Nonuniform spatial mesh adaptation using a posteriori error estimates: Applications to forward and inverse problems
The following tasks occurring in biomedicine are considered: Direct problem: Given a subset of potentials of the surface of the heart, or a description of the primary current sources within the heart. Find the electric and potential fields everywhere within the body and the voltages on the surface of the torso. Inverse problem I: Given a subset of voltages on the surface of the thorax. Find either the voltages on a closed surface bounding the heart or the primary currents within the volume of the heart. Inverse problem II: Given known currents or voltages which are applied from external sources. Find the distribution of applied current throughout the heart. Both of the inverse problems are ill-posed. The mathematical formulation of these problems leads to an elliptic equation of second order in a three-dimensional inhomogeneous, anisotropic domain with boundary conditions, respectively. For its solution the authors develop an adaptive meshing scheme based upon a posteriori error estimates from the finite element approximation. Furthermore, a brief description of its implementation and some results using these techniques are given.
three-dimensional inhomogeneous, anisotropic domain
scientific article; zbMATH DE number 609624