×

A numerical method for the inverse problem of cell traction in 3D. (English) Zbl 1252.92042

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.

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
Full Text: DOI Link