Electrical impedance tomography for imaging tissue electroporation

Electroporation is a method to introduce molecules, such as gene constructs or small drugs, into cells by temporarily permeating the cell membrane with electric pulses. In molecular medicine and biotechnology, tissue electroporation is performed with electrodes placed in the target area of the body. Currently, tissue electroporation, as with all other methods of molecular medicine, is performed without real-time control or near-term information regarding the extent and degree of electroporation. This paper expands the work from our previous study by implementing new ex vivo experimental data with "front-tracking" analysis for the image reconstruction algorithm. The experimental data is incorporated into numerical simulations of electroporation procedures and images are generated using the new reconstruction algorithm to demonstrate that electrical impedance tomography (EIT) can produce an image of the electroporated area. Combining EIT with electroporation could become an important biotechnological and medical technique to introduce therapeutic molecules into cells in tissue at predetermined areas of the body.     

Electrical impedance tomography

Electrical impedance tomography (EIT) is an imaging modality that estimates the electrical properties at the interior of an object from measurements made on its surface. Typically, currents are injected into the object through electrodes placed on its surface, and the resulting electrode voltages are measured. An appropriate set of current patterns, with each pattern specifying the value of the current for each electrode, is applied to the object, and a reconstruction algorithm uses knowledge of the applied current patterns and the measured electrode voltages to solve the inverse problem, computing the electrical conductivity and permittivity distributions in the object. This article focuses on the type of EIT called adaptive current tomography (ACT) in which currents are applied simultaneously to all the electrodes. A number of current patterns are applied, where each pattern defines the current for each electrode, and the subsequent electrode voltages are measured to generate the data required for image reconstruction. A ring of electrodes may be placed in a single plane around the object, to define a two-dimensional problem, or in several layers of such rings, to define a three-dimensional problem. The reconstruction problem is described and two algorithms are discussed, a one-step, two-dimensional (2-D) Newton-Raphson algorithm and a one-step, full three-dimensional (3-D) reconstructor. Results from experimental data are presented which illustrate the performance of the algorithms     

Electrical impedance tomography problem with inaccurately known boundary and contact impedances

In electrical impedance tomography (EIT) electric currents are injected into a body with unknown electromagnetic properties through a set of contact electrodes at the boundary of the body. The resulting voltages are measured on the same electrodes and the objective is to reconstruct the unknown conductivity function inside the body based on these data. All the traditional approaches to the reconstruction problem assume that the boundary of the body and the electrode-skin contact impedances are known a priori. However, in clinical experiments one usually lacks the exact knowledge of the boundary and contact impedances, and therefore, approximate model domain and contact impedances have to be used in the image reconstruction. However, it has been noticed that even small errors in the shape of the computation domain or contact impedances can cause large systematic artefacts in the reconstructed images, leading to loss of diagnostically relevant information. In a recent paper (Kolehmainen , 2006), we showed how in the 2-D case the errors induced by the inaccurately known boundary can be eliminated as part of the image reconstruction and introduced a novel method for finding a deformed image of the original isotropic conductivity using the theory of TeichmÜller mappings. In this paper, the theory and reconstruction method are extended to include the estimation of unknown contact impedances. The method is implemented numerically and tested with experimental EIT data. The results show that the systematic errors caused by inaccurately known boundary and contact impedances can efficiently be eliminated by the reconstruction method.      

Enhancing impedance imaging through multimodal tomography

Several noninvasive modalities including electrical impedance tomography (EIT), magnetic induction tomography (MIT), and induced-current EIT (ICEIT) have been developed for imaging the electrical conductivity distribution within a human body. Although these modalities differ in how the excitation and detection circuitry (electrodes or coils) are implemented, they share a number of common principles not only within the image reconstruction approaches but also with respect to the basic principle of generating a current density distribution inside a body and recording the resultant electric fields. In this paper, we are interested in comparing differences between these modalities and in theoretically understanding the compromises involved, despite the increased hardware cost and complexity that such a multimodal system brings along. To systematically assess the merits of combining data, we performed 3-D simulations for each modality and for the multimodal system by combining all available data. The normalized sensitivity matrices were computed for each modality based on the finite element method, and singular value decomposition was performed on the resultant matrices. We used both global and regional quality measures to evaluate and compare different modalities. This study has shown that the condition number of the sensitivity matrix obtained from the multimodal tomography with 16-electrode and 16-coil is much lower than the condition number produced in the conventional 16-channel EIT and MIT systems, and thus, produced promising results in terms of image stability. An improvement of about 20% in image resolution can be achieved considering feasible signal-to-noise ratio levels.     

