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Inverse Methods

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Skin Biophysics

Part of the book series: Studies in Mechanobiology, Tissue Engineering and Biomaterials ((SMTEB,volume 22))

Abstract

The mechanical properties of skin have been studied for several decades; yet, to this day reported stiffness values for full-thickness skin or individual layers such as the epidermis, papillary dermis, reticular dermis, and subcutis vary drastically. In vivo and ex vivo measurement techniques include extension, indentation, and suction tests. At the same time, several new imaging modalities emerged that visualize tissue microstructure at length scales ranging from the cell to the organ level. Informed by the experimental characterization of mechanobiological skin properties, computational skin models aim at predicting the soft tissue response under various physiological conditions such as skin growth, scar tissue formation, and surgical interventions. The identification of corresponding model parameters plays a major role in improving the predictive capabilities of such constitutive models. Here, we first provide an overview of the most common measurement techniques and imaging modalities. We then discuss popular methods used for model parameter identification based on inverse methods.

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References

  1. Jor JWY, Parker MD, Taberner AJ, Nash MP, Nielsen PMF (2013) Computational and experimental characterization of skin mechanics: identifying current challenges and future directions. Wiley Interdiscip Rev Syst Biol Med 5(5):539–556

    Google Scholar 

  2. Hani AFM (2014) Surface imaging for biomedical applications. CRC, Boca Raton

    Google Scholar 

  3. Forbes SJ, Rosenthal N (2014) Preparing the ground for tissue regeneration: from mechanism to therapy. Nat Med 20(8):857

    Google Scholar 

  4. Murphy PS, Evans GRD (2012) Advances in wound healing: a review of current wound healing products. Plast Surg Int 2012:8. https://doi.org/10.1155/2012/190436

    Article  Google Scholar 

  5. Rowan MP, Cancio LC, Eric A, Burmeister DM, Rose LF, Natesan S, Chan RK, Christy RJ, Chung KK (2015) Burn wound healing and treatment: review and advancements. Crit Care 19(1):243

    Google Scholar 

  6. Weickenmeier J, Wu R, Lecomte-Grosbras P, Witz J-F, Brieu M, Winklhofer S, Andreisek G, Mazza E (2014) Experimental characterization and simulation of layer interaction in facial soft tissues. In: Intrnational symposium on biomedical simulation. Springer, Cham, pp 233–241

    Google Scholar 

  7. Limbert G, Kuhl E (2018) On skin microrelief and the emergence of expression micro-wrinkles. Soft Matter 14(8):1292–1300

    Google Scholar 

  8. Buganza Tepole A, Joseph Ploch C, Wong J, Gosain AK, Kuhl E (2011) Growing skin: a computational model for skin expansion in reconstructive surgery. J Mech Phys Solids 59(10):2177–2190

    MathSciNet  MATH  Google Scholar 

  9. Zöllner AM, Buganza Tepole A, Gosain AK, Kuhl E (2012) Growing skin: tissue expansion in pediatric forehead reconstruction. Biomech Model Mechanobiol 11(6):855–867

    Google Scholar 

  10. Lee T, Turin SY, Gosain AK, Tepole AB (2018) Multi-view stereo in the operating room allows prediction of healing complications in a patient-specific model of reconstructive surgery. J Biomech 74:202–206

    Google Scholar 

  11. Weickenmeier J, Jabareen M, Mazza E (2015) Suction based mechanical characterization of superficial facial soft tissues. J Biomech 48(16):4279–4286

    Google Scholar 

  12. Limbert G (2017) Mathematical and computational modelling of skin biophysics: a review. Phil Trans R Soc A 473(2203):20170257

    MathSciNet  MATH  Google Scholar 

  13. Oomens C (2017) Mechanical behaviour of skin: the struggle for the right testing method. In: Avril S, Evans S (eds) Material parameter identification and inverse problems in soft tissue biomechanics. Springer, Cham, pp 119–132

    Google Scholar 

  14. Koehler MJ, Lange-Asschenfeldt S, Kaatz M (2011) Non-invasive imaging techniques in the diagnosis of skin diseases. Expert Opin Med Diagn 5(5):425–440

    Google Scholar 

  15. Wong R, Geyer S, Weninger W, Guimberteau J-C, Wong JK (2016) The dynamic anatomy and patterning of skin. Exp Dermatol 25(2):92–98

