A mathematical, in silico implemented, modular model for tumor growth in a spatially inhomogeneous, time-varying chemical environment (1st unrevised edition)

TL;DR

This paper presents a modular in silico mathematical model for early tumor growth that incorporates spatial and temporal variations in the chemical environment, aligning well with biological observations and adaptable to new hypotheses.

Contribution

The authors developed a flexible, modular mathematical model of tumor growth that integrates biological mechanisms and can utilize imaging data for enhanced understanding.

Findings

Model shows good qualitative agreement with biological data.

Reveals complex interactions between oxygen levels and cell mitosis.

Modular design facilitates hypothesis testing and model adjustments.

Abstract

During the last decades, medical observations and multiscale data concerning tumor growth are mounting. At the same time, contemporary imaging techniques well established in clinical practice, provide a variety of information on real-time, in-vivo tumor growth. Mathematical and in-silico modeling has been widely recruited to provide means for further understanding of pertinent biological phenomena. However, despite the vast amounts of new evidence compiled by medical doctors, there are still many aspects of tumor growth that remain largely unknown. There is still a large variety of mechanisms to be better understood and therefore, many hypotheses to be tested. To approach this problem, starting from mathematical elaborations, we have developed a model of the early phases of tumor growth consisting of several algorithmic modules, each one corresponding to a particular biological mechanism. The modularity of the model allows keeping track of the assumptions made in each step and facilitates re-adjustment, in case new hypotheses need to be considered. Simulations showed good qualitative agreement with biological observations, and revealed a non-trivial interplay between between oxygen requirements of cancer cells and their maximum mitosis rates. The proposed model has, at least in principle, the potential to exploit data from contemporary imaging techniques and is eligible for utilizing multicore computation.