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.     

Electrical impedance tomography of translationally uniform cylindrical objects with general cross-sectional boundaries

An algorithm is developed for electrical impedance tomography (EIT) of finite cylinders with general cross-sectional boundaries and translationally uniform conductivity distributions. The electrodes for data collection are assumed to be placed around a cross-sectional plane; therefore, the axial variation of the boundary conditions and the potential field are expanded in Fourier series. For each Fourier component a two-dimensional (2-D) partial differential equation is derived. Thus the 3-D forward problem is solved as a succession of 2-D problems, and it is shown that the Fourier series can be truncated to provide substantial savings in computation time. The finite element method is adopted and the accuracy of the boundary potential differences (gradients) thus calculated is assessed by comparison to results obtained using cylindrical harmonic expansions for circular cylinders. A 1016-element and 541-node mesh is found to be optimal. The algorithm is applied to data collected from phantoms, and the errors incurred from the several assumptions of the method are investigated.     

Anatomically constrained electrical impedance tomography forthree-dimensional anisotropic bodies

As shown previously for two-dimensional geometries, anisotropy effects should not be ignored in electrical impedance tomography (EIT) and structural information is important for the reconstruction of anisotropic conductivities. Here, we describe the static reconstruction of an anisotropic conductivity distribution for the more realistic three-dimensional (3-D) case. Boundaries between different conductivity regions are anatomically constrained using magnetic resonance imaging (MRI) data. The values of the conductivities are then determined using gradient-type-algorithms in a nonlinear-indirect approach. At each iteration, the forward problem is solved by the finite element method. The approach is used to reconstruct the 3-D conductivity profile of a canine torso. Both computational performance and simulated reconstruction results are presented together with a detailed study on the sensitivity of the prediction error with respect to different parameters. In particular, the use of an intracavity catheter to better extract interior conductivities is demonstrated     

Electrical impedance endo-tomography: imaging tissue from inside

This paper describes a new method for scanning the conductivity of a tissue or an organ using a multielectrode impedance probe placed at the center of the region of interest. The long-term objective of the study is the evaluation, using an urethral impedance probe, of the lesion produced by ultrasound ablathermy of localized prostate cancer. The probe consists of electrodes placed at the surface of an insulating cylinder. The injected current passes around the cylinder and spreads in the medium surrounding the probe. This paper presents the theoretical bases of this method, the calculated sensitivity distributions of electrode configurations involving a pair of diametrically opposed electrodes and an application in vitro. The experimental set-up consisted of a water tank and a 16-electrode prototype probe 50 mm in diameter. Data sets were collected in the presence of conductivity perturbations produced by small size insulators or conductors and a 7.5% constant perturbation model. The presented images, although reconstructed using a simple retro-projection algorithm, demonstrate the feasibility of the method. Improvements in data collection and image reconstruction are possible.     

An efficient forward solver in electrical impedance tomography by spectral element method

In electrical impedance tomography (EIT), a forward solver capable of predicting the voltages on electrodes for a given conductivity distribution is essential for reconstruction. The EIT forward solver is normally based on the conventional finite element method (FEM). One of the major problems of three-dimensional (3-D) EIT is its high demand in computing power and memory since high precision is required for obtaining a small secondary field which is typical for a small anomaly. This accuracy requirement is also set by the level of noise in the real data; although currently the noise level is still an issue, future EIT systems should significantly reduce the noise level to be capable of detecting very small anomalies. To accurately simulate the forward solution with the FEM, a mesh with large number of nodes and elements is usually needed. To overcome this problem, we proposed the spectral element method (SEM) for EIT forward problem. With the introduction of SEM, a smaller number of nodes and hence less computational time and memory are needed to achieve the same or better accuracy in the forward solution than the FEM. Numerical results demonstrate the efficiency of the SEM in 3-D EIT simulation.     

