Related papers: Mathematical models for cell migration: a nonlocal…
This work concerns with a class of chemotaxis models in which external sources, comprising nonlocal and gradient-dependent damping reactions, influence the motion of a cell density attracted by a chemical signal. The mechanism of the two…
Amoeboid motion is a dynamic mode of cell motility essential for processes such as the immune response and wound healing. This review examines recent developments in the mathematical and computational modeling of amoeboid crawling, focusing…
Collections of cells exhibit coherent migration during morphogenesis, cancer metastasis, and wound healing. In many cases, bigger clusters split, smaller sub-clusters collide and reassemble, and gaps continually emerge. The connections…
Chemotaxis and haptotaxis have been a main theme in the macroscopic study of bacterial and cellular motility. In this work we investigate the influence these processes have on the shape and motility of fast migrating cells. We note that…
We provide a short review of existing models with multiple taxis performed by (at least) one species and consider a new mathematical model for tumor invasion featuring two mutually exclusive cell phenotypes (migrating and proliferating).…
Cell migration plays a fundamental role in numerous physiological processes, including embryonic development, wound healing, and cancer metastasis. While cell-cell adhesion is known to regulate motion by shaping cell morphology and…
In this manuscript, we consider the modelling of cellular adhesions, which is a key interaction between biological cells. Continuum models of the diffusion-advection-reaction type have long been used in tissue modelling. In 2006, Armstrong,…
A slowly-varying or thin-layer multiscale assumption empowers macroscale understanding of many physical scenarios from dispersion in pipes and rivers, including beams, shells, and the modulation of nonlinear waves, to homogenisation of…
Mathematical modelling has a long history in the context of collective cell migration, with applications throughout development, disease and regenerative medicine. The aim of modelling in this context is to provide a framework in which to…
A two-dimensional mathematical model for cells migrating without adhesion capabilities is presented and analyzed. Cells are represented by their cortex, which is modelled as an elastic curve, subject to an internal pressure force. Net…
The phenomenological model for cell shape deformation and cell migration (Chen et.al. 2018; Vermolen and Gefen 2012) is extended with the incorporation of cell traction forces and the evolution of cell equilibrium shapes as a result of cell…
The capability of cells to form surface extensions to non-locally probe the surrounding environment plays a key role in cell migration. The existing mathematical models for migration of cell populations driven by this non-local form of…
From a systems biology perspective the majority of cancer models, although interesting and providing a qualitative explanation of some problems, have a major disadvantage in that they usually miss a genuine connection with experimental…
Based on symmetry consideration of migration and shape deformations, we formulate phenomenologically the dynamics of cell crawling in two dimensions. Forces are introduced to change the cell shape. The shape deformations induce migration of…
Collective cell migration plays a crucial role in numerous biological processes, including tumour growth, wound healing, and the immune response. Often, the migrating population consists of cells with various different phenotypes. This…
Cell migration is essential for regulating many biological processes in physiological or pathological conditions, including embryonic development and cancer invasion. In vitro and in silico studies suggest that collective cell migration is…
Cell migration is crucial to many physiological and pathological processes. During migration, a cell adapts its morphology, including the overall morphology and nucleus morphology, in response to various cues in complex microenvironments,…
Non-local advection is a key process in a range of biological systems, from cells within individuals to the movement of whole organisms. Consequently, in recent years, there has been increasing attention on modelling non-local advection…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
This paper is concerned with a non-homogeneous in space and non-local in time random walk model for anomalous subdiffusive transport of cells. Starting with a Markov model involving a structured probability density function, we derive the…