Related papers: A Model of Controlled Growth
We study the dynamics of proliferating cell collectives whose microscopic constituents' growth is inhibited by macroscopic growth-induced stress. Discrete particle simulations of a growing collective show the emergence of concentric-ring…
The mechanical behaviour of solid biological tissues has long been described using models based on classical continuum mechanics. However, the classical continuum theories of elasticity and viscoelasticity cannot easily capture the…
We study a shape evolution framework in which the deformation of shapes from time t to t + dt is governed by a regularized anisotropic elasticity model. More precisely, we assume that at each time shapes are infinitesimally deformed from a…
We derive a course grained, continuum model of the 2D vertex model, applicable for different underlying geometries, and allowing for analytical analysis of an otherwise numerical model. Using a geometric approach and out--of--equilibrium…
Tumor growth beyond a critical size relies on the development of a functional vascular network, which ensures adequate oxygen and nutrient supply. In this work, we present a modeling framework based on an optimization-based 3D-1D coupling…
An important question in biology is how the relative size of different organs is kept nearly constant during growth of an animal. This property, called proportionate growth, has received increased attention in recent years. We discuss our…
It is well established that the mechanical environment influences cell functions in health and disease. Here, we address how the mechanical environment influences tumor growth, in particular, the shape of solid tumors. In an in vitro tumor…
Cancer is a very complex phenomenon that involves many different scales and situations. In this paper we consider a free boundary problem describing the evolution of a tumor colony and we derive a new asymptotic model for tumor growth. We…
Cities are living organisms. They are out of equilibrium, open systems that never stop developing and sometimes die. The local geography can be compared to a shell constraining its development. In brief, a city's current layout is a step in…
Both compressible and incompressible porous medium models are used in the literature to describe the mechanical properties of living tissues. These two classes of models can be related using a stiff pressure law. In the incompressible…
In this paper a reduced one-dimensional moving boundary model is studied that describes the evolution of a biofilm driven by the presence of a reaction limiting substrate. Global well-posedness is established for the resulting parabolic…
A recent experiment on zebrafish blastoderm morphogenesis showed that the viscosity ({\eta}) of a non-confluent embryonic tissue grows sharply until a critical cell packing fraction ({\phi}S). The increase in {\eta} up to {\phi}S is similar…
Connecting cell behavior to tissue shape and mechanics is a key challenge in the physics of morphogenesis. Cytoskeletal turnover precludes a fixed reference state, and tensions are actively generated independently of strain; so conventional…
There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…
In this paper, we conduct a thorough mathematical analysis of a tumor growth model with treatments. The model is a system describing the evolution of metastatic tumors and the number of cells present in a primary tumor. The former evolution…
We investigate the evolutionary dynamics of an idealised model for the robust self-assembly of two-dimensional structures called polyominoes. The model includes rules that encode interactions between sets of square tiles that drive the…
Predictive modeling of the evolutionary dynamics of cancer is a challenge issue in computational cancer biology. In this paper, we propose a general mathematical model framework for the evolutionary dynamics of cancer with plasticity and…
From tumour invasion to cell sorting and animal territoriality, many biological systems rely on nonlocal interactions that drive complex spatial organisation. Partial differential equations (PDEs) with nonlocal advection are increasingly…
We introduce a formalism for the geometry of eukaryotic cells and organisms.Cells are taken to be star-convex with good biological reason. This allows for a convenient description of their extent in space as well as all manner of cell…
Cell proliferation, apoptosis, and myosin-dependent contraction can generate elastic stress and strain in living tissues, which may be dissipated by internal rearrangement through cell topological transition and cytoskeletal reorganization.…