IEEE Transactions on Medical Imaging

We compute unmeasured cone-beam projections from projections measured by a third-generation helical volumetric computed tomography system by solving a characteristic problem for an ultrahyperbolic differential equation [John (1938)]. By working in the Fourier domain, we convert the second-order PDE into a family of first-order ordinary differential equations. A simple first-order integration is used to solve the ODES.

This paper concerns the modeling and interpretation of harmonies observed as a result of the nonlinear electrical properties of biomedical electrode/electrolyte interfaces. The higher order harmonics have been calculated assuming that the nonlinearity of the interfacial impedance is dominated at low frequencies by the nonlinear faradaic charge transfer resistance. The harmonic distribution in the output signal is compared between 1) the author's theoretical model based on the Butler-Volmer equation and 2) Schwan's empirical model and results. The influence of different parameters such as the number of electrons involved in the faradaic reaction and the transfer coefficient was investigated in order to physically interpret the experimental results. A good agreement was found between the authors' model and some of the experimental data previously reported in the literature. Further, potentially productive areas of research have been identified.

We report an exact and fast Fourier-domain reconstruction algorithm for thermoacoustic tomography in a planar configuration assuming thermal confinement and constant acoustic speed. The effects of the finite size of the detector and the finite length of the excitation pulse are explicitly included in the reconstruction algorithm. The algorithm is numerically and experimentally verified. We also demonstrate that the blurring caused by the finite size of the detector surface is the primary limiting factor on the resolution and that it can be compensated for by deconvolution.

Electrical impedance spectroscopy (EIS) is a potential, noninvasive technique to image women for breast cancer. Studies have shown characteristic frequency dispersions in the electrical conductivity and permittivity of malignant versus normal tissue. Using a multifrequency EIS system, we imaged the breasts of 26 women. All patients had mammograms ranked using the American College of Radiology (ACR) BIRADS system. Of the 51 individual breasts imaged, 38 were ACR 1 negative, six had ACR 4-5 suspicious lesions, and seven had ACR 2 benign findings such as fibroadenomas or calcifications. A radially translatable circular array of 16 Ag/AgCl electrodes was placed around the breast while the patient lay prone. We applied trigonometric voltage patterns at ten frequencies between 10 and 950 kHz. Anatomically coronal images were reconstructed from this data using nonlinear partial differential equation methods. Typically, ACR 1-rated breasts were interrogated in a single central plane whereas ACR 2-5-rated breasts were imaged in multiple planes covering the region of suspicion. In general, a characteristic homogeneous image emerged for mammographically normal cases while focal inhomogeneities were observed in images from women with malignancies. Using a specific visual criterion, EIS images identified 83% of the ACR 4-5 lesions while 67% were detected using a numerical criterion. Overall, multifrequency electrical impedance imaging appears promising for detecting breast malignancies, but improvements must be made before the method reaches its full potential.

In the inverse conductivity problem, as in any ill-posed inverse problem, regularization techniques are necessary in order to stabilize inversion. A common way to implement regularization in electrical impedance tomography is to use Tikhonov regularization. The inverse problem is formulated as a minimization of two terms: the mismatch of the measurements against the model, and the regularization functional. Most commonly, differential operators are used as regularization functionals, leading to smooth solutions. Whenever the imaged region presents discontinuities in the conductivity distribution, such as interorgan boundaries, the smoothness prior is not consistent with the actual situation. In these cases, the reconstruction is enhanced by relaxing the smoothness constraints in the direction normal to the discontinuity. In this paper, we derive a method for generating Gaussian anisotropic regularization filters. The filters are generated on the basis of the prior structural information, allowing a better reconstruction of conductivity profiles matching these priors. When incorporating prior information into a reconstruction algorithm, the risk is of biasing the inverse solutions toward the assumed distributions. Simulations show that, with a careful selection of the regularization parameters, the reconstruction algorithm is still able to detect conductivities patterns that violate the prior information. A generalized singular-value decomposition analysis of the effects of the anisotropic filters on regularization is presented in the last sections of the paper.