Novel Large-Scale 3D Electrical Impedance Tomography Modeling of the Human Head

Abstract

With the advent of detailed numerical models, computing runtime can become excessive. We propose the facilitation of an innovative multi-level inverse-based LU preconditioning approach to improve computational efficiency while processing EIT system matrices. This combines static reordering and scaling, controlled growth of the inverse of triangular factors and approximation of the Schur-complement in a multi-level scheme. Comparison with conventional ILU factorization provided an increasing acceleration factor of up to 6 while preconditioning, and up to 12 in solution runtime for models with 12K–503K elements. In addition, a new approach of monopolar current sources is introduced. Current sources and sinks are represented by linear combinations of a compact monopolar sources basis. Only the corresponding monopolar solutions are processed. These solutions serve as a basis for construction of the entire excitation pattern. This counter-intuitive approach exploits the information content given in the system in an optimal manner and therefore avoids redundant computation.