Related papers: Continuous Time Random Walk and Migration Prolifer…

From footpaths to flight routes, human mobility networks facilitate the spread of communicable diseases. Control and elimination efforts depend on characterizing these networks in terms of connections and flux rates of individuals between…

We investigate the dynamics of a nonlinear model for tumor growth within a cellular medium. In this setting the "tumor" is viewed as a multiphase flow consisting of cancerous cells in either proliferating phase or quiescent phase and a…

Fractals are fascinating structures, not only for their aesthetic appeal, but also because they allow for the investigation of physical properties in non-integer dimensions. In these unconventional systems, a myriad of intrinsic features…

Diffuse low grade gliomas are slowly growing tumors that always recur after treatment. In this paper, we revisit the modeling of the tumor radius evolution before and after the radiotherapy process and propose a novel model that is simple,…

Directed cell motion in response to an external chemical gradient occurs in many biological phenomena such as wound healing, angiogenesis, and cancer metastasis. Chemotaxis is often characterized by the accuracy, persistence, and speed of…

Collective cell migration lies at the intersection of developmental biology and non-equilibrium physics, where active processes give rise to emergent patterns that are biologically relevant. Here, we investigate dilatational modes--cycles…

Interstitial fluid flow is a feature of many solid tumours. In vitro Experiments have shown that such fluid flow can direct tumour cell movement upstream or downstream depending on the balance between the competing mechanisms of tensotaxis…

In this article, the continuous time random walk on the circle is studied. We derive the corresponding generalized master equation and discuss the effects of topology, especially important when Levy flights are allowed. Then, we work out…

Multicellular migration and pattern formation play important roles in developmental biology, cancer metastasis and wound healing. To understand the collective cell dynamics in three dimensional extracellular matrix (ECM), we have developed…

We consider a mathematical model of cancer cell invasion of the extracellular matrix (ECM), comprising a strongly degenerate parabolic partial differential equation for the cell volume fraction, coupled with an ordinary differential…

Exploiting the coherent medium approximation, random walk among sites distributed randomly in space is investigated when the jump rate depends on the distance between two adjacent sites. In one dimension, it is shown that when the jump rate…

Cell-to-cell variability is inherent to numerous biological processes, including cell migration. Quantifying and characterizing the variability of migrating cells is challenging, as it requires monitoring many cells for long time windows…

Collective migration of eukaryotic cells is often guided by chemotaxis, and is critical in several biological processes, such as cancer metastasis, wound healing, and embryogenesis. Understanding collective chemotaxis has challenged…

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…

We suggest a modification of a comb model to describe anomalous transport in spiny dendrites. Geometry of the comb structure consisting of a one-dimensional backbone and lateral branches makes it possible to describe anomalous diffusion,…

Cell migration is an indispensable physiological and pathological process for normal tissue development and cancer metastasis, which is greatly regulated by intracellular signal pathways and extracellular microenvironment (ECM). However,…

We consider a phenotype-structured reaction-diffusion model of avascular glioma growth. The model describes the interaction dynamics between tumour cells and oxygen, and takes into account anisotropic cell movement and oxygen diffusion…

Collective motion of cells is common in many physiological processes, including tissue development, repair, and tumor formation. Recent experiments have shown that certain malignant cancer cells form clusters in a chemoattractant gradient,…

We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…

A number of biological processes, such as embryo development, cancer metastasis or wound healing, rely on cells moving in concert. The mechanisms leading to the emergence of coordinated motion remain however largely unexplored. Although…