Electrical impedance tomography using induced currents

The mathematical basis of a new imaging modality, induced current electrical impedance tomography (EIT), is investigated, The ultimate aim of this technique is the reconstruction of conductivity distribution of the human body, from voltage measurements made between electrodes placed on the surface, when currents are induced inside the body by applied time varying magnetic fields. In this study the two-dimensional problem is analyzed. A specific 9-coil system for generating nine different exciting magnetic fields (50 kHz) and 16 measurement electrodes around the object are assumed, The partial differential equation for the scaler potential function in the conductive medium is derived and finite element method (FEM) is used for its solution. Sensitivity matrix, which relates the perturbation in measurements to the conductivity perturbations, is calculated. Singular value decomposition of the sensitivity matrix shows that there are 135 independent measurements. It is found that measurements are less sensitive to changes in conductivity of the object's interior. While in this respect induced current EIT is slightly inferior to the technique of injected current EIT (using Sheffield protocol), its sensitivity matrix is better conditioned. The images obtained are found to be comparable to injected current EIT images In resolution. Design of a coil system for which parameters such as sensitivity to inner regions and condition number of the sensitivity matrix are optimum, remains to be made.     

Electrical Impedance Tomographic Imaging of Buried Landmines

A prototype confirmation landmine detector, based on electrical impedance tomography (EIT), which can operate under realistic environmental conditions, has been developed. Laboratory and field experiments demonstrated that it is possible to reliably reconstruct, on the scale of the electrode spacing (ES) (in width and depth), conductivity perturbations due to a shallow buried antitank mine or a similar object in a variety of soils (black earth, clay, sand) down to depths equal to the dimensions of the object (1–1.5 ES, equivalent to 14–21 cm for a 64-electrode 1 m$times$1 m array). These represent the first EIT images of real landmines computed from measured data. Occasional problems were encountered with the electrical contact in very dry soils, with excessive insertion pressure being required for reliable electrode contact. However, poor contacts could be detected, and the offending probe was either reinserted or compensation was applied. A matched filter detection algorithm based on a replica of the object of interest was developed and shown to effectively reduce the false alarm rate of the detector. EIT is especially suited for wet lands and underwater, where other mine detectors perform poorly. Experiments in a water-and sediment-filled tank have demonstrated that detection of minelike objects in such an environment with a submerged array is feasible. These experiments represent the first EIT measurements of targets using an electrode array submerged underwater. EIT may also have an application in locating intact mines in the berms formed by mine-clearing equipment. The EIT sensor head could be made cheaply enough to be disposable and remotely inserted to improve safety.     

静态阻抗断层图像重建新方法

阻抗断层图像重建是一个严重病态的非线性的逆问题,特别是在静态阻抗断层成像中,由于其图像重建模型误差和测量噪声的影响更为严重,因此常用的基于目标函数梯度信息不断迭代的改进的Newton-Raphson类重建算法,即使使用正则化技术,其稳定性仍较差,甚至发散.本文提出一种全新的静态阻抗断层图像重建方法,它利用基于生物自然选择与遗传机理的遗传算法去搜索阻抗图像重建问题的最优解,无需正则化技术,也不会象改进的Newton-Raphson类算法那样易陷入局部最优解.实验结果也表明基于遗传算法的图像重建方法重建的静态阻抗断层图像,其成像精度和空间分辨率都大大好于改进的Newton-Raphson类重建算法.     

Electrical conductivity imaging via contactless measurements

A new imaging modality is introduced to image electrical conductivity of biological tissues via contactless measurements. This modality uses magnetic excitation to induce currents inside the body and measures the magnetic fields of the induced currents. In this study, the mathematical basis of the methodology is analyzed and numerical models are developed to simulate the imaging system. The induced currents are expressed using the A-phi formulation of the electric field where A is the magnetic vector potential and phi is the scalar potential function. It is assumed that A describes the primary magnetic vector potential that exists in the absence of the body. This assumption considerably simplifies the solution of the secondary magnetic fields caused by induced currents. In order to solve phi for objects of arbitrary conductivity distribution a three-dimensional (3-D) finite-element method (FEM) formulation is employed. A specific 7 x 7-coil system is assumed nearby the upper surface of a 10 x 10 x 5-cm conductive body. A sensitivity matrix, which relates the perturbation in measurements to the conductivity perturbations, is calculated. Singular-value decomposition of the sensitivity matrix shows various characteristics of the imaging system. Images are reconstructed using 500 voxels in the image domain, with truncated pseudoinverse. The noise level is assumed to produce a representative signal-to-noise ratio (SNR) of 80 dB. It is observed that it is possible to identify voxel perturbations (of volume 1 cm3) at 2 cm depth. However, resolution gradually decreases for deeper conductivity perturbations.     

