medical image analysis

Medical Image AnalysisMedical Image AnalysisMedical Imaging Modalities: Magnetic Resonance Imaging

Figures come from the textbook: Medical Image Analysis, Second Edition, by Atam P. Dhawan, IEEE Press, 2011.

Magnetic Resonance Magnetic Resonance ImagingImagingNuclear magnetic resonance

◦The selected nuclei of the matter of the object

◦Blood flow and oxygenation◦Different parameters: weighted,

weighted, Spin-density◦Advance: MR Spectroscopy and

Functional MRI◦Fast signal acquisition of the order of

a fraction of a secondFigures come from the textbook: Medical Image Analysis, Second Edition, by Atam P. Dhawan, IEEE Press, 2011.

1T 2T


Figure comes from the Wikipedia, www.wikipedia.org.


Figure 4.12. MR images of a selected cross-section that are obtained simultaneously using a specific imaging technique. The images show (from left to right), respectively, the T1-weighted, T-2 weighted and the Spin-Density property of the hydrogen protons present in the brain.

Magnetic Resonance Magnetic Resonance ImagingImaging1H: high sensitivity and vast

occurrence in organic compounds13C: the key component of all organic15N: a key component of proteins and

DNA19F: high relative sensitivity31P: frequent occurrence in organic

compounds and moderate relative sensitivity

Adapted from the Wikipedia, www.wikipedia.org.

MR SpectroscopyMR Spectroscopy



Functional MRIFunctional MRI



MRI PrinciplesMRI Principles : spin-lattice relaxation time : spin-spin relaxation time : the spin density


1T

2T

MRI PrinciplesMRI Principles1. Great web sites

1. Simulations from BIGS - Lernhilfe für Physik und Technik

2. http://www.cis.rit.edu/class/schp730/bmri/bmri.htm


MRI PrinciplesMRI PrinciplesSpin

◦A fundamental property of nuclei with odd atomic weight and/or odd atomic numbers is the possession of angular moment

Magnetic moment◦The charged protons create a

magnetic field around them and thus act like tiny magnets


MRI PrinciplesMRI Principles : the spin angular moment : the magnetic moment : a gyromagnetic ratio, MHz/T

A hydrogen atom◦ :42.58 MHz/T


J

J


NN

SS

JJ

JJ

Figure 4.13. Left: A tiny magnet representation of a charged proton with angular moment, J. Right: A symbolic representation of a charged proton with angular moment, J and a magnetic moment, μ.

MRI PrinciplesMRI PrinciplesPrecession of a spinning proton

◦The interaction between the magnetic moment of nuclei with the external magnetic field

◦Spin quantum number of a spinning proton: ½

◦The energy level of nuclei aligning themselves along the external magnetic field is lower than the energy level of nuclei aligned against the external magnetic field



Figure 4.14 (a) A symbolic representation of a proton with precession that is experienced by the spinning proton when it is subjected to an external magnetic field. (b) The random orientation of protons in matter with the net zero vector in both longitudinal and transverse directions.


MRI PrinciplesMRI PrinciplesEquation of motion for isolated

spin

Solution:

J

kHHdtJd

00

kHdtd

0

00 H


Longitudinal Vector OX at the transverse position X

Net LongitudinalVector: Zero

Net TransverseVector: Zero

Net LongitudinalVector: Zero

Net TransverseVector: Zero


Lower EnergyLevel

Higher EnergyLevel

S

N

H

Lower EnergyLevel

Higher EnergyLevel

S

N

H0

Figure 4.15 (a). Nuclei aligned under thermal equilibrium in the presence of an external magnetic field. (b). A non-zero net longitudinal vector and a zero transverse vector provided by the nuclei precessing in the presence of an external magnetic field.


Non-zero Net Longitudinal Vector

x

y

z

x

y

zH0

Net Zero Transverse Vector

MRI PrinciplesMRI PrinciplesThe precession frequency

◦Depends on the type of nuclei with a specific gyromagnetic ratio and the intensity of the external magnetic field

◦This is the frequency on which the nuclei can receive the Radio Frequency (RF) energy to change their states for exhibiting nuclear magnetic resonance

◦The excited nuclei return to the thermal equilibrium through a process of relaxation emitting energy at the same precession frequency

MRI PrinciplesMRI Principles90-degree pulse

◦Upon receiving the energy at the Larmor frequency, the transverse vector also changes as nuclei start to precess in phase

◦Form a net non-zero transverse vector that rotates in the x-y plane perpendicular to the direction of the external magnetic field



S

N

S

N x

y

z

Figure 4.16. The 90-degree pulse causing nuclei to precess in phase with the longitudinal vector shifted clockwise by 90-degrees as a result of the absorption of RF energy at the Larmor frequency.

