Skip to main content

Advertisement

SpringerLink
Log in

The Incompatibility of Living Systems: Characterizing Growth-Induced Incompatibilities in Expanded Skin

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

Skin expansion is a common surgical technique to correct large cutaneous defects. Selecting a successful expansion protocol is solely based on the experience and personal preference of the operating surgeon. Skin expansion could be improved by predictive computational simulations. Towards this goal, we model skin expansion using the continuum framework of finite growth. This approach crucially relies on the concept of incompatible configurations. However, aside from the classical opening angle experiment, our current understanding of growth-induced incompatibilities remains rather vague. Here we visualize and characterize incompatibilities in living systems using skin expansion in a porcine model: We implanted and inflated two expanders, crescent, and spherical, and filled them to 225 cc throughout a period of 21 days. To quantify the residual strains developed during this period, we excised the expanded skin patches and subdivided them into smaller pieces. Skin growth averaged 1.17 times the original area for the spherical and 1.10 for the crescent expander, and displayed significant regional variations. When subdivided into smaller pieces, the grown skin patches retracted heterogeneously and confirmed the existence of incompatibilities. Understanding skin growth through mechanical stretch will allow surgeons to improve—and ultimately personalize—preoperative treatment planning in plastic and reconstructive surgery.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12

Similar content being viewed by others

References

  1. Ambrosi, D., G. A. Ateshian, E. M. Arruda, S. C. Cowin, J. Dumais, A. Goriely, G. A. Holzapfel, J. D. Humphrey, R. Kemkemer, E. Kuhl, J. E. Olberding, L. A. Taber, and K. Garikipati. Perspectives on biological growth and remodeling. J. Mech. Phys. Solids 59:863–883, 2011.

    Article  PubMed  PubMed Central  Google Scholar 

  2. Amini, R., C. E. Eckert, K. Koomalsingh, J. McGarvey, M. Minakawa, J. H. Gorman, R. C. Gorman, and M. S. Sacks. On the in vivo deformation of the mitral valve anterior leaflet: effects of annular geometry and referential configuration. Ann. Biomed. Eng. 40:1455–1467, 2012.

    Article  PubMed  PubMed Central  Google Scholar 

  3. Autodesk 123D Catch. Autodesk, Inc. http://www.123dapp.com/catch, 2014.

  4. Bao, G., Y. Bazilevs, J. H. Chung, P. Decuzzi, H. D. Espinosa, M. Ferrari, H. Gao, S. S. Hossain, T. J. R. Hughes, R. D. Kamm, W. K. Liu, A. Marsden, and B. Schrefler. USNCTAM perspectives on mechanics in medicine. J. R. Soc. Interface 11(97):20140301, 2014.

    Article  PubMed  PubMed Central  Google Scholar 

  5. Bartell, T. H., and T. A. Mustoe. Animal models of human tissue expansion. Plast. Reconstr. Surg. 83:681–686, 1989.

    Article  CAS  PubMed  Google Scholar 

  6. Beauchene, J. G., M. M. Chambers, A. E. Peterson, and P. G. Scott. Biochemical, biomechanical, and physical changes in the skin in an experimental animal model of therapeutic tissue expansion. J. Surg. Res. 47(6):507–514, 1989.

    Article  CAS  PubMed  Google Scholar 

  7. Belkoff, S. M., E. C. Naylor, R. Walshaw, E. Lanigan, L. Colony, and R. C. Haut. Effects of subcutaneous expansion on the mechanical properties of porcine skin. J. Surg. Res. 58(2):117–123, 1995.

    Article  CAS  PubMed  Google Scholar 

  8. Bhandari, P. S. Mathematical calculations in a spherical tissue expander. Ann. Plast. Surg. 62(2):200–204, 2009.

    Article  CAS  PubMed  Google Scholar 

  9. Brobmann, F., and J. Huber. Effects of different-shaped tissue expanders on transluminal pressure, oxygen tension, histopathologic changes, and skin expansion in pigs. Plast. Reconstr. Surg. 76(5):731–736, 1985.

    Article  CAS  PubMed  Google Scholar 

  10. Buganza Tepole, A., M. Gart, A. K. Gosain, and E. Kuhl. Characterization of living skin using multi view stereo and isogeometric analysis. Acta Biomat. 10:4822–4831, 2014.

