Related papers: Two-dimension tissue growth model based on circula…
Different types of interactions coexist and coevolve to shape the structure and function of a multiplex network. We propose here a general class of growth models in which the various layers of a multiplex network coevolve through a set of…
In this study, we explore a mathematical model for tissue growth focusing on the interplay between multiple cell subpopulations with distinct phenotypic characteristics. The model addresses the dynamics of tissue growth influenced by…
A connection is established between discrete stochastic model describing microscopic motion of fluctuating cells, and macroscopic equations describing dynamics of cellular density. Cells move towards chemical gradient (process called…
Nucleation and growth is the dominant relaxation mechanism driving first order phase transitions. In two-dimensional at systems nucleation has been applied to a wide range of problems in physics, chemistry and biology. Here we study…
We investigate a class of Young diagrams growing via the addition of unit cells and satisfying the constraint that the height difference between adjacent columns $\geq r$. In the long time limit, appropriately re-scaled Young diagrams…
We study a simple growth model for (d+1)-dimensional films of binary alloys in which atoms are allowed to interact and equilibrate at the surface, but are frozen in the bulk. The resulting crystal is highly anisotropic: Correlations…
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…
Two phase solid-fluid mixture models are ubiquitous in biological applications. For instance, models for growth of tissues and biofilms combine time dependent and quasi-stationary boundary value problems set in domains whose boundary moves…
Growth patterns of complex systems predict how they change in sizes, numbers, masses, etc. Understanding growth is important, especially for many biological, ecological, urban, and socioeconomic systems. One noteworthy growth behavior is…
The Whittaker 2d growth model is a triangular continuous Markov diffusion process that appears in many scientific contexts. It has been theoretically intriguing to establish a large deviation principle for this 2d process with a scaling…
We investigated the kinetics of domain growth on liposomes consisting of a ternary mixture (unsaturated phospholipid, saturated phospholipid, and cholesterol) by temperature jump. The domain growth process was monitored by fluorescence…
In order to describe two-dimensionally packed cells in epithelial tissues both mathematically and physically, there have been developed several sorts of geometrical models, such as the vertex model, the finite element model, the…
In this paper we analyse a differential system related to a Glioblastoma growth. Using numerical simulations, we prove that model captures different kind of growth changing adequately the parameters of the model. Firstly, we make an…
Growth (and resorption) of biological tissue is formulated in the continuum setting. The treatment is macroscopic, rather than cellular or sub-cellular. Certain assumptions that are central to classical continuum mechanics are revisited,…
Implant placement under soft tissues operation is described. In this operation tissues can reach such deformations that nonlinear properties are appeared. A mass-spring model modification for modeling nonlinear tissue operation is…
This paper presents a real-time simulation involving ''protozoan-like'' cells that evolve by natural selection in a physical 2D ecosystem. Selection pressure is exerted via the requirements to collect mass and energy from the surroundings…
The effects of a surfactant on two-dimensional pattern formation in epitaxial growth are explored theoretically using a simple model, in which an adatom becomes immobile only after overcoming a large energy barrier as it exchanges positions…
The mechanical properties of cells, which influence the properties of the tissue they belong to, are controlled by various mechanisms. Bi et al. theoretically demonstrated that density-independent rigidity transition occurs in…
In many tissues, cell type varies over single-cell length-scales, creating detailed spatial heterogeneities fundamental to physiological function. To gain understanding of this relationship between tissue function and detailed structure,…
The evolutionary transition to multicellularity transformed life on earth, allowing for the evolution of large, complex organisms. While multicellularity can be strongly advantageous, its earliest stages bring unique physical challenges.…