“A Finite Difference Model of Water Diffusion in 2D and 3D”
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Abstract: Diffusion-weighted MRI (DWMRI) allows non-invasive measurement of the motion of water in living tissue. Spatial maps of quantitative parameters, such as the apparent diffusion coefficient (ADC), can be obtained from DWMRI and are routinely used in clinical evaluation of neurological disease, such as stroke. More recently, the ADC has been used as an early predictor of response to chemotherapy in cancer. Despite the clinical utility of DWMRI and robustness of changes in ADC in stroke and cancer therapy, the biophysical mechanisms underlying ADC are not completely known. Different types of computational models have been proposed to aid in the understanding of DWMRI data. An accurate model of DWMRI must (1) realistically model the diffusion of water within a tissue and (2) account for how molecular diffusion and T2 decay effect MRI signal in a DWMRI experiment. We have developed a finite difference model (FDM) of molecular diffusion that considers cell size, intracellular volume fraction, cell membrane permeability, and compartment specific T2 and diffusion coefficients. In this work, we demonstrate the FDM in tissues composed of 2D square cells and 3D cubic cells.