Biomed Imaging Interv J 2006; 2(2):e24
doi: 10.2349/biij.2.2.e24
© 2006 Biomedical Imaging and
Intervention Journal
ORIGINAL ARTICLE
Assessment of electrical impedance endotomography for
hardware specification
J Jossinet, PhD,
A FournierDesseux, MSc,
A Matias
National Institute for Health and Medical Research, INSERM U556, Lyon, France
ABSTRACT
Purpose: The purpose of the study is the quantitative
assessment of Electrical Impedance Endotomography (EIE) for the specification
of hardware systems. EIE is a modality of Electrical Impedance Tomography (EIE)
where the electrodes are located on a probe placed in the middle of the region
of interest. The absence of material boundary to the explored volume and the
decrease in sensitivity away from the probe requires specific study.
Material and methods: The method is the derivation of
the equation linking explored medium�s conductivity, the sensitivity
distribution of the electrode patterns used for data collection and measuring
system�s noise and bandwidth. The assessment of EIE was achieved by means of simulations
based on realistic data of conductivity and noise level.
Results: The derived equation enabled the estimation
of the current needed under realistic operating condition corresponding to
prostate imaging. The generalisation to other organs is straightforward. The
image reconstructed from the simulated data and from bench experiments were in
agreement and showed that the two selected drive patterns, fan3 and adjacent,
gave images of similar quality in absence of noise and that adjacent drive
requires significantly higher measurement current.
Conclusion: The study confirmed the feasibility of
EIE with achievable hardware specifications. The derived equation enabled the
determination of design parameters for the specification of hardware systems
corresponding to any given application. The study also showed that EIE is more
appropriate for tissue characterisation than for high speed imaging. � 2006
Biomedical Imaging and Intervention Journal. All rights reserved.
Keywords: Electrical impedance tomography, drive pattern, sensitivity, noise, hardware design, urethral probe, prostate
INTRODUCTION
Electrical Impedance Tomography (EIT) produces images of a
body from impedance data collected using surface electrodes. The advantages of
this method in medical applications include harmlessness, easeofuse, high
time resolution and specificity for tissue characterisation [14]. The direct
problem obeys the second order differential equation ��(σ�u) = 0
with Neumann/Dirichlet mixed boundary conditions. The associated inverse
problem is illposed [5]. The small number of measurements limits the spatial
resolution of the reconstructed images. The reduction of sensitivity and
resolution from periphery towards the centre [6] makes EIT not well suited for
the imaging of small and deeplocated organs. The nature of the governing
equation and the low number of possible measurements with a workable number of
electrodes prevents significant improvement of spatial resolution.
In Electrical Impedance Endotomography (EIE), the electrodes are located on
a probe placed in the middle of the region of interest for local
measurements. An EIE probe consists of multiple linear electrodes
regularly spaced on the outer surface of an insulating core
(Figure 1). EIE was developed for prostate imaging aimed
at the evaluation of cancer treatment by therapeutic ultrasound
[79]. In the proposed application, the impedance
method is expected to compensate for the lack of specificity
of ultrasonic imaging in cancer detection and the low acoustic
contrast observed in the prostate between normal tissue and
tissue treated by ultrasound [1012]. This
approach has been supported by the known significant conductivity
differences between cancerous and normal tissue observed in
various organs [1318], including human prostate
[19, 20], and by recent studies reporting
significant conductivity changes in tissue exposed to ultrasound
energy [21, 22]. More generally, EIE can
potentially address a range of interstitial and intracanular
measurements such as in oesophageal and vascular studies.
The method, however, does not aim to compete with the
radiological methods of prostate imaging. The objective is to derive a
complementary technique for use in conjunction with ultrasound techniques. The
objective is to exploit the specificity of impedance measurements to improve
the characterisation of tissue before and after treatments with therapeutic
ultrasound.
EIE obeys the same governing equation as EIT but with
different boundary conditions. The boundary profile is unknown and variable in
EIT according to the morphology of the examined region and interpatient
variability while the surface bearing the electrodes is known by construction
in EIE. It is obvious that the volume actually sensed by the probe is finite
although there is no material boundary around the probe. The limit is the
distance beyond which noise overrides the contributions of distant points.
The determination of the computational domain is a key
problem in EIE. The absence of tangible limit for the domain sensed by the EIE
probe is one major difference compared with EIT. Therefore, the notions
formerly investigated in EIT are still relevant in EIE, due to the same
governing equation, but need to be revisited. For quantitative studies, the
geometry of an EIE probe suggested the use of a model with axial symmetry. In
this 2D model, an infinitely long cylinder represents the core of the probe and
infinitely long lines regularly spaced at the outer surface of this cylinder
represent the electrodes. This model enabled the derivation of analytical
equations for current density, field and potential created by EIE electrodes in
a medium of homogeneous conductivity.
According to the model, the field of a single electrode is
proportional to 1/d, where d is the distance to the centre of the probe. Hence,
the field of a pair of electrodes tends to vary as 1/d^{2} for large
distances to the probe. The consequence is a rapid falloff in sensitivity of
the order of 1/d^{4}. The measurements in a semiinfinite medium
