Efficient Stiff Ordinary Differential Equation Solvers for Quantitative Systems Pharmacology (QsP)
2019-07-25, 15:45–16:15, Elm A

QsP is a sophisticated and effective way to predict the interaction between drugs and the human body, however, simulating QsP models can take a long time because of the intrinsic stiffness in transient chemical reactions. Here we take a deep look at the efficiency of various stiff ordinary differential equation solvers in the JuliaDiffEq ecosystem applied to QsP models, and utilize benchmarks to summarize how the ecosystem is progressing and what kinds of advances we can expect in the near future.


The solution of the stiff ordinary differential equation (ODE) systems resulting from QsP models is a rate-limiting step in large-scale population studies. Here we review the ongoing efficiency developments within the JuliaDiffEq numerical differential equation solver ecosystem with a focus on ODEs derived from QsP models. These models have specific features that can be specialized in order to gain additional efficiency in the integration, such as their small size (normally <500 ODEs), frequent dosing events, and multi-rate behaviors. We demonstrate how new implementations of high order Rosenbrock methods with PI-adaptive time stepping, exponential propagation iterative methods (EPRIK) with adaptive Krylov expmv calculations, and implicit-explicit singly diagonally implicit Runge-Kutta methods (IMEX SDIRK) can be advantageous over classical schemes like LSODA and Sundials CVODE on these types of models and discuss the future directions.