Section: Application Domains

Cancer therapies and their optimisation

Drugs. 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 (i.e., this is not $L^2$ nor $L^1$, but $L^{\infty }$ optimisation) in healthy cell populations and avoiding the emergence of resistant cell clones in cancer cell populations [49] , [58] [4] , [40] . Prior to using optimisation methods, we design models of the targeted cell populations (healthy and tumour, including molecular or functional drug targets [48] ) by PDEs or agent-based models [3] , and molecular pharmacological (pharmacokinetic-pharmacodynamic, PK-PD) models of the fate and effects of the drugs used, usually by ODE models. A particular aspect of such modelling is the representation of multi-cellular spatio-temporal patterns emerging from therapies.

Radiotherapy. Radiation is still a major treatment in cancer. We have recently published new results on this topic, pleae refer to the New Results section.