present a certain similarity with the case of the rosette array of surface
electrodes used in EIT for monitoring gastric function [23]. In both cases, the
electrodes are grouped together, do not encircle the region of interest, and
explore a semiinfinite medium. The measurements carried out with the rosette
support the feasibility of EIE measurements.
It was found that for a total number of 16 electrodes, the
possible 4electrode patterns using an adjacent pair of voltage
electrodes can be sorted into 49 basic patterns from which any
pattern can be obtained by symmetry and rotation. The association
of the model with the lead field theory enabled the calculations
of sensitivity maps for the basic 49 patterns. The study of
these maps showed that the extension of sensitivity increases
with the angular spacing of source electrodes. These maps are
shown in the form of an animation (Figure 11). The drive pattern
giving the largest sensitivity range was selected based on these
sensitivity maps.
The purpose of this study is the quantitative assessment of
EIE as a whole including medium, electrodes and instrumentation. This differs
from the previous studies, which were limited to the comparison of drive
patterns to determine the widest sensitivity range. The novelty of the present
study is to encompass all the components involved in EIE data collection. This was
achieved by the derivation of an equation linking measurement, noise, magnitude
of injected current, electrode sensitivity distribution, medium conductivity
and conductivity contrast to be observed. The inclusion of noise enabled the
calculation of the volume actually sensed by the probe. The study is supported
by the comparison of adjacent and fan3 drive patterns using calculated data and
images reconstructed from computer and experimental data. Although particular
attention was given to prostate imaging, the study has been intended to enable generalisation
to other applications and the design of hardware systems.
DEFINITIONS
Electrode patterns
In this study, the measurements were carried out according
to the 4electrode technique with bipolar current patterns and differential
voltage sensing with all four electrodes located on the probe. The sensing pair
always consists of adjacent electrodes for hardware reasons including reduction
of common mode signal. The number of patterns with adjacent voltage electrodes
is N_{T} = (N_{E}‑3) (N_{E}‑2)N_{E}/2,
where N_{E} is the number of electrodes on the probe. The maximum
number of linearly independent patterns is (N_{E}3)N_{E}/2, as
this was formerly demonstrated in EIT. In this study, it was found convenient
to consider that the set of 4‑electrode patterns used for data
acquisition consists of the N_{E} angular duplications of a basic set
consisting of patterns comprising a given pair of voltage electrodes (pair
arbitrarily denoted {0,1} in this study) associated to different pairs of
current electrodes.
Reconstruction mesh
The reconstruction mesh consisted of N_{L}
concentric layers of N_{A} trapezoidal pixels. The outer radius of the
mesh was denoted R_{max}. The vertices of a pixel were located on two
circles of radii r_{n1} and r_{n}, with r_{n1} < r_{n},
r_{0}=1 and r_{NL} = R_{max}. The number of layers was
N_{C} = 14, the number of angular sectors was N_{A} = 64.
Hence, the number of pixels was N_{pix} = 896. The mesh was
designed, so that pixel dimensions were proportional to the distance from the
origin (Figure 2). This was achieved in the setting of the radial increment
equal to the length of the circular arc passing by the centre of the pixel.
This condition can be written under the form of (1):
_{}������������������������������ (1)
In this mesh design, the resolution is better for pixels of higher sensitivity
while the increase in pixel size with distance tends to compensate
for the sensitivity decrease. The radius of the reconstructed
domain was chosen according to the size of the domain explored
by the probe. If the reconstruction domain is too small, significant
elements would be ignored and attributed erroneously to pixels
located inside the mesh. If the reconstruction domain is too
wide, it would encompass points with negligible contributions.
In this study, the reconstruction domain was determined by considering
the diameters of urethral probes used in urological practice
and the size of the prostate. This 3cm high organ is approximately
conical in shape. It presents a base, an anterior, a posterior
and two lateral surfaces. The base applied to the inferior surface
of the bladder and the apex is directed downwards. The prostate
is about 4�2 cm^{2}
at the base (2 cm in anteroposterior diameter). From these
dimensions, the value of R_{max} chosen was equal to
4 times the radius of the probe. This justified the use
of 14layer mesh.
Sensitivity
Sensitivity is a general concept to quantify the change in
the measured signal when the conductivity within a given element,
∆τ, changes by ∆σ. The computation of sensitivity
normally requires the resolution of the governing equation knowing the original
and the perturbed distribution of conductivity in the medium. For small
perturbations, the lead field theory yields a linear approximation that has
been widely used in impedance imaging. This theory has enabled the derivation
of a general expression of change, ∆Z_{x}, in the measured
impedance, Z_{x}, due to the conductivity change in a given element
∆τ [24]. In the present study, the conductivity change was assumed
to be uniform within the volume element. Hence, the general expression of
∆Z_{x}, transforms into (2):
_{}������������������������� (2)
E_{volt}/I_{volt} is the field of the
voltage electrode in the initial medium. E'_{curr}/I_{curr} is
the lead field of the current electrodes in the medium perturbed by
∆σ in element ∆τ. If the element volume and the
conductivity change are small enough, it is convenient to consider that E'_{curr}
is approximately equal to the lead field of the current electrodes in the
nonperturbed medium. Using Ohm's law, the voltage changes due to the
conductivity change is given by (3), where I_{S} denotes the
measurement of the current injected across the source electrodes and σ the
