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Power type strain energy function model and prediction of the anisotropic mechanical properties of skin using uniaxial extension data

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Abstract

Many successful models to describe the biomechanical characteristics of planar biological soft tissues are based on strain energy function. However, the parameters in these models are determined by biaxial extension test, which might be difficult to exercise for certain types of soft tissue. This study presents a new constitutive model, the power type strain energy density function model (PTM), and a method to identify its material parameters for rabbit skin using uniaxial extension test of 4-direction strip samples. The abdominal skins from eight rabbits were taken to perform uniaxial tension tests in 7 different directions. The material parameters were identified for each subject based on any 4 out of 7 directions by applying some definite conditions of this issue. For each rabbit, the 35 groups of material parameters were consistent. The 7 material parameters in PTM were identified with root mean square errors <0.061. The results indicate that the material parameters of rabbit skin can be identified from uniaxial extension test data.

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References

  1. Alastrue V, Martinez MA, Doblare M, Menzel A (2009) Anisotropic microsphere-based finite elasticity applied to blood vessel modelling. J Mech Phys Solids 57(1):178–203

    Article  Google Scholar 

  2. Avril S, Badel P, Duprey A (2010) Anisotropic and hyperelastic identification of in vitro human arteries from full-field optical measurements. J Biomech 43(15):2978–2985

    Article  PubMed  Google Scholar 

  3. Azadani AN, Chitsaz S, Matthews PB, Jaussaud N, Leung J, Wisneski A, Ge L, Tseng EE (2012) Biomechanical comparison of human pulmonary and aortic roots. Eur J Cardio-Thorac 41(5):1111–1116

    Article  Google Scholar 

  4. Criscione JC, Sacks MS, Hunter WC (2003) Experimentally tractable, pseudo-elastic constitutive law for biomembranes: I. theory. J Biomech Eng 125(1):94–99

    Article  PubMed  Google Scholar 

  5. Criscione JC, Sacks MS, Hunter WC (2003) Experimentally tractable, pseudo-elastic constitutive law for biomembranes: II application. J Biomech Eng 125(1):100–105

    Article  PubMed  Google Scholar 

  6. Eilaghi A, Flanagan JG, Tertinegg I, Simmons CA, Brodland GW, Ethier CR (2010) Biaxial mechanical testing of human sclera. J Biomech 43(9):1696–1701

    Article  PubMed  Google Scholar 

  7. Federico S, Grillo A, Giaquinta G, Herzog W (2008) Convex Fung-type potentials for biological tissues. Meccanica 43(3):279–288

    Article  Google Scholar 

  8. Flynn C, McCormack BAO (2010) Simulating the wrinkling and aging of skin with a multi-layer finite element model. J Biomech 43(3):442–448

    Article  PubMed  Google Scholar 

  9. Fung YC (1993) Biomechanics: mechanical properties of living tissues. Springer, Berlin

    Google Scholar 

  10. Fung YC, Liu SQ (1995) Determination of the mechanical properties of the different layers of blood vessels in vivo. Proc Natl Acad Sci USA 92:2169–2173

    Article  PubMed  CAS  Google Scholar 

  11. Gambarotta L, Massabo R, Morbiducci R, Raposio E, Santi P (2005) In vivo experimental testing and model identification of human scalp skin. J Biomech 38(11):2237–2247

    Article  PubMed  CAS  Google Scholar 

  12. Harb N, Labed N, Domaszewski M, Peyraut F (2011) A new parameter identification method of soft biological tissue combining genetic algorithm with analytical optimization. Comput. Methods Appl Mec Eng 200:208–215

    Article  Google Scholar 

  13. Hernández B, Pena E, Pascual G, Rodriguez M, Calvo B, Doblaré M, Bellón M (2011) Mechanical and histological characterization of the abdominal muscle. A previous step to modelling hernia surgery. J Mech Behav Biomed 4(3):392–404

