Most processes in biology and medicine occur over different but inter-connected spatial and temporal scales - from genes to cells to tissues to organs to populations. Known as one of the "hallmarks of cancer", cancer invasion is a complex multi-scale phenomenon involving many inter-related genetic, biochemical, and cellular processes at many different spatial and temporal scales that play a crucial role in the overall cancer development. A key part in invasion is played by the various classes of matrix-degrading enzymes, secreted by the cancer cells, which degrade the surrounding tissue, enabling this way further tumour progression. Combining abnormal proliferation with favourable migratory conditions enabled by altered cell adhesion characteristics, the cancer cells actively spread locally into the surrounding tissue. These challenging multiscale phenomena lead naturally to a question concerning the establishment of an appropriate framework that would enable a rigorous analysis and modelling of cancer invasion. In this series of lectures we will present a series of novel modelling and analysis approaches for cancer invasion that will focus four major directions, namely: (1) tissue-scale cell adhesion modelling; (2) a new spatio-temporal-structural modelling of cell population dynamics incorporating membrane reactions; (3) a new multiscale moving boundary modelling framework for tumour invasion; and (4) a multiscale analysis platform, based on our new concept of "three-scale convergence". Finally, we will present computational simulations in each of these modelling directions and discuss a number of important fundamental properties that follows.
|Published - 2016
|CIMPA Summer Research School in "Mathematical modeling in Biology and Medicine” - Oriente University, Santiago de Cuba, Cuba
Duration: 8 Jun 2016 → 17 Jun 2016
|CIMPA Summer Research School in "Mathematical modeling in Biology and Medicine”
|Santiago de Cuba
|8/06/16 → 17/06/16