initial conductivity value within the pixel:
_{}��������������� (3)
Sensitivity Λ_{τ} is expressed in m^{1}
in general (3D) and dimensionless in 2D (translationally uniform model). In the
latter case, infinitely long lines model the electrodes and the measurement
current in (2) is in A/m, so that the dimensions in (2) and (3) remain
consistent.
The sensitivity of all pixels and all electrode patterns
used for data acquisition form the sensitivity matrix formed by N_{meas}
rows and N_{A}�N_{L}
columns. The socalled "fan3" electrode pattern has a larger
sensitivity domain than the other bipolar drive patterns tested: adjacent,
diametric and fan4 [25].
The adjacent drive pattern has widely been used in EIT. It
consists of 4electrode patterns where both voltage and current electrode pairs
consist of adjacent electrodes. Fan3 consists of 4electrode patterns where the
voltage electrodes are adjacent and source electrodes are of variable spacing
(Figure 3). In fan3, the two source electrodes are separated by the symmetry
axis of the voltage electrodes. The sixteen angular replications of these 13
patterns yields N_{meas} = 208 measurement patterns. Similar definition
applies to fan4 to fan8 patterns. However fan3 was found to give the largest
sensitivity range, so that the other fanX patterns were ignored in this study.
NOISE
Noise condition
This section describes the sources of noise and presents the
derivation of an equation for the measurement current. In the following, the
term "signal" denotes the change in the voltage difference across the
sensing electrodes in measuring the perturbed medium and the initial medium (du in (3)).
The correct measurement of a conductivity change,
∆σ, in an element implies that the sensitivity of this element is
above the noise level. It was assumed in this study that the minimum
conductivity change to be measured, denoted  ∆σ/σ _{min},
was the same for all pixels of the mesh. In all drive patterns, certain pixels
have low sensitivity values due to either their distance to the probe or the
local orthogonality of the lead fields. The contributions of such elements
remain under the noise level for any realistic value of the measurement
current. Hence, the noise condition used in this study was the following: any
pixel of the mesh is sensed by at least one of the N_{E} angular
replications of any basic electrode pattern. This condition is really a minimal
condition, for, if it were not satisfied, certain measurements would ignore
certain pixels. This condition means that for any basic pattern, the
contributions of at least N_{A}/N_{E} pixels per layer are
above noise level. Hence, with a 16electrode probe and the 64 angular sectors,
the relevant parameter is then the fourth largest sensitivity magnitude in each
layer of the mesh.
Noise sources
Three types of noise have been considered in the present
study: electrode noise, electronic noise and current noise. Electrode noise's
origin is electrochemical. In the frequency range of impedance measurements
(f>1 kHz), the general expression for such noise is similar to that of
thermal noise [2627]:
_{}�� (4)
where k is Boltzmann's constant, T absolute temperature (�K)
and � the real part of the interface
impedance and B system's bandwidth (Hz).
For the quantification of the noise generated in the current
injection circuit, the injecting circuit was considered as a
voltagetocurrent converter of transadmittance G/R_{S }(S/m),
where G is the voltage gain of the circuit and R_{s}
the resistance across which the feedback voltage is measured.
Figure 3 shows two circuits commonly used for voltagetocurrent
conversion: Howland's circuit and differencing amplifier.
The output current is I_{S}=V_{E}�G/R_{S}. G denotes the closed loop
voltage gain of the amplifier. Depending on the configuration of the circuit,
the noise gain, G_{noise}, can be different from G. Let Nf_{I}
be the noise figure (V/�Hz) at the
input of the circuit. The injected noise current, of rms value denoted i_{noise},
is then given by (5) where B is the bandwidth (Hz) of the system:
_{}������������������������������������ (5)
This noise current produces an error voltage across the
measured impedance Z_{x}. Considering that the measured impedance is
the quotient of the geometry factor g_{x} to the mean conductivity of
the medium, σ_{m}, the noise voltage due to the current source is
given by (6):
_{}���������������������������� (6)
The value of g_{x} can be either calculated for each
element and electrode pattern used by means of an appropriate model or derived
from experimental measurements of impedance Z_{x}, and medium's mean
conductivity σ_{m}. Table 1 shows the values of g_{x}
calculated using the described 2D model and measured in vitro. The
difference between measured and calculated values has been attributed to the
dispersion of current streamlines at the extremities of finite electrodes [9]
of length equal to the diameter of the probe as described in section
"Experimental setup".
The rms value of the amplifier input related noise voltage
is given by (7):
_{}������������������������������������������������������������ (7)
The noise figure Nf_{V} is given in technical data
sheets of operational amplifiers. Finally, using (4), (6) and (7), the total
noise rms voltage superimposed to the signal ∆v_{x} is given by:
_{}��������������������������� (8)
The coefficient √2 accounts for the fact that the
"signal" is the difference between two measurements.
Numerical application
The noise figure of the voltage amplifier is equal to
13nV/√Hz, which corresponds to standard opamps usable in EIE. The
contact impedance of one electrode of this probe in tap water of conductivity
0.039 S/m was 400 Ω at the used measurement frequency of
8 kHz [8]. In a urethral probe, the electrode surface would be reduced by
a factor of about 25 or less with respect to the mock‑up probe used in
bench experiments. The interface impedance would then become about 10 k
Ω in tap water. However, tissue conductivity is in general higher than
that of tap water, so that the interface impedance will presumably be lower in
tissue than in tap water. In the absence of literature data for urethral wall,
