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Sensitivity analysis based on non-intrusive regression-based polynomial chaos expansion for surgical mesh modelling

Abstrakt

The modelling of a system containing implants used in ventral hernia repair and human tissue suffers from many uncertainties. Thus, a probabilistic approach is needed. The goal of this study is to define an efficient numerical method to solve non-linear biomechanical models supporting the surgeon in decisions about ventral hernia repair. The model parameters are subject to substantial variability owing to, e.g., abdominal wall parameter uncertainties. Moreover, the maximum junction force, the quantity of interest which is worthy of scrutiny due to hernia recurrences, is non-smooth. A non-intrusive regression-based polynomial chaos expansion method is employed. The choice of regression points is crucial in such methods, thus we study the influence of this choice on the quantity of interest, and look for an efficient strategy. For this purpose, several aspects are studied : (i) we study the quality of the quantity of interest, i.e. accuracy of the mean and standard deviation, (ii) we perform a global sensitivity analysis using Sobol sensitivity indices. The influence of uncertainties of the chosen variables is presented. This study leads to the definition of an efficient numerical simulation dedicated to our model of implant.

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Informacje szczegółowe

Kategoria:
Publikacja w czasopiśmie
Typ:
artykuł w czasopiśmie wyróżnionym w JCR
Opublikowano w:
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION nr 57, wydanie 3, strony 1391 - 1409,
ISSN: 1615-147X
Język:
angielski
Rok wydania:
2018
Opis bibliograficzny:
Szepietowska K., Magnain B., Lubowiecka I., Florentin E.: Sensitivity analysis based on non-intrusive regression-based polynomial chaos expansion for surgical mesh modelling// STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION. -Vol. 57, iss. 3 (2018), s.1391-1409
DOI:
Cyfrowy identyfikator dokumentu elektronicznego (otwiera się w nowej karcie) 10.1007/s00158-017-1799-9
Bibliografia: test
  1. Acosta Santamaría, V., Siret, O., Badel, P., Guerin, G., Novacek, V., Turquier, F., Avril, S.: Material model calibration from planar tension tests on porcine linea alba. Journal of the Mechanical Behavior of Biomedical Materials 43, 26-34 (2015). DOI 10.1016/j.jmbbm.2014.12.003 otwiera się w nowej karcie
  2. de Aguiar, P., Bourguignon, B., Khots, M., Massart, D., Phan-Than-Luu, R.: D-optimal designs. Chemometrics and Intelligent Laboratory Systems 30(2), 199 -210 (1995). DOI http://dx.doi.org/10.1016/0169-7439(94)00076-X otwiera się w nowej karcie
  3. Antille, G., Weinberg, A., et al.: A Study of D-optimal Designs Efficiency for Polynomial Regression. Université de Genève/Faculté des sciences économiques et sociales (2000)
  4. Berveiller, M., Sudret, B., Lemaire, M.: Stochastic finite element: a non intrusive approach by regression. Revue européenne de mécanique numérique 15(1-3), 81-92 (2006). DOI 10.3166/remn.15.81-92 otwiera się w nowej karcie
  5. Blatman, G., Sudret, B.: An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis. Probabilistic Engineering Mechanics 25(2), 183-197 (2010). DOI 10.1016/j.probengmech.2009.10.003 otwiera się w nowej karcie
  6. Blatman, G., Sudret, B.: Efficient computation of global sensitivity indices using sparse polynomial chaos expansions. Reliability Engineering & System Safety 95(11), 1216-1229 (2010). DOI 10.1016/j.ress.2010.06.015 otwiera się w nowej karcie
  7. Blatman, G., Sudret, B.: Adaptive sparse polynomial chaos expansion based on least angle regression. Journal of Computational Physics 230(6), 2345-2367 (2011) otwiera się w nowej karcie
  8. Blatman, G., Sudret, B., Berveiller, M.: Quasi random numbers in stochastic finite element analysis. Mécanique & Industries 8(3), 289-297 (2007). DOI 10.1051/meca:2007051 otwiera się w nowej karcie
