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Characterizing Water Diffusion In Fixed Baboon Brain

In the Biomedical Medical Research laboratory in St. Louis Missouri there is an ongoing project to characterize water diffusion in fixed baboon brain using diffusion weighted magnetic res- onance imaging as a means of monitoring development throughout gestation. Magnetic resonance images can be made sensitive to diffusion by applying magnetic field gradients during the pulse sequence. Results from the analysis of diffusion weighted magnetic resonance images using a full diffusion tensor model do not fit the data well. The estimated standard deviation of the noise exhibit structures corresponding to known baboon brain anatomy. However, the diffusion tensor plus a con- stant model overfits the data: the residuals in the brain are smaller than in regions where there is no signal. Consequently, the full diffusion tensor plus a constant model has too many parameters and needs to be simplified. This model can be simplified by imposing axial symmetry on the diffusion tensor. There are three axially symmetric diffusion tensor models, prolate, oblate, and isotropic; and two other models, no signal and full diffusion tensor, that could characterize the diffusion weighted images. These five models may or may not have a constant offset, giving 10 total models that poten- tially describe the diffusion process. In this paper the Bayesian calculations needed to select which of the 10 models best characterizes the diffusion data are presented. The various outputs from the analysis are illustrated using one of our baboon brain data sets.