data for blood vessel and prostate were considered instead. From the data
published on the website of the Institute for Applied Physics "Nello Carrara"
[28], the magnitude of the calculated prostate admittivity (σ*=
σ_{0}+jωεε_{0}) varies from about
0.43 S/m to 0.58 S/m in the prostate and from 0.28 to 0.33 for blood
vessel in the range 10 kHz ‑ 1 MHz. Furthermore, the
possible presence of urine, wetting urethra wall, would presumably tend to
decrease the contact impedance.
The presence of urine of higher conductivity than the
surrounding tissue, can potentially affect the measurements. Besides the
reduction of electrode contact impedance due to the wet urethral wall, the
presence of urine could also cause adjacent electrodes to short circuit. It may
be expected that the amount of urine present during the measurements would be
limited by the preliminary draining of the urethra and the temporary
obstruction of the lumen by the tip of probe. The shorting impedance would depend
on the thickness of the conductive layer forming between the probe surface and
the urethral wall. A possible protection measure would be to give electrode
edges a slightly salient profile to locally increase the pressure to constrict
or divide the conductive layer. This issue can only be solved by a practical
measurement in situ.
Conductivity values for urine range from 2.5 S/m to 4.5 S/m
[29, 30]. In this study, in the worst case
the real part of the interface impedance of two electrodes in
series was finally maximised by 2500 Ω. The corresponding
electrode noise figure, Nf_{el}, is then about 6 nV√Hz.
The noise figure due to the current injecting circuit can be
derived from (6). With G_{noise} = 2, Nf_{I} = 13nV/√Hz,
g_{x} = 0.333 (maximal value in Table 1),
R_{S} = 1 kΩ and σ_{m} = 1 S/m,
the noise figure due to the current source is about 0.009nV/√Hz,
which is negligible compared with the other sources of noise.
The total noise figure in this numerical example is then about
14.3nV/√Hz.
Noise condition and measurement of current equation
The condition for the correct measurement of the
contribution of an element is that the contribution, δu, of this element
is above noise level. Assuming that the distribution of noise amplitude is
Gaussian, one may take 3.09�N_{f}
as arbitrary noise threshold, with the risk of 0.002 for the instantaneous
noise voltage, which is outside the interval �3.09�N_{f}. Using (4), (5), (6) in (8) and grouping the
terms corresponding to the probe, the instrumentation and the medium finally
gives the expression of the rms value of the injected current satisfying the
above noise condition:
_{}��������� (9)
The mean conductivity of the medium, σ_{m},
depends only on the explored medium, the conductivity change σ/σ on
the observed phenomena (tumour, treatment).
DESIGN PARAMETERS
The purpose of this section is to determine the realistic
design values for incorporation into (9) of the mean conductivity, σ_{m},
and minimal conductivity change ∆σ/σ_{min}. The mean
conductivity value determines the magnitude of the measured impedance Z_{x}.
and consequently that of a pixel's contribution, δu. For the prostate, Dawson
[31] reports a value of 0.4 S/m for studies at 60 Hz. This value is close
to the static conductivity σ_{0} of the prostate given by the IFAC
internet resource [28]. The conductivity values calculated in section
"Numerical application" from this resource for normal prostate tissue
(0.43 to 0.58) suggested 0.5 S/m as design value of σ_{m} in
(9).
The design value of ∆σ/σ_{min}
corresponds to the smaller change due to either the presence of cancer tissue
or the treatment of a tissue by therapeutic ultrasound. Several sources of data
enable the estimation of ∆σ/σ in presence of cancerous tissue. Blad
[32] has proposed a general conductivity ratio between normal tissue and cancer
tissue of about 0.69 (∆σ/σ = 0.31). Conductivity
ratios of 0.72 and 0.78 at 16 kHz and 125 kHz, respectively, were
observed between carcinoma and glandular tissue in excised breast tissue
samples [17, 18].
Dunning tumour in a Copenhagen rat is a commonly used model
for human prostate cancer [33]. The admittance of growing AT2 Dunning tumours
was monitored during 21 days [34]. The conductivity was estimated by modelling
the tumour with a cylindrical segment of length equal to its diameter with four
equally spaced electrodes. This yielded a rough estimate of tumour conductivity
of about 0.2 S/m at 9 kHz and 0.4 S/m at 1 MHz. Using the
figures and the values for reference prostate tissue of section "Numerical
application", the coarse estimates of conductivity ratios are about 0.47
and 0.69 at the two considered frequencies.
Lee [19] carried out impedance measurements at 100 kHz,
1 MHz, 2 MHz and 4 MHz in prostates exvivo using
bioimpedance needles. The conductivity was smaller in cancer tissue than in
prostate tissue at 100 kHz, 1 MHz and 2 MHz with conductivity
ratios of 0.86, 0.92 at and 0.8, respectively.
Smith, by measuring eddy currents using a magnetic coil at
2.14 MHz, compared the conductivity values in Dunning tumours from G, AT2 and
AT3 lines [20]. The conductivity was lower in AT2 and AT3 tumours (0.22 and
0.24 S/m) and G line (0.33 S/m) than in control tissue (0.35 S/m).
From the above data, the value of 10% was taken as representing the minimal
change ∆σ/σ_{min} resulting from the presence of
prostate cancer.
The energy deposited in tissue by therapeutic ultrasound produces
the irreversible necrosis of the tissue. In vitro experiments
showed noticeable changes in a tissue's impedance. Changes larger
than 20% were observed in tissue samples exposed in vitro
to high energy ultrasound [21] and muscle
tissue samples [22]. As these values were
larger than the value for cancer tissue, the latter (10%) was
finally taken as design value of ∆σ/σ_{min}
for incorporation into (9). Figure 4 shows the plot of
the measurement current satisfying the noise condition (9) with
the value of section "Numerical application� and ∆σ/σ_{min} = 0.1.
In this plot, the parameter varying with distance is Λ_{x},
the fourth largest sensitivity value calculated for each layer
of the mesh described in Figure 2.
