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Modelling of early lung cancer progression: influence of growth factor production and cooperation between partially transformed cells. (English) Zbl 1135.92019

Summary: The generally accepted S. H. Moolgavkar [Biologically motivated two-stage model for cancer risk assessment. Toxicol. Lett. 43, 139–150 (1988)] 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. 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. R. Axelrod et al. [Evolution of cooperation among tumour cells. Proc. Natl. Acad. Sci. U.S.A. 103, 13474–13479 (2006)] 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), a likely precursor of adenocarcinoma of the lung.
We explore the consequences of linking the model of spatial growth of precancerous cells 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 the cells considered may lead to diffusion-driven instability, which in turn may lead either to decay of both populations, 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.

MSC:

92C50 Medical applications (general)
35K57 Reaction-diffusion equations
92C37 Cell biology
35B40 Asymptotic behavior of solutions to PDEs
35B35 Stability in context of PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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