bioimpedance mapping of the cervix · 2010-06-09 · bioimpedance spectroscopy has shown potential...
TRANSCRIPT
QUEENSLAND UNIVERSITY OF TECHNOLOGY
SCHOOL OF PHYSICAL AND CHEMICAL SCIENCES
Bioimpedance Mapping
of the Cervix
Submitted by Jye Geoffrey SMITH to the School of Physical and Chemical Sciences, Queensland University of Technology, in partial fulfilment of the requirements of the degree of Doctor of Philosophy.
May 2008
Keywords
Bioimpedance, Mulitifrequency, Impedance, Cervical Cancer, Bovine Blood,
Haematocrit, Tetrapolar, Finite Element Analysis, Impedance Mapping, Mul-
tiplexer
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Abstract
Bioimpedance spectroscopy has shown potential as a method for characterising
biological tissue with the use of a tetrapolar electrode configuration. Brown
et al. (2000) demonstrated that the configuration is capable of distinguishing
between normal squamous epithelium and Cervical Intra-epithelial Neoplasia
(CIN). However little has been done to identify the volumes of tissue that
contribute to the measured impedance. Brown et al. employed a probe with
a single tetrapolar electrode set thus analysing single points of tissue. The
probe was required to be moved in order to “sample” other areas of tissue.
This method provides no spatial information of the lesion boundaries.
The overall objective of this research was to design and construct an impedance
mapping system (IMS) for objective virtual biopsy of lesions by bioimpedance
spectroscopy (BIS). Initially freshly excised cervical tissue was to be tested
however as the study progressed this proved problematic and bovine blood
was chosen as a suitable substitute.
Specific aims were to; Investigate the spatial sensitivity distribution of the tetrapolar electrode
configuration via finite element analysis (FEA).
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Design a novel front end multiplexing system and multi-electrode array
for mapping the impedance of the tissue of interest. Experimentally confirm the efficacy of the approach to identify regions of
different impedances and their boundaries using bioimpedance mapping.
The present study used finite element analysis (FEA) to investigate the
spatial variation in sensitivity of the tetrapolar electrode configuration and
identify which volumes of tissue were included in the measured impedance.
An impedance mapping device was also designed and constructed utilising
the tetrapolar electrode configuration in an expanded array of 25 electrodes.
This array allowed the surface of an area of tissue to be mapped and lesion
boundaries identified in an objective manner.
FEA was also used to model lesions in healthy tissue and the sensitivity
fields associated with the tetrapolar configuration. The FEA indicated that
anomalous results would be obtained when a lesion was located between a
drive and measurement electrode pair. In this case the lesion resulted in an
increase in impedance with respect to the impedance of healthy tissue, whereas
a lesion should result in a decrease in measured impedance relative to that of
healthy tissue. The anomaly was found to produce false negative results for
small lesions up to 0.4 mm and even a lesion with radius of approximately
0.75 mm could be undetected as the measured impedance spectrum for such
a lesion is similar to that of healthy tissue. Modelling also provided insight
into the sensitivity fields for an electrode array and its efficacy in accurately
measuring the surface impedance of tissue and lesions of interest.
The impedance mapping system (IMS) developed used an array of 25 (5x5)
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electrodes. The array allows 64 individual tetrapolar measurements to be
obtained at 16 locations, providing an impedance map of 49 mm2 on the surface
of a tissue sample. Multiple measurements at each location reduce the chance
of anomalous results since these can be identified and excluded. Software was
developed to display the measured impedance maps and regions of different
impedance were easily identified
Testing of the IMS using bovine blood showed separation of the measured
impedance for a range of haematocrit between 0 - 80%. Introduced volumes of
red blood cells (RBC) or clots (to mimic lesions) to the plasma (haematocrit
0%) were also clearly identified using the IMS. It was seen that measurements
made at the boundary of 2 different haematocrits (ie 2 volumes of different
impedance) resulted in an anomalous result as indicated by the FEA modelling.
However it was demonstrated that these anomalies can be used to objectively
identify the introduced RBC (lesion) boundaries.
A more efficient electrode stepping sequence was also developed taking
advantage of the reciprocal nature of the tetrapolar electrode configuration.
This development allows for the electrode array to be doubled in size using
the same components, and to sample twice the surface area in the same time
taken using the initially developed system.
In summary, an impedance mapping system has been modelled, designed
and developed for tissue characterisation by bioimpedance measurements. The
technique has been shown experimentally to be able to detect regions of differ-
ent impedance and is in agreement with the finite element analysis performed.
Further development of the IMS will allow progressive monitoring of suspect
lesions in-vivo and better identification of their spatial distribution for biopsy.
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List of publications
1. Smith, J. G., Thomas, B. J. & Cornish, B. H. (2004). FEA modelling: ef-
ficacy of tetrapolar electrode arrays in virtual biopsy-cervix, XII ICEBI.
2. Smith, J. G., Thomas, B. J. & Cornish, B. H. (2007). A Pilot Study For
Tissue Characterisation Using Bioimpedance Mapping, XII ICEBI.
3. Smith, J. G., Thomas, B. J. & Cornish, B. H. (2007). Queensland Univer-
sity of Technology. Impedance Measurement Process. Australian Patent
Application Number: 2007904287.
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Contents
1 Introduction 1
1.1 Cervical Cancer . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Bioelectrical Impedance Analysis . . . . . . . . . . . . . . . . . 3
1.2.1 Bioimpedance Background . . . . . . . . . . . . . . . . . 3
1.2.2 Biological Tissue Equivalent Circuit . . . . . . . . . . . . 5
1.2.3 Applications of BIA to Tissue Characterisation . . . . . 9
1.2.4 Tetrapolar Electrode Configuration . . . . . . . . . . . . 12
1.3 Finite Element Analysis (FEA) . . . . . . . . . . . . . . . . . . 13
1.4 Aims and Objectives . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Modelling of Sensitivity Distributions 17
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Lesion Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Sensitivity Fields . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.1 3-D Sensitivity Field Model . . . . . . . . . . . . . . . . 28
2.3.2 Electrode Array Sensitivity Fields . . . . . . . . . . . . . 36
3 Impedance Mapping System Overview, Operation and Test-
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ing 43
3.1 Current Source & Potential Measurement . . . . . . . . . . . . . 45
3.2 Multiplexers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3 Electrode Array . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.4 Impedance Data Analysis . . . . . . . . . . . . . . . . . . . . . 49
3.5 Impedance Mapping System Graphical Use Interface and Oper-
ation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.6 Impedance Mapping System Testing . . . . . . . . . . . . . . . 51
3.6.1 Testing of Multiplexer Ron Contribution . . . . . . . . . 51
3.6.2 RRC Circuits . . . . . . . . . . . . . . . . . . . . . . . . 56
3.6.3 Resistor Matrix . . . . . . . . . . . . . . . . . . . . . . . 59
3.6.4 Biological Tissue . . . . . . . . . . . . . . . . . . . . . . 62
3.6.5 Testing Summary . . . . . . . . . . . . . . . . . . . . . . 64
4 Bioimpedance Mapping - Results and Discussion 67
4.1 Effect of Tissue Sample Size . . . . . . . . . . . . . . . . . . . . 68
4.1.1 Electrode Array Coverage . . . . . . . . . . . . . . . . . 68
4.1.2 The Effect of Sample Thickness . . . . . . . . . . . . . . 71
4.2 Homogeneous Haematocrit Impedance Mapping . . . . . . . . . 73
4.3 Impedance Maps . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.3.1 Plasma with Introduced Red Blood Cells . . . . . . . . . 76
4.3.2 Plasma with Introduced Red Blood Cell Clot . . . . . . 80
4.4 Experimental Comparison with Modelled Sensitivity Field . . . 85
4.4.1 Anomalous Measurements . . . . . . . . . . . . . . . . . 85
4.4.2 Reciprocal Electrodes . . . . . . . . . . . . . . . . . . . . 87
4.5 Lesion Boundary Identification . . . . . . . . . . . . . . . . . . . 92
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
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5 Conclusion 97
Bibliography 101
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List of Figures
1.1 Schematic of modelled tissue when constructed of its basic com-
ponents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2 (a) Current pathways at low frequencies. (b) Current pathways
at high frequencies. . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Impedance spectrum for modelled tissue when constructed of
its basic components. . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Impedance spectrum for biological tissue with a depressed semi-
circle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 Changes in tissue structure associated with the progression of
CIN in cervical squamous epithelium (Walker et al., 2000). . . 10
1.6 Tetrapolar arrangement used for taking of bioelectrical impedance
measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.7 (a) Cross section of finite element model of single cell. (b) Finite
element tissue model (Walker et al., 2000, 2001a, 2001b) . . . . 14
2.1 (a) Tetrapolar electrode model with the lesion located between
a drive and measurement electrode. (b) 3D view showing the
lesion located immediately below the surface of healthy tissue. . 20
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2.2 Experimental electrode placement on the surface of a saline so-
lution and brass rod with radius ’r’ located (a) central to the
electrodes (b) between a drive and measurement electrode. . . . 21
2.3 Modelled results of tetrapolar electrode configuration for a le-
sion located centrally in the electrode configuration. . . . . . . . 24
2.4 Modelled results of tetrapolar electrode configuration for a le-
sion located midway between a drive and measurement electrode
(Legend displays frequency in kHz). . . . . . . . . . . . . . . . . 25
2.5 Modelled results of tetrapolar electrode configuration for a le-
sion located midway between a drive and measurement electrode
(Legend displays lesion radius in mm). . . . . . . . . . . . . . . 25
2.6 Measurement with (a) no lesion and (b) a lesion of radius 0.75
mm in otherwise healthy tissue. . . . . . . . . . . . . . . . . . . 26
2.7 Experimental and modelled results of the tetrapolar electrode
configuration for a brass rod located centrally in the electrode
configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.8 Experimental and modelled results of the tetrapolar electrode
configuration for a brass rod located midway between a drive
and measurement electrode. . . . . . . . . . . . . . . . . . . . . 27
2.9 3-D modelled tetrapolar configuration and current density con-
fined by the boundaries. . . . . . . . . . . . . . . . . . . . . . . 30
2.10 Sensitivity field at a depth of 0.0 mm. . . . . . . . . . . . . . . . 30
2.11 Sensitivity field at a depth of 0.2 mm. . . . . . . . . . . . . . . . 31
2.12 Sensitivity field at a depth of 0.4 mm. . . . . . . . . . . . . . . . 31
2.13 Sensitivity field at a depth of 0.6 mm. . . . . . . . . . . . . . . . 32
2.14 Sensitivity field at a depth of 0.8 mm. . . . . . . . . . . . . . . . 32
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2.15 Sensitivity field at a depth of 1.0 mm. . . . . . . . . . . . . . . . 33
2.16 Maximum sensitivity in each plane as a function of depth for
electrode spacing’s 0.2 mm, 0.4 mm, 0.6 mm, 0.8 mm and 1.0
mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.17 Sum of the absolute sensitivity in each plane as a function of
depth for electrode spacing’s 0.2 mm, 0.4 mm, 0.6 mm, 0.8 mm
and 1.0 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.18 Measured potential against tissue medium thickness for differing
electrode spacings. . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.19 The four unique electrode sites modelled. . . . . . . . . . . . . . 37
2.20 Maximum sensitivity in each plane as a function of depth for
electrode sites 1, 2, 3 and 4 (see figure 2.19). . . . . . . . . . . . 38
2.21 Sum of the absolute sensitivity in each plane as a function of
depth for electrode sites 1, 2, 3 and 4(see figure 2.19). Locations
1 and 3 are difficult to see due to overlap. . . . . . . . . . . . . 39
2.22 Sensitivity field at a depth of 0.1 mm for electrode site 1 shown
in figure 2.19. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.23 Measurement thickness for an array with 0.77 mm electrode
spacing and a single electrode configuration with the same spacing. 40
2.24 Sensitivity field at a depth of 0.1 mm for a tetrapolar electrode
configuration with inactive electrode inside the configuration. . . 41
3.1 Schematic of the bioimpedance mapping system. . . . . . . . . . 44
3.2 Functional block diagram and pin configuration of multiplexer
ADG732. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
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3.3 Multiplexer circuit diagram. Parallel port represented by Header
9 and electrode array socket by Header 25. SFB7 drive and mea-
surement electrodes connect through red, black and white, blue
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.4 PCB electrode array. . . . . . . . . . . . . . . . . . . . . . . . . 48
3.5 Electrode stepping sequence from 1 to 4; C1, C2 represent cur-
rent source and P1, P2 potential measurement. . . . . . . . . . 48
3.6 Impedance mapping system graphical user interface. Displayed
is a typical impedance map. . . . . . . . . . . . . . . . . . . . . 52
3.7 Flow chart of the IMS operational sequence. . . . . . . . . . . . 53
3.8 Measurement made with short circuited electrodes and no mul-
tiplexer front end. . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.9 Measurement made with short circuited electrodes through mul-
tiplexer front end. . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.10 RRC test circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.11 RRC test circuit attached to the electrode array. All resistor
values (R) are 100 Ω and capacitor value (C) 100 nF. . . . . . . 57
3.12 Typical Cole plots for RRC test circuit, measured data is rep-
resented by red circles and line of best fit by the broken blue
line. (a) Cole plot obtained without the multiplexers (b) Cole
plot obtained with the multiplexers. . . . . . . . . . . . . . . . . 58
3.13 Resistor matrix constructed with 1000 Ω resistors. . . . . . . . . 59
3.14 Typical Cole plot for a measurement made with a resistor ma-
trix, measured data is represented by red circles and line of best
fit by the broken blue line. This Cole plot was obtained from a
matrix constructed of 1000 Ω resistors. . . . . . . . . . . . . . . 61
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3.15 Impedance map obtained from a 1000 Ω resistor matrix, this is
representative of a typical matrix result. (a) R0 map. (b) R∞
map. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.16 Cole plot of pure plasma. . . . . . . . . . . . . . . . . . . . . . . 63
3.17 Impedance map of pure plasma. (a) R0 map. (b) R∞
map. . . . 64
4.1 Inadequate electrode coverage with bovine blood in the upper
right corner. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2 Impedance map with a higher impedance in the upper right
corner due to insufficient electrode coverage. . . . . . . . . . . . 70
4.3 Mean R0 of plasma for various sample thicknesses. . . . . . . . . 72
4.4 Homogeneous haematocrit impedance maps. The haematocrit
is given as a percentage and the colour legend displays the R0
value in ohms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.5 Mean R0 for homogeneous impedance maps. . . . . . . . . . . . 75
4.6 Region of red blood cells introduced to plasma. Lower left dark
area is where the cells were injected and the light grey is the
area of visible diffusion. . . . . . . . . . . . . . . . . . . . . . . . 77
4.7 Impedance map of plasma with red blood cells introduced in
lower left corner. . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.8 Impedance map of plasma with a larger volume of red blood
cells introduced in lower left corner. . . . . . . . . . . . . . . . . 79
4.9 Dispersion of introduced red blood cells into plasma over 2
minute intervals. (a) Measurement made immediately after the
introduction of RBC. (b) Measurement made at 2 minutes. (c)
Measurement made at 4 minutes. (d) Measurement made at 6
minutes. (e) Measurement made at 8 minutes. . . . . . . . . . . 81
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4.10 Impedance map of plasma with introduced red blood cell clot
covering central electrode. . . . . . . . . . . . . . . . . . . . . . 82
4.11 Impedance map of plasma with introduced red blood cell clot
covering the 4 electrodes associated with the region in the mid-
dle lower right. . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.12 Impedance map of plasma with introduced red blood cell clot
