Diffusion-MRI Monte-Carlo simulations need at least 5e5 particles, 1e4 time steps, and roughly 10,000 cylinders per substrate to avoid variance and bias that compromise their use as ground truth.
Random walk with barriers: Diffusion restricted by permeable membranes
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abstract
Restrictions to molecular motion by barriers (membranes) are ubiquitous in biological tissues, porous media and composite materials. A major challenge is to characterize the microstructure of a material or an organism nondestructively using a bulk transport measurement. Here we demonstrate how the long-range structural correlations introduced by permeable membranes give rise to distinct features of transport. We consider Brownian motion restricted by randomly placed and oriented permeable membranes and focus on the disorder-averaged diffusion propagator using a scattering approach. The renormalization group solution reveals a scaling behavior of the diffusion coefficient for large times, with a characteristically slow inverse square root time dependence. The predicted time dependence of the diffusion coefficient agrees well with Monte Carlo simulations in two dimensions. Our results can be used to identify permeable membranes as restrictions to transport in disordered materials and in biological tissues, and to quantify their permeability and surface area.
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Robust Monte-Carlo Simulations in Diffusion-MRI: Effect of the substrate complexity and parameter choice on the reproducibility of results
Diffusion-MRI Monte-Carlo simulations need at least 5e5 particles, 1e4 time steps, and roughly 10,000 cylinders per substrate to avoid variance and bias that compromise their use as ground truth.