    Google Scholar 

  16. Weissleder R (2011) A clearer vision for in vivo imaging. Nat Biotechnol 19:316–317

    Google Scholar 

  17. Blausen Medical (2014) Dermal circulation. WikiJ Med 1(2):10

    Google Scholar 

  18. LaTrenta G (2004) Atlas of aesthetic face and neck surgery. W.B. Saunders, Philadelphia

    Google Scholar 

  19. Aspres N, Egerton IB, Lim AC, Shumack SP (2003) Imaging of Skin. Australas J Dermatol 44(1):19–27

    Google Scholar 

  20. Mirrashed F, Sharp JC (2004) In vivo morphological characterisation of skin by MRI micro-imaging methods. Skin Res Technol 10(3):149–160

    Google Scholar 

  21. Barral JK, Bangerter NK, Hu BS, Nishimura DG (2010) In vivo high-resolution magnetic resonance skin imaging at 1.5 T and 3 T. Magn Reson Med 63(3):790–796

    Google Scholar 

  22. Van Mulder TJS, de Koeijer M, Theeten H, Willems D, Van Damme P, Demolder M, De Meyer GRY, Beyers KCL, Vankerckhoven V (2017) High frequency ultrasound to assess skin thickness in healthy adults. Vaccine 35(14):1810–1815

    Google Scholar 

  23. Kleinerman R, Whang TB, Bard RL, Marmur ES (2012) Ultrasound in dermatology: principles and applications. J Am Acad Dermatol 67(3):478–487

    Google Scholar 

  24. Wortsman, Ximena, Jacobo Wortsman, Laura Carreño, Claudia Morales, Ivo Sazunic, Gregor B. E. Jemec 2013 Sonographic anatomy of the skin, appendages, and adjacent structures. Springer, New York. https://link.springer.com/chapter/10.1007/978-1-4614-7184-4_2. Accessed 29 Apr 2018

  25. Weickenmeier J (2015) Investigation of the mechanical behavior of facial soft tissues. ETH Zurich, Zurich

    Google Scholar 

  26. Pensalfini M, Weickenmeier J, Rominger MB, Santoprete R, Distler O, Mazza E (2018) Location-specific mechanical response and morphology of facial soft tissues. J Mech Behav Biomed Mater 78:108–115

    Google Scholar 

  27. Pensalfini M, Ehret AE, Stüdeli S, Marino D, Kaech A, Reichmann E, Mazza E (2017) Factors affecting the mechanical behavior of collagen hydrogels for skin tissue engineering. J Mech Behav Biomed Mater 69:85–97

    Google Scholar 

  28. Chen Z, Rank E, Meiburger KM, Sinz C, Hodul A, Zhang E, Hoover E et al (2017) Non-invasive multimodal optical coherence and photoacoustic tomography for human skin imaging. Sci Rep 7(1):17975

    Google Scholar 

  29. Pensalfini M, Haertel E, Hopf R, Wietecha M, Werner S, Mazza E (2018) The mechanical fingerprint of murine excisional wounds. Acta Biomater 65:226–236

    Google Scholar 

  30. Bancelin S, Lynch B, Bonod-Bidaud C, Ducourthial G, Psilodimitrakopoulos S, Dokládal P, Allain J-M, Schanne-Klein M-C, Ruggiero F (2015) Ex vivo multiscale quantitation of skin biomechanics in wild-type and genetically-modified mice using multiphoton microscopy. Sci Rep 5(1):17635–17635

    Google Scholar 

  31. Yasui T, Takahashi Y, Ito M, Fukushima S, Araki T (2009) Ex vivo and in vivo second-harmonic-generation imaging of dermal collagen fiber in skin: comparison of imaging characteristics between mode-locked Cr:forsterite and Ti:sapphire lasers. Appl Opt 48(10):D88–D95

    Google Scholar 

  32. Adabi S, Hosseinzadeh M, Noei S, Conforto S, Daveluy S, Clayton A, Mehregan D, Nasiriavanaki M (2017) Universal in vivo textural model for human skin based on optical coherence tomograms. Sci Rep 7(1):17912

    Google Scholar 

  33. Avanaki MR, Hojjatoleslami A, Sira M, Schofield JB, Jones CA, Podoleanu AG (2013) Investigation of basal cell carcinoma using dynamic focus optical coherence tomography. Appl Opt 52(10):2116–2124

