Efficient Simultaneous Reconstruction of Time-Varying Images and Electrode Contact Impedances in Electrical Impedance Tomography.

Objective: In electrical impedance tomography (EIT), we apply patterns of currents on a set of electrodes at the external boundary of an object, measure the resulting potentials at the electrodes, and, given the aggregate dataset, reconstruct the complex conductivity and permittivity within the object. It is possible to maximize sensitivity to internal conductivity changes by simultaneously applying currents and measuring potentials on all electrodes but this approach also maximizes sensitivity to changes in impedance at the interface.

Methods: We have, therefore, developed algorithms to assess contact impedance changes at the interface as well as to efficiently and simultaneously reconstruct internal conductivity/permittivity changes within the body.

Adaptive techniques in electrical impedance tomography reconstruction.

We present an adaptive algorithm for solving the inverse problem in electrical impedance tomography. To strike a balance between the accuracy of the reconstructed images and the computational efficiency of the forward and inverse solvers, we propose to combine an adaptive mesh refinement technique with the adaptive Kaczmarz method. The iterative algorithm adaptively generates the optimal current patterns and a locally-refined mesh given the conductivity estimate and solves for the unknown conductivity distribution with the block Kaczmarz update step.

Adaptive Kaczmarz method for image reconstruction in electrical impedance tomography.

We present an adaptive Kaczmarz method for solving the inverse problem in electrical impedance tomography and determining the conductivity distribution inside an object from electrical measurements made on the surface. To best characterize an unknown conductivity distribution and avoid inverting the Jacobian-related term J(T)J which could be expensive in terms of computation cost and memory in large-scale problems, we propose solving the inverse problem by applying the optimal current patterns for distinguishing the actual conductivity from the conductivity estimate between each iteration of the block Kaczmarz algorithm. With a novel subset scheme, the memory-efficient reconstruction algorithm which appropriately combines the optimal current pattern generation with the Kaczmarz method can produce more accurate and stable solutions adaptively as compared to traditional Kaczmarz- and Gauss-Newton-type methods.

The development of biomedical engineering as experienced by one biomedical engineer.

This personal essay described the development of the field of Biomedical Engineering from its early days, from the perspective of one who lived through that development. It describes the making of a major invention using data that had been rejected by other scientists, the re-discovery of an obscure fact of physiology and its use in developing a major medical instrument, the development of a new medical imaging modality, and the near-death rescue of a research project. The essay concludes with comments about the development and present status of impedance imaging, and recent changes in the evolution of biomedical engineering as a field.

Methods for compensating for variable electrode contact in EIT.

Electrical impedance tomography (EIT) is an imaging modality that currently shows promise for the detection and characterization of breast cancer. A very significant problem in EIT imaging is the proper modeling of the interface between the body and the electrodes. We have found empirically that it is very difficult, in a clinical setting, to assure that all electrodes make satisfactory contact with the body.

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.

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.

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).

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.

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.

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.

Layered model for breasts in electrical impedance tomography.

We are presently using Electrical Impedance Tomography as a technique for breast cancer imaging, determining the admittivity distribution inside the breast. The admittivities we observed in compressed breasts in EIT were lower than those seen in earlier studies involving whole chest imaging. We attribute this to a thin low admittance skin layer which dominates in compressed breasts.

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.

The complete electrode model for imaging and electrode contact compensation in electrical impedance tomography.

Electrical Impedance Tomography (EIT) is an imaging modality which currently shows promise for the detection and characterization of breast cancer. A very significant problem in EIT imaging is the proper modeling of the interface between the body and the electrodes. We have found empirically that it is very difficult, in a clinical setting, to assure that all electrodes make satisfactory contact with the body.

The complete electrode model for EIT in a mammography geometry.

We have developed an EIT system for simultaneous use in a mammography examination, allowing for highly accurate co-registration between the two modalities. In this pre-clinical study, we investigate the importance of properly modeling the interface between the electrodes and the medium being imaged. We have implemented the complete electrode model for a parallel-plane mammography geometry, in which currents are injected into the medium through two planar sets of electrodes above and below the medium.

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.

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.

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.

Electrode boundary conditions and experimental validation for BEM-based EIT forward and inverse solutions.

In this paper, we present theoretical developments and experimental results for the problem of estimating the conductivity map inside a volume using electrical impedance tomography (EIT) when the boundary locations of any internal inhomogeneities are known. We describe boundary element method (BEM) implementations of advanced electrode models for the forward problem of EIT. We then use them in the inverse problem with known internal boundaries and derive the associated Jacobians.

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.

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.

Reconstructions of chest phantoms by the D-bar method for electrical impedance tomography.

The problem this paper addresses is how to use the two-dimensional D-bar method for electrical impedance tomography with experimental data collected on finitely many electrodes covering a portion of the boundary of a body. This requires an approximation of the Dirichlet-to-Neumann, or voltage-to-current density map, defined on the entire boundary of the region, from a finite number of matrix elements of the current-to-voltage map. Reconstructions from experimental data collected on a saline filled tank containing agar heart and lung phantoms are presented, and the results are compared to reconstructions by the NOSER algorithm on the same data.