Physiologically based mathematical models to optimize therapies against metastatic colorectal cancer: a mini-review

Understanding and improving the effects of combined drug treatments in metastatic colorectal Cancer (mCRC) is a multidisciplinary and multiscale problem, that can benefit from a systems biology approach. Although a quite limited number of active drugs have been approved for clinical applications, a variety of combined delivery regimen options are actually used in the clinic, so that choosing between them, or designing new ones, is not an obvious task, which calls for some rationalization based on physiological principles. We propose some physiologically based molecular pharmacokinetics-pharmacodynamics models for the main cytotoxic drugs used in the clinic and call for others describing more recently used agents, such as associated with monoclonal antibodies. We also advocate simultaneously designing models of the proliferating cell populations under therapeutic control, as cancer is primarily a disruption of physiological control on tissue proliferation. These two types of models are based on differential equations to continuously describe both the fate of drugs in the organism, from infusion until pharmacological effects, and their impact on the proliferation of cell populations, healthy and tumor. The multiscale nature of colorectal cancer, from the disruption of intracellular pathways to tumor growth observed at the macroscopic level, together with its frequent multilocal extension by simultaneous metastases in various healthy tissues of the organism at the time of diagnosis, and later, call for multiscale mathematical models. We thus propose a multi-level vision of cytotoxic drug use in the clinic, in which the weapon in the hands of clinicians, a drug combination regimen, the targets -wanted and unwanted -on which it exerts its effects, molecular pathways in proliferating cell populations, and the environment of the latter in a whole organism, are all considered in order to design a rationale for appropriate shooting, i.e., treatment optimization under patient-tailored constraints.