    Google Scholar 

  34. Yasui T, Tohno Y, Araki T (2004) Characterization of collagen orientation in human dermis by two-dimensional second-harmonic-generation polarimetry. J Biomed Opt 9(2):259–264

    Google Scholar 

  35. Chen X, Nadiarynkh O, Plotnikov SV, Campagnola PJ (2012) Second harmonic generation microscopy for quantitative analysis of collagen fibrillar structure. Nat Protoc 7(4):654–669

    Google Scholar 

  36. Chen S-Y, Chen S-U, Hai-Yin W, Lee W-J, Liao Y-H, Sun C-K (2010) In vivo virtual biopsy of human skin by using noninvasive higher harmonic generation microscopy. IEEE J Sel Top Quantum Electron 13(3):478–492

    Google Scholar 

  37. Shirshin EA, Gurfinkel YI, Priezzhev AV, Fadeev VV, Lademann J, Darvin ME (2017) Two-photon autofluorescence lifetime imaging of human skin papillary dermis in vivo: assessment of blood capillaries and structural proteins localization. Sci Rep 7(1):1171

    Google Scholar 

  38. Koehler MJ, Hahn S, Preller A, Elsner P, Ziemer M, Bauer A, König K, Bückle R, Fluhr JW, Kaatz M (2008) Morphological skin ageing criteria by multiphoton laser scanning tomography: non-invasive in vivo scoring of the dermal fibre network. Exp Dermatol 17(6):519–523

    Google Scholar 

  39. Pond D, McBride AT, Davids LM, Reddy BD, Limbert G (2018) Microstructurally-based constitutive modelling of the skin – linking intrinsic ageing to microstructural parameters. J Theor Biol 444:108–123

    MATH  Google Scholar 

  40. Achterberg VF, Buscemi L, Diekmann H, Smith-Clerc J, Schwengler H, Meister J-J, Wenck H, Gallinat S, Hinz B (2014) The nano-scale mechanical properties of the extracellular matrix regulate dermal fibroblast function. J Investig Dermatol 134(7):1862–1872

    Google Scholar 

  41. Annaidh AN, Bruyère K, Destrade M, Gilchrist MD, Otténio M (2012) Characterization of the anisotropic mechanical properties of excised human skin. J Mech Behav Biomed Mater 5(1):139–148

    Google Scholar 

  42. Dobrev H (2005) Application of Cutometer area parameters for the study ofhuman skin fatigue. Skin Res Technol 11(2):120–122

    Google Scholar 

  43. Luebberding S, Krueger N, Kerscher M (2014) Mechanical properties of human skin in vivo: a comparative evaluation in 300 men and women. Skin Res Technol 20(2):127–135

    Google Scholar 

  44. Krueger N, Luebberding S, Oltmer M, Streker M, Kerscher M (2011) Age-related changes in skin mechanical properties: a quantitative evaluation of 120 female subjects. Skin Res Technol 17(2):141–148

    Google Scholar 

  45. Ryu HS, Joo YH, Kim SO, Park KC, Youn SW (2008) Influence of age and regional differences on skin elasticity as measured by the Cutometer. Skin Res Technol 14(3):354–358

    Google Scholar 

  46. Diridollou S, Black D, Lagarde JM, Gall Y, Berson M, Vabre V, Patat F, Vaillant L (2000) Sex-and site-dependent variations in the thickness and mechanical properties of human skin in vivo. Int J Cosmet Sci 22(6):421–435

    Google Scholar 

  47. Barbarino GG, Jabareen M, Mazza E (2011) Experimental and numerical study on the mechanical behavior of the superficial layers of the face. Skin Res Technol 17(4):434–444

    Google Scholar 

  48. Luboz V, Promayon E, Payan Y (2014) Soft tissue finite element modeling and calibration of the material properties in the context of computer-assisted medical interventions. Ann Biomed Eng 42(11):2369–2378

    Google Scholar 

  49. Kim MA, Kim EJ, Lee HK (2018) Use of SkinFibrometer® to measure skin elasticity and its correlation with Cutometer® and DUB® Skinscanner. Skin Res Technol 24(3):466–471

