MATHEMATICAL MODELS IN PHARMACODYNAMICS

决定药物反应的主要因素是控制药代动力学的输入和处置速率、药物在作用部位（生物期）的分布、药物在改变介质或受体水平中的作用机制以及转导过程。我们认识到，不同的药效学效应可以用四种基本（和扩展的）间接反应模型来表征，这可能会改善药效学反应的定量。这些（和大多数）模型需要使用微分方程进行分析，而微分方程通常不能完全集成。该项目旨在表征和量化药物的性质，通过不同的机制。具体目标包括开发一个纲要，比较一系列相关的基于机制的PK/PD模型，进一步开发具有前体室的间接反应模型，包括反馈改变的发生；延长间接寿命模型的进化，以应用于自然细胞反应，包括骨髓刺激和/或细胞毒性等效应；以及非线性和时变转导模型的详细表征，这些模型可以应用于许多膜受体（例如g蛋白）介导的反应。将采用先进的演算和刺激方法来寻求这些模型的精确或近似解或行为，以确定如何控制响应的开始、程度、返回、持续时间、AUC和稳态阶段，更容易地从实验数据中恢复参数，并区分可用于描述典型数据的各种模型，并确定如何优化药物给药方案。这些努力将为理解和量化与主要作用机制相关的药物反应的时间过程提供见解、方法和资源。

The major factors determining drug responses are the input and disposition rates controlling pharmacokinetics, drug distribution to the site of action (biophase), the mechanism of drug action in altering mediator or receptor level, and transduction processes. May improvements in quantitating pharmacologic responses came from our recognition that diverse pharmacodynamic effects can be characterized using a family of four basic (and extended) indirect response models. These (and most) models require analysis using differential equations which usually cannot be fully integrated. This project seeks to characterize and quantify the properties of drugs acting by diverse mechanisms. Specific aims include development of a compendium with comparison of the array of relevant mechanism-based PK/PD models, further development of indirect response models with a precursor compartment including the occurrence of feedback alterations; evolution of extended indirect lifespan models for application to natural cell responses including effects such as bone marrow stimulation and/or cytotoxicity; and the detailed characterization of non-linear and time- dependent transduction models which may be applied to numerous membrane receptor (e.g., G-protein) mediated responses. Advanced methods of calculus and stimulations will be employed to seek exact or approximate solutions or behaviors for these models to identify how the onset, extent, return, duration, AUC, and steady-stage of responses are controlled, to recovery parameters more easily from experimental data, and to discriminate among diverse models available to describe typical data, and to determine how to optimize drug dosing regimens. These efforts will yield insights, methods, and resources for understanding and quantitating the time course of drug responses as related to major mechanisms of action.