Home Computer Science Computational Diffusion MRI: MICCAI Workshop, Athens, Greece, October 2016
The Bloch-Torrey equation is a lens through which different models in the diffusion MRI literature can be compared. We have attempted here to lay out the relationships between different approaches in terms of the underlying physics, avoiding discussion of inverse problems, machine learning, and other technical aspects which are commonly the focus elsewhere in the literature.
We can see that models assume different numbers of compartments and (often implicitly) different transport processes. We can also see that it is not possible to identify one particular approach as being superior to all others. In some cases we may wish to approach the signal with as few assumptions as possible, in others we may have extensive prior knowledge that it may be helpful to include in our models. Clinical constraints may enforce very short acquisition times or preclude more advanced acquisitions or processing and therefore require simpler methods.
In choosing a model or developing a new one it may be helpful to consider how natural a set of assumptions is. Although features such as direction anisotropy can be readily extracted from measurements, diffusion decay curves are extremely featureless. Although diffraction patterns are an exception to this, these patterns are only visible under very specific circumstances in which tissue geometry is highly regular. In more realistic situations tissue heterogeneity means that decay curves are very smooth, and we are faced with a problem of model degeneracy: given a sufficiently dense sampling of data we can, in principle, fit any (reasonably well- posed) model we choose. This makes model selection all the more important. We hope that looking at different models in terms of the physical assumptions is a useful aid.
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