Morphological stability for in silico models of avascular tumors

TL;DR

This paper presents a transparent, parsimonious in silico model of avascular tumor growth that combines stochastic and mean-field approaches, providing insights into tumor stability, progression, and potential instabilities due to nutrient starvation.

Contribution

It introduces a simple, first principles tumor model that links stochastic and PDE frameworks, enabling detailed analysis of growth stability and mechanisms.

Findings

Identified a novel instability caused by nutrient starvation.

Demonstrated the model's ability to reproduce known tumor behaviors.

Provided a framework for incorporating additional biological factors.

Abstract

The landscape of computational modeling in cancer systems biology is diverse, offering a spectrum of models and frameworks, each with its own trade-offs and advantages. Ideally, models are meant to be useful in refining hypotheses, to sharpen experimental procedures and, in the longer run, even for applications in personalized medicine. One of the greatest challenges is to balance model realism and detail with experimental data to eventually produce useful data-driven models. We contribute to this quest by developing a transparent, highly parsimonious, first principles silico model of a growing avascular tumor. We initially formulate the physiological considerations and the specific model within a stochastic cell-based framework. We next formulate a corresponding mean-field model using partial differential equations which is amenable to mathematical analysis. Despite a few notable differences between the two models, we are in this way able to successfully detail the impact of all parameters in the stability of the growth process and on the eventual tumor fate of the stochastic model. This facilitates the deduction of Bayesian priors for a given situation, but also provides important insights into the underlying mechanism of tumor growth and progression. Although the resulting model framework is relatively simple and transparent, it can still reproduce the full range of known emergent behavior. We identify a novel model instability arising from nutrient starvation and we also discuss additional insight concerning possible model additions and the effects of those. Thanks to the framework's flexibility, such additions can be readily included whenever the relevant data become available.