Non-regularised inverse finite element analysis for 3D traction force microscopy
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hdl:2117/99311
Tipus de documentArticle
Data publicació2016-06-10
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Abstract
The tractions that cells exert on a gel substrate from the observed
displacements is an increasingly attractive and valuable information in
biomedical experiments. The computation of these tractions requires in
general the solution of an inverse problem. Here, we resort to the discretisation
with finite elements of the associated direct variational formulation,
and solve the inverse analysis using a least square approach.
This strategy requires the minimisation of an error functional, which is
usually regularised in order to obtain a stable system of equations with
a unique solution. In this paper we show that for many common threedimensional
geometries, meshes and loading conditions, this regularisation
is unnecessary. In these cases, the computational cost of the inverse
problem becomes equivalent to a direct finite element problem. For the
non-regularised functional, we deduce the necessary and sufficient conditions
that the dimensions of the interpolated displacement and traction
fields must preserve in order to exactly satisfy or yield a unique solution
of the discrete equilibrium equations. We apply the theoretical results to
some illustrative examples and to real experimental data. Due to the relevance
of the results for biologists and modellers, the article concludes with
some practical rules that the finite element discretisation must satisfy.
CitacióMuñoz, J.J. Non-regularised inverse finite element analysis for 3D traction force microscopy. "International journal of numerical analysis and modeling", 10 Juny 2016, vol. 13, núm. 5, p. 763-781.
ISSN1705-5105
Versió de l'editorhttp://www.math.ualberta.ca/ijnam/Volume-13-2016/No-5-16/2016-05-07.pdf
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