Electrical impedance tomography using the extended Kalman filter

In this paper, we propose an algorithm that, using the extended Kalman filter, solves the inverse problem of estimating the conductivity/resistivity distribution in electrical impedance tomography (EIT). The algorithm estimates conductivity/resistivity in a wide range. The purpose of this investigation is to provide information for setting and controlling air volume and pressure delivered to patients under artificial ventilation. We show that, when the standard deviation of the measurement noise level raises up to 5% of the maximal measured voltage, the conductivity estimates converge to the expected vector within 7% accuracy of the maximal conductivity value, under numerical simulations, with spatial a priori information. A two-phase identification procedure is proposed. A cylindrical phantom with saline solution is used for experimental evaluation. An abrupt modification on the resistivity distribution of this solution is caused by the immersion of a glass object. Estimates of electrode contact impedances and images of the glass object are presented.     

A versatile high-permittivity phantom for EIT

Phantoms are frequently used in medical imaging systems to test hardware, reconstruction algorithms, and the interpretation of data. This report describes and characterizes the use of powdered graphite as a means of adding a significant reactive component or permittivity to useful phantom media for electrical impedance imaging. The phantom materials produced have usable complex admittivity at the electrical impedance tomography (EIT) frequencies from a few kilohertz to 1 MHz, as measured by our EIT system (ACT4) and by a commercial bioimpedance analyzer (BIS 4000, Xitron). We have also studied a commercial ultrasound coupling gel, which is highly electrically conductive and semisolid but that permits objects to move within it. The mixture of agar–graphite and gel–graphite, increases in permittivity and conductivity are proportional to the graphite concentration. We also report the use of a porous polymer membrane to simulate skin. A thin layer of this membrane increased resistance and the characteristic frequency of the phantoms, providing a promising candidate to simulate the effect of skin and the layered structure of a breast or other anatomical structure. The graphite also provides a realistic level of “speckle” in ultrasound images of the phantom, which may be useful in developing dual-mode imaging systems with ultrasound and the EIT.      

Nonrigid registration of 3-D free-hand ultrasound images of the breast

Three-dimensional (3-D) ultrasound imaging of the breast enables better assessment of diseases than conventional two-dimensional (2-D) imaging. Free-hand techniques are often used for generating 3-D data from a sequence of 2-D slice images. However, the breast deforms substantially during scanning because it is composed primarily of soft tissue. This often causes tissue mis-registration in spatial compounding of multiple scan sweeps. To overcome this problem, in this paper, instead of introducing additional constraints on scanning conditions, we use image processing techniques. We present a fully automatic algorithm for 3-D nonlinear registration of free-hand ultrasound data. It uses a block matching scheme and local statistics to estimate local tissue deformation. A Bayesian regularization method is applied to the sample displacement field. The final deformation field is obtained by fitting a B-spline approximating mesh to the sample displacement field. Registration accuracy is evaluated using phantom data and similar registration errors are achieved with (0.19 mm) and without (0.16 mm) gaps in the data. Experimental results show that registration is crucial in spatial compounding of different sweeps. The execution time of the method on moderate hardware is sufficiently fast for fairly large research studies.     

A broadband high-frequency electrical impedance tomography system for breast imaging.

