3D simulation of diffraction in ultrasonic computed tomography.

The contribution presents further results in developing the exact means for simulating the realistic situation in the USCT (ultrasonic computed tomography) imaging system, aiming both at evaluating the approximations used in the existing USCT image reconstruction methods as to their precision and also (in a longer perspective) at iterative improvement of the obtained images via continuum mechanics based feedback. The mathematical models, generalised in comparison with [1], emerging from the transparent physical background, are presented for inhomogeneous media incorporating both the object tissue and the surrounding fluid. The equations are already general enough to employ complex nonlinear phenomena in three-dimensional space; and linearised 3D simulations (giving rise to wave equation, WE) have been performed enabling first conclusions on the feasibility of this approach with respect to the available computing resources. Some of the results of the numerical solution of the WE in 3D by means of the finite-element method show in local detail the diffraction phenomena on acoustic-impedance inhomogeneities. The spatial extent of the simulations is basically limited only by the available computing resources. The hardware requirements and related practical limitations are mentioned together with a few examples of presently available results. Together with conclusions, further perspectives of this branch of the USCT research are suggested.