  9. Breuing, K., Butler, C.E., Ferzoco, S., Franz, M., Hultman, C.S., Kilbridge, J.F., Rosen, M., Silverman, R.P., Vargo, D., Group, V.H.W., et al.: Incisional ventral hernias: review of the literature and recommendations regarding the grading and technique of repair. Surgery 148(3), 544-558 (2010) otwiera się w nowej karcie
  10. Burnaev, E., Panin, I., Sudret, B.: Effective Design for Sobol Indices Estimation Based on Polynomial Chaos Expan- sions, pp. 165-184. Springer International Publishing, Cham (2016). DOI 10.1007/978-3-319-33395-3_12 otwiera się w nowej karcie
  11. Carter, S.A., Hicks, S.C., Brahmbhatt, R., Liang, M.K.: Recurrence and pseudorecurrence after laparoscopic ventral hernia repair: predictors and patient-focused outcomes. The American surgeon 80(2), 138-48 (2014)
  12. Chamoin, L., Florentin, E., Pavot, S., Visseq, V.: Robust goal-oriented error estimation based on the constitutive relation error for stochastic problems. Computers & Structures 106-107(i), 189-195 (2012). DOI 10.1016/j.compstruc. 2012.05.002 otwiera się w nowej karcie
  13. Cho, I., Lee, Y., Ryu, D., Choi, D.H.: Comparison study of sampling methods for computer experiments us- ing various performance measures. Structural and Multidisciplinary Optimization 55(1), 221-235 (2017). DOI 10.1007/s00158-016-1490-6 otwiera się w nowej karcie
  14. Choi, S.K., Grandhi, R.V., Canfield, R.A., Pettit, C.L.: Polynomial chaos expansion with latin hypercube sampling for estimating response variability. AIAA journal 42(6), 1191-1198 (2004) otwiera się w nowej karcie
  15. Cobb, W.S., Burns, J.M., Kercher, K.W., Matthews, B.D., Norton, H.J., Heniford, B.T.: Normal intraabdominal pressure in healthy adults. Journal of Surgical Research 129(2), 231-235 (2005) otwiera się w nowej karcie
  16. Cooney, G.M., Lake, S.P., Thompson, D.M., Castile, R.M., Winter, D.C., Simms, C.K.: Uniaxial and biaxial tensile stress-stretch response of human linea alba. Journal of the Mechanical Behavior of Biomedical Materials 63, 134-140 (2016) otwiera się w nowej karcie
  17. Crestaux, T., Le Maître, O., Martinez, J.M.: Polynomial chaos expansion for sensitivity analysis. Reliability Engineering & System Safety 94(7), 1161 -1172 (2009). Special Issue on Sensitivity Analysis otwiera się w nowej karcie
  18. Deeken, C.R., Thompson, D.M., Castile, R.M., Lake, S.P.: Biaxial analysis of synthetic scaffolds for hernia repair demonstrates variability in mechanical anisotropy, non-linearity and hysteresis. Journal of the mechanical behavior of biomedical materials 38, 6-16 (2014) otwiera się w nowej karcie
  19. Dubourg, V., Sudret, B., Bourinet, J.M.: Reliability-based design optimization using kriging surrogates and subset simulation. Structural and Multidisciplinary Optimization 44(5), 673-690 (2011). DOI 10.1007/s00158-011-0653-8 otwiera się w nowej karcie
  20. Fedorov, V.V.: Theory of optimal experiments. Academic Press, INC (english translation) (1972)
  21. Filomeno Coelho, R., Lebon, J., Bouillard, P.: Hierarchical stochastic metamodels based on moving least squares and polynomial chaos expansion. Structural and Multidisciplinary Optimization 43(5), 707-729 (2011). DOI 10.1007/ s00158-010-0608-5 otwiera się w nowej karcie
  22. Fishman, G.S.: Monte Carlo. Springer New York, New York, NY (1996). DOI 10.1007/978-1-4757-2553-7 otwiera się w nowej karcie
  23. Gao, Z., Zhou, T.: On the choice of design points for least square polynomial approximations with application to uncertainty quantification. Communications in Computational Physics 16(2), 365-381 (2014). DOI 10.4208/cicp. 130813.060214a otwiera się w nowej karcie
  24. Ghanem, R.G., Spanos, P.D.: Stochastic Finite Elements: A Spectral Approach. Springer-Verlag (1991) otwiera się w nowej karcie
  25. Hernández-Gascón, B., Mena, A., Pena, E., Pascual, G., Bellón, J., Calvo, B.: Understanding the passive mechanical behavior of the human abdominal wall. Annals of biomedical engineering 41(2), 433-444 (2013) otwiera się w nowej karcie
  26. Hernández-Gascón, B., Peña, E., Grasa, J., Pascual, G., Bellón, J.M., Calvo, B.: Mechanical response of the herniated human abdomen to the placement of different prostheses. Journal of biomechanical engineering 135(5), 051,004 (2013) otwiera się w nowej karcie
