Abstract
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.
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References
Alastrué V, Sáez P, MartÃnez 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):700–706
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):1666–1678
Bartlett LC (1985) Pressure necrosis is the primary cause of wound dehiscence. Can J Surg 28(1):27–30
Beeler T (2015) Passive spatiotemporal geometry reconstruction of human faces at high fidelity. IEEE Comput Graph Appl 35(3):82–90
Bilionis I, Zabaras N (2013) Solution of inverse problems with limited forward solver evaluations: a Bayesian perspective. Inverse Prob 30(1):015004
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 241:212–239
Bilionis I, Constantinescu EM, Anitescu M (2014) Data-driven model for solar irradiation based on satellite observations. Sol Energy 110:22–38
Bishop CM (2006) Machine learning and pattern recognition. Information science and statistics. Springer, Heidelberg
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 143:32–39
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 129–136
Cox H (1941) The cleavage lines of the skin. Br J Surg 29(114):234–240
Cua AB, Wilhelm K-P, Maibach HI (1990) Elastic properties of human skin: relation to age, sex, and anatomical region. Arch Dermatol Res 282:283–288
Daly CH, Odland GF (1979) Age-related changes in the mechanical properties of human skin. J Invest Dermatol 73(1):84–87
Du Q, Fowler JE (2007) Hyperspectral image compression using JPEG2000 and principal component analysis. IEEE Geosci Remote Sens Lett 4(2):201–205
Flynn C (2010) Finite element models of wound closure. J Tissue Viability 19(4):137–149
Forrester AI, Keane AJ (2009) Recent advances in surrogate-based optimization. Prog Aerosp Sci 45(1):50–79
Garn SM, Selby S, Young R (1954) Scalp thickness and the fat-loss theory of balding. A. M. A. Arch Dermatol Syphilol 70(5):601–608
Gasser TC, Ogden RW, Holzapfel GA (2006) Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J R Soc Interface 3(6):15–35
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):217–225
Higdon D, Gattiker J, Williams B, Rightley M (2008) Computer model calibration using high-dimensional output. J Am Stat Assoc 103(482):570–583
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):1–48
Rohrer TE, Bhatia A (2005) Transposition flaps in cutaneous surgery. Dermatol Surg 31:1014–1023
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):767–778
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):539–556
Kennedy MC, O’Hagan A (2001) Bayesian calibration of computer models. J R Stat Soc Ser B (Stat Methodol) 63(3):425–464
Lanir Y (1983) Constitutive equations for fibrous connective tissues. J Biomech 16(1):1–12
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 74:202–206
Limbert G (2017) Mathematical and computational modelling of skin biophysics: a review. Proc R Soc A 473(2203):20170257
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):2343–2358
LoGiudice J, Gosain AK (2004) Pediatric tissue expansion: indications and complications. Plast Surg Nurs 24(1):20–26
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):121
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):55–61
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):43
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 3:63
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):3672–3678
Rasmussen CE, Williams CK (2006) Gaussian processes for machine learning, vol 1. MIT Press, Cambridge
Richardson RR, Osborne MA, Howey DA (2017) Gaussian process regression for forecasting battery state of health. J Power Sources 357:209–219
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 1–8
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):5926–5942
Tripathy R, Bilionis I, Gonzalez M (2016) Gaussian processes with built-in dimensionality reduction: applications to high-dimensional uncertainty propagation. J Comput Phys 321:191–223
Weickenmeier J, Jabareen M, Mazza E (2015) Suction based mechanical characterization of superficial facial soft tissues. J Biomech 48(16):4279–4286
Weickenmeier J, Butler CA, Young PG, Goriely A, Kuhl E (2017) The mechanics of decompressive craniectomy: personalized simulations. Comput Methods Appl Mech Eng 314:180–195
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 169:422–436
Zöllner AM, Tepole AB, Gosain AK, Kuhl E (2012) Growing skin: tissue expansion in pediatric forehead reconstruction. Biomech Model Mechanobiol 11(6):855–867
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The authors thank Paul Berg for his contribution to the acquisition of the patient photographs.
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Lee, T., Turin, S.Y., Gosain, A.K. et al. Propagation of material behavior uncertainty in a nonlinear finite element model of reconstructive surgery. Biomech Model Mechanobiol 17, 1857–1873 (2018). https://doi.org/10.1007/s10237-018-1061-4
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DOI: https://doi.org/10.1007/s10237-018-1061-4