A robust image reconstruction algorithm and its parallel implementation in electrical impedance tomography

Suppressing interferences of EIT on synchronous recording EEG based on comb filter for seizure detection

Background and objective

The purpose of this study was to eliminate the interferences of electrical impedance tomography (EIT) on synchronous recording electroencephalography (EEG) for seizure detection.

Methods

The simulated EIT signal generated by COMSOL Multiphysics was superimposed on the clinical EEG signal obtained from the CHB-MIT Scalp EEG Database, and then the spectrum features of superimposed mixed signals were analyzed. According to the spectrum analysis, in addition to high-frequency interference at 51.2 kHz related to the drive current, there was also low-frequency interference caused by switching of electrode pairs, which were used to inject drive current. A low pass filter and a comb filter were used to suppress the high-frequency interference and low-frequency interference, respectively. Simulation results suggested the low-pass filter and comb filter working together effectively filtered out the interference of EIT on EEG in the process of synchronous monitoring.

Results

As a result, the normal EEG and epileptic EEG could be recognized effectively. Pearson correlation analysis further confirmed the interference of EIT on EEG was effectively suppressed.

Conclusions

This study provides a simple and effective interference suppression method for the synchronous monitoring of EIT and EEG, which could be served as a reference for the synchronous monitoring of EEG and other medical electromagnetic devices.

Low Cost, High Performance, 16-Channel Microwave Measurement System for Tomographic Applications

We have developed a multichannel software defined radio-based transceiver measurement system for use in general microwave tomographic applications. The unit is compact enough to fit conveniently underneath the current illumination tank of the Dartmouth microwave breast imaging system. The system includes 16 channels that can both transmit and receive and it operates from 500 MHz to 2.5 GHz while measuring signals down to −140 dBm. As is the case with multichannel systems, cross-channel leakage is an important specification and must be lower than the noise floors for each receiver. This design exploits the isolation inherent when the individual receivers for each channel are physically separate; however, these challenging specifications require more involved signal isolation techniques at both the system design level and the individual, shielded component level. We describe the isolation design techniques for the critical system elements and demonstrate specification compliance at both the component and system level.

Neural network-based supervised descent method for 2D electrical impedance tomography

OBJECTIVE

In this work, we study the application of the neural network-based supervised descent method (NN-SDM) for 2D electrical impedance tomography.

APPROACH

The NN-SDM contains two stages: offline training and online prediction. In the offline stage, neural networks are iteratively applied to learn a sequence of descent directions for minimizing the objective function, where the training data set is generated in advance according to prior information or historical data. In the online stage, the trained neural networks are directly used to predict the descent directions.

MAIN RESULTS

Numerical and experimental results are reported to assess the efficiency and accuracy of the NN-SDM for both model-based and pixel-based inversions. In addition, the performance of the NN-SDM is compared with the linear SDM (LSDM), an end-to-end neural network (E2E-NN) and the Gauss-Newton (GN) method. The results demonstrate that the NN-SDM achieves faster convergence than the LSDM and GN method, and achieves a stronger generalization ability than the E2E-NN.

SIGNIFICANCE

The NN-SDM combines the strong non-linear fitting ability of the neural network and good generalization capability of the supervised descent method (SDM), which also provides good flexibility to incorporate prior information and accelerates the convergence of iteration.

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.

Arts of electrical impedance tomographic sensing

This paper reviews governing theorems in electrical impedance sensing for analysing the relationships of boundary voltages obtained from different sensing strategies. It reports that both the boundary voltage values and the associated sensitivity matrix of an alternative sensing strategy can be derived from a set of full independent measurements and sensitivity matrix obtained from other sensing strategy. A new sensing method for regional imaging with limited measurements is reported. It also proves that the sensitivity coefficient back-projection algorithm does not always work for all sensing strategies, unless the diagonal elements of the transformed matrix, A(T)A, have significant values and can be approximate to a diagonal matrix. Imaging capabilities of few sensing strategies were verified with static set-ups, which suggest the adjacent electrode pair sensing strategy displays better performance compared with the diametrically opposite protocol, with both the back-projection and multi-step image reconstruction methods. An application of electrical impedance tomography for sensing gas in water two-phase flows is demonstrated. This article is part of the themed issue 'Supersensing through industrial process tomography'.

