Evaluation of Entropy and Fractal Dimension as Biomarkers for Tumor Growth and Treatment Response using Cellular Automata

TL;DR

This study uses cellular automata to simulate tumor growth and therapies, analyzing entropy and fractal dimension as biomarkers to evaluate their potential for monitoring cancer progression and treatment response.

Contribution

It introduces a cellular automata model for tumor growth with multiple therapies and assesses the dynamic behavior of entropy and fractal dimension as imaging biomarkers.

Findings

Fractal dimension increases rapidly during early tumor dissemination.

Entropy responds distinctly to different therapy modalities.

Biomarker changes reflect the spatial action of treatments.

Abstract

Cell-based models provide a helpful approach for simulating complex systems that exhibit adaptive, resilient qualities, such as cancer. Their focus on individual cell interactions makes them a particularly appropriate strategy to study the effects of cancer therapies, which often are designed to disrupt single-cell dynamics. In this work, we also propose them as viable methods for studying the time evolution of cancer imaging biomarkers (IBM). We propose a cellular automata model for tumor growth and three different therapies: chemotherapy, radiotherapy, and immunotherapy, following well-established modeling procedures documented in the literature. The model generates a sequence of tumor images, from which time series of two biomarkers: entropy and fractal dimension, is obtained. Our model shows that the fractal dimension increased faster at the onset of cancer cell dissemination, while entropy was more responsive to changes induced in the tumor by the different therapy modalities. These observations suggest that the predictive value of the proposed biomarkers could vary considerably with time. Thus, it is important to assess their use at different stages of cancer and for different imaging modalities. Another observation derived from the results was that both biomarkers varied slowly when the applied therapy attacked cancer cells in a scattered fashion along the automatons' area, leaving multiple independent clusters of cells at the end of the treatment. Thus, patterns of change of simulated biomarkers time series could reflect on essential qualities of the spatial action of a given cancer intervention.