Biomechanics and Modeling in Mechanobiology

, Volume 17, Issue 6, pp 1857–1873 | Cite as

Propagation of material behavior uncertainty in a nonlinear finite element model of reconstructive surgery

  • Taeksang Lee
  • Sergey Y. Turin
  • Arun K. Gosain
  • Ilias Bilionis
  • Adrian Buganza TepoleEmail author
Original Paper


Excessive mechanical stress following surgery can lead to delayed healing, hypertrophic scars, and even skin necrosis. Measuring stress directly in the operating room over large skin areas is not feasible, and nonlinear finite element simulations have become an appealing alternative to predict stress contours on arbitrary geometries. However, this approach has been limited to generic cases, when in reality each patient geometry and procedure are unique, and material properties change from one person to another. In this manuscript, we use multi-view stereo to capture the patient-specific geometry of a 7-year-old female undergoing cranioplasty and complex tissue rearrangement. The geometry is used to setup a nonlinear finite element simulation of the reconstructive procedure. A key contribution of this work is incorporation of material behavior uncertainty. The finite element simulation is computationally expensive, and it is not suitable for uncertainty propagation which would require many such simulations. Instead, we run only a few expensive simulations in order to build a surrogate model by Gaussian process regression of the principal components of the stress fields computed with these few samples. The inexpensive surrogate is then used to compute the statistics of the stress distribution in this patient-specific scenario.


Gaussian process regression Patient-specific simulation Multi-view stereo Nonlinear finite elements Principal component analysis Uncertainty propagation 



The authors thank Paul Berg for his contribution to the acquisition of the patient photographs.

Supplementary material

10237_2018_1061_MOESM1_ESM.docx (132 kb)
Supplementary material 1 (docx 131 KB)