Trackability evaluation of reconstruction algorithms to the change of measured objects in electrical tomography

The continuous monitoring of the changing process is an important application field of electrical tomography (ET). In this changing process, the size, position and shape of measured objects are always alterative. The trackability of algorithms to the change of measured objects is important to the application of ET. The single object model group and two-object-model group were established to simulate the change of measured objects. The single object model group includes the circle model group and square model group. The suitable evaluation parameters were designed to evaluate the trackability of the different algorithms quantitatively, which includes the single image parameter and group parameter. Evaluation software was developed, which can generate measured boundary data of different models, complete reconstructed image greying, calculate evaluation parameters and plot parameter curves, etc. Furthermore, the trackability of ten selected algorithms was evaluated by this evaluation software. The results show that the trackability of the different algorithms is different in the evaluation of the different model group. Therefore, the different model group should be established according to the application requirement. Then the suitable algorithm for a particular application could be chosen through the evaluation process.

Interpretation of the modality of touch on an artificial arm covered with an EIT-based sensitive skin

During social interaction humans extract important information from tactile stimuli that can improve their understanding of the interaction. The development of a similar capability in a robot will contribute to the future success of intuitive human–robot interaction. This paper presents a thin, flexible and stretchable artificial skin for robotics based on the principle of electrical impedance tomography. This skin, which can be used to extract information such as location, duration and intensity of touch, was used to cover the forearm and upper arm of a full-size mannequin. A classifier based on the ‘LogitBoost’ algorithm was used to classify the modality of eight different types of touch applied by humans to the mannequin arm. Experiments showed that the modality of touch was correctly classified in approximately 71% of the trials. This was shown to be comparable to the accuracy of humans when identifying touch. The classification accuracies obtained represent significant improvements over previous classification algorithms applied to artificial sensitive skins. It is shown that features based on touch duration and intensity are sufficient to provide a good classification of touch modality. Gender and cultural background were examined and found to have no statistically significant effect on the classification results.

Modelling of an oesophageal electrode for cardiac function tomography

There is a need in critical care units for continuous cardiopulmonary monitoring techniques. ECG gated electrical impedance tomography is able to localize the impedance variations occurring during the cardiac cycle. This method is a safe, inexpensive and potentially fast technique for cardiac output imaging but the spatial resolution is presently low, particularly for central locations such as the heart. Many parameters including noise deteriorate the reconstruction result. One of the main obstacles in cardiac imaging at the heart location is the high impedance of lungs and muscles on the dorsal and posterior side of body. In this study we are investigating improvements of the measurement and initial conductivity estimation of the internal electrode by modelling an internal electrode inside the esophagus. We consider 16 electrodes connected around a cylindrical mesh. With the random noise level set near 0.05% of the signal we evaluated the Graz consensus reconstruction algorithm for electrical impedance tomography. The modelling and simulation results showed that the quality of the target in reconstructed images was improved by up to 5 times for amplitude response, position error, resolution, shape deformation and ringing effects with perturbations located in cardiac related positions when using an internal electrode.