    Article  Google Scholar 

  14. Hoeltzel DA, Altman P, Buzard K, Choe K (1992) Strip extensiometry for comparison of the mechanical response of bovine, rabbit, and human corneas. J Biomech Eng 114:202–215

    Article  PubMed  CAS  Google Scholar 

  15. Holzapfel GA (2006) Determination of material models for arterial walls from uniaxial extension tests and histological structure. J Theor Biol 238(2):290–302

    Article  PubMed  Google Scholar 

  16. Holzapfel GA, Gasser TC, Ogden RW (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elasticity 61(1–3):1–48

    Article  Google Scholar 

  17. Holzapfel GA, Ogden RW (2009) On planar biaxial tests for anisotropic nonlinearly elastic solids. A continuum mechanical framework. Math Mech Solids 14(5):474–489

    Article  Google Scholar 

  18. Holzapfel GA, Ogden RW (2010) Constitutive modelling of arteries. P Roy Soc A-Math Phys 466(2118):1551–1597

    Article  Google Scholar 

  19. Holzapfel GA, Sommer G, Regitnig P (2004) Anisotropic mechanical properties of tissue components in human atherosclerotic plaques. J Biomech Eng 126(3):657–665

    Article  PubMed  Google Scholar 

  20. Holzapfel GA, Weizsacker HW (1998) Biomechanical behavior of the arterial wall and its numerical characterization. Comput Biol Med 28(4):377–392

    Article  PubMed  CAS  Google Scholar 

  21. Humphrey JD, Wells PB, Baek S, Hu J–J, McLeroy K, Yeh AT (2008) A theoretically-motivated biaxial tissue culture system with intravital microscopy. Biomech Model Mech 7(4):323–334

    Article  CAS  Google Scholar 

  22. Jayne BC (1988) Mechanical behaviour of snake skin. J Zool 214(1):125–140

    Article  Google Scholar 

  23. Kao PH, Lammers SR, Tian L, Hunter K, Stenmark KR, Shandas R, Qi HJ (2011) A microstructurally driven model for pulmonary artery tissue. J Biomech Eng 133:051002. doi:10.1115/1.4002698

    Article  PubMed  Google Scholar 

  24. Lanir Y, Fung YC (1974) Two-dimensional mechanical properties of rabbit skin—II: experimental results. J Biomech 7:171–182

    Article  PubMed  CAS  Google Scholar 

  25. Li L, Qian X, Yan S, Lei J, Wang X, Zhang H, Liu Z (2011) Determination of material parameters of the two-dimensional Holzapfel–Weizsäcker type model based on uniaxial extension data of arterial walls. Comput Method Biomech. doi:10.1080/10255842.2011.621121

  26. Li L, Qian X, Yan S, Hua L, Zhang H, Liu Z (2012) Determination of the material parameters of four-fibre family model based on uniaxial extension data of arterial walls. Comput Method Biomech doi:10.1080/10255842.2012.714374

  27. Lokshin O, Lanir Y (2009) Viscoelasticity and preconditioning of rat skin under uniaxial stretch: microstructural constitutive characterization. J Biomech Eng 131(3):031009–031010

    Article  PubMed  Google Scholar 

  28. NiAnnaidh A, Bruyere K, Destrade M, Gilchrist MD (2012) Characterization of the anisotropic mechanical properties of excised human skin. J Mech Behav Biomed Mater 5(1):139–148

    Article  Google Scholar 

  29. Reihsner R, Balogh B, Menzel EJ (1995) Two-dimensional elastic properties of human skin in terms of an incremental model at the in vivo configuration. Med Eng Phys 17(4):304–313

    Article  PubMed  CAS  Google Scholar 

  30. Schulze-Bauer CAJ, Holzapfel GA (2003) Determination of constitutive equations for human arteries from clinical data. J Biomech 36(2):165–169

