Biomechanics and Modeling in Mechanobiology

, Volume 11, Issue 6, pp 855–867 | Cite as

Growing skin: tissue expansion in pediatric forehead reconstruction

  • Alexander M. Zöllner
  • Adrian Buganza Tepole
  • Arun K. Gosain
  • Ellen KuhlEmail author
Original Paper


Tissue expansion is a common surgical procedure to grow extra skin through controlled mechanical over-stretch. It creates skin that matches the color, texture, and thickness of the surrounding tissue, while minimizing scars and risk of rejection. Despite intense research in tissue expansion and skin growth, there is a clear knowledge gap between heuristic observation and mechanistic understanding of the key phenomena that drive the growth process. Here, we show that a continuum mechanics approach, embedded in a custom-designed finite element model, informed by medical imaging, provides valuable insight into the biomechanics of skin growth. In particular, we model skin growth using the concept of an incompatible growth configuration. We characterize its evolution in time using a second-order growth tensor parameterized in terms of a scalar-valued internal variable, the in-plane area growth. When stretched beyond the physiological level, new skin is created, and the in-plane area growth increases. For the first time, we simulate tissue expansion on a patient-specific geometric model, and predict stress, strain, and area gain at three expanded locations in a pediatric skull: in the scalp, in the forehead, and in the cheek. Our results may help the surgeon to prevent tissue over-stretch and make informed decisions about expander geometry, size, placement, and inflation. We anticipate our study to open new avenues in reconstructive surgery and enhance treatment for patients with birth defects, burn injuries, or breast tumor removal.


Growth Residual stress Finite element analysis Skin Tissue expansion Reconstructive surgery 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Agache PG, Monneur C, Leveque JL, DeRigal J (1980) Mechanical properties and Young’s modulus of human skin in vivo. Arch Dermatol Res 269: 221–232CrossRefGoogle Scholar
  2. Ambrosi D, Ateshian GA, Arruda EM, Cowin SC, Dumais J, Goriely A, Holzapfel GA, Humphrey JD, Kemkemer R, Kuhl E, Olberding JE, Taber LA, Garikipati K (2011) on biological growth and remodeling. J Mech Phys Solids 59: 863–883MathSciNetCrossRefGoogle Scholar
  3. Argenta LC, Watanabe MJ, Grabb WC (1983) The use of tissue expansion in head and neck reconstruction. Ann Plast Surg 11: 31–37CrossRefGoogle Scholar
  4. Arneja JS, Gosain AK (2005) Giant congenital melanocytic nevi of the trunk and an algorithm for treatment. J Craniofac Surg 16: 886–893CrossRefGoogle Scholar
  5. Arneja JS, Gosain AK (2007) Giant congenital melanocytic nevi. Plast Reconstr Surg 120: 26e–40eCrossRefGoogle Scholar
  6. Barone FE, Perry L, Keller T, Maxwell GP (1992) The biomechanical and histopathologic effect of surface texturing with silicone and polyurethane in tissue implantation and expansion. Plast Reconstr Surg 90: 77–86CrossRefGoogle Scholar
  7. Bernardini F, Mittleman J, Rushmeiner H, Silva C, Taubin G (1999) The ball-pivoting algorithm for surface reconstruction. IEEE Trans Vis Comp Graph 5: 349–359CrossRefGoogle Scholar
  8. Buganza Tepole A, Ploch CJ, Wong J, Gosain AK, Kuhl E (2011) Growing skin—a computational model for skin expansion in reconstructive surgery. J Mech Phys Solids 59: 2177–2190MathSciNetCrossRefGoogle Scholar
