Multiscale problems are ubiquitous and fundamental in all biological phe- nomena that naturally emerge from the complex interaction of processes which occur at various levels. A number of both discrete and continuous mathematical models and methods have been developed to address such an intricate network of organization. One of the most suitable individual  cell-based model for this purpose is the well-known cellular Potts model (CPM, [1]). The CPM is a dis- crete, lattice-based, flexible technique that  is able to accurately identify  and describe the phenomenological  mechanisms which are responsible for innumer- able biological (and nonbiological) phenomena. In this presentation, we first give a brief overview of its biophysical basis and discuss its main limitations. We then propose  some innovative extensions, focusing on ways of integrating the basic CPM, operating at the mesoscopic scale, with continuous approaches accurately modeling microscopic dynamics. The aim is to create a nested and hybrid environment, where the evolution of a biological system is realistically driven by the constant  interplay  and flux of information  between the differ- ent levels of its organization [2, 3]. Our CPM extensions are then tested with sample applications that  show a qualitative  and quantitative  agreement  with experimental data [4, 5].In particular, we analyze cell migration within  fibrous extracellular matrices and bio-engineered microchannels,  showing the relevant role played by a compartmentalized represention of cells, i.e., differentiated in the nucleus and the cysolic region. Finally, we conclude by discussing further possible developments of the method.

References

[1] Glazier, J. A. and Graner, F., 1993. Simulation of the differential adhesion driven rearrangement of biological cells. Physical Rev E, 47, 2128 - 2154.

[2] Scianna, M. and Preziosi, L., 2012. Multiscale developments of the cellular

Potts model. Multiscale Model Simul, 10 (2), 342 - 382.

[3] Scianna, M., Preziosi, L.,2013.  Cellular Potts model: multiscale develop- ments and biological applications, Chapman & Hall/CRC  Press.

[4] Scianna, M., Munaron, L. and Preziosi, L., 2011. A multiscale hybrid ap- proach for vasculogenesis and related potential blocking therapies. Prog Bio- phys Mol Biol, 106 (2), 450 - 462.