Factorization method and its physical justification in frequency-difference electrical impedance tomography

Time-difference electrical impedance tomography (tdEIT) requires two data sets measured at two different times. The difference between them is utilized to produce images of time-dependent changes in a complex conductivity distribution inside the human body. Frequency-difference EIT (fdEIT) was proposed to image frequency-dependent changes of a complex conductivity distribution. It has potential applications in tumor and stroke imaging since it can visualize an anomaly without requiring any time-reference data obtained in the absence of an anomaly. In this paper, we provide a rigorous analysis for the detectability of an anomaly based on a constructive and quantitative physical correlation between a measured fdEIT data set and an anomaly. From this, we propose a new noniterative frequency-difference anomaly detection method called the factorization method (FM) and elaborate its physical justification. To demonstrate its practical applicability, we performed fdEIT phantom imaging experiments using a multifrequency EIT system. Applying the FM to measured frequency-difference boundary voltage data sets, we could quantitatively evaluate indicator functions inside the imaging domain, of which values at each position reveal presence or absence of an anomaly. We found that the FM successfully localizes anomalies inside an imaging domain with a frequency-dependent complex conductivity distribution. We propose the new FM as an anomaly detection algorithm in fdEIT for potential applications in tumor and stroke imaging.

A novel approach for EIT regularization via spatial and spectral principal component analysis

Electrical impedance tomography, EIT, is an imaging modality in which the internal conductivity distribution of an object is reconstructed based on voltage measurements on the boundary. This reconstruction problem is a nonlinear and ill-posed inverse problem, which requires regularization to ensure a stable solution. Most popular regularization approaches enforce smoothness in the inverse solution. In this paper, we propose a novel approach to build a subspace for regularization using a spectral and spatial multi-frequency analysis approach. The approach is based on the construction of a subspace for the expected conductivity distributions using principal component analysis. It is shown via simulations that the reconstructed images obtained with the proposed method are better than with the standard regularization approach. Using this approach, the percentage of misclassified finite elements was reduced up to twelve fold from the initial percentages after five iterations. The advantage of this technique is that prior information is extracted from the characteristic response of an object at different frequencies and spatially across the finite elements.

Application of conformal transformation to elliptic geometry for electric impedance tomography

Electrical impedance tomography (EIT) is a medical imaging modality that is used to compute the conductivity distribution through measurements on the cross-section of a body part. An elliptic geometry model, which defines a more general frame, ensures more accurate results in reconstruction and assessment of inhomogeneities inside. This study provides a link between the analytical solutions defined in circular and elliptical geometries on the basis of the computation of conformal mapping. The results defined as voltage distributions for the homogeneous case in elliptic and circular geometries have been compared with those obtained by the use of conformal transformation between elliptical and well-known circular geometry. The study also includes the results of the finite element method (FEM) as another approach for more complex geometries for the comparison of performance in other complex scenarios for eccentric inhomogeneities. The study emphasizes that for the elliptic case the analytical solution with conformal transformation is a reliable and useful tool for developing insight into more complex forms including eccentric inhomogeneities.

Neuromagnetic field strength outside the human head due to impedance changes from neuronal depolarization

The holy grail of neuroimaging would be to have an imaging system, which could image neuronal electrical activity over milliseconds. One way to do this would be by imaging the impedance changes associated with ion channels opening in neuronal membranes in the brain during activity. In principle, we could measure this change by using electrical impedance tomography (EIT) but it is close to its threshold of detectability. With the inherent limitation in the use of electrodes, we propose a new scheme based on recording the magnetic field resulting from an injected current with superconducting quantum interference devices (SQUIDs), used in magnetoencephalography (MEG). We have performed a feasibility study using computer simulation. The head was modelled as concentric spheres to mimic the scalp, skull, cerebrospinal fluid and brain using the finite element method. The magnetic field 1 cm away from the scalp was estimated. An impedance change of 1% in a 2 cm radius volume in the brain was modelled as the region of depolarization. A constant current of 100 microA was injected into the head from diametrically opposite electrodes. The model predicts that the standing magnetic field is about 10 pT and changed by about 3 fT (0.03%) on depolarization. The spectral noise density in a typical MEG system in the frequency band 1-100 Hz is about 7 fT, so this places the change at the limit of detectability. This is similar to electrical recording, as in conventional EIT systems, but there may be advantages to MEG in that the magnetic field directly traverses the skull and instrumentation errors from the electrode-skin interface will be obviated.

