Cellular Potts Models―Multiscale Extensions and Biological Applications

"All biological phenomena emerge from an intricate interconnection of multiple processes occurring at different levels of organization: namely, at the molecular, the cellular and the tissue level, see Figure 1. These natural levels can approximately be connected to a microscopic, mesoscopic, and macroscopic scale, respectively. The microscopic scale refers to those processes that occur at the subcellular level, such as DNA synthesis and duplication, gene dynamics, activation of receptors, transduction ofchemical signals, diffusion of ions and transport of proteins. The mesoscopic scale, on the other hand, can refer to cell-level phenomena, such as adhesive interactions between cells or between cells and ECM components, cell duplication and death and cell motion. The macroscopic scale finally corresponds to those processes that are typical of multicellular behavior, such as population dynamics, tissue mechanics and organ growth and development. It is evident that research in biology and medicine needs towork in a multiscale fashion. This brings many challenging questions and a complexity that can not be addressed in the classical way, but can take advantage of the increasing collaboration between natural and exact sciences (for more detailed comments the reader is referred to [90, 262]). On the other hand, the recent literature provides evidence of the increasing attention of the mathematical, statistical, computational and physical communities toward biological and biomedical modeling, consequence of the successful results obtained by a multidisciplinary approach to the Life Sciences problems"--

Marco Scianna is a post-doctoral fellow in the Department of Mathematical Sciences at the Politecnico di Torino. He earned a Ph.D. in complex systems in post-genomic biology from the University of Turin. His principal research focuses on mathematical multiscale models applied to biological and biomedical problems, with particular interest in the context of tumor growth, vascular network formation, and cell migration in extracellular matrix.

Luigi Preziosi is a professor of mathematical physics at the Politecnico di Torino. He earned a Ph.D. in mechanics from the University of Minnesota and in mathematics from the University of Naples. He has authored three books, more than 30 book chapters, and more than 100 articles in international journals. His recent research interests include multiphase models of tumor growth, the mechanics of tissue growth and regenerations, cell migration, and vascular network formation.