© 2016 aditya kumar kasinadhuni - university of...
TRANSCRIPT
MAPPING CURRENT DENSITY DUE TO ELECTRICAL STIMULATION USING
MAGNETIC RESONANCE ELECTRICAL IMPEDANCE TOMOGRAPHY
By
ADITYA KUMAR KASINADHUNI
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2016
© 2016 Aditya Kumar Kasinadhuni
To my parents, K A Shiva Prasad, K Mangala Gowri, and brother, Girija Kumar Raghava
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ACKNOWLEDGMENTS
I would like to extend my heartfelt thanks to my advisor Dr. Thomas Mareci for his
guidance and mentorship throughout my journey in graduate school. Dr. Mareci has been
instrumental in molding my thought process to pay attention to detail when planning
experiments. His meticulous nature taught me to analyze every problem closely and cultivated in
me the attitude to “question everything, assume nothing” which is critical to the development of
science. His astounding depth and breadth on all things MRI has and continues to inspire me to
constantly push the boundaries of my own knowledge in the field of magnetic resonance. I would
like to thank Dr. Rosalind Jane Sadleir for her constant support and for providing me a platform
to demonstrate my abilities in MRI. Dr. Sadleir has been a wonderful mentor who constantly
kept me on my toes and helped me develop an understanding of magnetic resonance electrical
impedance tomography (MREIT). I would like to thank Dr. Paul R. Carney who was highly
motivating and always willing to discuss current trends and literature pertaining to the field of
neuromodulation and neuroplasticity. His constant zeal and enthusiasm for the field kept me
inquisitive about the mysteries of the human brain and pushed me to understand the importance
of the work I embarked upon in my doctoral study. I would like to express my gratitude to Dr.
Stephen J Blackband, who was welcoming and allowed me unrestricted access to his lab so that I
could use his weighing balance, distilled water and hot plate when I needed them the most. Very
early in my Ph.D., Dr. Malisa Sarntinoranont instilled in me the importance of selecting a
practical and feasible project. Her advice to continue working towards my goals and make
whatever little progress in the wake of obstacles helped me stay ahead in my doctoral pursuits.
Dr. Aysegul Gunduz was highly accommodating and ever ready to listen to my efforts at
mapping electrical current density and was willing to help me out with any administration
problems.
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I would also like to thank Dr. Michael Schär for his help with the Philips pulse sequence
and for his prompt replies to my queries requesting clarity on the subtleties of the 3 T Philips
Achieva system at the McKnight Brain Institute. William Triplett was extremely supportive and
helpful with his ideas on image reconstructions, and provided the skeleton code to reconstruct
images from raw Philips data, which I built upon, for the MREIT data processing. Dr. Munish
Chauhan provided excellent guidance towards developing the imaging protocol for the human
imaging work and also helped with the reconstruction of current density from the measured
magnetic field maps.
I would like to extend my heartfelt thanks to the members of the Radio Frequency Lab at
the AMRIS facility in the McKnight Brain Institute who helped me with all problems
electronics. Malathy Elumalai was highly forthcoming and always ready to help me with
soldering small circuits and stimulated my thought process on numerous occasions when I
needed to troubleshoot my experiments. Kelly Jenkins was extremely encouraging and provided
valuable guidance during my efforts at repairing RF coils. Joshua Slade provided unquestioned
mechanical engineering support and guidance to help me construct numerous contraptions and
phantoms for research. Dr. Huadong Zeng and Tammy Nicholson were extremely
accommodating to work with my imaging schedules and always ready to help troubleshoot
problems pertaining to my experiments.
I would also like to thank my former and current labmates who played a vital role in
shaping my career in graduate school. Dr. Garrett Astary (General Electric, South Carolina) was
a great mentor and taught me how to use the Agilent system for imaging experiments. Dr. Luis
Colon Perez (Febo Lab, University of Florida) provided help with diffusion imaging and was a
source of continuous motivation. Guita Banan was a wonderful physics mentor on whose support
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I relied heavily to understand the complicated electromagnetic interactions in MREIT. Magdoom
Kulam has been a brother away from home providing constant brainstorming sessions and
helping me with data acquisition at the 3 T magnet for the human imaging work. Manish Amin is
a wonderful person in general and was willing to share his personal equipment for my use in the
lab for MREIT experiments. I would also like to thank Aprinda Indahlastari, Chris Anderson,
Kevin Castellano, Andrew Girard and Kevin Montes for their help and assistance with modeling,
administration and imaging experiments.
Finally I would like to thank my friends and family for believing in me and providing
great support in times of need. Bhargava Kandala, Anuj Goyal and Vijay Pappu were
instrumental in motivating me with excellent discussions on a variety of topics. Sunantha
Sethuraman provided constant support and motivation in every way possible and took great care
of me during my recovery from surgery. My brother, Girija Kumar, showed extreme love and
patience constantly supporting and shielding me so that I could fulfil my responsibilities. My
parents, Major Shiva Prasad and Mangala Gowri sacrificed a lot for me and showed
unconditional love and support all my life. They played a vital role in making me the person I am
today. I am extremely thankful and will remain forever grateful to them.
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TABLE OF CONTENTS
page
ACKNOWLEDGMENTS ...............................................................................................................4
LIST OF TABLES .........................................................................................................................10
LIST OF FIGURES .......................................................................................................................11
LIST OF ABBREVIATIONS ........................................................................................................14
ABSTRACT ...................................................................................................................................16
CHAPTER
1 MOTIVATION AND SPECIFIC AIMS ................................................................................18
1.1 Motivation .........................................................................................................................18 1.2 Specific Aims ....................................................................................................................20
1.2.1 Specific Aim1: Develop MR methodology for facilitating measurement of
low amplitude current induced magnetic fields in the presence of temporal drift
at 3 T MRI ....................................................................................................................20
1.2.2 Specific Aim 2: Measure at 3 T, current induced magnetic field maps and
current density distributions due to tACS like stimulation in healthy volunteers .......21
1.2.3 Specific Aim 3: In a DBS like experimental setup, determine feasible
electrode orientation for reliable measurement of magnetic fields due to low
amplitude current injection ..........................................................................................21
2 BACKGROUND AND PREVIOUS STUDIES ....................................................................22
2.1 Neurophysiology ...............................................................................................................22 2.2 Transcranial Electrical Stimulation ..................................................................................27
2.3 Magnetic Resonance Imaging ...........................................................................................31 2.4 Magnetic Resonance Electrical Impedance Tomography ................................................37
2.4.1 Signal and Noise in MREIT ............................................................................41 2.4.2 Magnitude noise ..............................................................................................43 2.4.3 Phase noise ......................................................................................................44
2.4.4 Optimization of imaging parameters to improve sensitivity ...........................46 2.4.5 Projected Current Density ...............................................................................48
3 DETERMINATION OF THE EFFECT OF TEMPORAL VARIATIONS IN THE
STATIC FIELD ON MREIT ACQUISITIONS .....................................................................53
3.1 Introduction .......................................................................................................................53 3.2 Theory ...............................................................................................................................54 3.3 Methods ............................................................................................................................57
3.3.1 Pilot Experiments ...................................................................................................57
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3.3.1.1 Phantom preparation. ...................................................................................57
3.3.1.2 Image acquisition. ........................................................................................57 3.3.1.3 Data inconsistencies .....................................................................................58 3.3.1.4 Troubleshooting data inconsistencies ...........................................................58
3.3.2 Field Corrected Experiments ..................................................................................59 3.3.3 Electrical Stimulation .............................................................................................59
3.3.3.1 Switching circuit. .........................................................................................60 3.3.3.2 Circuit description. .......................................................................................61
3.3.4. Data Processing .....................................................................................................62
3.4 Results...............................................................................................................................63 3.5 Discussion and Conclusion ...............................................................................................64
4 MEASUREMENT OF ELECTRICAL CURRENT DENSITY DUE TO
TRANSCRANIAL ALTERNATING CURRENT STIMULATION OF THE HUMAN
BRAIN AT 3 T .......................................................................................................................75
4.1 Introduction .......................................................................................................................75
4.2 Methods ............................................................................................................................78 4.2.1 Phantom Experiments .............................................................................................78
4.2.2 Human Experiments ...............................................................................................79 4.2.3 MR Imaging ............................................................................................................79 4.2.4 MREIT Data Processing .........................................................................................80
4.2.5 Image Segmentation ...............................................................................................81 4.2.6 Computational Modeling ........................................................................................82
4.3 Results and Discussion .....................................................................................................82 4.3.1 Gel Phantom ...........................................................................................................82
4.3.1.1 Field measurements ......................................................................................82 4.3.1.2 Optimization of magnetic field maps ...........................................................83
4.3.2 Healthy Volunteers .................................................................................................84 4.3.3 Quality of field maps ..............................................................................................86 4.3.4 Projected Current Density maps .............................................................................87
4.4 Conclusions.......................................................................................................................89
5 MEASUREMENT OF MAGNETIC FIELDS DUE TO LOW AMPLITUDE
INJECTION CURRENTS USING IMPLANTED ELECTRODES ....................................104
5.1 Introduction .....................................................................................................................104
5.2 Theory .............................................................................................................................104 5.2.1 Effect of background magnetic field on frequency encoding ..............................106
5.2.2 MREIT-ICNE .......................................................................................................108 5.3 Methods ..........................................................................................................................109
5.3.1 Field Stability measurements ...............................................................................109 5.3.2 Pilot Studies ..........................................................................................................110
5.3.2.1 Fabrication of carbon electrodes ................................................................110
5.3.2.2 Experimental setup .....................................................................................110 5.3.2.3 MR Imaging ...............................................................................................111
5.3.3 Extended Studies ..................................................................................................111
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5.3.3.1 Phantom preparation ..................................................................................111
5.3.2.2 Electrical Stimulation .................................................................................112 5.3.3.3 MR Imaging ...............................................................................................112
5.4 Results and Discussion ...................................................................................................113
5.5 Conclusions.....................................................................................................................115
6 CONCLUSIONS AND FUTURE WORK ...........................................................................124
6.1 Summary .........................................................................................................................124 6.2 Future Work ....................................................................................................................125
LIST OF REFERENCES .............................................................................................................128
BIOGRAPHICAL SKETCH .......................................................................................................135
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LIST OF TABLES
Table page
4-1 SNR values for volunteer MRI data and noise in measured magnetic field maps at
3T. ....................................................................................................................................102
5-1 Noise standard deviations for current induced field maps acquired with conventional
spin echo MREIT and spin echo MREIT with ICNE sequences. ....................................122
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LIST OF FIGURES
Figure page
2-1 Graphic representation of low frequency and high frequency current flow in tissue. .......50
2-2 Schematic for experimental setup in an MREIT experiment while injecting current
into a cylindrical agarose gel. ............................................................................................50
2-3 Representation of magnetization vector and the effect of noise on the phase (ϕ) of the
magnetization vector. A represents the magnetization in the absence of noise, and M,
in the presence of noise. For simplicity the deviation in ϕ due to noise is shown to. ........51
2-4 Distribution of phase noise for varying levels of magnitude signal-to-noise ratio. The
distribution begins to approximate to a Gaussian distribution for SNR values greater
than 3. .................................................................................................................................51
2-5 Spin echo pulse sequence for MREIT acquisition. The current polarity is reversed
after the 180° pulse to account for the phase reversal of spins. .........................................52
2-6 Spin echo sequence with current injection during the sampling interval altering the
linear relationship between the spin position and frequency. ............................................52
3-1 Gel phantom used in MR experiments. A) Freshly prepared agarose gel phantom
after removal from refrigerator. B) Experimental setup showing the electrodes
secured on the gel with a rubber strap. C) Schematic showing the placement of the. .......66
3-2 Spoiled multi gradient echo sequence (2D) used for data acquisition. The repetition
time (TR) was 50 ms. Current pulses Ic = ±1.5 mA in amplitude were injected for a
duration of 32 ms. The bandwidth of acquisition was 550 Hz/pixel while 100. ...............67
3-3 Layout of the experimental setup used for imaging. The current injected was
carefully monitored using the oscilloscope to ensure the synchronization of RF
trigger and injection pulses as well as the injection amplitude. The components of . .......68
3-4 Schematic of the switchbox circuit and layout of the different components used in
coalition for data acquisition. R-test is the test resistance of 1 KΩ across which the
stimulation is checked using an oscilloscope.....................................................................69
3-5 Preliminary experimental results from two identical acquisitions performed with 1
mA current injection through a wire placed in a gel phantom.. .........................................70
3-6 Oscilloscope recording during pilot experiments for 1 mA current injection. Each
division on the X-axis corresponds to 50 ms. The TTL signal (green trace) generated
after every RF excitation (see Figure 3-2) during imaging and corresponding .................70
3-7 Phase variation in a 30x30 pixel ROI across each of the complex divided datasets. ........71
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3-8 Regression fit for the phase values within a 30 x 30 pixel ROI drawn in the center of
the image for the first echo time across the ten volumes collected as part of the first
acquisition in the reversed experiments. Acquisition time for 1 volume was ...................72
3-9 Variation of the mean phase in a 20 x 20 pixel ROI drawn in the center of the image.
Each of the twenty-three plots represents the phase obtained by complex dividing
data of every repetition by its preceding one. The X-axis in each plot represents the ......73
3-10 Oscilloscope recording of the voltage across the test resistor (see Figure 3-4) due to
1.5 mA current injection (blue) alternating polarity with every incoming TTL signal
(green). ...............................................................................................................................73
3-11 Magnetic field maps for the first slice location obtained from field corrected
experiments by acquiring the positive and negative current injection data very close
in time. Identical maps across multiple current injection runs show measurement...........74
4-1 MR magnitude images from all 32 channels reconstructed by carrying out the inverse
Fourier transform of complex k-space data. The coil combined magnitude image can
be generated using a sum of squares approach with or without appropriate weighting. ...91
4-2 Representative images showing electrode placement, image reconstruction and
decrease in SNR with increasing echo times.. ...................................................................92
4-3 MR magnitude and phase images for the center slice location collected at the first
echo time. The increased sensitivity at the bottom of the magnitude image was due to
the proximity of the gel phantom to the bottom set of RF coils. .......................................92
4-4 Phase maps produced from complex division of acquired data scaled from -0.1
radians to 0.1 radians. ........................................................................................................93
4-5 Magnetic field maps computed from the measured phase changes (Figure 4-4) scaled
from -10 nT to 10 nT. ........................................................................................................93
4-6 MR magnitude data for all slices and their corresponding T2* maps computed from
data acquired without any current injection. The T2* maps are displayed in seconds
giving an average T2* of about 48 ms in the gel phantom. Volume fitting for all the .......94
4-7 Comparison of measured and simulated current-induced magnetic field maps in the
gel phantom. .......................................................................................................................95
4-8 Experimental setup and stimulation paradigm for transcranial electrical stimulation
on healthy volunteers.. .......................................................................................................96
4-9 Current-induced phase and magnetic field images for healthy volunteers. Note the
steady increase in phase across echoes. Electrical stimulation was performed from
right to left in the image. The static field direction is into the page. .................................97
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4-10 Current-induced phase and magnetic field maps for the Fpz-Oz direction. The phase
maps are scaled from -0.1 to 0.1 radians while the magnetic field maps cover a range
of -10nT to 10 nT. ..............................................................................................................98
4-11 Representative images of segmented T1 images, computational model generated and
comparison of simulated and measured magnetic fields. ..................................................99
4-12 Comparison of measured and simulated magnetic fields due to T3-T4 stimulation for
the central slice location. Good agreement can be observed in subjects 009 and 012.
Results from subjects 010 and 011could have contributions from motion. Magnetic.....100
4-13 Comparison of measured and simulated magnetic fields, following electrical
stimulation with electrodes placed at Fpz and Oz, for the central slice location .............101
4-14 Comparison of simulated current density images and current density maps computed
from measured magnetic field maps. Shown are the maps for X and Y components of
the current density vector and the corresponding norm calculated from the two ............102
4-15 Current density (norm) images for healthy volunteers shown in relation to their high
resolution T1 images. The current density maps were scaled from 0 – 0.7 A/m2. Also
shown are the current density maps overlaid onto the T1 images with 50%. ..................103
5-1 Asymmetric spin echo pulse sequence where the slice select 180° RF pulse is moved
from its original position to create a net phase accumulation due to free precession. .....117
5-2 Field stability measurements using the asymmetric spin echo sequence with varying
free precession delay times. .............................................................................................118
5-3 Demonstration of the dominant magnetic fields due to current in the electrodes.The
dissimilarity in the horizontal line plot across electrodes, was due to the electrodes
not being perfectly parallel to eachother. The image is scaled from -10 nT to 10 nT.. ...119
5-4 Current-induced magnetic field measurements for varying current amplitudes using
conventional spin echo measurements. ............................................................................120
5-5 Current-induced magnetic field measurements (in Tesla) using the Injection Current
Non-Linear Encoding (ICNE) approach with varying levels of current amplitude. ........121
5-6 Magnetic field maps (in Tesla) due to 0.25 mA current injection in three phantoms
with different orientations of copper electrodes. .............................................................123
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LIST OF ABBREVIATIONS
AMRIS advanced magnetic resonance imaging and spectroscopy
BLM bilayer lipid membrane
BW bandwidth
CNS central nervous system
CSF cerebrospinal fluid
DBS deep brain stimulation
DMSO dimethyl sulfoxide
EPI echo planar imaging
EIT electrical impedance tomography
fMRI functional magnetic resonance imaging
GE gradient echo
Gfe frequency encoding gradient
GM gray matter
Gpe phase encoding gradient
GRAPPA generalized auto-calibrating partially parallel acquisition
HARDI high angular resolution diffusion imaging
ICNE injection current non-linear encoding
MREIT magnetic resonance electrical impedance tomography
MRI magnetic resonance imaging
NMR nuclear magnetic resonance
nT nano tesla
PCD projected current density
PLA poly lactic acid
PVDF polyvinylidene fluoride
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RF radio frequency
SE spin echo
SENSE sensitivity encoding
SNR signal-to-noise ratio
SPGR spoiled gradient echo
T1 longitudinal relaxation time
T2 transverse relaxation time
tACS transcranial alternating current stimulation
Tc current injection time
tDCS transcranial direct current stimulation
TE echo time
tES transcranial electrical stimulation
TR repetition time
Ts sampling time
TTL transistor transistor logic
VNS vagal nerve stimulation
WM white matter
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Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
MAPPING CURRENT DENSITY DUE TO ELECTRICAL STIMULATION USING
MAGNETIC RESONANCE ELECTRICAL IMPEDANCE TOMOGRAPHY
By
Aditya Kumar Kasinadhuni
December 2016
Chair: Thomas Mareci
Major: Biomedical Engineering
Electrical stimulation therapies like Deep Brain Stimulation (DBS) and Vagal Nerve
Stimulation (VNS) have been widely used for the treatment of Parkinson’s Disease and Epilepsy.
Transcranial direct current stimulation (tDCS) has been shown to have the potential for being an
augmentative therapy and improve cognitive functions. However, the underlying mechanisms of
operation of these electrical stimulation therapies are still under debate and a sound working
hypothesis is still in want. Understanding the flow and distribution of injected currents can
provide information to improve the efficiency of these therapies. So far, computational models
using information from high resolution MR images have been used extensively for prediction
and estimation of current densities. Magnetic Resonance Electrical Impedance Tomography
(MREIT) can be used to visualize current distributions by tracking changes in magnetic fields
produced by the injected currents. The produced current density maps can help guide stimulation
therapies and validate existing modeling techniques. However, past implementations of MREIT
used high current amplitudes to reliably measure the induced magnetic fields and therefore were
not viable in in vivo studies due to safety considerations.
The magnetic fields generated by currents used in electrical stimulation therapies are
usually on the order of micro to nanoTesla which is a major deterrent to detecting the current
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induced magnetic fields. Reliable quantification of these fields is challenging requiring high
signal-to-noise ratio in the measurement that generally requires an increase in the imaging time.
Additionally, the miniscule nature of the fields makes the measurement susceptible to minor
variations in an otherwise static main magnetic field of the MR scanner. Appropriate imaging
methods were developed and necessary electronic circuitry was constructed to facilitate data
acquisition in a way that decreased the measurement sensitivity to temporal variations in the
static field.
Magnetic fields due to the current were measured in homogenous phantoms and healthy
individuals and compared against those generated from sample specific computational models.
The results show good correlation with discrepancies attributable to extraneous factors like
subject motion. Current density estimates from the measured magnetic fields and numerical
simulations were also compared. Finally, to understand the distribution of current density during
DBS-like stimulation, current induced magnetic fields while using implanted electrodes were
measured using different electrode orientations.
.
