| Contents |
| 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.
The process of invasion consists of cancer cells secreting various matrix-degrading enzymes, which degrade the surrounding tissue or the extracellular matrix. Combining abnormal proliferation with favourable migratory conditions enabled by altered cell-cell and cell-matrix adhesion characteristics, the cancer cells actively spread locally into the surrounding tissue.
As these multiscale phenomena lead naturally to a question concerning the establishment of a fundamental framework that would enable a rigorous analysis and modelling of cancer invasion, in this talk we will first present a novel multiscale modelling framework involving two scales - cell and tissue. This will be accompanied by a multiscale analysis framework, which is based on our new concept of "three-scale convergence". Finally, we will present computational simulations of our multiscale moving boundary model and discuss a number of important fundamental properties that follows. |
|