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In this paper, we formulate a geometric theory of the mechanics of arterial growth. An artery is modeled as a finite-length thick shell that is made of an incompressible nonlinear anisotropic solid. An initial radially-symmetric…
We describe a numerical model of faceted crystal growth using a cellular automata method that incorporates admolecule diffusion on faceted surfaces in addition to bulk diffusion in the medium surrounding the crystal. The model was developed…
In this paper the evolution of a binary mixture in a thin-film geometry with a wall at the top and bottom is considered. By bringing the mixture into its miscibility gap so that no spinodal decomposition occurs in the bulk, a slight…
In this paper we address some modelling issues related to biological growth. Our treatment is based on a recently-proposed, general formulation for growth within the context of Mixture Theory (Journal of the Mechanics and Physics of Solids,…
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 migratory dynamics of cells can be influenced by the complex micro-environment through which they move. It remains unclear how the motility machinery of confined cells responds and adapts to their micro-environment. Here, we propose a…
A mathematical model for tissue growth is considered. This model describes the dynamics of the density of cells due to pressure forces and proliferation. It is known that such cell population model converges at the incompressible limit…
We discuss several continuum cell-cell adhesion models based on the underlying microscopic assumptions. We propose an improvement on these models leading to sharp fronts and intermingling invasion fronts between different cell type…
Contact inhibition limits migration and proliferation of cells in cell colonies. We consider a multiphase field model to investigate the growth dynamics of a cell colony, composed of proliferating cells. The model takes into account the…
The hygro-mechanical behavior of a hierarchical cellular material, i.e. growth rings of softwood is investigated using a two-scale micro-mechanics model based on a computational homogenization technique. The lower scale considers the…
Cell-cell adhesion plays a vital role in the development and maintenance of multicellular organisms. One of its functions is regulation of cell migration, such as occurs, e.g. during embryogenesis or in cancer. In this work, we develop a…
Cell walls define a cell shape in bacteria. They are rigid to resist large internal pressures, but remarkably plastic to adapt to a wide range of external forces and geometric constraints. Currently, it is unknown how bacteria maintain…
We provide a short review of existing models with multiple taxis performed by (at least) one species and consider a new mathematical model for tumor invasion featuring two mutually exclusive cell phenotypes (migrating and proliferating).…
We present a model for mechanically-induced pattern formation in growing biological tissues and discuss its application to the development of leaf venation networks. Drawing an analogy with phase transitions in solids, we use a phase field…
We formulate a Hele-Shaw type free boundary problem for a tumor growing under the combined effects of pressure forces, cell multiplication and active motion, the latter being the novelty of the present paper. This new ingredient is…
Bacterial cells exhibit a diverse array of shapes and sizes, largely governed by their cell walls in conjunction with cytoskeletal proteins and internal turgor pressure. The present study develops a theoretical framework for modeling the…
Cell migration is important in many biological processes, including embryonic development, cancer metastasis, and wound healing. In these tissues, a cell's motion is often strongly constrained by its neighbors, leading to glassy dynamics.…
We introduce here a new diffuse interface thermodynamically consistent non-isothermal model for tumor growth in presence of a nutrient in a domain $\Omega \subset \mathbb{R}^3$. In particular our system describes the growth of a tumor…
The cell wall serves as a mechanical protection for the fungi and controls the traffic of molecules entering the cell. However, the optical role of the cell wall has not been fully investigated. In this work, we use a computational…
Developing clinically viable tissue-engineered cardiovascular implants remains a formidable challenge. Achieving reliable and durable outcomes requires a deeper understanding of the fundamental mechanisms driving tissue evolution during in…