Mathematical framework for traction force microscopy
Copyright policy )Mathematical framework for traction force microscopy
Summary: This paper deals with the \textit{Traction Force Microscopy} (TFM) problem. It consists in obtaining stresses by solving an inverse problem in an elastic medium, from known experimentally measured displacements. In this article, the application is the determination of the stresses exerted by a living cell at the surface of an elastic gel. We propose an abstract framework which formulates this inverse problem as a constrained minimization one. The mathematical constraints express the biomechanical conditions that the stress field must satisfy. From this framework, two methods currently used can be derived, the adjoint method (AM) and the Fourier Transform Traction Cytometry (FTTC) method. An improvement of the FTTC method is also derived using this framework. The numerical results are compared and show the advantage of the AM, in particular its ability to capture details more accurately.
Inverse problems, [PHYS.PHYS.PHYS-BIO-PH]Physics [physics]/Physics [physics]/Biological Physics [physics.bio-ph], Numerical solution to inverse problems in abstract spaces, Cell motility, cell motility, 510, Adjoint Method (AM), [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Biomechanics, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], Cell motility; Inverse problems; Tikhonov regularization; Adjoint Method (AM); Fourier Transform Traction Cytometry (FTTC); L–curve, Inverse problems in equilibrium solid mechanics, inverse problems, Tikhonov regularization, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], 620, adjoint method (AM), Cell movement (chemotaxis, etc.), \(L\)-curve, Fourier transform traction cytometry (FTTC), L -curve, Biomechanical solid mechanics, Fourier Transform Traction Cytometry (FTTC)
Inverse problems, [PHYS.PHYS.PHYS-BIO-PH]Physics [physics]/Physics [physics]/Biological Physics [physics.bio-ph], Numerical solution to inverse problems in abstract spaces, Cell motility, cell motility, 510, Adjoint Method (AM), [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Biomechanics, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], Cell motility; Inverse problems; Tikhonov regularization; Adjoint Method (AM); Fourier Transform Traction Cytometry (FTTC); L–curve, Inverse problems in equilibrium solid mechanics, inverse problems, Tikhonov regularization, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], 620, adjoint method (AM), Cell movement (chemotaxis, etc.), \(L\)-curve, Fourier transform traction cytometry (FTTC), L -curve, Biomechanical solid mechanics, Fourier Transform Traction Cytometry (FTTC)
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