    Article  Google Scholar 

  11. Buganza Tepole, A., M. Gart, C. A. Purnell, A. K. Gosain, and E. Kuhl. Multi-view stereo analysis reveals anisotropy of prestrain, deformation, and growth in living skin. Biomech. Model. Mechanobiol. 14(5):1007–1019, 2015.

    Article  PubMed  Google Scholar 

  12. Buganza Tepole, A., A. K. Gosain, and E. Kuhl. Stretching skin: the physiological limit and beyond. Int. J. Nonlinear Mech. 2012(47):938–949, 2012.

    Article  Google Scholar 

  13. Buganza Tepole, A., A. K. Gosain, and E. Kuhl. Computational modeling of skin: using stress profiles as predictor for tissue necrosis in reconstructive surgery. Comput. Struct. 143:32–39, 2014.

    Article  Google Scholar 

  14. Buganza Tepole, A., H. Kabaria, K. U. Bletzinger, and E. Kuhl. Isogeometric Kirchhoff-Love shell formulations for biological membranes. Comput. Methods Appl. Mech. Eng. 293(15):328–347, 2015.

    Article  Google Scholar 

  15. Buganza Tepole, A., C. J. Ploch, J. Wong, A. K. Gosain, and E. Kuhl. Growin skin: a computational model for skin expansion in reconstructive surgery. J. Mech. Phys. Solids 59:2177–2190, 2011.

    Article  Google Scholar 

  16. Cyganek, B., and J. P. Siebert. An Introduction to 3D Computer Vision Techniques and Algorithms. West Sussex: Wiley, 2009.

    Book  Google Scholar 

  17. Daly, C. H. Biomechanical properties of dermis. J. Invest. Dermatol. 79:17–20, 1982.

    Article  CAS  Google Scholar 

  18. De Filippo, R. E., and A. Atala. Stretch and growth: the molecular and physiologic influences of tissue expansion. Plast. Reconstr. Surg. 109:2450–2462, 2002.

    Article  PubMed  Google Scholar 

  19. Famaey, N., and J. Vander Sloten. Soft tissue modelling for applications in virtual surgery and surgical robotics. Comput. Methods Biomech. Biomed. Eng. 11:351–366, 2008.

    Article  Google Scholar 

  20. Fu, S., J. Fan, L. Liu, H. Jiao, C. Gan, J. Tian, W. Chen, Z. Yang, and Z. Yin. A uniaxial cell stretcher in vitro model simulating tissue expansion of plastic surgery. J. Craniofac. Surg. 24(4):1431–1435, 2013.

    Article  PubMed  Google Scholar 

  21. Furukawa, Y., and J. Ponce. Accurate, dense, and robust multi view stereopsis. IEEE Trans. Pattern Anal. 32:1362–1376, 2010.

    Article  Google Scholar 

  22. Genet, M., M. K. Rausch, L. C. Lee, S. Choy, X. Zhao, G. S. Kassab, S. Kozerke, J. M. Guccione, and E. Kuhl. Heterogeneous growth-induced prestrain in the heart. J. Biomech. 48(10):2080–2089, 2015.

    Article  CAS  PubMed  Google Scholar 

  23. Göktepe, S., O. J. Abilez, K. K. Parker, and E. Kuhl. A generic approach towards finite growth with examples of athlete’s heart, cardiac dilation, and cardiac wall thickening. J. Mech. Phys. Solids 58:1661–1680, 2010.

    Article  Google Scholar 

  24. Gosain, A. K., T. D. Santoro, D. L. Larson, and R. P. Gingrass. Giant congenital nevi: a 20-year experience and an algorithm for their management. Plast. Reconstr. Surg. 108:622–636, 2001.

    Article  CAS  PubMed  Google Scholar 

  25. Gosain, A. K., C. G. Zochowski, and W. Cortes. Refinements of tissue expansion for pediatric forehead reconstruction: a 13-year experience. Plast. Reconstr. Surg. 124(5):1559–1570, 2009.

    Article  CAS  PubMed  Google Scholar 

  26. Hiep, V., Keriven, P., Labatut, P., and J. P. Pons. Towards high-resolution large-scale multi view stereo. In: IEEE Conference on CVPR, 2009.

