Generalized diffusion models for transport in scattering and non-scattering regions

Guillaume Bal
Columbia University

Transport solutions in highly scattering media are known to be well- approximated by solutions to diffusion equations. As several numerical studies show, the presence of non-scattering areas, such as clear layers in optical tomography (a medical imaging technique based on photon propagation in human tissues), hampers the use of classical diffusion. This has resulted in some researchers abandoning diffusion equations to replace them by the numerically much more costly transport equations. I will show that ``generalized'' diffusion equations can still model transport fairly accurately for a large class of non-scattering inclusions. Such non-scattering areas include clear layers filled with cerebrospinal fluid and hematoma that need to be modeled carefully in optical tomography. Several numerical simulations will also be presented.

Presentation (PDF File)

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