A two-layered forward model of tissue for electrical impedance tomography

Electrical impedance tomography is being explored as a technique to detect breast cancer, exploiting the differences in admittivity between normal tissue and tumors. In this paper, the geometry is modeled as an infinite half space under a hand-held probe. A forward solution and a reconstruction algorithm for this geometry were developed previously by Mueller et al (1999 IEEE Trans. Biomed. Eng. 46 1379). In this paper, we present a different approach which uses the decomposition of the forward solution into its Fourier components to obtain the forward solution and the reconstructions. The two approaches are compared in terms of the forward solutions and the reconstructions of experimental tank data. We also introduce a two-layered model to incorporate the presence of the skin that surrounds the body area being imaged. We demonstrate an improvement in the reconstruction of a target in a layered medium using this layered model with finite difference simulated data. We then extend the application of our layered model to human subject data and estimate the skin and the tissue admittivities for data collected on the human abdomen using an ultrasound-like hand-held EIT probe. Lastly, we show that for this set of human subject data, the layered model yields an improvement in predicting the measured voltages of around 81% for the lowest temporal frequency (3 kHz) and around 61% for the highest temporal frequency (1 MHz) applied when compared to the homogeneous model.

Regional admittivity spectra with tomosynthesis images for breast cancer detection: preliminary patient study

It has been known for some time that many tumors have a significantly different conductivity and permittivity from surrounding normal tissue. This high "contrast" in tissue electrical properties, occurring between a few kilohertz and several megahertz, may permit differentiating malignant from benign tissues. Here we show the ability of electrical impedance spectroscopy (EIS) to roughly localize and clearly distinguish cancers from normal tissues and benign lesions. Localization of these lesions is confirmed by simultaneous, in register digital breast tomosynthesis (DBT) mammography or 3-D mammograms.

Robust linearized image reconstruction for multifrequency EIT of the breast

Electrical impedance tomography (EIT) is a developing imaging modality that is beginning to show promise for detecting and characterizing tumors in the breast. At Rensselaer Polytechnic Institute, we have developed a combined EIT-tomosynthesis system that allows for the coregistered and simultaneous analysis of the breast using EIT and X-ray imaging. A significant challenge in EIT is the design of computationally efficient image reconstruction algorithms which are robust to various forms of model mismatch. Specifically, we have implemented a scaling procedure that is robust to the presence of a thin highly-resistive layer of skin at the boundary of the breast and we have developed an algorithm to detect and exclude from the image reconstruction electrodes that are in poor contact with the breast. In our initial clinical studies, it has been difficult to ensure that all electrodes make adequate contact with the breast, and thus procedures for the use of data sets containing poorly contacting electrodes are particularly important. We also present a novel, efficient method to compute the Jacobian matrix for our linearized image reconstruction algorithm by reducing the computation of the sensitivity for each voxel to a quadratic form. Initial clinical results are presented, showing the potential of our algorithms to detect and localize breast tumors.

An analytical layered forward model for breasts in electrical impedance tomography

Electrical impedance tomography (EIT) can be used to determine the admittivity distribution within the breast from measurements made on its surface. It has been reported that the electrical impedance spectrum of normal breast tissue is significantly different from that of malignant tissue, making EIT a candidate technology for breast cancer detection. The inhomogeneous structure of breasts, with thin low-admittivity skin layers covering the relatively high-admittivity tissue inside, makes the breast imaging problem difficult. In addition, studies show that the electrical properties of skin vary considerably over frequency. This paper proposes a layered forward model which incorporates the presence of skin. Our layered model has three layers, thin low-admittivity top and bottom layers representing skin and a thicker high-admittivity middle layer representing breast tissue. We solve for the forward solution of the layered geometry and compare its behavior with the previously used homogeneous model. Next we develop an iterative method to estimate the skin and breast tissue admittivities from the measured data, and study the robustness and accuracy of the method for various simulated and experimental data. We then look at the reconstruction of a target embedded in a layered body when the homogeneous forward solution is replaced by the layered forward solution. Lastly, we demonstrate the improvement that the layered forward model produces over the homogeneous model when working with clinical data.

An electrical impedance spectroscopy system for breast cancer detection

This paper describes Rensselaer's ACT 4 electrical impedance tomography system which has been developed for breast cancer detection. ACT 4 acquires electrical impedance data at a set of discrete frequencies in the range from 3.33 kHz to 1 MHz and can support up to 72 electrodes. The instrument applies either voltages or currents to all the electrodes simultaneously and measures the resulting currents and/or voltages. Radiolucent electrode arrays are applied to the compression plates of an x-ray mammography system for collecting impedance data in register with x-ray images. The analog front-end electronics are supported with a distributed digital system, including a computer, Digital Signal Processors (DSPs) and Field-Programmable Gate Arrays (FPGAs). A Microsoft Visual C/C++ -based user interface controls the system operation. The overall system architecture is presented as well as performance results.

