Collaborative Research: Predicting the Release Kinetics of Matrix Tablets

本研究将扩展缓释基质片溶出与释放过程的两个数学模型。这些模型中的第一个在多个直径的随机密集球体的加权接触图上使用随机游动。第二个模型由反应扩散型偏微分方程组组成，分别为已解赋形剂和未解赋形剂和药物。我们将开发新的计算工具，借鉴图上随机游走理论、概率密度估计和数值偏微分方程。理论模型将以快速、健壮的代码实现，模型参数将与制药科学研究人员密切合作，根据实际数据进行校准。研究小组将开发数学和计算方法来预测缓释基质片的释放动力学。这些片剂用于输送活性药物，并在一段时间内逐渐释放。缓释片比速释片具有相当大的优势，即在患者体内保持更恒定的药物水平，同时减少每天需要服用的片剂数量。在之前的工作中，我们与新西兰的合作者（由NSF资助DMS-0737537发起）共同提出了溶解和释放过程的数学模型，预测了不同成分的粉末混合物的质量优异的释放曲线。这项研究将简化新的和更好的药物输送装置的设计过程，并将计算方法引入一个新的科学领域。所有程序都将用开源软件编写，并将免费在线提供给感兴趣的研究人员。

This work will extend two mathematical models for the dissolution and release process occurring in sustained release matrix tablets. The first of these models uses random walks on the weighted contact graph of a random dense packing of spheres of multiple diameters. The second model consists of a system of partial differential equations of reaction-diffusion type for the solved and unsolved excipient and drug, respectively. We will develop new computational tools, borrowing from theories of random walks on graphs, probability density estimation, and numerical partial differential equations. The theoretical models will be implemented in fast, robust code, and model parameters will be calibrated to actual data in close collaboration with researchers in the pharmaceutical sciences.The team of investigators will develop mathematical and computational methods to predict the release kinetics of sustained release matrix tablets. These tablets are used to deliver an active drug and to gradually release it over an extended period of time. Sustained release tablets offer considerable advantages over immediate release tablets, namely maintaining more constant drug levels in the patient's body while minimizing the number of tablets that need to be taken each day. In previous work, jointly with collaborators in New Zealand (initiated by NSF grant DMS-0737537), we have proposed mathematical models for the dissolution and release process, predicting qualitatively excellent release curves for different compositions of the powder mixture. This research will streamline the design process of new and better pharmaceutical delivery devices and will introduce computational methods into a new field of science. All programs will be written in open source software and will be freely available online to interested researchers.