Inverse Methods

  • Johannes WeickenmeierEmail author
  • Edoardo Mazza
Part of the Studies in Mechanobiology, Tissue Engineering and Biomaterials book series (SMTEB, volume 22)


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.


  1. 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):539–556Google Scholar
  2. 2.
    Hani AFM (2014) Surface imaging for biomedical applications. CRC, Boca RatonGoogle Scholar
  3. 3.
    Forbes SJ, Rosenthal N (2014) Preparing the ground for tissue regeneration: from mechanism to therapy. Nat Med 20(8):857Google Scholar
  4. 4.
    Murphy PS, Evans GRD (2012) Advances in wound healing: a review of current wound healing products. Plast Surg Int 2012:8. CrossRefGoogle Scholar
  5. 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):243Google Scholar
  6. 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 233–241Google Scholar
  7. 7.
    Limbert G, Kuhl E (2018) On skin microrelief and the emergence of expression micro-wrinkles. Soft Matter 14(8):1292–1300Google Scholar
  8. 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):2177–2190MathSciNetzbMATHGoogle Scholar
  9. 9.
    Zöllner AM, Buganza Tepole A, Gosain AK, Kuhl E (2012) Growing skin: tissue expansion in pediatric forehead reconstruction. Biomech Model Mechanobiol 11(6):855–867Google Scholar
  10. 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 74:202–206Google Scholar
  11. 11.
    Weickenmeier J, Jabareen M, Mazza E (2015) Suction based mechanical characterization of superficial facial soft tissues. J Biomech 48(16):4279–4286Google Scholar
  12. 12.
    Limbert G (2017) Mathematical and computational modelling of skin biophysics: a review. Phil Trans R Soc A 473(2203):20170257MathSciNetzbMATHGoogle Scholar
  13. 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 119–132Google Scholar
  14. 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):425–440Google Scholar
  15. 15.
    Wong R, Geyer S, Weninger W, Guimberteau J-C, Wong JK (2016) The dynamic anatomy and patterning of skin. Exp Dermatol 25(2):92–98Google Scholar
  16. 16.
    Weissleder R (2011) A clearer vision for in vivo imaging. Nat Biotechnol 19:316–317Google Scholar
  17. 17.
    Blausen Medical (2014) Dermal circulation. WikiJ Med 1(2):10Google Scholar
  18. 18.
    LaTrenta G (2004) Atlas of aesthetic face and neck surgery. W.B. Saunders, PhiladelphiaGoogle Scholar
  19. 19.
    Aspres N, Egerton IB, Lim AC, Shumack SP (2003) Imaging of Skin. Australas J Dermatol 44(1):19–27Google Scholar
  20. 20.
    Mirrashed F, Sharp JC (2004) In vivo morphological characterisation of skin by MRI micro-imaging methods. Skin Res Technol 10(3):149–160Google Scholar
  21. 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):790–796Google Scholar
  22. 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):1810–1815Google Scholar
  23. 23.
    Kleinerman R, Whang TB, Bard RL, Marmur ES (2012) Ultrasound in dermatology: principles and applications. J Am Acad Dermatol 67(3):478–487Google Scholar
  24. 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. Accessed 29 Apr 2018
  25. 25.
    Weickenmeier J (2015) Investigation of the mechanical behavior of facial soft tissues. ETH Zurich, ZurichGoogle Scholar
  26. 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 78:108–115Google Scholar
  27. 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 69:85–97Google Scholar
  28. 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):17975Google Scholar
  29. 29.
    Pensalfini M, Haertel E, Hopf R, Wietecha M, Werner S, Mazza E (2018) The mechanical fingerprint of murine excisional wounds. Acta Biomater 65:226–236Google Scholar
  30. 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):17635–17635Google Scholar
  31. 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–D95Google Scholar
  32. 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):17912Google Scholar
  33. 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):2116–2124Google Scholar
  34. 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):259–264Google Scholar
  35. 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):654–669Google Scholar
  36. 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):478–492Google Scholar
  37. 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):1171Google Scholar
  38. 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):519–523Google Scholar
  39. 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 444:108–123zbMATHGoogle Scholar
  40. 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):1862–1872Google Scholar
  41. 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):139–148Google Scholar
  42. 42.
    Dobrev H (2005) Application of Cutometer area parameters for the study ofhuman skin fatigue. Skin Res Technol 11(2):120–122Google Scholar
  43. 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):127–135Google Scholar
  44. 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):141–148Google Scholar
  45. 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):354–358Google Scholar
  46. 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):421–435Google Scholar
  47. 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):434–444Google Scholar
  48. 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):2369–2378Google Scholar
  49. 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):466–471MathSciNetGoogle Scholar
  50. 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 222–229Google Scholar
  51. 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):356–365Google Scholar
  52. 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):259–266Google Scholar
  53. 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):274–283Google Scholar
  54. 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):122–130Google Scholar
