Abstract
Skin, like all biological materials, adapts to mechanical cues. When expanded beyond its physiological regime over extended time periods, skin grows. This intuitive knowledge has been leveraged clinically in a widely used surgical technique called tissue expansion, in which a surgeon inserts a balloon-like device and inflates it gradually over months to grow skin for reconstructive purposes. However, it is currently not possible to anticipate how much of the deformation due to the expander is growth and how much of it is elastic strain, and tissue expansion protocols remain arbitrary, based on each physician’s experience and training, leading to an unacceptable frequency of complications. Here we show a continuum mechanics framework to describe skin growth based on the multiplicative split of the deformation gradient in to growth and elastic tensors. We present the corresponding finite element implementation, in which the growth component is an internal variable stored and updated at the integration points of the finite element mesh. The model is applied to study the deformation and growth patterns of skin for different expander shapes, as well as in patient specific scenarios, showing excellent qualitative agreement with clinical experience. Experimental methods to calibrate and validate the translation of the model to the clinical setting are briefly discussed. We expect that the proposed modeling framework will increase our fundamental understanding of how skin grows in response to stretch, and it will soon lead to personalized treatment plans to achieve the desired patterns of skin growth while minimizing complications.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Taber LA (1995) Biomechanics of growth, remodeling, and morphogenesis. Appl Mech Rev 48:487
Marcus J, Horan DB, Robinson JK (1990) Tissue expansion: past, present, and future. J Am Acad Dermatol 23:813–825
Neumann CG (1957) The expansion of an area of skin by progressive distention of a subcutaneousballoon: use of the method for securing skin for subtotal reconstruction of the ear. Plast Reconstr Surg 19:124–130
Manders EK, Schenden MJ, Furrey JA, Hetzler PT, Davis TS, Graham WP (1984) Soft-tissue expansion: concepts and complications. Plast Reconstr Surg 74(4):493–507
Bozkurt A, Groger A, O’Dey D, Vogeler F, Piatkowski A, Fuchs PC et al (2008) Retrospective analysis of tissue expansion in reconstructive burn surgery: evaluation of complication rates. Burns 34:1113–1118
LoGiudice J, Gosain AK (2003) Pediatric tissue expansion: indications and complications. J Craniofac Surg 14:866
Khalatbari B, Bakhshaeekia A (2013) Ten-year experience in face and neck unit reconstruction using tissue expanders. Burns 39:522–527
Gosain AK, Zochowski CG, Cortes W (2009) Refinements of tissue expansion for pediatric forehead reconstruction: a 13-year experience. Plast Reconstr Surg 124:1559–1570
Baker SR (1991) Fundamentals of expanded tissue. Head Neck 13:327–333
Pusic AL, Cordeiro PG (2003) An accelerated approach to tissue expansion for breast reconstruction: experience with intraoperative and rapid postoperative expansion in 370 reconstructions. Plast Reconstr Surg 111:1871–1875
Ronert MA, Hofheinz H, Manassa E, Asgarouladi H, Olbrisch RR (2004) The beginning of a new era in tissue expansion: self-filling osmotic tissue expander—four-year clinical experience. Plast Reconstr Surg 114:1025–1031
Schmidt SC, Logan SE, Hayden JM, Ahn ST, Mustoe TA (1991) Continuous versus conventional tissue expansion: experimental verification of a new technique. Plast Reconstr Surg 87:10–15
Gosain AK, Chepla KJ (2012) Giant nevus sebaceus: definition, surgical techniques, and rationale for treatment. Plast Reconstr Surg 130:296e–304e
Buganza Tepole A, Gart M, Purnell CA, Gosain AK, Kuhl E (2015) Multi-view stereo analysis reveals anisotropy of prestrain, deformation, and growth in living skin. Biomech Model Mechanobiol 14:1007–1019
De Filippo RE, Atala A (2002) Stretch and growth: the molecular and physiologic influences of tissue expansion. Plast Reconstr Surg 109:2450–2462
Buganza Tepole A, Gart M, Gosain AK, Kuhl E (2014) Characterization of living skin using multi-view stereo and isogeometric analysis. Acta Biomater 10:4822–4831
Eyckmans J, Boudou T, Yu X, Chen CS (2011) A hitchhiker’s guide to mechanobiology. Dev Cell 21:35–47
McGrath JA, Eady RAJ, Pope FM (2004) Anatomy and organization of human skin. In: Rook’s textbook of dermatology. Blackwell Science Ltd, Oxford, pp 45–128
