  A mathematical model for time development of metastases and their
distribution in size and carrying capacity is presented. The model is used to
theoretically investigate anti-cancer therapies such as surgery and chemical
treatments (cytotoxic or anti-angiogenic), in monotherapy or in combination.
Quantification of the effect of surgery on the size distribution of metastatic
colonies is derived. For systemic therapies, emphasis is placed on the
differences between the treatment of an isolated lesion and a population of
metastases. Combination therapy is addressed, in particular the problem of the
drugs administration sequence. Theoretical optimal schedules are derived that
show the superiority of a metronomic administration scheme (defined as a
continuous administration of a given amount of drug spread during the whole
therapeutic cycle) on a classical Maximum Tolerated Dose scheme (where the dose
is given as a few concentrated administrations at the beginning of the cycle),
for the total metastatic burden in the organism.

Tissues and Organs;Analysis of PDEs