MRI PrinciplesMRI Principles180-degree pulse

◦If enough energy is supplied, the longitudinal vector can be completely flipped over with a 180-degree clockwise shidf in the direction against the external magnetic field



S

N

S

N

x

y

z

Figure 4.17. The 180-degree pulse causing nuclei to precess in phase with the longitudinal vector shifted clockwise by 180-degrees as a result of the absorption of RF energy at the Larmor frequency.

MRI PrinciplesMRI PrinciplesRelaxation

◦The energy emitted during the relaxation process induces an electrical signal in a RF coil tuned at the Larmor frequency

◦The free induction decay of the electromagnetic signal in the PF coil is the basic signal that is used to create MR images

◦The nuclear excitation forces the net longitudinal and transverse magnetization vectors to move


MRI PrinciplesMRI PrinciplesA stationary magnetization

vector

The total response of the spin system


N

nnM

1

1

0

2

)( T

kMMT

jMiMHM

dtMd zzyx


Dephasing

RF Pulse

Random Phase (Zero Transverse Vector)

In Phase Spin

Relaxation

Figure 4.18. The transverse relaxation process of spinning nuclei.

MRI PrinciplesMRI PrinciplesThe longitudinal and transverse

magnetization vectors with respect to the relaxation times

where


tiTtyxyx eeMtM 02/

,, )0()(

11 //0 )0()1()( Ttz

Ttzz eMeMtM

piyxyx eMM 0)0()0( ',',


t

t

Mx,y (t)

Mz (t)

Figure 4.19. (a) Transverse and (b) longitudinal magnetization relaxation after the RF pulse.

MRI PrinciplesMRI PrinciplesThe RF pulse causes nuclear

excitation changing the longitudinal and transverse magnetization vectors

After the RF pulse is turned off, the excited nuclei go through the relaxation phase emitting the absorbed energy at the same Larmor frequency that can be detected as an electrical signal, called the Free Induction Decay (FID)


MRI PrinciplesMRI PrinciplesThe NMR spin-echo signal (FID

signal)


dxdydzezyxMS zyxizyx

zyx )(0 ),,(),,(

zyxzyxi

zyx dddeSMzyx zyx )(0 ),,(),,(

MR InstrumentationMR InstrumentationThe stationary external magnetic

field◦Provided by a large superconducting

magnet with a typical strength of 0.5 T to 1.5 T

◦Housing of gradient coils◦Good field homogeneity, typically on

the order of 10-50 parts per million◦A set of shim coils to compensate for

the field inhomogeneity Figures come from the textbook: Medical Image Analysis, Second Edition, by Atam P. Dhawan, IEEE Press, 2011.


Gradient Coils

Magnet

Gradient Coils

RFCoils

PatientPlatform

Monitor Data-AcquisitionSystem

Figure 4.20. A general schematic diagram of a MR imaging system.

MR InstrumentationMR InstrumentationAn RF coil

◦To transmit time-varying RF pulses◦To receive the radio frequency

emissions during the nuclear relaxation phase

◦Free Induction Decay (FID) in the RF coil


MR Pulse SequencesMR Pulse SequencesNMR signal

◦The frequency and the phaseSpatial encoding in MR imaging

◦Frequency encoding and phase encoding



x

z

y

y

xx

y

z

z

Sagital

Coronal

Axial

Figure 4.21 (a). Three-dimensional object coordinate system with axial, sagittal and coronal image views. (b): From top left to bottom right: Axial, coronal and sagittal MR images of a human brain.

MR Pulse SequencesMR Pulse Sequences


Z Gradient

90 RF Pulse(Slice Selection)

X Gradient

Phase-Encoding(x-scan selection)

Z Gradient

180 RF Pulse(Slice Echo Formation)

Y Gradient

Frequency Encoding(Read-Out Pulse)

Figure 4.22. (a): Three-dimensional spatial encoding for spin-echo MR pulse sequence. (b): A linear gradient field for frequency encoding. (c). A step function based gradient field for phase encoding.


