Comparison of classical tumour growth models for patient derived and cell-line derived xenografts using the nonlinear mixed-effects framework.

In this study we compare seven mathematical models of tumour growth using nonlinear mixed-effects which allows for a simultaneous fitting of multiple data and an estimation of both mean behaviour and variability. This is performed for two large datasets, a patient-derived xenograft (PDX) dataset consisting of 220 PDXs spanning six different tumour types and a cell-line derived xenograft (CDX) dataset consisting of 25 cell lines spanning eight tumour types. Comparison of the models is performed by means of visual predictive checks (VPCs) as well as the Akaike Information Criterion (AIC). Additionally, we fit the models to 500 bootstrap samples drawn from the datasets to expand the comparison of the models under dataset perturbations and understand the growth kinetics that are best fitted by each model. Through qualitative and quantitative metrics the best models are identified the effectiveness and practicality of simpler models is highlighted.

Stability of two competing populations in chemostat where one of the population changes its average mass of division in response to changes of its population.

This paper considers a novel dynamical behaviour of two microbial populations, competing in a chemostat over a single substrate, that is only possible through the use of population balance equations (PBEs). PBEs are partial integrodifferential equations that represent a distribution of cells according to some internal state, mass in our case. Using these equations, realistic parameter values and the assumption that one population can deploy an emergency mechanism, where it can change the mean mass of division and hence divide faster, we arrive at two different steady states, one oscillatory and one non-oscillatory both of which seem to be stable. A steady state of either form is normally either unstable or only attainable through external control (cycling the dilution rate). In our case no external control is used. Finally, in the oscillatory case we attempt to explain how oscillations appear in the biomass without any explicit dependence on the division rate (the function that oscillates) through the approximation of fractional moments as a combination of integer moments. That allows an implicit dependence of the biomass on the number of cells which in turn is directly dependent on the division rate function.

Derivation of Continuum Models from An Agent-based Cancer Model: Optimization and Sensitivity Analysis.

BACKGROUND: Agent-based models provide a formidable tool for exploring complex and emergent behaviour of biological systems as well as accurate results but with the drawback of needing a lot of computational power and time for subsequent analysis. On the other hand, equation-based models can more easily be used for complex analysis in a much shorter timescale. METHODS & OBJECTIVE: This paper formulates an ordinary differential equations and stochastic differential equations model to capture the behaviour of an existing agent-based model of tumour cell reprogramming and applies it to optimization of possible treatment as well as dosage sensitivity analysis. RESULTS: For certain values of the parameter space a close match between the equation-based and agent-based models is achieved. The need for division of labour between the two approaches is explored.