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Marth W.,Institute For Wissenschaftliches Rechnen | Voigt A.,Institute For Wissenschaftliches Rechnen | Voigt A.,TU Dresden | Voigt A.,Center for Systems Biology Dresden
Interface Focus | Year: 2016

We consider a generic model for cell motility. Even if a comprehensive understanding of cell motility remains elusive, progress has been achieved in its modelling using a whole-cell physical model. The model takes into account the main mechanisms of cell motility, actin polymerization, actin–myosin dynamics and substrate mediated adhesion (if applicable), and combines them with steric cell–cell and hydrodynamic interactions. The model predicts the onset of collective cell migration, which emerges spontaneously as a result of inelastic collisions of neighbouring cells. Each cell here modelled as an active polar gel is accomplished with two vortices if it moves. Upon collision of two cells, the two vortices which come close to each other annihilate. This leads to a rotation of the cells and together with the deformation and the reorientation of the actin filaments in each cell induces alignment of these cells and leads to persistent translational collective migration. The effect for low Reynolds numbers is as strong as in the non-hydrodynamic model, but it decreases with increasing Reynolds number. © 2016 The Author(s) Published by the Royal Society. All rights reserved.

Landsberg C.,Institute For Wissenschaftliches Rechnen | Voigt A.,Institute For Wissenschaftliches Rechnen
Computing and Visualization in Science | Year: 2010

We develop a multigrid finite element approach to solve PDE's on surfaces. The multigrid approach involves the same weights for restriction and prolongation as in the case of planar domains. Combined with the concept of parametric finite elements the approach thus allows to reuse code initially developed to solve problems on planar domains to solve the corresponding problem on surfaces. The method is tested on a non-linear reaction-diffusion system on stationary and evolving surfaces, with the normal velocity of the evolving surface depending on the reaction-diffusion system. As a reference model the Schnakenberg system is used, offering non-linearity and algebraic simplicity on one hand, and quantitative reference data on the other hand. © Springer-Verlag 2010.

Aland S.,Institute For Wissenschaftliches Rechnen | Voigt A.,Institute For Wissenschaftliches Rechnen
International Journal for Numerical Methods in Fluids | Year: 2012

Diffuse interface models for incompressible two-phase flow with large density ratios are tested on benchmark configurations for a two-dimensional bubble rising in liquid columns. The benchmark quantities circularity, center of mass, and mean rise velocity are compared with reference solutions from Hysing et al. © 2011 John Wiley & Sons, Ltd.

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