  9. Buganza Tepole A, Gosain AK, Kuhl E (2012) Stretching skin: the physiological limit and beyond. Int J Non-linear Mech. doi: 10.1016/j.ijnonlinmec.2011.07.006
  10. Castilla EE, daGraca Dutra M, Orioli-Parreiras IM (1981) Epidermiology of congenital pigmented naevi: I. Incidence rates and relative frequencies. Br J Dermatol 104: 307–315CrossRefGoogle Scholar
  11. De Filippo RE, Atala A (2002) Stretch and growth: the molecular and physiologic influences of tissue expansion. Plast Reconstr Surg 109: 2450–2462CrossRefGoogle Scholar
  12. Dervaux J, Ciarletta P, Ben Amar M (2009) Morphogenesis of thin hyperelastic plates: a constitutive theory of biological growth in the Föppl-von Karman limit. J Mech Phys Solids 57: 458–471MathSciNetzbMATHCrossRefGoogle Scholar
  13. Duits EHA, Molenaar J, van Rappard JHA (1989) The modeling of skin expanders. Plast Reconstr Surg 83: 362–367CrossRefGoogle Scholar
  14. Epstein M, Maugin GA (2000) Thermomechanics of volumetric growth in uniform bodies. Int J Plast 16: 951–978zbMATHCrossRefGoogle Scholar
  15. Garikipati K (2009) The kinematics of biological growth. Appl Mech Rev 62: 0308011–0308017CrossRefGoogle Scholar
  16. Göktepe S, Abilez OJ, Parker KK, Kuhl E (2010) A multiscale model for eccentric and concentric cardiac growth through sarcomerogenesis. J Theor Biol 265: 433–442CrossRefGoogle Scholar
  17. Göktepe S, Abilez OJ, Kuhl E (2010) A generic approach towards finite growth with examples of athlete’s heart, cardiac dilation, and cardiac wall thickening. J Mech Phys Solids 58: 1661–1680MathSciNetzbMATHCrossRefGoogle Scholar
  18. Goriely A, BenAmar M (2005) Differential growth and instability in elastic shells. Phys Rev Lett 94: 198103CrossRefGoogle Scholar
  19. Goriely A, BenAmar M (2007) On the definition and modeling of incremental, cumulative, and continuous growth laws in morphoelasticity. Biomech Model Mechanobiol 6: 289–296CrossRefGoogle Scholar
  20. Gosain AK, Santoro TD, Larson DL, Gingrass RP (2001) Giant congenital nevi: a 20-year experience and an algorithm for their management. Plast Reconstr Surg 108: 622–636CrossRefGoogle Scholar
  21. Gosain AK, Zochowski CG, Cortes W (2009) Refinements of tissue expansion for pediatric forehead reconstruction: a 13-year experience. Plast Reconstr Surg 124: 1559–1570CrossRefGoogle Scholar
  22. Himpel G, Kuhl E, Menzel A, Steinmann P (2005) Computational modeling of isotropic multiplicative growth. Comp Mod Eng Sci 8: 119–134zbMATHGoogle Scholar
  23. Kaplan EN (1974) The risk of malignancy in large congenital nevi. Plast Reconstr Surg 53: 421–428CrossRefGoogle Scholar
  24. Kobbelt LP, Vorsatz J, Labsik U, Seidel HP (1999) A shrink wrapping approach to remeshing polygonal surfaces. Comp Graph Forum 18: 119–130CrossRefGoogle Scholar
  25. Kroon W, Delhaas T, Arts T, Bovendeerd P (2009) Computational modeling of volumetric soft tissue growth: Application to the cardiac left ventricle. Biomech Model Mechanobiol 8: 301–309CrossRefGoogle Scholar
  26. Kuhl E, Steinmann P (2003a) Mass- and volume specific views on thermodynamics for open systems. Proc Royal Soc 459: 2547–2568MathSciNetzbMATHCrossRefGoogle Scholar
  27. Kuhl E, Steinmann P (2003b) On spatial and material settings of thermohyperelstodynamics for open systems. Acta Mech 160: 179–217zbMATHCrossRefGoogle Scholar