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CHAPTER 1
MOTIVATION AND SPECIFIC AIMS
1.1 Motivation
The brain is one of the most important and complex organs in the human body. Attempts
to understand brain anatomy and function date back to the prehistoric times as old as 4000 B.C.
when the Sumerians first documented the effects of poppy plant on the “mind”. In 300 B.C the
first dissection of a human body was performed by Alexandrian biologists who classified the
motor and sensory nerves. The basic anatomical classification of what we know to be the
“modern brain” was first established by Thomas Willis in 1664 A.D (in Cerebri Anatome),
known also for the discovery of the “Circle of Willis” which is a circular group of arteries on the
base of the brain.. Advances in experimentation and technology paved way for our understanding
of the brain anatomy and we now know it to comprise of billions of fundamental functional units
termed “neurons” that work together in coordination enabling us to operate in daily life. All our
experiences, emotions and thoughts are governed by electrochemical changes occurring in the
environment of these neurons. However, even to this day, in spite of the cornucopia of
knowledge and research on the brain, there is a lot we do not know about the brain’s function, its
connections and response to pathology.
Nerve and muscle tissue are collectively termed as “excitable” tissue and coordinate
activity in the human body through neuromuscular junctions (NMJ). The underlying
neurophysiology dictates that electrochemical impulses are responsible to bring about this
coordinated function which prompted early medical practitioners to use electrical and chemical
treatment strategies to restore function in cases of pathology. The idea was to use these treatment
strategies to alter the environment around the excitable tissue to promote or inhibit function. The
first form of electrical stimulation treatment was developed in the 1930s, called
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electroconvulsive therapy (ECT), for treatment of major depression and catatonia. The therapy
informally known as “shock treatment” was induced as a last option to control psychiatric
illnesses and is currently one among many techniques that are collectively termed
“neuromodulation” techniques. Today, neuromodulation is an extremely important field of
research that encompasses a gamut of interventional techniques aimed at long term activation,
inhibition, modification and/or regulation of neural activity, using electromagnetic, chemical and
optogenetic methodologies. Deep Brain Stimulation (DBS) which is a form of electrical
stimulation is an FDA approved technique for the treatment of medically intractable Parkinson’s
Disease. Over the past decade, Transcranial Direct Current Stimulation (tDCS) has been in the
spotlight promising the potential to improve working memory, stroke and a host of cognitive
functions (1,2). Transcranial Alternating Current Stimulation, one of the variants of tDCS, has
been shown to modulate the existing background neural activity promoting excitation or
inhibition of specific functions (3).
Despite the beneficial effects of these techniques, very little is understood with regards to
their mechanism of action. Treatments involving these techniques rely heavily on computational
models for guidance and selection of stimulation parameters. However generalized
computational models suffer as they are blind to variations in the head size and composition that
differ vastly across people. Subject specific models provide a more robust approach at accurate
current density predictions in different brain regions by utilizing information on the underlying
brain structure obtained through MRI or CT scans. However there is a dire need for the
validation of these computational models and MREIT or magnetic resonance electrical
impedance tomography is aptly placed to address this need.
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1.2 Specific Aims
The goal of this research is to develop an MR methodology to effectively map current
density for improved understanding of the mechanisms governing neuromodulation techniques
like tDCS and DBS. The developed technique can be used to validate existing models that aim to
describe current flow in the brain during electrical stimulation. This was achieved by tackling the
temporal drift in the static field of the MRI scanner by acquiring current injection datasets as
close in time as possible. Validation of magnetic field and current density maps from sample
specific computational models was performed. Finally, for characterization of current density in
DBS like setups, current injection using magnet wire to identify the most feasible electrode
orientation such that the magnetic field from current density in the electrodes does not mask that
in the sample will be presented.
1.2.1 Specific Aim1: Develop MR methodology for facilitating measurement of low
amplitude current induced magnetic fields in the presence of temporal drift at 3 Tesla
using MRI
Temporal drift in the static field of MRI scanners can adversely affect the measurement
of low amplitude current-induced magnetic fields by completely masking them. Data acquired
using a conventional MREIT approach and another approach to decrease the sensitivity to
background field drifts are presented. The field drift is characterized in the absence of current
injection and compared against manufacturer specifications. Necessary electronic circuitry to
synchronize electrical stimulation with image acquisition and enable data acquisition using the
second approach was designed and constructed. The reliability of measurements using the
second approach is presented.
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1.2.2 Specific Aim 2: Measure the current induced magnetic field maps and current density
distributions at 3 Tesla due to tACS like stimulation in healthy volunteers
Calculating current density distributions within the human head due to transcranial
electrical stimulation techniques requires reliable measurement of current-induced magnetic
fields. Using the method developed in specific aim 1, reliable determination of the minute fields
was performed in gel phantoms and extended to healthy volunteers who experienced electrical
stimulation in two orthogonal directions. Computational head models for the different volunteers
were generated from MR data and current-induced magnetic fields were calculated against which
the experimental data compared. Signal-to-noise ratio (SNR) was measured in the magnetic field
maps during the gel experiments to check the fidelity of MREIT measurements. Finally, current
density distributions generated from the measured magnetic fields were also compared against
their numerical simulations. The methods developed in this chapter can be used to validate
computational modeling techniques that are currently the guiding tools for electrical stimulation
therapies. Reliable characterization of induced current densities due to transcranial electrical
stimulation (tES) could bolster the efficiency of these therapies while simultaneously providing
insights into their mechanisms of operation.
1.2.3 Specific Aim 3: Using implanted electrodes, determine feasible electrode orientation
for reliable measurement of magnetic fields due to low amplitude current injection
Current injection using electrodes placed perpendicular to the static magnetic field of the
MR scanner can be detrimental to the observation of magnetic fields produced in tissue. Pilot
experiments elucidating this shortcoming are presented and current injection using different
electrode orientations was performed. Though challenging from a surgical standpoint, the
methods provide a compromise against tackling the problem of magnetic fields produced in
tissue being masked due to the strong magnetic fields from current in the electrodes.
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CHAPTER 2
BACKGROUND AND PREVIOUS STUDIES
2.1 Neurophysiology
The human brain that forms an integral part of the central nervous system (CNS) can be
divided into gray matter (GM), white matter (WM) and cerebrospinal fluid (CSF). The GM gets
its name from the grayish hue of the neuronal cell bodies while their axons, which are much
paler, constitute the WM. The brain is surrounded by CSF which provides it mechanical
protection and plays a vital role in cerebral blood flow and autoregulation. Knowledge of the
neuroanatomy and physiology is vital to our understanding of brain function and can provide
insights into the mechanisms of exogenous/endogenous current flow. Before understanding the
effect of induced current or electric field on the brain tissue, it is necessary to understand the
constituents of brain tissue and the environment surrounding neurons that make up the brain.
Neurons and glial cells make up the primary composition of the nervous system in the
human body. Neurons interact with each other through synaptic junctions while physical and
metabolic support is provided by the glial cells. Neurons can be classified structurally as
unipolar, bipolar, multipolar neurons. Functionally, they can be sensory (afferent) or motor
(efferent) neurons depending on whether they transmit signals from or to the target cells.
Interneurons are specialized neurons that connect other neurons to specific parts of the CNS. The
structure of a typical neuron consists of the cell body or “soma”, “dendrites” or fan like
projections that form synaptic connections with other neurons, and a long tail or “axon” which is
responsible for the transmission of signals. A neuron communicates with another neuron at the
synapse by releasing neurotransmitters (eg. gamma amino butyric acid or GABA and glutamate)
that adhere to special chemical receptor proteins present in the post-synaptic neuron. Neuronal
axons can sometimes be “myelinated” due to the glial cells that wrap around the neuron
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providing an insulating layer and improving its conduction velocity. Myelination in the
peripheral nervous system (PNS) is due to the outgrowth of Schwann cells, while that of
oligodendrocytes forms the myelin in CNS. Nerve and muscle cells are termed “excitable” due to
the existence of a constant voltage gradient across their cell membranes at rest. The interior of
these cells is maintained at a constant negative potential with respect to its exterior due to the
balance of net electrical and diffusional forces. This is termed as the resting membrane potential
(RMP) and is about -70 mV in a typical human cell (4). To understand the effect of induced
electrical fields on brain tissue, it is necessary to gain insight into the different processes
involved in maintenance of the voltage gradient.
The intracellular and extracellular spaces around a cell are separated from one another
through a very thin membrane (7-15 nm) consisting of a lipoprotein complex. This is called the
bilayer lipid membrane (BLM) and is impermeable to most ions as the fatty acid tails of lipids
exert hindrance to the polar molecules. A special layer of carbohydrates that covalently link with
the lipids and proteins of the BLM forms the “glycocalyx” and provides functions of structural
integrity, cellular identification and interaction. Many cells are connected to each other through
their membranes forming specialized junctions known as desmosomes, tight junctions and gap
junctions. Integral proteins embedded in the membrane extend into the cytoplasm and function as
transport channels for water and various ions. The phospholipids in the bilayer and the channel
proteins are not linked or bonded to each other and hence are free to move. This results in
random lateral movement of both the proteins and lipids parallel to surface of the bilayer. The
flow of ions across the cell membrane occurs due to passive or active transport. Passive transport
is due to the difference in concentration of ions across the cell membrane through integral
protein channels and the channels’ permeability to these ions. The concentration of sodium ions
24
is very high in the extracellular space while that of potassium is low. The reverse is true for the
interior of the cell. In addition, the permeability (number of open protein channels that facilitate
transport) for potassium ions is extremely high compared to sodium which creates a negative
potential inside the cell. Active transport of ions across the cell membrane is facilitated by the
presence of specific proteins in the lipid bilayer which utilize energy in the form of adenosine
triphosphate (ATP), to move the charged molecules against their concentration gradient. One
such example of proteins is the sodium-potassium pump or Na+-K+ ATPase which moves sodium
out of the cell and potassium into the cell, thus, establishing homeostasis by maintaining the
concentration of these ions in the intra and extracellular spaces. Thus the net membrane potential
in the resting state, measured as the difference of intra and extracellular potentials, is always
negative and equal to -70 mV. The overall expression for membrane potential therefore depends
on the concentration and membrane permeability (or conductance) to different ionic species.
This was first developed by Goldman (5) and later modified by Hodgkin and Katz (6) giving rise
to the famed Goldman-Hodgkin-Katz equation,
K Na Clo o i
K Na Cli i o
P K P Na P ClRTE ln
F P K P Na P Cl
(2-1)
In Equation 2-1, Pi refers to the permeability coefficient of the membrane to particular ionic
species ‘i’, E represents the equilibrium resting membrane potential (RMP), F is the Faraday
constant, R is the universal gas constant and T is the temperature of the medium. Even though, of
the diffusible ions, potassium, sodium and chloride are extensively studied due to their extremely
high concentrations, it is important to remember that there exist other charged particles like
bicarbonate, calcium, magnesium, phosphates, sulphates, amino acids and proteins in both the
25
intra and extracellular compartments which are vital to the maintenance of homeostasis of the
cell.
Bioimpedance. The concepts of bioimpedance and bioelectricity arise from the existence
of charged particles found abundantly in cells and their environment, and from the analysis of
changes in the resting membrane potential due to an external stimulus. The effect of electric
fields on biological systems can be quite complicated even while considering a simple system
like a biological fluid. Current flow in a biological fluid is given by the sum of drift and diffusion
currents of each component making up the fluid (water, proteins, lipids etc). The applied electric
fields can change the orientation of polar molecules and induce dipole moments in bound
molecules by distorting either their electron clouds or by causing displacement of ions relative to
each other. The latter is termed ionic polarization and occurs as a result of the shift in the
hydration layer surrounding an ion due to the application of the field. The influence of an electric
field on membranes can vary with the direction of application (7). This is because, parallel to the
membrane, the induced field will exert a force on the charged particles in the bilayer and cause
them to move freely along the surface whereas in the transverse direction, these particles are
bound within the bilayer. However, the transverse field can modulate the movement of ions
through the channels by altering the membrane conductance. A further complication arises when
considering the interactions of biological fluids and cell membranes as the electric field can alter
or modulate the way new molecules are bound to the membrane surface. Furthermore, the
exchange of ions or molecules between the membrane and the fluid can be affected (8). The
result is an alteration of the transport properties of the membrane thereby altering function of the
cell which directly affects the organ system of which the cell is a part. The first equivalent circuit
of an unmyelinated nerve fiber was given in the seminal paper by Hodgkin and Huxley (4). With
26
the resting membrane potential around -70 mV, and the approximate thickness of the membrane
around 7-15 nm, typical transverse electric fields in the order of tens of millions of volts/meter
exist in a resting cell. The resistivities of the intra and extracellular fluids are in the range of 0.5 -
2 Ωm with a relative dielectric constant of approximately 50-80. Cells can therefore be modeled
as a group of electronic components where the extracellular and intracellular spaces can be
represented as resistors while the BLM can be modeled as a capacitor. The first of such models
that is still considered a good approximation for the passive electrical nature of the cell was
given by Fricke in 1925 (9) where each infinitesimal portion of the extracellular and intracellular
space was modeled as a resistance and every infinitesimal portion of the membrane was modeled
as a capacitance. The capacitive membrane shields the interior of the cell from applied electric
fields that have a frequency less than 1 kHz and conducts current in the presence of high
frequency electric fields (MHz regime of the electromagnetic spectrum) (Figure 2-1). When
considering the effect of a low frequency electric field on a large cohort of cells, the overall
conductance of the system can be represented as the sum of individual conductance of all cells
while the effects of membrane capacitance and permittivity can be ignored (since the capacitors
act as open circuits at low frequencies). The current and voltage characteristics can then be
understood using Ohm’s law. At a macroscopic level, most predictions of electrical current flow
in biological tissue for diagnosis or therapy (10-14) are usually based on this simplified
representation of an otherwise complex, intricate and dynamic system.
Bidomain Model. The expressions for current density in the intra and extracellular
spaces can be described using Ohm’s law in a volume conductor. Assuming that these spaces are
isotropic, the conductivity tensors in these spaces can be represented by their scalar counterparts
(σi and σe) and the equations can be given by
27
i i
e e e
i U
J
J
U
(2-2)
where Ui and Ue are the electric potentials inside and outside the cell. If β represents the surface
to volume ratio of neurons in the tissue under consideration, then current entering and leaving the
intra and extracellular domains must be equal and opposite. Representing the transmembrane
current as Im, this can be written as,
i e mJ J I (2-3)
Defining the membrane potential as m i eU U U , the equations governing the extracellular and
intracellular potentials can be given as,
i m i e e
mi i m
U U
UU C
t
(2-4)
In Equation 2-4, Cm depicts the membrane capacitance and the membrane current, Im, is assumed
to be time independent. To understand the effect of injected currents on tissue at a macroscopic
level we assume that the difference in conductivities of the intra and extracellular spaces is
negligible. Thus for a tissue at rest, the solution to Equation 2-3 is given by mI 0 and
i eJ J 0 . This implies that there exists a constant potential difference between the two
domains and no activation of tissue occurs due to the externally applied current. This forms the
basis for understanding electrical current flow or distribution in tissue following stimulation.
2.2 Transcranial Electrical Stimulation
Over the past decade, electrical stimulation techniques like transcranial direct/alternating
current stimulation (tDCS/tACS) have shown great promise in the improvement of cognition and
working memory (15) and their success has been attributed to the modulation of excitability of
28
cell membranes (16,17) or by means of modulating the existing background activity (18).
Liebetanz et al. (19) pharmacologically investigated the mechanisms of action of tDCS that
contribute to neuroplasticity and concluded that changes in membrane excitability and NMDA
receptor activation played a major role in the after-effects of tDCS. Transcranial AC stimulation
has been researched extensively in an attempt to understand the modulating effect of applied
electric fields on underlying brain activity (18,20,21). Typically, these transcranial stimulation
techniques employ a pair of electrodes housed in a conducting medium (saline soaked sponges,
conductive electrode gel etc.) that facilitates the flow of current. The electrodes and conducting
medium are securely placed on the scalp of the subject for current injection. Until now, we have
discussed the presence of sodium and chloride ions in the intra and extracellular spaces.
However, the independent existence of sodium and chloride ions (without combining to form
sodium chloride) is because of the hydration ability of water due to its large dipole moment. The
hydration causes an effective increase in the size of the charged particles and hence the resulting
conductivity in tissue at low frequencies (or any ionic conductor, liquid or solid) which is due to
the motion of these hydrated ions, is governed greatly by their ionic mobilities and not so much
due to the number of charge carriers.
Electrode-Electrolyte interface. When an electrode is placed in an electrolyte, the
electrode metal being a source/sink of electrons exchanges charges with the arriving ions or
ionizes neutral substances. An electric double layer or an “interphase region” is formed as soon
as the electrode is placed in the electrolyte and transformation of electronic to ionic conduction
occurs at the electrode-electrolyte interface. In all such interphases, non-uniform distribution of
charge results in an electric potential across the interphase. Two kinds of charge transfer
mechanisms take place at the interface. One is a non-Faradaic charge transfer where there is no
29
electron exchange between the electrode and electrolyte. Charges in the bulk of the electrolyte
redistribute as the electrons in the metal attract counterions in the electrolyte. The second
mechanism is one which involves transfer of electrons from the electrode to the electrolyte
causing reduction or oxidation of chemical species in the electrolyte.
Capacitive charge transfer. The reason for the double layer formation is due to several
phenomena that include a transient transfer of charge carriers between the electrode and
electrolyte resulting in two oppositely charged layers (counterion phenomenon) in the
electrolyte. Some ionic species can also adsorb to the surface of the electrode thereby creating
charge separation. Polar molecules like water can exhibit preferential orientation at the electrode
that separates charge. When the charge on the “working electrode” (defined as the electrode one
is interested in studying) is reversed, redistribution of charges in the double layer and bulk of the
electrolyte occur. However, electroneutrality at the electrode interface and in the bulk of the
electrolyte is preserved. At the “counter electrode” (electrode necessary for circuit completion)
the opposite processes occur and even here the net charge in the double layer is zero. Thus when
the total delivered charge is small only charge redistribution occurs and when the polarity of the
voltage is reversed, the charge stored in the double layer capacitance can be recovered
effectively.
Faradaic charge transfer. Charge transfer can also occur due to the transfer of electrons
from the electrode to the electrolyte through processes of oxidation and reduction. This
phenomenon of charge transfer forms products in the solution which may or may not be
recovered by reversing the current direction. Faradaic charge transfer being chemical reactions
can also be reversible to some extent if the reaction rate is under kinetic control. This means that
if the reaction is governed by fast kinetics then the product formed does not move away from the
30
surface quickly (relative to the kinetic rate of the reaction) and hence when the current is
reversed, some of it can be converted to its initial form. However in a reaction with slow
kinetics, the reactants are able to diffuse to the surface of the electrode to support the kinetic rate
of the reaction and the formed products diffuse away quickly in comparison. These products that
have diffused away cannot be recovered and could be damaging to the electrode or the tissue
undergoing stimulation.
At equilibrium, the net electrochemical potential across the electrodes and the electrolytes
is zero and charge transfer is ceased. Now if current is injected using the electrodes, the net
current during electrical stimulation is defined by the sum of charge transfer following the above
two methods where the capacitive transfer depends on the rate of change of the equilibrium
potential while the Faradaic transfer is affected by shift of the potential from electrochemical
equilibrium. In most electrical stimulation applications, the stimulation is delivered using a
current controlled approach in the form of pulses. Stimulation using biphasic pulses causes the
second pulse to reverse any electrochemical processes occurring as a result of the first pulse. A
detailed understanding of the underlying processes and effect of different stimulation approaches
can be found in Merill et al. (22).
In spite of the simplified representation of the underlying processes that govern current
flow in the brain, there still remains ample complexity arising due to its heterogeneous nature
making it extremely challenging to design rigorous experimental paradigms that can faithfully
testify and corroborate the pros and cons of electrical stimulation techniques. Variations in the
site of electrode placement, intensity of stimulation and even duration of stimulation have been
shown to produce different effects and prompted researchers to establish specific scientific
guidelines for performing non-invasive brain stimulation (23). Computational models are widely
31
used as guiding tools for targeting areas of interest in the brain but these models are developed
on a general atlas of the head which may decrease the accuracy of prediction. For instance, an
atlas based model is blind to the variation in skull thicknesses or ventricle sizes across subjects
and hence attributing any observations solely to electrical stimulation would be inaccurate.
Subject specific computational models would serve as better estimates but this requires some sort
of a priori information about the subject’s head that can be obtained with the aid of Computed
Tomography (CT) or Magnetic Resonance Imaging (MRI). Even with this information, there
could be variation in the amount of hair across participants, information about which cannot be
obtained by these imaging methods. This could also affect current distribution. The need for
accurate segmentation of scalp and bone tissues, and taking into account the different anisotropy
of biological tissues make it extremely challenging for computational models to accurately
predict the injected current distribution, calling for new approaches that can accurately quantify
the localization of current density in different brain regions following electrical stimulation.
Magnetic Induction Tomography (MIT), Magneto Acoustic Tomography with Magnetic
Induction (MAT-MI), Magnetic Resonance Electrical Properties Tomography (MREPT) and
Electrical Impedance Tomography (EIT) are some of the techniques developed in the past to map
the conductivity of the imaging object and thereby understand the current distribution. Each of
the above techniques has its own merits and demerits in terms of portability and invasiveness of
measurement. Over the last decade, MRI coupled with EIT, called MREIT (24), has come into
prominence showing promise with its ability to reliably detect injected current distributions at
high spatial resolutions.