  27. Hughes, T. J. R., J. A. Cottrell, and Y. Bazilevs. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Eng. 194:4135–4195, 2005.

    Article  Google Scholar 

  28. Johnson, P. E., D. A. Kernahan, and B. S. Bauer. Dermal and epidermal response to soft-tissue expansion in the pig. Plast. Reconstr. Surg. 81:390–395, 1988.

    Article  CAS  PubMed  Google Scholar 

  29. Jor, J. W. Y., M. P. Nash, P. M. F. Nielsen, and P. J. Hunter. Estimating material parameters of a structurally based constitutive relation for skin mechanics. Biomech. Model. Mechanobiol. 10:767–778, 2010.

    Article  PubMed  Google Scholar 

  30. Jor, J. W. Y., M. D. Parker, A. J. Taberner, M. P. Nash, and P. M. F. Nielsen. Computational and experimental characterization of skin mechanics: identifying current challenges and future directions. Wiley Interdiscip. Rev. Syst. Biol. Med. 5:539–556, 2013.

    Article  PubMed  Google Scholar 

  31. Khalatbari, B., and A. Bakhshaeekia. Ten-year experience in face and neck unit reconstruction using tissue expanders. Burns 39(3):522–527, 2013.

    Article  PubMed  Google Scholar 

  32. Kuhl, E. Growing matter—a review of growth in living systems. J. Mech. Behav. Biomed. Mater. 29:529–543, 2014.

    Article  PubMed  Google Scholar 

  33. Langer, K. Zur Anatomie und Physiologie der Haut. I. Über die Spaltbarkeit der Cutis. Sitzungsbericht der mathematisch-naturwissenschaftlichen Classe der Kaiserlichen Academie der Wissenschaften, 1861, Abt. 44.

  34. Lim, K. H., S. Jeyapalina, H. N. Ho, C. M. Chew, P. C. Y. Chen, C. L. Teo, and B. H. Lim. Non-invasive prediction of skin flap shrinkage: a new concept based on animal experimental evidence. J. Biomech. 41:1668–1674, 2008.

    Article  CAS  PubMed  Google Scholar 

  35. Liu, S. Q., and Y. C. Fung. Relationships between hypertension, hypertrophy, and opening angle of zero-stress state of arteries following aortic constriction. J. Biomech. Eng. 111:325–335, 1989.

    Article  CAS  PubMed  Google Scholar 

  36. LoGiudice, J., and A. K. Gosain. Pediatric tissue expansion: indications and complications. J. Craniofac. Surg. 14:866–872, 2003.

    Article  PubMed  Google Scholar 

  37. Manders, E. K., M. J. Schenden, J. A. Furrey, P. T. Hetzler, T. S. Davis, and W. P. Graham. Soft-tissue expansion: concepts and complications. Plast. Reconstr. Surg. 74:493–507, 1984.

    Article  CAS  PubMed  Google Scholar 

  38. Marcus, J., D. Horan, and J. Robinson. Tissue expansion: past, present and future. J. Am. Acad. Dermatol. 23:813–825, 1990.

    Article  CAS  PubMed  Google Scholar 

  39. Menzel, A. Modelling of anisotropic growth in biological tissues. Biomech. Model. Mechanobiol. 3:147–171, 2005.

    Article  CAS  PubMed  Google Scholar 

  40. Menzel, A., and E. Kuhl. Frontiers in growth and remodeling. Mech. Res. Commun. 42:1–14, 2012.

    Article  PubMed  PubMed Central  Google Scholar 

  41. Meyer, W., K. Neurand, and B. Radke. Elastic fibre arrangement in the skin of the pig. Arch. Dermatol. Res. 270:391–401, 1981.

    Article  CAS  PubMed  Google Scholar 

  42. Meyer, W., K. Neurand, and B. Radke. Collagen fibre arrangement in the skin of the pig. J. Anat. 134:139–148, 1982.

    CAS  PubMed  PubMed Central  Google Scholar 

  43. Montagna, W., and J. S. Yun. The skin of the domestic pig. J. Invest. Dermatol. 43:11–21, 1964.

    Article  Google Scholar 

  44. Morykwas, M. J., M. W. Marks, and L. C. Argenta. Surface area and tissue volume increases with differential expansion. Ann. Plast. Surg. 28:311–314, 1992.