  28. Kuhl E, Menzel A, Steinmann P (2003) Computational modeling of growth - A critical review, a classification of concepts and two new consistent approaches. Comp Mech 32: 71–88zbMATHCrossRefGoogle Scholar
  29. Kuhl E, Steinmann P (2004) Computational modeling of healing—an application of the material force method. Biomech Model Mechanobiol 2: 187–203CrossRefGoogle Scholar
  30. Kuhl E, Garikipati K, Arruda EM, Grosh K (2005) Remodeling of biological tissue: mechanically induced reorientation of a transversely isotropic chain network. J Mech Phys Solids 53: 1552–1573MathSciNetzbMATHCrossRefGoogle Scholar
  31. Kuhl E, Menzel A, Garikipati K (2006) On the convexity of transversely isotropic chain network models. Philos Mag 86: 3241–3258CrossRefGoogle Scholar
  32. Kuhl E, Maas R, Himpel G, Menzel A (2007) Computational modeling of arterial wall growth: attempts towards patient-specific simulations based on computer tomography. Biomech Model Mechanobiol 6: 321–331CrossRefGoogle Scholar
  33. Kuhl E, Holzapfel GA (2007) A continuum model for remodeling in living structures. J Mater Sci 2: 8811–8823CrossRefGoogle Scholar
  34. Lee EH (1969) Elastic-plastic deformation at finite strains. J Appl Mech 36: 1–6zbMATHCrossRefGoogle Scholar
  35. Levi K, Kwan A, Rhines AS, Gorcea M, Moore DJ, Dauskardt RH (2010) Emollient molecule effects on the drying stresses in human stratum corneum. Br J Dermatol 163: 695–703CrossRefGoogle Scholar
  36. LoGiudice J, Gosain AK (2003) Pediatric tissue expansion: indications and complications. J Craniofac Surg 14: 866–872CrossRefGoogle Scholar
  37. Lubarda VA, Hoger A (2002) On the mechanics of solids with a growing mass. Int J Solids & Structures 39: 4627–4664zbMATHCrossRefGoogle Scholar
  38. Lubarda VA (2004) Constitutive theories based on the multiplicative decomposition of deformation gradient: thermoelasticity, elastoplasticity and biomechanics. Appl Mech Rev 57: 95–108CrossRefGoogle Scholar
  39. Mazza E, Papes O, Rubin MB, Bodner SR, Binur NS (2005) Nonlinear elastic-viscoplastic constitutive equations for aging facial tissues. Biomech Model Mechanobiol 4: 178–189CrossRefGoogle Scholar
  40. McMahon J, Goriely A (2010) Spontaneous cavitation in growing elastic membranes. Math Mech Solids 15: 57–77MathSciNetzbMATHCrossRefGoogle Scholar
  41. Menzel A (2005) Modelling of anisotropic growth in biological tissues—a new approach and computational aspects. Biomech Model Mechanobiol 3: 147–171CrossRefGoogle Scholar
  42. Menzel A (2007) A fibre reorientation model for orthotropic multiplicative growth. Biomech Model Mechanobiol 6: 303–320CrossRefGoogle Scholar
  43. Neumann CG (1959) The expansion of an area of skin by progressive distension of a subcutaneous balloon; use of the method for securing skin for subtotal reconstruction of the ear. Plast Reconstr Surg 19: 124–130CrossRefGoogle Scholar
  44. Pang H, Shiwalkar AP, Madormo CM, Taylor RE, Andriacchi TP, Kuhl E (2012) Computational modeling of bone density profiles in response to gait: a subject-specific approach. Biomech Model Mechanobiol. doi: 10.1007/s10237-011-0318-y
  45. Quaba AA, Wallace AF (1986) The incidence of malignant melanoma (0 to 15 years of age) arising in large congenital nevocellular nevi. Plast Reconstr Surg 78: 174–178CrossRefGoogle Scholar
  46. Radovan C (1982) Breast reconstruction after mastectomy using the temporary expander. Plast Reconstr Surg 69: 195–208CrossRefGoogle Scholar