covering the 2 lower right regions. . . . . . . . . . . . . . . . . . 84
4.13 Anomalous result due to positive and negative sensitivity fields.
Anomalous result is identified by arrows. . . . . . . . . . . . . . 86
4.14 Reciprocal nature of the tetrapolar electrode configuration. The
reciprocal pairs are grouped . . . . . . . . . . . . . . . . . . . . 88
4.15 Impedance map of plasma used to demonstrate the reciprocal
nature of the tetrapolar electrode configuration. . . . . . . . . . 89
4.16 New proposed electrode stepping sequence 1-8. Red/black and
white/blue represent drive and measurement electrodes respec-
tively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.17 Comparison of (a) new electrode stepping sequence with (b)
presently used. . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.18 Boundary identification via anomalies. . . . . . . . . . . . . . . 94
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List of Tables
1.1 Cell dimensions in µm used in models of normal tissue (Walker
et al., 2000). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.2 Electrical properties used in cell models (Walker et al., 2000). . 15
2.1 Tissue electrical properties as given by Brown et al, 2000. . . . . 19
4.1 R0 mean and variance for various electrode orientation combi-
nations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
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Statement of original authorship
The work contained in this thesis has not been previously submitted for a de-
gree or diploma at any other higher educational institution. To the best of my
knowledge and belief, the thesis contains no material previously published or
written by another person except where due reference is made.
Jye Geoffrey Smith
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Acknowledgements
Firstly I would like to thank my supervisor Assoc. Prof. Brian Thomas, or
as he is better know BJ. Without your support and guidance throughout this
project it would not have been possible. You never lost faith even when I
had and our meetings always left me motivated and ready to tackle the next
problem. If I had my time again I promise to use Word instead of LaTeX to
ease what seemed like the endless task of editing.
Assoc. Prof. Bruce Cornish, I am grateful for your help in problem solving,
not only academic but also administrative. Your support and friendly banter
made our meetings a pleasure.
Without the help of Elizabeth Stein and Margaret McBurney I may still
be stuck in a pile of administrative paper work, thankyou.
To everyone I have met, borrowed equipment from, has helped with ex-
periments and even the use of LaTeX throughout this journey I would like to
thank. However insignificant you feel it may have been you have made this
experience a pleasure.
To my darling wife Cheryl, it seemed this day would never come but your
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endless support and encouragement over the years has gotten me to where I
am today.
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List of Abbreviations
BIA Bioimpedance Analysis
MFBIA Multifrequency Bioimpedance Analysis
BIS Bioimpedance Spectroscopy
FEA Finite Element Analysis
CIN Cervical Intraepithelial Neoplasia
AC Alternating Current
DC Direct Current
IMS Impedance Mapping System
RBC Red Blood Cell
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Chapter 1
Introduction
1.1 Cervical Cancer
Cancer of the cervix is one of the most preventable and curable of all cancers
(Greenlee et al., 2000). In 2002 it was the second most common cancer in
women worldwide and it is estimated that up to 90 percent of the most common
type of cervical cancer (squamous cell carcinoma) may be prevented if cell
changes are detected and treated early (Gauthier et al., 1985, Hartikainen
et al., 2001, Koss 1989, Kottmeier 1961, Larsen 1994, Majeed et al., 1994,
Sasieni et al., 1995). Worldwide in 2002 more than 490,000 new cases of
cervical cancer were diagnosed with a mortality of over 270,000 (Parkin et al.,
2007). It is important to note that the death rate from cervical cancer amongst
developing countries is nearly 6 times that of developed countries (Parkin et
al., 2007). There are many reasons for these high death rates but a significant
reduction could be achieved if a device similar to that proposed in this study
1
2 CHAPTER 1. INTRODUCTION
was available for use in screening programs.
Cancer of the cervix affects the cells lining the cervix, which is the lower
part of the womb (uterus) as it joins the inner end of the vagina (Morrow and
Curtin 1998, Nguyen and Averette 1999). Like other cancers, cervical cancer
is a disease where normal cells change, begin to multiply out of control, and
form a growth, tumour or lesion. If not treated early, the growth can invade
local tissue and spread or metastasise to other parts of the body (Boyce et al.,
1984). The main symptoms of cervical cancer are unusual bleeding from the
vagina, and sometimes an unusual vaginal discharge (Raymond et al., 2001).
A cervical cancer may take 10 or more years to develop, but before this
the cells may show pre-cancerous changes. Brown et al. (2000a) and Quek
et al. (1998) proposed that bioimpedance analysis has the potential to detect
these changes and with early treatment there is an excellent chance of a full
recovery. Pre-cancerous lesions can be categorised into two levels of severity,
low-grade abnormalities and high-grade abnormalities, with the higher grade
lesions more likely to progress to a cancer. These are usually graded from warty
atypia (HPV effect), atypia, equivocal cervical intraepithelial neoplasia (CIN),
possible CIN, endocervical dysplasia NOS, CIN1 to CIN3, and carcinoma in
situ. Pre-cancerous changes are relatively easily treated and are cured in nearly
all cases (Baggish (1983)). The type of treatment depends on whether the
change observed is low or high grade, the woman’s age, general health, whether
she wants to have children, and her preferences (Houlard et al., 2002, Raymond
et al., 2001).
3
1.2 Bioelectrical Impedance Analysis
1.2.1 Bioimpedance Background
The Biological Impedance Analysis (BIA) method is an attractive tool as it
offers many opportunities for non-invasive assessment of human body com-
position and tissue characterisation in clinical investigation and patient care
(Baker 1989, Brodie et al., 1998, Chauveau et al., 1999, Rigaud et al., 1994,
Shinkarenko and Kostromina 1998). Advantages such as the non-invasive na-
ture, straightforward use, low cost, safety of operation and high level of re-
producibility provide a rationale for the application of this method (Lukaski
1999).
The use of electricity in medicine began with the discovery that electri-
cal sparks stimulated muscle contraction. This finding prompted investigators
to examine other biological responses to administered electrical current. Al-
though electricity was originally portrayed as a potential therapeutic method,
the measurement of body impedance was subsequently proposed as a use-
ful diagnostic indicator for the physician (King 1970). This hypothesis led
to the identification of physical maladies depicted as low impedance illnesses
and other conditions characterized as high impedance conditions (King 1970),
and has since been advanced to the detection of differing stages of cancerous
growth.
BIA is based upon the relationship between the volume of the conductor
(i.e. the human body or part there of), the conducting length, the compo-
nents of the conductor (e.g., fat or fat free mass, cellular composition) and
4 CHAPTER 1. INTRODUCTION
its impedance (Z) (Azcue et al. (1993)). Impedance itself reflects frequency-
dependent opposition to the flow of an alternating current, and comprises
resistive (R) and reactive (Xc) components. This impedance is frequency de-
pendent and is defined by equation 1.1 (Ackmann and Seitz 1984).
Z =√
R2 + X2c (1.1)
Both R and Xc components are found in biological systems, although Xc
is usually very small relative to Z at lower frequencies, <4 % (Baumgartner
1996).
It is recognized that the measurement of biological impedance is influenced
by other factors that should either be controlled or reported (Lukaski 1999).
The electrode configuration such as bipolar or tetrapolar is one important
factor (Lukaski 1993, Patterson et al., 1988, Ross et al., 1990).
Electrical conduction in biological systems is mainly ionic, and proportional
to fluid volume and the number of free electrolytic ions (Khaled et al., 1988).
It is also inversely proportional to temperature (Geddes and Baker 1989). This
infers that the bioelectrical resistance is affected by changes in body geometry,
volume, temperature, and electrolytic concentration, and these effects should
be taken into consideration (Geddes and Baker 1989, Khaled et al., 1988).
Biological tissues are inhomogeneous and have quite a complicated struc-
ture containing cells of different shapes and sizes in an extracellular fluid which
behaves as a pure resistance. The cell membranes act as capacitors of about
10 µF cm−2 for muscle cells and about 1 µF cm−2 for other cells, while intra-
cellular fluid presents a resistance to the flow of the electrical current (Kanai
5
1992).
As stated previously, the electrical properties of tissue depend on frequency
and are normally divided into three regions of dispersion: α-dispersion occurs
at low frequencies and is mainly affected by the ionic environment surrounding
the cells; β-dispersion which is a structural relaxation in the frequency range 1
kHz -10 MHz; and at higher frequencies the γ-dispersion which is caused by the
relaxation of the water molecules (Pethig 1987). For many applications the
α- and β-dispersion regions are particularly interesting, since most changes
between normal and pathological tissue seem to appear in these frequency
ranges. Furthermore it is more practical to design a system dedicated to the
low frequency measurement of cancerous tissue (Blad and Baldetorp 1996).
1.2.2 Biological Tissue Equivalent Circuit
The frequency-dependent electrical behaviour of a cellular medium is deter-
mined by the resistivity of the intra-cellular space, the volume of surrounding
extra-cellular fluid, and the capacitance of the membrane (Cole and Cole 1941,
Fricke and Morse 1925, Schwan 1957). The dimensions, internal structure, ar-
rangements of the constituent cells and tissue composition will thus determine
the complex electrical impedance of tissue. This is the basis for the general
application of BIA to assessment of the physiologic ’state’ of organs, and the
cervix (Walker et al., 2000, Walker et al., 2001b).
Significant distinction between normal and precancerous tissue has been
obtained in terms of the low-frequency resistance R0, where R0 is equal to the
extracellular resistance RE , and the high-frequency resistance R∞
, where R∞
is
6 CHAPTER 1. INTRODUCTION
RE
CRI
Figure 1.1: Schematic of modelled tissue when constructed of its basic com-ponents.
the total resistance at infinite frequency. This may be seen by considering the
electrical analogue RRC circuit for tissue as shown in figure 1.1. Biologically
this is represented in figure 1.2, at low frequencies the current can not pass
through the cell membrane due to it having a high impedance and must flow
through the extracellular space. As the frequency increases the cell membrane
impedance decreases allowing the current to flow through the intracellular
space, hence decreasing the measured tissue impedance.
(a) (b)
Cell Membrane Extracellular Space Intracellular Space
Figure 1.2: (a) Current pathways at low frequencies. (b) Current pathways athigh frequencies.
The impedance spectrum gathered from multifrequency bioimpedance anal-
7
ysis (MFBIA) can be plotted as reactance against resistance. This impedance
spectrum or locus is known as a Cole-Cole plot (figure 1.3), and represents the
impedance of the tissue for frequencies from zero to infinity (Cole and Cole
1941). The impedance at a particular frequency can be represented on the plot
by the phase angle between the vector and the R axis and the magnitude of the
impedance, represented by the length of the vector. Values for RE (extracel-
lular resistance), RI (intracellular resistance) and C (membrane capacitance)
may be deduced from the locus of the Cole-Cole plot and analogous circuit.
R0 as determined from the Cole-Cole plot is equal to the extracellular
resistance RE; and the resistance at infinite frequencies, R∞
, is the parallel
addition of RE and RI as given by equation 1.2.
R∞
=RIRE
RI + RE
(1.2)
IncreasingFrequency
Z
PhaseAngle
R∞
Ro
φ
Impedance atCharacteristic Frequency
Resistance (Ω)
-Reacta
nce
(Ω)
Figure 1.3: Impedance spectrum for modelled tissue when constructed of itsbasic components.
The Cole-Cole plot shown in figure 1.3 is more accurately represented by
equation 1.3 as given by Schwan and Kay (1957). This equation describes the
8 CHAPTER 1. INTRODUCTION
physical measurements of biological tissue which result in a depression of the
centre of the Cole-Cole semi-circle as shown in figure 1.4, where the centre is
not on the real axis. This depression is a result of varying cell size, structure
and type causing it to be an imperfect capacitor and to have a distribution of
time constants (Cole 1968, Fricke 1932, Schwan 1957).
