THE ROLE OF GROWTH-FACTORS IN AVASCULAR TUMOR-GROWTH

During avascular tumour growth, the balance between cell proliferation and cell loss determines the rate at which the tumour expands. Recent experimental results suggest that growth factors produced during cell proliferation manipulate the rate of natural cell death. In this pape r, we extend the standard model of avascular tumour growth to study th e effect that the production of such growth factors can have on a tumo ur's development. We assume that the growth factor is produced in inac tive form, and only becomes activated when it binds to a tumour cell; Two dependent variables are introduced to describe the levels of activ e and inactive growth factor. The model is studied using a combination of analytical and numerical techniques. These results show that the i nclusion into the model of growth factors endows the tumour with histo ry dependence, in that its evolution depends not only on its structure at a given instant, but also on its structure st earlier times. Numer ical simulations suggest that the manner in which the growth factor ac ts is crucial to the tumour's evolution. For example, a growth factor which enhances apoptosis does not alter the qualitative behaviour of t he tumour: it simply decreases the time taken to reach the equilibrium configuration in which the tumour may be present or absent. By contra st, a growth factor which inhibits apoptosis can dramatically alter th e tumour's behaviour, giving rise to asymmetric tumour pulsing. Here a single cycle comprises a long period of slow tumour growth followed b y a short period of tumour regression. Using asymptotic analysis, we i dentify regions of parameter space in which such periodic behaviour ar ises and show how they separate regions of unstable tumour growth from regions of bounded growth. The implications of our results are also d iscussed briefly.