During morphogenesis, hundreds of cells undergo large-scale movements, and the biological or mechanical regulatory factors involved are still poorly understood, despite intensive research. To better characterize the emergence of these movements, we propose a microscopic Vicsek-type model, combining the alignment of polarities and contact forces, and have studied the dynamics in confined...
Shigesada, Kawasaki, and Teramoto showed that introducing cross-diffusion into the spatial Lotka–Volterra competition model can destabilise homogeneous equilibria and generate spatial patterns. In this talk, I will consider populations with phenotype heterogeneity and introduce a general framework in which individuals’ movements and interactions are phenotype-dependent. Motivated by cellular...
The choroid is a densely vascularised layer of tissue of the eye, lying between the retina and the sclera (outer layer of the eye), which carries the majority of ocular blood flow. Vortex veins
drain blood out of the eye (to the orbit), crossing the sclera from the choroidal circulation.
Animal experiments have shown that pressure in these veins is tightly linked to intraocular pressure...
Since D'Arcy Thompson, the interplay between mechanics and shape in living organisms has been a central question in mathematical biology. In tissue mechanics, shape variation has been studied through growth, development, and wound healing with various modeling approaches and objectives (\cite{10.1088/1367-2630/adcd93,10.1039/d3sm01419c}).
We develop a variational approach to active...
Mathematical models present numerous advantages when studying biological issues, mainly because they enable us to explore hypotheses that cannot be tested in vitro and even less in vivo, such as evolutionary scenarii, possible alternative mechanisms or arbitrary setting of physiological parameters.
In this talk, we will use a 3D agents-based model to explore the question of how biological...
Epithelial tissues are densely packed, confluent systems whose organization and mechanics are commonly described mathematically using vertex models. While these approaches successfully capture membrane dynamics and cell–cell junction remodeling, they inherently lack the ability to explicitly account for intercellular attraction and/or repulsion forces. As a result, key aspects of tissue...
In this talk, PDE models for the growth of heterogeneous cell populations will be considered. Both models with discrete phenotype states, which consist of coupled systems of nonlinear PDEs, and models wherein the phenotype enters as a continuous structuring variable, which are formulated as non-local PDEs, will be examined. Focusing on scenarios where cells with different phenotypes are...
Tissues in health and disease are inherently dynamic, adaptive, and driven by processes that operate away from classical equilibrium assumptions. Integrating mechanistic models with experimental data (spanning in-vitro systems, organoids, live imaging, and in-vivo measurements) is key to unraveling how physiological function emerges and how dysregulation leads to pathology. However,...