An Algorithm for Applying Multiple Currents Using Voltage Sources in Electrical Impedance Tomography

A method to produce a desired current pattern in a multiple-source EIT system using voltage sources is presented. Application of current patterns to a body is known to be superior to the application of voltage patterns in terms of high spatial frequency noise suppression, resulting in high accuracy in conductivity and permittivity images. Since current sources are difficult and expensive to build, the use of voltage sources to apply the current pattern is desirable. An iterative algorithm presented in this paper generates the necessary voltage pattern that will produce the desired current pattern. The convergence of the algorithm is shown under the condition that the estimation error of the linear mapping matrix from voltage to current is small. Simulation results are presented to illustrate the convergence of the output current.

Regional admittivity spectra with tomosynthesis images for breast cancer detection

Because the electrical properties of many breast tumors are different from those of surrounding, normal tissue, imaging these properties may provide useful diagnostic information. At the present time, X-ray mammography is the standard imaging modality used for breast cancer screening. The interpretation of EIT imaging is thus enhanced by its use together with x-ray mammography in the same geometry. This paper reports the ability of Electrical Impedance Spectroscopy (EIS) to localize and distinguish cancers from normal tissues. These findings are confirmed by simultaneous, co-registered 3-D mammograms or tomosynthesis images and are verified with biopsy reports.

L-type voltage-operated Ca(+2) channels modulate transient Ca(+2) influx triggered by activation of Sertoli cell surface L-selectin

Near the base of mammalian seminiferous epithelium, Sertoli cells are joined by tight junctions, which constitute the blood-testis barrier. Differentiating germ cells are completely enveloped by Sertoli cells and must traverse the tight junctions during spermatogenic cycle. Following the specific ligand activation of L-selectin, the up-regulated Rho family small G-proteins have been implicated as important modulators of tight junctional dynamics. Although the activation of L-selectin transmits subsequent intracellular signals in a Ca(+2)-dependent fashion in various cell types, little is understood regarding the signaling pathways utilized by L-selectin in Sertoli cells. Therefore, we have examined the possible resultant calcium influx triggered by specific ligand-activation of cell surface L-selectin receptors or by cross-linking of L-selectin with anti-L-selectin. Spectrofluorimetric studies demonstrate increase of intracellular Ca(+2) levels immediately after the treatment of the L-selectin ligands, fucoidan and sialyl Lewis-a, or after treatment with anti-L-selectin antibody. We then determined the mechanism of Ca(+2) influx by investigating L- and T-type voltage-operated Ca(+2) channels, which have been suggested to present in the membranes of Sertoli cells. Data demonstrate that Sertoli cells treated with L-type voltage-operated Ca(+2) channel antagonists, nifedipine, diltiazem, or verapamil, lead to dose-dependent blockage of L-selectin-induced Ca(+2) influx. Cells treated with mibedradil, a T-type voltage-operated Ca(+2) channel antagonist, results in little or no blocking effect. Therefore, we conclude that activation of Sertoli cell L-selectin induces Ca(+2) influx, which is at least partially regulated by L-type voltage-operated Ca(+2) channels.

A compensated radiolucent electrode array for combined EIT and mammography

Electrical impedance tomography (EIT), a non-invasive technique used to image the electrical conductivity and permittivity within a body from measurements taken on the body's surface, could be used as an indicator for breast cancer. Because of the low spatial resolution of EIT, combining it with other modalities may enhance its utility. X-ray mammography, the standard screening technique for breast cancer, is the first choice for that other modality. Here, we describe a radiolucent electrode array that can be attached to the compression plates of a mammography unit enabling EIT and mammography data to be taken simultaneously and in register. The radiolucent electrode array is made by depositing thin layers of metal on a plastic substrate. The structure of the array is presented along with data showing its x-ray absorbance and electrical properties. The data show that the electrode array has satisfactory radiolucency and sufficiently low resistance.

