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.

中文翻译：

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模拟结合动力学对大脑中空间药物分布的影响

开发了一个 3 维数学模型，以确定药物结合动力学对大脑内药物空间分布的影响。关键组成部分，即跨血脑屏障 (BBB) 的运输、脑细胞外液 (ECF) 中的药物分布和药物结合动力学与脑 ECF 的双向整体流动相结合，以增强药物浓度的可视化在大脑中。该模型是基于大脑单位的立方体积开发的，它是三个子域的联合：大脑 ECF、BBB 和血浆。该模型是一组偏微分方程以及相关的初始和边界条件，通过这些条件描述了上述子域中的药物分布过程。通过改变非特异性和特异性结合位点的结合参数值来研究药物结合动力学的影响。讨论了结合参数值的所有变化，结果显示了结合动力学对大脑内药物分布影响的改进可视化。为了更逼真的可视化，我们建议合并更多的大脑组件，以构成大量的脑组织。