Introduction to Mathematical Oncology

Chapter 3

Spatially Structured Tumor Growth

3.1 Introduction

In Chapter 2, we introduced Laird’s notion of Gompertzian tumor growth [9, 10] as a phenomenological idea. In contrast, Gyllenberg and Webb’s model [7] (Section 2.4) is mechanistic in that it suggests an explanation—quiescence— of Gompertz-like dynamics. In 1966, Alan Burton proposed an alternative hypothesis [2]. Based on William Mayneord’s [13] studies of a type of sarcoma, Burton suggested that necrosis causes Gompertz-like growth. Specifically, as tumors grow, necrotic regions form and expand faster than the tumor does.

To explore this idea, Burton modeled tumors as ideal spheres with nutrient diffusing into the interior from the surface (Fig. 3.1). He further suggested that necrosis ...