A review of mathematics determining solute uptake at the blood–brain barrier in normal and pathological conditions

The blood–brain barrier (BBB) limits movement of solutes from the lumen of the brain microvascular capillary system into the parenchyma. The unidirectional transfer constant, K_in, is the rate at which transport across the BBB occurs for individual molecules. Single and multiple uptake experiments are available for the determination of K_in for new drug candidates using both intravenous and in situ protocols. Additionally, the single uptake method can be used to determine K_in in heterogeneous pathophysiological conditions such as stroke, brain cancers, and Alzheimer’s disease. In this review, we briefly cover the anatomy and physiology of the BBB, discuss the impact of efflux transporters on solute uptake, and provide an overview of the single-timepoint method for determination of K_in values. Lastly, we compare preclinical K_in experimental results with human parallels.