Mathematical Modeling of Pharmaceuticals: Predictive Design for Better Medicines
Massachusetts Institute of Technology
Smart designs of drug molecules and pharmaceutical formulations can target treatments to specific tissues, reduce side effects, and improve patient quality of care. Computational models for evaluating pharmaceutical formulations can narrow the range of experiments needed to identify successful designs by predicting performance, thus reducing development time and driving down costs. Models coupled with sophisticated process control strategies allow for careful manufacturing monitoring to reduce materials and energy waste and adhere to quality standards. I will overview mathematical modeling efforts in several pharmaceutical domains and highlight work related to predicting drug release from controlled-release formulations that administer medicine over extended periods with a single dose. I will show how coupled, nonlinear partial differential equations can be used to capture the complex dynamic interactions between simultaneous chemical reactions and mass transfer. I will describe mathematical techniques that can reduce the system size from thousands of equations to just a few while still resolving biodegradation of the pharmaceutical formulation that strongly influences drug release dynamics. These techniques can help design improved controlled-release formulations.