Iterative reconstruction methods using regularization and optimal current patterns in electrical impedance tomography

A Point-Matching Method of Moment with Sparse Bayesian Learning Applied and Evaluated in Dynamic Lung Electrical Impedance Tomography

Dynamic lung imaging is a major application of Electrical Impedance Tomography (EIT) due to EIT's exceptional temporal resolution, low cost and absence of radiation. EIT however lacks in spatial resolution and the image reconstruction is very sensitive to mismatches between the actual object's and the reconstruction domain's geometries, as well as to the signal noise. The non-linear nature of the reconstruction problem may also be a concern, since the lungs' significant conductivity changes due to inhalation and exhalation. In this paper, a recently introduced method of moment is combined with a sparse Bayesian learning approach to address the non-linearity issue, provide robustness to the reconstruction problem and reduce image artefacts. To evaluate the proposed methodology, we construct three CT-based time-variant 3D thoracic structures including the basic thoracic tissues and considering 5 different breath states from end-expiration to end-inspiration. The Graz consensus reconstruction algorithm for EIT (GREIT), the correlation coefficient (CC), the root mean square error (RMSE) and the full-reference (FR) metrics are applied for the image quality assessment. Qualitative and quantitative comparison with traditional and more advanced reconstruction techniques reveals that the proposed method shows improved performance in the majority of cases and metrics. Finally, the approach is applied to single-breath online in-vivo data to qualitatively verify its applicability.

An efficient Point-Matching Method-of-Moments for 2D and 3D Electrical Impedance Tomography Using Radial Basis functions

AbstractObjective: The inverse problem of computing conductivity distributions in 2D and 3D objects interrogated by low frequency electrical signals, which is called Electrical Impedance Tomography (EIT), is treated using a Method-of-Moment technique.

METHODS

A Point-Matching-Method-of-Moment technique is used to formulate a global integral equation solver. Radial Basis Functions are adopted to express the conductivity distribution. Single-step quadratic-norm (L2) and iterative total variation (L1) regularization techniques are exploited to solve the inverse problem.

RESULTS

Simulation and experimental tests on a circular reconstruction domain show satisfactory performance in deriving conductivity distribution, achieving a Correlation Coefficient (CC) up to 0:863 for 70 dB voltage SNR and 0:842 for 40 dB voltage SNR. The proposed methodology with L2-norm regularization provided better results than traditional iterative Gauss-Newtons approach, whereas with L1-norm regularization it showed promising performance. Moreover, 3D reconstructions on a cylindrical cavity demonstrated superior results near the electrodes planes compared to those of the conventional linearized approach. Finally, application to EIT medical data for dynamic lung imaging successfully revealed the breath-cycle conductivity changes.

CONCLUSION

The results show that the proposed method can be effective for both 2D and 3D EIT and applicable to many applications.

SIGNIFICANCE

Strong conductivity variations are successfully tackled with a very good Correlation Coefficient. In contrast to conventional EIT solutions based on weak-form and linearization on small conductivity changes, the proposed method requires only one step to converge with L2-norm regularization. The proposed method with L1-norm regularization also achieves good reconstruction quality with a low number of iterations.

Simultaneous Imaging of Bio- and Non-Conductive Targets by Combining Frequency and Time Difference Imaging Methods in Electrical Impedance Tomography

As a promising medical imaging modality, electrical impedance tomography (EIT) can image the electrical properties within a region of interest using electrical measurements applied at electrodes on the region boundary. This paper proposes to combine frequency and time difference imaging methods in EIT to simultaneously image bio- and non-conductive targets, where the image fusion is accomplished by applying a wavelet-based technique. To enable image fusion, both time and frequency difference imaging methods are investigated regarding the reconstruction of bio- or non-conductive inclusions in the target region at varied excitation frequencies, indicating that none of those two methods can tackle with the scenarios where both bio- and non-conductive inclusions exist. This dilemma can be resolved by fusing the time difference (td) and appropriate frequency difference (fd) EIT images since they are complementary to each other. Through simulation and in vitro experiment, it is demonstrated that the proposed fusion method can reasonably reconstruct both the bio- and non-conductive inclusions within the lung models established to simulate the ventilation process, which is expected to be beneficial for the diagnosis of lung-tissue related diseases by EIT.

