Abstract
The development of drugs that target the brain is very challenging. A quantitative understanding is needed of the complex processes that govern the concentration–time profile of a drug (pharmacokinetics) within the brain. So far, there are no studies on predicting the drug concentration within the brain that focus not only on the transport of drugs to the brain through the blood–brain barrier (BBB), but also on drug transport and binding within the brain. Here, we develop a new model for a 2D square brain tissue unit, consisting of brain extracellular fluid (ECF) that is surrounded by the brain capillaries. We describe the change in free drug concentration within the brain ECF, by a partial differential equation (PDE). To include drug binding, we couple this PDE to two ordinary differential equations that describe the concentration–time profile of drug bound to specific as well as non-specific binding sites that we assume to be evenly distributed over the brain ECF. The model boundary conditions reflect how free drug enters and leaves the brain ECF by passing the BBB, located at the level of the brain capillaries. We study the influence of parameter values for BBB permeability, brain ECF bulk flow, drug diffusion through the brain ECF and drug binding kinetics, on the concentration–time profiles of free and bound drug.
Highlights
The development of drugs that target the brain and reach the target site in adequate levels is very challenging
As the main barrier of the brain, the blood–brain barrier (BBB) separates the blood from the brain extracellular fluid (ECF), which may cause the drug concentration–time profiles in blood and brain to be substantially different from each other (Hladky and Barrand 2014)
We model the transport of a drug through the brain ECF within a unit by diffusion and brain ECF bulk flow
Summary
The development of drugs that target the brain and reach the target site in adequate levels is very challenging. As a step towards such understanding, we formulate a 2D brain tissue unit model, where drug transport across the BBB and within the brain ECF, and the interaction of a drug with both specific (target) and non-specific binding sites are incorporated. The existing models on compound distribution within the brain have different properties They may focus on compartmental exchange, transport in the (brain) ECF or binding kinetics. In a recent work by McGinty and Pontrelli (2016) that focuses on local drug delivery to biological tissue such as the arterial wall, the diffusion equation that describes the concentration changes in free drug in the (non-brain) ECF is coupled to two ODEs that describe the concentration changes in drug bound to specific and non-specific binding sites (Tzafriri et al 2012; McGinty and Pontrelli 2015, 2016).
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