  27. Hu, C., Youn, B.D.: Adaptive-sparse polynomial chaos expansion for reliability analysis and design of complex engineer- ing systems. Structural and Multidisciplinary Optimization 43(3), 419-442 (2011). DOI 10.1007/s00158-010-0568-9 otwiera się w nowej karcie
  28. Huang, X., Liu, Y., Zhang, Y., Zhang, X.: Reliability analysis of structures using stochastic response surface method and saddlepoint approximation. Structural and Multidisciplinary Optimization pp. 1-10 (2016). DOI 10.1007/s00158-016-1617-9 otwiera się w nowej karcie
  29. Huberts, W., Donders, W., Delhaas, T., Vosse, F.: Applicability of the polynomial chaos expansion method for person- alization of a cardiovascular pulse wave propagation model. International Journal for numerical methods in biomedical engineering 30(12), 1679-1704 (2014) otwiera się w nowej karcie
  30. Isukapalli, S.S.: Uncertainty analysis of transport-transformation models. Ph.D. thesis, Graduate School New Brunswick (1999) otwiera się w nowej karcie
  31. Junge, K., Klinge, U., Prescher, A., Giboni, P., Niewiera, M., Schumpelick, V.: Elasticity of the anterior abdominal wall and impact for reparation of incisional hernias using mesh implants. Hernia 5(3), 113-118 (2001)
  32. Le Maître, O.P., Knio, O.M.: Spectral Methods for Uncertainty Quantification. Scientific Computation. Springer Netherlands, Dordrecht (2010). DOI 10.1007/978-90-481-3520-2 otwiera się w nowej karcie
  33. Le Maître, O.P., Reagan, M.T., Najm, H.N., Ghanem, R.G., Knio, O.M.: A stochastic projection method for fluid flow: Ii. random process. Journal of Computational Physics 181(1), 9 -44 (2002). DOI http://dx.doi.org/10.1006/jcph. 2002.7104 otwiera się w nowej karcie
  34. Lee, S.H., Chen, W.: A comparative study of uncertainty propagation methods for black-box-type problems. Structural and Multidisciplinary Optimization 37(3), 239 (2008). DOI 10.1007/s00158-008-0234-7 otwiera się w nowej karcie
  35. Lubowiecka, I.: Mathematical modelling of implant in an operated hernia for estimation of the repair persistence. Computer methods in biomechanics and biomedical engineering 18(4), 438-445 (2015) otwiera się w nowej karcie
  36. Lubowiecka, I., Szepietowska, K., Szymczak, C., Tomaszewska, A.: Preliminary study on the optimal choice of an implant and its orientation in ventral hernia repair. Journal of Theoretical and Applied Mechanics 54(2), 411-421 (2016). DOI 10.15632/jtam-pl.54.2.411 otwiera się w nowej karcie
  37. Lyons, M., Mohan, H., Winter, D., Simms, C.: Biomechanical abdominal wall model applied to hernia repair. British Journal of Surgery 102(2), e133-e139 (2015) otwiera się w nowej karcie
  38. Maurer, M., Röhrnbauer, B., Feola, A., Deprest, J., Mazza, E.: Mechanical biocompatibility of prosthetic meshes: A comprehensive protocol for mechanical characterization. Journal of the mechanical behavior of biomedical materials 40, 42-58 (2014) otwiera się w nowej karcie
  39. McKay, M.D., Beckman, R.J., Conover, W.J.: 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 (2000) otwiera się w nowej karcie
  40. Morokoff, W.J., Caflisch, R.E.: Quasi-Random Sequences and Their Discrepancies. SIAM J. SCl. COMPUT 15(6), 1251-1279 (1994). DOI 10.1137/0915077 otwiera się w nowej karcie
  41. Redhe, M., Forsberg, J., Jansson, T., Marklund, P.O., Nilsson, L.: Using the response surface methodology and the d- optimality criterion in crashworthiness related problems. Structural and Multidisciplinary Optimization 24(3), 185-194 (2002). DOI 10.1007/s00158-002-0228-9 otwiera się w nowej karcie
  42. Schobi, R., Sudret, B., Wiart, J.: Polynomial-Chaos-based Kriging. International Journal for Uncertainty Quantification 5(2), 171-193 (2015). DOI 10.1615/Int.J.UncertaintyQuantification.2015012467 otwiera się w nowej karcie
  43. Simón-Allué, R., Calvo, B., Oberai, A., Barbone, P.: Towards the mechanical characterization of abdominal wall by inverse analysis. Journal of the Mechanical Behavior of Biomedical Materials 66, 127-137 (2017) otwiera się w nowej karcie
