Abstract
The development of drugs targeting the brain still faces a high failure rate. One of the reasons is a lack of quantitative understanding of the complex processes that govern the pharmacokinetics (PK) of a drug within the brain. While a number of models on drug distribution into and within the brain is available, none of these addresses the combination of factors that affect local drug concentrations in brain extracellular fluid (brain ECF). Here, we develop a 3D brain unit model, which builds on our previous proof-of-concept 2D brain unit model, to understand the factors that govern local unbound and bound drug PK within the brain. The 3D brain unit is a cube, in which the brain capillaries surround the brain ECF. Drug concentration-time profiles are described in both a blood-plasma-domain and a brain-ECF-domain by a set of differential equations. The model includes descriptions of blood plasma PK, transport through the blood-brain barrier (BBB), by passive transport via paracellular and transcellular routes, and by active transport, and drug binding kinetics. The impact of all these factors on ultimate local brain ECF unbound and bound drug concentrations is assessed. In this article we show that all the above mentioned factors affect brain ECF PK in an interdependent manner. This indicates that for a quantitative understanding of local drug concentrations within the brain ECF, interdependencies of all transport and binding processes should be understood. To that end, the 3D brain unit model is an excellent tool, and can be used to build a larger network of 3D brain units, in which the properties for each unit can be defined independently to reflect local differences in characteristics of the brain.
Highlights
The brain capillary bed is the major site of drug exchange between the blood and the brain
We describe the distribution of drug within the brain extracellular fluid (ECF) by a partial differential equation (PDE) and couple this to two ordinary differential equations (ODEs) to account for specific and non-specific drug binding
(iv) All drug distributes within the brain ECF and we only have extracellular binding sites. (v) The total concentration of specific and non-specific binding sites is constant. (vi) The specific and non-specific binding sites are evenly distributed over the 3D brain unit and do not change position. (vii) The specific and non-specific binding sites lie on the outside of cells and the drug does not have to cross cell membranes in order to bind to binding sites. (viii) Drug binding is reversible and drugs associate and dissociate from their binding sites
Summary
The brain capillary bed is the major site of drug exchange between the blood and the brain. The most recent and comprehensive brain drug distribution model is the physiologically-based pharmacokinetic model for the rat and for human [27, 28] This model takes multiple compartments of the central nervous system (CNS) into account, including plasma PK, passive paracellular and transcellular BBB transport, active BBB transport, and distribution between the brain ECF, intracellular spaces, and multiple CSF sites, on the basis of CNS-specific and drug-specific parameters. The 3D brain unit model encompasses blood plasma PK, the BBB, brain ECF, brain ECF bulk flow, diffusion, and binding to specific and non-specific binding sites [29, 30] within the brain This 3D piece of brain tissue can be considered the smallest physiological unit of the brain in terms of drug transport. BBB transport, diffusion, brain ECF bulk flow, specific binding of a drug at its target site and non-specific binding of a drug to components of the brain.
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