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

Background and Objective: The validation of mathematical models of tumour growth is frequently hampered by the 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 the present study, we investigated the performance of several mathematical models of tumour growth, including classical logistic, fractional and novel multiscale models, in terms of quantifying in-vitro tumour growth in the presence and absence of therapy. We further examined the effect of genes associated with changes in chemosensitivity in cell death rates. Methods: The multiscale expansion of logistic growth models was performed by coupling gene expression profiles to the cell death rates. State-of-the-art Bayesian inference, likelihood maximisation and uncertainty quantification techniques allowed a thorough evaluation of model performance. Results: 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) yielded the best fit for 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. Conclusions: Overall, the present study demonstrates that model performance can be improved by incorporating multiscale measurements of tumour growth when high-dose treatment is involved. •Classical logistic growth models performed best in no treatment and low treatment dose conditions.•Increasing the number of cell populations in the model did not improve predictive performance.•Expression of genes related to the alteration of chemosensitivity suggested transient response to treatment.•Multiscale model accounting for both cell population size and gene expression performed best in high treatment doses.•The knowledge of the gene expression profiles is necessary for a practically identifiable multiscale model.