    Article  PubMed  CAS  Google Scholar 

  31. Smuts AN, Blaine DC, Scheffer C, Weich H, Doubell AF, Dellimore KH (2011) Application of finite element analysis to the design of tissue, leaflets for a percutaneous aortic valve. J Mech Behav Biomed 4(1):85–98

    Article  CAS  Google Scholar 

  32. Sun W, Sacks MS, Sellaro TL, Slaughter WS, Scott MJ (2003) Biaxial mechanical response of bioprosthetic heart valve biomaterials to high in-plane shear. J Biomech Eng 125(3):372–380

    Article  PubMed  Google Scholar 

  33. Sun W, Sacks MS (2005) Finite element implementation of a generalized Fung-elastic constitutive model for planar soft tissues. Biomech Model Mech 4(2–3):190–199

    Article  Google Scholar 

  34. Tanaka ML, Weisenbach CA, Miller MC, Kuxhaus L (2011) A Continuous method to compute model parameters for soft biological materials. J Biomech Eng 133(7):074502. doi:10.1115/1.4004412

    Article  PubMed  Google Scholar 

  35. Taylor CA, Humphrey JD (2009) Open problems in computational vascular biomechanics: hemodynamics and arterial wall mechanics. Comput Method Appl Mech Eng 198:3514–3523

    Article  Google Scholar 

  36. Vande Geest JP, Sacks MS, Vorp DA (2006) The effects of aneurysm on the biaxial mechanical behavior of human abdominal aorta. J Biomech 39(7):324–1334

    Article  Google Scholar 

  37. Yip CP, Walker D, Fernlund G, Pinder K (2007) Role of dermal fibroblasts in rat skin tissue biomechanics. Bio-Med Mater Eng 17(2):109–117

    CAS  Google Scholar 

  38. Yoder JH, Elliott DM (2010) Nonlinear and anisotropic tensile properties of graft materials used in soft tissue applications. Clin Biomech 25(4):378–382

    Article  Google Scholar 

  39. Zeng Y, Liu Y, Xu C, Xu X, Xu H, Sun G (2004) Biomechanical properties of skin in vitro for different expansion methods. Clin Biomech 19(8):853–857

    Article  Google Scholar 

  40. Zhang W, Kassab GS (2007) A bilinear stress–strain relationship for arteries. Biomaterials 28(6):1307–1315

    Article  PubMed  CAS  Google Scholar 

  41. Zhang W, Wang C, Kassab GS (2007) The mathematical formulation of a generalized Hooke’s law for blood vessels. Biomaterials 28(24):3569–3578

    Article  PubMed  CAS  Google Scholar 

  42. Zhao J, Liao D, Chen P, Kunwald P, Gregersen H (2008) Stomach stress and strain depend on location, direction and the layered structure. J Biomech 41(16):3441–3447

    Article  PubMed  Google Scholar 

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Acknowledgments

This research was supported in part by the National Natural Science Foundation of China (30900288; 31070840), Beijing Municipal Education Commission Foundation (KM201010025007) and Beijing Leading Academic Discipline Project of Beijing Municipal Education Commission (PHR201110506).

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Authors and Affiliations

  1. School of Biomedical Engineering, Capital Medical University, Beijing, 100069, China

    Lin Li, Lin Hua, Haixia Zhang & Zhicheng Liu

  2. Biomechanics Research Center, Capital Medical University, Beijing, 100069, China

    Xiuqing Qian, Hui Wang & Zhicheng Liu

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  1. Lin Li
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  2. Xiuqing Qian
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  3. Hui Wang
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  4. Lin Hua
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  5. Haixia Zhang
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  6. Zhicheng Liu
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Correspondence to Zhicheng Liu.

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Li, L., Qian, X., Wang, H. et al. Power type strain energy function model and prediction of the anisotropic mechanical properties of skin using uniaxial extension data. Med Biol Eng Comput 51, 1147–1156 (2013). https://doi.org/10.1007/s11517-013-1098-6

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  • DOI: https://doi.org/10.1007/s11517-013-1098-6

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