    Article  CAS  PubMed  Google Scholar 

  45. Neumann, C. G. The expansion of an area of skin by progressive distension of a subcutaneous balloon. Plast. Reconstr. Surg. 19:124–130, 1957.

    Article  CAS  Google Scholar 

  46. Nikkhah, D., L. Yildirimer, and N. W. Bulstrode. Tissue Expansion. Plastic and Reconstructive Surgery: Approaches and Techniques. Hoboken: Wiley, 2015.

    Google Scholar 

  47. Osman, O. S., J. L. Selway, P. E. Harikumar, C. J. Stocker, E. T. Wargent, M. A. Cawthorne, S. Jassim, and K. Langlands. A novel method to assess collagen architecture in skin. BMC Bioinformatics 14(1):260, 2013.

    Article  PubMed  PubMed Central  Google Scholar 

  48. Pamplona, D. C., and C. R. Carvalho. Characterization of human skin through skin expansion. J. Mech. Mater. Struct. 7:641–655, 2012.

    Article  Google Scholar 

  49. Pamplona, D. C., and D. E. J. S. Mota. Numerical and experimental analysis of inflating a circular hyperelastic membrane over a rigid and elastic foundation. Int. J. Mech. Sci. 65:18–23, 2012.

    Article  Google Scholar 

  50. Pamplona, D. C., R. Q. Velloso, and H. N. Radwanski. On skin expansion. J. Mech. Behav. Biomed. Mater. 29:655–662, 2014.

    Article  CAS  PubMed  Google Scholar 

  51. Piegl, L., and W. Tiller. Curve and surface constructions using rational B-splines. Comput. Aided Des. 19:485–498, 1987.

    Article  Google Scholar 

  52. Pietramaggiori, G., P. Liu, S. S. Scherer, A. Kaipainen, M. J. Prsa, H. Mayer, J. Newalder, M. Alperovich, S. J. Mentzer, M. A. Konerding, S. Huang, D. E. Ingber, and D. P. Orgill. Tensile forces stimulate vascular remodeling and epidermal cell proliferation in living skin. Ann. Surg. 246:896–902, 2007.

    Article  PubMed  Google Scholar 

  53. Rausch, M. K., N. Famaey, T. O’Brien Shultz, W. Bothe, D. C. Miller, and E. Kuhl. Mechanics of the mitral valve: a critical review, an in vivo parameter identification, and the effect of prestrain. Biomech. Model. Mechanobiol. 12:1053–1071, 2013.

    Article  PubMed  PubMed Central  Google Scholar 

  54. Rausch, M. K., and E. Kuhl. On the effect of prestrain and residual stress in thin biological membranes. J. Mech. Phys. Solids 61:1955–1969, 2013.

    Article  PubMed  PubMed Central  Google Scholar 

  55. Rivera, R., J. LoGiudice, and A. K. Gosain. Tissue expansion in pediatric patients. Clin. Plast. Surg. 32:35–44, 2005.

    Article  PubMed  Google Scholar 

  56. Rodreiguez, E. K., A. Hoger, and A. D. McCulloch. Stress-dependent finite growth in soft elastic tissues. J. Biomech. 27:455–467, 1994.

    Article  Google Scholar 

  57. Rose, E. H., G. A. Ksander, and L. M. Vistnes. Skin tension lines in the domestic pig. Plast. Reconstr. Surg. 57:729–732, 1976.

    Article  CAS  PubMed  Google Scholar 

  58. Seitz, S. M., B. Curless, J. Diebel, D. Scharstein, and R. Szeliski. A comparison and evaluation of multi-view stereo reconstruction algorithms. IEEE Conf. CVPR. 1:519–528, 2006.

    Google Scholar 

  59. Shively, R. E. Skin expander volume estimator. Plast. Reconstr. Surg. 77:482–483, 1986.

    Article  CAS  PubMed  Google Scholar 

  60. Silver, F. H., L. M. Siperko, and G. P. Seehra. Mechanobiology of force transduction in dermal tissue. Skin Res. Technol. 9:3–23, 2003.