Induced current electrical impedance tomography system: experimental results and numerical simulations

In electrical impedance tomography (EIT), measurements of developed surface potentials due to applied currents are used for the reconstruction of the conductivity distribution. Practical implementation of EIT systems is known to be problematic due to the high sensitivity to noise of such systems, leading to a poor imaging quality. In the present study, the performance of an induced current EIT (ICEIT) system, where eddy current is applied using magnetic induction, was studied by comparing the voltage measurements to simulated data, and examining the imaging quality with respect to simulated reconstructions for several phantom configurations. A 3-coil, 32-electrode ICEIT system was built, and an iterative modified Newton-Raphson algorithm was developed for the solution of the inverse problem. The RMS norm between the simulated and the experimental voltages was found to be 0.08 +/- 0.05 mV (<3%). Two regularization methods were implemented and compared: the Marquardt regularization and the Laplacian regularization (a bounded second-derivative regularization). While the Laplacian regularization method was found to be preferred for simulated data, it resulted in distinctive spatial artifacts for measured data. The experimental reconstructed images were found to be indicative of the angular positioning of the conductivity perturbations, though the radial sensitivity was low, especially when using the Marquardt regularization method.

Elliptic Cylinder Geometry for Distinguishability Analysis in Impedance Tomography

Electrical impedance tomography (EIT) is a technique that computes the cross-sectional impedance distribution within the body by using current and voltage measurements made on the body surface. It has been reported that the image reconstruction is distorted considerably when the boundary shape is considered to be more elliptical than circular as a more realistic shape for the measurement boundary. This paper describes an alternative framework for determining the distinguishability region with a finite measurement precision for different conductivity distributions in a body modeled by elliptic cylinder geometry. The distinguishable regions are compared in terms of modeling error for predefined inhomogeneities with elliptical and circular approaches for a noncircular measurement boundary at the body surface. Since most objects investigated by EIT are noncircular in shape, the analytical solution for the forward problem for the elliptical cross section approach is shown to be useful in order to reach a better assessment of the distinguishability region defined in a noncircular boundary. This paper is concentrated on centered elliptic inhomogeneity in the elliptical boundary and an analytic solution for this type of forward problem. The distinguishability performance of elliptical cross section with cosine injected current patterns is examined for different parameters of elliptical geometry.

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).

Estimation of anomaly location and size using electrical impedance tomography

We developed a new algorithm that estimates locations and sizes of anomalies in electrically conducting medium based on electrical impedance tomography (EIT) technique. When only the boundary current and voltage measurements are available, it is not practically feasible to reconstruct accurate high-resolution cross-sectional conductivity or resistivity images of a subject. In this paper, we focus our attention on the estimation of locations and sizes of anomalies with different conductivity values compared with the background tissues. We showed the performance of the algorithm from experimental results using a 32-channel EIT system and saline phantom. With about 1.73% measurement error in boundary current-voltage data, we found that the minimal size (area) of the detectable anomaly is about 0.72% of the size (area) of the phantom. Potential applications include the monitoring of impedance related physiological events and bubble detection in two-phase flow. Since this new algorithm requires neither any forward solver nor time-consuming minimization process, it is fast enough for various real-time applications in medicine and nondestructive testing.

J-substitution algorithm in magnetic resonance electrical impedance tomography (MREIT): phantom experiments for static resistivity images

Recently, a new static resistivity image reconstruction algorithm is proposed utilizing internal current density data obtained by magnetic resonance current density imaging technique. This new imaging method is called magnetic resonance electrical impedance tomography (MREIT). The derivation and performance of J-substitution algorithm in MREIT have been reported as a new accurate and high-resolution static impedance imaging technique via computer simulation methods. In this paper, we present experimental procedures, denoising techniques, and image reconstructions using a 0.3-tesla (T) experimental MREIT system and saline phantoms. MREIT using J-substitution algorithm effectively utilizes the internal current density information resolving the problem inherent in a conventional EIT, that is, the low sensitivity of boundary measurements to any changes of internal tissue resistivity values. Resistivity images of saline phantoms show an accuracy of 6.8%-47.2% and spatial resolution of 64 x 64. Both of them can be significantly improved by using an MRI system with a better signal-to-noise ratio.

