arXiv subjects

Sebastian Aland

Publications and source records attributed to Sebastian Aland.

24 records · Page 2Linked to original sources

arXiv2019

The Poisson ratio of the cellular actin cortex is frequency-dependent

Cell shape changes are vital for many physiological processes such as cell proliferation, cell migration and morphogenesis. They emerge from an orchestrated interplay of active cellular force generation and passive cellular force response - both crucially influenced by the actin cytoskeleton. To model cellular force response and deformation, cell mechanical models commonly describe the actin cytoskeleton as a contractile isotropic incompressible material. However, in particular at slow frequencies, there is no compelling reason to assume incompressibility as the water content of the cytoskeleton may change. Here we challenge the assumption of incompressibility by comparing computer simulations of an isotropic actin cortex with tunable Poisson ratio to measured cellular force response. Comparing simulation results and experimental data, we determine the Poisson ratio of the cortex in a frequency-dependent manner. We find that the Poisson ratio of the cortex decreases with frequency likely due to actin cortex turnover leading to an over-proportional decrease of shear stiffness at larger time scales. We thus report a trend of the Poisson ratio similar to that of glassy materials, where the frequency-dependence of jamming leads to an analogous effect.

physics.bio-ph↗

arXiv2018

A Phase-Field Model for Fluid-Structure-Interaction

In this paper, we develop a novel phase-field model for fluid-structure interaction (FSI), that is capable to handle very large deformations as well as topology changes like contact of the solid to the domain boundary. The model is based on a fully Eulerian description of the velocity field in both, the fluid and the elastic domain. Viscous and elastic stresses in the Navier-Stokes equations are restricted to the corresponding domains by multiplication with their characteristic functions. To obtain the elastic stress, an additional Oldroyd-B - like equation is solved. Thermodynamically consistent forces are derived by energy variation. The convergence of the derived equations to the traditional sharp interface formulation of fluid-structure interaction is shown by matched asymptotic analysis. The model is evaluated in a challenging benchmark scenario of an elastic body traversing a fluid channel. A comparison to reference values from Arbitrary Lagrangian Eulerian (ALE) simulations shows very good agreement. We highlight some distinct advantages of the new model, like the avoidance of re-triangulations and the stable inclusion of surface tension. Further, we demonstrate how simple it is to include contact dynamics into the model, by simulating a ball bouncing off a wall. We extend this scenario to include adhesion of the ball, which to our knowledge, cannot be simulated with any other FSI model. While we have restricted simulations to fluid-structure interaction, the model is capable to simulate any combination of viscous fluids, visco-elastic fluids and elastic solids.

physics.comp-ph↗

arXiv2017

Simulating Organogenesis in COMSOL: Comparison Of Methods For Simulating Branching Morphogenesis

During organogenesis tissue grows and deforms. The growth processes are controlled by diffusible proteins, so-called morphogens. Many different patterning mechanisms have been proposed. The stereotypic branching program during lung development can be recapitulated by a receptor-ligand based Turing model. Our group has previously used the Arbitrary Lagrangian-Eulerian (ALE) framework for solving the receptor-ligand Turing model on growing lung domains. However, complex mesh deformations which occur during lung growth severely limit the number of branch generations that can be simulated. A new Phase-Field implementation avoids mesh deformations by considering the surface of the modelling domains as interfaces between phases, and by coupling the reaction-diffusion framework to these surfaces. In this paper, we present a rigorous comparison between the Phase-Field approach and the ALE-based simulation.

q-bio.QM↗

arXiv2016

Simulating Organogenesis in COMSOL: Phase-Field Based Simulations of Embryonic Lung Branching Morphogenesis

Organogenesis has been studied for decades, but fundamental questions regarding the control of growth and shape remain unsolved. We have recently shown that of all proposed mathematical models only ligand-receptor based Turing models successfully reproduce the experimentally determined growth fields of the embryonic lung and thus provide a mechanism for growth control during embryonic lung development. Turing models are based on at least two coupled non-linear reaction-diffusion equations. In case of the lung model, at least two distinct layers (mesenchyme and epithelium) need to be considered that express different components (ligand and receptor, respectively). The Arbitrary Lagrangian-Eulerian (ALE) method has previously been used to solve this Turing system on growing and deforming (branching) domains, where outgrowth occurs proportional to the strength of ligand-receptor signalling. However, the ALE method requires mesh deformations that eventually limit its use. Therefore, we incorporate the phase field method to simulate 3D embryonic lung branching with COMSOL.

q-bio.QM↗

arXiv2013

Diffuse interface models of locally inextensible vesicles in a viscous fluid

We present a new diffuse interface model for the dynamics of inextensible vesicles in a viscous fluid. A new feature of this work is the implementation of the local inextensibility condition in the diffuse interface context. Local inextensibility is enforced by using a local Lagrange multiplier, which provides the necessary tension force at the interface. To solve for the local Lagrange multiplier, we introduce a new equation whose solution essentially provides a harmonic extension of the local Lagrange multiplier off the interface while maintaining the local inextensibility constraint near the interface. To make the method more robust, we develop a local relaxation scheme that dynamically corrects local stretching/compression errors thereby preventing their accumulation. Asymptotic analysis is presented that shows that our new system converges to a relaxed version of the inextensible sharp interface model. This is also verified numerically. Although the model does not depend on dimension, we present numerical simulations only in 2D. To solve the 2D equations numerically, we develop an efficient algorithm combining an operator splitting approach with adaptive finite elements where the Navier-Stokes equations are implicitly coupled to the diffuse interface inextensibility equation. Numerical simulations of a single vesicle in a shear flow at different Reynolds numbers demonstrate that errors in enforcing local inextensibility may accumulate and lead to large differences in the dynamics in the tumbling regime and differences in the inclination angle of vesicles in the tank-treading regime. The local relaxation algorithm is shown to effectively prevent this accumulation by driving the system back to its equilibrium state when errors in local inextensibility arise.

math-ph↗

arXiv2013

Time integration for diffuse interface models for two-phase flow

We propose a variant of the $θ$-scheme for diffuse interface models for two-phase flow, together with three new linearization techniques for the surface tension. These involve either additional stabilizing force terms, or a fully implicit coupling of the Navier-Stokes and Cahn-Hilliard equation. In the common case that the equations for interface and flow are coupled explicitly, we find a time step restriction which is very different to other two-phase flow models and in particular is independent of the grid size. We also show that the proposed stabilization techniques can lift this time step restriction. Even more pronounced is the performance of the proposed fully implicit scheme which is stable for arbitrarily large time steps. We demonstrate in a Taylor flow application that this superior coupling between flow and interface equation can render diffuse interface models even computationally cheaper and faster than sharp interface models.

math.NA↗