I have a preliminary observation: are you referring to miroscopic scale (i.e. at the scale of the division of a single tumor cells) or at mesoor macro scales (i.e. at the scale of a population of tumor cells) ?
If you are referring at the tumor scale, my answer is: ** no **, for a series of reasons of various nature. First, seldom a tumor growth model is adequately described by a discete dynamical system (one exception is my paper: d'Onofrio and Tomlinson, J Theor Biol ,2007); Second, the chaotic bifurcation diagram of the logistic map is often the result of the discretization of a continuous model by adopting an excessively large time-step; Third (and main) reason: the tumor growth is (unfortunately) progressive and (apart some cases of highly immunogenic tumors) very seldom characterized by the wild oscillations that are a landmark of the vast majority of chaotic phenomena.
There are some chaotic models of tumor growth, where, however, chaos stems from other biological processes (e.g. in some cases: the interplay with the immune system) mirrored by other mathematical propserties.
Kind regards,
Alberto d'Onofrio
Thank You Dr. Onofrio. I was thinking in terms of single cells at the microscopic scale so that one could model/predict primary tumor size. I was thinking whether tumor size is related to the ability of cells to escape the primary tumor and spread/metastasize.
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