SIMULATION
This section describes the simulation of an EIE application
using calculated and experimental data. The conductivity ratio (σ/σ_{0})
was set to 1.1 for the simulation of biological conditions and to zero to
simulate the plastic rods used in bench experiments. The model described below
was used for the simulation of two conductivity perturbations, of radius 0.2 and
0.3 and centred on the Oy axis at (0,2) and (0,3), respectively. The
experimental data were collected using the bench model described in section
"Experimental setup".
Software model
The signal, the change in the measured potential difference
across a pair of sensing electrodes, was calculated using the 2D software model
developed for the project [35]. In this model, infinitely long lines represent
the electrodes and all quantities are assumed constant by translation along one
direction. This models yields analytical equations for electric field and
potential. The conductivity perturbations were assumed to be infinitely long
cylinders parallel to the axis of the probe and projecting on the calculation
plane as circular disks of conductivity σ=σ_{0}+∆σ.
The voltage change at the sensing electrodes was calculated using the image
theory [36] considering the series of images of the initial source electrodes
in the perturbing cylinder and in the probe. This forms sequences of sources
with rapid convergence of potential and electric field.
The addition of noise to calculated data was achieved
according to (11):
_{}����� (11)
∆u_{2} is the 2‑norm of the data
vector calculated for I_{s}/σ_{m} equal to unity. N_{L}
denotes the noise level (dimensionless) and X a normal Gaussian variable.
Hence, assuming that the variance of sample X_{k} is equal to the
variance of the distribution, the relation between total noise, ε_{T}
and added noise is given by (12):
_{}���������������������������� (12)
Inverse problem
In the linear approximation, the measured potential changes
are assumed proportional to the conductivity changes. The images were
reconstructed solving the normal matrix equation:
������� (13)
∆σ is the unknown vector of conductivity changes, ∆u
is the vector of the measured potential changes and Λ
the sensitivity matrix. The sensitivity matrix is illconditioned.
The plot of singular values shows that the maximal rank of this
matrix is 104 with 16 electrodes (Figure 5), which corresponds
to the number of linearly independent measurements. Fan3 and
fan4 show very similar sets of singular values. Experimental
measurements confirmed that these two types of drive have equivalent
performances so that fan4 was ignored in the following sections.
The largest singular value of adjacent drive is about four times
smaller than that of fan3.
Reconstruction method
The equation was solved as an optimisation problem using Tikhonov's
regularisation method, searching for a vector b minimising the functional F
defined by:
_{}������������ (14)
Symbol w_{p} denote the pnorm of a vector
w and λ is the regularisation parameter. The optimal
value of the regularisation parameter λ was determined
automatically for each data set using the "Lcurve"
procedure. The lower limit of λ (10^{15}) was
determined by successive trials using simulated data. For this
value, the images reconstructed from simulated noiseless data
could not be distinguished from reconstruction noise. The upper
limit (10^{4}) corresponded to clearly excessive image
smoothing producing lobes spreading over the entire image. In
practice, the values found by the automatic Lcurve procedure
ranged roughly from 10^{9 }to 10^{12} for
noiseless simulated data and from 10^{6} to 10^{8}
for experimental data. Regularised matrices were precalculated
using three values of λ per decade. Image reconstruction
therefore consisted of matrixvector products and calculation
of the radius of curvature of the Lcurve. The calculation was
carried out using the circular mesh of Figure 2 using
specific software written in Borland Delphi. The cartesian mesh
for 3D plots of Figures 8 to 10 were obtained by linear interpolation.
With a 1.6 MHz laptop PC computer the image was available
in about 20 seconds.
EXPERIMENTAL SETUP
The experimental data set were collected using a bench system that comprised
a 16electrode mockup probe, 50 mm in diameter, immersed in
a tank filled with tap water modelling a uniform conductivity
medium and the purposebuilt experimental instrumentation [9].
The electrodes, made of brass, formed 50�2
mm^{2} conducting stripes regularly spaced around the
probe. The measurement frequency was 8 kHz [8].
This frequency was chosen for bench experiments as it ensured
satisfactory compromise between the increase of electrodemedium
interface impedance at low frequency and the onset of error
due to stray capacitance with increasing measurement frequency.
The magnitude of the measurement current was 1mA pp. The contact
impedance was about 400 ohms per electrode in tap water.
Tap water has been widely used in EIT as a uniform
conductivity model, especially for feasibility studies and test of
instrumentation, even though it does not have the same electric and dielectric
properties as human body tissues. As a matter of fact, there is no really
satisfactory model of the conductivity of cellular medium. The conductivity of
tap water was 0.039 S/m in this study. Furthermore, the use of a liquid model
makes it easier to place conductivity perturbations in the medium.
The adaptable frontend system (Figure 6) comprised a
controlled amplitude current source based on the circuit of
Figure 3a, 16 input differential voltage amplifiers, 4 multiplexers
for the 16 to 1 selection of electrodes. In this study, the
demodulator produced a DC signal proportional to the magnitude
of the measured voltage. This voltage was digitized with a resolution
equivalent to 17 bits. This was achieved by means of a twostage
system reducing the DC offset of the signal using a D/A converter
and sampling the amplified residual with a 12bit A/D converter.
RESULTS
Images reconstructed from noiseless calculated data
Figure 8 shows the images reconstructed according to (14).
The drive patterns fan3 and adjacent give similar images. For