Zf = R∞
+R0 − R
∞
1 + jωτ 1−α(1.3)
α(π/2)
R∞
Ro
Resistance (Ω)
-Reacta
nce
(Ω)
Figure 1.4: Impedance spectrum for biological tissue with a depressed semi-circle.
At low frequencies, the capacitive cell membranes have high impedance,
and current in cervical tissue is confined to the narrow extracellular pathways
of the highly structured epithelium. This results in a high electrical resistance
(Brown et al., 2000a, Walker et al., 2000). However, in pathological tissue,
these pathways are significantly wider (White and Gohari 1984). In addition,
the reduction in cell volume reduces the most difficult pathways around the
highly flattened cells present in normal epithelium and increases the extracel-
lular space. The expected effect of these changes is a large reduction in low
9
frequency impedance and this suggests that electrical impedance techniques
may provide a method of distinguishing between normal and abnormal cervi-
cal tissue structure (Brown et al., 2000a, Walker et al., 2000).
1.2.3 Applications of BIA to Tissue Characterisation
Cancerous Tissues
Cancer cells in culture show an increased nucleus-to-cytoplasm ratio charac-
terized by increased nuclear size, enlarged nucleoli, and irregular chromatin
distribution (Anderson et al. (1992), Assenheimer et al. (2001) , Blad (1998),
Gonzlez-Correa et al., 1999, Keshtkar et al., 2001, Raymond et al., 2001). In
situations concerning the cervix, cancerous cells appear to be more rounded in
overall shape in contrast to non-cancerous cells, which are flattened along the
growth surface and present a highly structured brick like pattern (Raymond et
al., 2001, Walker et al., 2001a). Figure 1.5 displays the rounded appearance of
cancerous cells that is linked to changes in the structural organisation of actin
polymers (Colgan et al., 2001, Raymond et al., 2001).
Initial clinical trials on an electrical impedance method of diagnosis for
cervical neoplasia have already been undertaken in Sheffield (Brown et al.,
2000a) and by Quek et al. (1998). However Quek also makes use of optical
spectroscope along with bioimpedance. The results of Brown et al. (2000a)
reported clear colposcopy results and good impedance data for 756 measure-
ments made on 124 women. From the data 236 measurements were rejected
due to the tissue not clearly being identified by biopsy or by colposcopy, or
on technical grounds. From comparison of colposcopic and histological results,
10 CHAPTER 1. INTRODUCTION
Figure 1.5: Changes in tissue structure associated with the progression of CINin cervical squamous epithelium (Walker et al., 2000).
there were 370 measurements from normal squamous epithelium, one from an
invasive cancer, 126 from CIN2/3 (high grade), 63 from CIN1 (low grade),
64 classified as mature metaplasia, 98 classified as immature metaplasia, and
34 classified as columnar tissue. The results demonstrated that BIA provided
significant distinction between normal and precancerous tissue (Brown et al.,
2000a, Mould et al., 1997).
The clinical trials of Brown et al. (2000a) used a tetrapolar configuration
but did not indicate any research conducted towards determining whether
this was the optimum electrode configuration for sampling the required tissue
volumes, even though correct electrode configuration is vital for application
of BIA. The tetrapolar probe utilised by Brown et al. (2000a) provided a
check on small samples of tissue and hence did not provide a impedance map
of an ‘area’ of the cervical tissue. The probe was required to be moved if
additional sampling was required. Quek et al. (1998), although utilising a
different electrode configuration, also only used a single point measurement
11
system and again the probe was required to be moved to sample additional
areas of the tissue surface.
Wound Mapping
Although developed for a different purpose, a method for monitoring the heal-
ing process of wounds involves a similar concept to that of the current research.
The method was introduced by McCullough et al. (2004) at the XII Interna-
tional Conference On Electrical Bioimpedance & V Electrical Impedance To-
mography. A tripolar electrode configuration implemented into a bandage and
applied to the wound was proposed, with one of the drive electrodes placed onto
the back during measurement. This allowed for the wound to be monitored
over time without the need for the bandage to be removed for examination.
No clinical or experimental data has been presented or published to date.
Breast Cancer
The T-SCAN developed by Assenheimer et al. (2001), and currently approved
by the Food and Drug Administration (FDA), produces two-dimensional maps
of breast tissue impedance via the detection of electrical currents at the surface
of the breast tissue. The T-SCAN injects a current between the patients
breast of interest and arm. Changes in tissue impedance are detected via
the use of an electrode array applied to the breast. These measured changes
are a result of bulk spatial inhomogeneities and may be used to discriminate
between various pathological states. The publication does not state the spatial
resolution required for the early detection of breast lesions.
12 CHAPTER 1. INTRODUCTION
1.2.4 Tetrapolar Electrode Configuration
The tetrapolar electrode configuration has been accepted as one standard in
virtual biopsy, which is the use of bioimpedance in tissue characterisation.
The tetrapolar surface electrode configuration, consists of two drive electrodes
between which is injected a current, and two measurement electrodes that
record the potential (see Figure 1.6). The ratio of the measured potential to
the amplitude of the imposed current is used to determine the tissue impedance
(Brown et al., 2000).
Drive Electrodes
Measurement Electrodes
Figure 1.6: Tetrapolar arrangement used for taking of bioelectrical impedancemeasurements.
Different electrode configurations have been utilised, for example a tripolar
configuration (McCullough et al., 2004). However the tetrapolar configuration
is that most commonly used. Major advantages of the tetrapolar configuration
are the significant reduction in electrode artefacts (Ragheb et al., 1992), and
that the effect of electrode impedance is removed (Gersing 2001). However
the tetrapolar configuration has a complex pattern of sensitivity within the
13
conductor volume, an important consideration in virtual biopsy since it is
important to know which volume of tissue is being sampled
The relatively few reports of the application of BIA to virtual biopsy have
noted the importance of electrode configuration but have not investigated what
volumes of tissue are being measured. This study will investigate this essen-
tial part of virtual biopsy by means of finite element analysis to model the
tetrapolar configuration.
1.3 Finite Element Analysis (FEA)
Although FEA has a relatively long history in such disciplines as structural
mechanics (Akin 1986, Kardestuncer and Norrie 1987, Holland 1974, Strang
and Fix 1973), its application to field problems in physiology is very recent
(Miller and Henriquez 1990, Pavlin et al., 2001, Radai et al., 1999). The 1982
review article by Heringa et al. (1982) discussed only three methods of solution
for bioelectrical field problems, one of which was the finite element method.
One of the first papers reporting application of FEA to modelling of electrical
characteristics of tissue with reference to virtual biopsy was by Kanai (1992),
with work on frequency characteristics of electrical properties of living tissue
and its clinical applications.
Walker et al. (2000) have used the FEA technique to construct models of
the different cells that occupy multiple layers in normal or cancerous epithelium
of the cervix. A cross-section of a modelled single cell used by Walker et al.
(2000) is shown in Figure 1.7. The cells dimensions were assigned from the
14 CHAPTER 1. INTRODUCTION
values given by (Friedrich and Morse, 1925), and electrical properties based
on conductivities and capacitance quoted by Irimajiri et al., (1978) and Pethig
(1984). These properties are shown in Tables 1.1 and 1.2 respectively.
CytoplasmExtracellular
Space
Nucleus
(a) (b)
40mm
40mm
Electrodes
Stroma (5mm)
Basement
Membrane (100nm)
Epithelial
Layer (0.3mm)
Figure 1.7: (a) Cross section of finite element model of single cell. (b) Finiteelement tissue model (Walker et al., 2000, 2001a, 2001b)
In the studies of Walker et al. the models suggested that current flow
was confined to the epithelium. However these results did not identify which
volumes of tissue produced the majority of the impedance spectrum detected.
There is an apparent need to investigate these volumes such that the tissues
sampled are those of importance to the biopsy required.
Table 1.1: Cell dimensions in µm used in models of normal tissue (Walker etal., 2000).
15
Table 1.2: Electrical properties used in cell models (Walker et al., 2000).
1.4 Aims and Objectives
The overall objective of this research was to design and construct an impedance
mapping system (IMS) for objective virtual biopsy of lesions by bioimpedance
spectroscopy (BIS). Initially freshly excised cervical tissue was to be tested
however as the study progressed this proved problematic and bovine blood
was chosen as a suitable substitute.
Specific aims were to; Investigate the spatial sensitivity distribution of the tetrapolar electrode
configuration via finite element analysis (FEA). Design a novel front end multiplexing system and multi-electrode array
for mapping the impedance of the tissue of interest. Experimentally confirm the efficacy of the approach to identify regions of
different impedances and their boundaries using bioimpedance mapping.
16 CHAPTER 1. INTRODUCTION
Chapter 2
Modelling of Sensitivity
Distributions
2.1 Introduction
The tetrapolar electrode configuration is commonly used for tissue characteri-
sation by bioimpedance and involves injecting a constant drive current between
an adjacent pair of electrodes (drive electrodes), and measurement of the re-
sulting potential between another pair of adjacent electrodes (measurement
electrodes). This measured potential is dependent on the electrical charac-
teristics of the volume of tissue under investigation. This study looks at how
various volumes of tissue and their location with respect to the electrodes affect
the resulting measurement.
Finite element analysis (FEA) was used to model the sensitivity of the
tetrapolar electrode configuration with an emphasis on the sensitivity for de-
17
18 CHAPTER 2. MODELLING OF SENSITIVITY DISTRIBUTIONS
tecting a cancerous lesion on the surface of healthy cervical tissue. The elec-
trodes were modelled in contact with the surface of the tissue. It was found that
the sensitivity varied with differing lesion locations, and when modelled with
the lesion located between a drive and measurement electrode pair, anomalous
results were obtained. The existence of the anomaly was confirmed experi-
mentally.
Sensitivity Fields for the tetrapolar configuration were also modelled in 3
dimensions using the approach as described by Grimnes and Martinsen (2006).
The model confirmed the existence of the anomaly and provided additional in-
sight into current density and sensitivity as a function of depth for the tetrap-
olar configuration.
2.2 Lesion Modelling
2.2.1 Methodology
FEA
The FEA method had been previously validated during research undertaken as
part of the Bachelor of Applied Science Honours degree. The tetrapolar elec-
trode configuration was modelled on physical dimensions that are achievable
when constructing probes (Brown et al, 2000). Electrodes were modelled as 1
mm in diameter and separated by 0.2 mm as shown in figure 2.1. Electrodes
were given ideal electrical properties of zero resistivity and contact impedance
with the modelled tissue. As the interest of this study was the volume of tis-
19
sue on and just below the surface, the lesion was modelled as a hemisphere
located immediately below the surface of healthy tissue. Two arrangements
were modelled; (a) with a lesion central to the electrode configuration and
(b) with the lesion situated between a drive and measurement electrode. This
latter arrangement is shown in figure 2.1.
Tissues were assigned mean electrical properties as described in Brown et
al, 2000 (Table 2.1) and applied by equation 2.1 (Schwan and Kay 1957).
Where R0 = RE and R∞
and Fc were calculated by equations 1.2 and 2.2
respectively. In this equation Fc is the characteristic frequency and defined
as the frequency where the reactance is greatest. The frequency of the drive
current is F and for the purpose of this study α (figure 1.4) was given the value
of zero since the cell membrane was modelled as a perfect capacitor.
Z = R∞
+(R0 − R
∞)
(1 + [jF/Fc])1−α(2.1)
Fc =1
2πC(RE + RI)(2.2)
Table 2.1: Tissue electrical properties as given by Brown et al, 2000.
The lesion was modelled with various radii from 0 mm (no lesion present,
only healthy tissue) to 1.05 mm. For the lesion modelled central to the elec-
trodes a direct current (DC) was injected and the potential between mea-
surement electrodes calculated. For the lesion located between a drive and
20 CHAPTER 2. MODELLING OF SENSITIVITY DISTRIBUTIONS
Drive
Electrodes
Measurement
Electrodes
Lesion
mm
mm
(a)
(b)
Figure 2.1: (a) Tetrapolar electrode model with the lesion located betweena drive and measurement electrode. (b) 3D view showing the lesion locatedimmediately below the surface of healthy tissue.
21
measurement electrode, the modelling was expanded to comprise a frequency
spectrum of 600, 1200, 2400, 4800, 9600, 19200, 38400, 76800, 153600, 307200
and 614400 Hz and the real part of the potential between measurement elec-
trodes determined. The magnitude of the drive current was kept constant
throughout.
Experimental Verification
Experimental verification of the modelled tetrapolar electrode configuration
was difficult due to the small size of the electrodes and lesion. For this reason
the electrode size was altered but the same tetrapolar configuration main-
tained. The experimental verification was performed for the case of a lesion
located (a) central to the electrodes and (b) between a measurement and drive
electrode i.e. where the modelling indicated an anomalous result for the mea-
sured impedance. The experimental setup is shown in figure 2.2.
50 mm
50
mm rDrive Electrodes
(Luer needles)
Measurement Electrodes
(Luer needles)
(a) (b)
Figure 2.2: Experimental electrode placement on the surface of a saline solutionand brass rod with radius ’r’ located (a) central to the electrodes (b) betweena drive and measurement electrode.
The electrodes (16 G (1.2 mm) Luer needles) were separated by 50 mm (in a
50 mm square) and held in place with a non-conducting epoxy. The electrode
22 CHAPTER 2. MODELLING OF SENSITIVITY DISTRIBUTIONS
configuration was then placed on the surface of a saline solution with the
needles penetrating 4 mm into the solution. The saline solution represented
a large medium of healthy tissue. Brass rods of various diameters were used
to represent lesions of lower resistance compared to healthy tissue (saline).
