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Number of Pages : X, Skip to main content. Search SpringerLink Search. Editors: view affiliations J. Buying options eBook EUR Softcover Book EUR Hardcover Book EUR Learn about institutional subscriptions. Table of contents 18 chapters Search within book Search.

Page 1 Navigate to page number of 2. Front Matter Pages i-ix. Tang Pages Pages Enz, A. El-Hoiydi, J. Decotignie, A. Porret, T. Melly, V. Peiris Pages 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 [ 7 - 9 ]. 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 [ 10 - 12 ]. This approach has been supported by the known significant conductivity differences between cancerous and normal tissue observed in various organs [ 13 - 18 ], 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. Sketch of the tip of a electrode probe for EIE. The insulating core may consist of a cylindrical tube enabling to pass electrode leads. 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.

The boundary profile is unknown and variable in EIT according to the morphology of the examined region and inter-patient 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. 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.

The measurements in a semi-infinite 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 semi-infinite 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 4-electrode 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 The drive pattern giving the largest sensitivity range was selected based on these sensitivity maps. This animation displays successively the sensitivity maps of the 49 basic patterns from which any electrode pattern can be derived by symmetry and rotation.

This animation does not display any time varying process. The purpose is to illustrate the influence of drive pattern on the sensitivity distribution around an EIE probe comprising 16 electrodes. The red colours show positive values of sensitivity and blue colours to negative ones. The highest magnitude values are near the electrode. The change is 10 dB from one colour level to the next. The central, background colour corresponds to low absolute values of sensitivity, either positive or negative.

As there are 11 levels, the background corresponds to sensitivity smaller than 50 dB compared to the maximum. The maps were drawn varying the current injection pair of electrodes and keeping constant the sensing pair. The radius of the mapped zone is 3 times the radius of the probe. 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.

In this study, the measurements were carried out according to the 4-electrode 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 reconstruction mesh consisted of N L concentric layers of N A trapezoidal pixels. The outer radius of the mesh was denoted R max. 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 :. Reconstruction mesh used in this study. The central area corresponds to the insulating core of the probe. There are 14 layers and 64 angular sectors forming trapezoidal pixels of constant profile but varying dimensions.

In this mesha 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 3-cm 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. From these dimensions, the value of R max chosen was equal to 4 times the radius of the probe. This justified the use of layer mesh. 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.

In the present study, the conductivity change was assumed to be uniform within the volume element. 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 non-perturbed medium. The so-called "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 4-electrode patterns where both voltage and current electrode pairs consist of adjacent electrodes. Fan3 consists of 4-electrode 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.

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. Construction of fan3 pattern. The current injection circuit, S , is successively connected to the pairs of source electrodes.

Fan3 comprises two groups of patterns. The first group uses electrode 3 successively associated to electrodes 9 to 15 7 patterns. The second group not shown in this figure for clarity consists of symmetrical patterns versus the axis of symmetry of the voltage electrodes.

In this group electrode 14 is successively associated to electrodes 2 to 8. This section describes the sources of noise and presents the derivation of an equation for the measurement current. It was assumed in this study that the minimum conductivity change to be measured, denoted? 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.

Hence, with a electrode probe and the 64 angular sectors, the relevant parameter is then the fourth largest sensitivity magnitude in each layer of the mesh. Three types of noise have been considered in the present study: electrode noise, electronic noise and current noise. Electrode noise's origin is electrochemical. Figure 3 shows two circuits commonly used for voltage-to-current conversion: Howland's circuit and differencing amplifier. 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. The injected noise current, of rms value denoted i noise , is then given by 5 where B is the bandwidth Hz of the system:. This noise current produces an error voltage across the measured impedance Z x. 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".

Limit values of the 2D-calculated and experimental geometry factors for fan3 and adjacent drive patterns. The rms value of the amplifier input related noise voltage is given by 7 :. The noise figure Nf V is given in technical data sheets of operational amplifiers. The contact impedance of one electrode of this probe in tap water of conductivity 0. 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.

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?

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. The noise figure due to the current injecting circuit can be derived from 6. The total noise figure in this numerical example is then about Assuming that the distribution of noise amplitude is Gaussian, one may take 3.

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:. The mean conductivity value determines the magnitude of the measured impedance Z x. For the prostate, Dawson [ 31 ] reports a value of 0.

The conductivity values calculated in section "Numerical application" from this resource for normal prostate tissue 0. Blad [ 32 ] has proposed a general conductivity ratio between normal tissue and cancer tissue of about 0. Conductivity ratios of 0. 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. Using the figures and the values for reference prostate tissue of section "Numerical application", the coarse estimates of conductivity ratios are about 0.

The conductivity was smaller in cancer tissue than in prostate tissue at kHz, 1 MHz and 2 MHz with conductivity ratios of 0. Smith, by measuring eddy currents using a magnetic coil at 2. The conductivity was lower in AT2 and AT3 tumours 0. 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. Two circuits for voltage-to-current conversion commonly used in impedance measurement.

