Home Computer Science Computational Diffusion MRI: MICCAI Workshop, Athens, Greece, October 2016
The Flux Terms: Transport Processes
Different choices of flux lead to different solutions of Eq. (15), and in many cases to different specific MR imaging techniques. We will give solutions in terms of the q-space approximation, assuming a Fourier relationship between spatial variables x and displacement spatial frequencies q = ylG. In most cases solutions are found via the Fourier-Laplace method applied to the Bloch-Torrey equation in question.
This section reviews the diffusion MRI modelling literature in the context of the theoretic framework developed above. We will show how many existing techniques stem from choices of flux terms of generalised Bloch-Torrey equations and demonstrates that the framework acts as a unifying principle across what can otherwise appear a bewildering maze of different models. We will also see that the common assumption that the phase information is not important is only valid in particular special cases (The different combinations are summarised in Table 1).
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