A cellular automata model for avascular solid tumor growth under the effect of therapy

TL;DR

This paper introduces a probabilistic cellular automata model to simulate avascular solid tumor growth, capturing Gompertzian dynamics, tumor morphology, necrosis, and therapy effects, providing insights into tumor progression and treatment response.

Contribution

It presents a novel two-dimensional cellular automata model that incorporates nutrient competition, growth patterns, and therapy effects to analyze tumor development and response.

Findings

Transitions between necrotic and non-necrotic phases identified

Therapy can induce tumor cure or non-cure states

Inner necrotic core and therapy-induced tumor destruction observed

Abstract

Tumor growth has long been a target of investigation within the context of mathematical and computer modelling. The objective of this study is to propose and analyze a two-dimensional probabilistic cellular automata model to describe avascular solid tumor growth, taking into account both the competition between cancer cells and normal cells for nutrients and/or space and a time-dependent proliferation of cancer cells. Gompertzian growth, characteristic of some tumors, is described and some of the features of the time-spatial pattern of solid tumors, such as compact morphology with irregular borders, are captured. The parameter space is studied in order to analyze the occurrence of necrosis and the response to therapy. Our findings suggest that transitions exist between necrotic and non-necrotic phases (no-therapy cases), and between the states of cure and non-cure (therapy cases). To analyze cure, the control and order parameters are, respectively, the highest probability of cancer cell proliferation and the probability of the therapeutic effect on cancer cells. With respect to patterns, it is possible to observe the inner necrotic core and the effect of the therapy destroying the tumor from its outer borders inwards.