Mathematical Modeling in the Social and Life Sciences

CHAPTER 5

Tumor Growth Models

What we call growth of even a simple organism is a tremendously complex phenomenon from the biochemical, physiological, cytological and morphological viewpoints. There are, however, certain aspects that are amenable to quantitative analysis, and such an approach appears to lead to some insight into the connections between metabolism and growth, and to some answer to the seemingly trivial, but in fact hardly explored question, “Why does an organism grow at all, and why, after a certain time, does its growth come to a stop?”

—Ludwig von Bertalanffy

I. Introduction

Cancer is a leading cause of cause of death worldwide, accounting for nearly 8 million deaths per year. Experts predict that deaths globally will continue rising, with an estimated 9 million people dying from cancer in 2015 and 11.4 million succumbing in 2030. Thus, cancer poses major public health questions.

Cancer is a generic term for a large class of diseases that can affect any part of the body; malignant tumors and neoplasms are often used as synonyms. A characteristic feature of cancer is the rapid creation of abnormal cells growing beyond their usual boundaries and often invading adjoining parts of the body, spreading to other organs. Many cancers can be detected early and powerful treatments exist. Yet our understanding of cancer is far from complete, and a diagnosis of cancer often results in great anxiety and fear for the patient. The writer Susan Sontag has noted how frequently ...