Hybrid cell-centred/vertex model for multicellular systems

This thesis presents a hybrid vertex/cell-centred approach to mechanically simulate planar cellular monolayers undergoing cell reorganisation. Cell centres are represented by a triangular nodal network, while the cell boundaries are formed by an associated vertex network. The two networks are coupled through a kinematic constraint which we allow to relax progressively. Cell-cell connectivity changes due to cell reorganisation or remodelling events, are accentuated. These situations are handled by using a variable resting length and applying an Equilibrium-Preserving Mapping (EPM) on the new connectivity, which computes a new set of resting lengths that preserve nodal and vertex equilibrium. As a by-product, the proposed technique enables to recover fully vertex or fully cell-centred models in a seamless manner by modifying a numerical parameter of the model. The properties of the model are illustrated by simulating monolayers subjected to imposed extension and during a wound healing process. The evolution of forces and the EPM are analysed during the remodelling events.Esta tesis presenta un modelo híbrido para la simulación mecánica de monocapas celulares. Este modelo combina métodos de vértices y centrados en la célula, y está orientado al análisis de deformaciones con reorganización celular. Los núcleos vienen representados por nodos que forman una malla triangular, mientras que las contornos (membranas y córtex) forman una malla poligonal de vértices. Las dos mallas se acoplan a través de una restricción cinemática que puede ser relajada de forma controlada. El estudio hace especial hincapié en los cambios de conectividad, tanto debidos a la reorganización celular como el remodelado del citoesqueleto. Estas situaciones se abordan a través de una longitud de referencia variable y aplicando un Mapeo con Conservación de Equilibrio (EPM) que minimiza el error en el equilibrio nodal y en los vértices. La técnica resultante puede ser adaptada progresivamente a través de un parámetro, dando lugar a un modelo exclusivamente de vértices o a uno de centros. Sus propiedades se ilustran en simulaciones de monocapas sujetas a una extensión impuesta y durante el proceso de cicatrizado de heridas. La evolución de las fuerzas y los efectos del EPM durante el remodelado se analizan en estos ejemplos

Computational tools for multicellular systems

Macroscopic deformations in embryonic soft tissues are due to the intra-cellular remodelling and cell intercalation. We here present a computational approach that can handle the two types of deformations, and also take into account the active cell response. The model resorts to cell centred techniques, where particles represent cell nuclei, and to vertex models, where the vertices represent cell boundaries. This hybrid approach allows to consider separately intra-cellular and inter-cellular forces, and at the same time impose cell incompressibility. The model is applied to simulate the active stretching of epithelium

Hybrid cell-centred/vertex model for multicellular systems with equilibrium-preserving remodelling

We present a hybrid cell‐centred/vertex model for mechanically simulating planar cellular monolayers undergoing cell reorganisation. Cell centres are represented by a triangular nodal network, while the cell boundaries are formed by an associated vertex network. The two networks are coupled through a kinematic constraint which we allow to relax progressively. Special attention is paid to the change of cell‐cell connectivity due to cell reorganisation or remodelling events. We handle these situations by using a variable resting length and applying an Equilibrium‐Preserving Mapping on the new connectivity, which computes a new set of resting lengths that preserve nodal and vertex equilibrium. We illustrate the properties of the model by simulating monolayers subjected to imposed extension and during a wound healing process. The evolution of forces and the Equilibrium‐Preserving Mapping are analysed during the remodelling events. As a by‐product, the proposed technique enables to recover fully vertex or fully cell‐centred models in a seamless manner by modifying a numerical parameter of the model

Hybrid cell centred/vertex model for large tissue deformations

Macroscopic deformations in embryonic soft tissues are due to the intra-cellular remodelling and cell intercalation. We here present a computational approach that can handle the two types of deformations, and also take into account the active cell response. The model resorts to cell-centred techniques, where particles represent cell nuclei, and to vertex models, where the vertices represent cell boundaries. This hybrid approach allows to consider separately intracellular and inter-cellular forces, and at the same time impose cell incompressibility. In the proposed model, the cell boundaries (defined by vertices) and cell nuclei (or cellcentres) networks are coupled through an interpolation scheme, which is eventually relaxed in order to smooth the cell boundaries. We show that this coupling between the two networks modifies the equilibrium equations and stabilises the vertex network. Incompressibility is implemented through a penalty method. The resulting model can be implemented in two- and three-dimensions, and is complemented with active rheological models. We apply the model to simulate the stretching and relaxation of cell monolayers, and to simulate wound healing process in the wing disc of Drosophila fly embryo. We show that the numerical results agree with the experimental measurements.Postprint (published version

