  Molecular circadian clocks, that are found in all nucleated cells of mammals,
are known to dictate rhythms of approximately 24 hours (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 tumour 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 are at work fighting tumor
growth.
