Related papers: Modeling fungal hypha tip growth via viscous sheet…
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…
A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…
Biological transport networks adapt through dynamic interactions between material transport and structural modification during growth and development. In this work, we present a model of transport network growth driven by local material…
Models of tumor growth, now commonly used, present several levels of complexity, both in terms of the biomedical ingredients and the mathematical description. The simplest ones contain competition for space using purely fluid mechanical…
We consider a partial differential equation model for the growth of heterogeneous cell populations subdivided into multiple distinct discrete phenotypes. In this model, cells preferentially move towards regions where they feel less…
The present work investigates environmental effects on the growth of fungal colonies of P. vitreus by using a lattice-free discrete modelling approach called FGM (Fuhr et al. (2010), arXiv:1101.1747), in which hyphae and nutrients are…
A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for…
The mycelium of a filamentous fungus is a growing, branching network of numerous entangled hyphae exhibiting polarised apical growth. Expansion occurs during the vegetative phase from a single ascospore, driven by the need to explore and…
This paper proposes a model for the growth two interacting populations of cells that do not mix. The dynamics is driven by pressure and cohesion forces on the one hand and proliferation on the other hand. Following earlier works on the…
Growth pattern dynamics lie at the heart of morphogenesis. Here, we investigate the growth of plant leaves. We compute the conformal transformation that maps the contour of a leaf at a given stage onto the contour of the same leaf at a…
Based upon apical growth and hyphal branching, the two main processes that drive the growth pattern of a fungal network, we propose here a two-dimensions simulation based on a binary-tree modelling allowing us to extract the main…
Cell colonies of bacteria, tumour cells and fungi, under nutrient limited growth conditions, exhibit complex branched growth patterns. In order to investigate this phenomenon we present a simple hybrid cellular automaton model of cell…
The orientation of cell division is a major determinant of three-dimensional plant morphogenesis. Whether and how a simple division orientation rule explains the establishment of symmetric body plans is a fundamental question. Testing such…
Growth and folding in one-layered model tissue sheets are studied in a stochastic, lattice-free single cell model which considers the discrete cellular structure of the tissue, and a coarse grained analytical approach. The polarity of the…
The topological organisation of cells in a model of living tissue (the crypt of intestinal epithelium) is identical to the topological organisation of atoms in carbon nanotubes. The existing models of growth of these two structures contain…
A one-dimensional cellular automaton with a probabilistic evolution rule can generate stochastic surface growth in $(1 + 1)$ dimensions. Two such discrete models of surface growth are constructed from a probabilistic cellular automaton…
Various models of tumor growth are available in the litterature. A first class describes the evolution of the cell number density when considered as a continuous visco-elastic material with growth. A second class, describes the tumor as a…
We model the growth of a cell population using a piecewise deterministic Markov branching tree. In this model, each cell splits into two offspring at a division rate $B(x)$, which depends on its size $x$. The size of each cell increases…
In this work, we introduce a spatial branching process to model the growth of the mycelial network of a filamentous fungus. In this model, each filament is described by the position of its tip, the trajectory of which is solution to a…
Motivated by the phenomenology of transport through the Golgi apparatus of cells, we study a multi-species model with boundary injection of one species of particle, interconversion between the different species of particle, and driven…