    Article  PubMed  Google Scholar 

  61. Socci, L., G. Pennati, F. Gervaso, and P. Vena. An axisymmetric computational model of skin expansion and growth. Biomech. Model. Mechanobiol. 6:177–188, 2007.

    Article  CAS  PubMed  Google Scholar 

  62. Taber, L. Biomechanics of growth, remodeling, and morphogenesis. Appl. Mech. Rev. 48:487–545, 1995.

    Article  Google Scholar 

  63. Tonge, T. K., L. S. Atlan, L. M. Voo, and T. D. Nguyen. Full-field bulge test for planar anisotropic tissues: Part I: Experimental methods applied to human skin tissue. Acta Biomater. 9(4):5913–5925, 2013.

    Article  PubMed  Google Scholar 

  64. Tong, P., and Y. C. Fung. The stress-strain relationship for the skin. J. Biomech. 9:649–657, 1976.

    Article  CAS  PubMed  Google Scholar 

  65. van Rappard, J. H. A., J. Molenaar, K. van Doorn, G. J. Sonneveld, and J. M. H. M. Borghouts. Surface-area increase in tissue expansion. Plast. Reconstr. Surg. 82:833–839, 1988.

    Article  PubMed  Google Scholar 

  66. Wang, J. H. C., B. P. Thampatty, J. S. Lin, and H. J. Im. Mechanoregulation of gene expression in fibroblasts. Gene 391:1–15, 2007.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  67. Wong, V. W., K. Levi, S. Akaishi, G. Schultz, and R. H. Dauskardt. Scar zones: region-specific differences in skin tension may determine incisional scar formation. Plast. Reconstr. Surg. 129:1272–1276, 2012.

    Article  CAS  PubMed  Google Scholar 

  68. Zeng, Y. J., Y. H. Liu, C. Q. Xu, X. H. Xu, H. Xu, and G. C. Sun. Biomechanical properties of skin in vitro for different expansion methods. Clin. Biomech. 19:853–857, 2004.

    Article  Google Scholar 

  69. Zöllner, A. M., A. Buganza Tepole, A. K. Gosain, and E. Kuhl. Growing skin—tissue expansion in pediatric forehead reconstruction. Biomech. Model. Mechanobiol. 11:855–867, 2012.

    Article  PubMed  PubMed Central  Google Scholar 

  70. Zöllner, A. M., A. Buganza Tepole, and E. Kuhl. On the biomechanics and mechanobiology of growing skin. J. Theor. Biol. 297:166–175, 2012.

    Article  PubMed  PubMed Central  Google Scholar 

  71. Zöllner, A. M., M. A. Holland, K. S. Honda, A. K. Gosain, and E. Kuhl. Growth on demand—reviewing the mechanobiology of stretched skin. J. Mech. Behav. Biomed. Mater. 28:495–509, 2013.

    Article  PubMed  Google Scholar 

Download references

Acknowledgments

This work was supported by the CONACyT Fellowship, the Stanford Graduate Fellowship, and the DARE Doctoral Fellowship to Adrian Buganza Tepole and by the National Science Foundation CAREER award CMMI 0952021, by the National Science Foundation INSPIRE Grant 1233054, and by the National Institutes of Health Grant U01 HL119578 to Ellen Kuhl.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Stanford University, Stanford, CA, 94305, USA

    Adrian Buganza Tepole

  2. Lurie Children’s Hospital, Northwestern University Feinberg School of Medicine, Chicago, IL, 60611, USA

    Michael Gart, Chad A. Purnell & Arun K. Gosain

  3. Departments of Mechanical Engineering, Bioengineering, and Cardiothoracic Surgery, Stanford University, Stanford, CA, 94305, USA

    Ellen Kuhl

Authors
  1. Adrian Buganza Tepole
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael Gart
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chad A. Purnell
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Arun K. Gosain
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ellen Kuhl
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Adrian Buganza Tepole.

Additional information

Associate Editor Michael Gower oversaw the review of this article.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Buganza Tepole, A., Gart, M., Purnell, C.A. et al. The Incompatibility of Living Systems: Characterizing Growth-Induced Incompatibilities in Expanded Skin. Ann Biomed Eng 44, 1734–1752 (2016). https://doi.org/10.1007/s10439-015-1467-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-015-1467-4

Keywords

Search

Navigation