MULTILEVEL PRECONDITIONING FOR 3D LARGE-SCALE SOFT-FIELD MEDICAL APPLICATIONS MODELLING

Soft-field imaging methods, such as Optical Tomography (OT) and Electrical Impedance Tomography (EIT) have significant potential for medical imaging as they are non-invasive, portable and inexpensive. Possible clinical applications include epilepsy monitoring, cerebral stroke differentiation and screening for breast cancer. Recent advances in data acquisition instrumentation and image reconstruction algorithms raise the requirement to handle multiple large datasets from detailed large-scale geometric descriptions of biological objects. Thus, a major bottleneck lies in processing a large number of linear equations that result from the Finite-Element formulation of soft-field problems. Common numerical tools are not suited for large-scale problems, therefore alternative approaches are required. We propose the facilitation of an innovative multi-level inverse-based incomplete LU preconditioning approach to improve computational efficiency in processing EIT and OT 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 incomplete LU factorisation provided a speed improvement of up to 11 times in preconditioner setup time, and up to 12 times in solution runtime for large-scale models. 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 approach exploits the information content given in the system in an optimal manner and therefore avoids redundant computation.