Related papers: A two species hyperbolic-parabolic model of tissue…
The self-organization of cells into complex tissues relies on a tight coordination of cell behavior. Identifying the cellular processes driving tissue growth is key to understanding the emergence of tissue forms and devising targeted…
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…
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…
Partial differential equations are a convenient way to describe reaction- advection-diffusion processes of signalling models. If only one cell type is present, and tissue dynamics can be neglected, the equations can be solved directly.…
We derive and study a new hyperbolic two-phase model of a porous deformable medium saturated by a viscous fluid. The governing equations of the model are derived in the framework of Symmetric Hyperbolic Thermodynamically Compatible (SHTC)…
We consider the time evolution of the supercritical Galton-Watson model of branching particles with extra parameter (mass). In the moment of the division the mass of the particle (which is growing linearly after the birth) is divided in…
Several recent papers have addressed modelling of the tissue growth by the multi-phase models where the velocity is related to the pressure by one of the physical laws (Stoke's, Brinkman's or Darcy's). While each of these models has been…
We study an optimal control problem for a stochastic model of tumour growth with drug application. This model consists of three stochastic hyperbolic equations describing the evolution of tumour cells. It also includes two stochastic…
In this paper, we study a nonlinear system of first order partial differential equations describing the macroscopic behavior of an ensemble of interacting self-propelled rigid bodies. Such system may be relevant for the modelling of bird…
Cell proliferation and diffusion can be modeled through reaction-diffusion systems describing the space-time evolution of a density variable. In this work, we present non-linear transformations of heat equation solutions to model cellular…
We use a three-dimensional formulation of the cell vertex model to describe the mechanical properties of a confluent planar monolayer of prismatic cells. Treating cell height as a degree of freedom, we reduce the model to a two-dimensional…
Mechanical models for tumor growth have been used extensively in recent years for the analysis of medical observations and for the prediction of cancer evolution based on imaging analysis. This work deals with the numerical approximation of…
In this paper we study a model describing the growth of necrotic tumors in different regimes of vascularisation. The tumor consists of a necrotic core of death cells and a surrounding nonnecrotic shell. The corresponding mathematical…
In this paper we study a cross-diffusion system whose coefficient matrix is non-symmetric and degenerate. The system arises in the study of tissue growth with autophagy. The existence of a weak solution is established. We also investigate…
We study a strongly coupled system consisting of a parabolic equation and a singular Hamilton-Jacobi equation in one space dimension. This system describes the dynamics of dislocation densities in a material submitted to an exterior applied…
The simulation of growth processes within soft biological tissues is of utmost importance for many applications in the medical sector. Within this contribution we propose a new macroscopic approach fro modelling stress-driven volumetric…
This paper addresses the existence and regularity of weak solutions for a fully parabolic model of chemotaxis, with prevention of overcrowding, that degenerates in a two-sided fashion, including an extra nonlinearity represented by a…
We investigate avascular tumour growth as a two-phase process consisting of cells and liquid. Based on the one-dimensional continuum moving-boundary model formulated by (Byrne, King, McElwain, Preziosi, Applied Mathematics Letters, 2003,…
We use drifted Brownian motion in warped product model spaces as comparison constructions to show $p$-hyperbolicity of a large class of submanifolds for $p\ge 2$. The condition for $p$-hyperbolicity is expressed in terms of upper support…
We introduce a nonlinear and nonlocal model that describes the range expansion of a population resulting from growth and competition for space. This type of phenomenon underlies the expansion of colonies of immotile cells which motivated…