2024-03-28T08:10:52Zhttps://www.tdx.cat/oai/requestoai:www.tdx.cat:10803/3927162017-09-19T05:43:07Zcom_10803_183col_10803_328726
nam a 5i 4500
Rheological models for tissue relaxation and fluidisation
[Barcelona] :
Universitat Politècnica de Catalunya,
2016
Accés lliure
http://hdl.handle.net/10803/392716
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Asadipour, Nina,
autor
1 recurs en línia (93 pàgines)
Tesi
Doctorat
Universitat Politècnica de Catalunya. Departament de Matemàtiques
2016
Universitat Politècnica de Catalunya. Departament de Matemàtiques
Tesis i dissertacions electròniques
Muñoz Romero, José Javier,
supervisor acadèmic
TDX
We present a cell-centred model for the simulation of multicellular soft tissues that takes into account the underlying active process at the cytoskeletal level, and allows for active and passive cell-cell reorganisation and intercalation. In the cell centred model, each cell is treated as a discrete entity and adjacent cell centres are connected by bar elements holding the rheological properties of cell-cell interactions. Cell-cell connectivity is determined with Delaunay triangulation of the cell-centres (nuclei). We use Voronoi tessellation and barycentric tessellation in order to represent the cell domains.
We develop a viscoelastic bar element that can handle multiple rheological laws with non-linear elastic and non-linear viscous material models. The bar element is built by joining in series an elastic and viscous bar, constraining the middle node position to the bar axis with a reduction method, and statically condensing the internal degrees of freedom. Also, we develop a new rheological model based on dynamical changes of the resting length which mimics the viscoelastic response.
It has been experimentally observed that cells exhibit a fluidisation process when subjected to a transient stretch, with an eventual recovery of the mechanical properties upon removal of the applied deformation. This fluidisation process is characterised by a decrease of the stored modulus and an increase of the phase angle. We propose a rheological model which is able to reproduce this combined mechanical response. The model is described in the context of continua and adapted to a cell-centred particle system that simulates the cell-cell interaction. Mechanical equilibrium is coupled with two evolution laws: (i) one for the reference configuration, and (ii) another for the porosity or polymer density. The first law depends on the actual elastic strain of the tissue, while the second assumes different remodelling rates during porosity increase and decrease. The theory is implemented on the particle based model and tested on a stretching numerical simulation, which agrees with the experimental measurements for different stretching magnitudes.
The rheological law is also applied to simulate the stress relaxation that suspended monolayers undergo when subjected to a constant stretch. The numerical model is here applied on in multiple branches, so that the response with different characteristic times is reproduced.
By using Delaunay triangulations and Voronoi tessellations, the model presented in this thesis also opens the possibility to test different combined rheological laws in cytoskeletal and cortical regions of cellular networks.
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