Using a difference amplifier b , the voltage gain and noise gain are both equal to unity. This section describes the simulation of an EIE application using calculated and experimental data. The model described below was used for the simulation of two conductivity perturbations, of radius 0.

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 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 :. N L denotes the noise level dimensionless and X a normal Gaussian variable. In the linear approximation, the measured potential changes are assumed proportional to the conductivity changes. The images were reconstructed solving the normal matrix equation:. The sensitivity matrix is ill-conditioned. The plot of singular values shows that the maximal rank of this matrix is 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. The equation was solved as an optimisation problem using Tikhonov's regularisation method, searching for a vector b minimising the functional F defined by:. 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 L-curve procedure ranged roughly from 10 -9 to 10 for noiseless simulated data and from 10 -6 to 10 -8 for experimental data. Image reconstruction therefore consisted of matrix-vector products and calculation of the radius of curvature of the L-curve.

The calculation was carried out using the circular mesh of Figure 2 using specific software written in Borland Delphi. With a 1. Images reconstructed from calculated noiseless data for adjacent and fan3 drive patterns. In this figure, the sign of the reconstructed values has been inversed to display the upward negative perturbations of conductivity. The experimental data set were collected using a bench system that comprised a electrode mock-up probe, 50 mm in diameter, immersed in a tank filled with tap water modelling a uniform conductivity medium and the purpose-built experimental instrumentation [ 9 ].

The measurement frequency was 8 kHz [ 8 ]. This frequency was chosen for bench experiments as it ensured satisfactory compromise between the increase of electrode-medium 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 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. Furthermore, the use of a liquid model makes it easier to place conductivity perturbations in the medium. The adaptable front-end 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.

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It is the value of these two resistors that govern the gain of the operational amplifier circuit as they determine the level of feedback. The gain of the non-inverting circuit for the operational amplifier is easy to determine. The calculation hinges around the fact that the voltage at both inputs is the same. This arises from the fact that the gain of the amplifier is exceedingly high. If the output of the circuit remains within the supply rails of the amplifier, then the output voltage divided by the gain means that there is virtually no difference between the two inputs.

As the input to the op-amp draws no current this means that the current flowing in the resistors R1 and R2 is the same. The voltage at the inverting input is formed from a potential divider consisting of R1 and R2, and as the voltage at both inputs is the same, the voltage at the inverting input must be the same as that at the non-inverting input.

Hence the voltage gain of the circuit Av can be taken as:. As an example, an amplifier requiring a gain of eleven could be built by making R2 47 k ohms and R1 4. For most circuit applications any loading effect of the circuit on previous stages can be completely ignored as it is so high, unless they are exceedingly sensitive.

This is a significant difference to the inverting configuration of an operational amplifier circuit which provided only a relatively low impedance dependent upon the value of the input resistor. In most cases it is possible to DC couple the circuit. Where AC coupling is required it is necessary to ensure that the non-inverting has a DC path to earth for the very small input current that is needed to bias the input devices within the IC.

This can be achieved by inserting a high value resistor, R3 in the diagram, to ground as shown below. If this resistor is not inserted the output of the operational amplifier will be driven into one of the voltage rails.

The cut off point occurs at a frequency where the capacitive reactance is equal to the resistance. Similarly the output capacitor should be chosen so that it is able to pass the lowest frequencies needed for the system. In this case the output impedance of the op amp will be low and therefore the largest impedance is likely to be that of the following stage.

Operational amplifier circuits are normally designed to operate from dual supplies, e. Negative sign implies that the output signal is negated. The circuit diagram of a basic inverting amplifier using opamp is shown below. The input and output waveforms of an inverting amplifier using opamp is shown below. The graph is drawn assuming that the gain Av of the amplifier is 2 and the input signal is a sine wave.

A simple practical inverting amplifier using IC is shown below. It can be used in a verity of applications like integrator, differentiator, voltage follower, amplifier etc. The IC has an integrated compensation network for improving stability and has short circuit protection. Signal to be amplified is applied to the inverting pi pin2 of the IC. Non inverting pin pin3 is connected to ground.

R1 is the input resistor and Rf is the feedback resistor. Rf and R1 together sets the gain of the amplifier. RL is the load resistor and the amplified signal will be available across it. POT R2 can be used for nullifying the output offset voltage.

If you are planning to assemble the circuit, the power supply must be well regulated and filtered.

1) The op amp has infinite open-loop gain. source.) golden rule 2. output so that the voltage difference between the + and − inputs is zero (V+ = V−). When operating at unity gain (no amplification), the noninverting amplifier reduces to a voltage follower, where the output voltage is identical to the input. A synthesis procedure based on the signal flow graph for generating biquadratic active filters using operational transconductance amplifiers and grounded.