A Review of Mathematics Determining Solute Uptake at the Blood-Brain Barrier in Normal and Pathological Conditions

Abstract

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.

Keywords: blood–brain barrier; brain; magnetic-resonance imaging; pharmacokinetics; preclinical models.

Figure 1

Anatomical differences between (A) blood–brain barrier vasculature and (B) disrupted BBB. The BBB is characterized by presence of endothelial tight junctions, formed by the tight junction proteins and the adjacent pericytes, microglia and astrocytic foot processes.

Figure 2

Correlation of solute BBB permeability, indicated by its permeability surface area (PS) product, with the Log(P÷√MW). Compounds with higher lipophilicity have a greater tendency to traverse the BBB. Compounds in the green-shaded area are those with values of 80% of reported cerebral blood flow or high. Compounds in the yellow shaded region indicate those with PS values between 20 and 80% of cerebral blood flow. Compounds with PS values in the red-shaded area are those with reported PS values which are less than 20% of cerebral blood flow. Values compiled from literature reported values of PS [14,15,16,17] R² = 0.78.

Figure 3

A schematic representation of (A) extraction-limited and (B) flowlimited solute transfer across the BBB. The physicochemical properties of compounds having extraction-limited permeability are not amenable to BBB transport. Conversely, the transport of highly permeable solutes across the BBB is generally quick, and only limited by how rapidly they are presented to the BBB.

Figure 4

Differential tracer uptake in various imaging modalities. Accumulation of Texas Red 3K (A) and 14C-aminoisobutyric acid (B) in brain metastases of breast cancer using fluorescent and phosphorescent quantitative imaging. (C)T1 cortical Turbo Spin Echo MRI indicating gadavist enhancement in lesions within the brain.