both types of drive, the resolution is better near the probe
and deteriorates for increasing distance from the probe.
Images reconstructed from calculated data with added
noise
Gaussian noise was added to the calculated data according to
(11). The simulated real part of electrode contact impedance
was 400 Ω, simulating the value measured in vitro.
The amplifier's input related noise figure was taken equal to
13 nV/√Hz. Current noise was ignored. The resulting
total noise figure was 13.2 nV/√Hz. The bandwidth
was B = 208. Figure 9 shows the corresponding
images. The conductivity perturbation does not distinguish from
noise artefact, excepted for fan3 drive pattern at distance
d = 2. This figure illustrates the influence of noise
and the different susceptibility to noise of adjacent and fan3
drive patterns.
Images reconstructed from experimental data
The experimental data sets were collected using the setup
described above. The perturbation used in this study was an
insulating PVC, 16 mm in diameter (normalised radius of
0.32) and located at distance d = 3 from the axis
of the probe. Figure 10 shows the images reconstructed
from the in vitro data and from calculated noiseless
data modelling the same perturbation.
DISCUSSION
The above data and design parameters confirm that EIE is
particularly sensitive to noise. This is mainly due to the rapid decrease of
sensitivity with increasing distance from the probe due to the simultaneous
reduction of the lead fields of current and voltage electrodes. The results
obtained in this study are compatible with prostate size. The noise of the
current injection circuit is negligible compared to the other sources of noise.
The predominant source of noise is the input related noise of the voltage
amplifier. The second largest source of noise is electrode noise. This gives
particular importance to electrode technology in a miniaturised probe.
For tissue characterisation, there is no particular need for high data acquisition
speed. The parameter bandwidth (B) in (9) accounts for measurement
time. The above numerical examples were based on the rate of
1 frame per second with 208 values per frame. The increase of
the total acquisition time by, for instance, a factor of 16,
would be practically acceptable and would increase by 12dB the
signaltonoise ratio. With the limit falloff in 1/d^{4}
of the sensitivity this would theoretically increase by two
the sensitivity range, reduce the measurement current or improve
the quality of the reconstructed images. One possible technique
would be the averaging of 16 successive images. The use of a
series of images would also enable the detection of transient
artefact during data acquisition.
The limit size for the detection of a tumour depends on the conductivity of
the medium, the conductivity contrast of the tumour, the sensitivity
distribution of the used drive pattern, the measurement noise
and the magnitude of the applied current. There is therefore
no unique answer to the question of limit size for detection.
However, the plots in Figure 4 enable the calculation
of estimates under the conditions of example numerical application.
These plots correspond to the limit measurement conditions for
the pixels of the mesh of Figure 2. Straightforward considerations
based on equation 9 yield a value for given current magnitude
and tumour location. Table 2 shows the values obtained with
a conductivity ratio ∆σ/σ = 10%� for 1mA and
10mA currents at the distance of three times the radius of the
probe, assumed as typical range for EIE measurements. For extrapolation
of the figures of table 2 to conductivity changes than 0.1,
the conductivity ratio q=∆σ/σ should be replaced
with the quantity 2q/(q+2) ratio in equation 9 to account for
nonlinearity [35].
The two selected bipolar drive patterns were adjacent and fan3. Adjacent drive
has widely been used in EIT due to its minimal number of measurements
and its full ranked sensitivity matrix. Fan3 was selected in
previous studies for its sensitivity range that was found larger
than that of the other tested patterns [9, 26].
The required number of measurements in fan3 is twice that of
adjacent drive and the sensitivity matrix is not full rank.
However, the additional linearly dependent data can be seen
as an averaging improving signaltonoise ratio in the same
way as the full set of 208 measurements used in EIT to compensate
for reciprocity error. The reconstructed images indicate that
adjacent and fan3 give images of similar quality in absence
of noise. Adjacent drive requires a four time larger measurement
current for a given signaltonoise ratio (Figure 4). This can
be compensated by sufficient current magnitude and measurement
time. Under these conditions, the above noise equation shows
that both types of drive can be used. Preference would then
be given to adjacent drive due to its better matrix conditioning.
In practice, however, the use of small size electrodes could
potentially limit the actual magnitude of the applied current
below the maximal limit of 10 mA rms. Furthermore, the impedance
of electrodes and the output swing of the current source can
also limit the magnitude of the measurement current. Table 2
shows that fan3 enable the detection of larger tumour than fan3
for given measurement conditions. This argument may be decisive
in selecting the drive pattern to be implemented. In any case,
electrode technology will be crucial in the design of probes
and that, finally, EIE seems more appropriate to tissue characterisation
than to high speed imaging.
CONCLUSION
The simulation of operating conditions enabled the quantification of the magnitude
of the measurement current ensuring appropriate signalnoise
ratio. Measurement current of about 1 mA satisfying the
noise condition derived in this study is feasible in practice.
This study also showed that fan3 and adjacent drive patterns
give similar results with noiseless data, but that adjacent
drive requires significantly higher measurement current than
fan3. The equation derived in this study enables the specification
of the hardware system given the operating condition of a given
application.
REFERENCES