2.3 Magnetic Resonance Imaging
Magnetic Resonance Imaging, commonly referred to as MRI, is a diagnostic imaging
approach that facilitates the generation of non-invasive high resolution images of an object and is
32
currently the gold standard for imaging soft tissue in the human body. MRI in its various forms
(diffusion MRI, functional MRI, quantitative MRI, etc.) has proven to be extremely useful in
diagnosing a wide gamut of disorders in their incipient stages.
At its root, MRI stems from a thorough understanding of Nuclear Magnetic Resonance or
NMR which was measured and described for the first time by Isador Rabi (25) in 1938, which
won him the Nobel Prize in Physics. Felix Bloch (26,27) and Edward Purcell (28,29) extended
this work to liquids and solids and were jointly awarded the Nobel prize in 1952. In 1948, the
BPP theory (30), named after its formulators and renowned physicists Nicolaas Bloembergen,
Edward Purcell and Robert Pound, explained and demonstrated the interaction between nuclei
immersed in an external field with their surrounding lattice and neighboring nuclei based on
which modern day diagnostic MRI is understood. NMR received a major thrust and its
diagnostic potential came to light with the work of Raymond Damadian (31) who showed that it
was possible to identify cancerous lesions by their sufficiently long relaxation times. With the
advent of computers and computerized tomography, Damadian attempted to build a prototype of
the modern MR scanner. However, it was the pioneering work of Paul Lauterbur in 1973 (32)
and Sir Peter Mansfield (33-35) who realized that a spatially varying magnetic field in the form
of magnetic field gradients produced a distribution of spatially varying nuclear spins and that
helped create the first proton density images which paved the way for modern day Magnetic
Resonance Imaging.
Spin is an intrinsic quantum property of atomic nuclei. The overall spin of the nucleus is
determined by the spin quantum number ‘s’ and can be ±1/2 (or their integral multiples), referred
to as the spin-up and spin-down states. When the total number of neutrons and protons in a
nucleus are equal, the overall spin can be considered to be zero. Hydrogen ion (H+) has a total
33
positive charge due to the presence of just the one proton in the nucleus giving H+ a total spin of
+1/2. The human body comprises of an abundance of protons whose spins can be detected and
localized using MRI making proton MRI the most viable methodology for diagnostic imaging. In
the remainder of this dissertation, for simplicity, proton MRI will be explained using a classical
approach and referred to as simply MRI.
The spin-up and spin-down states have the same energy and hence the number of protons
(or simply spins) occupying these states are equal in conditions of thermal equilibrium. When
these spins are placed in an external magnetic field B , the densities of spins in the two states are
altered (described by Boltzmann statistics) such that there is an excess of spins occupying the
lower energy state (parallel to the external field). Though this value is extremely small, the sheer
number of protons available in biological tissue makes up for this smallness giving rise to a net
magnetic moment (magnetization) that precesses around the external field with an angular
frequency that is dependent on the gyromagnetic ratio γ of H+ and the strength of the external
field, B . The coordinate frame used to describe this precession is a right handed system and so
we can write the precession frequency (ω) as,
(2-5)
A key point of significance is that the frequency of precession, also called the Larmor frequency,
happens to be proportional to the difference in the energy of the two spin states of the proton.
This frequency is in the MHz range and therefore, in order to excite the spins and create a
resonance condition, it is imperative that the energy deposited falls in the radio frequency range
of the electromagnetic spectrum. Therefore, an RF coil can be used to generate sufficient energy
to tip the spins away from the external field (along z direction) at any arbitrary angle θ thereby
even causing them to precess in the transverse plane (xy plane). The net magnetization of these
34
precessing spins will induce a small voltage signal in a nearby coil following Faraday’s laws of
electromagnetic induction. This induced signal is then mixed with a reference frequency equal to
the Larmor frequency of the spins to enable recording (this is equivalent to looking at the spins
from a frame of reference rotating at their precession frequency) and then digitized for storage.
The precessing magnetization will return to its equilibrium value Mo along the z direction, upon
the removal of the RF field due to the interactions of the spin with its surrounding lattice
(longitudinal relaxation) and due to its interaction with the neighboring spins (transverse
relaxation). These two mechanisms can be described as exponential regrowth and decay of the
magnetization with time constants T1 and T2. The time evolution of the precessing magnetization
can be understood from the Bloch equation, Equation 2-6, that captures the effect of these
relaxation parameters and is given as,
x y o z
2 1
ˆ ˆ ˆM x M y M M zdMM B
dt T T
(2-6)
where Mo is the magnitude of the equilibrium magnetization, x y zˆ ˆ ˆM M x M y M z and
ˆB B z .
Image formation. In MRI we use three orthogonal magnetic field gradients that produce
a variation in the z-component of the main magnetic field along the three coordinate axes, in
order to create a distribution of spins that precess with different Larmor frequencies. This can be
written as,
z z zˆ ˆ ˆˆr B z G.r where GB B
i jB
x y z
k
(2-7)
35
where r is a position vector in space, Bz represents the magnitude of the net magnetic field along
the z direction and G is the gradient of Bz. The complex time-dependent signal detected at the
end of the receiver chain of an MRI system, ignoring relaxation effects, can be represented by,
i r, t
r des t r
(2-8)
In Equation 2-8, ρ refers to the spin density, ϕ is the phase accumulated by the magnetization
vector in the transverse plane over the time interval t. The phase ϕ can be written as 2 k.r
where t
0
k G t dt2
and is called the wave vector which represents the spatial frequencies
present in the image. A very basic explanation (without much math) for generation of a two-
dimensional (2D) image along the z direction in the sample is as follows: the magnetic field
gradient applied along the z direction (Gz) creates a spatial variation of the precession
frequencies along the z direction described by the following the equation
zz B G z (2-9)
In reality it is not possible to create a perfect 2D slice, and the applied RF pulses excite a band of
frequencies (band-limited) thereby providing a finite thickness to the “slice”. Therefore as the
bandwidth of the RF pulse increases, we obtain thicker slices as we now excite a bigger region of
precessing spins. The slice thickness can be related to the RF excitation bandwidth as,
o zB G z (2-10)
If the RF excitation pulse (with a frequency content Δω) is applied along x, it will tip the spins in
the region Δz oriented along z, towards the –y direction causing them to precess in the xy plane,
while those that are off-resonance i.e spins that are not defined by the precession frequency range
Δω, remain largely unaffected by the pulse. Ignoring relaxation effects, this effectively produces
36
a slab of spins precessing in the xy plane. A subsequent field gradient turned on for a brief period
of time τ along the x-direction will cause the slab of spins to precess with varying frequencies
along the gradient direction effectively creating rows of spins along the x direction that are
precessing with the same Larmor frequency. However, since the gradient is turned on only for a
brief period of time, the spins experience this additional field gradient only for the period τ,
accumulating a net phase, γGxτ. Upon removal of the gradient, the spins begin to precess with
their initial Larmor frequencies but can now be distinguished due to their differences in phase.
This is termed as “phase encoding”. A third gradient now applied perpendicular to the initial two
gradients, causes the spins along each row in the slab to vary in frequency thereby creating a slab
of spins where each spin is unique in terms of its frequency and phase. This is called “frequency
encoding”. A receive coil used to detect the signal from the entire slab at each frequency
encoding step. The frequency content of the detected signal can be analyzed using a 2D inverse
Fourier transformation which enables us to localize the various detected frequencies in 2D space.
Mathematically, the entire process can be summarized as,
x yi2 k x k y
x yS k ,k x, y e dxdy
(2-11)
The inverse Fourier transformation operation yielding the desired spatial distribution of spins
(proton density), can then be written as,
i2 k rr S k e dk
(2-12)
Note that although the slice, phase and frequency encoding directions were assumed to be along
z, y and x directions, it is completely reasonable to switch around the directions of encoding. For
this reason it is always convenient in MRI to refer to the data acquisition in terms of the axes of
encoding (frequency, phase and slice) as opposed to the laboratory coordinate axes.
37
2.4 Magnetic Resonance Electrical Impedance Tomography
In Electrical Impedance Tomography (EIT), conductivity of the underlying tissue is
extracted by measuring potentials at the boundary of the object. This represents an ill-posed
problem which can be solved using additional information obtained from the MRI scanner.
Therefore the combination of the two techniques gave birth to MREIT (Magnetic Resonance
Electrical Impedance Tomography). The approach bears roots in the ability to produce current
induced magnetic field maps using a conventional MRI scanner, first shown possible in the
1990s by Scott et al. (36,37). The authors computed the injected current density J, by measuring
the magnetic field map Bc, produced by the current. To estimate all three components of the
magnetic field vector Bc, they rotated the object in three orthogonal directions. The idea behind
MREIT is that the z component of Bc interacts with Boz of the scanner and produces a change in
the spatial distribution of main magnetic field that can be measured as a variation in the phase of
the measured MR signal. The measured 2D spatial distribution of spins in MRI is described by
Equation 2-11, where the term x yi2 k x k y
e
refers to the phase of the measured MR signal
resulting from the phase and frequency encoding gradients. The current induced magnetic field
imparts an additional phase term to the precessing spins, described by c cT , where Tc is
the total duration of current injection. Equation 2-11 can then be modified as,
x y c ci2 k x k y i T
x yS k ,k x, y e e dxdy
(2-13)
The MR acquisition is repeated with an alternating current polarity, and the resulting datasets are
complex divided to extract the magnetic field image (38). The following equations describe the
process of magnetic field extraction from MRI data where So represents the MR signal in the
absence of current injection, ρ is the 2D spin density, kx & ky are the wave vectors in the phase
and frequency encoding directions. S+ and S- represent the MR signal in the presence of positive
38
and negative current injections applied for time Tc within one repetition time TR of the pulse
sequence. ϕc represents the additional phase imparted by Bc to the MRI signal.
x y
c c
c c
i2 k x k y
o
i
c c c
T
o
i T
o
S x, y e dxdy
S S e
S S e
Sarctan B2
ST
(2-14)
From Equation 2-14, one component of the current induced magnetic field can be measured as,
cc
c
B2 T
(2-15)
Figure 2-2 shows a typical arrangement of an MREIT experiment using a cylindrical agarose gel
phantom doped with sodium chloride and copper sulphate, and placed in the bore of an MRI
scanner. The idea is to inject current from left to right thereby creating the magnetic field Bc
which interacts with Bo. Seo et al. (24) analyzed the distribution of current density within the
phantom and formulated the following equations,
J = 0 inside the phantom (Ω
ˆJ.n = g on the boundary ( Ω)
)
(2-16)
The first equation in Equation 2-16 describes the conservation of current owing to preservation
of electro neutrality of the phantom. In the second equation, ‘g’ is the Neumann boundary
condition due to injected current describing the presence of current near only the electrodes and
is zero everywhere else on the boundary of the phantom (since no current is radiating out of the
phantom, ˆJ n 0 , except at the electrodes). The magnetic field produced due to this distribution
of current density J, can be described using the Biot-Savart equation as.
3
r rB r J r dr
4 r r
(2-17)
39
By treating the phantom as a volume conductor, the current density can be linearly related to the
electric potential (U) as J U and thus the problem in MREIT becomes that of estimation
of σ from the measured component of B(r) (39). This is a very complicated problem due to the
unavailability of the full B vector and also because σ is generally a macroscopic parameter that
can be anisotropic, complex (has real and imaginary parts) and depends on both temporal and
spatial frequencies. Making an assumption that the underlying conductivity is isotropic, using the
steady-state Maxwell’s equations, it can be shown that,
1
n JJ J l
(2-18)
From Equation 2-18, the nature of the component of ln that is parallel to J is unclear. It is
for this reason that in traditional MREIT acquisitions, current is injected in two non-collinear
directions. It is important to note that if the conductivity is believed to be anisotropic, then the
conductivity tensor can be estimated by injecting current in seven different directions (40). There
exist numerous reconstruction algorithms developed to compute σ or J, from the measured field
maps. Seo et al., Oh et al. and Park et al. (39,41) used the harmonic Bz algorithm which
computes the conductivity images based on the relation between 2B U . Nam et al.
proposed the J substitution algorithm (42) while Birgul et al. used the current constrained voltage
scaled reconstruction (CCVSR) (43). The harmonic Bz algorithm is advantageous in that no
rotations of the imaging object are necessary for the computation of J. Park et al. analyzed the
projected current density approach (PCD) (44) to reconstruct two dimensional current density
with some approximations. One advantage of using the harmonic Bz algorithm and the PCD
approach is that they work by incorporating the Laplacian of the current induced magnetic field
which remains unaffected by the magnetic field produced due to surface currents on the
40
electrodes and the current in lead wires. This can be proved by using the Biot-Savart equation
described in Equation 2-17. For a current density J, within a domain Ω, the magnetic field due to
that current density can be calculated using the Biot-Savart equation. As the gradient of 1/r can
be written as –r/|r|3, Equation 2-17 can be written as,
o
J r 'B r dr '
4 r r
(2-19)
where J is the current density inside the domain Ω. From the expansion of curl of curl of a vector
field, given that J 0 and fg f g f g , we can write Equation 2-19 as
21 1B J r dr J r dr r
4 r r 4 r r
(2-20)
Using the identities, 1 1
r r r r
and 2 14 r r
r r
, gives us,
oo
o
1B J r dr J r , and integrating by parts results in,
4 r r
J rBJ r dr , r
4 r r
(2-21)
Using the divergence theorem, the above can be written as,
o
ˆJ r n rBJ r dS
4 r r
(2-22)
Since the current J in the domain Ω can be expressed aso
B
, the second term on the right hand
side of Equation 2-22 can be written as,
l
o
B r r ˆJ r n rdS
4 r r
(2-23)
41
where Bϵ and Bl represent the magnetic field due to surface currents on the electrodes and the
magnetic field due to the current in the lead wires, such that, lB B B B . The influence of
Bϵ and Bl can be reflected to the boundary condition ˆJ.n g , implying,
l
2
2
B r B r 0 , r as,
10 r r
r r
(2-24)
Since the reconstructed conductivity and current density images rely on the fidelity of the
Laplacian of induced magnetic field maps, it is imperative that the measured field maps are
ideally noise-free.
2.4.1 Signal and Noise in MREIT
In MREIT, the reliability of the reconstructed conductivity or current density map is
governed by the noise characteristics of the measured induced magnetic field which is a scaled
form of the measured phase of the MR signal. Therefore we rely on the optimization of pulse
sequences and imaging parameters to generate phase changes that are above the image noise
floor. In general, noise in MR images can arise due to a multitude of sources making it
problematic to observe the tissues of interest. The precessing transverse magnetization is
detected by a receiver coil and the induced voltage is manipulated through a series of electronic
circuitry collectively called the receiver chain. As with any measurements, systematic noise in
the measuring apparatus, in this case the electronics, affects the signal-to-noise ratio (SNR) that
can be achieved. In MRI, SNR is dependent on various factors not limited to imaging parameters
like voxel size, number of averages, bandwidth of the low pass filter present during signal
readout (BWread), thermal fluctuations in the sample being imaged and the impedance of the
42
receive coil dictated by the amount of loading due to the sample. The measured k-space MR
signal for 2D imaging represented by Equation 2-11, can be extended to 3D and re-written as,
2 k rk dS r e r (2-25)
where the term ρ(r) represents the effective spin density. Equation 2-25 represents the continuous
sampling of the signal while in reality, the MR signal is sampled as a discrete set of points in 3D
k-space. If the total image comprises of Nf, Np and Ns data points each separated by Δkf, Δkp and
Δks in k-space, then the signal in a voxel of the reconstructed image can be written as,
f p s
mm' nn ' pp 'i2
N N N
f p s
m',n ',p 'f p s
1m f ,n p,p s S m ' k ,n ' k ,p ' k e
N N N
(2-26)
Equation 2-26 shows the relation between the reconstructed signal in a particular voxel and its
corresponding k-space counterpart (45). This reconstructed signal is proportional to the volume
Δf.Δp.Δs and as the volume of voxels, which is controllable in an MR experiment, is increased,
the net signal is also increased thereby increasing the SNR. As the Fourier transform is a linear
operation and the recorded signal comprises of the true signal along with a noise component, the
variance of the measured signal due to noise also depends on the volume of the voxel. The
variance of the induced voltage in the receiver chain can be written as 4kT R BW where R
represents the effective impedance due to the sample, coil and the electronics. This noise is
considered to be “white” as it is equally distributed in power across all frequencies within the
readout bandwidth. As white noise can be characterized as a Gaussian distribution with zero
mean and variance, σm2, the variance of noise (white) in the image domain (σo
2) can be written
as,
2
m
f p sN N N
(2-27)
43
i.e noise in the image domain is spread equally over all the voxels and is considerably lower.
Repeated measurements of the imaging experiment can further decrease the noise level and the
variance of the measured noise is decreased proportional to the number of measurements (Navgs).
The overall SNR in a voxel can then be written as,
avgs
f p s
f p s N
BW
N N
N
N
AS R
(2-28)
To better understand the signal and noise characteristics in an MR image, it is necessary to pay
attention to the two components that make up the image, namely the magnitude and phase.
2.4.2 Magnitude noise
The magnitude images are constructed from the real and imaginary images produced
from the mixing stage of the receiver chain as the square root of sum of their squares. This is a
non-linear mapping and therefore the noise in magnitude images no longer follows a Gaussian
distribution but can be represented using a Rician distribution. The Rice density (46,47) can be
represented as,
2
2
2M A
2M 2 2o
M A MP (M) e I
(2-29)
where, ‘PM’ is the probability distribution for the measured pixel intensity ‘M’. ‘A’ is the image
pixel intensity in the absence of noise. Io is the zeroth order Bessel function of the first kind and
‘σ’ is the standard deviation of Gaussian noise in the real and imaginary images. The Rician
distribution starts to approximate to Gaussian distribution for SNR values that are greater than
three. In the regions outside the sample (background in the image), since there is no “true” MR
signal, A in Equation 2-29 becomes zero and we get,
44
2
2
2
M
2M
MP (M) e
(2-30)
Equation 2-30 describes a Rayleigh distribution. The standard deviation of such a distribution
can be related to the Gaussian distributed white noise, σo, as 0.655σo.
2.4.3 Phase noise
The phase images are generated by calculating the four quadrant arctangent of the ratio of
imaginary and real images which, like the magnitude calculation, is also a non-linear function,
and hence the distribution of noise is no longer expected to be Gaussian. The distribution of
phase noise (Δθ) can be given by,
2 2 22
2 2
A
2
Acos
A cos x
2 21 A
P e 1 2 c1
e e do x2
s2
(2-31)
Though the above expression seems extremely complicated, in the limits A = 0 and A ≫ σ the
distribution can be understood much more easily. In regions with only noise, A=0 and the above
equation converges to 1/(2π) as long as -π < Δθ < π. This is equivalent to a circle in the complex
plane since the noise vector is equally likely to point in any direction. The phase noise
distribution as a function of Δθ in Equation 2-31 is shown in Figure 2-4. When A ≫ σ, the
integral in Equation 2-31 reaches 1 and the distribution can be written as,
2
2
2
2 2A 1 cos2
2
2 AA c
2
A
os 1P e e
2
(2-32)
which represents a Gaussian distribution. This result corroborates the idea that if one is to
represent the magnetization as a vector in the complex plane, the variance in the magnetization
due to noise can be decomposed into parallel and perpendicular vectors along the magnetization,
45
and given that the magnitude of the magnetization is very large, the parallel component can be
ignored. The perpendicular component is then responsible for the deviation of the magnetization
from the real axis thereby causing an uncertainty in the phase of the magnetization (Figure 2-3).
Using the approximation that tan for a small angle δ, the uncertainty can be linearized as
σp/A where σp represents the perpendicular component of noise. The standard deviations for the
phase noise can then be given as 1
SNR
when A
A (45) and
22 if 0
3
A .Therefore, in
MREIT, the noise standard deviation of the magnetic field calculated as in Equation 2-15 can be
written as,
c
cB
c c
1
2 T 2 T SNR
(2-33)
From Equation 2-33, it is clear that the noise in the induced field maps can be decreased by
increasing the signal-to-noise ratio in magnitude MR images. Another factor determining the
noise levels is the current injection time. As the current injection time increases, greater phase
accumulation due to the current’s magnetic field occurs increasing our ability to characterize
magnetic fields produced by low amplitude currents. For currents in the order of hundreds of
microampere the accumulated phase is restricted to the interval [-π,π] and phase unwrapping
algorithms are not necessary. However, the increase in Tc is limited by the T2 of the sample
being imaged which controls the degree of magnetization available thereby controlling the SNR
in the magnitude image. Thus there exists a tradeoff between increasing the current injection
time (Tc) and achieving the best possible SNR that dictates the reliability of measured phase
change for a given MREIT acquisition.
