Hybrid cell-centred/vertex model for multicellular systems

• Autores: Payman Mosaffa
• Directores de la Tesis: José Javier Muñoz Romero (dir. tes.)
• Lectura: En la Universitat Politècnica de Catalunya (UPC) ( España ) en 2017
• Idioma: español
• Tribunal Calificador de la Tesis: Marino Arroyo Balaguer (presid.), Blas Echebarría Domínguez (secret.), Xavier Trepat Guixer (voc.), Yanyan Cao (voc.), José Manuel García Aznar (voc.)
• Programa de doctorado: Programa de Doctorado en Matemática Aplicada por la Universidad Politécnica de Catalunya
• Materias:
  • Matemáticas
    • Análisis y análisis funcional
      • Ecuaciones diferenciales ordinarias
    • Ciencia de los ordenadores
      • Simulación
  • Ciencias de la vida
    • Biofísica
      • Biomecánica
• Enlaces
  • Tesis en acceso abierto en: TDX
• Resumen

  • 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.