Methods for simulations with thousands of interacting objects to model mass transport in the brain

Clearance of toxic species that may cause neurodegenerative diseases relies on convection and diffusion of mass around cells in the central nervous system. In this manuscript, methods that allow the nanoscale modeling of mass transport around cells in the brain at a resolution of 8 nm are described. The cells are modeled as surface meshes and a parallelization scheme is used to solve the diffusion equation directly on the surface mesh of each biological cell independently. This is followed by mass exchange between biological cells that are in direct contact. The analysis volume size is fixed at 4 μm x 4 μm x 4 μm but arrays of analysis volumes of arbitrary size may be analyzed, with fluxes across analysis volume boundaries updated at each time step by a semi-implicit formulation. Setup of the discretized equations is described, along with the ‘face matching’ that allows mass transfer between cells. Parallelization is via a manager/worker framework. One-sided RMA communication in MPI is used to coordinate the efforts of multiple workers, with common information handled by the manager. This specialized framework is suitable for analyzing diffusional transport around thousands of interacting objects simultaneously. The framework is implemented with custom code developed in Julia, which is used here as a rapid prototyping language. Using model geometries, the accuracy of the discretization methods are demonstrated, with limitations and next steps described.