Related papers: A Model of Controlled Growth
Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed…
Modeling the spontaneous evolution of morphology in natural systems and its preservation by proportionate growth remains a major scientific challenge. Yet, it is conceivable that if the basic mechanisms of growth and the coupled kinetic…
In this paper, a two-dimensional model for the growth of multi-layer tumors is presented. The model consists of a free boundary problem for the tumor cell membrane and the tumor is supposed to grow or shrink due to cell proliferation or…
Morphogenesis, the process by which an adult organism emerges from a single cell, has fascinated humans for a long time. Modelling this process can provide novel insights into development and the principles that orchestrate the…
Based on a recently proposed non-equilibrium mechanism for spatial pattern formation [cond-mat/0312366] we study how morphogenesis can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of…
I consider how cell shape and environmental geometry affect the rate of nutrient capture and the consequent maximum growth rate of a cell, focusing on rod-like species like \textit{E.\ coli}. Simple modeling immediately implies that it is…
We study the optimal control problem of a free boundary PDE model describing the growth of multilayered tumor tissue in vitro. We seek the optimal amount of tumor growth inhibitor that simultaneously minimizes the thickness of the tumor…
Understanding the rules underlying organismal development is a major unsolved problem in biology. Each cell in a developing organism responds to signals in its local environment by dividing, excreting, consuming, or reorganizing, yet how…
A free boundary value problem related to the genesis of multispecies granular biofilms is presented. The granular biofilm is modelled as a spherical free boundary domain with radial symmetry. The proposed model is conceived in the framework…
This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly…
Morphogen transport is a biological process, occurring in the tissue of living organisms, which is a determining step in cell differentiation. We present rigorous analysis of a simple model of this process, which is a system coupling…
One of the major challenges in biology concerns the integration of data across length and time scales into a consistent framework: how do macroscopic properties and functionalities arise from the molecular regulatory networks - and how can…
Space-saving design is a requirement that is encountered in biological systems and the development of modern technological devices alike. Many living organisms dynamically pack their polymer chains, filaments or membranes inside of…
Shape is one of the important characteristics for the structures observed in living organisms. Whereas biologists have proposed models where the shape is controlled on a molecular level [1], physicists, following Turing [2] and d'Arcy…
Using linearized elasticity as a convenient mechanical framework, we show that volumetric growth can be formulated as an optimization-driven process in which the growth tensor is determined implicitly by constrained optimization rather than…
We present a theory of pattern formation in growing domains inspired by biological examples of tissue development. Gradients of signaling molecules regulate growth, while growth changes these graded chemical patterns by dilution and…
In this paper, we propose a tumor growth model to incorporate and investigate the spatial effects of autophagy. The cells are classified into two phases: normal cells and autophagic cells, whose dynamics are also coupled with the nutrients.…
Based on a non-equilibrium mechanism for spatial pattern formation we study how position information can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing…
Recently, much attention has been given to a noteworthy property of some soft tissues: their ability to grow. Many attempts have been made to model this behaviour in biology, chemistry and physics. Using the theory of finite elasticity,…
This work studies a variational formulation and numerical solution of a regularized morphoelasticity problem of shape evolution. The foundation of our analysis is based on the governing equations of linear elasticity, extended to account…