New Methodology and Modelling in Magnetic Resonance Imaging

The partial differential equations employed in this chapter are those based on the Bloch NMR flow equations and NMR diffusion equation. Each physical problems solved in this chapter are described by a Bloch related equation based on close observation of how the system usually behaves in the presence of NMR magnetic fields. A few numbers of realistic assumptions have been made in order to obtain a solution to each differential equation that has been developed for each problem identified. Justification for the choice of solution may not be presented in detail. However, basic information is appropriately provided. The solutions are obtained based on the following two properties (i) ability of the solution (describing the NMR transverse magnetisation) to demonstrate significant tissue contrast based on the unique relaxation times (ii) ability of the solution to give a significant value of NMR Signal when the spatial resolution is very small. Meanwhile, it may not be quite easy to achieve these criteria in all situations; however, at least one of these criteria was met in the model developed. In terms of methodology employed, the first two steps of developing a model (setting up a model in terms of differential equations and seeking for their mathematical/computational solutions) is adequately captured.