Related papers: Mathematical models for cell migration: a nonlocal…
We formulate haptotaxis models of cancer invasion wherein the infiltrating cancer cells can occupy a spectrum of states in phenotype space, ranging from `fully mesenchymal' to `fully epithelial'. The more mesenchymal cells are those that…
Migrating cells choose their preferential direction of motion in response to different signals and stimuli sensed by spanning their external environment. However, the presence of dense fibrous regions, lack of proper substrate, and cell…
Adhesion-independent migration is a prominent mode of cell motility in confined environments, yet the physical principles that guide such movement remain incompletely understood. We present a phase-field model for simulating the motility of…
There is increasing interest in the analysis of biological tissue, its organization and its dynamics with the help of mathematical models. In the ideal case emergent properties on the tissue scale can be derived from the cellular scale.…
Non-locality is being intensively studied in various PDE-contexts and in variational problems. The numerical approximation also looks challenging, as well as the application of these models to Continuum Mechanics and Image Analysis, among…
Local cancer cell invasion is a complex process involving many cellular and tissue interactions and is an important prerequisite for metastatic spread, the main cause of cancer related deaths. Occurring over many different temporal and…
We propose and study a strongly coupled PDE-ODE system with tissue-dependent degenerate diffusion and haptotaxis that can serve as a model prototype for cancer cell invasion through the extracellular matrix. We prove the global existence of…
In this thesis we develop minimal models of the relationship between motility, growth, and evolution of cancer cells. We utilise simple simulations of a population of individual cells in space to examine how changes in mechanical properties…
The migration of cells is relevant for processes such as morphogenesis, wound healing, and invasion of cancer cells. In order to move, single cells deform cyclically. However, it is not understood how these shape oscillations influence…
We discuss several continuum cell-cell adhesion models based on the underlying microscopic assumptions. We propose an improvement on these models leading to sharp fronts and intermingling invasion fronts between different cell type…
Cell migration is a fundamental process involved in physiological phenomena such as the immune response and morphogenesis, but also in pathological processes, such as the development of tumor metastasis. These functions are effectively…
We investigate micro-to-macroscopic derivations in two models of living cells, in presence to cell-cell adhesive interactions. We rigorously address two PDE-based models, one featuring non-local terms and another purely local, as a a result…
Morphogenesis, tissue regeneration and cancer invasion involve transitions in tissue morphology. These transitions, caused by collective cell migration (CCM), have been interpreted as active wetting/de-wetting transitions. This phenomenon…
Formation of organs and specialized tissues in embryonic development requires migration of cells to specific targets. In some instances, such cells migrate as a robust cluster. We here explore a recent local approximation of nonlocal…
We propose and study a strongly coupled PDE-ODE-ODE system modeling cancer cell invasion through a tissue network under the go-or-grow hypothesis asserting that cancer cells can either move or proliferate. Hence our setting features two…
In this paper, we consider a mathematical model for the invasion of host tissue by tumour cells in a $d$-dimensional bounded domain, $d\leq 3$. This model consists of a system of differential equations describing the evolution of cancer…
Over the past decades, nonlocal models have been widely used to describe aggregation phenomena in biology, physics, engineering, and the social sciences. These are often derived as mean-field limits of attraction-repulsion agent-based…
Partial differential equations (PDEs) are used, with huge success, to model phenomena arising across all scientific and engineering disciplines. However, across an equally wide swath, there exist situations in which PDE models fail to…
This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly…
Partial differential equation (PDE) models for infectious diseases, while less common than their ordinary differential equation (ODE) counterparts, have found successful applications for many years. Such models are typically of…