Electromagnetic impedance tomography (EMIT): a new method for impedance imaging

We propose a new impedance imaging method, electromagnetic impedance tomography (EMIT), in which the boundary electric potential measurements in electrical impedance tomography (EIT) are augmented by measurements of the exterior magnetic field induced by the currents excited in the object by the standard EIT procedures. These magnetic measurements can be obtained reliably and inexpensively by simple pickup coils located around the imaged cross section. We derive expressions for the forward problem and for the Jacobian of the measurements, and propose an iterative reconstruction algorithm using a squared error cost function. The performance of EMIT and EIT is compared in numerical simulations using a finite-element model for the conductivity distribution of several phantoms. Evaluation of the rank and condition of the Jacobian demonstrates that the additional magnetic measurements provided by a few pickup coils in EMIT turn an underdetermined EIT problem into a well-posed one with reasonable condition, or significantly improve the conditioning of the EIT problem when it is already fully determined. Reconstructions of various phantoms reveal that EMIT provides particularly significant visual and quantitative improvement (threefold to tenfold reduction in the root-mean-squared error) in the sensitivity at the center of the object, which is the area most difficult to image using EIT.

A comparison of methods for measurement of spatial resolution in two-dimensional circular EIT images

The literature concerning measurement of spatial resolution in electrical impedance tomography (EIT) is vague. Different groups often use their own method or a modified version of a better known method, thus hindering a generalized resolution measurement which could be useful for gauging the performance of one system against another. Measurement of spatial resolution in EIT is further complicated by its spatial variant nature and hence cannot be expressed simply with a single parameter as it can be in other imaging modalities (such as nuclear medicine or MRI for example). If the performance of each acquisition and image reconstruction system in EIT is to be compared objectively then there needs to be a common standard. In this paper the results of different methods for calculating spatial resolution are compared and an improved method is proposed which aims to fulfil this role.

A multi-shell algorithm to reconstruct EIT images of brain function

Electrical impedance tomography (EIT) may be used to image brain function, but an important consideration is the effect of the highly resistive skull and other extracerebral layers on the flow of injected current. We describe a new reconstruction algorithm, based on a forward solution which models the head as four concentric, spherical shells, with conductivities of the brain, cerebrospinal fluid, skull and scalp. The model predicted that the mean current travelling in the brain in the diametric plane for current injection from polar electrodes was 5.6 times less than if the head was modelled as a homogeneous sphere; this suggests that an algorithm based on this should be more accurate than one based on a homogeneous sphere model. In images reconstructed from computer-simulated data or data from a realistic saline-filled tank containing a real skull, a Perspex rod was localized to within 17% or 20% of the tank diameter of its true position, respectively. Contrary to expectation, the tank images were less accurate than those obtained with a reconstruction algorithm based on a homogeneous sphere. It is not yet clear if the theoretical advantages of this algorithm will yield practical advantages for head EIT imaging; it may be necessary to proceed to more complex algorithms based on numerical models which incorporate realistic head geometry. If so, this analytical forward model and algorithm may be used to validate numerical solutions.

Magnetic resonance electrical impedance tomography (MREIT): simulation study of J-substitution algorithm

We developed a new image reconstruction algorithm for magnetic resonance electrical impedance tomography (MREIT). MREIT is a new EIT imaging technique integrated into magnetic resonance imaging (MRI) system. Based on the assumption that internal current density distribution is obtained using magnetic resonance imaging (MRI) technique, the new image reconstruction algorithm called J-substitution algorithm produces cross-sectional static images of resistivity (or conductivity) distributions. Computer simulations show that the spatial resolution of resistivity image is comparable to that of MRI. MREIT provides accurate high-resolution cross-sectional resistivity images making resistivity values of various human tissues available for many biomedical applications.