The rods were 30 mm in length and varied in radius from 2.5 mm to 22.5
mm. They were placed upright in the saline solution just below the surface. A
SEAC SFB3 body composition meter was used to supply a constant current
at frequencies of 10, 15, 20, 25, 35, 55, 65, 80, 120 and 310 kHz between the
drive electrodes and the potential between measurement electrodes recorded
when each rod was positioned as indicated above.
The experimental setup was also modelled using the FEA method. The
model included dimensions as described above in the experimental setup and
the conductive mediums were given electrical properties of saline and brass.
2.2.2 Results
FEA
All potentials were normalized against the potential measured for homogeneous
healthy tissue at DC (0 Hz). For a lesion located central to the electrodes the
potential decreased as the radius of the lesion with lower impedance increased
(figure 2.3). However for a lesion located between a drive and measurement
electrode the results (figures 2.4 & 2.5) clearly demonstrate a rise in measured
potential (particularly at the lower frequencies) as the lesion increased in radius
up to approximately 0.4 mm followed by a decrease in potential. Shown in
figure 2.6 is the potential versus frequency for (a) healthy tissue and (b) healthy
23
tissue with a lesion 0.75 mm in radius located between a drive and measurement
electrode.
The detection of precancerous changes using BIA relies upon detecting the
reduced impedance of these changes at low frequencies compared with that
of healthy tissue. The expected effect was noticed when a region of lower
impedance was introduced into the centre of the tetrapolar electrode configu-
ration. The results of the FEA modelling displayed in figure 2.3 show that a
lesion of 0.4 mm radius reduced the measured impedance by 30 % and a 0.8
mm lesion would approach an impedance measured for a lesion alone. How-
ever an increase in measured potential was noted in the modelled results with
the introduction of a region of lower impedance midway between a drive and
measurement electrode. In the modelled results (figure 2.4) the increase at DC
was a maximum for a lesion of radius 0.4 mm. For larger radii the impedance
decreased as expected but did not reach the impedance for a lesion alone until
a radius greater than 1.0 mm. This anomaly was absent in the case of a lower
impedance medium central to the electrodes. This anomaly could cause a pre-
cancerous lesion to be identified as healthy tissue as demonstrated in figure 2.6
where results with a relatively large lesion of 0.75 mm in radius situated be-
tween a drive and measurement electrode are similar to that of healthy tissue.
Experimental Results
All potentials for the experimental and modelled experimental results were
normalized against their respective potentials measured for the pure saline
24 CHAPTER 2. MODELLING OF SENSITIVITY DISTRIBUTIONS
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.4
0.5
0.6
0.7
0.8
0.9
1
1.1
Lesion Radius (mm)
Nor
mal
ised
Pot
entia
l
Figure 2.3: Modelled results of tetrapolar electrode configuration for a lesionlocated centrally in the electrode configuration.
solution. Results for a centrally located brass rod (representing a lesion) are
shown in figure 2.7. The measured potential is seen to decrease as the radius of
the rod increased in a similar manner to that indicated by the FEA modelling.
Again as predicted by the FEA modelling, the experimental results show an
initial rise in measured potential as the radius of the brass rod increased when
the rod was located between a drive and measurement electrode (figure 2.8).
Figure 2.8 also shows the results of FEA modelling of the experimental
electrode configuration. The position of the maximum potential is similar in
the experimental and modelled results. However the magnitude of the potential
is consistently less than the experimental results for both brass rod locations
(central to the electrodes and between a drive and measurement electrode).
The agreement between the modelled and experimental results in indicating
the position of the maximum provides confidence that the results of FEA
25
0 0.2 0.4 0.6 0.8 1 1.2 1.40
0.5
1
1.5
Lesion Radius (mm)
Nor
mal
ised
Pot
entia
l
00.61.22.44.89.619.238.476.8153.6307.2614.4
Figure 2.4: Modelled results of tetrapolar electrode configuration for a lesionlocated midway between a drive and measurement electrode (Legend displaysfrequency in kHz).
10−1
100
101
102
103
0
0.5
1
1.5
Frequency (kHz)
Nor
mal
ised
Pot
entia
l
0.000.050.150.250.350.450.550.650.750.850.951.05
Figure 2.5: Modelled results of tetrapolar electrode configuration for a lesionlocated midway between a drive and measurement electrode (Legend displayslesion radius in mm).
26 CHAPTER 2. MODELLING OF SENSITIVITY DISTRIBUTIONS
10−1
100
101
102
103
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
Frequency (kHz)
Nor
mal
ised
Pot
entia
l0.00 mm0.75 mm
Figure 2.6: Measurement with (a) no lesion and (b) a lesion of radius 0.75 mmin otherwise healthy tissue.
modelling are realistic.
0 5 10 15 200.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
Lesion Radius, mm
Nor
mal
ised
Pot
entia
l
ExperimentalModelled
Figure 2.7: Experimental and modelled results of the tetrapolar electrode con-figuration for a brass rod located centrally in the electrode configuration.
27
0 5 10 15 200.9
1
1.1
1.2
1.3
1.4
1.5
Lesion Radius, mm
Nor
mal
ised
Pot
entia
l
ExperimentalModelled
Figure 2.8: Experimental and modelled results of the tetrapolar electrode con-figuration for a brass rod located midway between a drive and measurementelectrode.
2.3 Sensitivity Fields
Sensitivity fields have been used to describe the tetrapolar configuration pre-
viously by Brown et al., 2000 and more recently by Grimnes and Martinsen,
2006. However in neither case were the electrodes modelled in a realistic square
configuration for tissue characterisation applications; Brown et al. modelled a
square tetrapolar electrode configuration using point electrodes and Grimnes
and Martinsen modelled using a line configuration. In the present study a real-
istic square electrode configuration was modelled. The geometry and electrode
properties were the same as previously described (see section 2.2.1) with the
exception that the electrodes had a diameter of 1 mm. The electrode spacing
was varied and the sensitivity determined as a function of depth into the test
medium.
28 CHAPTER 2. MODELLING OF SENSITIVITY DISTRIBUTIONS
The sensitivity of a volume of medium is a measure of how much this volume
contributes to the total measured impedance. Geselowitz (1971) showed that
the sensitivity, S, at a point within the model can be defined as the scalar
product of the vector current densities (equation 2.3). Here the current density
J1 at any point is found by injecting the current, I, between the drive electrodes.
J2 is the current density found by now injecting the same current between the
measurement electrodes.
S =J1 · J2
I2(2.3)
The resultant field can have volumes of positive and negative sensitivity. If
positive then a drop in measured impedance will result if a medium of lower
resistivity is located in this volume. Whereas a negative value would result
in an increase in measured impedance. The measured impedance will likewise
increase and decrease for positive and negative sensitivity values respectively
when a medium with a higher resistivity is introduced. The change in measured
impedance is also dependent on the magnitude of the sensitivity value.
2.3.1 3-D Sensitivity Field Model
Modelling used the same electrode dimensions as previously described (1 mm
diameter electrodes) with a larger conductive medium to reduce the effect of
confined current flow on the results. A confined current flow would distort the
current density as demonstrated in figure 2.9 resulting with incorrect sensitivity
fields. Sensitivity fields were also found for models with an electrode spacing of
0.4 mm, 0.6 mm, 0.8 mm and 1.0 mm to investigate the relationship between
29
electrode spacing and measurement depth. The injected current is between
the upper and lower left electrodes and has an amplitude of 1 A.
Figure 2.10 through to figure 2.15 display the sensitivity fields for a model
with an electrode spacing of 0.2 mm and for a depth of 0.0 (surface of the
conductive medium), 0.2, 0.4, 0.6, 0.8 and 1.0 mm. The electrode positions on
the surface are represented in the figures by black circles.
The fields show very localised areas of positive sensitivity between the drive
or measurement electrode pairs and more importantly negative sensitivity be-
tween drive and measurement electrode pairs. These areas of negative sen-
sitivity become significantly larger with increasing depth but the magnitude
decreases substantially (a factor greater than 10 at 0.2 mm depth). The area
of positive sensitivity (shown in red on figures 2.10 - 2.15) also increases in
size with depth but not to the same extent. The lack of sensitivity on the sur-
face central to the electrodes explains the relatively insensitive nature of the
measurement for small lesions (see figures 2.3 and 2.7). The lesion must be of
sufficient size to overlap regions of sensitivity deeper into the tissue and to the
sides before being detected. Negative fields between the drive and measure-
ment electrode pairs agree with the results obtained from modelling lesions and
experimental verification. This negative sensitivity field shows that a lesion of
lower resistance located here will result in an increase in measured impedance
(i.e. anomalous results).
The maximum of the sensitivity over the plane at each depth is plotted in
figure 2.16 and the sum of the absolute sensitivity in the plane in figure 2.17.
It can be seen that the maximum sensitivity decreases significantly at a depth
of 0.1 mm and is less than 10 % of the maximum at 0.2 mm. The sum of the
30 CHAPTER 2. MODELLING OF SENSITIVITY DISTRIBUTIONS
D
D
Figure 2.9: 3-D modelled tetrapolar configuration and current density confinedby the boundaries.
5 10 15 20 25 30 35 40 45 50 55 60
5
10
15
20
25
30
35
40
45
50
55
60
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
Figure 2.10: Sensitivity field at a depth of 0.0 mm.
31
5 10 15 20 25 30 35 40 45 50 55 60
5
10
15
20
25
30
35
40
45
50
55
60
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
Figure 2.11: Sensitivity field at a depth of 0.2 mm.
5 10 15 20 25 30 35 40 45 50 55 60
5
10
15
20
25
30
35
40
45
50
55
60
-6
-4
-2
0
2
4
6
x 10 -3
Figure 2.12: Sensitivity field at a depth of 0.4 mm.
32 CHAPTER 2. MODELLING OF SENSITIVITY DISTRIBUTIONS
5 10 15 20 25 30 35 40 45 50 55 60
5
10
15
20
25
30
35
40
45
50
55
60
-2.5
2-
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
x 10 -3
Figure 2.13: Sensitivity field at a depth of 0.6 mm.
5 10 15 20 25 30 35 40 45 50 55 60
5
10
15
20
25
30
35
40
45
50
55
60
-1
-0.5
0
0.5
1
x 10 -3
Figure 2.14: Sensitivity field at a depth of 0.8 mm.
33
5 10 15 20 25 30 35 40 45 50 55 60
5
10
15
20
25
30
35
40
45
50
55
60
-4
-2
0
2
4
6
x 10 -4
Figure 2.15: Sensitivity field at a depth of 1.0 mm.
absolute sensitivity over the planes with respect to depth approaches a value
less than 10 % of the original for depths greater than 0.4 mm.
Sensitivity fields have confirmed the existence of the anomaly (negative
sensitivity) within the tetrapolar electrode configuration and that it is confined
to the regions between drive and measurement electrode pairs. It can also be
seen that the sensitivity fields indicate that the measured impedance is limited
to the surface layers, predominantly to a depth of less than 0.4 mm, making
the tetrapolar configuration ideal for detection of surface lesion.
Grimnes and Martinsen (2006) note that equation 2.3 demonstrates the
reciprocal nature of the tetrapolar configuration. Under linear conditions (e.g.
same drive and measurement electrode size) the drive and measurement elec-
trode are interchangeable without a change in measured impedance. This is
also shown in the symmetrical nature of the sensitivity fields since the same
34 CHAPTER 2. MODELLING OF SENSITIVITY DISTRIBUTIONS
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Depth, mm
Sen
sitiv
ity
0.2 mm0.4 mm0.6 mm0.8 mm1.0 mm
Figure 2.16: Maximum sensitivity in each plane as a function of depth forelectrode spacing’s 0.2 mm, 0.4 mm, 0.6 mm, 0.8 mm and 1.0 mm.
sensitivity field is produced independent of which electrode pair (left or right)
are the drive electrodes.
Later in chapter 4 it will be shown that the anomaly produced by negative
sensitivity is present in the impedance maps and that it may be noted for
further analysis.
Electrode Spacing and Measurement Depth
To confirm the use of sensitivity as an indicator of measurement depth, the
tetrapolar configuration was again modelled with a range of electrode spacing’s
and the measurement medium thickness varied. Each electrode spacing was
modelled with a medium thickness of 0.2, 0.4, 0.6, 0.8 and 1.0 mm. The
35
0 0.2 0.4 0.6 0.8 10
2
4
6
8
10
12
14
Depth, mm
Sen
sitiv
ity
0.2 mm0.4 mm0.6 mm0.8 mm1.0 mm
Figure 2.17: Sum of the absolute sensitivity in each plane as a function ofdepth for electrode spacing’s 0.2 mm, 0.4 mm, 0.6 mm, 0.8 mm and 1.0 mm.
resulting potentials were normalised to one and are shown in figure 2.18.
It can be seen that with increasing medium thickness the measured po-
tential decreases until a medium thickness of 5 to 6 mm. This thickness is
significantly different to that given by the maximum or sum of the absolute
sensitivity (0.2 & 0.4 mm). It is later experimentally verified that the thick-
ness must be at least 4 to 5 mm thick so as not to distort the impedance
measurements (see section 4.1.2). This result suggests that sensitivity is not
a good indicator of measurement depth and should only be used for mapping
positive and negative sensitivity fields.
