Section: Application Domains

Cancer modelling

Evolution of healthy or cancer cell populations under environmental pressure; drug resistance. Considering cancer as an evolutionary disease – evolution meaning here Darwinian evolution, but also Lamarckian instruction, of populations structured according to relevant phenotypes – in collaboration with our biologist partners within the Institut Universitaire de Cancérologie (IUC) of UPMC, we tackle the problem of understanding and limiting: a) the evolution from pre-malignancy to malignancy in cell populations (in particular we study early leukaemogenesis, leading to acute myeloid leukaemia), and b) in established cancer cell populations, the evolution towards (drug-induced) drug resistance. The environmental pressure guiding evolution has many sources, including signalling molecules induced by the peritumoral stroma (e.g., between a breast tumour and its adipocytic stroma), and anticancer drugs and their effects on both the tumour and its stromal environment. The models we use [82] , [81] , [23] , [41] are close to models used in ecology for adaptive dynamics.

Multi-scale modelling of EMT. The major step from a benign tumour that can be eradicated by surgery and an invasive cancer is the development step at which cells detach from the tumour mass and invade individually the surrounding tissue (Weinberg, The biology of cancer, Garland, 2007). The invasion is preceded by a transition (called EMT - epithelial mesenchymal transition) of the cancer phenotype from an epithelial type to a mesenchymal type cell. We have so far worked on multi-scale modelling of EMT (Ramis-Conde, Drasdo, Anderson, Chaplain, Biophys. J., 2008), and the step by which invading cancer cells enter blood vessels, called intravasation (Ramis-Conde, Chaplain, Anderson, Drasdo, Phys. Biol. 2009). We currently perform in vitro simulations of cancer cell invasion for non-small cell lung cancer (NSCLC) cells having a 5-year survival fraction of about 20%, and for breast cancer. Under development (in collaboration with our biologist partners within the IUC for the experimental part) is also a phenotype-structured PDE model of the interactions between colonies of MCF7 breast cancer and adipocyte stromal support populations (see below, in “New results”, Lung and breast cancer).

Drugs: pharmacokinetics-pharmacodynamics, therapy optimisation. We focus on multi-drug multi-targeted anticancer therapies aiming at finding combinations of drugs that theoretically minimise cancer cell population growth with the constraint of limiting unwanted toxic side effects under an absolute threshold (this is not $L^2$ nor $L^1$, but $L^{\infty }$ optimisation, i.e. the constraints as well as the objective function are $L^{\infty }$) in healthy cell populations and avoiding the emergence of resistant cell clones in cancer cell populations [62] , [81] , [63] , [80] . Prior to using optimisation methods, we design models of the targeted cell populations (healthy and tumour, including molecular or functional drug targets [61] ) by PDEs or agent-based models [59] , and molecular pharmacological (pharmacokinetic-pharmacodynamic, PK-PD) models of the fate and effects in the organism of the drugs used, usually by ODE models. A special aspect of such modelling is the representation of multi-cellular spatio-temporal patterns emerging from therapies.