Dynamic modelling and evaluation of preclinical trials in acute leukaemia

Abstract

Dynamic models are widely used to mathematically describe biological phenomena that evolve over time. One important area of application is leukaemia research, where leukaemia cells are genetically modified in preclinical studies to explore new therapeutic targets for reducing leukaemic burden. In advanced experiments, these studies are often conducted in mice and generate time-resolved data, the analysis of which may reveal growth-inhibiting effects of the investigated gene modifications. However, the experimental data is often times evaluated using statistical tests which compare measurements from only two different time points. This approach does not only reduce the time series to two instances but also neglects biological knowledge about cell mechanisms. Such knowledge, translated into mathematical models, expands the power to investigate and understand effects of modifications on underlying mechanisms based on experimental data. We utilise two population growth models -- an exponential and a logistic growth model -- to capture cell dynamics over the whole experimental time horizon and to consider all measurement times jointly. This approach enables us to derive modification effects from estimated model parameters. We demonstrate that the exponential growth model recognises simulated scenarios more reliably than the other candidate model and than a statistical test. Moreover, we apply the population growth models to evaluate the efficacy of candidate gene knockouts in patient-derived xenograft (PDX) models of acute leukaemia.