Related papers: A continuum mathematical model of substrate-mediat…
A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion…
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…
A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for…
We propose a simple mathematical model to describe the mechanical relaxation of cells within a curved epithelial tissue layer represented by an arbitrary curve in two-dimensional space. This model generalises previous one-dimensional models…
The study and characterization of the diversity of spatiotemporal patterns generated when a rectangular layer of fluid is locally heated beneath its free surface is presented. We focus on the instability of a stationary cellular pattern of…
We investigate morphologies of proliferating cellular tissue using a newly developed numerical simulation model for mechanical cell division. The model reproduces structures of simple multi-cellular organisms via simple rules for selective…
This paper is concerned with traveling waves to an diffusive SIR model with delay placed in the diffusion terms as well as nonlinear incidence rate with delay. Using a cross iteration scheme and partial monotone conditions it will be shown…
Out-of-equilibrium systems, inherently complex and challenging to understand, are prevalent across various disciplines, including physics where they arise in contexts such as fluid dynamics. In particular, critical out-of-equilibrium…
This letter is concerned with asymptotic analysis of a PDE model for motility of a eukaryotic cell on a substrate. This model was introduced in [1], where it was shown numerically that it successfully reproduces experimentally observed…
Although tissues are usually studied in isolation, this situation rarely occurs in biology, as cells, tissues, and organs, coexist and interact across scales to determine both shape and function. Here, we take a quantitative approach…
In this paper, we study the existence and stability of travelling wave solutions of a kinetic reaction-transport equation. The model describes particles moving according to a velocity-jump process, and proliferating thanks to a reaction…
A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion…
At the continuous level, we consider two types of tumor growth models: the cell density model, which is based on the fluid mechanical construction, is more favorable for scientific interpretation and numerical simulations; and the free…
Several mathematical models of tumor growth are now commonly used to explain medical observations and predict cancer evolution based on images. These models incorporate mechanical laws for tissue compression combined with rules for…
We consider a minimal go-or-grow model of cell invasion, whereby cells can either proliferate, following logistic growth, or move, via linear diffusion, and phenotypic switching between these two states is density-dependent. Formal analysis…
A mathematical model is developed to analyze the growth/decay rate of surface perturbations of an ultrathin metal film on an amorphous substrate (SiO_{2}). The formulation combines the approach of Mullins [J. Appl. Phys. v30, 77, 1959] for…
We consider a model for the dynamics of growing cell populations with heterogeneous mobility and proliferation rate. The cell phenotypic state is described by a continuous structuring variable and the evolution of the local cell population…
Most biological tissues grow by the synthesis of new material close to the tissue's interface, where spatial interactions can exert strong geometric influences on the local rate of growth. These geometric influences may be mechanistic, or…
Reaction-diffusion waves in multiple spatial dimensions advance at a rate that strongly depends on the curvature of the wave fronts. These waves have important applications in many physical, ecological, and biological systems. In this work,…
In this paper, we derive an effective macroscale description suitable to describe the growth of biological tissue within a porous tissue-engineering scaffold. As in our recent work (Holden \textit{et al.} "A multiphase multiscale model for…