Fuchs E, Raghavan S (2002) Getting under the skin of epidermal morphogenesis. Nat Rev Genet 3:199–209
Epstein WL, Maibach HI (1965) Cell renewal in human epidermis. Arch Dermatol 92:462
Lechler T, Fuchs E (2005) Asymmetric cell divisions promote stratification and differentiation of mammalian skin. Nature 437:275–280
Reichelt J (2007) Mechanotransduction of keratinocytes in culture and in the epidermis. Eur J Cell Biol 86:807–816
Margadant C, Charafeddine RA, Sonnenberg A (2010) Unique and redundant functions of integrins in the epidermis. FASEB J 24:4133–4152
Stupack DG, Cheresh DA (2002) Get a ligand, get a life: integrins, signaling and cell survival. J Cell Sci 115:3729–3738
Hertle M, Adams J, Watt F (1991) Integrin expression during human epidermal development in vivo and in vitro. Development 112:193–206
Runswick SK, O’Hare MJ, Jones L, Streuli CH, Garrod DR (2001) Desmosomal adhesion regulates epithelial morphogenesis and cell positioning. Nat Cell Biol 3:823–830
Schultz GS, Wysocki A (2009) Interactions between extracellular matrix and growth factors in wound healing. Wound Repair Regen 17:153–162
Kippenberger S, Bernd A, Loitsch S, Guschel M, Müller J, Bereiter-Hahn J et al (2000) Signaling of mechanical stretch in human keratinocytes via MAP kinases. J Invest Dermatol 114:408–412
Grinnell F (2003) Fibroblast biology in three-dimensional collagen matrices. Trends Cell Biol 13:264–269
Driskell RR, Lichtenberger BM, Hoste E, Kretzschmar K, Simons BD, Charalambous M et al (2013) Distinct fibroblast lineages determine dermal architecture in skin development and repair. Nature 504:277–281
Jiang C, Shao L, Wang Q, Dong Y (2012) Repetitive mechanical stretching modulates transforming growth factor-β induced collagen synthesis and apoptosis in human patellar tendon fibroblasts. Biochem Cell Biol 90:667–674
Silver FH, Siperko LM, Seehra GP (2003) Mechanobiology of force transduction in dermal tissue. Skin Res Technol 9:3–23
Prajapati RT, Chavally-Mis B, Herbage D, Eastwood M, Brown RA (2000) Mechanical loading regulates protease production by fibroblasts in three-dimensional collagen substrates. Wound Repair Regen 8:226–237
Limbert G (2017) Mathematical and computational modelling of skin biophysics: a review. Proc R Soc A Math Phys Eng Sci 473:20170257
Buganza Tepole A, Vaca EE, Purnell CA, Gart M, McGrath J, Kuhl E et al (2017) Quantification of strain in a porcine model of skin expansion using multi-view stereo and isogeometric kinematics. J Vis Exp 2017(122):55052
Himpel G, Kuhl E, Menzel A (2005) Computational modelling of isotropic multiplicative growth. Comput Model Eng Sci 8:119–134
Rodriguez EK, Hoger A, McCulloch AD (1994) Stress-dependent finite growth in soft elastic tissues. J Biomech 27:455–467
Lee EH (1969) Elastic-plastic deformation at finite strains. J Appl Mech 36(1):1–6
Göktepe S, Abilez OJ, Parker KK (2010) A multiscale model for eccentric and concentric cardiac growth through sarcomerogenesis. J Theor Biol 265(3):433–442
Roose T, Chapman SJ, Maini PK (2007) Mathematical models of avascular tumor growth. Siam Rev 49:179–208
Cowin SC (1996) Strain or deformation rate dependent finite growth in soft tissues. J Biomech 29:647–649
Ambrosi D, Ateshian GA, Arruda EM, Cowin S, Dumais J, Goriely A et al (2011) Perspectives on biological growth and remodeling. J Mech Phys Solids 59:863
Socci L, Pennati G, Gervaso F, Vena P (2006) An axisymmetric computational model of skin expansion and growth. Biomech Model Mechanobiol 6:177–188
Buganza Tepole A, Kabaria H, Bletzinger K-U, Kuhl E (2015) Isogeometric Kirchhoff-Love shell formulations for biological membranes. Comput Methods Appl Mech Eng 293:328–347
Cermelli P, Gurtin ME (2001) On the characterization of geometrically necessary dislocations in finite plasticity. J Mech Phys Solids 49:1539–1568
Buganza Tepole A, Gart M, Purnell CA, Gosain AK, Kuhl E (2016) The incompatibility of living systems: characterizing growth-induced incompatibilities in expanded skin. Ann Biomed Eng 44:1734–1752
Liu SQ, Fung YC (1988) Zero-stress states of arteries. J Biomech Eng 110:82–84
Ambrosi D, Mollica F (2002) On the mechanics of a growing tumor. Int J Eng Sci 40:1297–1316
Rausch MK, Kuhl E (2013) On the effect of prestrain and residual stress in thin biological membranes. J Mech Phys Solids 61:1955–1969
Zöllner AM, Buganza Tepole A, Kuhl E (2012) On the biomechanics and mechanobiology of growing skin. J Theor Biol 297:166–175
Kuhl E, Steinmann P (2003) Mass- and volume-specific views on thermodynamics for open systems. Proc R Soc A Math Phys Eng Sci 459:2547–2568
