Inverse Reconstruction of Cell Proliferation Laws in Cancer Invasion Modelling

The process of local cancer cell invasion the surrounding tissue is key for overall tumour growth and spread within human body, past 3 decades witnessing intense mathematical modelling efforts in these regards. However, a deep understanding studies require robust data assimilation approaches. While being crucial importance assimilating potential clinical data, inverse problems approaches are still their early stages, with questions regarding retrieval characteristics cells motility, mutations, population proliferation, remaining widely open. This study deals identification reconstruction usually unknown proliferation law from macroscopic snapshot collected at some later stage evolution. Considering two basic configurations, associated case one subpopulations that exercise dynamics extracellular matrix, we combine Tikhonov regularisation gaussian mollification finite element differences approximations to reconstruct laws each sub-populations both exact noisy measurements. Our problem formulation accompanied by numerical examples several used modelling.