Hybrid cell centred/vertex model for cellular nanolayers

Macroscopic deformations in embryonic soft tissues are due to the intra-cellular remodelling and cell intercalation. We here present a computational approach that can handle the two types of deformations, and also take into account the active cell response. The model resorts to cell centred techniques, where particles represent cell nuclei, and to vertex models, where the vertices represent cell boundaries. This hybrid approach allows to consider separately intra-cellular and inter-cellular forces, and at the same time impose cell incompressibility. The model is applied to simulate the active stretching of epithelium.Peer ReviewedPostprint (author's final draft

Cell-centred model for the simulation of curved cellular monolayers

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.Postprint (published version

Hybrid cell-centred/vertex model for multicellular systems

This thesis presents a hybrid vertex/cell-centred approach to mechanically simulate planar cellular monolayers undergoing cell reorganisation. Cell centres are represented by a triangular nodal network, while the cell boundaries are formed by an associated vertex network. The two networks are coupled through a kinematic constraint which we allow to relax progressively. Cell-cell connectivity changes due to cell reorganisation or remodelling events, are accentuated. These situations are handled by using a variable resting length and applying an Equilibrium-Preserving Mapping (EPM) on the new connectivity, which computes a new set of resting lengths that preserve nodal and vertex equilibrium. As a by-product, the proposed technique enables to recover fully vertex or fully cell-centred models in a seamless manner by modifying a numerical parameter of the model. The properties of the model are illustrated by simulating monolayers subjected to imposed extension and during a wound healing process. The evolution of forces and the EPM are analysed during the remodelling events.Esta tesis presenta un modelo híbrido para la simulación mecánica de monocapas celulares. Este modelo combina métodos de vértices y centrados en la célula, y está orientado al análisis de deformaciones con reorganización celular. Los núcleos vienen representados por nodos que forman una malla triangular, mientras que las contornos (membranas y córtex) forman una malla poligonal de vértices. Las dos mallas se acoplan a través de una restricción cinemática que puede ser relajada de forma controlada. El estudio hace especial hincapié en los cambios de conectividad, tanto debidos a la reorganización celular como el remodelado del citoesqueleto. Estas situaciones se abordan a través de una longitud de referencia variable y aplicando un Mapeo con Conservación de Equilibrio (EPM) que minimiza el error en el equilibrio nodal y en los vértices. La técnica resultante puede ser adaptada progresivamente a través de un parámetro, dando lugar a un modelo exclusivamente de vértices o a uno de centros. Sus propiedades se ilustran en simulaciones de monocapas sujetas a una extensión impuesta y durante el proceso de cicatrizado de heridas. La evolución de las fuerzas y los efectos del EPM durante el remodelado se analizan en estos ejemplos

Hybrid cell-centred/vertex model for multicellular systems

This thesis presents a hybrid vertex/cell-centred approach to mechanically simulate planar cellular monolayers undergoing cell reorganisation. Cell centres are represented by a triangular nodal network, while the cell boundaries are formed by an associated vertex network. The two networks are coupled through a kinematic constraint which we allow to relax progressively. Cell-cell connectivity changes due to cell reorganisation or remodelling events, are accentuated. These situations are handled by using a variable resting length and applying an Equilibrium-Preserving Mapping (EPM) on the new connectivity, which computes a new set of resting lengths that preserve nodal and vertex equilibrium. As a by-product, the proposed technique enables to recover fully vertex or fully cell-centred models in a seamless manner by modifying a numerical parameter of the model. The properties of the model are illustrated by simulating monolayers subjected to imposed extension and during a wound healing process. The evolution of forces and the EPM are analysed during the remodelling events.Esta tesis presenta un modelo híbrido para la simulación mecánica de monocapas celulares. Este modelo combina métodos de vértices y centrados en la célula, y está orientado al análisis de deformaciones con reorganización celular. Los núcleos vienen representados por nodos que forman una malla triangular, mientras que las contornos (membranas y córtex) forman una malla poligonal de vértices. Las dos mallas se acoplan a través de una restricción cinemática que puede ser relajada de forma controlada. El estudio hace especial hincapié en los cambios de conectividad, tanto debidos a la reorganización celular como el remodelado del citoesqueleto. Estas situaciones se abordan a través de una longitud de referencia variable y aplicando un Mapeo con Conservación de Equilibrio (EPM) que minimiza el error en el equilibrio nodal y en los vértices. La técnica resultante puede ser adaptada progresivamente a través de un parámetro, dando lugar a un modelo exclusivamente de vértices o a uno de centros. Sus propiedades se ilustran en simulaciones de monocapas sujetas a una extensión impuesta y durante el proceso de cicatrizado de heridas. La evolución de las fuerzas y los efectos del EPM durante el remodelado se analizan en estos ejemplos

Cell-centred model for non-linear tissue rheology and active remodelling

Soft active tissues exhibit softening, hardening, and reversible fluidisation. The result of these non-linear behaviour is due to multiple processes taking part at different scales: active protein motors that actuate at the polymeric structure of the cell, (de)polymerisation and remodelling of the cytoskeleton, and cell-cell connectivity changes that take place at the tissue level.Peer Reviewe