  55. 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):85–89Google Scholar
  56. 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):208–212Google Scholar
  57. 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):55–67Google Scholar
  58. 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 28:474–483Google Scholar
  59. 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):1603–1610Google Scholar
  60. 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):1274–1280Google Scholar
  61. 61.
    Zahouani H, Boyer G, Pailler-Mattéi C, Ben Tkaya M, Vargiolu R (2011) Effect of human ageing on skin rheology and tribology. Wear 271:2364–2369Google Scholar
  62. 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):2851–2862Google Scholar
  63. 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):4123–4129Google Scholar
  64. 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):1176–1181Google Scholar
  65. 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 45:133Google Scholar
  66. 66.
    Langer K (1978) On the anatomy and physiology of the skin: I. The cleavability of the cutis. Br J Plast Surg 31(1):3–8Google Scholar
  67. 67.
    Rubin MB, Bodner SR (2002) A three-dimensional nonlinear model for dissipative response of soft tissue. Int J Solids Struct 39(19):5081–5099zbMATHGoogle Scholar
  68. 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):59–70Google Scholar
  69. 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):1384–1402Google Scholar
  70. 70.
    Yang W, Sherman VR, Gludovatz B, Schaible E, Stewart P, Ritchie RO, Meyers MA (2015) On the tear resistance of skin. Nat Commun 6:6649Google Scholar
  71. 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):610–619Google Scholar
  72. 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):1935–1946Google Scholar
  73. 73.
    Sanders R (1973) Torsional elasticity of human skin in vivo. Pflügers Archiv Eur J Phys 342(3):255–260Google Scholar
  74. 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):353–357Google Scholar
  75. 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):5913–5925Google Scholar
  76. 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 28:462–470Google Scholar
  77. 77.
    Mazza E, Ehret AE (2015) Mechanical biocompatibility of highly deformable biomedical materials. J Mech Behav Biomed Mater 48:100–124Google Scholar
  78. 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 49:197–219Google Scholar
  79. 79.
    Boissieux L, Kiss G, Thalmann NM, Kalra P 2000 Simulation of skin aging and wrinkles with cosmetics insight. Accessed 8 Apr 2018
  80. 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 82:224–234Google Scholar
  81. 81.
    Lanir Y (1983) Constitutive equations for fibrous connective tissues. J Biomech 16(1):1–12Google Scholar
  82. 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):1002Google Scholar
  83. 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):152–164zbMATHGoogle Scholar
  84. 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):337–345Google Scholar
  85. 85.
    Lanir Y, Fung YC (1974) Two-dimensional mechanical properties of rabbit skin—II. Experimental results. J Biomech 7(2):171–174Google Scholar
  86. 86.
    Lanir Y, Fung YC (1974) Two-dimensional mechanical properties of rabbit skin—I. Experimental system. J Biomech 7(1):29–34Google Scholar
  87. 87.
    Kvistedal YA, Nielsen PMF (2009) Estimating material parameters of human skin in vivo. Biomech Model Mechanobiol 8(1):1–8Google Scholar
  88. 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):13–27Google Scholar
  89. 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 18:167–180Google Scholar
  90. 90.
    Rivlin R (1948) Large elastic deformations of isotropic materials. IV. Further developments of the general theory. Phil Trans R Soc A 241(835):379–397MathSciNetzbMATHGoogle Scholar
  91. 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):565–584zbMATHGoogle Scholar
  92. 92.
    Tong P, Fung YC (1976) The stress-strain relationship for the skin. J Biomech 9(10):649–657Google Scholar
  93. 93.
    Weiss JA, Maker BN, Govindjee S (1996) Finite element implementation of incompressible, transversely isotropic hyperelasticity. Comput Methods Appl Mech Eng 135:107–128zbMATHGoogle Scholar
  94. 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):645–652Google Scholar
  95. 95.
    Limbert G (2011) A mesostructurally-based anisotropic continuum model for biological soft tissues–decoupled invariant formulation. J Mech Behav Biomed Mater 4(8):1637–1657Google Scholar
  96. 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):1793–1811zbMATHGoogle Scholar
  97. 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 37–66Google Scholar
  98. 98.
    Koziel S, Yang X-S (2011) Computational optimization, methods and algorithms. Springer, Berlin HeidelbergzbMATHGoogle Scholar
  99. 99.
    Conn AR, Scheinberg K, Vicente LN (2009) Introduction to derivative-free optimization. SIAM, PhiladelphiazbMATHGoogle Scholar
  100. 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):112–147MathSciNetzbMATHGoogle Scholar
  101. 101.
    Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7:308–313MathSciNetzbMATHGoogle Scholar
  102. 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):231–241Google Scholar
  103. 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):767–778Google Scholar
  104. 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 48:381–402Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringStevens Institute of TechnologyHobokenUSA
  2. 2.Department of Mechanical and Process EngineeringETHZurichSwitzerland
  3. 3.Swiss Federal Laboratories for Materials Science and TechnologyEMPADuebendorfSwitzerland

Personalised recommendations