Reseach Interests
Reseach Interests
My main focus lies in the development of mathematical models in the field of Mathematical Oncology. At the moment, my aim is extending our knowledge on cancer metastasis through multiscale mathematical modelling techniques, starting from the solitary cancer cell migration to the holistic representation of the organism.
Publications
D. Katsaounis, M.A.J. Chaplain & N. Sfakianakis, Stochastic differential equation modelling of cancer cell migration and tissue invasion. J. Math. Biol. 87, 8 (2023). https://doi.org/10.1007/s00285-023-01934-4
Invasion of the surrounding tissue is a key aspect of cancer growth and spread involving a coordinated effort between cell migration and matrix degradation, and has been the subject of mathematical modelling for almost 30 years. In this current paper we address a long-standing question in the field of cancer cell migration modelling. Namely, identify the migratory pattern and spread of individual cancer cells, or small clusters of cancer cells, when the macroscopic evolution of the cancer cell colony is dictated by a specific partial differential equation (PDE). We show that the usual heuristic understanding of the diffusion and advection terms of the PDE being one-to-one responsible for the random and biased motion of the solitary cancer cells, respectively, is not precise. On the contrary, we show that the drift term of the correct stochastic differential equation (SDE) scheme that dictates the individual cancer cell migration, should account also for the divergence of the diffusion of the PDE. We support our claims with a number of numerical experiments and computational simulations.
2. D. Katsaounis, N. Harbour, T. Williams, M.A.J. Chaplain & N. Sfakianakis, A genuinely hybrid, multiscale 3D cancer invasion and metastasis modelling framework. Bull Math Biol 86, 64 (2024). https://doi.org/10.1007/s11538-024-01286-0
We introduce in this paper substantial enhancements to a previously proposed hybrid multiscale cancer invasion modelling framework to better reflect the biological reality and dynamics of cancer. These model updates contribute to a more accurate representation of cancer dynamics, they provide deeper insights and enhance our predictive capabilities. Key updates include the integration of porous medium-like diffusion for the evolution of Epithelial-like Cancer Cells and other essential cellular constituents of the system, more realistic modelling of Epithelial-Mesenchymal Transition and Mesenchymal-Epithelial Transition models with the inclusion of Transforming Growth Factor beta within the tumour microenvironment, and the introduction of Compound Poisson Process in the Stochastic Differential Equations that describe the migration behaviour of the Mesenchymal-like Cancer Cells. Another innovative feature of the model is its extension into a multi-organ metastatic framework. This framework connects various organs through a circulatory network, enabling the study of how cancer cells spread to secondary sites.
Understanding the dynamics of cancer cell dormancy and reactivation is crucial for predicting metastatic potential and improving treatment outcomes in cancer research. This study evaluates a cancer growth model incorporating cell death, dormancy reactivation, and proliferation to capture the duration of dormancy and the frequency of reactivation events. By testing various statistical distributions against experimental data on mice, we identified models that effectively represent the asymmetry and variability observed in dormancy durations. Notably, the estimated cancer cell death rate remained consistent across all tested distributions, supporting its biological relevance as a robust parameter for modelling dormancy survival dynamics. Among the distributions, the most suitable ones feature heavy-tailed behaviour and asymmetric skewness aligned with the prolonged and rare dormancy periods expected of cancer cells. Our findings underscore the importance of selecting appropriate statistical models for dormancy, in aiding predictions of cancer cell reactivation events, and potentially informing therapeutic strategies to manage dormancy-driven metastasis.