Electrical Impedance Tomography-Based Abdominal Subcutaneous Fat Estimation Method Using Deep Learning

This paper proposes a deep learning method based on electrical impedance tomography (EIT) to estimate the thickness of abdominal subcutaneous fat. EIT for evaluating the thickness of abdominal subcutaneous fat is an absolute imaging problem that aims at reconstructing conductivity distributions from current-to-voltage data. Existing reconstruction methods based on EIT have difficulty handling the inherent drawbacks of strong nonlinearity and severe ill-posedness of EIT; hence, absolute imaging may not be possible using linearized methods. To handle nonlinearity and ill-posedness, we propose a deep learning method that finds useful solutions within a restricted admissible set by accounting for prior information regarding abdominal anatomy. We determined that a specially designed training dataset used during the deep learning process significantly reduces ill-posedness in the absolute EIT problem. In the preprocessing stage, we normalize current-voltage data to alleviate the effects of electrodeposition and body geometry by exploiting knowledge regarding electrode positions and body geometry. The performance of the proposed method is demonstrated through numerical simulations and phantom experiments using a 10 channel EIT system and a human-like domain.

Three-Dimensional Electrical Impedance Tomography With Multiplicative Regularization

OBJECTIVE

The multiplicative regularization scheme is applied to three-dimensional electrical impedance tomography (EIT) image reconstruction problem to alleviate its ill-posedness.

METHODS

A cost functional is constructed by multiplying the data misfit functional with the regularization functional. The regularization functional is based on a weighted L²-norm with the edge-preserving characteristic. Gauss-Newton method is used to minimize the cost functional. A method based on the discrete exterior calculus (DEC) theory is introduced to formulate the discrete gradient and divergence operators related to the regularization on unstructured meshes.

RESULTS

Both numerical and experimental results show good reconstruction accuracy and anti-noise performance of the algorithm. The reconstruction results using human thoracic data show promising applications in thorax imaging.

CONCLUSION

The multiplicative regularization can be applied to EIT image reconstruction with promising applications in thorax imaging.

SIGNIFICANCE

In the multiplicative regularization scheme, there is no need to set an artificial regularization parameter in the cost functional. This helps to reduce the workload related to choosing a regularization parameter which may require expertise and many numerical experiments. The DEC-based method provides a systematic and rigorous way to formulate operators on unstructured meshes. This may help EIT image reconstructions using regularizations imposing structural or spatial constraints.

Impedance imaging with first-order TV regularization

EIT problem is a typical inverse problem with serious ill-posedness. In general, regularization techniques are necessary for such ill-posed inverse problems. To overcome ill-posedness, the total variation (TV) regularization is widely used and it is also successfully applied to EIT. For realtime monitoring, a fast and robust image reconstruction algorithm is required. By exploiting recent advances in optimization, we propose a first-order TV algorithm for EIT, which simply consists of matrix-vector multiplications and in which the sparse structure of the system can be easily exploited. Furthermore, a typical smoothing parameter to overcome nondifferentibility of the TV term is not needed and a closed form solution can be applied in part using soft thresholding. It shows a fast reconstruction in the beginning. Numerical experiments using simulated data and real experimental data support our claim.

Precise two-dimensional D-bar reconstructions of human chest and phantom tank via sinc-convolution algorithm

BACKGROUND

Electrical Impedance Tomography (EIT) is used as a fast clinical imaging technique for monitoring the health of the human organs such as lungs, heart, brain and breast. Each practical EIT reconstruction algorithm should be efficient enough in terms of convergence rate, and accuracy. The main objective of this study is to investigate the feasibility of precise empirical conductivity imaging using a sinc-convolution algorithm in D-bar framework.