Varying Spatially DependentLarmor Frequency

S

N

S

N

Linear Gradient

Precessing Nuclei

External Magnet

Positive PhaseChange

Negative PhaseChange

Phase -EncodingGradientStep

MR Pulse SequencesMR Pulse SequencesFrequency encoding

◦A linear gradient is applied throughout the imaging space a long a selected direction

◦The effective Larmor frequency of spinning nuclei is also spatially encloded along the direction of the gradient

◦Slice selection for axial imaging


MR Pulse SequencesMR Pulse SequencesThe phase-encoding gradient

◦Applied in steps with repeated cycles◦If 256 steps are to be applied in the

phase-encoding gradient, the readout cycle is repeated 256 times, each time with a specific amount of phase-encoding gradient


Spin Echo ImagingSpin Echo Imaging :

◦Between the application of the 90 degree pulse and the formation of echo (rephasing of nuclei

:◦Between the 90 degree pulse and

180 degree pulse


ET

2/ET


RF Energy: 90 Deg Pulse

Zero Net Vector:Random Phase

RelaxationDephasing


Echo -Formation


Zero Net Vector:Random Phase

In Phase

Rephasing

Echo -Formation

In Phase

Figure 4.23. The transverse relaxation and echo formation of the spin echo MR pulse sequence.

Spin Echo ImagingSpin Echo ImagingK-space

◦The placement of raw frequency data collected through the pulse sequences in a multi-dimensional space

◦By taking the inverse Fourier transform of the k-space data, an image about the object can be reconstructed in the spatial domain

◦The NMR signals collected as frequency-encoded echoes can be placed as horizontal lines in the corresponding 2-D k-space


Spin Echo ImagingSpin Echo ImagingK-space

◦As multiple frequency encoded echoes are collected with different phase-encoding gradients, they are placed as horizontal lines in the corresponding k-space with the vertical direction representing the phase-encoding gradient values


Spin Echo ImagingSpin Echo Imaging : the cycle repetition time weighted

◦A long and a long weighted

◦A short and a shortSpin-density

◦A long and a short


RT2T

RT ET1T

RT ET

RT ET


90 deg RF pulse

180 deg RF pulse

Gz: Slice Selection Frequency EncodingGradient

Gx: Phase EncodingGradient

Gy: Readout Frequency EncodingGradient

TE /2

TE /2

TE

RF pulseTransmitter

NMRRF FIDSignal

Figure 4.24. A spin echo pulse sequence for MR imaging.

Spin Echo ImagingSpin Echo Imaging

The effective transverse relaxation time from the field inhomogeneities


12 1),,(),,( 0TT

TT RE

eezyxzyx

2 11

2*

2

HTT

Spin Echo ImagingSpin Echo ImagingThe effective transverse

relaxation time from a spatial encoding gradient


2 11

*2

**2

GdTT

Inversion Recovery Inversion Recovery ImagingImagingIR imaging

◦IR imaging pulse sequence allows relaxation of some or all of before spins are rephased through 90-degree pulse and therefore emphasizes the effect of longitudinal magnetization

◦ 180-degree pulse is first applied along with the slice selection frequency encoding gradientFigures come from the textbook: Medical Image Analysis, Second Edition, by Atam P. Dhawan, IEEE Press, 2011.

1T

Echo Planar ImagingEcho Planar ImagingA single-shot fast-scanning methodSpiral Echo Planar Imaging (SEPI)

◦where

)(1)( tdtdtG xx

)(1)( tdtdtG yy

tttx cos )(

ttty sin )(


90 deg RF pulse

90 deg RF pulse


Gx: OscillatingGradient

Gy: Readout Gradient

RF pulseTransmitter

NMRRF FIDSignal

Figure 4.25. A single shot EPI pulse sequence.


gy

gx

x

y

Figure 4.26. The k-space representation of the EPI scan trajectory.


x

y

SEPI Trajectory

Data SamplingPoints

Figure 4.27. The spiral scan trajectory of SEPI pulse sequence in the k-space.


90 deg RF pulse

180 deg RF pulse


Gx Gradient

Gy Gradient

TE /2

TE /2

TE

RF pulseTransmitter

NMRRF FIDSignal

TD

Figure 4.28. The SEPI pulse sequence


Figure 4.29. MR images of a human brain acquired through SEPI pulse sequence.

