Supercomputer simulations in the problem of ultrasound diagnostics with the use of analytical approaches

Abstract

This is a study of ultrasound radiation in the environment and the solution of the direct and inverse problems of ultrasound tomography. The interaction of radiation with inhomogeneities is modeled by two methods: finite-difference and analytic. This allows us to estimate the limits of applicability of the considered models and evaluate the accuracy of the calculations. The use of two independent methods helps to check the reliability of methods for solving direct and inverse problems. Mathematical modeling methods investigated the effects of the density of the substance to the possibility of reconstruction. Choice of model parameters are oriented to the problem of differential diagnosis of breast diseases. The used algorithms are based on the direct calculation of the gradient of the residual functional. The problem of the large amount of computation for solving the inverse problem is overcome by using a supercomputer cluster-type on the basis of MPI technology. Used explicit finite difference scheme is ideally suited for parallelization. The results of model calculations are shown that demonstrate the effectiveness of the proposed approaches.