46
2.4.4 Optimization of imaging parameters to improve sensitivity
A typical spin echo MREIT sequence is shown in Figure 2-5. The magnetization signal
detected in MRI depends on the longitudinal and transverse relaxation times, T1 and T2, of the
precessing spins and is given by the solution to Equation 2-6 at echo time as,
1 2
TR TE
T TM x, y x, y 1 e e
(2-34)
Expressing the echo time (TE) of the imaging sequence in terms of RF pulse width duration
(assuming the 90° and 180° pulse have the same pulse width, τ), sampling time interval and the
current injection time we have,
srfc
TT
2T
2
3E
(2-35)
Since the SNR of the experiment is dependent on T2 and is directly proportional to the square
root of sampling time, Ts, the noise standard deviation in Equation 2-33 can be rewritten as,
2
c
TE
T
B
rfc c
e
3T 2 TE T
2
(2-36)
Differentiating Equation 2-36 with respect to Tc to obtain the optimal pulse width for
minimizing the noise standard deviation, we obtain the optimal value as,
rc f
2T TE 3
3 (2-37)
This gives an optimal sampling time that corresponds to the current injection time as,
rs cf
2T TE 3 T
3 (2-38)
Injecting current into the sampling interval was performed by Kwon et al. in 2007 (Figure 2-6).
Though the injected currents inside the sampling interval distort the linear relation between spin
47
position and precession frequency, the magnetic fields due to injected currents are extremely
small when considering traditional image resolutions (millimeter) and their effects can be
ignored. However, taking into account the non-linear mapping could potentially improve the
sensitivity of measurement considerably (as high as 40 %). For such an experiment, the authors
predicted the optimal current injection time and sampling times to be,
rfc
fs r
2
33 3T TE
3
2 3T TE 3
3
(2-39)
The above equations describe the optimization of the injection current pulse width to obtain the
best possible noise characteristics in the induced magnetic field map. Assuming perfect
electronics, increasing the sampling time to decrease the bandwidth of the image acquisition
could lead to unwanted off-resonance effects like chemical shift artifacts. Decreasing the noise
standard deviation in the induced field map can also be achieved by improving the SNR of the
magnitude image. One possible way for achieving this is to use a multi-echo sequence as
opposed to a single echo and using the relaxation time envelope governing the signal over the
multiple echoes to obtain an average map that has the best SNR characteristic. However with
multiple RF spin echoes, imperfect 180° pulses pose a problem and could cause an inherent
signal loss affecting the SNR of the image. Recently Oh et al. (48) employed a multiple gradient-
echo sequence to decrease the noise standard deviation of the current induced field maps that
showed great promise for the measurement of small magnetic fields due to low amplitude current
injections.
48
2.4.5 Projected Current Density
In MREIT, reconstruction of conductivity distribution requires the use of at least two
independent currents to tackle the problem of uniqueness as described by Equation 2-18.
However in 2007, Park et al. (44) developed the projected current density approach that
facilitates the reconstruction of current density using just one injection current, under
assumptions of a transversal two-dimensional internal current distribution (for example in the
XY plane).
For a cylindrical imaging domain Ω that can be represented by the union of ‘m’ thin
slices, Ωt where t 1,m , Jp is a projection of the internal current density J inside the domain Ωt.
Jp can be uniquely determined and decomposed into curl free and divergence free components Jo
and J*. Under the assumption that the component of current density perpendicular to the slice Ωt
is the same for both J and Jp, it can be shown that J =Jp can be estimated from measuring Bz in
just one direction. The curl free component of Jp, Jo, is a two-dimensional current density due to
a homogenous potential α and can be represented by . J* (divergence free component) can
be represented by the curl of a two dimensional field β. Using Equation 2-16, α and β then satisfy
the following equations,
2
22 c
o
0 in
ˆ ˆn J.n on
BJ in
0 in
n 0 on
(2-40)
where Bc is the calculated current induced magnetic field from Equation 2-15 and n is the
outward normal vector on the boundary ∂Ω. Park et al. (44) showed that the measured projection
of J, Jp, is unique and independent of the conductivity of the sample being imaged as long as the
49
internal current is predominantly planar in Ωt. For a three-dimensional distribution of J, the
difference vector pJ J is calculated and the authors show that the norm of the difference vector
pJ J up to some tolerance is dependent on the norm of the difference of z-components of J
and Jp. The reconstruction of projected current density is carried out using the following steps.
1. Assuming a uniform conductivity, σo = 1 S/m, calculate the internal current density oJ
and the magnetic field o
cB due to oJ , using a computational model.
2. Using the calculated o
cB and the measured Bc, calculate the projected current density given
by Park et al.(44) as
o
m o m o
c c c c
o
B B B B1J
xJ 0
y, ,
(2-41)
3. Iterate the reconstruction procedure to improve the reconstruction of J using the
measured Bc by reducing the error between J and oJ till desired tolerance is achieved.
50
Figure 2-1. Graphic representation of low frequency and high frequency current flow in tissue.
Figure 2-2. Schematic for experimental setup in an MREIT experiment while injecting current
into a cylindrical agarose gel.
51
Figure 2-3. Representation of magnetization vector and the effect of noise on the phase (ϕ) of the
magnetization vector. A represents the magnetization in the absence of noise, and M,
in the presence of noise. For simplicity the deviation in ϕ due to noise is shown to
increase ϕ though in reality it could decrease ϕ as well.
Figure 2-4. Distribution of phase noise for varying levels of magnitude signal-to-noise ratio. The
distribution begins to approximate to a Gaussian distribution for SNR values greater
than 3.
52
Figure 2-5. Spin echo pulse sequence for MREIT acquisition. The current polarity is reversed
after the 180° pulse to account for the phase reversal of spins.
Figure 2-6. Spin echo sequence with current injection during the sampling interval altering the
linear relationship between the spin position and frequency.
53
CHAPTER 3
DETERMINATION OF THE EFFECT OF TEMPORAL VARIATIONS IN THE STATIC
FIELD ON MREIT ACQUISITIONS
3.1 Introduction
The field of neuromodulation has gained immense popularity over the past decade. In
particular, transcranial electrical stimulation techniques have been in the spotlight as a result of
the concerted effort from several research groups attempting to understand transcranial
direct/alternating current stimulation (tDCS/tACS). tDCS and tACS have been shown to be able
to modulate cortical activity and hence might serve as augmentative therapies to promote
rehabilitation if carefully controlled. tDCS is hypothesized to operate by modulating the resting
membrane potential of neurons making them either hyper or hypo excitable (17), whereas tACS
works by modulating the background neuronal activity occurring in the brain (18). Effects of
these types of electrical stimulations have been predominantly studied by understanding the
behavior of participants undergoing electrical stimulation and few research groups have
attempted to quantify current induced changes on the brain tissue (49). There exists ample
literature showing the use of tDCS in the MRI scanner (23) where researchers have attempted to
capture changes in brain connectivity during electrical stimulation. However, given the
complexity of brain connections and the concept of functional connectivity which addresses the
relation between two different regions of the brain involved in the same functional task (50),
understanding the distribution of induced electric currents becomes extremely challenging. (51).
Scott et al., in the late 80s, imaged current flowing in a gel phantom using the concept of MRI,
thus laying the foundation for current density imaging. It was later improved in the early 2000s
and came to be called as Magnetic Resonance Electrical Impedance Tomography (MREIT) (36).
MREIT relies on changes produced in the phase of the detected MR signal caused by injected
currents. These phase changes are reflective of the local magnetic field from which the current
54
density can be calculated. Further, computational models to predict the distribution of current
inside the human head have been developed (52). Given the conductivity of brain tissue and
applied current amplitude, currents that reach the cortex and subcortical structures are extremely
small and so are the magnetic fields due to such small currents. Therefore, measurements of
these fields are easily corrupted by the presence of noise and any variations in the field
homogeneity or stability. Moreover, there exists an inherent drift in the static magnetic field of
superconducting magnets owing to imperfect construction joints which is usually quoted in the
magnet’s specifications. Fast imaging sequences could cause heating of resistive magnet
structures such as existing passive shims and alter their calibration for generating a homogenous
field. For high amplitude current injections, shifts in the proton resonance frequency due to
current-induced local heating could also pose a serious problem. In MREIT, the phase change in
the MR signal due to injected current is calculated as the four quadrant inverse tangent of the
complex division of positive and negative current injected datasets (36).
This chapter addresses the effect of variations in the static magnetic field on MREIT
measurements and the development of necessary electronics for facilitating acquisitions that are
relatively insensitive to the magnetic field inconsistencies. Experimental data following data
collection using two methods is presented and the usefulness of the second method in
circumventing sources of static field inhomogeneity is demonstrated.
3.2 Theory
Variations in the static magnetic field of an MR scanner can be calculated directly from
measured phase in the MR image, which is advantageous to MREIT. By measuring phase
changes relative to a baseline condition, the net change in image phase can be calculated which
is reflective of the applied current-induced inhomogeneity in the static field. The MRI signal
equation for a two dimensional image acquired without any current injection can be written as,
55
oi
o
x,yS x, y S x, y e
(3-1)
where ϕo represents the background phase occurring due to various sources including the RF
pulse used to create the image, sample loading on the detection coil, variations in electronics etc.
In gradient echo imaging, the measured signal is affected by two important parameters. One is
the T2 effect due to spin-spin relaxation and the other is the presence of any local field
inhomogeneity that could cause a dephasing of spins in the affected voxel. The final
reconstructed image at the echo time (TE) can then be written as,
ooi , TE
o
i B x yS x, y S x, y e e
(3-2)
The background inhomogeneity can be extracted by performing repeated measurements
at varying time intervals and estimating the variation via the image phases (53). Since the
temporal variation of the main magnetic field is unknown, the time dependent phase evolution of
spins can be written as,
1
2
t
1 1 o o
0
t
2 2 o o
0
o
x, y, t x, y B x, y, t dt
x, y, t x, y B x, y, t dt
x, y, tB x, y, t
t
(3-3)
In Equation 3-3, Δϕ refers to the net phase change in the time interval 2 1t t t . The temporal
drift of the main magnetic field can be assumed to be linear in the absence of variations
occurring due to heating of resistive structures. This allows us to drop the integral representation
for describing the phase of spins and write the net change in magnetic field as the last equation in
Equation 3-3. Repeated measurements can be made at different intervals either by using a fixed
echo time and creating fresh transverse magnetization for each measurement (Equation 3-3) or
56
by following the transverse magnetization phase at multiple echo times for a single excitation as
in a multi-echo acquisition,
o
x, y,TEB x, y,TE
TE
(3-4)
A shift in the phase of an MR image can also be generated by shifting the 180° RF pulse of a
spin echo sequence. Such a shift causes a difference in the durations of precession before and
after the 180° pulse resulting in the accumulation of phase due to existing background field
inhomogeneities that can be specifically measured according to the equation,
1,2 1,2
o o fp
o fp
x, y, t x, y 2 B x, y, t
x, y, t 2 B x, y, t
(3-5)
where, τfp is called the free-precession delay term (54). In MREIT, in addition to any existing
background field inhomogeneity, we impress an additional current-induced magnetic field in
order to extract it (which is an inhomogeneity in the static field) as a change in the phase of the
signal. The equations for the complex divided image in MREIT and the current induced field can
be given as,
c co o
c c
i B x,y Ti B TE
B x,y
i
o
i2
c
T
c
S x, y S x, y e
S x, ye
S x, y
S x, yarctan
S x, yB x, y
2
e e
T
(3-6)
where Bc is the magnitude of the current induced magnetic field and Tc is the duration for which
the induced magnetic field persists. Due to the complex division to extract the current induced
magnetic field, static field inhomogeneities that remain unchanged during the acquisition of the
positive and negative current injection scans do not affect MREIT measurements. The work
57
detailed in this chapter focuses on the effect of temporal changes in the static magnetic field on
MREIT acquisitions and the development and use of an acquisition protocol that helps mitigate
these effects in current injection experiments.
3.3 Methods
3.3.1 Pilot Experiments
3.3.1.1 Phantom preparation
An agar gel phantom was prepared by mixing 25 g of agar in 1200 ml distilled water. 3 g
of NaCl and 0.3 g of CuSO4 were added to the solution to increase its conductivity and facilitate
conduction of injected current. The mixture was heated in a microwave for uniform heating.
Dissolution of the agar resulted in some frothing causing the liquid to rise. At this time the
microwave was turned off and the mixture was allowed to drop back to its initial level. This
process of heating and cooling was repeated until all of agar (seen as a precipitate in the bottom
of the beaker) was completely dissolved. Once the solution no longer rose but boiled in place, it
was taken out, cleared of froth, and was poured into a 3 liter beaker with an approximate
diameter of 16 cm. The beaker was covered to trap the heat and maintain the liquid state of the
mixture while another identical solution of 1200 ml was prepared and combined with it to
achieve a total volume of 2400 ml. The mixture was left to gel for over 6 hours at room
temperature following which it was refrigerated until it was hard facilitated easy removal from
the beaker. The phantom was allowed to remain at room temperature for at least a couple of
hours prior to use in the imaging experiments.
3.3.1.2 Image acquisition
The phantom was placed in the bore of a 3 Tesla Philips Achieva magnet and a spoiled
gradient echo sequence with ten echoes (Figure 3-2) was used to acquire 2D axial images using a
32 channel head coil. The imaging resolution was 2.24 x 2.24 mm using a matrix size of 100 x
58
100. The bandwidth used was 550 Hz/pixel. A repetition time (TR) of 50 ms was used for
acquisition of each phase encode step where the ten echoes were collected.
3.3.1.3 Data inconsistencies
Electrode cables were attached to the exposed ends of magnet wire that was driven into
the gel phantom and current was injected using the experimental setup shown in Figure 3-3.
Current of one polarity was injected throughout the acquisition for every phase encoding step
and the 2D axial images were acquired at ten different slice locations. The time taken for
acquiring one such volume of data was approximately 50 seconds. To improve the signal-to-
noise ratio, 4 such 3D volumes (dynamics) were acquired amounting to a total acquisition time
of approximately 3½ minutes. This entire acquisition was repeated for the opposite current
polarity and magnetic field maps were calculated from these two current injection datasets using
the Equation 3-6. The contribution of current-induced fields during the sampling interval was
predicted to be extremely small and therefore not accounted for in the data processing. The
resulting field maps are shown in Figure 3-5. When repeated measurements were performed with
identical imaging and electrical stimulation parameters, very different magnetic field maps were
obtained (Figure 3-5) which indicated a temporally unstable static magnetic field. Variations in
the static magnetic field could alter the reference against which the current-induced field maps
were computed thereby producing inconsistent results.
3.3.1.4 Troubleshooting data inconsistencies
To understand the inconsistencies observed, experiments using the same acquisition
method as in the pilot experiments were performed without any current injection to map the
temporal variation of the static magnetic field. To characterize the temporal variation, each
volume (3D) of acquisition was repeatedly acquired (n = 40) with the first ten acquisitions
collecting two volumes each while the next two acquisitions collected ten volumes each. In a
59
separate experiment, these scans were performed in a reverse order and an additional acquisition
with ten volumes was performed at the end (total n = 50) to check if the observed inconsistencies
were dependent on the order of acquisitions. The total time for each experiment was
approximately 30 minutes.
3.3.2 Field Corrected Experiments
To circumvent the sources of inconsistencies observed during pilot experiments a new
acquisition method was used where the same spoiled gradient echo sequence with ten echoes was
employed to collect 2D axial images at three different slice locations, while collecting repeated
measurements (n = 24) of each phase encoded step as opposed to the full 3D volume. This
ensured that each repetition in the data was interlaced to be closest in time to the preceding one
thereby greatly minimizing the time window for any substantial background inhomogeneity to
influence measurements. The rationale behind this approach was that injection of currents of
opposing polarity for each repeated measurement would maintain the fidelity of the computed
current-induced magnetic field maps. First, the stability of the static magnetic field over time was
measured using the acquisition method employed in pilot experiments and compared against that
specified by the manufacturer. Next, current injection experiments using the two acquisition
methods were compared.
3.3.3 Electrical Stimulation
Electrical stimulation was delivered through conductive rubber electrodes housed in
saline soaked sponges using an MRI compatible, battery driven, constant current source
(NeuroConn DCMC, Ilmenau, Germany). The stimulator was triggered using a TTL signal
generated by the MRI scanner following the installation of a custom patch and the current was
injected at 1.5 mA using pulse widths of 32 ms. The stimulator was positioned outside the
magnetic field in the operator room. Current was administered via two RF filter boxes, one
60
placed closed to the filter panel connecting the scanner room with the operator room and the
other was placed inside the bore of the MRI scanner to which electrode leads were attached. A
switching circuit (developed in-house) was also used between the stimulator and the outer filter
box in order to deliver fixed-duration current pulses during the time interval following RF
excitations. The complete experimental setup is as depicted in Figure 3-4. For the experiments
using approach two, the stimulation polarity was alternated at each RF excitation with the help of
an onboard programmable microcontroller which was a part of the switching circuit. No such
alternation was performed until the completion of the scan during the pilot experiments. Anode
and cathode leads coming out of the inner filter box housed two 5 kΩ resistors to prevent
induction of high voltages from RF pulses produced during imaging. It was ensured that the
electrode cable emanating from the inner filter box ran parallel to the static field by securing it in
place using sand bags.
3.3.3.1 Switching circuit
The NeuroConn DC MC stimulator posed two major challenges. First, it was not possible
for the stimulator to be triggered by an external device (MRI scanner in this case) and hence it
was not possible to precisely control the delivery of current. Second, it did not allow for sub-
second stimulation durations which meant that the minimum TR usable in the MR acquisitions
was at least one second which drastically increased the scanning time. To address these
shortcomings, a switching circuit was developed in-house which would enabled us to capture the
5V TTL signal from the MRI scanner and gate the electrical stimulation appropriately. With the
ability to gate the stimulation, controlling the duration of stimulation meant controlling the
gating interval which was easily achieved with the use of a microcontroller. The switching
circuit also played an integral role in allowing us to control the polarity of the applied
stimulation.
61
3.3.3.2 Circuit description
The circuit schematic is shown in Figure 3-4. All components are represented as boxes
with gray shadings and where possible, anode cables are shown in red and cathode cables in
blue. LCB110 and LH1540 are optocouplers that depend on the bias of an available light
emitting diode and sensor pair for break/make type contacts. In the default state, LCB110 is a
normally closed switch (NC) and LH1540 is a normally open switch (NO). LCC110 is an
integrated chip that possesses both NC and NO connections whose states can be toggled by
forward/reverse biasing its light emitting diode. The microcontroller used is a commercially
available MSP430G2553 microcontroller housed on a MSP-EXP430G2 launch pad built by
Texas Instruments. The circuit also includes a test resistance (R-test) in order to monitor the
delivered electrical stimulation on an oscilloscope (also shown in figure). Since the
MSP430G2553 microcontroller has a maximum input operating voltage of 3V, the 5V TTL
signal was reduced using a voltage dividing circuit.
Working. The constant-current stimulator was set at the appropriate current rating and
configured to deliver a continuous DC current of the desired amplitude. The working of the
circuit can be divided into three states depending on the TTL input from the magnet: no TTL,
odd numbered TTL and even numbered TTL
No TTL. This is the default or initial state of the system in which no current injection
was desired and the output of the stimulator was fed to LCB110 which operates as a “normally
closed” switch, thereby completing the current path from anode to cathode of the stimulator.
Odd numbered TTL. For all odd-numbered TTL pulses, the microcontroller was
programmed to generate a “HIGH” (3 V signal) on pin 17 in response to the received TTL signal
on pin 25. This signal generated sufficient voltage to forward bias the diode in the optocoupler
LH1540 (normally open switch) closing the switch and creating a route for the current from
62
anode to the outer box. After accounting for the switching time to complete this routing, the
microcontroller generated a high signal to change the state of LCB110 to open circuit. This
ensured that the current from the stimulator now traversed along the path; anode-LCC110 (top)-
LH1540-outerbox-subject-outerbox-Rtest-LCC110 (bottom)-cathode. This status was maintained
for the duration of current injection time (Tc) following which the states of LH1540 and LCB110
were restored to their default condition. This ensured that the phantom received current injection
for the desired time Tc.
Even numbered TTL. For the even numbered TTLs, in addition to the process described
above, the microcontroller was programmed to also toggle the states of LCC110s by sending a
high signal on pin 23 that was input to the LCC110s. Toggling the states of LCC110
optocouplers altered the route of input stimulation so as to make it traverse along the path;
anode-LCC110 (bottom)-Rtest-outerbox-subject-outerbox-LH1540-LC110 (top)-anode. This
effectively switched the direction of the current injection perceived by the imaging object and
enabled us to achieve a bipolar stimulation during the imaging session.
Apart from enabling triggering, the circuit also provided the facility for polarity
switching of the stimulator output on the timescales of the repetition time of MR acquisitions.
The TTL trigger and current waveforms used for stimulation in both acquisition methods are
shown in Figure 3-6.
