[Camino-users] Unexpected Monte Carlo Diffusion Simulations

[Slater David]

Hi everyone,

I've been working with the Camino Monte Carlo diffusion simulator. To check things were working correctly I tried some simple tests of diffusion around hexagonally packed cylinders. Spins were placed only in the extracellular space by using the 'extra' option. However even with these simple tests I've got some unexpected results.

I created a number of substrates with different axon radii while keeping the ratio of cylinder separation to axon radius constant. In this way we scale up and down the characteristic length scales of the system while keeping the intra- and extra-cellular volume fractions constant.

By applying the same scheme to each substrate with (Δ-δ/3)=30ms we would expect radial diffusivity to approach free diffusivity in systems with very large length scales (i.e. relatively few membrane interactions) while radial diffusivity should approximate theoretical tortuosity model predictions in systems with very small characteristic length scales.

In fact what we find from the simulations is that radial diffusivity can go up as the axon radius and axonal spacing go down. See the attached figure. This seems physically implausible to me: how is it that extracellular diffusivity can increase in systems with more membranes per unit length?

Here are example commands that I used to create the .traj files and to generate the synthetic measurements:

datasynth -walkers 200000 -tmax 5000 -p 0 -voxels 1 -initial extra -duration 0.04 -diffusivity 17E-10 -substrate cylinder -packing hex -cylinderrad 9.01E-07 -cylindersep 2.22E-06 -trajfile ic60_diam1p8E-06_extra_hex_dura40ms.traj

scan -trajfile ic60_diam1p8E-06_extra_hex_dura40ms.traj -schemefile J30_DELTA30.scheme2 | float2txt > ic60_diam1p8E-06_extra_hex_dura40ms_J30_DELTA30.txt

I have also attached the .scheme2 file that was used.

What might be leading to these unexpected results? Do you have any suggestions for where I might be going wrong?

Any help or suggestions will be greatly appreciated.

Thanks,
David
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