Vitale, G.; Preziosi, L.; Ambrosi, D. A numerical method for the inverse problem of cell traction in 3D. (English) Zbl 1252.92042 Inverse Probl. 28, No. 9, Article ID 095013, 17 p. (2012). Summary: 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. 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. Cited in 5 Documents MSC: 92C55 Biomedical imaging and signal processing 92C37 Cell biology 82B80 Numerical methods in equilibrium statistical mechanics (MSC2010) 92C05 Biophysics 49N90 Applications of optimal control and differential games PDFBibTeX XMLCite \textit{G. Vitale} et al., Inverse Probl. 28, No. 9, Article ID 095013, 17 p. (2012; Zbl 1252.92042) Full Text: DOI Link