3.3.4. Data Processing
For the measurements obtained without current injection, in both the pilot and corrected
experiments, the acquired raw k-space multi-echo data was first read into IDL 8.1 as an 8D array
of complex floating point values. The k-space lines along the frequency encoding direction were
flipped to account for the negative readout gradient and inverse Fourier transformed to calculate
the complex MR image data. The pilot and corrected measurement data were then partitioned
63
into 40 and 24 volumes respectively to obtain a time-series of multi-channel complex images.
Each of those volumes was complex divided by its preceding volume in the time series and the
multi-coil data was combined following the method described by Bernstein et al. (55). Complex
dividing the multichannel data prior to coil combination removed any fluctuations in the coil
phase and ensured that the coil sensitivity maps were not required for the reconstruction (56).
Following coil combination, the phase of the coil combined dataset was computed as the four
quadrant arc tangent for every slice location and echo collected. The magnetic field
inhomogeneity was measured from the computed phase maps at different echo times using
Equation 3-4.
3.4 Results
To address data inconsistencies, each of the 40 volumes of data collected by repeated
acquisitions without current injection was complex divided by its preceding volume to generate
39 datasets. Phase maps for these 39 datasets were computed and a region of interest (ROI) 30
pixels by 30 pixels in size was drawn in each of these datasets. Figure 3-7 shows a plot of the
mean and standard deviation of phase in the region of interest for the center slice and first and
last echo times of the original and reversed experiments. The haphazard variation observed in the
mean phase within the region of interest followed acquisition order when the experiments were
reversed, indicating that the inconsistency was directly related to the acquisition itself and not
due to heating of gradients or tissue relaxation between acquisitions. In addition, the low inter-
scan variability as evident from the first part of the plots suggested that it would be better to
acquire the desired data within a single acquisition. Phase values in the region of interest when
plotted as a function of echo number (as opposed to divided datasets) revealed a linear variation
of phase across echo times indicating the presence of a static field inhomogeneity in the
background. The precession frequency shift (γΔBo) due to the presence of the static field
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inhomogeneity was calculated as the slope of the linear fit across repetitions using the first echo
time according to Equation 3-3 to be 0.57 Hz/hr (Figure 3-8). However, in the field-corrected
experiments, the variation of the mean phase over the repetitions was quite stable (Figure 3-9)
indicating that these measurements would be less sensitive to the changing static magnetic field
and MREIT data acquired using this style would be more accurate.
Current injection scans acquired using 1.5 mA and a bipolar approach as shown in Figure
3-10 provided more stable measurements for the current-induced magnetic field. Figure 3-11
shows the consistency in the current induced field map for the center slice across three repeated
acquisitions of the 24-volume dataset.
3.5 Discussion and Conclusion
The results presented in this chapter demonstrate the influence of temporal drift in the
static field on MREIT acquisitions. MREIT or Current Density Imaging (CDI) acquisitions
typically involve the complex division of two datasets that differ only in the polarity of current
injection (37). Therefore, static field inhomogeneities are less concerning in MREIT than
temporal fluctuations. As per the specification sheet of the Philips Achieva scanner, the field
drift was approximately 1.28 Hz/hr and that measured in this work was close to 0.57 Hz/hr or
approximately 0.01 Hz/min. Magnetic fields produced due to milliampere current injections are
in the nanoTesla range which corresponds to frequency shifts of about 0.043 Hz. Therefore, for
the successful characterization of the current-induced fields, it is necessary that the MREIT data
acquired for complex division is collected over very short timescales. In the work presented here,
this effect is well established as the temporal changes in the static field have been shown to be
strong enough to mask the effects of injected currents.
It has been shown that the noise in the current-induced magnetic field is inversely
proportional to the current injection time and SNR of the magnitude MR image (57). Repeated
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measurements, if stable, can be averaged for each acquisition, thereby improving the SNR and
hence the reliability of detecting minute fields. All data acquisitions were performed after
allowing for at least two hours of rest for the MRI scanner. This duration was hypothesized to be
a sufficient time for any field inhomogeneities from eddy currents generated during prior use to
subside. Observed results support this hypothesis and indicate that the major contributor which
masks the current-induced magnetic field is the temporal drift of the scanner. Another approach
to mitigate the effect of temporal inhomogeneity would be to use the field fluctuation
information from a distant region that is known to be unaffected by the applied current (58). The
best approach to compensate for the field variation would be to quickly characterize the Bo map
in between the MREIT acquisitions. This was however not feasible due to limitations on
scanning time. By acquiring the two datasets that need to be complex divided extremely close in
time (averaging over each individual phase encoding step), even though the static field varies to
a large degree over the length of the full k-space acquisition, we believe that this effect is
diffused similarly in both the datasets and is cancelled more efficiently. This is apparent from
Figure 3-9 which shows considerable stability to the temporal variations in the static field.
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Figure 3-1. Gel phantom used in MR experiments. A) Freshly prepared agarose gel phantom
after removal from refrigerator. B) Experimental setup showing the electrodes
secured on the gel with a rubber strap. C) Schematic showing the placement of the gel
phantom in the MR scanner.
A B C
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Figure 3-2. Spoiled multi gradient echo sequence (2D) used for data acquisition. The repetition
time (TR) was 50 ms. Current pulses Ic = ±1.5 mA in amplitude were injected for a
duration of 32 ms. The bandwidth of acquisition was 550 Hz/pixel while 100 samples
were collected during the frequency encoding. The echo spacing was 3 ms.
(Method 1): 1.5 mA was injected till the completion of all frequency and phase encoding steps
for all slice locations to generate a 3D volume. This 3D volume was repeated for the
required number of averages before -1.5 mA was injected to collect data in a similar
fashion. The first echo time (TE1) was 6 ms.
(Method 2) The required averages were collected for each phase encoding step with +1.5 mA
and -1.5 mA alternatingly injected for each average. A delay time (Td) of 4 ms was
used to allow polarity switching. The phase encoding step size was incremented after
collecting all averages until a full slice acquisition was completed. The first out of ten
echo times (TE1) was 7 ms.
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Figure 3-3. Layout of the experimental setup used for imaging. The current injected was
carefully monitored using the oscilloscope to ensure the synchronization of RF trigger
and injection pulses as well as the injection amplitude. The components of the
stimulator commercially available are shown in orange while the in house
components added to the circuit are shown in gray.
69
Figure 3-4. Schematic of the switchbox circuit and layout of the different components used in coalition for data acquisition. R-test is
the test resistance of 1 KΩ across which the stimulation is checked using an oscilloscope.
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Figure 3-5. Preliminary experimental results from two identical acquisitions performed with 1
mA current injection through a wire placed in a gel phantom. A) Images acquired
during acquisition 1. B) Images acquired using identical acquisition parameters as in
A, showing data inconsistency due to magnetic field instability.
Figure 3-6. Oscilloscope recording during pilot experiments for 1 mA current injection. Each
division on the X-axis corresponds to 50 ms. The TTL signal (green trace) generated
after every RF excitation (see Figure 3-2) during imaging and corresponding
stimulation voltage (blue trace) recorded across the test resistor due to injected
current (Ic+ in Figure 3-2) are shown.
A
B
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Figure 3-7. Phase variation in a 30x30 pixel ROI across each of the complex divided datasets. A)
The first 19 datasets corresponding to data acquired as two volumes per acquisition,
and the next 20 to data collected as 10 volumes per acquisition. B) Data from similar
experiments as in A, acquired in reverse order along with an additional 9 datasets
from the repeated 10 volume acquisition.
A
B
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Figure 3-8. Regression fit for the phase values within a 30 x 30 pixel ROI drawn in the center of
the image for the first echo time across the ten volumes collected as part of the first
acquisition in the reversed experiments. Acquisition time for 1 volume was
approximately 52 seconds. The measured frequency drift from the regression fit was
0.57 Hz/hr.
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Figure 3-9. Variation of the mean phase in a 20 x 20 pixel ROI drawn in the center of the image.
Each of the twenty-three plots represents the phase obtained by complex dividing data
of every repetition by its preceding one. The X-axis in each plot represents the echo
number. A total of 24 repetitions/averages were acquired during the field corrected
experiments.
Figure 3-10. Oscilloscope recording of the voltage across the test resistor (see Figure 3-4) due to
1.5 mA current injection (blue) alternating polarity with every incoming TTL signal
(green).
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Figure 3-11. Magnetic field maps for the first slice location obtained from field corrected experiments by acquiring the positive and
negative current injection data very close in time. Identical maps across multiple current injection runs show measurement
reliability and insensitivity to temporal drift of the static magnetic field.
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CHAPTER 4
MEASUREMENT OF ELECTRICAL CURRENT DENSITY DUE TO TRANSCRANIAL
ALTERNATING CURRENT STIMULATION OF THE HUMAN BRAIN AT 3 T
4.1 Introduction
The effect of electrical stimulation of the human brain has been a hot topic of research for
quite some time and there have been numerous efforts in understanding the spatial distribution
and temporal variation of the applied electric field. Given that the brain is a complex and
intricate network of neurons, neuronal activation thresholds and integration characteristics of
neurons to enable firing also play a major role in the observed effects of electrical stimulation.
Knowledge of the applied electric field provides insights into the different regions affected due
to stimulation, the extent to which they are influenced spatially and how strongly the affected
regions are modulated by it. The applied electric field causes free ions in tissue to move,
constituting a current density which is defined as the charge flowing through a cross sectional
area per second and is related to the applied field via Ohm’s law EJ .
Electrical conductivity or σ is a property of the underlying tissue and is defined as the
amount of resistance faced by the moving ions under the influence of applied field. Under the
assumptions that there are no sources or sinks present in the volume of tissue, total current
entering the volume should be equal to the net current exiting the volume, i.e. J 0 . The
presence of free and bound charges in the tissue gives rise to conduction and displacement
currents that can be described by the conductivity and permittivity of brain tissue. In the range of
excitation frequencies spanning 0 – 10 kHz, the conductivity of brain tissue is largely determined
by the extracellular conductivity. A comprehensive review of the dielectric properties of
biological tissue was given by Gabriel et al. (59-61).The human head comprises of different
tissue types (fat, skin, muscle, white matter and gray matter etc.) and transcranial stimulation
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applied using surface electrodes gives rise to different current densities in these tissues. For
instance, muscle tissue comprises of a collection of muscle spindles or fibers that have varying
conductivities in parallel (0.624 S/m) and perpendicular directions (0.131 S/m) (60,62,63).
Therefore muscles under the electrode area will strongly shunt the electrical stimulation
decreasing the amount of current entering the brain. In addition to the muscle, fat, which has a
low conductivity (0.025 S/m), will also decrease the applied electric field in the brain. Skin is a
multilayered tissue where the outer layers are dry and resistive (2x10-5S/m) while the deeper
layers are conductive (0.3 S/m) (64). The skull is probably the greatest barrier that hinders the
applied stimulation from reaching the brain. It comprises of three different layers of bone tissue,
a spongy cancellous layer enclosed between two hard cortical layers. Moreover the thickness of
the skull varies in different parts of the head giving rise to inhomogeneous conductivity. The
skull also comprises of immovable joints called sutures that provide low resistance paths for
applied current. Akhtari et al. measured the conductivity of the three skull layers in preserved
(65) and live tissue (66) and concluded that live tissue was more conductive by at least a factor
of 1.5. Baumann et al. measured the electrical conductivity of cerebrospinal fluid at room
temperature (25° C, 1.45 S/m) and body temperature (37° C, 1.79 S/m). They reported that these
values differed by approximately 25% and that these values were constant over the range of
frequencies from 10 Hz – 10 kHz. Brain tissue, categorized as gray and white matter, is
heterogeneous and importantly anisotropic like the skull. The gray matter can be assumed to be
isotropic and homogeneous with an average conductivity value of approximately 0.4 S/m (67).
Nicholson (68) measured the impedance of white matter in cats’ internal capsules, and reported
that the conductivity along the length of the track was approximately 10 times larger than that
perpendicular to the track. When compared to gray matter, the conductivity of white matter is
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greater along the length of the fiber (1.13 S/m) but the transverse conductivity is lower.(0.13
S/m). In addition to anisotropy, the heterogeneity of tissue has a significant effect on the induced
electric field distribution. Since the electric field across different tissues is constant but their
conductivities vary, charge accumulation occurs at the interface of different tissue types that
generates a secondary field which opposes the flow of charge in the high conductivity region. As
a result, the current density normal to the interface in the high conductivity region decreases such
that the current density on either side of the interface becomes the same. At this juncture, the
amount of charge entering and leaving the interface is the same. This process in biological tissue
occurs in the time span of microseconds and can be considered instantaneous, thus validating
assumptions that the tissue is purely resistive. Miranda et al. (69) showed that the secondary field
generated at these interfaces is a significant fraction of the applied field and cannot be neglected.
Plonsey and Heppner (70) presented several approximations to compute the electric field
distribution at low frequency (DC – 10 kHz). They neglected propagation effects, i.e. the electric
field in the brain was assumed to vary without any significant phase differences or delays in
response to the stimulation and the tissue was considered to be purely resistive. Under these
assumptions, the spatial and temporal variations of induced electric field can be represented by
separate functions with the temporal variation characterized by injected current from the constant
current source.
Mapping the spatial distribution of the electric field or current density however is much
more challenging. Using MRI, Scott and colleagues (36), developed current density imaging, a
methodology to reconstruct injected current density by extracting the three components of the
magnetic flux density vector following rotations of sample in the MR scanner. Assuming sample
conductivity to be isotropic, Seo et al. (39) extended the idea of current density imaging by
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reconstructing maps of injected current using only one component of the magnetic flux density
vector eliminating the need for subject rotation. Kwon et al. (71) extracted tissue properties by
exploiting the relation between conductivity and magnetic field. Recently, Jog et al. (72)
quantified the magnetic field induced due to injected currents in the human brain by tracking
changes in phase of the MRI signal in the presence and absence of current injection and
analyzing them using a generalized linear model.
The work detailed in this chapter is based on the experimental design from chapter 3 and
extends the experiments from phantoms to healthy volunteers. Current-induced magnetic fields
from the experiments are qualitatively compared against those simulated from realistic head
models. In addition the inverse problem of reconstructing electrical current density distribution
from measured magnetic fields in the human brain is solved using the projected current density
approach introduced by Park et al.(44). Aprinda Indahlastari performed the image segmentation
and generation of computational models against which the experimental data compared. Munish
Chauhan reconstructed the projected current density maps. My role was to recruit the
participants, handle the electrical stimulation, perform MR imaging and develop the necessary
data processing software for analysis of the acquired data.
4.2 Methods
4.2.1 Phantom Experiments
A homogeneous agar gel phantom of uniform conductivity was prepared following the
protocol outlined in subsection 3.3.1.1. Electrode cables with carbon rubber electrodes housed in
0.9 % saline soaked sponges were attached diametrically opposite to each other. The entire setup
was then placed in the bore of a 3 T Philips Achieva magnet and MREIT data with 1.5 mA
current injection was collected following the installation of a custom-built patch that enabled
triggering of the constant current source.
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4.2.2 Human Experiments
Healthy volunteers (n = 6) between the ages 18-30 years, without any history of mental
health issues, predominantly right handed, had no history of prior seizures and did not have any
metallic implants that could interfere with the MR imaging, were recruited for participation after
they were duly consented. Handedness was determined by the Edinburgh handedness inventory
test. A Mini Mental examination was performed to assess the IQ of participants. The volunteers
also completed an MRI screening form to ascertain their compliance with the MR imaging
procedure and answered a questionnaire to assess their mood both prior to and following the
imaging session. All participants received electrical stimulation at 1.5 mA via conductive rubber
electrodes enclosed in saline soaked sponges that were placed on predetermined locations
marked on their scalp following the 10-20 system of electrode placement. Current injection
during the imaging was performed along two directions, Fpz – Oz and T7 – T8. The current
polarity was alternated with every RF excitation used in the MR acquisition which corresponded
to a frequency of stimulation of approximately 10 Hz. Subject recruitment, preparation and
imaging were performed in accordance with the experimental protocol (IRB201600695)
approved by the University of Florida Institutional Review Board.
4.2.3 MR Imaging
MREIT measurements were performed using a Philips Achieva 3 T MRI scanner. A
custom patch was installed on the scanner to provide a TTL pulse following each RF pulse
generated in the pulse sequence. A 32 channel head coil was used for signal reception. High
resolution T1 weighted 3D FLASH acquisition, at 1 mm isotropic resolution, was acquired to
facilitate image segmentation and generation of computational models. MREIT measurements
were made using a 2D spoiled gradient echo sequence (SPGR) at a resolution of 2.24 x 2.24
mm2. Three slices at a thickness of 5 mm each were acquired without any gap such that the
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imaged region contained all the four electrodes. The data was collected as multi-echo single slice
acquisitions with a repetition time of 50 ms within which 10 echoes were acquired. The first
echo time was 7 ms and the echo spacing was set to 3 ms. The first echo time was set so as to
allow the switching of current polarity, as needed, following every RF excitation. The k-space
data was collected so as to acquire 24 averages of the same phase encoding step, while altering
the current injection polarity for every average. This ensured that the positive and negative
current injection datasets were acquired as closely in time as possible, thereby minimizing the
effect of the static magnetic field drift. A hundred phase encoded steps were acquired so that the
scan time for each slice was two minutes. This amounted to a total scan time of six minutes per
acquisition.
For each current injection direction, two such acquisitions were performed which were
averaged in the data-processing for better signal-to-noise ratio. One acquisition with the above
parameters was performed without any current injection to serve as the control dataset. For the
experiments with healthy volunteers, the total imaging time for MREIT scans with and without
current injection was approximately 30 minutes. High angular resolution diffusion imaging
(HARDI) data with b values of 100 (in 6 directions) and 1000 (in 64 directions) was also
collected so that the principal Eigen vector of the processed diffusion tensors from this data
could be used in computational modeling.
4.2.4 MREIT Data Processing
Raw k-space data (.DATA and .LIST) files were exported from the Philips scanner and
processed using software developed in-house in IDL. The raw data was read as a
multidimensional dataset comprising of frequency, phase, slice, echoes, averages, and coils as
the dimensional parameters. First, the raw data pertaining to every other echo in the multiple
echo acquisition was flipped in k-space to account for the negative gradient encoding. Spatial
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domain data was then computed by performing the inverse Fourier transform in the frequency
and phase encoding directions. The current induced magnetic field within the sampling window
during data readout was assumed to be negligible in comparison to the magnitude of readout
gradient and therefore, the distortion caused by it was not accounted for during image
reconstruction. Positive and negative current information was encoded in the repetitions as the
polarity of current injection alternated for every repetition of the phase encoding step. To
account for this, the complex reconstructed dataset was split into two datasets comprising of 12
averages each of positive and negative current encoding followed by complex division of
positive data by the negative data. Complex division of the datasets prior to combining the
multiple coil data ensured that the individual coil sensitivities need not be taken into account (56)
and any differences in the phase across coils did not affect the measured data. Magnitude data
was then reconstructed using the sum of squares reconstruction as suggested by Roemer et al.
(73). To calculate the phase of the combined dataset, the individual coil phases were summed
assuming that noise variances in the different channels were identical. The four quadrant
arctangent of this complex divided dataset was calculated to generate phase images. Magnetic
field maps were computed by taking into account the appropriate current injection times for each
of the measured ten echoes.
4.2.5 Image Segmentation
A combination of automatic and manual processes was used to segment a single human
head into ten tissue types. The high resolution T1 dataset was imported into Freesurfer image
processing software to resample the T1 data into an isotropic resolution of 1mm3 and a matrix
size of 256 x 256 x 256. Freesurfer was also used to auto-segment the human head into white and
gray matter. SPM was used to auto-segment bone, skin and air. The remaining tissue types
comprising of cerebrospinal fluid (CSF), muscle, eyes, fat and blood, along with the attached
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electrodes, were segmented manually with Scan IP, Simpleware Ltd, using an atlas of the human
brain as reference. All automatic segmentation outputs were manually corrected in ScanIP
according to the human atlas.
4.2.6 Computational Modeling
The 3D segmented head model derived from high resolution T1 MR images was meshed
in ScanFE, Simpleware Ltd. and exported into the modeling software COMSOL 5.0. Literature
referenced conductivity values for the different tissue types were then assigned to the segmented
3D head model (52) prior to simulation. Finite element calculations, to solve the Laplace
equation with mixed boundary values at the surface of the head model was performed via
COMSOL-MATLAB Livelink Interface. Current density results from finite element simulation
were interpolated into a fine stencil (1001x1001x91, 0.5mm resolution) and were used to
calculate Bz based on the Biot-Savart equation. The Jx and Jy data were used to compute the z-
component of magnetic field having the same dimensions such that,
x y
z 3
y y J r x x J rB r dr
4 r r
(4-1)
Finally, the simulated magnetic field was averaged over each voxel volume and resampled into
2.24 x 2.24 x 5 mm3 resolution to register them to the experimentally measured field maps.
Corresponding slices in the final registered simulated maps were extracted and compared against
the measured magnetic field values obtained from experiments.
