Approximate Repeated Administration Models for Pharmacometrics

Improving performance through parallelization, while a common approach to reduce running-times in high-performance computing applications, is only part of the story. At some point, all available parallelism is exploited and performance improvements need to be sought elsewhere. As part of drug development trials, a compound is periodically administered, and the interactions between it and the human body are modeled through pharmacokinetics and pharmacodynamics by a set of ordinary differential equations. Numerical integration of these equations is the most computationally intensive part of the fitting process. For this task, parallelism brings little benefit. This paper describes how to exploit the nearly periodic nature of repeated administration models by numerical application of the method of averaging on the one hand and reusing previous computational effort on the other hand. The presented method can be applied on top of any existing integrator while requiring only a single tunable threshold parameter. Performance improvements and approximation error are studied on two pharmacometrics models. In addition, automated tuning of the threshold parameter is demonstrated in two scenarios. Up to 1.7-fold and 70-fold improvements are measured with the presented method for the two models respectively.