Towards Precise Modelling of Diffusion Across the Blood-Brain Barrier.

In this chapter, we outline the key components of modelling passive solute fluxes across the blood-brain barrier (BBB). An overview of BBB anatomy is provided, and physiological parameters at transport interfaces are quantified. We highlight the scarcity of approaches to passive diffusion that directly integrate biophysics into comprehensive differential models. To address this, we investigate solute transport dynamics at the BBB using a physiological model of parabolic partial differential equations (PDEs).Analytical and numerical solutions to our PDE system are obtained, and we use initial conditions to incorporate characteristic features of the transport process. Solute properties and BBB permeability values are considered in conjunction with appropriate boundary conditions. A PDE stability analysis is performed to ensure the model's accuracy and utility. We extend our investigation by directly comparing our PDE model to a semi-physiological, compartmental ODE model sourced from the literature.The convergence of temporal concentration values for mannitol and sucrose is demonstrated, and the inherent advantage of our PDE methodology in predicting spatial concentration values is outlined. The proposed PDE model offers unique computational advantages in studies of pharmaceutical targeting for neurological disorders: it can be further developed to model passive diffusion in both steady and unsteady states across multiple dimensions; it incorporates physiological and pharmaceutical parameters directly; and it provides both spatial and temporal predictions of solute diffusion across the BBB.