Journal
INVERSE PROBLEMS
Volume 28, Issue 9, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0266-5611/28/9/095013
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Categories
Funding
- PRIN project Mathematics and Mechanics of Biological Assemblies and Soft Tissues
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Force traction microscopy is an inversion method that allows us to obtain the stress field applied by a living cell on the environment on the basis of a pointwise knowledge of the displacement produced by the cell itself. This classical biophysical problem, usually addressed in terms of Green's functions, can be alternatively tackled in a variational framework. In such a case, a variation of the error functional under suitable regularization is operated in view of its minimization. This setting naturally suggests the introduction of a new equation, based on the adjoint operator of the elasticity problem. In this paper, we illustrate a numerical strategy of the inversion method that discretizes the partial differential equations associated with the optimal control problem by finite elements. A detailed discussion of the numerical approximation of a test problem (with known solution) that contains most of the mathematical difficulties of the real one allows a precise evaluation of the degree of confidence that one can achieve in the numerical results.
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