Bio-electric impedance signatures arise primarily from differences in cellular morphologies within an organ and can be used to differentiate benign and malignant pathologies, specifically in the breast. Electrical impedance tomography (EIT) is an imaging modality that determines the impedance distribution within tissue and has been used in prior work to map the electrical properties of breast at signal frequencies ranging from a few kHz to 1 MHz. It has been suggested that by extending the frequency range, additional information of clinical significance may be obtained. We have, therefore, developed a new EIT system for breast imaging which covers the frequency range from 10 kHz to 10 MHz. The instrument developed here is a distributed processor tomograph with 64 channels, capable of generating and measuring voltages and currents. Electrical benchmarking has shown the system to have a SNR greater than 94 dB up to 2 MHz, 90 dB up to 7 MHz, and 65 dB at 10 MHz. In addition, the system measures impedances to an accuracy of 99.7 % and has channel-to-channel variations of less than 0.05 %. Phantom imaging has demonstrated the ability to image across the entire frequency range in both single- and multiplane configurations. Further, 96 women have participated safely in breast exams with the system and the associated conductivity spectra obtained from 3-D image reconstructions range from 0.0237 S/m at 10 kHz to 0.2174 S/m at 10 MHz. These findings are consistent with impedance values reported in the literature.     

Electrical impedance tomography for piecewise constant domains using boundary element shape-based inverse solutions

Shape-based solutions have recently received attention for certain ill-posed inverse problems. Their advantages include implicit imposition of relevant constraints and reduction in the number of unknowns, especially important for nonlinear ill-posed problems. We apply the shape-based approach to current-injection electrical impedance tomography (EIT) reconstructions. We employ a boundary element method (BEM) based solution for EIT. We introduce two shape models, one based on modified B-splines, and the other based on spherical harmonics, for BEM modeling of shapes. These methods allow us to parameterize the geometry of conductivity inhomogeneities in the interior of the volume. We assume the general shape of piecewise constant inhomogeneities is known but their conductivities and their exact location and shape is not. We also assume the internal conductivity profile is piecewise constant, meaning that each region has a constant conductivity. We propose and test three different regularization techniques to be used with either of the shape models. The performance of our methods is illustrated via both simulations in a digital torso model and phantom experiments when there is a single internal object. We observe that in the noisy environment, either simulated noise or real sources of noise in the experimental study, we get reasonable reconstructions. Since the signal-to-noise ratio (SNR) expected in modern EIT instruments is higher than that used in this study, these reconstruction methods may prove useful in practice.     

Real-Time Management of Faulty Electrodes in Electrical Impedance Tomography

Completely or partially disconnected electrodes are a fairly common occurrence in many electrical impedance tomography (EIT) clinical applications. Several factors can contribute to electrode disconnection: patient movement, perspiration, manipulations by clinical staff, and defective electrode leads or electronics. By corrupting several measurements, faulty electrodes introduce significant image artifacts. In order to properly manage faulty electrodes, it is necessary to: (1) account for invalid data in image reconstruction algorithms and (2) automatically detect faulty electrodes. This paper presents a two-part approach for real-time management of faulty electrodes based on the principle of voltage-current reciprocity. The first part allows accounting for faulty electrodes in EIT image reconstruction without a priori knowledge of which electrodes are at fault. The method properly weights each measurement according to its compliance with the principle of voltage-current reciprocity. Results show that the algorithm is able to automatically determine the valid portion of the data and use it to calculate high-quality images. The second part of the approach allows automatic real-time detection of at least one faulty electrode with 100% sensitivity and two faulty electrodes with 80% sensitivity enabling the clinical staff to fix the problem as soon as possible to minimize data loss.     

An active microwave imaging system for reconstruction of 2-Delectrical property distributions

The goal of this work is to develop a microwave-based imaging system for hyperthermia treatment monitoring and assessment. Toward this end, a 4-transmit channel and 4-receive channel hardware device and concomitant image reconstruction algorithm have been realized. The hardware is designed to measure electric fields (i.e., amplitude and phase) at various locations in a phantom tank with and without the presence of various heterogeneities using standard heterodyning principles. Particular attention has been paid to designing a receiver with better than 115 dB of linear dynamic range which is necessary for imaging biological tissue which often has very high conductivity, especially for tissues with high water content. A calibration procedure has been developed to compensate for signal loss due to 3-dimensional radiation in the measured data, since the reconstruction process is only 2-dimensional at the present time. Results are shown which demonstrate the stability and accuracy of the measurement system, the extent to which the forward computational model agrees with the measured field distribution when the electrical properties are known, and image reconstructions of electrically unknown targets of varying diameter. In the latter case, images of both the reactive and resistive component of the electrical property distribution have been recoverable. Quantitative information on object location, size, and electrical properties results when the target is approximately one-half wavelength in size. Images of smaller objects lack the same level of quantitative information, but remain qualitatively correct