METHODS

At the first step, synthetic and experimental data were used to compute an intermediate object named scattering transform. Next, this object was used in a two-dimensional integral equation which was precisely and rapidly solved via sinc-convolution algorithm to find the square root of the conductivity for each pixel of image. For the purpose of comparison, multigrid and NOSER algorithms were implemented under a similar setting. Quality of reconstructions of synthetic models was tested against GREIT approved quality measures. To validate the simulation results, reconstructions of a phantom chest and a human lung were used.

RESULTS

Evaluation of synthetic reconstructions shows that the quality of sinc-convolution reconstructions is considerably better than that of each of its competitors in terms of amplitude response, position error, ringing, resolution and shape-deformation. In addition, the results confirm near-exponential and linear convergence rates for sinc-convolution and multigrid, respectively. Moreover, the least degree of relative errors and the most degree of truth were found in sinc-convolution reconstructions from experimental phantom data. Reconstructions of clinical lung data show that the related physiological effect is well recovered by sinc-convolution algorithm.

CONCLUSIONS

Parametric evaluation demonstrates the efficiency of sinc-convolution to reconstruct accurate conductivity images from experimental data. Excellent results in phantom and clinical reconstructions using sinc-convolution support parametric assessment results and suggest the sinc-convolution to be used for precise clinical EIT applications.

In vivo impedance imaging with total variation regularization

We show that electrical impedance tomography (EIT) image reconstruction algorithms with regularization based on the total variation (TV) functional are suitable for in vivo imaging of physiological data. This reconstruction approach helps to preserve discontinuities in reconstructed profiles, such as step changes in electrical properties at interorgan boundaries, which are typically smoothed by traditional reconstruction algorithms. The use of the TV functional for regularization leads to the minimization of a nondifferentiable objective function in the inverse formulation. This cannot be efficiently solved with traditional optimization techniques such as the Newton method. We explore two implementations methods for regularization with the TV functional: the lagged diffusivity method and the primal dual-interior point method (PD-IPM). First we clarify the implementation details of these algorithms for EIT reconstruction. Next, we analyze the performance of these algorithms on noisy simulated data. Finally, we show reconstructed EIT images of in vivo data for ventilation and gastric emptying studies. In comparison to traditional quadratic regularization, TV regularization shows improved ability to reconstruct sharp contrasts.

A reconstruction algorithm for breast cancer imaging with electrical impedance tomography in mammography geometry

The conductivity and permittivity of breast tumors are known to differ significantly from those of normal breast tissues, and electrical impedance tomography (EIT) is being studied as a modality for breast cancer imaging to exploit these differences. At present, X-ray mammography is the primary standard imaging modality used for breast cancer screening in clinical practice, so it is desirable to study EIT in the geometry of mammography. This paper presents a forward model of a simplified mammography geometry and a reconstruction algorithm for breast tumor imaging using EIT techniques. The mammography geometry is modeled as a rectangular box with electrode arrays on the top and bottom planes. A forward model for the electrical impedance imaging problem is derived for a homogeneous conductivity distribution and is validated by experiment using a phantom tank. A reconstruction algorithm for breast tumor imaging based on a linearization approach and the proposed forward model is presented. It is found that the proposed reconstruction algorithm performs well in the phantom experiment, and that the locations of a 5-mm-cube metal target and a 6-mm-cube agar target could be recovered at a target depth of 15 mm using a 32 electrode system.