Dawids SG. Evaluation of applied potential tomography: a clinician's view. Clin Phys Physiol Meas 1987;8 Suppl A:17580.
[Medline]

Jongschaap HC, Wytch R, Hutchison JM, et al. Electrical impedance tomography: a review of current literature. Eur J Radiol 1994;18(3):16574.
[Medline]

Dijkstra AM, Brown BH, Leathard AD, et al. Clinical applications of electrical impedance tomography. J Med Eng Technol 1993;17(3):8998.
[Medline]

Boone K, Barber D, Brown B. Imaging with electricity: report of the European Concerted Action on Impedance Tomography. J Med Eng Technol 1997;21(6):20132.
[Medline]

Breckon WR, Pidcock MK. Mathematical aspects of impedance imaging. Clin Phys Physiol Meas 1987;8 Suppl A:7784.
[Medline]

Seagar AD, Barber DC, Brown BH. Theoretical limits to sensitivity and resolution in impedance imaging. Clin Phys Physiol Meas 1987;8 Suppl A:1331.
[Medline]

Molebny V, Jossinet J, Skipa O, et al. IIT Inverse Impedance Tomography: Modelling contrast sensitivity. Riu J, Rosell J, Bragos R, et al, eds. Proc Int Conf on Electrical BioImpedance. Barcelona, Spain: Publication Office of UPC, 1998: 4158.

Jossinet J, Marry E, Montalibet A. Electrical impedance endotomography: imaging tissue from inside. IEEE Trans Med Imaging 2002;21(6):5605.
[Medline]

Jossinet J, Marry E, Matias A. Electrical impedance endotomography. Phys Med Biol 2002;47(13):2189202.
[Medline]

Kirkland TA, Lathem JE. The role of transrectal ultrasound (TRUS) in the evaluation of cancer of the prostate. J S C Med Assoc 1994;90(5):2179.
[Medline]

Schmitz G, Ermert H, Senge T. Tissue characterization of the prostate using radio frequency ultrasonic signals. IEEE Trans Ultrason Ferroelectr Freq Control 1999;46:12638.

