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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 phenotypes relevant to describe their heterogeneity at stake in studies led 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  [63], [79], [80], [81] are close to models used in ecology for adaptive dynamics.

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  [59], [80], [60], [79]. Prior to using optimisation methods, we design models of the targeted cell populations (healthy and tumour, including molecular or functional drug targets  [58]) by PDEs or agent-based models  [56], 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.

Multi-scale modelling of cancer invasion. The major step from a benign tumour to 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). We performed in vitro simulations of cancer cell invasion for breast cancer evaluating under which conditions the observed migration pattern occurs. (In collaboration with our biologist partners within the Institut Curie)