Evaluation of an iterative reconstruction method for quantitative elastography

This paper describes an inverse reconstruction technique based on a modified Newton Raphson iterative scheme and the finite element method, which has been developed for computing the spatial distribution of Young's modulus from within soft tissues. Computer simulations were conducted to determine the relative merits of reconstructing tissue elasticity using knowledge of (a) known displacement boundary conditions (DBC), and (b) known stress boundary conditions (SBC). The results demonstrated that computing Young's modulus using knowledge of SBC allows accurate quantification of Young's modulus. However, the quality of the images produced using this reconstruction approach was dependent on the Young's modulus distribution assumed at the start of the reconstruction procedure. Computing Young's modulus from known DBC provided relative estimates of tissue elasticity which, despite the disadvantage of not being able to accurately quantify Young's modulus, formed images that were generally superior in quality to those produced using the known SBC, and were not affected by the trial solution. The results of preliminary experiments on phantoms demonstrated that this reconstruction technique is capable in practice of improving the fidelity of tissue elasticity images, reducing the artefacts otherwise present in strain images, and recovering Young's modulus images that possess excellent spatial and contrast resolution.

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.

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.

Electrical impedance tomography of complex conductivity distributions with noncircular boundary

Electrical impedance tomography (EIT) uses low-frequency current and voltage measurements made on the boundary of a body to compute the conductivity distribution within the body. Since the permittivity distribution inside the body also contributes significantly to the measured voltages, the present reconstruction algorithm images complex conductivity distributions. A finite element model (FEM) is used to solve the forward problem, using a 6017-node mesh for a piecewise-linear potential distribution. The finite element solution using this mesh is compared with the analytical solution for a homogeneous field and a maximum error of 0.05% is observed in the voltage distribution. The boundary element method (BEM) is also used to generate the voltage data for inhomogeneous conductivity distributions inside regions with noncircular boundaries. An iterative reconstruction algorithm is described for approximating both the conductivity and permittivity distributions from this data. The results for an off-centered inhomogeneity showed a 35% improvement in contrast from that seen with only one iteration, for both the conductivity and the permittivity values. It is also shown that a significant improvement in images results from accurately modeling a noncircular boundary. Both static and difference images are distorted by assuming a circular boundary and the amount of distortion increases significantly as the boundary shape becomes more elliptical. For a homogeneous field in an elliptical body with axis ratio of 0.73, an image reconstructed assuming the boundary to be circular has an artifact at the center of the image with an error of 20%. This error increased to 37% when the axis ratio was 0.64. A reconstruction algorithm which used a mesh with the same axis ratio as the elliptical boundary reduced the error in the conductivity values to within 0.5% of the actual values.

Impedance imaging of lung ventilation: do we need to account for chest expansion?

Electrical impedance tomography (EIT) uses surface electrical measurements to image changes in the conductivity distribution within a medium. When used to measure lung ventilation, however, measurements depend both on conductivity changes in the thorax and on rib cage movement. Given that currently available reconstruction techniques assume that only conductivity changes are present, certain errors are introduced. A finite element model (FEM) is used to calculate the effect of chest expansion on the reconstructed conductivity images. Results indicate that thorax expansion accounts for up to 20% of the reconstructed image amplitude and introduces an artifact in the center of the image tending to "move" the reconstructed lungs closer together. Although this contribution varies depending on anatomical factors, it is relatively independent of inspiration depth. For certain applications in which one is only interested in changes in the level of physiological activity, the effect of the expansion can be neglected because it varies linearly with impedance changes. We conclude that chest expansion can contribute significantly to the conductivity images of lung ventilation and should be taken into account in the interpretation of these images.