    MathSciNet  Google Scholar 

  50. Nava A, Mazza E, Kleinermann F, Avis NJ, McClure J (2003) Determination of the mechanical properties of soft human tissues through aspiration experiments. In: International Conference on Medical Image Computing and Computer-Assisted Intervention. Springer, New York, pp 222–229

    Google Scholar 

  51. Iivarinen JT, Korhonen RK, Julkunen P, Jurvelin JS (2013) Experimental and computational analysis of soft tissuemechanical response under negative pressure in forearm. Skin Res Technol 19(1):356–365

    Google Scholar 

  52. Hendriks F, Brokken D, Oomens C, Bader D, Baaijens F (2006) The relative contributions of different skin layers to the mechanical behavior of human skin in vivo using suction experiments. Med Eng Phys 28(3):259–266

    Google Scholar 

  53. Hendriks F, Brokken D, Van Eemeren J, Oomens C, Baaijens F, Horsten J (2003) A numerical-experimental method to characterize the non-linear mechanical behaviour of human skin. Skin Res Technol 9(3):274–283

    Google Scholar 

  54. Schlangen LJM, Brokken D, Van Kemenade PM (2003) Correlations betwen small aperture skin suction parameter- statistical analysis and mechanical model. Skin Res Technol 9(2):122–130

    Google Scholar 

  55. Bonaparte JP, Chung J (2014) The effect of probe placement on inter-trial variability when using the Cutometer MPA 580. J Med Eng Technol 38(2):85–89

    Google Scholar 

  56. Bonaparte JP, Ellis DA, Chung J (2013) The effect of probe to skin contact force on Cutometer MPA 580 measurements. J Med Eng Technol 37(3):208–212

    Google Scholar 

  57. Boyer G, Laquièze L, Le Bot A, Laquièze S, Zahouani H (2009) Dynamic indentation on human skin in vivo: ageing effects. Skin Res Technol 15(1):55–67

    Google Scholar 

  58. Pailler-Mattei C, Debret R, Vargiolu R, Sommer P, Zahouani H (2013) In vivo skin biophysical behaviour and surface topography as a function of ageing. J Mech Behav Biomed Mater 28:474–483

    Google Scholar 

  59. Delalleau A, Josse G, Lagarde J-M, Zahouani H, Bergheau J-M (2006) Characterization of the mechanical properties of skin by inverse analysis combined with the indentation test. J Biomech 39(9):1603–1610

    Google Scholar 

  60. Zahouani H, Vargiolu R, Boyer G, Pailler-Mattéi C, Laquièze L, Mavon A (2009) Friction noise of human skin in vivo. Wear 267(2):1274–1280

    Google Scholar 

  61. Zahouani H, Boyer G, Pailler-Mattéi C, Ben Tkaya M, Vargiolu R (2011) Effect of human ageing on skin rheology and tribology. Wear 271:2364–2369

    Google Scholar 

  62. Tupin S, Molimard J, Cenizo V, Hoc T, Sohm B, Zahouani H (2016) Multiscale approach to characterize mechanical properties of tissue engineered skin. Ann Biomed Eng 44(9):2851–2862

    Google Scholar 

  63. Grant CA, Twigg PC, Tobin DJ (2012) Static and dynamic nanomechanical properties of human skin tissue using atomic force microscopy: effect of scarring in the upper dermis. Acta Biomater 8(11):4123–4129

    Google Scholar 

  64. Geerligs M, van Breemen L, Peters GWM, Ackermans PAJ, Baaijens FF, Oomens C (2011) In vitro indentation to determine the mechanical properties of epidermis. J Biomech 44(6):1176–1181

    Google Scholar 

  65. Langer K (1862) Zur Anatomie und Physiologie der Haut -- II -- Die spannung der cutis. Sitzungsberchte der Mathematisch-naturwissenschaftlicher Classe der. Kaiserlichen Akademie der Wissenschaften 45:133

    Google Scholar 

  66. Langer K (1978) On the anatomy and physiology of the skin: I. The cleavability of the cutis. Br J Plast Surg 31(1):3–8

    Google Scholar 

  67. Rubin MB, Bodner SR (2002) A three-dimensional nonlinear model for dissipative response of soft tissue. Int J Solids Struct 39(19):5081–5099

    MATH  Google Scholar 

  68. Har-Shai Y, Bodner SR, Egozy-Golan D, Lindenbaum ES, Ben-Izhak O, Mitz V, Hirshowitz B (1996) Mechanical properties and microstructure of the superficial musculoaponeurotic system. Plast Reconstr Surg 98(1):59–70