Usefulness of ultrasonic strain measurement-based shear modulus reconstruction for diagnosis and thermal treatment

We previously reported an ultrasonic strain measurement-based one-dimensional (1-D) shear modulus reconstruction technique using a regularization method for differential diagnosis of malignancies on human superficial tissues (e.g., breast tissues). Here, ultrasonic strain measurement-based 2-D and 3-D shear modulus reconstruction techniques are described, and the 1-D technique is reviewed and subsequently applied to various human in vivo tissues, including deeply situated tissues (e.g., liver). Because soft tissues are deformed in 3-D space by externally situated arbitrary mechanical sources, the accuracy of the low-dimensional (i.e., 1-D or 2-D) reconstructions is lower to that of 3-D reconstruction due to occurrence of erroneous reconstruction artifacts (i.e., the reconstructed modulus is different than reality). These artifacts are confirmed on simulated inhomogeneous cubic phantoms containing a spherical homogenous inclusion using numerically calculated deformation data. The superiority of quasi-real-time imaging of the shear modulus is then demonstrated by comparing it with conventional B-mode imaging and strain imaging from the standpoints of monitoring the effectiveness of minimally invasive thermal therapy as well as differential diagnosis. Because the 2-D and 3-D techniques require special ultrasonic (US) equipment, the 1-D technique using conventional US imaging equipment is used, even though erroneous artifacts will occur. Specifically, the 1-D technique is applied as a diagnostic tool for differentiating malignancies in human in vivo liver and breast tissue, and a monitoring technique for determining the effectiveness of interstitial electromagnetic wave (micro and rf) thermal therapy on human in vivo liver and calf in vitro liver. Even when using the 1-D technique, reconstructed shear moduli were confirmed to be a suitable measure for monitoring thermal treatment as well as differential diagnosis. These results are encouraging in that they will promote use of 2-D and 3-D reconstruction techniques.

Dynamic electrical impedance imaging with the interacting multiple model scheme

In this paper, an effective dynamical EIT imaging scheme is presented for on-line monitoring of the abruptly changing resistivity distribution inside the object, based on the interacting multiple model (IMM) algorithm. The inverse problem is treated as a stochastic nonlinear state estimation problem with the time-varying resistivity (state) being estimated on-line with the aid of the IMM algorithm. In the design of the IMM algorithm multiple models with different process noise covariance are incorporated to reduce the modeling uncertainty. Simulations and phantom experiments are provided to illustrate the proposed algorithm.

Induced-current electrical impedance tomography: a 2-D theoretical simulation

A reconstruction algorithm, based on the modified Newton-Raphson algorithm, was developed for induced-current electrical impedance tomography and studied in theoretical two-dimensional geometry representing a human thorax. The finite-volume method was applied for the discretization of the physical domain, resulting in a symbolic representation of the Jacobian matrix, which is accurate and fast to construct. Several system configurations, differing in the number of excitation coils and electrodes, were simulated, and the performance in thoracic imaging was studied. It was found that a six-coil system shows a significant 40% improvement of conductivity values reconstruction over the three-coil system (an error of 2.06 omega(-1) compared with 3.44 omega(-1)). A number of 32 electrodes was found to be sufficient, being the smallest number of electrodes to still provide a reasonable performance (only 4.2% degradation in average conductivity error compared with the maximum possible 106-electrode system).

An algorithm using projection onto subspace of prior distributions for long-wavelength sound wave CT

The stationary long-wavelength sound wave computed tomography is a nonlinear inverse problem that requires the use of prior information of the object. However, the prior assumptions that are usually used in similar inverse problems are more or less inappropriate. In this paper, a new reconstruction algorithm using the prior information is proposed and compared with subspace regularization method and Marquardt reconstruction algorithms. The simulation shows that the proposed algorithm can give a better reconstructed result whether the actual distribution is compatible or incompatible with the prior distributions.

