Related papers: Continuous Approximation of Stochastic Maps for Mo…
The emergence of spatial patterns and organized growth is a hallmark of developing tissues. While symmetry-breaking and scaling laws govern these processes, how cells coordinate spatial patterning with size regulation remains unclear. Here,…
Stem cells, through their ability to produce daughter stem cells and differentiate into specialized cells, are essential in the growth, maintenance, and repair of biological tissues. Understanding the dynamics of cell populations in the…
A microscopic agent dynamical model for diploid age-structured populations is used to study evolution of polymorphism and sympatric speciation. The underlying ecology is represented by a unimodal distribution of resources of some width.…
Stem cells are characterized by their ability to self-renew, as well as to differentiate and give rise to new populations of cells. Stem cell divisions are crucial for generative processes that occur during early development, and later in…
An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…
We present a systematic study of the influence of cell geometry on the orientational distribution of microtubules (MTs) nucleated from a single microtubule organizing center (MTOC). For simplicity we consider an elliptical cell geometry, a…
Cell growth, division and death are defining features of biological tissues that contribute to morphogenesis. In hydrodynamic descriptions of cohesive tissues, their occurrence implies a non-zero rate of variation of cell density. We show…
Understanding how genetically encoded rules drive and guide complex neuronal growth processes is essential to comprehending the brain's architecture, and agent-based models (ABMs) offer a powerful simulation approach to further develop this…
An extension of coupled maps is given which allows for the growth of the number of elements, and is inspired by the cell differentiation problem. The growth of elements is made possible first by clustering the phases, and then by…
Automated cell segmentation has become increasingly crucial for disease diagnosis and drug discovery, as manual delineation is excessively laborious and subjective. To address this issue with limited manual annotation, researchers have…
We take up the challenge of designing realistic computational models of large interacting cell populations. The goal is essentially to bring Gillespie's celebrated stochastic methodology to the level of an interacting population of cells.…
The Gierer-Meinhardt system occurs in morphogenesis, where the development of an organism from a single cell is modelled. One of the steps in the development, is the formation of spatial patterns of the cell structure, starting from an…
In this paper we propose a systematic approach to construct mathematical models describing populations of cancer-cells at different stages of disease development. The methodology we propose is based on stochastic Concurrent Constraint…
We consider an age-size structured cell population model based on the cell cycle length. The model is described by a first order partial differential equation with initial-boundary conditions. Using the theory of semigroups of positive…
The Gompertz model describes the growth in time of the size of significant quantities associated to a large number of systems, taking into account nonlinearity features by a linear equation satisfied by a nonlinear function of the size.…
We consider two division models for structured cell populations, where cells can grow, age and divide. These models have been introduced in the literature under the denomination of `mitosis' and `adder' models. In the recent years, there…
We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated…
We present a continuous time model of maturation and survival, obtained as the limit of a compartmental evolution model when the number of compartments tends to infinity. We establish in particular an explicit formula for the law of the…
A thin shell finite element approach based on Loop's subdivision surfaces is proposed, capable of dealing with large deformations and anisotropic growth. To this end, the Kirchhoff-Love theory of thin shells is derived and extended to allow…
We deal with a continuous-time Ehrenfest model defined over an extended star graph, defined as a lattice formed by the integers of $d$ semiaxis joined at the origin. The dynamics on each ray are regulated by linear transition rates, whereas…