Step-by-step comparison of ordinary differential equation and agent-based approaches to pharmacokinetic-pharmacodynamic models

Mathematical models in oncology aid in the design of drugs and understanding of their mechanisms of action by simulation of drug bio-distribution, drug effects, and interaction between tumour and healthy cells. The traditional approach in pharmacometrics is to develop and validate ordinary differential equation models to quantify trends at the population level. In this approach, time-course of biological measurements is modelled continuously, assuming a homogenous population. Another approach, agent-based models focus on the behaviour and fate of biological entities at the individual level which subsequently could be summarized to reflect the population level. Heterogeneous cell populations and discrete events are simulated, and spatial distribution can be incorporated. In this tutorial, an agent-based model is presented and compared to an ordinary differential equation model for a tumour efficacy model inhibiting the pERK pathway. We highlight strengths, weaknesses, and opportunities of each approach.