  44. Simón-Allué, R., Hernández-Gascón, B., Lèoty, L., Bellón, J., Peña, E., Calvo, B.: Prostheses size dependency of the mechanical response of the herniated human abdomen. Hernia 20(6), 839-848 (2016) otwiera się w nowej karcie
  45. Smith, K.: On the standard deviations of adjusted and interpolated values of an observed polynomial function and its constants and the guidance they give towards a proper choice of the distribution of observations. Biometrika 12(1-2), 1-85 (1918). DOI 10.1093/biomet/12.1-2.1 otwiera się w nowej karcie
  46. Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation 55(1-3), 271-280 (2001). DOI 10.1016/S0378-4754(00)00270-6 otwiera się w nowej karcie
  47. Song, C., Alijani, A., Frank, T., Hanna, G., Cuschieri, A.: Elasticity of the living abdominal wall in laparoscopic surgery. Journal of biomechanics 39(3), 587-591 (2006) otwiera się w nowej karcie
  48. Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93(7), 964-979 (2008). DOI 10.1016/j.ress.2007.04.002 otwiera się w nowej karcie
  49. Suryawanshi, A., Ghosh, D.: Reliability based optimization in aeroelastic stability problems using polynomial chaos based metamodels. Structural and Multidisciplinary Optimization 53(5), 1069-1080 (2016). DOI 10.1007/ s00158-015-1322-0 otwiera się w nowej karcie
  50. Szymczak, C., Lubowiecka, I., Szepietowska, K., Tomaszewska, A.: Two-criteria optimisation problem for ventral hernia repair. Computer Methods in Biomechanics and Biomedical Engineering 20(7), 760-769 (2017) otwiera się w nowej karcie
  51. Szymczak, C., Lubowiecka, I., Tomaszewska, A., Śmietański, M.: Modeling of the fascia-mesh system and sensitivity analysis of a junction force after a laparascopic ventral hernia repair. Journal of Thoretical and Applied Mechanics 48(4), 933-950 (2010)
  52. Szymczak, C., Lubowiecka, I., Tomaszewska, A., Śmietański, M.: Investigation of abdomen surface deformation due to life excitation: implications for implant selection and orientation in laparoscopic ventral hernia repair. Clinical biomechanics (Bristol, Avon) 27(2), 105-10 (2012). DOI 10.1016/j.clinbiomech.2011.08.008 otwiera się w nowej karcie
  53. Szymczak, C., Śmietański, M.: Selected problems of laparoscopic ventral hernia repair -modeling and simulation. alfa-medica press Gdańsk (2012) otwiera się w nowej karcie
  54. Tomaszewska, A., Lubowiecka, I., Szymczak, C., Śmietański, M., Meronk, B., Kłosowski, P., Bury, K.: Physical and mathematical modelling of implant-fascia system in order to improve laparoscopic repair of ventral hernia. Clinical Biomechanics 28(7), 743 -751 (2013). DOI http://dx.doi.org/10.1016/j.clinbiomech.2013.06.009 otwiera się w nowej karcie
  55. Tran, D., Mitton, D., Voirin, D., Turquier, F., Beillas, P.: Contribution of the skin, rectus abdominis and their sheaths to the structural response of the abdominal wall ex vivo. Journal of biomechanics 47(12), 3056-3063 (2014) otwiera się w nowej karcie
  56. Tran, D., Podwojewski, F., Beillas, P., Ottenio, M., Voirin, D., Turquier, F., Mitton, D.: Abdominal wall muscle elasticity and abdomen local stiffness on healthy volunteers during various physiological activities. Journal of the mechanical behavior of biomedical materials 60, 451-459 (2016) otwiera się w nowej karcie
  57. Wiener, N.: The homogeneous chaos. American Journal of Mathematics 60(4), 897-936 (1938) otwiera się w nowej karcie
  58. Winkelmann, K., Górski, J.: The use of response surface methodology for reliability estimation of composite engineering structures. Journal of Theoretical and Applied Mechanics 52(4), 1019-1032 (2014) otwiera się w nowej karcie
  59. Xiu, D., Karniadakis, G.E.: The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations. SIAM Journal on Scientific Computing 24(2), 619-644 (2002). DOI 10.1137/S1064827501387826 otwiera się w nowej karcie
  60. Zein, S., Colson, B., Glineur, F.: An Efficient Sampling Method for Regression-Based Polynomial Chaos Expansion. Communications in Computational Physics 13(4), 1173-1188 (2012). DOI 10.4208/cicp.020911.200412a otwiera się w nowej karcie
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Politechnika Gdańska

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