Uncertainty quantification for personalized analyses of human proximal femurs

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• 作者：Hagen Wille^a ; ^{hagen.wille@tum.de" class="auth_mail" title="E-mail the corresponding author} ; Martin Ruess^b ; ^{m.ruess@tudelft.nl" class="auth_mail" title="E-mail the corresponding author} ; Ernst Rank^a ; ^d ; ^{ernst.rank@tum.de" class="auth_mail" title="E-mail the corresponding author} ; Zohar Yosibash^c ; ^{zohary@bgu.ac.il" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Femur ; Personalized medicine ; Uncertainty quantification ; Polynomial chaos ; Finite cell method
• 刊名：Journal of Biomechanics
• 出版年：2016
• 出版时间：29 February 2016
• 年：2016
• 卷：49
• 期：4
• 页码：520-527
• 全文大小：3089 K

文摘

Computational models for the personalized analysis of human femurs contain uncertainties in bone material properties and loads, which affect the simulation results. To quantify the influence we developed a probabilistic framework based on polynomial chaos (PC) that propagates stochastic input variables through any computational model. We considered a stochastic E–ρ relationship and a stochastic hip contact force, representing realistic variability of experimental data. Their influence on the prediction of principal strains (ϵ₁ and ϵ₃) was quantified for one human proximal femur, including sensitivity and reliability analysis. Large variabilities in the principal strain predictions were found in the cortical shell of the femoral neck, with coefficients of variation of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021929015006430&_mathId=si0020.gif&_user=111111111&_pii=S0021929015006430&_rdoc=1&_issn=00219290&md5=2cadcc5f7552647a9b4f53e9f7c17d4c" title="Click to view the MathML source">≈40%class="mathContainer hidden">class="mathCode">$\approx 40\%$. Between 60 and 80% of the variance in ϵ₁ and ϵ₃ are attributable to the uncertainty in the E–ρ   relationship, while class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021929015006430&_mathId=si0021.gif&_user=111111111&_pii=S0021929015006430&_rdoc=1&_issn=00219290&md5=27785c726717ce6ef58e42dd5b97e906" title="Click to view the MathML source">≈10%class="mathContainer hidden">class="mathCode">$\approx 10\%$ are caused by the load magnitude and 5–30% by the load direction. Principal strain directions were unaffected by material and loading uncertainties. The antero-superior and medial inferior sides of the neck exhibited the largest probabilities for tensile and compression failure, however all were very small (class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021929015006430&_mathId=si0022.gif&_user=111111111&_pii=S0021929015006430&_rdoc=1&_issn=00219290&md5=7d2a8f62c5796808ff22800c79ac4fc7" title="Click to view the MathML source">p_f<0.001class="mathContainer hidden">class="mathCode">$p_f<0.001$). In summary, uncertainty quantification with PC has been demonstrated to efficiently and accurately describe the influence of very different stochastic inputs, which increases the credibility and explanatory power of personalized analyses of human proximal femurs.