Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Muslov S. A., Arutyunov S. D., Sukhochev P. Y., Chizhmakov E. A. Calculation of parameters of elastic and hyperelastic facial skin models. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2025, vol. 25, iss. 1, pp. 91-105. DOI: 10.18500/1816-9791-2025-25-1-91-105, EDN: TJSGIS

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
28.02.2025
Full text:
download
(downloads: 57)
Language: 
Russian
Heading: 
Mathematics
Article type: 
Article
UDC: 
517.98
DOI: 
10.18500/1816-9791-2025-25-1-91-105
EDN: 
TJSGIS

Calculation of parameters of elastic and hyperelastic facial skin models

Autors: 
Muslov Sergey A., Evdokimov Moscow State University of Medicine and Dentistry
Arutyunov Sergey D., Evdokimov Moscow State University of Medicine and Dentistry
Sukhochev Pavel Yu., Lomonosov Moscow State University
Chizhmakov Evgeny A., Evdokimov Moscow State University of Medicine and Dentistry
Abstract: 

The results of uniaxial mechanical tests of the facial (forehead) skin in vitro were compared with linear, bilinear and non-linear exponential, as well as five hyperelastic models. The results showed that the deformation properties of tissues are best described by the exponential function. Linear and bilinear elastic models are considered and the numerical values of the model parameters are determined. To study the hyperelastic properties of the skin, neohookean, Mooney – Rivlin, Ogden, polynomial and Veronda – Westmann phenomenological models were used. In order to find the most advanced algorithms for calculating the parameters of hyperelastic models, calculations were performed in the Mathcad 15 computer algebra system and the Ansys 2022 R2 multi-purpose software package. The parameters of the models and the closeness of the correlation between the exponential curve and the calculated data were determined, the correlation coefficient was used as a criterion for the correspondence of the models. The polynomial model and the Ogden model demonstrated the highest correlation with the experimental values, and the neohookean one demonstrated the lowest correlation. The values of Young's moduli and other elastic and hyperelastic characteristics of tissues were compared to study the factors affecting the mechanical behavior of human facial skin, and can be used in calculations in finite element analysis and in the development of replacement materials for plastic surgery.

