A Spatially Distributed Model of Brain Metabolism Highlights the Role of Diffusion in Brain Energy Metabolism

TL;DR

This paper introduces a detailed spatially distributed computational model of brain metabolism that incorporates diffusion processes in extracellular space and astrocyte networks, highlighting their roles in energy supply during neuronal activity.

Contribution

The study presents a novel multidomain model with a homogenization approach for diffusion, integrating biochemical and spatial transport processes in brain metabolism modeling.

Findings

Diffusion in ECS and astrocyte networks significantly affects energy metabolism.

Gap junction strength influences metabolite distribution and brain energy supply.

Spatial anisotropy alters diffusion effects and metabolic efficiency.

Abstract

The different active roles of neurons and astrocytes during neuronal activation are associated with the metabolic processes necessary to supply the energy needed for their respective tasks at rest and during neuronal activation. Metabolism, in turn, relies on the delivery of metabolites and removal of toxic byproducts through diffusion processes and the cerebral blood flow. A comprehensive mathematical model of brain metabolism should account not only for the biochemical processes and the interaction of neurons and astrocytes, but also the diffusion of metabolites. In the present article, we present a computational methodology based on a multidomain model of the brain tissue and a homogenization argument for the diffusion processes. In our spatially distributed compartment model, communication between compartments occur both through local transport fluxes, as is the case within local astrocyte-neuron complexes, and through diffusion of some substances in some of the compartments. The model assumes that diffusion takes place in the extracellular space (ECS) and in the astrocyte compartment. In the astrocyte compartment, the diffusion across the syncytium network is implemented as a function of gap junction strength. The diffusion process is implemented numerically by means of a finite element method (FEM) based spatial discretization, and robust stiff solvers are used to time integrate the resulting large system. Computed experiments show the effects of ECS tortuosity, gap junction strength and spatial anisotropy in the astrocyte network on the brain energy metabolism.