The boundary element method in the forward and inverse problem of electrical impedance tomography

In this paper, a new formulation of the reconstruction problem of electrical impedance tomography (EIT) is proposed. Instead of reconstructing a complete two-dimensional picture, a parameter representation of the gross anatomy is formulated, of which the optimal parameters are determined by minimizing a cost function. The two great advantages of this method are that the number of unknown parameters of the inverse problem is drastically reduced and that quantitative information of interest (e.g., lung volume) is estimated directly from the data, without image segmentation steps. The forward problem of EIT is to compute the potentials at the voltage measuring electrodes, for a given set of current injection electrodes and a given conductivity geometry. In this paper, it is proposed to use an improved boundary element method (BEM) technique to solve the forward problem, in which flat boundary elements are replaced by polygonal ones. From a comparison with the analytical solution of the concentric circle model, it appears that the use of polygonal elements greatly improves the accuracy of the BEM, without increasing the computation time. In this formulation, the inverse problem is a nonlinear parameter estimation problem with a limited number of parameters. Variants of Powell's and the simplex method are used to minimize the cost function. The applicability of this solution of the EIT problem was tested in a series of simulation studies. In these studies, EIT data were simulated using a standard conductor geometry and it was attempted to find back this geometry from random starting values. In the inverse algorithm, different current injection and voltage measurement schemes and different cost functions were compared. In a simulation study, it was demonstrated that a systematic error in the assumed lung conductivity results in a proportional error in the lung cross sectional area. It appears that our parametric formulation of the inverse problem leads to a stable minimization problem, with a high reliability, provided that the signal-to-noise ratio is about ten or higher.

An iterative Newton-Raphson method to solve the inverse admittivity problem

By applying electrical currents to the exterior of a body using electrodes and measuring the voltages developed on these electrodes, it is possible to reconstruct the electrical properties inside the body. This technique is known as electrical impedance tomography. The problem is nonlinear and ill conditioned meaning that a large perturbation in the electrical properties far away from the electrodes produces a small voltage change on the boundary of the body. This paper describes an iterative reconstruction algorithm that yields approximate solutions of the inverse admittivity problem in two dimensions. By performing multiple iterations, errors in the conductivity and permittivity reconstructions that result from a linearized solution to the problem are decreased. A finite-element forward-solver, which predicts voltages on the boundary of the body given knowledge of the applied current on the boundary and the electrical properties within the body, is required at each step of the reconstruction algorithm. Reconstructions generated from numerical data are presented that demonstrate the capabilities of this algorithm.

A robust numerical solution to reconstruct a globally relative shear modulus distribution from strain measurements

To noninvasively quantify tissue elasticity for differentiating malignancy of soft tissue, we previously proposed a two-dimensional (2-D) mechanical inverse problem in which simultaneous partial differential equations (PDE's) represented the target distribution globally of relative shear moduli with respect to reference shear moduli such that the relative values could be determined from strain distributions obtained by conventional ultrasound (US) or nuclear magnetic resonance (NMR) imaging-based analysis. Here, we further consider the analytic solution in the region of interest, subsequently demonstrating that the problem is inevitably ill-conditioned in real-world applications, i.e., noise in measurement data and improper configurations of mechanical sources/reference regions make it impossible to guarantee the existence of a stable and unique target global distribution. Next, based on clarification of the inherent problematic conditions, we describe a newly developed numerical-based implicit-integration approach that novelly incorporates a computationally efficient regularization method designed to solve this differential inverse problem using just low-pass filtered spectra derived from strain measurements. To evaluate method effectiveness, reconstructions of the global distribution are carried out using intentionally created ill-conditioned models. The resultant reconstructions indicate the robust solution is highly suitable, while also showing it has high potential to be applied in the development of an effective yet versatile diagnostic tool for quantifying the distribution of elasticity in various soft tissues.

Nonlinear reconstruction constrained by image properties in electrical impedance tomography

It is proposed that image quality, for example the degree of roughness, in electrical impedance tomography is the essential measure required to regularize nonlinear reconstruction. Most previously published work has addressed efficiency, stabilization and speed of reconstruction and has overlooked the targeted image qualities. The measure of quality adopted is the mean square gradient of the logarithm of resistivity which, in combination with the chi2 statistic as a measure of the fit to the data, is minimized by iteration until convergence to a stable image is achieved. This penalty function is invariant to the scale of the resistivity and to the interchange of resistivity and conductivity. The algorithm is tested on computer simulated data and on measurements from a cylindrical tank of electrolyte. The results demonstrate the increased image definition that it would be possible to achieve as data acquisition systems are improved. The images show how a reduction in resolution can be traded for reduced noise artefacts, by selecting an appropriate target chi2.