Key words: 
skin
face
Langer lines
elastic properties
hyperelastic models
References: 
  1. Yamaguchi T. Study on the strength of human skin. Journal of Kyoto Prefectural University of Medicine, 1960, vol. 67, pp. 347–379.
  2. Yamada H. Strength of biological materials. Baltimore, Krieger Publ., 1973. 297 p.
  3. Jacquemoud C., Bruyere-Garnier K., Coret M. Methodology to determine failure characteristics of planar soft tissues using a dynamic tensile test. Journal of Biomechanics, 2007, vol. 40, iss. 2, pp. 468–475. https://doi.org/10.1016/j.jbiomech.2005.12.010
  4. Joodaki H., Panzer M. B. Skin mechanical properties and modeling: A review. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, 2018, vol. 232, iss. 4, pp. 323–343. https://doi.org/10.1177/0954411918759801
  5. Laurino C., Palmieri B., Coacci A. Efficacy, safety, and tolerance of a new injection technique for high- and low-molecular-weight hyaluronic acid hybrid complexes. ePlasty, 2015, vol. 15, pp. 427–437.
  6. Lynch B., Pageon H., Le Blay H., Brizion S., Bastien P., Bornschlögl T., Domanov Y. A mechanistic view on the aging human skin through ex vivo layer-by-layer analysis of mechanics and microstructure of facial and mammary dermis. Scientific Reports, 2022, vol. 12, art. 849. https://doi.org/10.1038/s41598-022-04767-1
  7. Fedorov A. E., Samartsev V. A., Kirillova T. A. On mechanical properties of human skin. Russian Journal of Biomechanics, 2006, vol. 10, iss. 2, pp. 29–42 (in Russian). EDN: JWTICT
  8. Griffin M. F., Leung B. C., Premakumar Y., Szarko M., Butler P. E. Comparison of the mechanical properties of different skin sites for auricular and nasal reconstruction. Journal of Otolaryngology – Head & Neck Surgery, 2017, vol. 46, art. 33. https://doi.org/10.1186/s40463-017-0210-6
  9. Wood J. M., Soldin M., Shaw T. J., Szarko М. The biomechanical and histological sequelae of common skin banking methods. Journal of Biomechanics, 2014, vol. 47, iss. 5, pp. 1215–1219. https://doi.org/10.1016/j.jbiomech.2013.12.034
  10. Annaidh A. N., Bruyère K., Destrade M., Gilchrist M. D., Otténio M. Characterizing the anisotropic  mechanical properties of excised human skin. Journal of the Mechanical Behavior of Biomedical Materials, 2012, vol. 5, iss. 1, pp. 139–148. https://doi.org/10.1016/j.jmbbm.2011.08.016
  11. Muslov S. A., Pertsov S. S., Arutyunov S. D. Fiziko-mekhanicheskiye svoystva biologicheskikh tkaney [Physical and mechanical properties of biological tissues]. Moscow, Practiсheskaya Meditsina, 2023. 456 p. (in Russian). EDN: MNOSIQ
  12. Manan N. F. A., Ramli M. H. M., Patar M. N. A. A., Holt C., Evans S., Chizari M. Determining hyperelastic parameters of human skin using 2D finite element modelling and simulation. 2012 IEEE Symposium on Humanities, Science and Engineering Research. Kuala Lumpur, Malaysia, 2012, pp. 805–809. https://doi.org/10.1109/shuser.2012.6268996
  13. Othman N. L. A., Isa K. M., Manssor N. A. S. Hyperelastic models of sheep skin under uniaxial tensile test. Proceedings of Mechanical Engineering Research Day, 2022, vol. 2022, pp. 242–243.
  14. Gasson P., Lapeer R. Fitting hyperelastic material models to stress-strain data from an in-vitro experiment on human skin. Proceedings of the Internation Conference on Polymers and Moulds Innovations (PMI) 17–18 September 2009. Ghent, Belgium, 2009, pp. 127–133.
  15. Azizzati S., Mahmud J. Skin prestretch evaluation adapting Mooney – Rivlin model. Journal of Medical and Bioengineering, 2015, vol. 4, iss. 1, pp. 31–35. https://doi.org/10.12720/jomb.4.1.31-35
  16. Chanda A. Biomechanical modeling of human skin tissue surrogates. Biomimetics, 2018, vol. 3, iss. 3, art. 18. https://doi.org/10.3390/biomimetics3030018
  17. Groves R. B., Coulman S. A., Birchall J. C., Evans S. L. An anisotropic, hyperelastic model for skin: Experimental measurements, finite element modelling and identification of parameters for human and murine skin. Journal of the Mechanical Behavior of Biomedical Materials, 2013, vol. 18, pp. 167–180. https://doi.org/10.1016/j.jmbbm.2012.10.021
  18. Li W., Luo X. Y. An invariant-based damage model for human and animal skins. Annals of Biomedical Engineering, 2016, vol. 44, iss. 10, pp. 3109–3122. https://doi.org/10.1007/s10439-016-1603-9
  19. Flynn C., Taberner A. J., Nielsen P. M. F., Fels S. Simulating the three-dimensional deformation of in vivo facial skin. Journal of the Mechanical Behavior of Biomedical Materials, 2013, vol. 28, pp. 484–494. https://doi.org/10.1016/j.jmbbm.2013.03.004
