Computation of forces from deformed visco-elastic biological tissues

José J. Munoz, David Amat, Vito Conte

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Abstract

We present a least-squares based inverse analysis of visco-elastic biological tissues. The proposed method computes the set of contractile forces (dipoles) at the cell boundaries that induce the observed and quantified deformations. We show that the computation of these forces requires the regularisation of the problem functional for some load configurations that we study here. The functional measures the error of the dynamic problem being discretised in time with a second-order implicit time-stepping and in space with standard finite elements. We analyse the uniqueness of the inverse problem and estimate the regularisation parameter by means of an L-curved criterion. We apply the methodology to a simple toy problem and to an in vivo set of morphogenetic deformations of the Drosophila embryo.

Original languageEnglish
Article number044001
Number of pages19
JournalInverse Problems
Volume34
Issue number4
DOIs
Publication statusPublished - Apr 2018
Externally publishedYes

Bibliographical note

Special issue: Dynamic inverse problems: modelling, regularization, numerics

Keywords

  • dipoles
  • embryogenesis
  • finite elements
  • tissue mechanics
  • tractions
  • viscoelasticity

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