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Cell-centred model for the simulation of curved cellular monolayers
Mosaffa, Payman; Asadipour, Nina; Millán, Raúl Daniel; Rodríguez Ferran, Antonio; Muñoz Romero, José
Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental; Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria
This paper presents a cell-centred model for the simulation of planar and curved multicellular soft tissues. We propose a computational model that includes stress relaxation due to cell reorganisation (intercellular connectivity changes) and cytoskeleton remodelling (intracellular changes). Cells are represented by their cell centres, and their mechanical interaction is modelled through active non-linear elastic laws with a dynamically changing resting length. Special attention is paid to the handling of connectivity changes between cells, and the relaxation that the tissues exhibit under these topological changes. Cell--cell connectivity is computed by resorting to a Delaunay triangulation, which is combined with a mapping technique in order to obtain triangulations on curved manifolds. Our numerical results show that even a linear elastic cell--cell interaction model may induce a global non-linear response due to the reorganisation of the cell connectivity. This plastic-like behaviour is combined with a non-linear rheological law where the resting length depends on the elastic strain, mimicking the global visco-elastic response of tissues. The model is applied to simulate the elongation of planar and curved monolayers.
Àrees temàtiques de la UPC::Enginyeria biomèdica::Biomecànica
Biomechanics
Biomecànica
Morfogènesi
Geometria combinatòria
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/publishedVersion
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