Modelling of early lung cancer progression: Influence of growth factor production and cooperation between partially transformed cells

The generally accepted Moolgavkar's theory of carcinogenesis assumes that all cancers are clonal, i.e. that they arise from progressive genetic deregulation in a cell pedigree originating from a single ancestral cell. ¹⁸ However, recently the clonal theory has been challenged by the field theory of carcinogenesis, which admits the possibility of simultaneous changes in tissue subject to carcinogenic agents, such as tobacco smoke in lung cancer. Axelrod et al.¹ formulated a more detailed framework, in which partially transformed cells depend in a mutualistic way on growth factors they produce, in this way enabling these cells to proliferate and undergo further transformations. On the other hand, the field theory assumes spatial distribution of precancerous cells and indeed there exists evidence that early-stage precancerous lesions in lung cancer progress along linear, tubular, or irregular surface structures. This seems to be the case for the atypical adenomatous hyperplasia (AAH),¹⁰ a likely precursor of adenocarcinoma of the lung. In this paper we explore the consequences of linking the model of spatial growth of precancerous cells,12 with the mutualistic hypothesis. We investigate the solutions of the model using analytical and computational techniques. The picture emerging from our modelling indicates that production of growth factors by cells considered may lead to diffusion-driven instability, which in turn may lead either to decay of both population, or to emergence of local growth foci, represented by spike-like solutions. Mutualism may, in some situations, increase the stability of solutions. One important conclusion is that models of field carcinogenesis, which include spatial effects, generally have very different behaviour compared to ODE models.