36 CHAPTER 2. MODELLING OF SENSITIVITY DISTRIBUTIONS
2 3 4 5 6 7 8 9 100
0.2
0.4
0.6
0.8
1
Tissue Thickness, mm
Nor
mal
ised
Pot
entia
l
0.2 mm0.4 mm0.6 mm0.8 mm1.0 mm
Figure 2.18: Measured potential against tissue medium thickness for differingelectrode spacings.
2.3.2 Electrode Array Sensitivity Fields
The 3 dimensional model was expanded to include surrounding inactive elec-
trodes as would be the case for the impedance mapping system (IMS) described
in chapter 4. The electrode spacing was also increased to 0.77 mm which is
representative of the spacing used in the instrumentation later developed. The
maximum and sum of the sensitivity in each plane for a range of depths was
found for each of the four unique electrode sites shown in figure 2.19. All of
the other electrode sites located on the array can be represented by one of the
four by rotation, reflection and taking into account the reciprocal nature of
the electrode configuration.
Figures 2.20 & 2.21 show that the maximum and sum of the absolute sen-
sitivity decrease to 10 % of the original value much deeper into the model (0.6
37
D
D
M
M
D
D
M
M
D D
MM
D
D
M
M
(1) (2)
(3) (4)
Figure 2.19: The four unique electrode sites modelled.
& 0.4 mm respectively) compared to the single tetrapolar electrode model (see
figures 2.16 & 2.17 for comparison). The maximum sensitivity has also de-
creased to 5 % of the original value modelled without the inactive electrodes.
This large decrease indicates that the inactive array is altering the current dis-
tribution, however the sensitivity fields produced (figure 2.22) still show strong
areas of positive and negative sensitivity directly below the active electrodes.
Each of the four unique electrode sites display similar plots for maximum
and sensitivity sum (figures 2.20 & 2.21). Indicating that impedance measure-
ments taken on a homogeneous medium will be similar whether taken with an
electrode set inside or on the border of the array.
38 CHAPTER 2. MODELLING OF SENSITIVITY DISTRIBUTIONS
0 0.2 0.4 0.6 0.8 10
0.002
0.004
0.006
0.008
0.01
0.012
Depth, mm
Sen
sitiv
ity
Location 1Location 2Location 3Location 4
Figure 2.20: Maximum sensitivity in each plane as a function of depth forelectrode sites 1, 2, 3 and 4 (see figure 2.19).
Electrode Array Measurement Depth
The effect of inactive electrodes on measurement depth was modelled using site
1 (figure 2.19) and an electrode spacing of 0.77 mm which is the experimental
electrode spacing. The medium was increased in thickness from 0.2 mm to
1.0 mm and the results are shown in figure 2.23. The results for a single
tetrapolar electrode configuration of electrode spacing 0.77 mm are also shown
in figure 2.23.
With a small medium thickness the results for the single electrode config-
uration and the array are identical, with the array plot overlaying the plot
for a single electrode. This result shows that the array of inactive electrodes
has little effect on the resultant measurement depth as previously indicated by
the plots of maximum sensitivity and sum of absolute sensitivity (figures 2.16,
39
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
1.2
1.4
Depth, mm
Sen
sitiv
ity
Location 1Location 2Location 3Location 4
Figure 2.21: Sum of the absolute sensitivity in each plane as a function ofdepth for electrode sites 1, 2, 3 and 4(see figure 2.19). Locations 1 and 3 aredifficult to see due to overlap.
5 10 15 20 25 30 35 40 45 50 55 60
5
10
15
20
25
30
35
40
45
50
55
60
14
12
10
8
6
4
2
0
2
D
D M
M
x 10-3
Figure 2.22: Sensitivity field at a depth of 0.1 mm for electrode site 1 shownin figure 2.19.
40 CHAPTER 2. MODELLING OF SENSITIVITY DISTRIBUTIONS
0 2 4 6 8 100.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
Thickness, mm
Nor
mal
ised
Pot
entia
l
Single Electrode ConfigurationArray
Figure 2.23: Measurement thickness for an array with 0.77 mm electrode spac-ing and a single electrode configuration with the same spacing.
2.17, 2.20 & 2.21). Figure 2.23 also shows that the measurement depth is much
greater than that indicated by the plot of sensitivity against depth. Once again
confirming that sensitivity is not appropriate as an indicator of measurement
depth.
Effect Of Inactive Electrodes Inside The Tetrapolar Configuration
The tetrapolar electrode configuration was modelled as an array with inactive
electrodes within the active set to determine if the inactive electrodes would
affect measurements of a larger surface area. Figure 2.24 displays the resultant
field at a depth of 0.1 mm.
It can be seen that the inactive electrodes between the drive and measure-
41
5 10 15 20 25 30 35 40 45 50 55 60
5
10
15
20
25
30
35
40
45
50
55
60
6
4
2
0
2
4
6
8
10
x 10 -4
D
D M
M
Figure 2.24: Sensitivity field at a depth of 0.1 mm for a tetrapolar electrodeconfiguration with inactive electrode inside the configuration.
ment electrodes result in an area of larger negative sensitivity underneath their
location (this may not be clear in the hard copy, please refer to the electronic
copy provided on the CD). Any measurements made with inactive electrodes
within the active set would therefore be affected and could produce misleading
results similar to the anomaly previously found. This is due to the inactive
electrodes being located in regions of negative sensitivity.
However large surface area measurements such as this are not necessary for
the proposed impedance mapping system. If high imaging resolution of the
surface tissue is to be achieved then the electrode spacing must be as small as
42 CHAPTER 2. MODELLING OF SENSITIVITY DISTRIBUTIONS
possible. Allowing smaller surface areas to be analysed and lesion boundaries
more accurately identified.
Chapter 3
Impedance Mapping System
Overview, Operation and
Testing
Tissue characterisation by bioimpedance analysis has to date been single point,
where a large tissue sample was analysed at a single point and no attempt was
made to identify the boundaries of any lesion. Sampling of a single point also
means that precancerous changes might not be detected if the point chosen for
sampling was healthy tissue and other areas were indeed precancerous. This
study aims to reduce the possibility of not detecting areas of precancerous
change by identifying boundaries of any change detected by means of develop-
ing a novel impedance mapping system (IMS) to sample a large area of tissue.
The IMS will make use of the tetrapolar electrode configuration in a repeated
array allowing measurements to be taken over the surface of a tissue sample.
BIA of individual measurement locations can then be visually displayed and
43
44CHAPTER 3. IMPEDANCE MAPPING SYSTEM OVERVIEW,
OPERATION AND TESTING
boundaries of a suspected lesion identified. This approach of display will also
allow for easy identification of anomalous results which, as discussed in chapter
2, can result if a lesion is located between a drive and measurement electrode.
The IMS developed for this study is shown schematically in figure 3.1. The
current source and potential measurements are switched through multiplexers
which allow them to be directed to any electrode on the array. A PC based
program was written in Visual Basic (VB) to switch the multiplexers and
complete all data analysis through Matlab for the visual display. An array
consisting of 25 electrodes allows 16 measurement sites over the surface of a
medium and 4 tetrapolar measurements at each site. This provides a total of
64 measurements on the area of medium covered by the array.
PC
SFB7 Multiplexers Electrode Array
Figure 3.1: Schematic of the bioimpedance mapping system.
45
3.1 Current Source & Potential Measurement
An Imp SFB7 from Impedimed (www.impedimed.com) was used as the current
source and for potential measurement. The SFB7 is a single channel, tetra po-
lar bioimpedance spectroscopy (BIS) device with 265 frequencies in the range
of 4 kHz to 1000 kHz. The SFB7 has an impedance accuracy of +/- 1.0% in
the range 50 to 1100 Ω and allows access to the full raw data of resistance and
reactance.
3.2 Multiplexers
Current and potential probes from the SFB7 were directed to the appropriate
electrode in the array via 32-channel ADG732 (figure 3.2) multiplexers from
Analog Devices. The ADG732 was chosen as they have a low ‘on’ resistance
(Ron) of 4 Ω through each channel. The Ron resistance can be considered
negligible since when in series with the source probes a constant current is
always driven. Ron is also negligible with the potential probes since they draw
no current and this results in no change to the measured potential.
Multiplexer switching is by 5-bit binary parallel inputs and switching may
be enabled or disabled (switching locked) with the addition of another input.
The parallel inputs and disable function make them ideal for control with a
parallel port found on any desktop personal computer. Figure 3.3 shows the
multiplexer circuit diagram with parallel port (Header 9) and electrode array
socket (Header 25). Pins Red and Black are SFB7 current source connections
and pins White and Blue are SFB7 potential measurement connections.
46CHAPTER 3. IMPEDANCE MAPPING SYSTEM OVERVIEW,
OPERATION AND TESTING
Figure 3.2: Functional block diagram and pin configuration of multiplexerADG732.
3.3 Electrode Array
The electrode array consisted of 25, 1 mm diameter electrodes separated by
0.77 mm in a 5x5 square as shown in figure 3.4. The use of 25 electrodes instead
of 32, which is the total available multiplexer channels, allowed for the array
to be constructed on a single sided printed circuit board (PCB). The use of a
larger array would require a double sided PCB and further difficulties coupling
with the multiplexers. FEA modelling showed that the measurable depth was
independent of electrode spacing, so the electrodes were positioned as close as
possible to increase the imaging resolution. A PCB edge connector (Header
25, figure 3.3) allows easy removal of the electrodes from the multiplexers.
Using a PCB made manufacturing the electrode arrays cheap and disposable
for single use or if needed they could be autoclaved and sterilised for repeated
uses, which was the original intent.
Measurements were made using the tetrapolar configuration with 4 mea-
47
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
D D
C C
B B
A A
Title
Number RevisionSize
A3
Date: 7/07/2007 Sheet of
File: F:\Latex\Thesis exers4x.SCHDOC Drawn By:
+5 +5
+5
+5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Header 25
pin3
pin4
pin5
pin6
pin7
pin8
pin9
pin1
0
pin1
1
pin1
2
pin1
3
pin1
4
pin1
5
pin1
6
pin1
7
pin18
pin1
pin2
pin3
pin4
pin5
pin6
pin7
pin8
pin9
pin10
pin11
pin12
pin13
pin14
pin15
pin16
pin17
pin18
pin19
pin20
pin21
pin22
pin23
pin24
pin25 pin1
pin2
pin3
pin4
pin5
pin6
pin7
pin8
pin9
pin1
0
pin1
1
pin1
2
pin1
3
pin1
4
pin1
5
pin1
6
pin17
pin18
pin19
pin20
pin21
pin22
pin23
pin24
pin25
pin1
pin2
pin3
pin4
pin5
pin6
pin7
pin8
pin9
pin1
0
pin1
1
pin1
2
pin1
3
pin1
4
pin1
5
pin1
6
pin1
7
pin1
8
pin1
9
pin2
0
pin2
1
pin2
2
pin2
3
pin2
4
pin2
5
pin1
pin2
pin19
pin20
pin21
pin22
pin23
pin24
pin25
pin1
pin2
pin3
pin4
pin5
pin6
pin7
pin8
pin9
pin1
0
pin1
1
pin1
2
pin1
3
pin1
4
pin1
5
pin1
6
pin1
7
pin18
pin19
pin20
pin21
pin22
pin23
pin24
pin25
11
22
33
44
55
66
77
88
99
1010
1111
1212
1313
1414
IN1
15
IN2
16
IN3
17
IN4
18
IN5
19
IN6
20
WRb
ar21
ENba
r22
GND
23
Vss
24
NC25
NC26
NC27
NC28
NC29
NC30
NC31
3232
3333
3434
3535
3636
3737
3838
3939
4040
NC41
NC42
D43
NC44
4545
4646
4747
4848
Multiplexer - ADG732
Top_Driver
Multiplexer
11
22
33
44
55
66
77
88
99
1010
1111
1212
1313
1414
IN1
15
IN2
16
IN3
17
IN4
18
IN5
19
IN6
20
WRb
ar21
ENba
r22
GND
23
Vss
24
NC25
NC26
NC27
NC28
NC29
NC30
NC31
3232
3333
3434
3535
3636
3737
3838
3939
4040
NC41
NC42
D43
NC44
4545
4646
4747
4848
Multiplexer - ADG732
Under_Driver
Multiplexer
11
22
33
44
55
66
77
88
99
1010
1111
1212
1313
1414
IN1
15
IN2
16
IN3
17
IN4
18
IN5
19
IN6
20
WRb
ar21
ENba
r22
GND
23
Vss
24
NC25
NC26
NC27
NC28
NC29
NC30
NC31
3232
3333
3434
3535
3636
3737
3838
3939
4040
NC41
NC42
D43
NC44
4545
4646
4747
4848
Multiplexer - ADG732
Top_Potential
Multiplexer
11
22
33
44
55
66
77
88
99
1010
1111
1212
1313
1414
IN1
15
IN2
16
IN3
17
IN4
18
IN5
19
IN6
20
WRb
ar21
ENba
r22
GND
23
Vss
24
NC25
NC26
NC27
NC28
NC29
NC30
NC31
3232
3333
3434
3535
3636
3737
3838
3939
4040
NC41
NC42
D43
NC44
4545
4646
4747
4848
Multiplexer - ADG732
Under_Potential
Multiplexer
Blac
k
Red W
hite
Blue
dn3
dn4
dn5
dn6
dn7
dn8
dn9
dn3
dn4
dn5
dn6
dn7
cn1
cn2
cn1
cn2
0.1uF
C190.1uF
C18
0.1uF
C17
0.1uF
C16
1 2 3 4 5 6 7 8 9
Header 9
dn3
dn4
dn5
dn6
dn7
dn8
dn9
dn3
dn4
dn5
dn6
dn7
dn3
dn4
dn5
dn6
dn7
Figu
re3.3:
Multip
lexer
circuit
diagram
.Parallel
port
represen
tedby
Head
er9
and
electrode
arrayso
cketby
Head
er25.
