Model-based elastography is fraught with problems owing to the ill-posed nature of the inverse elasticity problem. To overcome this limitation, we have recently developed a novel inversion scheme that incorporates a priori information concerning the mechanical properties of the underlying tissue structures, and the variance incurred during displacement estimation in the modulus image reconstruction process. The information was procured by employing standard strain imaging methodology, and introduced in the reconstruction process through the generalized Tikhonov approach. In this paper, we report the results of experiments conducted on gelatin phantoms to evaluate the performance of modulus elastograms computed with the generalized Tikhonov (GTK) estimation criterion relative to those computed by employing the un-weighted least-squares estimation criterion, the weighted least-squares estimation criterion and the standard Tikhonov method (i.e., the generalized Tikhonov method with no modulus prior). The results indicate that modulus elastograms computed with the generalized Tikhonov approach had superior elastographic contrast discrimination and contrast recovery. In addition, image reconstruction was more resilient to structural decorrelation noise when additional constraints were imposed on the reconstruction process through the GTK method.

Traditionally, image reconstruction in electrical impedance tomography (EIT) has been based on Laplace's equation. However, at high frequencies the coupling between electric and magnetic fields requires solution of the full Maxwell equations. In this paper, a formulation is presented in terms of the Maxwell equations expressed in scalar and vector potentials. The approach leads to boundary conditions that naturally align with the quantities measured by EIT instrumentation. A two-dimensional implementation for image reconstruction from EIT data is realized. The effect of frequency on the field distribution is illustrated using the high-frequency model and is compared with Laplace solutions. Numerical simulations and experimental results are also presented to illustrate image reconstruction over a range of frequencies using the new implementation. The results show that scalar/vector potential reconstruction produces images which are essentially indistinguishable from a Laplace algorithm for frequencies below 1 MHz but superior at frequencies reaching 10 MHz.

We develop a statistical criterion for optimal patterns in planar circular electrical impedance tomography. These patterns minimize the total variance of the estimation for the resistance or conductance matrix. It is shown that trigonometric patterns (Isaacson, 1986), originally derived from the concept of distinguishability, are a special case of our optimal statistical patterns. New optimal random patterns are introduced. Recovering the electrical properties of the measured body is greatly simplified when optimal patterns are used. The Neumann-to-Dirichlet map and the optimal patterns are derived for a homogeneous medium with an arbitrary distribution of the electrodes on the periphery. As a special case, optimal patterns are developed for a practical EIT system with a finite number of electrodes. For a general nonhomogeneous medium, with no a priori restriction, the optimal patterns for the resistance and conductance matrix are the same. However, for a homogeneous medium, the best current pattern is the worst voltage pattern and vice versa. We study the effect of the number and the width of the electrodes on the estimate of resistivity and conductivity in a homogeneous medium. We confirm experimentally that the optimal patterns produce minimum conductivity variance in a homogeneous medium. Our statistical model is able to discriminate between a homogenous agar phantom and one with a 2 mm air hole with error probability (p-value) 1/1000.

Electrical impedance tomography (EIT) has been used in the recent past for a number of clinical applications. In this work we present recent tomographic and spectroscopic findings for breast imaging from clinical exams completed at Dartmouth. The results presented here are based on 18 normal and 24 abnormal subjects. The participants were classified as normal or abnormal using the American College of Radiology (ACR) indexing system for mammograms. The EIT data were collected for ten discrete frequencies in the range 10 kHz-1 MHz using a single array of 16 electrodes. The finite element method was used to reconstruct the images. The images were examined visually and were compared with mammograms. The results were also analyzed based on zonal averages of property values and breast tissue radiodensities. Statistical analysis showed a significance difference between the mean conductivity and permittivity values of normal and abnormal subjects for various zones defined on the reconstructed images. Tissues with high radiodensity also had increased conductivity and permittivity.