    Google Scholar 

  69. Shergold OA, Fleck NA, Radford D (2006) The uniaxial stress versus strain response of pig skin and silicone rubber at low and high strain rates. Int J Impact Eng 32(9):1384–1402

    Google Scholar 

  70. Yang W, Sherman VR, Gludovatz B, Schaible E, Stewart P, Ritchie RO, Meyers MA (2015) On the tear resistance of skin. Nat Commun 6:6649

    Google Scholar 

  71. Flynn C, Taberner AJ, Nielsen PMF (2011) Measurement of the force–displacement response of in vivo human skin under a rich set of deformations. Med Eng Phys 33(5):610–619

    Google Scholar 

  72. Flynn C, Taberner A, Nielsen P (2011) Modeling the mechanical response of in vivo human skin under a rich set of deformations. Ann Biomed Eng 39(7):1935–1946

    Google Scholar 

  73. Sanders R (1973) Torsional elasticity of human skin in vivo. Pflügers Archiv Eur J Phys 342(3):255–260

    Google Scholar 

  74. Escoffier C, de Rigal J, Rochefort A, Vasselet R, Lévêque J-L, Agache PG (1989) Age-related mechanical properties of human skin- an in vivo study. J Investig Dermatol 93(3):353–357

    Google Scholar 

  75. Tonge TK, Atlan LS, Voo LM, Nguyen TD (2013) Full-field bulge test for planar anisotropic tissues: part I--experimental methods applied to human skin tissue. Acta Biomater 9(4):5913–5925

    Google Scholar 

  76. Lamers E, T.H.S v K, F.P.T B, G.W.M P, C.W.J O (2013) Large amplitude oscillatory shear properties of human skin. J Mech Behav Biomed Mater 28:462–470

    Google Scholar 

  77. Mazza E, Ehret AE (2015) Mechanical biocompatibility of highly deformable biomedical materials. J Mech Behav Biomed Mater 48:100–124

    Google Scholar 

  78. Leyva-Mendivil MF, Page A, Bressloff NW, Limbert G (2015) A mechanistic insight into the mechanical role of the stratum corneum during stretching and compression of the skin. J Mech Behav Biomed Mater 49:197–219

    Google Scholar 

  79. Boissieux L, Kiss G, Thalmann NM, Kalra P 2000 Simulation of skin aging and wrinkles with cosmetics insight. https://link.springer.com/chapter/10.1007/978-3-7091-6344-3_2. Accessed 8 Apr 2018

  80. Lee T, Vaca EE, Ledwon JK, Bae H, Topczewska JM, Turin SY, Kuhl E, Gosain AK, Buganza A (2018) Improving tissue expansion protocols through computational modeling. J Mech Behav Biomed Mater 82:224–234

    Google Scholar 

  81. Lanir Y (1983) Constitutive equations for fibrous connective tissues. J Biomech 16(1):1–12

    Google Scholar 

  82. Ehret AE, Bircher K, Stracuzzi A, Marina V, Zündel M, Mazza E (2017) Inverse poroelasticity as a fundamental mechanism in biomechanics and mechanobiology. Nat Commun 8(1):1002

    Google Scholar 

  83. Delalleau A, Josse G, Lagarde J-M, Zahouani H, Bergheau J-M (2008) A nonlinear elastic behavior to identify the mechanical parameters of human skin in vivo. Skin Res Technol 14(2):152–164

    MATH  Google Scholar 

  84. Evans SL, Holt CA (2009) Measuring the mechanical properties of human skin in vivo using digital image correlation and finite element modelling. J Strain Anal Eng Des 44(5):337–345

    Google Scholar 

  85. Lanir Y, Fung YC (1974) Two-dimensional mechanical properties of rabbit skin—II. Experimental results. J Biomech 7(2):171–174

    Google Scholar 

  86. Lanir Y, Fung YC (1974) Two-dimensional mechanical properties of rabbit skin—I. Experimental system. J Biomech 7(1):29–34

    Google Scholar 

  87. Kvistedal YA, Nielsen PMF (2009) Estimating material parameters of human skin in vivo. Biomech Model Mechanobiol 8(1):1–8