SFB
7drive
and
measu
remen
telectro
des
connect
throu
ghred
,black
and
white,
blu
eresp
ectively.
48CHAPTER 3. IMPEDANCE MAPPING SYSTEM OVERVIEW,
OPERATION AND TESTING
Electrodes
Figure 3.4: PCB electrode array.
P2 C2
P1 C1
P1 P2
C1 C2
C1 P1
C2 P2
C2 C1
P2 P1
(1) (2)
(3) (4)
Figure 3.5: Electrode stepping sequence from 1 to 4; C1, C2 represent currentsource and P1, P2 potential measurement.
49
surements being made for each measurement site on the surface of the test
medium. As shown in figure 3.5 measurements were made by switching the
current and potential electrodes such that the tetrapolar configuration was
effectively rotated by 90o for each successive measurement. The tetrapolar
configuration was then shifted to the right by one column and another 4 mea-
surements taken. This was repeated for all columns and moved down one row
at a time and repeated. This gives a total of 64 separate measurements to
be taken at 16 different locations and an impedance map of 49 mm2 on the
surface of a test medium.
3.4 Impedance Data Analysis
Measurements were made via stepping through the electrode array sequence
as detailed previously and values for resistance and reactance were taken with
the SFB7 and imported to Matlab. A circular locus of best fit to reactance
versus resistance was determine by applying equation 3.1.
R2 + X2− aR − bX + c = 0 (3.1)
R2+X2 can be substituted for Z2 and equation 3.2 solved by multiple re-
gression (Cornish, 1994).
Z2 = aR + bX − c (3.2)
Values a, b and c describe the circle of best fit (equation 3.3 and equa-
tion 3.4) and were used to determine the cole parameters R0 and R∞
by equa-
50CHAPTER 3. IMPEDANCE MAPPING SYSTEM OVERVIEW,
OPERATION AND TESTING
tion 3.5 and equation 3.6.
centre = (a
2,b
2) (3.3)
radius =
√
a2
2+
b2
2− c (3.4)
R0 =a
2−
√
radius2− (
b
2)2 (3.5)
R∞
=a
2+
√
radius2− (
b
2)2 (3.6)
3.5 Impedance Mapping System Graphical Use
Interface and Operation
The IMS graphical user interface (GUI) shown in figure 3.6 was developed
as part of this study in Visual Basic to control the multiplexer front end
stepping sequence. The GUI was also used as a visual display for the impedance
measurements and mapping of the 16 regions on the surface of the medium
measured. ‘Gather’ starts the mapping process and multiplexers switching.
The array of 25 squares represent the electrode array and change colours to
indicate where the electrode stepping sequence is currently present. Red and
black represent drive electrodes and white and blue measurement electrodes.
When this sequence is finished the ’Data Analysis’ button starts the Matlab
analysis of the raw resistance and reactance data. The 64 R0 values calculated
in Matlab are imported into the GUI and displayed in 4 smaller impedance
51
maps, representing each of the tetrapolar electrode orientations as shown in
figure 3.5. The maps electrode orientation is indicated by red, white, blue
and black squares above each map. The four electrode orientation maps are
averaged to present the larger impedance map. Figure 3.7 shows a flow chart
that more simply presents the IMS GUI operational sequence. The attached
CD contains a copy of the IMS program with a set of real data which is later
displayed in figure 4.7.
Impedance maps may also be displayed for R∞
and capacitance of the test
medium. This feature can be expanded to present any of the Cole or user
defined parameters.
The colour bar legend is scaled for each impedance map so that the range
is always from the smallest to largest R0 (or user defined parameter) value.
Scaling in this manner will insure that the greatest colour contrast possible is
presented in the map.
3.6 Impedance Mapping System Testing
3.6.1 Testing of Multiplexer Ron Contribution
The 32 channel ADG732 multiplexers were chosen due to their low resistance
(Ron) when a channel was in use. Theoretically this resistance should play
no part in measurements due to the resistance being in series with the drive
electrodes which pass a constant current and in series with the measurement
electrodes which draw no current. To test this hypothesis short circuited mea-
52CHAPTER 3. IMPEDANCE MAPPING SYSTEM OVERVIEW,
OPERATION AND TESTING
Figure 3.6: Impedance mapping system graphical user interface. Displayed isa typical impedance map.
surements (no impedance load used) were made in the frequency range 4 kHz to
1000 kHz with and without the multiplexer front end. Measurements without
and with the multiplexers and are presented in figures 3.8 and 3.9 respectively.
53
Open Impedance Mapping System
Start data collecting sequence
Switch SFB7 electrodes via
multiplexers to next tetrapolar set
SFB7 Impedance measurement
Rotate electrode orientation by 90o
Are all
electrode orientations
complete?
Are all
tetrapolar sets
complete?
Export raw impedance data to Matlab
Perform data analysis and
R0 calculations
Import R0 values to IMS program
Scale map ledgend for greatest
image contrast
Display impedance maps
No
Yes
Yes
No
Figure 3.7: Flow chart of the IMS operational sequence.
54CHAPTER 3. IMPEDANCE MAPPING SYSTEM OVERVIEW,
OPERATION AND TESTING
−1.5 −1 −0.5 0 0.5 1 1.5 2 2.5
−2
−1.5
−1
−0.5
0
0.5
Resistance Ohms
− R
eact
ance
Ohm
s
Figure 3.8: Measurement made with short circuited electrodes and no multi-plexer front end.
An analysis of variance (ANOVA) was performed on the data gathered for
resistance and reactance components to determine if a significant difference
was measured with and without the multiplexer front end. For analysis of
resistance the F statistic was 1.10, with a p-value of 0.30. Since this is greater
than 0.05 (or equivalently the observed F statistic is smaller than its critical
value of 3.86) it can be concluded that there is no significant difference between
the measured resistance with and without the multiplexers.
Analysis of the reactance produced a F statistic of 5.57, with a p-value
of 0.02. Since this is less than 0.05 (or equivalently the observed F statistic
is greater than its critical value of 3.86) it can be concluded that there is a
55
significant difference between the measured reactance with and without the
multiplexers.
−2 −1 0 1 2 3
−3.5
−3
−2.5
−2
−1.5
−1
−0.5
0
0.5
Resistance Ohms
− R
eact
ance
Ohm
s
Figure 3.9: Measurement made with short circuited electrodes through multi-plexer front end.
The result of no significant difference with resistance demonstrates the mul-
tiplexers Ron does not alter the resistive measurements. However significant
difference was found between the reactance values. This difference is due to
the close proximity of the multiplexers to each other and the electrode paths
taken on the PCB to the electrode array. This close proximity of the electrodes
needed to map small tissue sample has resulted in capacitive coupling of the
electrodes at high frequencies.
56CHAPTER 3. IMPEDANCE MAPPING SYSTEM OVERVIEW,
OPERATION AND TESTING
3.6.2 RRC Circuits
Various electrical circuits representative of biological tissue were used to test
the frequency response of the multiplexer front end. Figure 3.10 shows one
such RRC circuit consisting of a 100 Ω resistor in parallel with an in series
100 Ω resistor and 100 nF capacitor. The RRC circuits were measured with a
SFB7 in the range of 4 kHz to 1 MHz, with and without the multiplexer front
end attached. With the front end attached the RRC circuit was attached to
the first 4 multiplexer channels on the PCB electrode array board as shown
in figure 3.11. Buffer resistors of 100 Ω were used between the drive and
measurement electrodes. Typical Cole plots obtained with and without the
multiplexers are shown in figure 3.12.
100 Ω
100 nF100 Ω
Figure 3.10: RRC test circuit.
Measurements made without the multiplexer front end agreed within 1.5%
with the theoretical values for R0 and R∞
of 100 Ω and 50 Ω respectively.
This is not the case with the multiplexers attached, a second arc is produced
at frequencies higher than 90 kHz. This is due to the design of the printed
circuit boards manufactured for the multiplexers and electrode array. For a
small surface electrode array to be constructed the paths taken by the drive
57
R R
R
R C
Drive
Electrodes
Measurement
Electrodes
Figure 3.11: RRC test circuit attached to the electrode array. All resistorvalues (R) are 100 Ω and capacitor value (C) 100 nF.
and measurement electrodes must be very close. The close proximity of these
electrode paths results in a capacitive coupling, effectively ’shunting’ the RRC
test circuit at high frequencies.
Capacitive coupling of the electrodes may be modelled and taken into ac-
count during the data analysis, subsequently removing its effect. This will be
shown in following sections to be more difficult than anticipated and was not
the solution pursued. Alternatively higher frequencies (above 90 kHz) can be
removed from analysis. When this was done the resulting Cole plot agreed
within 1.5 % with theoretical R0 and R∞
values.
58CHAPTER 3. IMPEDANCE MAPPING SYSTEM OVERVIEW,
OPERATION AND TESTING
40 50 60 70 80 90
5
0
5
10
15
20
25
30
35
40
Ri = 48.2291 Ro = 99.6802
50 55 60 65 70 75 80 85 90 95
5
0
5
10
15
20
25
30
Ri = 49.9059 Centre = (74.2563,0.26315) Ro = 98.6066
Fc = 1.4379e008
R = 98.6066ohms S = 101.0467ohms C = 55439265446.6937uFF
igur
e 1
Resistance Ohms
Resistance Ohms
- R
eacta
nce O
hm
s-
Reacta
nce O
hm
s
(a)
(b)
90 kHz
Figure 3.12: Typical Cole plots for RRC test circuit, measured data is repre-sented by red circles and line of best fit by the broken blue line. (a) Cole plotobtained without the multiplexers (b) Cole plot obtained with the multiplex-ers.
59
3.6.3 Resistor Matrix
Mapping capabilities of the system were tested using an array of resistors con-
structed onto the electrode PCB, this resistor matrix is shown schematically
in figure 3.13. Measurements of a resistor matrix allowed testing of the mul-
tiplexers stepping sequence and the usable frequency range. The following
results are for a 1000 Ω resistor matrix and are typical of results also obtained
for 150, 330 and 560 Ω resistor matrices.
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
RR RR RR
RR
RR
RR
Figure 3.13: Resistor matrix constructed with 1000 Ω resistors.
A typical Cole plot and impedance map for measurements made with the
entire frequency spectrum (4 to 1000 kHz) are displayed in figures 3.14 and 3.15
respectively. The Cole plot no longer displays the second arc in the frequencies
above 90 kHz as previously seen with RRC circuits (figure 3.12b). This lack
of a second arc is due to the resistor matrix being non-complex (no reactive
component) as opposed to the RRC circuits, hence it is not the high frequency
60CHAPTER 3. IMPEDANCE MAPPING SYSTEM OVERVIEW,
OPERATION AND TESTING
arc (as seen in figure 3.12b) that is absent but the low frequency arc between
4 to 90 kHz.
The capacitive coupling of the electrode paths is still very evident in fig-
ure 3.14. Ideally all of the measured points should lie on the resistance axis
(zero reactance) at a single point. The measurements at high frequencies con-
tain a very small resistive component and a large reactive component. The
Cole plot obtained indicates that the majority of the current flow at these
frequencies is between the electrode PCB paths and not through the resistor
matrix. Capacitive coupling is typically overcome by shielding the electrodes,
however this was not possible due to size constraints.
Impedance mapping of a resistor matrix as shown in figure 3.15 also demon-
strates the effect of capacitive coupling in the map of R∞
. For a non-complex
electrical component, high frequency measurements should remain the same,
producing the same map as R0. Modelling the capacitive coupling effect and
taking this into account during the data analysis stage is a possible solution
for this problem. However with 64 independent measurements, each having a
unique PCB path through the multiplexers and onto the electrode array this
approach becomes time consuming and much larger than the scope of this
study. Limiting the frequency range used to less than 90 kHz will also not be
of use, as previously described with RRC circuits, since capacitive coupling
will still distort the measurements.
Variation in calculated values for R0 shown in figure 3.15a are not a result
of this capacitive coupling but size restrictions in the resistor matrix. If the
matrix was to be expanded the outer measurement will become closer to that
of the central values due to more resistors being in parallel.
61
-50 0 50 100 150
20
0
20
40
60
80
100
120
Ri = -57.0581 Ro = 152.8678
1 MHz
Resistance Ohms
-R
eact
ance
Ohm
s
4 kHz
Figure 3.14: Typical Cole plot for a measurement made with a resistor matrix,measured data is represented by red circles and line of best fit by the brokenblue line. This Cole plot was obtained from a matrix constructed of 1000 Ωresistors.
The lack of resistors becomes more evident when comparing the four smaller
maps of R0 obtained with different electrode orientations. The smaller maps
on the left have a higher resistance on the left and right sides due to more
current being forced to pass through the resistor between the measurement
electrodes. This current induces a larger voltage and resulting impedance
calculated. The same effect is seen with the maps on the right however their
electrode orientation produces regions of higher impedance on the upper and
lower sides.
The use of a resistor matrix has demonstrated that the electrode stepping
62CHAPTER 3. IMPEDANCE MAPPING SYSTEM OVERVIEW,
OPERATION AND TESTING
(a) (b)
Figure 3.15: Impedance map obtained from a 1000 Ω resistor matrix, this isrepresentative of a typical matrix result. (a) R0 map. (b) R
∞map.
sequence works and the results can be displayed as a surface map. However the
high frequency component of the measurement spectrum is still unreliable, but
the calculated Cole parameter R0 that relies on low frequency measurements
is still useable.