  1. Alastrué V, Sáez P, Martínez M, Doblaré M (2010) On the use of the Bingham statistical distribution in microsphere-based constitutive models for arterial tissue. Mech Res Commun 37(8):700–706CrossRefGoogle Scholar
  2. Annaidh AN, Bruyère Karine, Destrade M, Gilchrist MD, Maurini C, Otténio M, Saccomandi G (2012) Automated estimation of collagen fibre dispersion in the dermis and its contribution to the anisotropic behaviour of skin. Ann Biomed Eng 40(8):1666–1678CrossRefGoogle Scholar
  3. Bartlett LC (1985) Pressure necrosis is the primary cause of wound dehiscence. Can J Surg 28(1):27–30Google Scholar
  4. Beeler T (2015) Passive spatiotemporal geometry reconstruction of human faces at high fidelity. IEEE Comput Graph Appl 35(3):82–90CrossRefGoogle Scholar
  5. Bilionis I, Zabaras N (2013) Solution of inverse problems with limited forward solver evaluations: a Bayesian perspective. Inverse Prob 30(1):015004MathSciNetCrossRefGoogle Scholar
  6. Bilionis I, Zabaras N, Konomi BA, Lin G (2013) Multi-output separable gaussian process: towards an efficient, fully Bayesian paradigm for uncertainty quantification. J Comput Phys 241:212–239MathSciNetCrossRefGoogle Scholar
  7. Bilionis I, Constantinescu EM, Anitescu M (2014) Data-driven model for solar irradiation based on satellite observations. Sol Energy 110:22–38CrossRefGoogle Scholar
  8. Bishop CM (2006) Machine learning and pattern recognition. Information science and statistics. Springer, HeidelbergzbMATHGoogle Scholar
  9. Buganza Tepole A, Gosain AK, Kuhl E (2014) Computational modeling of skin: using stress profiles as predictor for tissue necrosis in reconstructive surgery. Comput Struct 143:32–39CrossRefGoogle Scholar
  10. Cignoni P, Callieri M, Corsini M, Dellepiane M, Ganovelli F, Ranzuglia G (2008) MeshLab: an open-source mesh processing tool. In: Sixth Eurographics Italian chapter conference, pp 129–136Google Scholar
  11. Cox H (1941) The cleavage lines of the skin. Br J Surg 29(114):234–240CrossRefGoogle Scholar
  12. Cua AB, Wilhelm K-P, Maibach HI (1990) Elastic properties of human skin: relation to age, sex, and anatomical region. Arch Dermatol Res 282:283–288CrossRefGoogle Scholar
  13. Daly CH, Odland GF (1979) Age-related changes in the mechanical properties of human skin. J Invest Dermatol 73(1):84–87CrossRefGoogle Scholar
  14. Du Q, Fowler JE (2007) Hyperspectral image compression using JPEG2000 and principal component analysis. IEEE Geosci Remote Sens Lett 4(2):201–205CrossRefGoogle Scholar
  15. Flynn C (2010) Finite element models of wound closure. J Tissue Viability 19(4):137–149CrossRefGoogle Scholar
  16. Forrester AI, Keane AJ (2009) Recent advances in surrogate-based optimization. Prog Aerosp Sci 45(1):50–79CrossRefGoogle Scholar
  17. Garn SM, Selby S, Young R (1954) Scalp thickness and the fat-loss theory of balding. A. M. A. Arch Dermatol Syphilol 70(5):601–608CrossRefGoogle Scholar
  18. Gasser TC, Ogden RW, Holzapfel GA (2006) Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J R Soc Interface 3(6):15–35CrossRefGoogle Scholar
  19. Gurtner GC, Dauskardt RH, Wong VW, Bhatt KA, Wu K, Vial IN, Padois K, Korman JM, Longaker MT (2011) Improving cutaneous scar formation by controlling the mechanical environment: large animal and phase I studies. Ann Surg 254(2):217–225CrossRefGoogle Scholar
  20. Higdon D, Gattiker J, Williams B, Rightley M (2008) Computer model calibration using high-dimensional output. J Am Stat Assoc 103(482):570–583MathSciNetCrossRefGoogle Scholar
  21. Holzapfel GA, Gasser TC, Ogden RW (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elast Phys Sci Solids 61(1–3):1–48MathSciNetzbMATHGoogle Scholar
  22. Rohrer TE, Bhatia A (2005) Transposition flaps in cutaneous surgery. Dermatol Surg 31:1014–1023CrossRefGoogle Scholar
  23. Jor JW, Nash MP, Nielsen PM, Hunter PJ (2011) Estimating material parameters of a structurally based constitutive relation for skin mechanics. Biomech Model Mechanobiol 10(5):767–778CrossRefGoogle Scholar
  24. Jor JW, Parker MD, Taberner AJ, Nash MP, Nielsen PM (2013) Computational and experimental characterization of skin mechanics: identifying current challenges and future directions. Wiley Interdiscip Rev Syst Biol Med 5(5):539–556CrossRefGoogle Scholar
  25. Kennedy MC, O’Hagan A (2001) Bayesian calibration of computer models. J R Stat Soc Ser B (Stat Methodol) 63(3):425–464MathSciNetCrossRefGoogle Scholar
  26. Lanir Y (1983) Constitutive equations for fibrous connective tissues. J Biomech 16(1):1–12CrossRefGoogle Scholar
  27. Lee T, Turin SY, Gosain AK, Tepole AB (2018) Multi-view stereo in the operating room allows prediction of healing complications in a patient-specific model of reconstructive surgery. J Biomech 74:202–206CrossRefGoogle Scholar
  28. Limbert G (2017) Mathematical and computational modelling of skin biophysics: a review. Proc R Soc A 473(2203):20170257MathSciNetCrossRefGoogle Scholar
  29. Limbert G, Taylor M (2002) On the constitutive modeling of biological soft connective tissues: a general theoretical framework and explicit forms of the tensors of elasticity for strongly anisotropic continuum fiber-reinforced composites at finite strain. Int J Solids Struct 39(8):2343–2358CrossRefGoogle Scholar
  30. LoGiudice J, Gosain AK (2004) Pediatric tissue expansion: indications and complications. Plast Surg Nurs 24(1):20–26CrossRefGoogle Scholar
  31. Ma W-C, Jones A, Chiang J-Y, Hawkins T, Frederiksen S, Peers P, Vukovic M, Ouhyoung M, Debevec P (2008) Facial performance synthesis using deformation-driven polynomial displacement maps. ACM Trans Graph (TOG) 27(5):121CrossRefGoogle Scholar
  32. McKay MD, Beckman RJ, Conover WJ (2000) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 42(1):55–61CrossRefGoogle Scholar
  33. Mitchell N, Sifakis E et al (2015) GRIDiron: an interactive authoring and cognitive training foundation for reconstructive plastic surgery procedures. ACM Trans Graph (TOG) 34(4):43CrossRefGoogle Scholar
  34. Paul SP (2016) The golden spiral flap: a new flap design that allows for closure of larger wounds under reduced tension how studying nature’s own design led to the development of a new surgical technique. Front Surg 3:63CrossRefGoogle Scholar
  35. Rajabi A, Dolovich AT, Johnston JD (2015) From the rhombic transposition flap toward Z-plasty: an optimized design using the finite element method. J Biomech 48(13):3672–3678CrossRefGoogle Scholar
  36. Rasmussen CE, Williams CK (2006) Gaussian processes for machine learning, vol 1. MIT Press, CambridgezbMATHGoogle Scholar
  37. Richardson RR, Osborne MA, Howey DA (2017) Gaussian process regression for forecasting battery state of health. J Power Sources 357:209–219CrossRefGoogle Scholar
  38. Strecha C, von Hansen W, Van Gool L, Fua P, Thoennessen U (2008) On benchmarking camera calibration and multi-view stereo for high resolution imagery. In: 2008 IEEE conference on computer vision and pattern recognition, pp 1–8Google Scholar
  39. Tonge TK, Voo LM, Nguyen TD (2013) Full-field bulge test for planar anisotropic tissues: part II—a thin shell method for determining material parameters and comparison of two distributed fiber modeling approaches. Acta Biomater 9(4):5926–5942CrossRefGoogle Scholar
  40. Tripathy R, Bilionis I, Gonzalez M (2016) Gaussian processes with built-in dimensionality reduction: applications to high-dimensional uncertainty propagation. J Comput Phys 321:191–223MathSciNetCrossRefGoogle Scholar
  41. Weickenmeier J, Jabareen M, Mazza E (2015) Suction based mechanical characterization of superficial facial soft tissues. J Biomech 48(16):4279–4286CrossRefGoogle Scholar
  42. Weickenmeier J, Butler CA, Young PG, Goriely A, Kuhl E (2017) The mechanics of decompressive craniectomy: personalized simulations. Comput Methods Appl Mech Eng 314:180–195CrossRefGoogle Scholar
  43. Wu X, Kozlowski T, Meidani H (2018) Kriging-based inverse uncertainty quantification of nuclear fuel performance code BISON fission gas release model using time series measurement data. Reliab Eng Syst Saf 169:422–436CrossRefGoogle Scholar
  44. Zöllner AM, Tepole AB, Gosain AK, Kuhl E (2012) Growing skin: tissue expansion in pediatric forehead reconstruction. Biomech Model Mechanobiol 11(6):855–867CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mechanical EngineeringPurdue UniversityWest LafayetteUSA
  2. 2.Feinberg School of MedicineNorthwestern UniversityChicagoUSA
  3. 3.Weldon School of Biomedical EngineeringPurdue UniversityWest LafayetteUSA

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