Gradient Echo ImagingGradient Echo ImagingFast low angle shot (FLASH) imaging

◦Utilize low-flip angle RF pulses to create multiple echoes in repeated cycles to collect the data required for image reconstruction

◦A low-flip angle (as low as 20 degrees)◦The readout gradient is inverted to re-

phase nuclei leading to the gradient echo during the data acquisition

◦The entire pulse sequence time is much shorter than the spin echo pulse sequence



Low Flip Angle RF pulse


RF pulseTransmitter


Gy: Readout Frequency EncodingGradient TE

NMRRF FIDSignal

Figure 4.30. The FLASH pulse sequence for fast MR imaging.

Flow ImagingFlow ImagingTracking flow

◦Diffusion (incoherent flow) and perfusion (partially coherent flow)

◦The FID signal generated in the RF receiver coil by the moving nuclei and velocity-dependent factors

MR angiography



90 deg RF pulse

180 deg (selective)RF pulse




TE /2

TE

RF pulseTransmitter

NMRRF FIDSignal

Figure 4.31. A flow imaging pulse sequence with spin echo.


Figure 4.32: Left: A proton density image of a human brain. Right: The corresponding perfusion image.


90 degree RF pulse


RF pulseTransmitter



TE NMRRF FIDSignal

Next 90 degree RF pulse

TR

Figure 4.33. Gradient echo based MR pulse sequence for 3-D MR volume angiography.


Figure 4.34. An MR angiography image.

Flow ImagingFlow Imaging


angiography image

FMRIFMRIfMRI imaging

◦Measure blood oxygen level during sensory stimulation or any task that causes a specific neural activity

◦Visual or auditory stimulation, finger movement, or a cognitive task

◦Blood oxygenated level dependence (BOLD)

◦Oxygenated hemoglobin ( ) is diamagnetic, while deoxygenated hemoglobin ( ) is paramagnetic

2HbO

Hb

FMRIFMRIfMRI imaging

◦A reduction of the relative deoxy-hemoglobin concentration due to an increase of blood flow and hence increased supply of fresh oxy-hemoglobin during neural activity is measured as an increase in or weighted MR signals

2T2T

Diffusion ImagingDiffusion ImagingDiffusion process

◦Water molecules spread out over time that is represented by Brownian motion

◦An anisotropic Gaussian distribution along a given spatial axis such that the spread of the position of molecules after a time along a spatial axis can be represented with a variance of

◦where is diffusion coefficient in the tissue

Tx

D

DTx 22


DTI color image


◦Anisotropic diffusion in the white matter◦Isotropic diffusion in the gray matter◦Motion probing gradients (MPG) to

examine the motion of water molecules in the diffusion process in a specific direction

◦The MR FID signal is decreased for healthy tissue, and increased with trapped-in water molecules


◦where is the gyromagnetic ratio, is diffusion coefficient, and is the strength of two MPG gradients each with duration separated by applied in spatial directions

DNGeSS )/(0

222

DG

N


z

y

x

zzzyzx

yzyyyx

xzxyxx

zyx

uuu

DDDDDDDDD

uuuD ),,(

321][trace zzyyxx DDDD

3

2

1


◦Fractional anisotropy (FA)

◦Multiple sclerosis, strokes, tumors, Parkinson’s and Alzheimer’s disease

◦Attention deficit hyperactivity disorder (ADHS)

23

22

21

213

232

221 )()()(

21

FA

Contrast, Spatial Resolution, Contrast, Spatial Resolution, and SNRand SNRSpin-echo imaging pulse

sequence

Inversion recovery (180-90-180) imaging pulse sequence

211 TT

TT ER

eekS

21121 TT

TT

TT ERI

eeekS

Contrast, Spatial Resolution, Contrast, Spatial Resolution, and SNRand SNRGradient echo imaging pulse

sequence

1

*21

cos1

sin1

TT

TT

TT

R

ER

e

ee

kS

Contrast, Spatial Resolution, Contrast, Spatial Resolution, and SNRand SNRParamagnetic contrast agent

◦gadolinium (Gd) to change the susceptibility of the net magnetization vector

◦Reduces relaxation time and increases the signal intensity of -weighted images

Noise and field inhomogeneities◦RF noise, field inhomogeneities,

motion, chemical shift

1T1T

Contrast, Spatial Resolution, Contrast, Spatial Resolution, and SNRand SNRChemical shift

◦The deviation of its effective resonance frequency in the presence of other nuclei from a standard reference without any other nuclei with their local magnetic fields present

◦ppmref

ref

610)(

Contrast, Spatial Resolution, Contrast, Spatial Resolution, and SNRand SNR

◦Induced magnetic field in alkenes

◦Induced magnetic field in alkynes


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