Abstract

Mathematical and computational modeling have been increasingly applied in many areas of cancer research, aiming to improve the understanding of tumorigenic mechanisms and to suggest more effective therapy protocols. The mathematical description of the tumor growth dynamics is often made using the exponential, logistic, and Gompertz models. However, recent literature has suggested that the Allee effect may play an important role in the early stages of tumor dynamics, including cancer relapse and metastasis. For a model to provide reliable predictions, it is necessary to have a rigorous evaluation of the uncertainty inherent in the modeling process. In this work, our main objective is to show how a model framework that integrates sensitivity analysis, model calibration, and model selection techniques can improve and systematically characterize model and data uncertainties. We investigate five distinct models with different complexities, which encompass the exponential, logistic, Gompertz, and weak and strong Allee effects dynamics. Using tumor growth data published in the literature, we perform a global sensitivity analysis, apply a Bayesian framework for parameter inference, evaluate the associated sensitivity matrices, and use different information criteria for model selection (First- and Second-Order Akaike Information Criteria and Bayesian Information Criterion). We show that such a wider methodology allows having a more detailed picture of each model assumption and uncertainty, calibration reliability, ultimately improving tumor mathematical description. The used in vivo data suggested the existence of both a competitive effect among tumor cells and a weak Allee effect in the growth dynamics. The proposed model framework highlights the need for more detailed experimental studies on the influence of the Allee effect on the analyzed cancer scenario.

Highlights

  • Cancer is a generic term that refers to various diseases characterized mainly by abnormal cell growth, affecting different tissues and organs of the body

  • To account for parameter and model uncertainties, here we put forward a model framework that integrates sensitivity analysis, model calibration, and model selection methods

  • At the end of the process, we identify the evidence towards the model that better supports the data, we quantify the uncertainty on estimated parameter values given the data, and how these uncertainties impact the tumor growth

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Summary

Introduction

Cancer is a generic term that refers to various diseases characterized mainly by abnormal cell growth, affecting different tissues and organs of the body It is the second leading cause of death in the world, accounting for approximately 9.6 million deaths in 2018 [16, 34]. Understanding its growth dynamics is a challenge and may contribute to a better knowledge of the mechanisms involved and new developments of more effective therapy protocols In this context, mathematical and computational modeling has been widely applied in many cancer research areas [4]. Uncertainties are present in almost all practical problems, especially in biological processes They are manifested in various ways including the variability associated with knowledge (or lack of knowledge) about the parameters and the model uncertainty, that is, the uncertainty associated with the representation of reality by the mathematical model. To account for parameter and model uncertainties, here we put forward a model framework that integrates sensitivity analysis, model calibration, and model selection methods

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