  20. Flynn C., Taberner A., Nielsen P. Mechanical characterisation of in vivo human skin using a 3D forcesensitive micro-robot and finite element analysis. Biomechanics and Modeling in Mechanobiology, 2011, vol. 10, pp. 27–38. https://doi.org/10.1007/s10237-010-0216-8
  21. Lapeer R. J., Gasson P. D., Karri V. A. Hyperelastic finite-element model of human skin for interactive realtime surgical simulation. IEEE Transactions on Biomedical Engineering, 2011, vol. 58, iss. 4, pp. 1013–1022. https://doi.org/10.1109/tbme.2009.2038364
  22. Browell R., Lin G. The power of nonlinear materials capabilities. Part 1 of 2 on modeling materials with nonlinear characteristics // ANSYS Solutions, 2000, vol. 2, iss. 1. Available at: https://studizba.com/show/1050594-1-ray-browell-the-power-of-nonlinear.html (accessed Seprtember 05, 2023).
  23. Bruyaka V. A. (ed.). Inzhenernyy analiz v Ansys Workbench [Engineering analysis in Ansys Workbench]: tutorial. Part 1. Samara : Samara State Technical University Publ., 2010. 271 p. (in Russian). EDN: QMHFYZ
  24. Liu F., Li C., Liu S., Genin G. M., Huang G., Lu T. J., Xu F. Effect of viscoelasticity on skin pain sensation. Theoretical and Applied Mechanics Letters, 2015, vol. 5, iss. 6, pp. 222–226. https://doi.org/10.1016/j.taml.2015.11.002
  25. Fung Y. C. Biomechanics: Mechanical properties of living tissues. 2nd ed. New York, NY, Springer, 1993. 586 p. https://doi.org/10.1007/978-1-4757-2257-4
  26. Lyamets L. L. Application of exponential polynomials for structural biomechanical analysis of the vascular wall. Mathematical Morphology: Electronic Mathematical and Medical-Biological Journal, 1997, vol. 2, iss. 1, pp. 71–82 (in Russian). EDN: ADBYXD
  27. Markenscoff X., Yannas I. On the stress-strain relation for skin. Journal of Biomechanics, 1979, vol. 12, pp. 127–129. https://doi.org/10.1016/0021-9290(79)90151-9
  28. Shmurak M. I., Kuchumov A. G., Voronova N. O. Hyperelastic models analysis for description of soft human tissues behavior. Master’s Journal, 2017, iss. 1, pp. 230–243 (in Russian). EDN: YUOPFB
  29. Melly S. K., Liu L., Liu Y., Leng J. A review on material models for isotropic hyperelasticity. International Journal of Mechanical System Dynamics, 2021, vol. 1, pp. 71–88. https://doi.org/10.1002/msd2.12013
  30. Kumar N., Rao V. Hyperelastic Mooney – Rivlin Model: Determination and physical interpretation of material constants. MIT International Journal of Mechanical Engineering, 2016, vol. 6, iss. 1, pp. 43–46.
  31. Ogden R. W. Large deformation isotropic elasticity — on the correlation of theory and experiment for incompressible rubberlike solids. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1972, vol. 326, iss. 1567, pp. 565–584. https://doi.org/10.1098/rspa.1972.0026
  32. Shergold O. A., Fleck N. A. Mechanisms of deep penetration of soft solids, with application to the injection and wounding of skin. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 2004, vol. 460, iss. 2050, pp. 3037–3058. https://doi.org/10.1098/rspa.2004.1315
  33. Shergold O. A., Fleck N. A., Radford D. The uniaxial stress versus strain response of pig skin and silicone rubber at low and high strain rates. International Journal of Impact Engineering, 2006, vol. 32, iss 9, pp. 1384–1402. https://doi.org/10.1016/j.ijimpeng.2004.11.010
  34. Lim J., Hong J., Chen W. W., Weerasooriya T. Mechanical response of pig skin under dynamic tensile loading. International Journal of Impact Engineering, 2011, vol. 38, iss. 2–3, pp. 130–135. https://doi.org/10.1016/j.ijimpeng.2010.09.003
  35. Rackl M. Curve fitting for Ogden, Yeoh and polynomial models. ScilabTEC 2015, 7th International Scilab Users Conference. Paris, France, 21st and 22nd May 2015. 18 p.
  36. Calvo-Gallego J. L., Martinez-Reina J., Dominguez J. A polynomial hyperelastic model for the mixture of fat and glandular tissue in female breast. International Journal for Numerical Methods in Biomedical Engineering, 2015, vol. 31, iss. 9, art. e02723. https://doi.org/10.1002/cnm.2723
  37. Lapeer R., Gasson P., Karri V. Simulating plastic surgery: From human skin tensile tests, through hyperelastic finite element models to real-time haptics. Progress in Biophysics and Molecular Biology, 2010, vol. 103, iss. 2–3, pp. 208–216. https://doi.org/10.1016/j.pbiomolbio.2010.09.013
  38. Veronda D., Westmann R. Mechanical characterizations of skin-finite deformations. Journal of Biomechanics, 1970, vol. 3, iss. 1, pp. 111–124. https://doi.org/10.1016/0021-9290(70)90055-2
Received: 
05.10.2023
Accepted: 
04.12.2023
Published: 
28.02.2025
  • 114 reads