  47. Rausch MK, Bothe W, Kvitting JP, Göktepe S, Miller DC, Kuhl E (2011a) In vivo dynamic strains of the ovine anterior mitral valve leaflet. J Biomech 44: 1149–1157CrossRefGoogle Scholar
  48. Rausch MK, Dam A, Göktepe S, Abilez OJ, Kuhl E (2011b) Computational modeling of growth: systemic and pulmonary hypertension in the heart. Biomech Model Mechanobiol. doi: 10.1007/s10237-010-0275-x
  49. Rivera R, LoGiudice J, Gosain AK (2005) Tissue expansion in pediatric patients. Clin Plast Surg 32: 35–44CrossRefGoogle Scholar
  50. Rodriguez EK, Hoger A, McCulloch AD (1994) Stress-dependent finite growth in soft elastic tissues. J Biomech 27: 455–467CrossRefGoogle Scholar
  51. Schmid H, Pauli L, Paulus A, Kuhl E, Itskov M (2011) How to utilise the kinematic constraint of incompressibility for modelling adaptation of soft tissues.Comp Meth Biomech Biomed Eng. doi: 10.1080/10255842.2010.548325
  52. Serup J, Jemec GBE, Grove GL (2003) Handbook of Non-Invasive Methods and the Skin. Informa HealthcareGoogle Scholar
  53. Shively RE (1986) Skin expander volume estimator. Plast Reconstr Surg 77: 482–483CrossRefGoogle Scholar
  54. Silver FH, Siperko LM, Seehra GP (2003) Mechanobiology of force transduction in dermal tissue. Skin Res Tech 9: 3–23CrossRefGoogle Scholar
  55. Socci L, Pennati G, Gervaso F, Vena P (2007) An axisymmetric computational model of skin expansion and growth. Biomech Model Mechanobiol 6: 177–188CrossRefGoogle Scholar
  56. Taber LA (1995) Biomechanics of growth, remodeling and morphogenesis. Appl Mech Rev 48: 487–545CrossRefGoogle Scholar
  57. Takei T, Mills I, Arai K, Sumpio BE (1998) Molecular basis for tissue expansion: clinical implications for the surgeon. Plast Reconstr Surg 102: 247–258CrossRefGoogle Scholar
  58. Taylor RL (2011) FEAP - A Finite Element Analysis Program. Version 8.3, User Manual, University of California at BerkeleyGoogle Scholar
  59. van der Kolk CA, McCann JJ, Knight KR, O’Brien BM (1987) Some further characteristics of expanded tissue. Clin Plast Surg 14: 447–453Google Scholar
  60. van Rappard JHA, Molenaar J, van Doorn K, Sonneveld GJ, Borghouts JMHM (1988) Surface-area increase in tissue expansion. Plast Reconstr Surg 82: 833–839CrossRefGoogle Scholar
  61. Wollina U, Berger U, Stolle C, Stolle H, Schubert H, Zieger M, Hipler C, Schumann D (1992) Tissue expansion in pig skin—a histochemical approach. Anat Histol Embryol 21: 101–111CrossRefGoogle Scholar
  62. Wu KS, van Osdol WW, Dauskardt RH (2006) Mechanical properties of human stratum corneum: effects of temperature, hydration, and chemical treatment. Biomaterials 27: 785–795CrossRefGoogle Scholar
  63. Zeng Y, Xu C, Yang J, Sun G, Xu X (2003) Biomechanical comparison between conventional and rapid expansion of skin. Br Assoc Plast Surg 56: 660–666CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Alexander M. Zöllner
    • 1
  • Adrian Buganza Tepole
    • 1
  • Arun K. Gosain
    • 2
  • Ellen Kuhl
    • 1
    • 3
    • 4
    Email author
  1. 1.Department of Mechanical EngineeringStanford UniversityStanfordUSA
  2. 2.Rainbow Babies and Children’s Hospital, Case Western Reserve UniversityClevelandUSA
  3. 3.Department of BioengineeringStanford UniversityStanfordUSA
  4. 4.Department of Cardiothoracic SurgeryStanford UniversityStanfordUSA

Personalised recommendations