A new framework for analyzing mass transport in cortical brain tissue at <10 nm resolution

Transmission electron microscopy of brain tissue yields high resolution maps of the spatial organization of cells in the central nervous system. Automated segmentation identifies distinct biological cells and the resulting segmented images are easily converted into surface meshes. The surface meshes are structural models of cell surfaces, providing a framework for modeling of mass transport within the interstitial fluid of brain tissue that surrounds the cells. Our goal is to model the production and clearance of proteins implicated in the development of Alzheimer’s Disease. This work introduces a new custom computational framework to allow massive parallelization of the solution of the mathematical equations of mass transfer. The diffusion equation was solved directly on the surface meshes of multiple biological cells in parallel, with exchange of mass across co-localized faces at the end of each time step. Mass transfer across the interfaces of multiple analysis volumes was incorporated using a semi-implicit approach. To demonstrate the capabilities of the framework, unsteady mass transfer along cell surfaces was modeled in an array of eight 4 x 4 x 4 μm analysis volumes containing 2175 biological cells at 8 nm resolution, consisting of 313 million face elements. Areas of enhanced and hindered diffusive transport were identified, suggesting structural motifs that may contribute to the development of insoluble plaques. The tortuosity and fractional anisotropy were consistent with Diffusion Tensor Imaging (DTI) measurements in cortical tissue. This new framework allows modeling of diffusive mass transport while preserving anatomical details at <10 nm resolution.