Multiscale extensions of the cellular Potts models: toward a nested-hybrid approach

Multiscale problems are ubiquitous in all biological phenomena, which emerge from the complex interaction between processes happening at various levels. A number of mathematical approaches have been developed to address such an intricate network of organization. Among others, the cellular Potts model is particularly well-known and widespread. The CPM is a discrete, lattice-based, flexible technique able to accurately identify and describe the phenomenological mechanisms responsible for innumerable biological phenomena. This work discusses some innovative extensions of the method, whose aim is to increase its accuracy and to create a multilevel framework able to deal with the multiscale organization typical of biological development. Such CPM extensions are finally tested with sample applications, that show their potential and biological realism.