Related papers: A Model of Controlled Growth
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…
Tissue homeostasis, the biological process of maintaining a steady state in tissue via control of cell proliferation, death, and metabolic function, is essential for the development, growth, maintenance, and proper function of living…
A multiscale mathematical model is presented to describe the de novo granulation and the evolution of multispecies granular biofilms within a continuous reactor. The granule is modelled as a spherical free boundary domain with radial…
This paper is concerned with a multi-dimensional free boundary problem modeling the growth of a tumor with two species of cells: proliferating cells and quiescent cells. This free boundary problem has a unique radial stationary solution. By…
We present a model for cell growth, division and packing under soft constraints that arise from the deformability of the cells as well as of a membrane that encloses them. Our treatment falls within the framework of diffuse interface…
We present a mathematical model that describes how tumour heterogeneity evolves in a tissue slice that is oxygenated by a single blood vessel. Phenotype is identified with the stemness level of a cell, $s$, that determines its proliferative…
A new model for biological growth is introduced that couples the geometry of an organism (or part of the organism) to the flow and deposition of material. The model has three dynamical variables (a) a Riemann metric tensor for the geometry,…
Morphogenesis emerges from dynamic feedback among geometry, mechanics, and chemistry; however, disentangling these contributions in living systems remains challenging. Here, we focus on the interplay between geometry and mechanics by…
We present a framework for shape matching in computational anatomy allowing users control of the degree to which the matching is diffeomorphic. This control is given as a function defined over the image and parameterises the template…
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 a distributed optimal control problem for a diffuse interface model for tumor growth. The model consists of a Cahn-Hilliard type equation for the phase field variable coupled to a reaction diffusion equation for the…
We propose a two-scale model to resolve essential features of developmental tissue deformations. The model couples individual cellular behavior to the mechanics at tissue scale. This is realized by a multiphase-field model addressing the…
The multiplicative decomposition model is widely employed for predicting residual stresses and morphologies of biological tissues due to growth. However, it relies on the assumption that the tissue is initially in a stress-free state, which…
We study the equilibrium configurations related to the growth of an elastic fibre in a confining flexible ring. This system represents a paradigm for a variety of biological, medical, and engineering problems. We consider a simplified…
Topological defects determine the collective properties of anisotropic materials. How their configurations are controlled is not well understood however, especially in 3D. In living matter moreover, 2D defects have been linked to biological…
The process of morphogenesis, which can be defined as an evolution of the form of an organism, is one of the most intriguing mysteries in the life sciences. It is clear, that gene expression patterns cannot explain the development of the…
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…
We present a two-dimensional continuum model of tumor growth, which treats the tissue as a composition of six distinct fluid phases; their dynamics are governed by the equations of mass and momentum conservation. Our model divides the…
Morphogenesis is a tightly regulated process that has been studied for decades. We are developing data-based and image-basd mechanistic models for a range of developmental processes with a view to integrate the available knowledge and to…
We consider a class of tumor growth models under the combined effects of density-dependent pressure and cell multiplication, with a free boundary model as its singular limit when the pressure-density relationship becomes highly nonlinear.…