Brask

Compressed Sensing for Traction Force Microscopy

Talk by Jonatan Bohr Brask, University of Geneva
Friday, 28th of February, 14.15, Venue: Seminarraum Westabau

Abstract

In this talk, I will explain how ideas for sparse signal
recovery, coming from compressed sensing, can help reveal
the forces excerted by living cells.

Cell movement is important for many biological processes
such as the development and regeneration of tissue. Errors
in regulation of cell motility will contribute to diseases
including cancers, osteoporosis, and mental retardation.
Hence understanding cell movement is important both
fundamentally and for development of treatments.

Traction force microscopy aims to measure the physical
forces excerted by cells on their surroundings, forces
which are a fundamental component of cell motility. To this
end, cells are placed on a deformable substrate with known
mechanical properties and observed under a microscope. The
technique visualises the deformations which the substrate
undergoes as the cells move, and it is then possible to
reconstruct the forces excerted by the cells, by inverting
the continuum mechanics equations which describe how the
medium responds to applied force.

In in-vitro experiments, the substrate is a linear elastic
and incompressible material, and the displacements are
resolved on a grid. Force reconstruction therefore becomes
a discrete, linear inversion problem. Traditional methods
solve this problem either by least-squares minimisation or
by inversion in Fourier space, resulting in reconstructed
force fields with the same spatial resolution as the
displacement fields, respecting the Nyquist-Shannon
sampling theorem. However, there is good reason to expect
that the force fields are spatially sparse, because the
cells mainly exert force through localised attachment
points, known as focal adhesions. This indicates that
methods for sparse signal recovery borrowed from compressed
sensing may be useful, and in particular that it may be
possible to reconstruct force fields of higher resolution
than the observed displacement fields.

I will cover the background necessary to cast traction
force microscopy as a sparse signal recovery problem. I
will then show results of preliminary simulations which
demonstrate that it is indeed possible to increase the
resolution using compressed sensing techniques, and I will
touch upon upcoming proof-of-principle experiments.