A method for analyzing electrical impedance spectroscopy data from breast cancer patients

Research on freshly-excised malignant breast tissues and surrounding normal tissues in an in vitro impedance cell has shown that breast tumors have different conductivity and permittivity from normal or non-malignant tissues. This contrast may provide a basis for breast cancer detection using electrical impedance imaging. This paper describes a procedure for collecting electrical impedance spectroscopy data simultaneously and in register with tomosynthesis data from patients. We describe the methods used to analyze the data in order to determine if the electrodes are making contact with the breast of the patient. Canonical voltage patterns are applied and used to synthesize the data that would have resulted from constant voltage patterns applied to each of two parallel mammography plates. A type of Cole-Cole plot is generated and displayed from each of the currents measured on each of the electrodes for each of the frequencies (5, 10, 30, 100 and 300 kHz) of applied voltages. We illustrate the potential usefulness of these displays in distinguishing breast cancer from benign lesions with the Cole-Cole plots for two patients--one having cancer and one having a benign lesion--by comparing these graphs with electrical impedance spectra previously found by Jossinet and Schmitt in tissue samples taken from a variety of patients.

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.

A simplified model of mammography geometry for breast cancer imaging with electrical impedance tomography

One recent application area of EIT is the detection of breast cancer by imaging the conductivity and the permittivity distribution inside the breast. The present "gold standard" for breast cancer detection is X-ray mammography, and it is desirable that the EIT and the X-ray mammography use the same geometry. This work presents a simplified model of the mammography geometry for EIT imaging. 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 the homogeneous conductivity distribution and validated by experiment using a phantom tank. The effect of unmodeled surface on the sides of the electrodes is studied.

Reducing boundary effects in static EIT imaging

Electrical impedance tomography (EIT) is a non-invasive technique used to image the electrical conductivity and permittivity within a body from measurements taken on the body's surface. High-quality static images are required for many medical imaging applications. Forming such images usually requires an accurate way to calculate the expected voltages on the surface resulting from the application of known currents to that surface. This is described as the forward problem. This paper introduces a new method to improve static images by using an improved forward solution which estimates a different conductivity value for each applied current pattern. This method, creating an automatically adjusting forward solution, can improve the sensitivity of static images under many EIT imaging applications. It does so by reducing the boundary effects caused by electrodes and any layered structures near them such as skin. The drawback of this method is that circularly symmetric structures of interest may be suppressed or eliminated from the images. The performance of this method is illustrated in a 2D circular phantom with simulation data from both a FEM model and experimental data.

Dynamic electrical impedance imaging of a chest phantom using the Kalman filter

A dynamic complex impedance imaging technique is developed with the aid of the linearized Kalman filter (LKF) for real-time reconstruction of the human chest. The forward problem is solved by an analytical method based on the separation of variables and Fourier series. The inverse problem is treated as a state estimation problem. The nonlinear measurement equation is linearized about the best homogeneous impedivity value as an initial guess, and the impedivity distribution is estimated with the aid of the Kalman estimator. The Kalman gain matrix is pre-computed and stored off-line to minimize the on-line computational time. Simulation and phantom experiment are reported to illustrate the reconstruction performances in the sense of spatio-temporal resolution in a simplified geometry of the human chest.

A 3D reconstruction algorithm for EIT using a handheld probe for breast cancer detection

A 3D reconstruction algorithm for electrical impedance tomography is presented for determining the distribution of electrical properties inside the body, given electrical measurements made on the surface. A linearized reconstruction algorithm using planar electrode arrays in a handheld probe geometry developed by Mueller et al (1999 IEEE Trans. Biomed. Eng. 46 1379-86) has been refined and extended in this paper. This algorithm is based on linearizing the conductivity about a constant value. We have extended the distance below the electrodes at which a target can be imaged by using a combination of two regularization schemes and a weighted mesh. An appropriate combination of Tikhonov and NOSER regularization produces satisfactory static images of a 2 cm cube placed 2 cm below the array, and difference images of a 1 cm cube 4 cm away from the array. The weighted mesh allows use of fixed regularization parameters for all depths of the target.

Distinguishability of inhomogeneities using planar electrode arrays and different patterns of applied excitation

Electrical impedance tomography (EIT) is a non-invasive technique used to image the electrical conductivity and permittivity within a body from measurements taken on the body surface. Four methods are being investigated for breast cancer diagnosis by EIT today: Single voltage source, single current source and multiple current sources with a fixed pre-determined 'canonical' pattern of currents and an adaptively determined 'optimal' pattern of currents. To determine which of these four methods might yield the best distinguishability using planar electrode arrays for breast cancer detection, we placed electrode arrays on a saline tank and used each excitation pattern to detect a conducting target placed at the centre of a flat electrode array in two geometries: mammography geometry and single probe geometry. The result was that the multiple current sources method had higher distinguishability than either the SCS or the SVS method. In both these electrode geometries, the optimal current pattern had higher distinguishability than the other patterns at all distances.