10,464 research outputs found
Measuring cellular traction forces on non-planar substrates
Animal cells use traction forces to sense the mechanics and geometry of their
environment. Measuring these traction forces requires a workflow combining cell
experiments, image processing and force reconstruction based on elasticity
theory. Such procedures have been established before mainly for planar
substrates, in which case one can use the Green's function formalism. Here we
introduce a worksflow to measure traction forces of cardiac myofibroblasts on
non-planar elastic substrates. Soft elastic substrates with a wave-like
topology were micromolded from polydimethylsiloxane (PDMS) and fluorescent
marker beads were distributed homogeneously in the substrate. Using feature
vector based tracking of these marker beads, we first constructed a hexahedral
mesh for the substrate. We then solved the direct elastic boundary volume
problem on this mesh using the finite element method (FEM). Using data
simulations, we show that the traction forces can be reconstructed from the
substrate deformations by solving the corresponding inverse problem with a
L1-norm for the residue and a L2-norm for 0th order Tikhonov regularization.
Applying this procedure to the experimental data, we find that cardiac
myofibroblast cells tend to align both their shapes and their forces with the
long axis of the deformable wavy substrate.Comment: 34 pages, 9 figure
Hybrid finite difference/finite element immersed boundary method
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian
description of the structural deformations, stresses, and forces along with an Eulerian description of the
momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary
methods described immersed elastic structures using systems of flexible fibers, and even now, most
immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This
work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian
variables that facilitates independent spatial discretizations for the structure and background grid. This
approach employs a finite element discretization of the structure while retaining a finite difference scheme
for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively
contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases
in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors
that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes.
The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse
structural meshes with the immersed boundary method. This work also contrasts two different weak forms
of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations
facilitated by our coupling approach
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