Related papers: Simulation of morphogen and tissue dynamics
This paper studies an evolving bulk--surface finite element method for a model of tissue growth, which is a modification of the model of Eyles, King and Styles (2019). The model couples a Poisson equation on the domain with a forced mean…
Since its introduction in 1952, Turing's (pre-)pattern theory ("the chemical basis of morphogenesis") has been widely applied to a number of areas in developmental biology. The related pattern formation models normally comprise a system of…
Many cellular processes involve information processing and decision making. We can probe these processes at increasing molecular detail. The analysis of heterogeneous data remains a challenge that requires new ways of thinking about cells…
With the rise of computers, simulation models have emerged beside the more traditional statistical and mathematical models as a third pillar for ecological analysis. Broadly speaking, a simulation model is an algorithm, typically…
Rapid advance of experimental techniques provides an unprecedented in-depth view into complex developmental processes. Still, little is known on how the complexity of multicellular organisms evolved by elaborating developmental programs and…
In this paper, we present a spatio-temporal mathematical model for simulating the formation and growth of a thrombus. Blood is treated as a multi-constituent mixture comprised of a linear fluid phase and a thrombus (solid) phase. The…
Radiation therapy is one of the most common cancer treatments, and dose optimization and targeting of radiation are crucial since both cancerous and healthy cells are affected. Different mathematical and computational approaches have been…
Morphogen gradients play an essential role in the spatial regulation of cell patterning during early development. The classical mechanism of morphogen gradient formation involves the diffusion of morphogens away from a localized source…
The phase field model can accurately simulate the evolution of microstructures with complex morphologies, and it has been widely used for cell modeling in the last two decades. However, compared to other cellular models such as the…
Mathematical Modelling has a long history in developmental biology. Advances in experimental techniques and computational algorithms now permit the development of increasingly more realistic models of organogenesis. In particular, 3D…
In this paper, we propose a fractional differential equation of order one-half, to model the evolution through time of the dynamics of accumulation and elimination of the contaminant in human organism with a deficient immune system, during…
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…
A number of factors, such as, cell-cell interactions and self-propulsion of cells driven by cytoskeletal forces determine tissue morphologies and dynamics. To explore the interplay between these factors in controlling the dynamics at the…
A numerical method based on Matrix Product Formalism is proposed to study the phase transitions and shock formation in the Asymmetric Simple Exclusion Process with open boundaries and parallel dynamics. By working in a canonical ensemble,…
Plastic deformation of most crystalline materials is due to the motion of lattice dislocations. Therefore, the simulation of the interaction and dynamics of these defects has become state-of-the-art method to study work hardening, size…
In this paper we propose a "discrete in continuous" mathematical model for the morphogenesis of the posterior lateral line system in zebrafishes. Our model follows closely the results obtained in recent biological experiments. We rely on a…
Thermogenesis is a physiological activity of releasing heat that originates from intracellular biochemical reactions. Recent experimental studies discovered that externally applied heat changes intracellular signaling locally, resulting in…
We present some existence results for three-dimensional quasistatic morphoelasticity. The state of the growing body is described by its deformation and the underlying growth tensor and is ruled by the interplay of hyperelastic energy…
Microelectronic morphogenesis is the creation and maintenance of complex functional structures by microelectronic information within shape-changing materials. Only recently has in-built information technology begun to be used to reshape…
Stochastic agent-based models can account for millions of cells with spatiotemporal movement that can be a function of different factors. However, these simulations can be computationally expensive. In this work, we develop a novel…