Computation of forces from deformed visco-elastic biological tissues. (English) Zbl 1459.74178


74S05 Finite element methods applied to problems in solid mechanics
74L15 Biomechanical solid mechanics
74H75 Inverse problems in dynamical solid mechanics
74D05 Linear constitutive equations for materials with memory
92C10 Biomechanics
92-08 Computational methods for problems pertaining to biology


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[1] Alves C J S and Ha-Duong T 1999 Inverse scattering for elastic plane cracks Inverse Problems15 91-7 · Zbl 0929.35170
[2] Ambrosi D 2006 Cellular traction as an inverse problem SIAM J. Appl. Math.66 2049-60 · Zbl 1107.92013
[3] Andreieux S, Ben-Abda A and Bui H D 1999 Reciprocity principle and crack identification Inverse Problems15 59-65 · Zbl 0920.35165
[4] Beilina L, Thành N T, Klibanov M V and Fiddy M A 2014 Reconstruction from blind experimental data for an inverse problem for a hyperbolic equation Inverse Problems30 025002 · Zbl 1292.78011
[5] Bonnet M and Constantinescu A 2005 Inverse problems in elasticity Inverse Problems21 R1-50
[6] Brodland G W, Conte V, Cranston P G, Veldhuis J H, Narasimhan S, Hutson M S, Jacinto A, Ulrich F, Baum B and Miodownik M 2010 Video force microscopy reveals the mechanics of ventral furrow invagination in Drosophila Proc. Natl Acad. Sci. USA107 22111-6
[7] Brodland G W, Veldhuis J H, Kim S, Perrone M, Mashburn D and Hutson M S 2014 Cellfit: a cellular force-inference toolkit using curvilinear cell boundaries PLoS One9 e99116
[8] Brugués A, Anon E, Conte V, Veldhuis J H, Gupta M, Collombelli J, Muñoz J J, Brodland G W, Ladoux B and Trepat X 2014 Forces driving epithelial wound healing Nat. Phys.10 683-90
[9] Campàs O, Mammoto T, Hasso S, Sperling R A, O’Connell D, Bischof A G, Maas R, Weitz D A, Mahadevan L and Ingber D E 2014 Quantifying cell-generated mechanical forces within living embryonic tissues Nat. Mat.11 183-9
[10] Ciarlet P G 1988 Mathematical Elasticity(Studies in Mathematics and its Applications vol 1) (Amsterdam: Elsevier)
[11] Cranston P G, Veldhuis J H, Narasimhan S and Brodland G W 2010 Cinemechanometry (CMM): a method to determine the forces that drive morphogenetic movements from time-lapse images Ann. Biomed. Eng.38 2937-47
[12] Doubrovinski K, Swan M, Polyakov O and Wieschaus E F 2017 Measurement of cortical elasticity in Drosophila melanogaster embryos using ferrofluids Proc. Natl Acad. Sci. USA114 1051-6
[13] Franck C, Maskarinec S A, Tirrell D A and Ravichandran G 2011 Three-dimensional traction force microscopy: a new tool for quantifying cell-matrix interactions PLoS One6 e17833
[14] Grasso E, Chaillat S, Semblat J F and Bonnet M 2011 Méthode multipôle rapide multi-niveaux en visco-élastodynamique 3D. Giens, France. 10e Colloque National en Calcul des Structures (CSMA) (https://hal.archives-ouvertes.fr/hal-00592883)
[15] Hanke M 1996 Limitations of the L-method in ill-posed problems BIT Numer. Math.36 287-301
[16] He B, Doubrovinski K, Polyakov O and Wieschaus E 2014 Apical constriction drives tissue-scale hydrodynamic flow to mediate cell elongation Nature508 392-6
[17] Heisenberg C P and Bellaïche Y 2013 Forces in tissue morphogenesis and patterning Cell153 948-62
[18] Humphrey J D, Dufresne E R and Schwartz M A 2014 Mechanotransduction and extracellular matrix homeostasis Nat. Rev. Mol. Cell Biol.15 802-12
