User:Jadrian Miles/Diffusion simulation

• Axon gauges in range 0.25 -- 10 μm (wzhou cite 1). "Extra-thick" axons (~20μm) are rare; about 3% occurrence at most, and only in certain structures.
• Hindered diffusion differs from free diffusion by a "tortuosity" value (Nicholson "Diffusion and related transport mechanisms" '01)
• Volume fraction is ~80% intra? (Nilsson MRI '08)
• Extracellular free D ~= 1.08 μm²/ms (ibid)
• τ_intra ~= 306 ms (but authors claim it's a bad fit) (ibid) (exchange times; see page 178 and ref 35)

Human histology would be useful: hand-compute volume fraction of intracellular fluid, extracellular fluid, and myelin, as well as axon gauges.

What about parallel DWIs and microscale histology on a sheep or macaque brain?

Parameters:

• direction: 1, 2, n
• directional coherence: ignore, scalar
• exchange: ignore, constant, per-compartment
• isotropic D: constant globally, constant intra / extra, per-compartment
• gauge: constant, per-compartment, fixed distribution, distribution per-compartment
• volume fraction: intra / extra, per-compartment

The experiment:

1. Generate lots of detailed 1-voxel numerical phantoms and run diffusion simulation on them to generate DWIs in a dense sampling of q-space. Now you have ground truth (kinda).
2. For a given phantom, fix all parameters but two at known correct values and then analyze the ambiguity between the free parameters. Treat one as independent and vary its assumed value; find the value of the other that best recreates the DWIs. Your output is a dependent-variable value and a DWI error.
3. For each pair of parameters, scatter-plot (or multi-line plot) the relationship between them over all phantoms.
4. Generalize some ambiguity rules and theorize about 'em.