MATHEMATICAL MODELS IN PHARMACODYNAMICS

决定药物反应的主要因素是控制药物动力学的输入和处置速率、药物在作用部位(生物相)的分布、药物改变介体或受体水平的作用机制以及转导过程。我们认识到，可以使用四种基本(和扩展的)间接反应模型来表征不同的药效学效应，这可能是量化药理反应的改进。这些(和大多数)模型需要使用通常不能完全集成的微分方程式进行分析。该项目旨在描述和量化通过不同机制发挥作用的药物的特性。具体目标包括开发一系列相关的基于机制的PK/PD模型的比较概要，进一步开发包括反馈改变的前体室的间接反应模型，进化应用于自然细胞反应的延长的间接寿命模型，包括骨髓刺激和/或细胞毒性等效应，以及可应用于许多膜受体(例如G蛋白)介导的反应的非线性和时间依赖的转导模型的详细表征。将使用先进的微积分和刺激方法为这些模型寻找准确或近似的解决方案或行为，以确定如何控制反应的开始、程度、返回、持续时间、AUC和稳定阶段，更容易地从实验数据中恢复参数，并在可用于描述典型数据的不同模型中进行区分，并确定如何优化给药方案。这些努力将产生洞察力、方法和资源，以了解和量化与主要作用机制有关的药物反应的时间进程。

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.