The model muddle: in search of tumour growth laws

TL;DR

This paper reviews the historical development of tumour growth laws, highlighting the evolution from simple exponential models to more complex formulations, emphasizing the need for further research to understand tumour growth intricacies.

Contribution

It provides a comprehensive survey of tumour growth models, analyzing their assumptions, developments, and the necessity for new models to better understand tumour dynamics.

Findings

Historical models range from exponential to complex differential equations

Current models have limitations in capturing tumour growth intricacies

Further development of models is needed for better understanding

Abstract

In this article we shall trace the historical development of tumour growth laws, which in a quantitative fashion describe the increase in tumour mass/volume over time. These models are usually formulated in terms of differential equations that relate the growth rate of the tumour to its current state, and range from the simple one-parameter exponential growth model, to more advanced models that contain a large number of parameters. Understanding the assumptions and consequences of such models is important, since they often underpin more complex models of tumour growth. The conclusion of this brief survey is that although much improvement has occurred over the last century, more effort and new models are required if we are to understand the intricacies of tumour growth.