3.6.4 Biological Tissue
The impedance mapping system was tested using bovine blood as a biological
tissue. This was readily available and if needed could be obtained in large
volumes. Bovine blood fitted the RRC circuit shown in figure 3.10 with plasma
63
representing the resistive extracellular space and the red blood cells having a
capacitive membrane and resistive intracellular space.
Preliminary testing was performed using plasma extracted from bovine
blood. Plasma can be treated as a non-complex electrical component like a
resistor, since no red blood cells (or insignificant numbers) are present to act
as capacitors. BIS measurements should result in a single resistance value
(R0) with no reactance. Figure 3.16 displays a Cole plot obtained from an
impedance map measurement, and the same arc seen with the resistor matrix
is once again seen here due to capacitive coupling. The first arc present in the
RRC Cole plots is not present here because of the absence of red blood cells
to act as capacitance and intracellular resistance.
0 10 20 30 40 50
10
5
0
5
10
15
20
25
30
35
Ri = 5.1502 Resistance Ohms Ro = 53.8929
Rea
ctan
ce O
hms
1 MHz
4 kHz
Figure 3.16: Cole plot of pure plasma.
64CHAPTER 3. IMPEDANCE MAPPING SYSTEM OVERVIEW,
OPERATION AND TESTING
Impedance maps of R0 and R∞
are given in figure 3.17. Again the results
are similar to those for the resistor matrix, with R0 producing reliable values.
However the impedance map of R∞
produces values much less than expected
due to measurements being greatly affected by capacitive coupling.
(a) (b)
Figure 3.17: Impedance map of pure plasma. (a) R0 map. (b) R∞
map.
3.6.5 Testing Summary
Testing of the impedance mapping system on electrical circuits used to mimic
the electrical response of biological tissue, has shown that the multiplexer front
end is susceptible to producing erroneous results. Capacitive coupling of the
electrodes through the multiplexer and electrode array PCB was unavoidable
65
due to size constraints and hence close proximity of the electrode paths. How-
ever further advances in the multiplexer PCB design and construction may be
able to include shielding for the electrode paths, greatly reducing the effect of
capacitive coupling. Removal of the capacitance effect through modelling and
further data analysis would also prove difficult due to the multiple (64) indi-
vidual electrode paths. It is also not possible to just use the lower frequency
range below 90 kHz which was less effected in RRC circuits but clearly effected
when measurements over the entire array were made.
As an outcome of these results all further work conducted in this study will
concentrate on the R0 value. It is the least effected by capacitive coupling and
still provides significant change in measurable impedance, as will be demon-
strated in chapter 4. R0 also provides the greatest accuracy to extracellular
resistance compared to using a single frequency measurement (Cornish et al.,
1993). Measurements at lower frequencies are also where the majority of the
impedance change is seen between healthy and cancerous tissue. Brown et al.
(2000a) presented mean R0 values of 19.0 and 3.85 Ω m for normal squamous
epithelium and CIN 2/3 respectively. Whereas intracellular resistance, which
is determined from R∞
only has a range of 2.31 to 6.10 Ω m for normal squa-
mous epithelium and CIN 2/3. This larger range seen between extracellular
resistance will provide more accurate identification of suspected lesions.
66CHAPTER 3. IMPEDANCE MAPPING SYSTEM OVERVIEW,
OPERATION AND TESTING
Chapter 4
Bioimpedance Mapping -
Results and Discussion
The aim of this study was to gather impedance maps of freshly excised cervical
tissue. However as the project developed it became evident that this aim could
not be realised and an alternate approach to establishing the efficacy of the
bioimpedance mapping technique was necessary. Specific issues were identified
as problematic in the in-vitro assessment of excised tissue but which would not
be of concern in-vivo. Sample size of the excised tissue would not sufficiently
cover the electrode array or be of great enough thickness. In addition the
limited size of excised tissue would confine the current flow injected from drive
electrodes and result in erroneous impedance measurements, particularly on
the periphery of the sample.
For these reasons the efficacy of the bioimpedance mapping technique was
tested using bovine blood. The blood for each trial was collected from the
67
68CHAPTER 4. BIOIMPEDANCE MAPPING - RESULTS AND
DISCUSSION
same animal and treated with 70 mg/L of heparine to prevent coagulation.
Blood for each measurement was prepared in the same manner by allowing
it to cool to room temperature (22 degrees Celsius) and the red blood cells
separated via a centrifuge. The separated red blood cells and plasma could
then be mixed in appropriate proportions to obtain the required haematocrit
for testing. Samples were also collected and allowed to coagulate, these were
used to represent a high impedance tissue medium at R0 due to the small
extracellular space.
4.1 Effect of Tissue Sample Size
4.1.1 Electrode Array Coverage
FEA modelling indicated that it is important for the sample to sufficiently
cover the electrode array so the current flow is not confined as seen in figure 2.9.
Figure 4.1 shows an example of insufficient coverage in the upper right corner.
The result of this inadequate coverage is that a smaller volume of conductive
medium is available for the current to flow through, increasing the measured
impedance in the upper right corner in relation to the rest of the impedance
map. The increase in impedance (Z) is due to it being inversely proportion to
the conductor volume (V) as given in equation 4.1 (ρ = resistivity and L =
conductor length).
Z =ρL2
V(4.1)
69
Figure 4.1: Inadequate electrode coverage with bovine blood in the upper rightcorner.
Figure 4.2 displays the impedance map produced when the volume of
plasma in the upper right corner is reduced. The thickness of the sample
was 4 mm. The effect of varying the sample thickness is considered in the
following section 4.1.2. Here the dam that is used to contain the bovine blood
in place on the electrode array has been brought closer to the upper right
corner of the electrode array, reducing the amount of plasma overlap on the
electrodes. The increase in measured impedance, with respect to the rest of
the map, in this corner is clearly seen.
If biopsy samples were to be used, they must be of a sufficient size to
eliminate these impedance distortions. This would not have been feasible in
a clinical trial as the typical sample taken at biopsy is smaller than the area
of the electrode array. With a biopsy sample not covering the electrode ar-
70CHAPTER 4. BIOIMPEDANCE MAPPING - RESULTS AND
DISCUSSION
Figure 4.2: Impedance map with a higher impedance in the upper right cornerdue to insufficient electrode coverage.
71
ray, tetrapolar electrode sets on the boundary of the sample will have partial
coverage resulting in heavily distorted impedance measurements.
4.1.2 The Effect of Sample Thickness
FEA modelling showed that the sensitivity decreased rapidly with depth and
that the thickness of the sample must be at least 5 to 6 mm (figure 2.23).
This was tested experimentally by confining the plasma sample with a glass
cover slip attached to a micrometer which could be used to alter the sample
thickness. Use of the glass plate and micrometer permitted a sample of known
thickness to be measured. Figure 4.3 shows the average R0 measurement made
for plasma at thicknesses of 0.25, 0.50, 1.00, 2.00, 3.00, 4.00 and 5.00 mm.
With an increase in plasma thickness the R0 value decreases substantially
to a constant value at a thickness of 4 to 5 mm. This is consistent with
the thickness indicated by the FEA modelling of 5 to 6 mm. Thus although
the thickness of the cervix is greater than 6 mm the bioimpedance technique
samples the surface layer where any precancerous changes occur. As a result
of this observation all following impedance maps were taken with a minimum
sample thickness of 4 mm.
It is evident that virtual biopsy of small tissue sizes will be prone to prob-
lems of confined current flow. If impedance mapping is to be continued for
use on excised tissue then a sample size sufficient to more than cover the array
will be needed to avoid distorted maps at the tissue boundaries and edges of
the electrode array. The thickness of the sample would also need to be at least
4-5 mm. As mentioned above, biopsy samples of cervical tissue are unlikely to
72CHAPTER 4. BIOIMPEDANCE MAPPING - RESULTS AND
DISCUSSION
0 1 2 3 4 540
50
60
70
80
90
100
Thickness (mm)
Mean
R 0
Figure 4.3: Mean R0 of plasma for various sample thicknesses.
73
meet these requirements. However further development of the instrumentation
such as miniaturisation and wireless communication between a personal com-
puter and recording device would allow for measurements to be made in-situ,
minimising the distortion of impedance measurements as a result of insufficient
sample size.
4.2 Homogeneous Haematocrit Impedance Map-
ping
The sensitivity of the impedance mapping system (as described in chapter 3)
to changes in impedance values (R0) was studied using blood samples with a
range of haematocrit values. A significant impedance range would ensure an
impedance map with differing haematocrits would show defined boundaries.
Impedance maps were obtained using homogeneous blood samples with a
range of prepared haematocrit values (0, 20, 40, 60, 80%). A haematocrit of
0% represents pure plasma. The individual haematocrit samples were placed
on the electrode array one at a time, with a volume large enough to completely
cover the electrode array and 4 mm in thickness.
Figure 4.4 shows the resultant impedance maps for the samples. It can be
seen that the impedance maps display constant R0 values for individual maps
(CV = 3 %). This confirms the results for testing the Ron contribution in
section 3.6.1. If Ron was to contribute to the measured impedance it would
result in variations of R0 values throughout the map.
74CHAPTER 4. BIOIMPEDANCE MAPPING - RESULTS AND
DISCUSSION
0
250
0%
20%
40%
60%
80%
Figure 4.4: Homogeneous haematocrit impedance maps. The haematocrit isgiven as a percentage and the colour legend displays the R0 value in ohms.
75
0 10 20 30 40 50 60 70 8040
60
80
100
120
140
160
180
200
Haematocrit %
Me
an
R0
R2 = 0.97
Figure 4.5: Mean R0 for homogeneous impedance maps.
76CHAPTER 4. BIOIMPEDANCE MAPPING - RESULTS AND
DISCUSSION
The constant R0 values also show that the inactive electrodes are not inter-
acting with the active measurement by creating a short circuit. If this was the
case a different impedance would have been measured in the outer 12 regions
to that of the 4 inner regions.
A plot of mean R0 for each impedance map against haematocrit (figure 4.5)
shows a large increase in impedance with haematocrit. The plot follows an
exponential trend as expected since the R0 value of a sample with haematocrit
of 100 % would approach infinity due to the very small extracellular space. The
range of haematocrit values has also shown to have a significant and measurable
change in R0. This was vital if impedance maps were to be measured with two
or more volumes of blood with differing haematocrits.
4.3 Impedance Maps
4.3.1 Plasma with Introduced Red Blood Cells
Impedance maps of samples of non-homogeneous haematocrits were measured
in the same manner as used for homogeneous haematocrits to investigate if
a region of different haematocrit in an otherwise homogeneous sample could
be identified. The electrode array was covered with plasma (0% haematocrit)
and regions of higher haematocrit introduced onto the electrode array via a
hypodermic syringe. This was not a stable arrangement as the introduced
RBC diffused through the plasma. Figure 4.6 demonstrates a region of red
blood cells (100% haemotcrit) introduced in the lower left corner of a plasma
sample and the associated diffusion through the plasma.
77
Figure 4.6: Region of red blood cells introduced to plasma. Lower left darkarea is where the cells were injected and the light grey is the area of visiblediffusion.
Cells were introduced via a hypodermic syringe onto the lower left electrode
as a region of higher impedance and to mimic a lesion on the surface of healthy
tissue. Impedance maps were obtained immediately after the red blood cells
were introduced and examples of typical results obtained from this process
are shown in figure 4.7 and 4.8. More red blood cells were introduced for the
impedance map shown in figure 4.8.
A clear distinction between the impedance of the upper right corner (pure
plasma) can be seen compared with the lower left corner (introduced red
blood cells). In both impedance maps the region of introduced cells can be
clearly identified by regions of high impedance. Figure 4.8 indicates a higher
impedance in the lower left as a result of more introduced RBC compared to
78CHAPTER 4. BIOIMPEDANCE MAPPING - RESULTS AND
DISCUSSION
Figure 4.7: Impedance map of plasma with red blood cells introduced in lowerleft corner.
79
figure 4.7. However the boundaries are not clear due to the dispersion of red
blood cells into the plasma. The dispersion is identified by the gradual change
in impedance between the upper right and lower left corners. A schematic of
dispersion is shown in figure 4.6.
Figure 4.8: Impedance map of plasma with a larger volume of red blood cellsintroduced in lower left corner.
80CHAPTER 4. BIOIMPEDANCE MAPPING - RESULTS AND
DISCUSSION
Red Blood Cell Dispersion
The dispersion of red blood cells throughout the plasma was expected to affect
the impedance measurements by continuously changing the impedance mea-
sured in each region. To measure this effect red blood cells were introduced in
the lower left corner of the plasma and measurements made at 2 minute inter-
vals (the time taken for one measurement). Figure 4.9 shows the 5 maps taken
over a ten minute period and the resulting decrease in measured impedance
over time in the lower left corner.
The continual change in impedance is not desirable since a single measure-
ment can take 2 minutes and impedance values will change during this single
measurement. The dispersion effect would not be seen in a biopsy and in-vivo
measurements.
4.3.2 Plasma with Introduced Red Blood Cell Clot
To stop the dispersion of red blood cells a clot was introduced to the plasma
in place of the RBC. This should result in regions of higher impedance and
more defined boundaries, with no gradual change in impedance from the region
of the clot to regions of plasma. Figures 4.10, 4.11 and 4.12 display typical
impedance maps with clots introduced in various regions on the electrode array.
The maps measured show clear impedance changes at the boundaries of the
red blood cell clots due to minimal dispersion of RBC. With defined boundaries
it is now possible to accurately mimic a surface lesion and precisely identify
the size of a lesion and monitor its growth or change in shape over time.
