Konzeption und Realisierung eines skalierbaren Simulators für die Magnetresonanz-Tomographie

Abstract

In research activities regarding Magnetic Resonance Imaging in medicine, simulation tools with a universal approach are rare. Usually, simulators are developed and used which tend to be restricted to a particular, small range of applications. This led to the design and implementation of a new simulator PARSPIN, the subject of this thesis. In medical applications, the Bloch equation is a well-suited mathematical model of the underlying physics with a wide scope. In this thesis, it is shown how analytical solutions of the Bloch equation can be found, which promise substantial execution time advantages over numerical solution methods. From these analytical solutions of the Bloch equation, a new formalism for the description and the analysis of complex imaging experiments is derived, the K-t formalism. It is shown that modern imaging methods can be better explained by the K-t formalism than by observing and analysing the magnetization of each spin of a spin ensemble. Various approaches for a numerical simulation of Magnetic Resonance imaging are discussed. It is shown that a simulation tool based on the K-t formalism promises a substantial gain in execution time. Proper spatial discretization according to the sampling theorem, a topic rarely discussed in literature, is universally derived from the K-t formalism in this thesis. A spin-based simulator is an application with high demands to computing facilities even on modern hardware. In this thesis, two approaches for a parallelized software architecture are designed, analysed and evaluated with regard to a reduction of execution time. A number of possible applications in research and education are demonstrated. For a choice of imaging experiments, results produced both experimentally and by simulation are compared