My main goal is developing multiscale mathematical methods for modelling multicellular systems such as tissues, bacterial colonies, tumours etc. Many mathematical models rely on phenomenological relationships between model parameters and variables. While these relationships may be fitted to experimental data, they do not incorporate functions of directly measurable quantities at the cell scal. Multiscale models equip directly measurable quantities at the cell scale inform the model parameters at the continuum scale through upscaling techniques making multiscale models, in principle, predictive because the data used for calibration is distinct from that used for validation. Bridging these scales is a significant challenge.
Biological Lattice-Gas Cellular Automata (BIO-LGCA)
Cellular automata (CA) can be viewed as simple models of self-organizing complex systems in which collective behavior can emerge out of an ensemble of many interacting “simple” components. They were introduced by J. von Neumann and S. Ulam in the 1950s in an attempt to model biological self-reproduction. I have mainly worked in the development of biological lattice-gas cellular automat (BIO-LGCA), which is specific class of CA. In contrast to traditional CA, BIO-LGCA provide a straightforward and intuitive implementation of particle transport and interactions. Additionally, the structure of LGCA facilitates the mathematical analysis of their behavior. For more details please refer to the designated Wikipedia page.
Multicellular Density Functional Theory (MDFT)
I am interested in a new mesoscopic framework based on an extended Dynamic Density Functional Theory (DDFT), for the first time, to the dynamics of living tissues by accounting for cell density correlations, different cell types, phenotypes and cell birth/death processes, in order to provide a biophysically consistent description of processes across the scales. The basis of this framework is the appropriate definition of a “free energy” functional. Recently, based on the DDFT model, we have developed a phase-field crystal method for multicellular systems.