Abstract
A 3-dimensional mathematical model is developed to determine the effect of drug binding kinetics on the spatial distribution of a drug within the brain. The key components, namely, transport across the blood-brain barrier (BBB), drug distribution in the brain extracellular fluid (ECF), and drug binding kinetics are coupled with the bidirectional bulk flow of the brain ECF to enhance the visualization of drug concentration in the brain. The model is developed based on the cubical volume of a brain unit, which is a union of three subdomains: the brain ECF, the BBB, and the blood plasma. The model is a set of partial differential equations and the associated initial and boundary conditions through which the drug distribution process in the mentioned subdomains is described. Effects of drug binding kinetics are investigated by varying the binding parameter values for both nonspecific and specific binding sites. All variations of binding parameter values are discussed, and the results show the improved visualization of the effect of binding kinetics in the drug distribution within the brain. For more realistic visualization, we suggest incorporating more brain components that make up the large volume of the brain tissue.
Highlights
The drug distribution is the process by which the drug molecules are delivered from the bloodstream to various body compartments, especially where the drug effect is needed [1]
The drug exchange between the blood plasma and the brain extracellular fluid (ECF) is described by both passive and active transport across the blood-brain barrier (BBB) in both directions (viii) Drug within the brain ECF is transported through the brain ECF bulk flow and diffusion (ix) Tortuosity is taken into consideration to account for the obstruction imposed to diffusion by the brain cells (x) The rectangular Cartesian coordinate system is used to indicate the direction of the bulk flow of the brain ECF
The drug distribution in the 3-dimensional brain unit is studied by plotting the concentration of drug in the blood plasma, drug binding sites, and the brain extracellular fluid for various time instances
Summary
The drug distribution is the process by which the drug molecules are delivered from the bloodstream to various body compartments, especially where the drug effect is needed [1]. The drug distribution in the human body is significant in a sense that it results into exposing the targeted sites to the drug being administered. Drugs can only induce their therapeutic effects if they properly associate with the molecular targets within the body [2]. When the drug is administered to target the central nervous system, its distribution is usually varied due to various factors such as blood perfusion, permeability of the bloodbrain barrier (BBB), diffusion, bulk flow of the brain extracellular fluid (ECF), metabolism, and drug binding [3, 4]. The delivery of drug substances into the brain is strongly controlled by the semipermeable brain border that is the BBB [5,6,7]. The ability of the drug to pass across the BBB largely depends on both biological features such as transporters and enzymes, as well as the drug compound physicochemical properties like molecular weight, lipophilicity, and hydrogen bonding capacity [8, 9]
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