    Google Scholar 

  88. Meijer RR, Douven LL, Oomens CC (1999) Characterisation of anisotropic and non-linear behaviour of human skin in vivo. Comput Methods Biomech Biomed Eng 2(1):13–27

    Google Scholar 

  89. Groves RB, Coulman S, Birchall J, Evans SL (2013) An anisotropic, hyperelastic model for skin: experimental measurements, finite element modelling and identification of parameters for human and murine skin. J Mech Behav Biomed Mater 18:167–180

    Google Scholar 

  90. Rivlin R (1948) Large elastic deformations of isotropic materials. IV. Further developments of the general theory. Phil Trans R Soc A 241(835):379–397

    MathSciNet  MATH  Google Scholar 

  91. Ogden R (1972) Large deformation isotropic elasticity – on the correlation of theory and experiment for incompressible rubberlike solids. Proc R Soc Lond A Math Phys Sci 326(1567):565–584

    MATH  Google Scholar 

  92. Tong P, Fung YC (1976) The stress-strain relationship for the skin. J Biomech 9(10):649–657

    Google Scholar 

  93. Weiss JA, Maker BN, Govindjee S (1996) Finite element implementation of incompressible, transversely isotropic hyperelasticity. Comput Methods Appl Mech Eng 135:107–128

    MATH  Google Scholar 

  94. Bischoff JE, Arruda EM, Grosh K (2000) Finite element modeling of human skin using an isotropic, nonlinear elastic constitutive model. J Biomech 33(6):645–652

    Google Scholar 

  95. Limbert G (2011) A mesostructurally-based anisotropic continuum model for biological soft tissues–decoupled invariant formulation. J Mech Behav Biomed Mater 4(8):1637–1657

    Google Scholar 

  96. Flynn C, Rubin MB, Nielsen PMF (2011) A model for the anisotropic response of fibrous soft tissues using six discrete fibre bundles. Int J Numer Meth Biomed Eng 27(11):1793–1811

    MATH  Google Scholar 

  97. Avril S (2017) Overview of identification methods of mechanical parameters based on full-field measurements. In: Avril S, Evans S (eds) Material parameter identification and inverse problems in soft tissue biomechanics, vol 573. Springer, Cham, pp 37–66

    Google Scholar 

  98. Koziel S, Yang X-S (2011) Computational optimization, methods and algorithms. Springer, Berlin Heidelberg

    MATH  Google Scholar 

  99. Conn AR, Scheinberg K, Vicente LN (2009) Introduction to derivative-free optimization. SIAM, Philadelphia

    MATH  Google Scholar 

  100. Lagarias JC, Reeds JA, Wright MH, Wright PE (1998) Convergence properties of the Nelder-Mead simplex method in low dimensions. SIAM J Optim 9(1):112–147

    MathSciNet  MATH  Google Scholar 

  101. Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7:308–313

    MathSciNet  MATH  Google Scholar 

  102. Hendriks F, Brokken D, Oomens C, Baaijens F (2004) Influence of hydration and experimental length scale on the mechanical response of human skin in vivo, using optical coherence tomography. Skin Res Technol 10(4):231–241

    Google Scholar 

  103. Jor JWY, Nash MP, Nielsen PMF, Hunter PJ (2011) Estimating material parameters of a structurally based constitutive relation for skin mechanics. Biomech Model Mechanobiol 10(5):767–778

    Google Scholar 

  104. Avril S, Bonnet M, Bretelle A-S, Grédiac M, Hild F, Ienny P, Latourte F et al (2008) Overview of identification methods of mechanical parameters based on full-field measurements. Exp Mech 48:381–402

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken, NJ, USA

    Johannes Weickenmeier

  2. Department of Mechanical and Process Engineering, ETH, Zurich, Switzerland

    Edoardo Mazza

  3. Swiss Federal Laboratories for Materials Science and Technology, EMPA, Duebendorf, Switzerland

    Edoardo Mazza

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  1. Johannes Weickenmeier
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  2. Edoardo Mazza
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Correspondence to Johannes Weickenmeier .

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Editors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering and Physical Sciences, University of Southampton, Southampton, UK

    Georges Limbert

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Weickenmeier, J., Mazza, E. (2019). Inverse Methods. In: Limbert, G. (eds) Skin Biophysics. Studies in Mechanobiology, Tissue Engineering and Biomaterials, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-030-13279-8_6

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