4.3 Results and Discussion
4.3.1 Gel Phantom
4.3.1.1 Field measurements
Multichannel MR magnitude images of the gel phantom for the first echo and center slice
location obtained from the inverse Fourier transformation of the complex k-space raw data are
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shown in Figure 4-1. The reconstructed magnitude and phase images following the sum of
squares reconstruction are shown in Figure 4-3. shows the binary mask generated from the high
resolution T1 data and the different slices for the first echo in the multiple echo dataset. Also
shown in are the different echoes for the center slice location. Figure 4-4 and Figure 4-5 show
phase and magnetic field maps generated from the complex division of data acquired with and
without current injection. The increased sensitivity to induced phase and magnetic field, across
echoes, due to increased current injection duration is clear from these images. Patterns of the
magnetic field observed with a darkish hue on one side and a brighter pattern on the other, are
consistent with those reported in literature. This is to be expected because when the current
travels from left to right (or right to left) the magnetic field perpendicular to the slice adds or
subtracts from the static field thus producing the dark and light patterns.
4.3.1.2 Optimization of magnetic field maps
The multiple echo dataset acquired without any current injection was used to generate T2*
maps of the different slices. These maps are shown in Figure 4-6 along with their corresponding
magnitude slices. Each of the magnetic field maps for every echo was multiplied by a weighting
factor (48) that took into account the signal decay due to relaxation and field inhomogeneities.
Moreover, the weighting function was also adapted to take into account the increase in current
induced field which is dependent on the current injection time Tc. Optimized field maps for the
three different slices are shown in Figure 4-7. Figure 4-7 also shows the comparison of measured
magnetic field maps against numerical simulations from a computational model. The
experimental and simulated magnetic field maps show similar range of variation but the
experimental value seemed to be affected by a global offset of 1nT. It is possible that this offset
existed in MREIT experiments by other research groups mentioned in the literature (41,49) but
was not appreciable given the high amplitudes of current used in those studies. Possible sources
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of this offset are the surface currents on electrodes pads or magnetic fields due to currents in the
lead wires.
4.3.2 Healthy Volunteers
The data from two participants (MREIT-005 and MREIT-006) who had electrodes placed
at T3, T4, Fpz, Oz locations showed large noise levels in the computed magnetic field maps and
were hence not further analyzed. This variability was believed to be due to poor electrode
contact with the scalp owing to much denser hair in these participants. For clinical studies, it
would be beneficial to shave the hair of patients at the electrode locations in order to ensure good
contact. This could eliminate confounds/variability due to improper electrode contact area.
Figure 4-8 shows the electrode locations on a healthy volunteer along with the stimulation
waveform used. The frequency of stimulation as revealed by the Fourier transform was
approximately 10 Hz. Experimentally measured current-induced phase changes and magnetic
field maps at the central slice location for four different volunteers along T3 – T4 direction is
shown in Figure 4-9. Phase and field maps due to current injection along the Fpz-Oz direction are
shown in Figure 4-10. Optimized magnetic field maps were computed using T2* maps similar to
phantom experiments. A realistic head model along with electrode locations generated by
segmenting the high resolution T1 dataset into multiple regions is shown in Figure 4-11. The
head model comprised of ten different tissue types which are GM, WM, CSF, skin, air, bone,
muscle, fat eyes and blood. The current-induced magnetic fields calculated from numerical
simulations performed on the generated head model compared against the optimized magnetic
field maps are also shown in Figure 4-11. The simulated magnetic field values for T3-T4
stimulation varied from -1 nT to 1.5 nT while the experimental values varied from -1 nT to 3 nT.
For the current injection along Fpz-Oz the simulations predicted field changed from -2 nT to 2
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nT while the experiment recorded -0.5 nT to 0.5 nT. Qualitative comparisons of the experimental
and simulated magnetic field maps in the two current injection directions for four volunteers are
shown in Figure 4-12 and Figure 4-13 respectively.
The experimental and simulated field maps were in good agreement for subjects 009 and
012, but not so much for subjects 010 and 011. This can be attributed to the subjects’ experience
during electrical stimulation especially along the Fpz-Oz direction. Subjects 010 and 011, when
questioned, reported discomfort during Fpz-Oz stimulation which was reflected in their ratings
of stimulation perception. Retinal phosphenes, or flashes of light in the field of vision, consistent
with those reported in tACS literature were observed in all participants in addition to a
tingling/pricking sensation under the electrodes. Subject 009 however did not report strong
perception for current injection in either direction but 010, 011 and 012 reported feeling the
phosphenes strongly. Subject 010 and 011 claimed that they moved their head during image
acquisition to reduce discomfort from the electrical stimulation. This would have generated
motion artifacts that can easily compromise the fidelity of the measured MR signal phase. The
improvement in the comparisons for subject 012 is believed to be due to strongly persuading the
participant not to move during the imaging and rigorously securing that participant in the head
coil. In addition to subject movement, cardiac pulsing and changes in size of the thoracic cavity
due to respiration are known to affect the precession frequency of spins due to changes in
susceptibility.
Since the majority of the MR signal resides in the center of k-space, the influence of
respiratory and cardiac fluctuations can be understood by analyzing the variation of phase of the
k-space central point over time. Fourier analysis was performed to extract the different
frequencies present in the time series of k-space center following twenty-four repetitions and
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contained a large peak only at the zero frequency. This revealed that the physiological noise due
to cardiac fluctuations usually observed in fMRI acquisitions did not influence the MREIT
measurement process. However, typical frequency of respiration, which is around 0.2 – 0.5 Hz,
was smaller than the best frequency resolution possible with the employed acquisition technique
and therefore the effect of respiration could not be quantitatively addressed.
4.3.3 Quality of field maps
As reviewed in Section 2.4, signal-to-noise ratio is critical in MREIT acquisitions for the
reliable measurement of current induced magnetic fields. Twenty-four repetitions of each phase
encoding step of the MREIT scan were acquired to improve signal-to-noise ratio. SNR is
typically calculated using a two-region approach and is evaluated using the statistics of the signal
and noise in these regions. This approach is however based on two conditions. First, the noise is
spatially homogeneous over the entire image and second, the distribution of noise is known so
that statistics measured from a background region can be used to calculate its behavior inside the
imaging object. The noise distribution in magnitude images for single channel receivers was
shown to follow a Rician distribution (Section 2.4). Constantinides et al. (74) showed that for
phased array coils that use ‘n’ receiver channels, noise is no longer Rician distributed but follows
a noncentral chi distribution inside the imaging object. In regions without any signal
(background) the noise statistics change and can be described by a central chi distribution.
Dietrich and colleagues (75) compared four different SNR measurement methods and showed
that SNR calculated from two identical acquisitions provided the best results. In this approach
SNR was calculated as the ratio of mean and standard deviation in a region containing the object,
where the mean was computed in a combined map of two identical acquisitions and the standard
deviation was measured in a difference map of the two acquisitions. The inverse relation
between the SNR in magnitude images and the noise in phase images is still valid and a
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theoretical estimate for the noise in phase maps obtained during current injection can be
calculated. Magnitude SNR for the phantom and human datasets was measured using the
difference method (75) for datasets with and without current injection as shown in Table 4.1.
Sadleir et al. (57) developed an analytical approach to test the fidelity of MREIT
experiments using a method that relates the Laplacian of current induced magnetic field to the
Laplacian of noise for homogeneous phantoms. The noise standard deviation of the magnetic
field map can be calculated as,
2
c
c
B
B
4 4
s
20 6
(4-2)
In Equation 4-2, Bc refers to the current induced magnetic field without noise and Bc is the
current-induced magnetic field in the presence of noise. Δ represents the pixel width along the
frequency and phase directions (assuming they are equal) and Δs refers to the slice thickness.
Theoretical and experimental values of the noise standard deviations of the averaged current
induced field for the first and last echo were 1.07 nT, 0.7 nT and 0.16 nT, 0.15 nT respectively.
4.3.4 Projected current density maps
The projected current density map computed as gradient of the magnetic field map
following the description in subsection 2.4.5 for the phantom experiment is shown in Figure 4-
14. Since the electrodes used for injecting current spanned the entire field of view used for
MREIT current injections, the projection of true current density, Jp, was expected to match the
true current density J in the imaging field of view. Moreover, as the current density was
calculated using a Laplacian operation on the measured magnetic field, any global offset
affecting the measured magnetic field did not cause problems in the estimation of current
density. This is evident from the similarity between current patterns in gel phantom despite the
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1nT offset that was observed when comparing numerical simulations to measured magnetic
fields. Figure 4-15 shows the projected current densities for healthy volunteers. This figure also
shows an overlay of current densities on T1 images to help understand/visualize the regions
affected by the applied current.
Since the electric and magnetic fields corresponding to the applied current are always
orthogonal to each other, judging from the measured magnetic field maps, the projected current
density maps seem to provide reasonable estimates of current density distributions. In all four
volunteers the results are consistent with the hypothesis that the largest current densities in the
brain are obtained closest to the electrodes (76). Sadleir et al. (63) reported current densities as
high as 0.8 A/m2 in a realistic head model when using injection current densities of 0.45 A/m2.
Reconstructed current densities in the work presented here also vary within a comparable range
(0-0.7 A/m2). Recently, some researchers performed invasive current density measurements on
cadavers and reported that the majority of current (90%) during tACS was shunted through the
scalp. However, the conductivity of living tissue is higher than that of dead tissue and the work
detailed here shows that a significant amount of applied current distributes within the brain.
Nevertheless the current density was still small and incapable of eliciting action potentials. The
apparent variation in current density across the volunteers could be due to the difference in
electrode placement or leakage of saline from the sponges increasing the effective area of the
electrode. Gel or conductive paste as the interface medium between the electrode and tissue has
been widely used in the literature but the work presented here has not yet taken into account the
effect of electrolytic medium. It is possible that gel electrodes could present a better alternative
for saline soaked sponges for localizing the area of contact for the electrodes during MRI.
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Bone has a very short T2 relaxation time and the signal from bone tissue is completely
lost for conventional echo times used in MR imaging. Therefore, extracting the distribution
within the bone tissue presents a great challenge and novel pulse sequences like ultrashort echo
time, UTE (77), could be tailored for use with MREIT to enable extracting the current density
information in bone tissue. The work presented in this chapter utilizes bipolar current injection
pulses that correspond to roughly 10 Hz stimulation. However extrapolating this work to
mapping current density during tDCS will require careful selection of stimulation parameters and
experimental design. Jog et al. (72) mapped magnetic fields due to varying amplitudes of tDCS
stimulation by injecting current while simultaneously mapping the static magnetic field Bo.
However, the interaction of current-induced magnetic fields with RF fields used for slice
selection in MR imaging was not addressed which is crucial for high resolution imaging.
An interesting observation in the projected current density maps was the high current
density localization in the ventricles during Fpz - Oz stimulation for subjects 009 and 011. This
could be explained by the high conductivity of CSF in comparison with other tissues. However
this was not immediately appreciable in the density maps due to T3 – T4 stimulation indicating a
complex interplay between the current injection direction and tissue conductivity. In addition,
large current densities were observed for subject 009 in the posterior part of the brain between
the two hemispheres. Whether this was the result of magnetic field measurements close to the
noise floor or due to tissue interfaces dictating current density localization remains to be
determined.
4.4 Conclusions
In this chapter the methodology for mapping current density distribution in the in vivo
human brain following a tACS like stimulation was presented. While researchers in the past have
measured current density in inanimate objects, and more recently magnetic fields due to in vivo
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tDCS in the human brain was performed by (72), the results in this chapter are the first
measurements of current density in the human brain performed in vivo. Projected current density
was computed for a two dimensional dominant current distribution in an agarose gel phantom
and healthy volunteers. The projected current density maps calculated from measured magnetic
fields were in good agreement with current densities simulated using computational models for
the phantom data. Though the modeling enlisted heterogeneous conductivity values presented in
literature for different regions of the head, the anisotropy of certain tissue types (muscle, white
matter etc) was not taken into consideration. Improving the computational models by
incorporating diffusion tensor information to account for the underlying anisotropies would
result in more precise comparisons of the measured and simulated current densities. The
variation of measured current distributions within subjects underlines the importance of carefully
controlling various experimental parameters like electrode location, contact area and subject
motion.
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Figure 4-1. MR magnitude images from all 32 channels reconstructed by carrying out the inverse Fourier transform of complex k-
space data. The coil combined magnitude image can be generated using a sum of squares approach with or without
appropriate weighting.
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Figure 4-2. Representative images showing electrode placement, image reconstruction and
decrease in SNR with increasing echo times. A) Binary mask generated from the high
resolution T1 data showing the location of electrodes. B) Sum of squares
reconstructed magnitude MR images for each of the three slice locations. C)
Magnitude MR images for the center slice showing all echoes in the acquisition. Note
the decrease in SNR in the images going from left to right.
Figure 4-3. MR magnitude and phase images for the center slice location collected at the first
echo time. The increased sensitivity at the bottom of the magnitude image was due to
the proximity of the gel phantom to the bottom set of RF coils.
A
C
B
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Figure 4-4. Phase maps produced from complex division of acquired data scaled from -0.1
radians to 0.1 radians. A) Phase maps when no current was injected into the phantom.
Figures B, C, and D show the phase maps computed when 1.5 mA current with
alternating polarity was injected into the phantom. Note the consistency of results
across B, C and D.
Figure 4-5. Magnetic field maps computed from the measured phase changes (Figure 4-4) scaled
from -10 nT to 10 nT. A) Magnetic field maps without any current injection. B, C and
D show magnetic field maps computed when 1.5 mA current was injected with
alternating polarity. The sensitivity to current induced magnetic field is higher for the
later echoes due to greater current injection duration (Tc).
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Figure 4-6. MR magnitude data for all slices and their corresponding T2* maps computed from
data acquired without any current injection. The T2* maps are displayed in seconds
giving an average T2* of about 48 ms in the gel phantom. Volume fitting for all the
voxels was performed using the Levenberg Marquardt algorithm.
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Figure 4-7. Comparison of measured and simulated current-induced magnetic field maps in the
gel phantom. A) Magnetic field images generated following optimal combination of
the multi-echo field maps for all slice locations. B) Comparison of measured and
simulated magnetic fields, in the central slice, along the lines drawn at the same
regions in both images. The field values are shown in Tesla.
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Figure 4-8. Experimental setup and stimulation paradigm for transcranial electrical stimulation
on healthy volunteers. A) Photographs depicting the electrode placement at T3, T4,
Fpz, Oz locations following the 10-20 EEG system. B) Oscilloscope recording
showing the trigger pulse (green) and the stimulation waveform (blue). C) Fourier
transform of the waveform shown in B. Note that maximum power in the frequency
spectrum corresponded with ±10 Hz stimulation.
A
B
C
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Figure 4-9. Current-induced phase and magnetic field images for healthy volunteers. Note the
steady increase in phase across echoes. Electrical stimulation was performed from
right to left in the image. The static field direction is into the page.
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Figure 4-10. Current-induced phase and magnetic field maps for the Fpz-Oz direction. The phase
maps are scaled from -0.1 to 0.1 radians while the magnetic field maps cover a range
of -10nT to 10 nT.
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Figure 4-11. Representative images of segmented T1 images, computational model generated and comparison of simulated and
measured magnetic fields. A) Computational model generated from manually segmented tissue types obtained from the
high resolution T1 data. B) T1 data resampled to facilitate easy segmentation and segmented T1 images are shown. C)
Experimental and simulated magnetic field maps scaled from -5nT to 5 nT and profile plots along the black lines for both
the current injection directions. (Model and segmentation images generated by Aprinda Indahlastari.)
A
B
C
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Figure 4-12. Comparison of measured and simulated magnetic fields due to T3-T4 stimulation
for the central slice location. Good agreement can be observed in subjects 009 and
012. Results from subjects 010 and 011could have contributions from motion.
Magnetic field maps are scaled from -10 nT to 10 nT.
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Figure 4-13. Comparison of measured and simulated magnetic fields, following electrical
stimulation with electrodes placed at Fpz and Oz, for the central slice location
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Table 4-1. SNR values for volunteer MRI data and noise in measured magnetic field maps at 3T.
SNR in magnitude data Theoretical σBc Measured σBc
No Current T3-T4 Fpz-Oz T3-T4 Fpz-Oz T3-T4
Gel phantom 454 503 - 0.15 nT - 0.18 nT
MREIT 009 348 330 395 0.26 nT 0.22 nT -
MREIT 010 432 406 307 0.21 nT 0.29 nT -
MREIT 011 380 388 436 0.22 nT 0.20 nT -
MREIT 012 521 525 495 0.17 nT 0.18 nT -
Figure 4-14. Comparison of simulated current density images and current density maps
computed from measured magnetic field maps. Shown are the maps for X and Y
components of the current density vector and the corresponding norm calculated from
the two components. The units of scaling are in ampere per square meter or A/m2.
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Figure 4-15. Current density (norm) images for healthy volunteers shown in relation to their high
resolution T1 images. The current density maps were scaled from 0 – 0.7 A/m2. Also
shown are the current density maps overlaid onto the T1 images with 50%
transparency. The highest current densities were observed underneath the electrode
contact regions (Figures generated by Munish Chauhan).
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CHAPTER 5
MEASUREMENT OF MAGNETIC FIELDS DUE TO LOW AMPLITUDE INJECTION
CURRENTS USING IMPLANTED ELECTRODES
5.1 Introduction
This chapter details with the work involved in the measurement of magnetic fields due to
very low amplitude injection currents using implanted electrodes. The measurements were
performed using a 4.7 T Agilent magnet system housed in the McKnight Brain Institute,
University of Florida. Magnetic field measurements due to varying levels of current injection in
gel phantoms, using spin echo techniques are presented. Data acquisition using copper wires and
fabricated carbon electrodes are presented. Effects of large current densities in the electrodes on
measured field distributions inside the gel phantom are discussed. Extended studies using current
injections with three different electrode orientations are discussed.
5.2 Theory
Current injection due to implanted electrodes must typically be maintained under a
certain threshold in order to avoid damage to the local tissue as a result of Joule heating. More
importantly, the implanted electrode should not react with the surrounding tissue and should
possess a magnetic susceptibility that is close to water in order to avoid artifacts in MR imaging
(since brain tissue is predominantly composed of water). The magnetic field due to current
passing through an infinitely long wire at a distance ‘a’ away from the wire can be written using
Ampere’s law as,
ocB
ar
I
2
(5-1)
For wires with finite length, the magnetic field associated due to current in the wires is
given by the Biot-Savart equation.
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or r
B r J r drc 34 r r
(5-2)
Stimulation using implanted electrodes results in current travelling through a well-
defined path (through the electrode) and then into the tissue while stimulation using surface
electrodes results in a more distributed current. The result is that in the electrodes the current
density is large, resulting in a large magnetic field associated with the current injection.
Depending on the orientation of the electrode during stimulation, this large magnetic field can
mask the distribution of magnetic field due to the current flow in the tissue. The effect can be
pronounced depending on the spacing between the electrodes which can be tailored in order to
decrease this effect. As the current-induced magnetic field is measured as a change in the main
magnetic field of the MRI scanner, interaction of the current induced field with the static field
can be controlled by varying the orientation of electrodes with respect to each other and the static
magnetic field so as to minimize the effect of field due to current inside the electrodes.
The magnetic field changes in the sample due to injected currents can be quantified with
a conventional spin echo sequence imaging sequence as described by Scott et al.(36). Recall
from Section 2.4 that as the current induced magnetic field imparts an additional phase to the
spins without altering the encoding generated by the imaging gradients, the resulting datasets can
be complex divided to extract the field due to current injection. A more sensitive approach to
measuring the induced magnetic fields was developed by Kwon et al., termed as the injection
current non-linear encoding method (78). The “non-linear” in the name stems from injection of
current during the data acquisition period thereby changing the one-one mapping of spin
precession frequency with position. To understand the ICNE approach, a detailed understanding
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of the effect of background gradients on frequency and phase encoding of precessing spins is
necessary.
5.2.1 Effect Of Background Magnetic Field On Frequency Encoding
The effect of a background magnetic field can be assumed to be caused due to a
stationary gradient applied in conjunction with the frequency encoding gradient. For simplicity,
let us consider that the inhomogeneity exists only along the frequency encoding direction.
Without loss of generality we can assume that the frequency encoding is performed along x and
the phase encoding is performed in the y direction. Then the precession frequency of spins in the
rotating frame can be described by the equation
x= G .x (5-3)
In the presence of the magnetic field inhomogeneity Equation 5-3 can be written as,
x x= G .x G .x (5-4)
The phase of precessing spins can be given by the relation 2 k.rt . Using the wave
vector t
0
k t2
G dt
to describe the spatial frequencies in the image, the measured signal at a
particular frequency encoding step, kx, in the presence of the background field can be represented
by,
x
xx
Gk xi2
x o
1G
S k S e
(5-5)
This causes a local distortion in the image since the spins that are at position ‘x’ are now
misappropriated to be present at x′ due to the additional gradient present during the sampling
interval. As a result the original field of view, L, given by x
1 2
k G tL
changes to L′ such
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that the local effective field of view is now scaled by inverse ratio of the term involving
gradients in Equation 5-5. The scaling factor can be expressed as,
x
x x
G
G G
(5-6)
Depending on the magnitude and sign of the background field gradient, signal enhancement
could occur as a result of the mispositioning of spins upon image reconstruction. This effect is
particularly strong in gradient echo imaging where the background gradient is not refocused at
echo time. In the case of spin echo sequences, the additional 180° RF pulse ensures that the
background gradient is refocused at the gradient echo time.
