A calibration and uncertainty quantification analysis of classical, fractional and multiscale logistic models of tumour growth

Abstract

The validation of mathematical models of tumour growth is typically hampered by a lack of sufficient experimental data, resulting in qualitative rather than quantitative studies. Recent approaches to this problem have attempted to extract information about tumour growth by integrating multiscale experimental measurements, such as longitudinal cell counts and gene expression data. In this study, we investigated the fitness of several mathematical models of tumour growth, including classical logistic, fractional and novel multiscale models, with respect to measurements ofin-vitrotumour growth in the presence and absence of therapy and the expression profiles of genes associated with changes in chemosensitivity. State-of-the-art Bayesian inference, likelihood maximisation and uncertainty quantification techniques allowed a thorough evaluation of the model fitness. The results suggest that the classical single-cell population model (SCPM) was the best fit for the untreated and low-dose treatment conditions, while the multiscale model with a cell death rate symmetric with the expression profile of OCT4 (Sym-SCPM) showed the best fit with the high-dose treatment data. Further identifiability analysis showed that the multiscale model was both structurally and practically identifiable under the condition of known OCT4 expression profiles. Overall, this study demonstrates that model performance can be improved by incorporating multiscale measurements of tumour growth.