Experimental evaluation of two iterative reconstruction methods for induced current electrical impedance tomography

The Newton-Raphson (N-R) with two different regularization methods: the Levenberg-Marquardt (N-R-LM) and the Hachtel's Augmented Matrix (N-R-HAM), were used to reconstruct images of conductivity changes in a cylindrical medium by Induced Current Electrical Impedance Tomography (ic-EIT). Experimental data were obtained from an 8-cm high, 19.2-cm diameter tank with 16 electrodes on the boundary surface and surrounded by eight 50-cm diameter coils. The coils were angularly displaced by 45 degrees and offset 12.4 cm from the center of the tank. They were driven by a 150-mA (peak) 20-kHz sine wave. Potential differences between adjacent electrodes were measured with phase-sensitive demodulators. The scalar potential field in the electrode plane of the conducting medium, resulting from eddy currents generated by each coil, was computed by the Finite Element Method. Image reconstruction by the N-R-HAM method was found to provide higher resolution and better noise immunity than the N-R-LM method. Two 2.2-cm diameter nonconducting rods located 3.9 cm from the center of the tank, 180 degrees from each other, were clearly resolved. Spatial resolution is estimated at 15% of the tank diameter and is comparable to the resolution obtained by conventional EIT using the Sheffield protocol. Higher resolution could be achieved with more coils and/or electrodes. A 16-coil system should present no construction problems. However, voltages induced by stray magnetic flux through the electrode leads and measurement circuits are significant and may limit the ability of ic-EIT to perform static imaging of conductivity distributions.

Electrical impedance tomography: regularized imaging and contrast detection

Dynamic electrical impedance tomography (EIT) images changes in the conductivity distribution of a medium from low frequency electrical measurements made at electrodes on the medium surface. Reconstruction of the conductivity distribution is an under-determined and ill-posed problem, typically requiring either simplifying assumptions or regularization based on a priori knowledge. This paper presents a maximum a posteriori (MAP) approach to linearized image reconstruction using knowledge of the noise variance of the measurements and the covariance of the conductivity distribution. This approach has the advantage of an intuitive interpretation of the algorithm parameters as well as fast (near real time) image reconstruction. In order to compare this approach to existing algorithms, the authors develop figures of merit to measure the reconstructed image resolution, the noise amplification of the image reconstruction, and the fidelity of positioning in the image. Finally, the authors develop a communications systems approach to calculate the probability of detection of a conductivity contrast in the reconstructed image as a function of the measurement noise and the reconstruction algorithm used.

Anatomically constrained electrical impedance tomography for anisotropic bodies via a two-step approach

Discusses the inclusion of anatomical constraints and anisotropy in static Electrical Impedance Tomography (EIT) using a two-step approach to EIT. In the first step, the boundaries between regions of different conductivities are anatomically constrained using Magnetic Resonance Imaging (MRI) data. In the second step, the conductivity values in different regions are determined. Anisotropic conductivity regions are included to allow better modeling of the muscle regions (e.g., skeletal muscle) which exhibit a greater conductivity in the direction parallel to the muscle fiber. This two-step approach is used to reconstruct the conductivity profile of a canine torso, illustrating its potential application in extracting conductivity values for bioelectric modeling.

A neural network image reconstruction technique for electrical impedance tomography

Reconstruction of images in electrical impedance tomography requires the solution of a nonlinear inverse problem on noisy data. This problem is typically ill-conditioned and requires either simplifying assumptions or regularization based on a priori knowledge. The authors present a reconstruction algorithm using neural network techniques which calculates a linear approximation of the inverse problem directly from finite element simulations of the forward problem. This inverse is adapted to the geometry of the medium and the signal-to-noise ratio (SNR) used during network training. Results show good conductivity reconstruction where measurement SNR is similar to the training conditions. The advantages of this method are its conceptual simplicity and ease of implementation, and the ability to control the compromise between the noise performance and resolution of the image reconstruction.