Title: The Mathematics of Metaprograms and Personalized Pharmacometric Analytics

Abstract: One application of systems biology is for the understanding of disease and drug dynamics in human patients. In this talk we will look into applications of pharmacometric chemical reaction models for the purpose of personalized drug dosage prediction, including physiologically-based pharmacokinetic (PBPK) and quantitative systems pharmacology (QsP) models. These models involve a nonlinear mixed effect model (NLME) over a differential equation system for predicting internal drug concentrations from easily identifiable patient covariates. Optimal design of patient care will be introduced and methods for identifying optimal times for taking patient vitals and optimal dosing schedules will be shown to translate to a maximum likelihood estimation problem. However, these likelihood optimizations require new algorithms in order to scale to size required for our clinical trials. As a solution to this problem, we will introduce an atomic mathematics on metaprograms, programs which output programs, as a way to describe efficient algorithms for calculating parameter derivatives and uncertainty quantification without sampling. The audience will leave with a good understanding of how systems biology is being translated to clinical applications and the mathematical issues required to complete this translation to clinical practice.