Mathematical Models of Cancer

Abstract

Modelling and simulation are indispensable for the study of biological systems as dynamical ensembles, made up of a large number of interacting components and exhibiting complex non-linear behaviour. These methods provide the tools for data and knowledge-based in silico predictions of tumour behaviour and hypothesis formulation in both preclinical and clinical settings (see also Chapter 1 and later chapters in this section).The number of mathematical models that describe solid tumour dynamics has increased dramatically since the first instances in the 1920s, and more rapid advances have become possible through the arrival of accessible and fast computation. However, there are no universally accepted models yet, although a large number exist, and none are capable of satisfactorily capturing the rich dynamic behaviour of tumours. Therefore, a real clinical use of mathematical modelling has not yet materialized, and critics have warned that most models of cancer systems are too simplistic and therefore potentially too dangerous for use in the medical field (Byrne, 1999;Gatenby and Maini, 2003). With the advent of post-genomic cancer research, a multidisciplinary research ethos and new computational approaches, this situation is set to change rapidly. Modellers have now reached a juncture where tumour biology is meeting face-to-face with systems science. This chapter will provide an overview of existing mathematical cancer models and the methodologies applied for their development. Ordinary, partial and stochastic differential equation models, as well as phenomenological methods, will be discussed critically and compared with discrete, interaction-based approaches such as cellular automata.Cancer Bioinformatics: From therapy design to treatment Edited by Sylvia Nagl

Biología sintética: Sobre el desarrollo de circuitos genéticos y su aplicación en biociencias y en biocombustibles

“…In 1984, a mathematical model for the growth of breast cancer was proposed (Botesteanu, Lipkowitz, Lee & Levy, 2016), and it was found that different individual tumors grew according to Gompertz parameters. With this basic growth model, it was possible to estimate that a cancerous cell would take eight years to be detected, referring to the fact that a tumor is a group of cells that grow without control and its growth is limited to the space and resources available (Patel & Nagl, 2006), which makes it more complicated to describe its growth and behavior as opposed to growth under an exponential model. Hence, from that day forward, the use of the Gompertz model has been widely used in cancer research.…”