Tumour Growth Modelling at ICIAM 99September 23, 1999
Cancer can arise from any cell type in the body and is one of the major causes of death in the developing world. Medically, cancer can be defined as an inappropriate, excessive, and continuous proliferation of transformed cells. One type of cancer that lends itself to mathematical study (because of its spherical shape) is the cancer of the epithelium that manifests as palpable "lumps" of tissue. The cancerous cells in these lumps grow rapidly and then form (or coalesce) into small compact groups of cells, or solid tumours, which continue to expand. If the solid tumour can induce the growth of pre-existing neighbouring blood vessels (angiogenesis), it can grow even larger, invade the surrounding tissue, and enter the body's blood and lymph systems. As a result, secondary tumours may arise in distant sites of the body. Treatment then becomes difficult.
Like the subject itself, the mathematical modelling of tumour growth is a rapidly expanding area of applied mathematics, witnessed by the interest shown in two mini-symposia devoted to the topic at ICIAM 99 in Edinburgh. Indeed, so successful were the minisymposia that due to overcrowding pressures in the original seminar room, the minisymposia were relocated and the participants were forced to "invade" larger premises at a (not so) distant room in another building.
The speakers in the minisymposia covered a wide range of problems associated with cancer growth, from the early avascular stages, through the process of angiogenesis, to the vascular, invasive phase. Some speakers considered the modelling of chemotherapy treatment of cancer. A similarly wide range of mathematical techniques was on display. Partial differential equation models, continuum mechanics models, dynamical systems theory, bifurcation theory, stochastic differential equations, numerical analysis were all used in the modelling of this important area in mathematical biology. Many of the speakers presented models in which actual clinical data had been used, and it was clear that there was much quality collaboration with clinicians and experimentalists with the aim of using advanced mathematical techniques to provide a deeper understanding of a complicated biological and medical problem.---Mark Chaplain, Department of Mathematics, University of Dundee.