Tikhonov regularization and prior information in electrical impedance tomography

The solution of impedance distribution in electrical impedance tomography is a nonlinear inverse problem that requires the use of a regularization method. The generalized Tikhonov regularization methods have been popular in the solution of many inverse problems. The regularization matrices that are usually used with the Tikhonov method are more or less ad hoc and the implicit prior assumptions are, thus, in many cases inappropriate. In this paper, we propose an approach to the construction of the regularization matrix that conforms to the prior assumptions on the impedance distribution. The approach is based on the construction of an approximating subspace for the expected impedance distributions. It is shown by simulations that the reconstructions obtained with the proposed method are better than with two other schemes of the same type when the prior is compatible with the true object. On the other hand, when the prior is incompatible with the true object, the method will still give reasonable estimates.

Regularized reconstruction in electrical impedance tomography using a variance uniformization constraint

This paper describes a new approach to reconstruction of the conductivity field in electrical impedance tomography. Our goal is to improve the tradeoff between the quality of the images and the numerical complexity of the reconstruction method. In order to reduce the computational load, we adopt a linearized approximation to the forward problem that describes the relationship between the unknown conductivity and the measurements. In this framework, we focus on finding a proper way to cope with the ill-posed nature of the problem, mainly caused by strong attenuation phenomena; this is done by devising regularization techniques well suited to this particular problem. First, we propose a solution which is based on Tikhonov regularization of the problem. Second, we introduce an original regularized reconstruction method in which the regularization matrix is determined by space-uniformization of the variance of the reconstructed condictivities. Both methods are nonsupervised, i.e., all tuning parameters are automatically determined from the measured data. Tests performed on simulated and real data indicate that Tikhonov regularization provides results similar to those obtained with iterative methods, but with a much smaller amount of computations. Regularization using a variance uniformization constraint yields further improvements, particularly in the central region of the unknown object where attenuation is most severe. We anticipate that the variance uniformization approach could be adapted to iterative methods that preserve the nonlinearity of the forward problem. More generally, it appears as a useful tool for solving other severely ill-posed reconstruction problems such as eddy current tomography.

Impedance tomography: computational analysis based on finite element models of a cylinder and a human thorax

A direct image reconstruction method of electrical impedance tomography (EIT) is evaluated using three-dimensional (3-D) finite element models of cylindrical and torso-shaped volume conductors. The cylindrical model is used to examine the effect of electrode configurations and the sensitivity to off-plane objects and to noise in the measured data. It is also used to validate the modeling procedures by comparison with experimental data acquired from a similar cylindrical tank filled with saline. Simulation results show only minor differences in performance between the various electrode configurations. In the second part, a realistic human thorax model constructed from CT images is used to evaluate monitoring of pulmonary edema by EIT. The conductivity, volume, and vertical position of an abnormal region in the lungs are varied to simulate the progress of edema. Dynamic EIT images are reconstructed from data computed for the inhomogeneous thorax (heart and lungs) as the reference set and a realistic amount of noise is added to reproduce the conditions in which the technique would be used in practice. Simulation results show that a 10 ml edema region with a conductivity equal to that of blood can be detected at a 40 dB signal-to-noise ratio (SNR). Detection of a smaller volume, in the order of 2 ml, should be possible by improving either the instrumentation to achieve 60 dB SNR or the performance of reconstruction algorithms.