[19] Isaacson E and Keller H B 1966 Analysis of Numerical Methods (New York: Dover) · Zbl 0168.13101
[20] Malvern L E 1969 Introduction to the Mechanics of Continuous Medium (Englewood Cliffs, NJ: Prentice-Hall) · Zbl 0181.53303
[21] Marin L and Johansson B T 2015 A relaxation method of an alternating iterative algorithm for the Cauchy problem in linear isotropic elasticity Comput. Methods Appl. Mech. Eng.199 3179-96 · Zbl 1225.74116
[22] Marin L and Lesnic D 2003 BEM first-order regularisation method in linear elasticity for boundary identification Comput. Methods Appl. Mech. Eng.192 2059-71 · Zbl 1041.74075
[23] Moeendarbary E, Valon L, Fritzsche M, Harris A R, Moulding D A, Thrasher A J, Stride E, Mahadevan L and Charras G T 2013 The cytoplasm of living cells behaves as a poroelastic material Nat. Mat.12 253-61
[24] Morozov V A 1966 On the solution of functional equations by the method of regularization Sov. Math. Dokl.7 414-7
[25] Muñoz J J 2016 Non-regularised inverse finite element analysis for 3D traction force microscopy. Int. J. Numer. Anal. Mod.13 763-81
[26] Paleologu C, Benesty J and Ciochin S 2008 A robust variable forgetting factor recursive least-squares algorithm for system identification Signal Proc. Lett.15 597-600
[27] Savitzky A and Golay M J E 1964 Smoothing and differentiation of data by simplified least squares procedures Anal. Chem.36 1627-39
[28] Schwarz U S, Balaban N Q, Riveline D, Bershadsky A, Geiger B and Safran S A 2002 Calculation of forces at focal adhesions from elastic substrate data: the effect of localized force and the need for regularization Biophys. J.83 1380-94
[29] Serra-Picamal X, Conte V, Sunyer R, Muñoz J J and Trepat X 2015 Mapping forces and kinematics during collective cell migration Methods Cell Biol.125 309-30
[30] Sugimura K, Lenne P F and Graner F 2016 Measuring forces and stresses in situ in living tissues Development143 186-96
[31] Sunyer R et al 2016 Collective cell durotaxis emerges from long-range intercellular force transmission Science353 1157-61
[32] Toyjanova J, Hannen E, Bar-Kochba E, Darling E M, Henanna D L and Franck C 2014 3D viscoelastic traction force microscopy Soft Matter10 8095-106
[33] Veldhuis J H, Ehsandar A, Maître J L, Hiiragi T, Cox S and Brodland G W 2017 Inferring cellular forces from image stacks Philos. Trans. R Soc. Lond. B 372 20160261
[34] Vitale G, Preziosi L and Ambrosi D 2012 Force traction microscopy: an inverse problem with pointwise observations J. Math. Anal. Appl.395 788-801 · Zbl 1398.92064
[35] Vitale G, Preziosi L and Ambrosi D 2012 A numerical method for the inverse problem of cell traction in 3D Inverse Problems28 095013 · Zbl 1252.92042
[36] Vogel C R 1996 Non-convergence of the L-curve regularization parameter method Inverse Problems12 535-47 · Zbl 0867.65025
[37] Wahba G 1977 Practical approximate solution to linear operator equations when the data is noisy SIAM J. Numer. Anal.14 651-67 · Zbl 0402.65032
[38] Wozniak M A and Chen C S 2009 Mechanotransduction in development: a growing role for contractility Nat. Rev. Mol. Cell Biol.10 34-43
[39] Yeih W C, Koya T and Mura T 1993 An inverse problem in elasticity with partially overspecied boundary conditions. I. Theoretical approach Trans. ASME J. Appl. Mech.60 595-600 · Zbl 0795.73015
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