Matrix analysis
Mathematical and Computer Modelling: An International Journal
Preface: Mathematical methods and modelling of biophysical phenomena
Mathematical and Computer Modelling: An International Journal
Mathematics and Computers in Simulation
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Molecular circadian clocks, that are found in all nucleated cells of mammals, are known to dictate rhythms of approximately 24 h (circa diem) to many physiological processes. This includes metabolism (e.g., temperature, hormonal blood levels) and cell proliferation. It has been observed in tumor-bearing laboratory rodents that a severe disruption of these physiological rhythms results in accelerated tumor growth. The question of accurately representing the control exerted by circadian clocks on healthy and tumor tissue proliferation to explain this phenomenon has given rise to mathematical developments, which we review. The main goal of these previous works was to examine the influence of a periodic control on the cell division cycle in physiologically structured cell populations, comparing the effects of periodic control with no control, and of different periodic controls between them. We state here a general convexity result that may give a theoretical justification to the concept of cancer chronotherapeutics. Our result also leads us to hypothesize that the above mentioned effect of disruption of circadian rhythms on tumor growth enhancement is indirect, that is, this enhancement is likely to result from the weakening of healthy tissue that is at work fighting tumor growth.