New Mathematical Model for the Diffusion Time Dependent ADC

DMRI has been established as a useful tool to obtain voxel-level information on tissue microstructure. An important quantity measured in dMRI is the apparent diffusion coefficient (ADC), and it has been well established by in-vivo brain imaging experiments that the ADC depends significantly on the diffusion time. To aid in understanding and interpreting the experimentally measured ADC, we derive a new mathematical model of the voxel-level ADC that is diffusion time-dependent and accurate over a large range of diffusion times, using a linearization of the Bloch-Torrey equation around low b-values. The goal is to use this time-dependent ADC model in the future to identify parameters of tissue microstructure from the experimentally measured ADC at different diffusion times.

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