81
(a) (b)
(c) (d)
(e)
Figure 4.9: Dispersion of introduced red blood cells into plasma over 2 minuteintervals. (a) Measurement made immediately after the introduction of RBC.(b) Measurement made at 2 minutes. (c) Measurement made at 4 minutes.(d) Measurement made at 6 minutes. (e) Measurement made at 8 minutes.
82CHAPTER 4. BIOIMPEDANCE MAPPING - RESULTS AND
DISCUSSION
Figure 4.10: Impedance map of plasma with introduced red blood cell clotcovering central electrode.
83
Figure 4.11: Impedance map of plasma with introduced red blood cell clotcovering the 4 electrodes associated with the region in the middle lower right.
84CHAPTER 4. BIOIMPEDANCE MAPPING - RESULTS AND
DISCUSSION
Figure 4.12: Impedance map of plasma with introduced red blood cell clotcovering the 2 lower right regions.
85
4.4 Experimental Comparison with Modelled
Sensitivity Field
4.4.1 Anomalous Measurements
Evidence of the anomaly found in FEA modelling (see section 2.2.2) and as a
result of the tetrapolar configuration’s complex sensitivity field is also shown in
the experimental impedance maps. Figure 4.13 presents results obtained from
the introduction of red blood cells to plasma and with subsequent dispersion
as displayed in figure 4.6. The map shows the red blood cell density and re-
sulting impedance is higher between the 2 lower electrodes associated with the
4 electrodes used to measure the region identified by the arrows in figure 4.13.
The sensitivity region between these 2 electrodes is positive for the smaller
maps on the right, resulting in a increased measured impedance if a higher
impedance medium is here. This increase in impedance is clearly seen in the
two maps on the right and indicated by arrows. The two maps on the left show
a decrease in impedance because the region between the lower electrode pair
is of negative sensitivity, resulting in a decreased measured impedance when a
higher impedance medium is located in the region.
This measured anomaly was seen in nearly every impedance map recorded
and agrees with the sensitivity fields modelled with FEA. However it does not
alter the averaged impedance map since the R0 value in this region of the
larger map (average impedance) is not anomalous i.e. the R0 value follows the
decreasing impedance gradient from the lower left corner to the upper right.
86CHAPTER 4. BIOIMPEDANCE MAPPING - RESULTS AND
DISCUSSION
(1) (2)
(3) (4)
Figure 4.13: Anomalous result due to positive and negative sensitivity fields.Anomalous result is identified by arrows.
87
4.4.2 Reciprocal Electrodes
The reciprocal nature of the tetrapolar electrode configuration as indicated
by FEA modelling is clearly seen in figure 4.14. The two smaller electrode
orientation maps on the left are the same as are the pair on the right. The only
differences within the pairs are that the drive and measurement electrodes have
been interchanged. This can be explained by consideration of the symmetrical
nature of the sensitivity fields as shown in section 2.3.
The reciprocal nature of the tetrapolar electrode configuration suggests
that the impedance map might be obtained using only two electrode orienta-
tions rather than the four currently proposed. The number of required mea-
surements could therefore be halved. However the uncertainty in the measured
impedance is also important.
The uncertainty was tested using an impedance map obtained for a pure
plasma sample (figure 4.15). The average of all four is the current proposed
approach (1+2+3+4), and the average of new electrode orientations usable
are 1+2, 3+4, 1+4 and 3+2. The mean and variance of R0 for these averages
are presented in table 4.1.
Combined Maps Mean Variance
1,2,3,4 49.59 1.961,2 49.57 2.063,4 49.61 1.911,4 49.61 1.673,2 49.58 2.35
Table 4.1: R0 mean and variance for various electrode orientation combina-tions.
Analysis of variance (ANOVA) for R0 produced a F statistic of 0.002, with
88CHAPTER 4. BIOIMPEDANCE MAPPING - RESULTS AND
DISCUSSION
Figure 4.14: Reciprocal nature of the tetrapolar electrode configuration. Thereciprocal pairs are grouped
89
21
3 4Figure 4.15: Impedance map of plasma used to demonstrate the reciprocalnature of the tetrapolar electrode configuration.
90CHAPTER 4. BIOIMPEDANCE MAPPING - RESULTS AND
DISCUSSION
a p-value of 1.0. Since the p-value is greater than 0.05 (or equivalently the ob-
served F statistic is smaller than its critical value of 2.494) it can be concluded
that there is no significant difference between the measured mean R0 values
using the different pairs of electrode orientations and the original approach of
using all 4 orientations. Similar results were also obtained for other impedance
maps analysed.
Since the averages were shown to be not statistically different it can be
accepted that only 2 impedance measurements are required at each region.
These measurements can also be of any electrode orientation as long as they
are 90o to each other. Any anomalies present will also still be removed by
averaging since there is no difference between averaging 4 measurements where
there are infact only 2 unique measurements, or just averaging these 2 unique
measurements.
Efficient Electrode Stepping
As shown above there is no advantage in reproducibility in averaging four
rather than two maps. It is now possible to take advantage of the reciprocal
nature of the tetrapolar configuration and utilise a more efficient electrode
stepping sequence. Figure 4.16 displays an alternative method for stepping
through the electrode array, here the number of electrodes can be double that
of the available multiplexer channels.
Using this presented sequence a 25 electrode array may be constructed
with only 12 channel multiplexers. Electrodes white (measurement) and black
(drive) will require only 12 channels each, while the other blue measurement
91
(1) (2)
(3) (4)
(5) (6)
(7) (8)
Figure 4.16: New proposed electrode stepping sequence 1-8. Red/black andwhite/blue represent drive and measurement electrodes respectively.
92CHAPTER 4. BIOIMPEDANCE MAPPING - RESULTS AND
DISCUSSION
electrode requires 9 channels and the red even less with only 4 channels. This
stepping sequence was applied to an impedance map and is show in figure 4.17
along with the map obtained using an average of 4 measurements.
Comparison of the impedance maps show only minor changes in R0 values,
with some differences due to rounding in the data analysis. However the region
of higher impedance in the lower left corner is still clearly identifiable.
4.5 Lesion Boundary Identification
The anomaly confirmed in section 4.4.1 is only found in regions where a
medium of different impedance is located under the electrodes. A possible
method for detection of lesion boundaries is now available since 2 measure-
ments using orthogonal electrode orientations, at a region of non-homogeneity,
will produce different measured impedances. Whereas a region of homogeneity
will produce the same measurements. The impedance map of plasma with in-
troduced RBC shown in figure 4.13 was used for the following example. Smaller
maps 1 & 3 have been averaged , the same process was used for maps 2 & 4.
The difference between these 2 maps is presented in figure 4.18.
A lesion’s boundary can now be identified in the resultant map as a region
with a non-zero R0 value. For example a boundary map of homogeneous
plasma will result in values close to zero since there is no difference in the
medium under the electrodes. However in figure 4.18 it can be seen in the
region of dispersed blood there are high values due to different haematocrits
being located under each of these electrode sets. In the lower left a value of
93
(a)
(b)
Figure 4.17: Comparison of (a) new electrode stepping sequence with (b)presently used.
94CHAPTER 4. BIOIMPEDANCE MAPPING - RESULTS AND
DISCUSSION
Figure 4.18: Boundary identification via anomalies.
95
zero is seen due to a high but homogeneous haematocrit sample being located
under the electrode set. This is the location of the injected RBC. The upper
right region of homogeneity is also close to zero due to the sample under the
electrode sets being homogeneous plasma, the RBC have not dispersed into
this region. This has identified a method for objectively determining lesion
boundaries.
4.6 Summary
Virtual biopsy of small tissue sizes will be prone to problems of confined cur-
rent flow. If impedance mapping is to be continued for use on excised tissue
then minimum size requirement will be needed to avoid distorted maps at the
tissue boundaries and edges of the electrode array. Further development of the
instrumentation and electrodes would allow for measurements to be made in-
situ, eliminating all effects and distorted impedance measurements as a result
of insufficient sample size.
The use of bovine blood as a substitute for freshly excised tissue proved to
be acceptable. A significant change in impedance was seen with a change in
haematocrit and these impedance changes were measurable in the mapping.
The advantage of using a clot to confine the regions of high impedance and
provide distinct boundaries also proved useful.
Anomalous results indicated during modelling of the tetrapolar configu-
rations sensitivity fields in chapter 2 are also present in the experimental
impedance maps. However they are only found when lesion boundaries or
96CHAPTER 4. BIOIMPEDANCE MAPPING - RESULTS AND
DISCUSSION
changes in medium impedance are located underneath the electrodes. These
anomalies did not appear to alter the resultant impedance map once averaged.
This negated the need to remove and discard this measurement as previously
expected. A surprising side effect of the anomaly is the ability to now detect
boundaries of lesions or changes in impedance. This allows a non-subjective
method for determining lesion size and possible biopsy margins.
The reciprocal nature of the electrodes shown by modelling of the sen-
sitivity fields agree with the experimental impedance maps measured. This
also provides a method for increasing the number of electrodes in the array
while still using multiplexers with the same number of channels. Reducing the
number of measurements required at each region will also minimise the time
taken to acquire an impedance map. However, despite halving the number of
measurements from four to two at each region statistically there is no decrease
in the measurement accuracy.
Chapter 5
Conclusion
Virtual biopsy by bioimpedance spectroscopy is a relatively new technique.
This study investigated the sensitivity fields of the commonly used tetrapolar
electrode configuration and expanded it to consider the sensitivity of a 25
electrode array. The use of an array allowed further characterisation of a lesion
of interest by identifying spatial information, importantly lesion boundaries.
This work into mapping the surface impedance of a lesion has not previously
been undertaken as other investigations of virtual biopsy have used single point
measurements on a region of interest, with no additional information gathered
about the lesion dimensions.
Finite element analysis (FEA) was used to study the sensitivity for the
measurement of impedance of tissue using the tetrapolar electrode configura-
tion with simulated lesions located in healthy tissue. As expected, a decrease
in measured impedance resulted when a lesion was introduced, except for the
case of a lesion located between a drive and measurement electrode pair. In
97
98 CHAPTER 5. CONCLUSION
this latter case, the measured impedance was found to initially increase when
small lesions were present and then decrease as the lesion size increased. This
“delayed” decrease in measured impedance could lead to a false negative re-
sult, leaving the lesion undetected and subsequently not identified for further
treatment.
Modelling of sensitivity fields provided insight of the distribution of areas
of positive and negative sensitivity. These fields were found to agree with and
explain the previous anomalous results indicated by the modelled lesions. The
rapid decrease in sensitivity with depth confirmed the efficacy of using the
tetrapolar electrode configuration for surface measurements. Results showed
that the magnitude decreased to near zero at a depth of 5 mm, confirming the
measurement sensitivity to the surface layers.
A multi-electrode array showed surprising results in that the inactive elec-
trodes surrounding the active electrodes had little effect on the measured
impedance. Modelled sensitivity fields indicated additional regions of pos-
itive sensitivity between the active and inactive electrodes. However these
had a magnitude 10 times less than those found within the active electrodes,
explaining their lack of effect on measured impedance. They were shown, ex-
perimentally, to not affect the measured impedance in maps of homogeneous
haematocrit samples
Instrumentation has been designed and constructed allowing for the use of
an electrode array with a commercially available impedance measuring device.
The multiplexer front end developed in this project allows for the drive and
measurement electrodes of the commercial device to be switched to any of the
25 electrodes in the array. The front end is also designed to be used on a
99
desktop personal computer without the need for any specialised equipment.
A printed circuit board based electrode array was developed and imple-
mented. A PCB based electrode arrays also makes manufacturing of arrays
readily available and disposable, but autoclavable for repeated use if desired.
Automation of the multiplexing front end and data analysis process was
performed via Matlab and a Visual Basic program. The Visual Basic program
provided an objective display of the measured impedance map for the user.
Testing of the multiplexer front end showed that it suffers from capaci-
tive coupling. This did not allow for accurate impedance measurements at
high frequencies and the use of R∞
as an analysis parameter. However R0
was unaffected by the capacitive coupling and still usable to provide detailed
impedance maps with high contrast between regions of different impedance.
A small tissue sample size was determined to be a problem and trials with
freshly excised cervical tissue would not be possible since adequate coverage
of the electrode array by the sample is required as well as adequate sample
thickness. It was shown that if these size conditions were not met then confined
current flow throughout the tissue medium would result in distorted impedance
measurements.
A substitute tissue medium was found in bovine blood and mapping of
homogeneous haematocrit demonstrated a large range of impedance values
that would be suitable for impedance mapping. The Impedance Mapping
System (IMS) was shown to measure these regions of impedance change when
red blood cells and clots were introduced to plasma, displaying them clearly
in the maps produced. Changes in impedance at the boundaries resulted in
100 CHAPTER 5. CONCLUSION
anomalous impedance measurement as modelled in FEA. It was thought these
anomalous results would need to be removed from further analysis to prevent
altering the final outcome. However averaging of the maps obtained with
electrodes rotated by 90o showed no evidence of anomalous effects. A method
for objectively identifying lesion boundaries utilising these anomalous results
was developed.
Taking advantage of the reciprocal nature of the tetrapolar electrode config-
uration a more efficient electrode stepping sequence was developed. Without
changes to the present instrumentation the number of measurements, com-
pared to that initially considered, may be halved without any detrimental
effects to the measurement quality, resulting in faster measurement times and
data analysis.
In summary, an impedance mapping system has been modelled, designed
and developed for tissue characterisation by bioimpedance measurements. The
technique has been shown experimentally to be able to detect regions of differ-
ent impedance and is in agreement with the finite element analysis performed.
Further development of the IMS will allow progressive monitoring of suspect
lesions in-vivo and better identification of their spatial distribution for biopsy.
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