Deterministic Mathematical Modelling for Cancer Chronotherapeutics: Cell Population Dynamics and Treatment Optimization

Abstract

In this short review paper, I will present the mathematical models that have been designed in the frame of continuous deterministic cell population dynamics that aim at optimization of cancer treatments using chronotherapeutics. Many authors have dealt with chronobiology of cancer, less with continuous mathematical models and even less with the declared aim to optimize chronotherapeutics. The biological and theoretical bases for these models are sketched, started from a historical viewpoint, and the main theoretical results are presented, with biological suggestions to account for them. Chronotherapeutics that leads to therapeutic optimization with the constraint of limiting unwanted toxicity of anticancer drugs towards healthy cell populations is put in a medical perspective together with the other main pitfall of cancer therapeutics, for which optimization procedures should have little to do with circadian biology, i.e., emergence of drug resistance in cancer cell populations, which is amenable to the use of other sorts of models, that are briefly mentioned.

Cell population heterogeneity and evolution towards drug resistance in cancer: Biological and mathematical assessment, theoretical treatment optimisation

“…becomes a problem with two populations, healthy and cancer, that are partly proliferating, partly dying, both evolving under the same drug insult, however with structural dynamic differences between them. This question has been the object of several studies [17,27,30,50,51,52], taking into account for some of them heterogeneity with respect to age phases in the cell division cycle [27,28,29,30], but so far heterogeneity with respect to phenotypes determining drug resistance had only been sketched as prospective work [27,51].…”

Contextualizing the Genes Altered in Bladder Neoplasms in Pediatric and Teen Patients Allows Identifying Two Main Classes of Biological Processes Involved and New Potential Therapeutic Targets

“…Consequently, these two GO terms do share logical connections, being light an abiotic stimulus and a visual cue. As a matter of fact, the link between cyclic rhythms (which depend on the alternation of light and darkness) and human diseases (including cancer) or health issues is not a novelty and has been investigated by chronobiology [ 84 , 85 ]. Even the young age of the patients that are the focus of our analyses does not seem to be a limitation, except possibly for the youngest cases (see, for instance, Table 2 , row 27), since the emergence of important biological rhythms has been shown within 18 weeks from birth [ 86 ].…”

Mathematics of Pharmacokinetics and Pharmacodynamics: Diversity of Topics, Models and Methods

“…Its originality is that it is coupled with an ODE model for the PK-PD of the two main drugs used in colorectal cancer: 5-fluorouracil and oxaliplatin. It has been originally designed in the framework of chronotherapeutics (chrono-PK-PD) [25], but it can also be used outside of this framework, provided that the time differences in gating at the cell cycle checkpoints between healthy and cancer cell populations are preserved.…”