Temperature field estimation using electrical impedance profiling methods. I. Reconstruction algorithm and simulated results

Algorithmic methods for estimating complete temperature fields during hyperthermia treatments based on surface and internal electrical measurements are presented. The techniques utilized draw upon impedance imaging concepts, but rather than limit the measurements to positions on the body surface, internal impedance recording sites are allowed. Theoretical simulations show that this strategy improves the reconstructed image in the target region when either internal measurement locations are added to a given number of external recording sites or some external measurement locations are replaced by internal recording positions. The algorithms developed are tested on a set of problems with increasing levels of complexity. The culmination of these investigations is a complete simulation of a hyperthermia treatment and reconstruction of a thermal image for a body cross-section of an actual cancer patient. The results of this work suggest that the surface plus internal measurement approach holds some promise as a method for estimating temperature distributions during hyperthermia treatments. However, the simulations while promising are idealizations in that they are two-dimensional with modest levels of additive noise. In a companion paper, we explore the viability of this approach in several laboratory phantom experiments which include both static and heat-induced transient electrical property profiles.

Bayesian approach with the maximum entropy principle in image reconstruction from microwave scattered field data

Microwave imaging is of great interest in medical applications owing to its high sensitivity with respect to dielectric properties. It allows detection of very small inhomogeneities. The image reconstruction employing the microwave inverse scattering consists of reconstructing the image of an object from the scattered field measured behind the object. This reconstruction runs up against the nonuniqueness of the solution of the inverse scattering problem. The authors propose to solve the ill-posed inverse problem by a statistical regularization method based on the Bayesian maximum a posteriori estimation where the principle of maximum entropy is used for assigning the a priori laws. The results obtained demonstrate the power and potential of this method in image reconstruction.

Time-harmonic impedance tomography using the T-matrix method

A time-harmonic formulation for the electrical impedance tomography (EIT) inverse problem accounting for electrodynamic effects is derived. This work abandons the standard electrostatic impedance model for a full-wave T-matrix model. The advantage of this method is an accurate physical model that includes finite frequency effects, such as diffusion phenomena, and electrode contact impedance effects. This model offers the potential for increased resolution and larger invertible contrast objects than other methods when used on experimental data, because it may represent a more realistic physical model. Also, an accurate gradient matrix is used in the Newton iterative method so the image reconstruction converges in a few iterations. These advantages are realized with no increase in the computational complexity of this algorithm, compared to the static finite element model. A calibration technique is suggested for measurement systems, to test the validity of a theoretical model that includes electrode contact impedance effects.

Finite element modeling of electrode-skin contact impedance in electrical impedance tomography

In electrical impedance tomography (EIT), we inject currents through and measure voltages from an array of surface electrodes. The measured voltages are sensitive to electrode-skin contact impedance because the contact impedance and the current density through this contact impedance are both high. We used large electrodes to provide a more uniform current distribution and reduce the contact impedance. A large electrode differs from a point electrode in that it has shunting and edge effects which cannot be modeled by a single resistor. We used the finite element method (FEM) to study the electric field distributions underneath an electrode, and developed three models: a FEM model, a simplified FEM model and a weighted load model. We showed that the FEM models considered both shunting and edge effects and matched closely the experimental measurements. FEM models for electrodes can be used to improve the performance of an electrical impedance tomography reconstruction algorithm.

Using compound electrodes in electrical impedance tomography

In electrical impedance tomography, we inject currents and measure voltages to estimate an object's resistivity distribution. The electrode configuration affects measured voltage data because the electrode-skin contact impedance is high and varies with electrode location. We developed a compound electrode which is composed of two electrodes: a large outer electrode to inject current and a small inner electrode to sense voltage. We used these compound electrodes to measure voltages from a physical phantom. We showed that the measured voltages from the compound electrodes are smaller in amplitude than those from conventional electrodes. This demonstrates that the compound electrode can minimize contact impedance voltage drop from the measured data. We used a finite element model for the compound electrode and incorporated the model into the regularized Newton-Raphson reconstruction algorithm. We performed a sensitivity study and showed that the reconstructed resistivity distributions are less dependent on the unknown contact resistance values for a compound electrode than a conventional electrode and that the use of a compound electrode results in improved images for the reconstruction algorithm.