Feleppa EJ, Ennis RD, Schiff PB, et al. Spectrumanalysis and neural networks for imaging to detect and treat prostate cancer. Ultrason Imaging 2001;23(3):13546.
[Medline]

Stoy RD, Foster KR, Schwan HP. Dielectric properties of mammalian tissues from 0.1 to 100 MHz: a summary of recent data. Phys Med Biol 1982;27(4):50113.
[Medline]

Foster KR, Schwan HP. Dielectric properties of tissues and biological materials: a critical review. Crit Rev Biomed Eng 1989;17(1):25104.
[Medline]

Surowiec AJ, Stuchly SS, Barr JB, et al. Dielectric properties of breast carcinoma and the surrounding tissues. IEEE Trans Biomed Eng 1988;35(4):25763.
[Medline]

Morimoto T, Kimura S, Konishi Y, et al. A study of the electrical bioimpedance of tumors. J Invest Surg 1993;6(1):2532.
[Medline]

Jossinet J. Variability of impedivity in normal and pathological breast tissue. Med Biol Eng Comput 1996;34(5):34650.
[Medline]

Jossinet J. The impedivity of freshly excised human breast tissue. Physiol Meas 1998;19(1):6175.
[Medline]

Lee BR, Roberts WW, Smith DG, et al. Bioimpedance: novel use of a minimally invasive technique for cancer localization in the intact prostate. Prostate 1999;39(3):2138.
[Medline]

Smith DG, Potter SR, Lee BR, et al. In vivo measurement of tumor conductiveness with the magnetic bioimpedance method. IEEE Trans Biomed Eng 2000;47(10):14035.
[Medline]

Jossinet J, Trillaud C, Chesnais S. Impedance changes in liver tissue exposed in vitro to highenergy ultrasound. Physiol Meas 2005;26(2):S4958.
[Medline]
[CrossRef]

Ekstrand V, Wiskell H. Variation in electrical admittivitty after exposure to different types of acoustic energy, an in vitro study. Physica Medica 2004;20:138.

Erol RA, Cherian P, Smallwood RH, et al. Can electrical impedance tomography be used to detect gastrooesophageal reflux? Physiol Meas 1996;17 Suppl 4A:A1417.
[Medline]

Geselowitz DB. An application of electrocardiographic lead theory to impedance plethysmography. IEEE Trans Biomed Eng 1971;18(1):3841.
[Medline]

Jossinet J, Desseux A. Electrical impedance endotomography: sensitivity distribution against bipolar current patterns. Physiol Meas 2004;25(1):35564.
[Medline]

Barker C. Noise connected with electrode process. J Electroanal Chem 1969;21:12736.

Huigen E, Peper A, Grimbergen CA. Investigation into the origin of the noise of surface electrodes. Med Biol Eng Comput 2002;40(3):3328.
[Medline]

Andreucetti, D, Fossi, R, Petrucci, C. Internet resource for the calculation of the dielectric properties of body tissues in frequency range 10 Hz100 GHz [Web Page]. Available at http://niremfifaccnrit/tissprop/. (Accessed September 2005).

Geddes LA, Baker LE. The specific resistance of biological materiala compendium of data for the biomedical engineer and physiologist. Med Biol Eng 1967;5(3):27193.
[Medline]

Nyboer J. Electrorheometric properties of tissues and fluids. Ann N Y Acad Sci 1970;170:41020.

Dawson TW, Caputa K, Stuchly MA. A comparison of 60 Hz uniform magnetic and electric induction in the human body. Phys Med Biol 1997;42(12):231929.
[Medline]

Blad B, Baldetorp B. Impedance spectra of tumour tissue in comparison with normal tissue; a possible clinical application for electrical impedance tomography. Physiol Meas 1996;17 Suppl 4A:A10515.
[Medline]

Tennant TR, Kim H, Sokoloff M, et al. The Dunning model. Prostate 2000;43(4):295302.
[Medline]

Jossinet J, Moulin V, Matias A, et al. In vivo spectrometry of Dunning prostate tumours. Grimmes S, Martinsen OG, Bruvoll H, eds. Proc 11th Int Conf on Electrical BioImpedance. Oslo, Norway: in collaboration with Unipub Vorlag, 2001: 2858.

Jossinet J, Matias A. Nonlinear software phantom for conductivity perturbations in Electrical Impedance Endotomography. EMBEC'05, 3rd European Medical & Biological Engineering Conference. CDROM paper 2415.

Binns KJ, Lawrenson PJ, Trowbridge CW. Charge or current near a circular boundary. The analytical and numerical solution of electric and magnetic field. Chichester, UK: John Wiley and Sons, 1992:2142.
Received 27 September 2005; received in revised form 13 January 2006; accepted 28 March 2006
Correspondence:
Inserm, U556, 151 Cours Albert Thomas, 69424 Lyon cedex 03, France. Tel.: (33) 472681946; Fax: (33) 472681931; Email: jossinet@lyon.inserm.fr (Jacques Jossinet)
Please cite as: Jossinet J, FournierDesseux A, Matias A, Assessment of electrical impedance endotomography for hardware specification, Biomed Imaging Interv J 2006;2(2):e24
<URL: http://www.biij.org/2006/2/e24/>
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