Another important effect that occurs due to the presence of background inhomogeneity is
a shift in position of the echo during readout. This effectively causes the echo to no longer be
centered in the sampling window and depending on the strength of the background gradient, the
echo could be completely pushed out of the readout interval leading to a complete loss of
measured signal. If the background field is not sufficient to move the echo out of the sampling
interval, the time shift in the echo upon image reconstruction can be observed as a shift in the
image phase. For a fixed echo time, the time shift due to the background gradient creates phase
dispersion over the length of the imaging voxel leading to an increased transverse relaxation rate
that directly translates to a decrease in signal. The phase dispersion produced across the voxel as
a result of echo shift in k-space can be written as,
s
2 t 2 t
T N t
(5-7)
where δt corresponds to time shift of the echo and Ts (sampling time) is the total time required to
collect N data points along the frequency encoding direction evenly spaced at Δt interval. Since
the readout is sampled as a discrete set of points, the background field induced shift of the echo
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can be represented by the number of points by which the echo shifted. This can be written
mathematically as,
x
x
G Tn
G t
E
G
(5-8)
The important thing to note here is the shift in the echo occurs to the right resulting in an
effective echo time TE′ where TE < TE′ when the background gradient has a negative sign with
respect to the readout gradient. The reverse is true when the polarity of the background gradient
is positive with respect to the readout gradient. In low amplitude MREIT current injections, the
magnetic field produced by the current (nT – μT regime) is orders of magnitude smaller than the
frequency encoding gradient (mT/m) and therefore the image distortion and phase dispersion are
minimal and can be ignored during the reconstruction process.
5.2.2 MREIT-ICNE
The current-induced magnetic field that exists as a background gradient during the image
acquisition, if extracted, can provide additional sensitivity to the MREIT experiment enabling the
decrease in the injected current amplitude that is crucial when delivering current directly to the
brain tissue. This is achieved using the ICNE method and the formulation is as described below.
Since the one-one linear relationship between the precession frequency of spins and their
position is no longer preserved, a linear operation like the Fourier transform can no longer be
applied for image reconstruction. The k-space signal from the ICNE approach where the current
is applied during the sampling interval (Ts) can be described by,
csx yc c
x
B x,yT i2 k x k yi T B x,yGi x,y 2
x y x, y e e e dS k xdy,k
(5-9)
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where c c sT T T .Taking the difference of the positive and negative k-space signals, defining
s xc
x
T kT 2
2 G
and finally dividing by the term 2iα, we can obtain,
x yx y x y i2 k x k yci x,y
c
c
sin B x, yx, y e B x, y e
S k ,k S k ,k
2idxdy
B x, y
(5-10)
Using the expansion of sin(θ)/θ, and since αBc is extremely small, we can write the final relation
for Bc(x,y) as,
1 x
,
y x y
c i x y
S k ,k S kB x, y
,k1FT
2ix, y e
(5-11)
where, s xc
x
T kT 2
2 G
. Compared to the conventional method of measuring Bc(x,y),
the ICNE method has been shown to decrease the noise in the measured magnetic field map by
approximately 42% (78).
5.3 Methods
5.3.1 Field Stability Measurements
In tubes of 50 ml capacity, 2 % agar gel doped with sodium chloride and copper sulphate
were prepared using the same procedure described in Section 3.3.1. The tube was left at room
temperature for a whole day and in the evening, T1, T2 relaxation times were quantified using a
4.7 T Agilent magnet system. Background magnetic fields were characterized using an
asymmetric spin echo sequence (Figure 5-1) with free precession delay times (Tfp) of 0, 0.5, 1,
1.5, 2 ms. The repetition and echo times for the experiment were 1000 and 14 ms. The in-plane
resolution was 250 x 250 μm2 and the slice thickness was 1 mm. A total of 10 slices were
acquired. The entire experiment set was repeated two more times and differences in background
field maps were computed to ensure the temporal stability of the static magnetic field.
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5.3.2 Pilot Studies
5.3.2.1 Fabrication of carbon electrodes
Carbon has a magnetic susceptibility close to that of water. In the form of graphite, is
highly conductive due to its layered structure thus making it a viable option for use in building
electrodes for electrical stimulation. Carbon fiber tows consisting of 12000 individual filaments
(Formosa Plastics, Taiwan) were used to make the electrodes using a procedure similar to that of
Dunn et al. (79). Polyvinylidene fluoride (PVDF), a biocompatible polymer (solid at room
temperature) was used to coat the carbon fibers to provide insulation. Pellets of PVDF were
dissolved in 99% dimethyl sulfoxide (DMSO) by heating at approximately 70° C and stirring
constantly at 340 rpm. Complete dissolution of the polymer occurred over a period of 14 hours,
yielding a clear dark yellow solution. The solution was continually stirred to prevent
precipitation or clumping of polymer. Groups of carbon fiber strands (12000 strands) were
manually isolated and soaked in 0.9 % saline solution to prevent splaying. The thickness of the
groups was qualitatively estimated under a magnifying glass and those roughly 200 μm
(measured against a scale) in thickness were selected. The soaking also ensured that the
interstitial spaces between the filaments were filled with conductive medium. Soaked carbon
fibers were dipped into the PVDF solution for approximately 30 seconds to allow adequate
coating. The fibers were then heated in a conventional oven at 200° C for 15 minutes to
evaporate the DMSO and concentrate the fibers with PVDF plastic. The entire process was
repeated two more times to ensure thorough coating of PVDF on the carbon fibers.
5.3.2.2 Experimental setup
Carbon fiber electrodes fabricated using the procedure described above, were crushed at
one end to expose the fibers that were attached to a brass screw using a conductive silver epoxy.
A 40 x 40 x 40 mm box with a cap attachment was printed in 3D using PLA (poly lactic acid)
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with a Makerbot Replicator 2. Two holes matching the diameter of the screws were drilled on the
cap approximately 1 cm apart. The electrodes along with screws were inserted into the box
through the holes such that the screw heads were flushed against the cap surface. The screws
were epoxied in place and the exposed ends of insulated copper wires were soldered to the screw
heads. The box was filled with 2 % agar gel doped with NaCl and CuSO4. The entire
experimental setup was placed in the bore of a 4.7 T Agilent magnet system at the AMRIS
facility in University of Florida. The cores of coaxial cables were soldered to the other ends of
insulated wires and were attached to the front of the magnet’s bore using BNC connectors.
Coaxial cables carrying current from a constant current source developed at Kyung Hee
University, South Korea were attached to the other end of the BNC connectors.
5.3.2.3 MR imaging
Spin echo MREIT measurements using the sequence shown in Figure 5-1 were
performed using a current injection of 0.2 mA. A TR of 2000 ms was used along with a TE of 50
ms to facilitate current injection pulse widths of 20 ms each, prior to and following the 180° RF
pulse. The total current injection time was 40 ms. Twelve slices 1 mm thick were acquired along
the axial direction with an in-plane resolution of approximately 0.35 x 0.35 mm2.
5.3.3 Extended Studies
5.3.3.1 Phantom preparation
0.5 mm holes were drilled into a 50 ml cylindrical tube (Fisherbrand) in diametrically
opposite positions and insulated magnet wire (AWG 25) with only the tips exposed were inserted
through them until the wires were at 1 cm distance from each other. Epoxy was applied at the
holes to secure the wires in place and the setup was left overnight to dry. Two percent agar
solution doped with NaCl and CuSO4 was prepared and the mixture was poured into the
cylindrical tube to form a gel. Using similar approach, two more gel phantoms, one with the
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wires inserted parallel to the cylinder’s length and another where the wires were at right angles to
each other, were also constructed. Electrical stimulation was performed and current-induced
magnetic fields were mapped.
5.3.2.2 Electrical stimulation
Electrical stimulation was performed using a commercially available stimulator system
built by Tucker Davis Technologies, Alachua, Florida. The system consisted of an IZ2H
electrical stimulator that was synchronized with the magnet for stimulation using a RZ5D control
station. The control station was configured to accept a TTL input from the Agilent magnet
system and stimulation programmed to switch polarities for every incoming TTL signal. Initial
testing of experimental setup was performed by injecting current at 0.1, 0.2, 0.3, 0.5 and 0.75
mA into the phantom with wire ends placed diametrically opposite. Current of 0.25 mA was
injected into all three phantoms while simultaneously monitoring the stimulation waveforms.
5.3.3.3 MR imaging
Using the phantom with diametrically opposite wire ends, MREIT measurements using
the approach developed by Scott and colleagues (36) were performed at five different current
ratings (0.1, 0.2, 0.3, 0.5, 0.75 mA). MREIT-ICNE measurements were also performed at three
different current ratings (0.1, 0.2, 0.3 mA) to compare against standard MREIT measurements.
An echo time of 50 ms was used to inject current for a duration of 40 ms. Multi-slice acquisitions
with ten slices at 2 mm slice thickness were performed. A TR of 2 seconds was used to collect
data with an in-plane resolution of 0.33 x 0.33 mm2. The total acquisition time for each
measurement was 3 minutes. In all three phantoms, a current of 0.25 mA was injected and a total
of 5 averages were acquired to compare the current induced field maps across multiple averages.
In all experiments, a readout bandwidth of 16 KHz was used to improve the signal-to-noise ratio.
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5.4 Results and Discussion
T1 and T2 relaxation times for the 2% Agar gel phantom at 4.7 T ranged as 717 ± 19 ms
and 44.6 ± 0.8 ms. Maps of the static field inhomogeneity are presented in Figure 5-2 along with
their difference maps. The absence of any temporal drift over the time scale of MR acquisitions
was apparent from the difference maps. Magnetic field maps due to current injection using
fabricated carbon fiber electrodes are shown in Figure 5-3. The overwhelming effect of large
magnetic fields from current in the electrodes is evident in the region towards the top of the
phantom. Current induced magnetic field maps acquired using the conventional spin echo
sequence and the ICNE approach are shown in Figure 5-4 and Figure 5-5 for different ratings of
current. The increase in magnetic field intensity with current is clearly depicted. The results
indicated that for a given SNR during image acquisition and a set current injection time at 40 ms,
reliable measurements of magnetic field can be made using 0.3 mA of current injection. Current
injection times typically used in electrical stimulation techniques like DBS are orders of
magnitude lower than those used here. However, though electrical conductivity in tissue is
frequency dependent, for the frequencies used in DBS (60-150 Hz) or that used in this study (5 -
10Hz), the difference in conductivity values is extremely small and can be ignored. Therefore,
current injection using varying pulse lengths should produce similar magnetic fields and ergo
current distribution patterns. Therefore though it may not yet be possible to use MREIT for real
time measurements of current distributions during DBS yet, it is definitely possible to obtain a
sense of the volume of tissue activated during the procedure thereby working towards the
improvement of currently used computational models. Using very low amplitude injected
currents requires excellent image quality to ensure reliability which usually means longer
imaging times. The ICNE approach (Section 5.2.2) is one way to increase sensitivity in the
magnetic field measurement without the need for increased imaging times. This is apparent from
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the noise standard deviations within computed current-induced magnetic field maps given in
Table 5-1. However this approach relies on the use of increased sampling times and hence is
highly susceptible to off-resonance effects like chemical shift effects. In addition, since the one-
one mapping of spin position and precession frequency no longer holds, image reconstruction
using a linear operator like the Fourier transform is no longer viable and approximations about
the injected field magnitude become necessary to facilitate extraction of the current-induced
fields (Section 5.2.2). Faster pulse sequences adapted to perform MREIT (48,80) or parallel
imaging approaches like sensitivity encoding (SENSE) (81) or generalized auto-calibrating
partially parallel acquisition (GRAPPA) (82) can also be employed to circumvent the problem of
longer imaging times. Custom made array coils can be developed to further increase the image
quality while employing parallel imaging (83).
The greatest challenge for extending the current methodologies for in vivo imaging in
rodents is, however, the effect of large current densities in the electrode leads that can easily
mask the magnetic fields due to currents in tissue thereby affecting our calculation of current
densities. Figure 5-6 shows the magnetic field characterization following a current injection of
0.25 mA using different orientations of electrodes with respect to the static field of the MRI
scanner. Magnetic fields due to the electrodes angled in plane at 90° to each other seem to
produce fairly unbiased results. The diametrically opposite electrode orientation though optimal
for measuring current-induced magnetic fields within the region between the electrodes, it
presents complex options for surgery making it extremely challenging. Interestingly, for
electrodes oriented parallel to the main magnetic field, the current-induced magnetic fields inside
the gel phantom are completely masked by the noise levels in the image. Magnetic field changes
are observable only at the tip of the electrode where the current density is significantly high.
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Characterizing field changes in this kind of a stimulation setup is quite challenging as the tip of
the electrode is masked by image distortions due to susceptibility differences between the
electrode and surrounding medium. Electrodes fabricated from materials that are similar in
magnetic susceptibility to surrounding tissues could provide a better understanding of current
distributions and magnetic field changes close to the tip of the electrodes (84). Though MREIT
measurement using electrodes parallel to the static field of an MRI scanner is highly impractical
in in vivo imaging due to the requirement of inserting the electrodes through the eyes/olfactory
bulb of the rodent, the approach poses intriguing questions about the distribution of current
induced magnetic fields and the sensitivity of currently performed MREIT measurements.
5.5 Conclusions
Current induced magnetic fields due to diametrically opposite electrodes were mapped at
different current ratings to understand the sensitivity of spin echo and spin echo ICNE MREIT
approaches. Theoretical noise standard deviations, computed using the relation given by Sadleir
et al. (57), agree well with the experimentally measured noise standard deviation values. Current
induced magnetic fields due to varying electrode orientations were investigated and targeting
regions of the brain using electrodes placed at large angles with respect to each other seems to be
the best approach. Future studies should focus on improvement of the sensitivity of MREIT
measurements while employing smaller current pulse widths and faster imaging times. Parallel
imaging techniques should be explored thoroughly in order to improve the measurement
reliability and enable the feasibility of real-time MREIT measurements. Though distant, in the
future, these techniques would also provide the ability to integrate MREIT within the framework
of fMRI acquisitions to track conductivity changes due to neural activity. As the greatest changes
in current density can be expected close to the electrode tips, fabrication of electrodes that are
116
susceptibility matched to the surrounding in combination with zoom MRI (85) can provide better
understanding of magnetic field and current density distributions.
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Figure 5-1. Asymmetric spin echo pulse sequence where the slice select 180° RF pulse is moved
from its original position to create a net phase accumulation due to free precession.
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Figure 5-2. Field stability measurements using the asymmetric spin echo sequence with varying
free precession delay times. A) The static field inhomogeneity fits for the acquired
data following three sets of repetition using Equation 3-5. B) Difference maps
computed from the ΔBo measurements showing good stability of Bo field over
experiment timescales of 30 minutes. The units are in Tesla.
A
B
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Figure 5-3. Demonstration of the dominant magnetic fields due to current in the electrodes.The
dissimilarity in the horizontal line plot across electrodes, was due to the electrodes not
being perfectly parallel to eachother. The image is scaled from -10 nT to 10 nT. The
Y-axis in the line plots represents magnetic field in Tesla while the X-axis indicates
position along the lines shown in the figures. The lines on the figure are drawn for the
entire length and width of the phantom. The discrepancies in the axes of the
experimental and simulated lineplots are due to the variation in the size of the
experimental phantom and the generated model.
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Figure 5-4. Current-induced magnetic field measurements for varying current amplitudes using conventional spin echo measurements.
A) Magnetic field maps showing that field patterns remain the same irrespective of current strengths. B) Magnetic field
values along the lines shown in A. Using fixed durations of current (40 ms) and identical imaging parameters, these results
show the reliability in magnetic field measurements with varying current amplitudes. The magnetic field values are shown
in Tesla.
A
B
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Figure 5-5. Current-induced magnetic field measurements (in Tesla) using the Injection Current Non-Linear Encoding (ICNE)
approach with varying levels of current amplitude. A) Magnetic field maps for different current ratings. B) Corresponding
magnetic field values plotted along the line shown in A. The difference in field maps at 0.3 mA obtained with conventional
spin echo (Figure 5-4) and the spin echo ICNE sequence can be attributed to non-linear reconstruction approach used in
ICNE.
B
A
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Table 5-1. Noise standard deviations for current induced field maps acquired with conventional spin echo MREIT and spin echo
MREIT with ICNE sequences.
Theoretical σBc (nT) Experimental σBc (nT)
0.1mA 0.2mA 0.3mA 0.5mA 0.75mA 0.1mA 0.2mA 0.3mA 0.5mA 0.75mA
Conventional 1.02 0.96 0.92 0.81 0.97 1.54 1.58 1.72 1.82 1.64
ICNE 1.03 0.89 0.86 - - 1.27 1.29 1.21 - -
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Figure 5-6. Magnetic field maps (in Tesla) due to 0.25 mA current injection in three phantoms
with different orientations of copper electrodes. A) Magnetic field maps for different
electrode orientations. B) Magnetic field values plotted along the lines shown in A.
The direction of static magnetic field is into the page in this figure. All data were
collected with five averages and the improvement in SNR for the angled case was due
to better positioning of the sample within the RF coil.
A
B
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CHAPTER 6
CONCLUSIONS AND FUTURE WORK
6.1 Summary
The work detailed in this dissertation addresses the dire need for quantifying current
density distribution in the human brain following transcranial electrical stimulation therapies. An
experimental methodology to reliably detect the minute magnetic fields due to low current
amplitudes using MREIT was developed. Additionally current-induced magnetic fields were
detected in phantoms and healthy volunteers to validate computational modeling techniques and
contribute to their development. Current density estimates from the measured magnetic fields
were obtained and compared against those produced from numerical simulations. Finally the
approach to understand magnetic field distributions was extended to electrical stimulation
techniques utilizing implanted electrodes like DBS. The best orientation of the stimulating
electrodes with respect to the static magnetic field of MRI machine was explored using a set of
three possible orientations.
In Chapter 3, discrepancies in MREIT acquisitions in pilot studies were addressed by
analyzing repeated acquisitions without any current injection. The analysis revealed the presence
of a magnetic field inhomogeneity that varied with time affecting the determination of current-
induced magnetic fields. The effect of static magnetic field drift with time was estimated and a
different acquisition style to collect imaging data that was insensitive to temporal drift was
employed. Necessary electronic circuitry was adapted to facilitate image acquisition and the
results indicated reliable measurement of current-induced magnetic fields.
In Chapter 4, the work done in Chapter 3 was extended to measure the low magnetic
fields and injected current densities in gel phantoms and healthy volunteers. This is the first
study in literature presenting injected current density maps in healthy volunteers. Current
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induced magnetic fields characterized in the gel phantom revealed an offset in the measurement
which could be due to extremely small imbalances in the amplitudes of the different current
polarities. The extreme sensitivity of these fields to electrode location, contact area and subject
motion was apparent from the results. Reproducible results were obtained in two participants
while quite different field patterns were obtained in two others during current injection along one
of the two directions. All the volunteers showed expected patterns (with very minor
discrepancies) for stimulation using T3, T4 electrode locations. Though the measurements
depicted the detectability of current induced magnetic fields using diametrically opposite
electrode locations in the head, the methods can easily be extended to study magnetic field or
current density patterns due to stimulation from arbitrary electrode locations.
In Chapter 5 characterization of magnetic fields was extended to implanted electrodes
with the aim to understand stimulation techniques like DBS. Different electrode orientations with
respect to the main magnetic field in MRI were explored to avoid the problem of magnetic fields
due to high current densities in electrodes masking the magnetic fields due to current flow within
the brain. Electrode orientation parallel to the field would produce least susceptibility image
distortion while those place diametrically opposite give best estimates of magnetic field due to
current injection but are both impractical for in vivo animal imaging. Angled electrodes provide
the best of both worlds and successful mapping of magnetic fields in such an orientation paves
way for improving our understanding of brain response due to cortical stimulation
6.2 Future Work
Quantifying current densities within different regions of the brain following electrical
stimulation has been a long standing goal in the field of neuroscience. Electrical stimulation
therapies rely on realistic computational models and validating these models is a giant leap that
could challenge/alter longstanding approaches and assumptions. The primary focus of this
126
dissertation has been to provide evidence of small but measurable currents localized in the brain
due to transcranial stimulation. Successful characterization of currents and their magnetic fields
opens up innumerable prospects for the improvement of existing neuromodulation techniques.
