Multiscale modelling of acid-mediated cancer cell migration with random dynamics
Final Report Abstract
In the broad active field of cancer cell migration, this project was particularly motivated by the respective influence of acidosis on both neoplastic and normal tissue. Indeed, cancer cells exhibit excess use of glycolysis both in hypoxic and normoxic conditions, and the intra- and extracellular pH values have a significant effect on the malignant phenotype. We proposed and studied several classes of new mathematical models, some of them including stochasticity, as the latter is a relevant feature inherent to most biological processes and in particular to those related to acid-mediated tumor invasion. The models couple various types of differential equations (parabolic and/or hyperbolic PDEs with ODEs, SDEs or random ODEs) acting on different scales (subcellular, mesoscopic, macroscopic). They are highly nonlinear and can even exhibit certain types of degeneracy and even blow-up phenomena, their analysis thus raising serious challenges; in particular, such nonlinear couplings between PDEs and SDEs/RODEs were so far widely unknown. Also new (from the modeling as well as analytical viewpoints) is our setting involving a cell-state-structured population model with nonlinear diffusion, pH-taxis, cell-cell and cell-tissue adhesions, also incorporating proliferation mediated by the cell state, along with the evolution of the normal tissue hosting the tumor. The numerical simulations performed for the models introduced in this project confirmed the experimentally and/or clinically observed (mainly qualitative, one of the models also quantitative) behavior of tumor cells subjected to various conditions in their biochemical environment, acidosis being thereby one important issue. The models open the way for predictions about the tumor development and its invasion into the tissue and for enhancing the therapy planning; there is yet a need of reliable data for quantitatively validating these models. The contribution of our project goes, however, beyond investigating the mentioned biomedical problem; it also extends to advancing the mathematical understanding of such systems arising from the modeling process.
Publications
- On a class of multiscale cancer cell migration models: Well-posedness in less regular function spaces, Mathematical Models and Methods in the Applied Sciences 24 (2014) 2383–2436
T. Lorenz and C. Surulescu
(See online at https://doi.org/10.1142/S0218202514500249) - A multiscale model for pH-tactic invasion with time-varying carrying capacities, IMA Journal of Applied Mathematics 80 (2015) 1300–1321
C. Stinner, C. Surulescu, and G. Meral
(See online at https://doi.org/10.1093/imamat/hxu055) - A stochastic model featuring acid-induced gaps during tumor progression, Nonlinearity 29 (2016) 851–914
S. Hiremath and C. Surulescu
(See online at https://doi.org/10.1088/0951-7715/29/3/851) - On a coupled SDE-PDE system modeling acid-mediated tumor invasion, preprint, TU Kaiserslautern, 2016, 26 pages
S. Hiremath, S. Sonner, C. Surulescu, and A. Zhigun
