This preprint presents a model which looks like a merge of two previous models on different biological scales: one is a tumour growth model by Hahnfeldt et al. the other is a model of metastatic spread in terms of a transport equation originally formulated by Iwata et al. With this new model the authors investigate the efficacy of different schedules for chemotherapy.

Quantitative Analysis of the Tumor/Metastasis System and its Optimal Therapeutic Control

Sebastien Benzekry (CCSB, INRIA Bordeaux - Sud-Ouest), Dominique Barbolosi (CRO2), Assia Benabdallah (LATP), Florence Hubert (LATP), Philip Hahnfeldt (CCSB)

(Submitted on 20 Jun 2013)

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.