However to begin with, the reliability and reproducibility of this work across individuals
should be established using a larger sample space. Carefully controlled experiments with
minimal variation in parameters such as electrode location, contact area and minimal subject
motion during imaging can improve the consistency of results. The beneficial effects of electrical
stimulation therapies are known to vary with stimulation strength, area of stimulation and
stimulus duration. All these factors should be meticulously addressed and controlled across
subjects to provide a comprehensive comparison against published literature. The work presented
in this dissertation does not provide rigorous statistical comparisons while validating the
computational models. Models taking into account the anisotropic nature of different regions in
the brain should be developed to better compare against measurement values. Neurovascular
coupling can potentially confound the measurement of current-induced magnetic fields
indicating the need for carefully designed experiments that control for such effects. As the
magnetic fields due to current injection are extremely small, it is possible that they produce
negligible distortion of the B1 field used in MR imaging. Imaging slice distortions with varying
amplitudes and durations of current injection should be quantified. Such characterizations can
improve the measurement of current-induced magnetic fields providing capabilities of extending
this work to direct current applications. Fast imaging sequences like echo planar imaging or fast
spin echo sequences coupled with parallel imaging techniques can significantly improve the
measurement process by increasing the volume of imaging. Currents measured in the work
presented in this dissertation depict a highly distributed path across the brain. Validated
127
computational models can be employed to simulate current densities using an array of electrodes
to increase current density in deeper brain regions of brain tissue. The data from such
experiments can then once again be validated using the methods developed in this dissertation.
To obtain absolute validations of the current density imaging techniques presented in this work,
invasive measurements of underlying sample conductivity and ergo current density could be
made in freshly dead tissue. However, these measurements would have to take into account the
time for which the tissue was dead and the resulting change in tissue conductivity. MR
thermometry techniques can be applied to measure the change in temperature as a result of
decreased perfusion to the tissue and help augment the accuracy of conductivity/current density
measurements.
Current density characterization could be extended to stimulation using implanted
electrodes. Electrodes constructed from materials whose susceptibility is close to that of brain
tissue can provide excellent characterization of current-induced magnetic fields following the
details outlined in Chapter 5. The advantage of implanted electrodes is that, though invasive,
they can provide greater control over the region of brain stimulated and can therefore be used to
probe specific tissue properties while simultaneously providing deeper insights into the
mechanisms behind current distribution in the brain. Meticulously designed experiments can
improve our understanding by providing quantitative estimates of the degree of blood-brain
barrier disruption, information that can be utilized in drug delivery techniques. MREIT, by virtue
of its ability to generate high resolution conductivity maps, can also be used for cancer diagnosis.
Many studies have looked at feasibility and the promise of MREIT in successfully detecting
breast or prostate cancers (86,87). Current density imaging can also be used in non-biological
applications, like measuring the currents in a printed circuit board (88).
128
LIST OF REFERENCES
1. Nitsche MA, Seeber A, Frommann K, Klein CC, Rochford C, Nitsche MS, Fricke K,
Liebetanz D, Lang N, Antal A, Paulus W, Tergau F. Modulating parameters of
excitability during and after transcranial direct current stimulation of the human motor
cortex. J Physiol 2005;568(Pt 1):291-303.
2. Clark VP, Coffman BA, Mayer AR, Weisend MP, Lane TD, Calhoun VD, Raybourn EM,
Garcia CM, Wassermann EM. TDCS guided using fMRI significantly accelerates
learning to identify concealed objects. Neuroimage 2012;59(1):117-128.
3. Antal A, Paulus W. Transcranial alternating current stimulation (tACS). Front Hum
Neurosci 2013;7(317):1-4.
4. Hodgkin AL, Huxley AF. A quantitative description of membrane current and its
application to conduction and excitation in nerve. J Physiol 1952;117(4):500-544.
5. Goldman DE. Potential, impedance and rectification in membranes. J Gen Physiol
1943;27(1):37-60.
6. Hodgkin AL, Katz B. The effect of sodium ions on the electrical activity of giant axon of
the squid. J Physiol 1949;108(1):37-77.
7. Singer SJ, Nicolson GL. The fluid mosaic model of the structure of cell membranes.
Science 1972;175(4023):720-731.
8. Poo M. In situ electrophoresis of membrane components. Annu Rev Biophys Bioeng
1981;10:245-276.
9. Fricke H. A mathematical treatment of the electric conductivity and capacity of disperse
systems ii. The capacity of a suspension of conducting spheroids surrounded by a non-
conducting membrane for a current of low frequency. Physical Review 1925;26(5):678-
681.
10. Datta A, Bikson M, Fregni F. Transcranial direct current stimulation in patients with skull
defects and skull plates: high-resolution computational FEM study of factors altering
cortical current flow. Neuroimage 2010;52(4):1268-1278.
11. Dmochowski JP, Datta A, Bikson M, Su Y, Parra LC. Optimized multi-electrode
stimulation increases focality and intensity at target. J Neural Eng 2011;8(4):1-16.
12. Datta A, Baker JM, Bikson M, Fridriksson J. Individualized model predicts brain current
flow during transcranial direct-current stimulation treatment in responsive stroke patient.
Brain Stimul 2011;4(3):169-174.
13. Bikson M, Rahman A, Datta A. Computational models of transcranial direct current
stimulation. Clin EEG Neurosci 2012;43(3):176-183.
129
14. Truong DQ, Huber M, Xie X, Datta A, Rahman A, Parra LC, Dmochowski JP, Bikson
M. Clinician accessible tools for GUI computational models of transcranial electrical
stimulation: BONSAI and SPHERES. Brain Stimul 2014;7(4):521-524.
15. Fregni F, Boggio PS, Nitsche M, Bermpohl F, Antal A, Feredoes E, Marcolin MA,
Rigonatti SP, Silva MT, Paulus W, Pascual-Leone A. Anodal transcranial direct current
stimulation of prefrontal cortex enhances working memory. Exp Brain Res
2005;166(1):23-30.
16. Nitsche MA, Paulus W. Sustained excitability elevations induced by transcranial DC
motor cortex stimulation in humans. Neurology 2001;57(10):1899-1901.
17. Nitsche MA, Paulus W. Excitability changes induced in the human motor cortex by weak
transcranial direct current stimulation. J Physiol 2000;527(3):633-639.
18. Antal A, Boros K, Poreisz C, Chaieb L, Terney D, Paulus W. Comparatively weak after-
effects of transcranial alternating current stimulation (tACS) on cortical excitability in
humans. Brain Stimul 2008;1(2):97-105.
19. Liebetanz D, Nitsche MA, Tergau F, Paulus W. Pharmacological approach to the
mechanisms of transcranial DC-stimulation-induced after-effects of human motor cortex
excitability. Brain 2002;125(10):2238-2247.
20. Kanai R, Chaieb L, Antal A, Walsh V, Paulus W. Frequency-dependent electrical
stimulation of the visual cortex. Curr Biol 2008;18(23):1839-1843.
21. Zaghi S, de Freitas Rezende L, de Oliveira LM, El-Nazer R, Menning S, Tadini L, Fregni
F. Inhibition of motor cortex excitability with 15Hz transcranial alternating current
stimulation (tACS). Neurosci Lett 2010;479(3):211-214.
22. Merrill DR, Bikson M, Jefferys JG. Electrical stimulation of excitable tissue: design of
efficacious and safe protocols. J Neurosci Methods 2005;141(2):171-198.
23. Woods AJ, Antal A, Bikson M, Boggio PS, Brunoni AR, Celnik P, Cohen LG, Fregni F,
Herrmann CS, Kappenman ES, Knotkova H, Liebetanz D, Miniussi C, Miranda PC,
Paulus W, Priori A, Reato D, Stagg C, Wenderoth N, Nitsche MA. A technical guide to
tDCS, and related non-invasive brain stimulation tools. Clin Neurophysiol
2016;127(2):1031-1048.
24. Seo JK, Kwon O, Woo EJ. Magnetic resonance electrical impedance tomography
(MREIT): conductivity and current density imaging. Journal of Physics: Conference
Series 2005;12(1):140-155.
25. Rabi II, Zacharias JR, Millman S, Kusch P. A new method of measuring nuclear
magnetic moment. Physical Review 1938;53(4):318.
26. Bloch F, Hansen W, Packard M. The nuclear induction experiment. Physical Review
1946;70(7,8):474-485.
130
27. Bloch F. Nuclear induction. Physical Review 1946;70(7,8):460-474.
28. Purcell EM, Torrey HC, Pound RV. Resonance absorption by nuclear magnetic moments
in a solid. Physical Review 1946;69:37-38.
29. Purcell EM. Spontaneous emission probabilities at radio frequencies. Physical Review
1946;69:681.
30. Bloembergen N, Purcell EM, Pound RV. Relaxation effects in nuclear magnetic
resonance absorption. Physical Review 1948;73(7):679-712.
31. Damadian R. Tumor detection by nuclear magnetic resonance. Science
1971;171(976):1151-1153.
32. Lauterbur PC. Image formation by induced local interactions. Examples employing
nuclear magnetic resonance. Clin Orthop Relat Res 1973;244:3-6.
33. Mansfield P, Maudsley AA, Baines T. Fast scan proton density imaging by NMR.
Journal of Physics E-Scientific Instruments 1976;9(4):271-278.
34. Garroway AN, Grannell PK, Mansfield P. Image formation using nuclear magnetic
resonance. US Patents 1977;610436(4021726):1-12.
35. Mansfield P, Pykett IL. Biological and medical imaging by NMR. Journal of Magnetic
Resonance 1978;29:355-373.
36. Scott GC, Joy MLG, Armstrong RL, Henkelman RM. Measurement of nonuniform
current density by magnetic resonance. IEEE Transactions on Medical Imaging
1991;10(3):362-374.
37. Scott GC, Joy MLG, Armstrong RL, Henkelman RM. Sensitivity of magnetic-resonance
current-density imaging. Journal of Magnetic Resonance 1992;97(2):235-254.
38. Lee BI, Park C, Pyo HC, Kwon O, Woo EJ. Optimization of current injection pulse width
in MREIT. Physiol Meas 2007;28(1):N1-7.
39. Seo JK, Yoon JR, Woo EJ, Kwon O. Reconstruction of conductivity and current density
images using only one component of magnetic field measurements. IEEE Trans Biomed
Eng 2003;50(9):1121-1124.
40. Seo JK, Pyo HC, Park C, Kwon O, Woo EJ. Image reconstruction of anisotropic
conductivity tensor distribution in MREIT: computer simulation study. Phys Med Biol
2004;49(18):4371-4382.
41. Park C, Kwon OI. Current density imaging using directly measured harmonic Bz data in
MREIT. Comput Math Methods Med 2013;381507:1-9.
131
42. Nam HS, Lee BI, Choi J, Park C, Kwon OI. Conductivity imaging with low level current
injection using transversal J-substitution algorithm in MREIT. Phys Med Biol
2007;52(22):6717-6730.
43. Birgul O, Eyuboglu BM, Ider YZ. Current constrained voltage scaled reconstruction
(CCVSR) algorithm for MR-EIT and its performance with different probing current
patterns. Phys Med Biol 2003;48(5):653-671.
44. Park C, Lee BI, Kwon OI. Analysis of recoverable current from one component of
magnetic flux density in MREIT and MRCDI. Phys Med Biol 2007;52(11):3001-3013.
45. Haacke EM, Brown RW, Thompson MR, Venkatesan R. Magnetic Resonance Imaging
Physical Principles and Sequence Design. New York: John Wiley & Sons; 1999.
46. Andersen AH. On the Rician distribution of noisy MRI data. Magn Reson Med
1996;36(2):331-333.
47. Gudbjartsson H, Patz S. The Rician distribution of noisy MRI data. Magn Reson Med
1995;34(6):910-914.
48. Oh TI, Jeong WC, Kim JE, Sajib SZ, Kim HJ, Kwon OI, Woo EJ. Noise analysis in fast
magnetic resonance electrical impedance tomography (MREIT) based on spoiled multi
gradient echo (SPMGE) pulse sequence. Phys Med Biol 2014;59(16):4723-4738.
49. Woo EJ, Seo JK. Magnetic resonance electrical impedance tomography (MREIT) for
high-resolution conductivity imaging. Physiological Measurement 2008;29(10):R1-26.
50. Polania R, Paulus W, Antal A, Nitsche MA. Introducing graph theory to track for
neuroplastic alterations in the resting human brain: a transcranial direct current
stimulation study. Neuroimage 2011;54(3):2287-2296.
51. Antal A, Bikson M, Datta A, Lafon B, Dechent P, Parra LC, Paulus W. Imaging artifacts
induced by electrical stimulation during conventional fMRI of the brain. Neuroimage
2014;85:1040-1047.
52. Sadleir RJ, Vannorsdall TD, Schretlen DJ, Gordon B. Target optimization in transcranial
direct current stimulation. Front Psychiatry 2012;3(90):1-13.
53. El-Sharkawy A, Schär M, Bottomley P, Atalar E. Monitoring and correcting spatio-
temporal variations of the MR scanner’s static magnetic field. Magnetic Resonance
Materials in Physics, Biology and Medicine 2006;19(5):223-236.
54. Astary GW, Peprah MK, Fisher CR, Stewart RL, Carney PR, Sarntinoranont M, Meisel
MW, Manuel MV, Mareci TH. MR measurement of alloy magnetic susceptibility:
Towards developing tissue-susceptibility matched metals. Journal of Magnetic
Resonance 2013;233:49-55.
132
55. Bernstein MA, King KE, Zhou XJ. Handbook of MRI Pulse Sequences: Academic Press;
2004.
56. Parker DL, Payne A, Todd N, Hadley JR. Phase reconstruction from multiple coil data
using a virtual reference coil. Magn Reson Med 2014;72(2):563-569.
57. Sadleir R, Grant S, Zhang SU, Lee BI, Pyo HC, Oh SH, Park C, Woo EJ, Lee SY, Kwon
O, Seo JK. Noise analysis in magnetic resonance electrical impedance tomography at 3
and 11 T field strengths. Physiol Meas 2005;26(5):875-884.
58. Rieke V, Vigen KK, Sommer G, Daniel BL, Pauly JM, Butts K. Referenceless PRF shift
thermometry. Magn Reson Med 2004;51(6):1223-1231.
59. Gabriel C, Gabriel S, Corthout E. The dielectric properties of biological tissues: I.
Literature survey. Phys Med Biol 1996;41(11):2231-2249.
60. Gabriel S, Lau RW, Gabriel C. The dielectric properties of biological tissues: II.
Measurements in the frequency range 10 Hz to 20 GHz. Phys Med Biol
1996;41(11):2251-2269.
61. Gabriel S, Lau RW, Gabriel C. The dielectric properties of biological tissues: III.
Parametric models for the dielectric spectrum of tissues. Phys Med Biol
1996;41(11):2271-2293.
62. van Dongen R, Burger HC. Specific electric resistance of body tissues. Physics in
Medicine and Biology 1961;5(4):431-449.
63. Sadleir RJ, Vannorsdall TD, Schretlen DJ, Gordon B. Transcranial direct current
stimulation (tDCS) in a realistic head model. Neuroimage 2010;51(4):1310-1318.
64. Heethaar RM, Faes TJC, Meij HA, de Munck JC. The electric resistivity of human tissues
(100 Hz-10 MHz): a meta-analysis of review studies. Physiological Measurement
1999;20(4):R1-10.
65. Akhtari M, Bryant HC, Mamelak AN, Heller L, Shih JJ, Mandelkern M, Matlachov A,
Ranken DM, Best ED, Sutherling WW. Conductivities of three-layer human skull. Brain
Topogr 2000;13(1):29-42.
66. Akhtari M, Bryant HC, Mamelak AN, Flynn ER, Heller L, Shih JJ, Mandelkern M,
Matlachov A, Ranken DM, Best ED, DiMauro MA, Lee RR, Sutherling WW.
Conductivities of three-layer live human skull. Brain Topogr 2002;14(3):151-167.
67. Logothetis NK, Kayser C, Oeltermann A. In vivo measurement of cortical impedance
spectrum in monkeys: implications for signal propagation. Neuron 2007;55(5):809-823.
68. Nicholson PW. Specific impedance of cerebral white matter. Experimental Neurology
1965;13(4):386-401.
133
69. Miranda PC, Hallett M, Basser PJ. The electric field induced in the brain by magnetic
stimulation: a 3-D finite-element analysis of the effect of tissue heterogeneity and
anisotropy. IEEE Trans Biomed Eng 2003;50(9):1074-1085.
70. Plonsey R, Heppner DB. Considerations of quasi-stationarity in electrophysiological
systems. Bull Math Biophys 1967;29(4):657-664.
71. Kwon OI, Jeong WC, Sajib SZ, Kim HJ, Woo EJ, Oh TI. Reconstruction of dual-
frequency conductivity by optimization of phase map in MREIT and MREPT. Biomed
Eng Online 2014;13(24):1-15.
72. Jog MV, Smith RX, Jann K, Dunn W, Lafon B, Truong D, Wu A, Parra L, Bikson M,
Wang DJJ. In vivo imaging of magnetic fields induced by transcranial direct current
stimulation (tDCS) in human brain using MRI. Scientific Reports 2016;6(34385):1-10.
73. Roemer PB, Edelstein WA, Hayes CE, Souza SP, Mueller OM. The NMR phased array.
Magn Reson Med 1990;16(2):192-225.
74. Constantinides CD, Atalar E, McVeigh ER. Signal-to-noise measurements in magnitude
images from NMR phased arrays. Magn Reson Med 1997;38(5):852-857.
75. Dietrich O, Raya JG, Reeder SB, Reiser MF, Schoenberg SO. Measurement of signal-to-
noise ratios in MR images: influence of multichannel coils, parallel imaging, and
reconstruction filters. J Magn Reson Imaging 2007;26(2):375-385.
76. Miranda PC, Lomarev M, Hallett M. Modeling the current distribution during
transcranial direct current stimulation. Clinical Neurophysiology 2006;117(7):1623-1629.
77. Du J, Carl M, Bydder M, Takahashi A, Chung CB, Bydder GM. Qualitative and
quantitative ultrashort echo time (UTE) imaging of cortical bone. J Magn Reson
2010;207(2):304-311.
78. Kwon OI, Lee BI, Nam HS, Park C. Noise analysis and MR pulse sequence optimization
in MREIT using an injected current nonlinear encoding (ICNE) method. Physiol Meas
2007;28(11):1391-1404.
79. Dunn JF, Tuor UI, Kmech J, Young NA, Henderson AK, Jackson JC, Valentine PA,
Teskey GC. Functional brain mapping at 9.4T using a new MRI-compatible electrode
chronically implanted in rats. Magn Reson Med 2009;61(1):222-228.
80. Hamamura MJ, Muftuler LT. Fast imaging for magnetic resonance electrical impedance
tomography. Magnetic Resonance Imaging 2008;26(6):739-745.
81. Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P. SENSE: Sensitivity encoding
for fast MRI. Magn Reson Med 1999;42(5):952-962.
82. Sodickson DK, McKenzie CA. A generalized approach to parallel magnetic resonance
imaging. Med Phys 2001;28(8):1629-1643.
134
83. Muftuler LT, Chen G, Hamamura MJ, Ha SH. MREIT with SENSE acceleration using a
dedicated RF coil design. Physiol Meas 2009;30(9):913-929.
84. Astary GW, Peprah MK, Fisher CR, Stewart RL, Carney PR, Sarntinoranont M, Meisel
MW, Manuel MV, Mareci TH. MR measurement of alloy magnetic susceptibility:
towards developing tissue-susceptibility matched metals. J Magn Reson 2013;233:49-55.
85. Setser RM, Kotys M, Bolen MA, Muthupillai R, Flamm SD. High resolution imaging of
the right ventricle using ZOOM MRI. Journal of Cardiovascular Magnetic Resonance
2010;12(1):1-2.
86. Li G, Chen R, Hao L, Lin L. Three dimensional MREIT for breast cancer detection on
open MRI scanners. IEEE International Conference on Information and Automation
2012:446-450.
87. Liu Y, Zhang Y. A feasibility study of magnetic resonance electrical impedance
tomography for prostate cancer detection. Physiol Meas 2014;35(4):567-581.
88. Pesikan P, Joy MLG, Scott GC, Henkelman RM. Two-dimensional current density
imaging. IEEE Transactions on Instrumentation and Measurement 1990;39(6):1048-
1053.
135
BIOGRAPHICAL SKETCH
Aditya Kumar Kasinadhuni was born in Hyderabad, a metropolitan city in South India.
He completed his schooling from the Hyderabad Public School, Begumpet in 2003 and earned
his Bachelor of Engineering degree from Osmania University (O.U) in the field of Biomedical
Engineering in 2009.While at O.U, he gained hands on expertize in Biomedical Instrumentation
during his internship with CARE Hospitals and developed image processing skills as part of his
undergraduate research in Apollo Gleneagles PET-CT center under the guidance of Dr. Jyotsna
Rao. He moved to the United States of America in 2009 to pursue his Master of Science degree
in Biomedical Engineering and achieved successful completion in 2011 from the University of
Florida, Gainesville. In the same year he embarked on his doctoral degree under the mentorship
of Dr. Thomas Mareci to study the development and applications of Magnetic Resonance
Imaging for mapping electrical current density in the brain. He received his Ph.D. in Biomedical
Engineering from the University of Florida in the fall of 2016.