Kuhl E, Steinmann P (2003) On spatial and material settings of thermo-hyperelastodynamics for open systems. Acta Mech 160:179–217
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 59:2177–2190
Buganza Tepole A, Kuhl E, Gosain AK (2012) Stretching skin: the physiological limit and beyond. Int J Non Linear Mech 47:938–949
Buganza Tepole A (2017) Computational systems mechanobiology of wound healing. Comput Methods Appl Mech Eng 314:46–70
Rivera R, LoGiudice J, Gosain AK (2005) Tissue expansion in pediatric patients. Clin Plast Surg 32:35–44
Chin MS, Ogawa R, Lancerotto L, Pietramaggiori G, Schomacker KT, Mathews JC et al (2010) In vivo acceleration of skin growth using a servo-controlled stretching device. Tissue Eng Part C Methods 16:397–405
Pamplona DC, Velloso RQ, Radwanski HN (2014) On skin expansion. J Mech Behav Biomed Mater 29:655–662
Austad ED, Pasyk KA, McClatchey KD, Cherry GW (1982) Histomorphologic evaluation of guinea pig skin and soft tissue after controlled tissue expansion. Plast Reconstr Surg 70:704–710
Erba P, Miele LF, Adini A, Ackermann M, Lamarche JM, Orgill BD et al (2011) A morphometric study of mechanotransductively induced dermal neovascularization. Plast Reconstr Surg 128:288e–299e
Derderian CA, Bastidas N, Lerman OZ, Bhatt KA, Lin S-E, Voss J et al (2005) Mechanical strain alters gene expression in an in vitro model of hypertrophic scarring. Ann Plast Surg 55:69–75. discussion 75
Flynn C, Taberner AJ, Nielsen PMF, Fels S (2013) Simulating the three-dimensional deformation of in vivo facial skin. J Mech Behav Biomed Mater 28:484–494
Flynn C, Taberner A, Nielsen P (2011) Mechanical characterisation of in vivo human skin using a 3D force-sensitive micro-robot and finite element analysis. Biomech Model Mechanobiol 10:27–38
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 58:1661–1680
Zöllner AM, Holland MA, Honda KS, Gosain AK, Kuhl E (2013) Growth on demand: reviewing the mechanobiology of stretched skin. J Mech Behav Biomed Mater 28:495–509
Lee T, Vaca EE, Ledwon JK, Bae H, Topczewska JM, Turin SY et al (2018) Improving tissue expansion protocols through computational modeling. J Mech Behav Biomed Mater 82:224–234
Patel P a, Elhadi HM, Kitzmiller WJ, Billmire D a, Yakuboff KP (2014) Tissue expander complications in the pediatric burn patient: a 10-year follow-up. Ann Plast Surg 72:150–154
Cordeiro PG, McCarthy CM (2006) A single surgeon’s 12-year experience with tissue expander/implant breast reconstruction: part I. A prospective analysis of early complications. Plast Reconstr Surg 118:825–831
Zöllner AM, Tepole AB, Gosain AK (2011) Growing skin: tissue expansion in pediatric forehead reconstruction. Biomech Model Mechanobiol 11:855–877
van Rappard JH, Molenaar J, van Doorn K, Sonneveld GJ, Borghouts JM (1988) Surface-area increase in tissue expansion. Plast Reconstr Surg 82:833–839
McCauley RL (2005) Tissue expansion reconstruction of the scalp. Semin Plast Surg 19:143–152
Gosain AK, Cortes W (2007) Pediatric tissue expansion for forehead reconstruction: a 13-year review and an algorithm for its use. Am Soc Plast Surg. Baltimore, Abstract 13288
Zöllner AM, Buganza Tepole A, Kuhl E (2012) On the biomechanics and mechanobiology of growing skin. J Theor Biol 297:166–175
Baker SR, Swanson NA (1990) Clinical applications of tissue expansion in head and neck surgery. Laryngoscope 100(3):313–319
Yang M, Li Q, Sheng L, Li H, Weng R, Zan T (2011) Bone marrow—derived mesenchymal stem cells transplantation accelerates tissue expansion by promoting skin regeneration during expansion. Ann Surg 253:202–209
Chen L, Nguyen-Thanh N, Nguyen-Xuan H, Rabczuk T, Bordas SPA, Limbert G (2014) Explicit finite deformation analysis of isogeometric membranes. Comput Methods Appl Mech Eng 277:104–130
Beauchene JG, Chambers MM, Peterson AE, Scott PG (1989) Biochemical, biomechanical, and physical changes in the skin in an experimental animal model of therapeutic tissue expansion. J Surg Res 47:507–514
Bartell TH, Mustoe TA (1989) Animal models of human tissue expansion. Plast Reconstr Surg 83:681–686
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Tepole, A.B., Gosain, A.K. (2019). Constitutive Modelling of Skin Growth. In: Limbert, G. (eds) Skin Biophysics. Studies in Mechanobiology, Tissue Engineering and Biomaterials, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-030-13279-8_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-13279-8_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-13278-1
Online ISBN: 978-3-030-13279-8
eBook Packages: EngineeringEngineering (R0)