title: Uncertainty quantification for personalized analyses of human proximal femurs.
abstract: 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 ≈40%. Between 60 and 80% of the variance in ϵ1 and ϵ3 are attributable to the uncertainty in the E-ρ relationship, while ≈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 (pf<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.
authors.affiliation: Chair for Computation in Engineering, Technische Universität München, Munich, Germany. Electronic address: hagen.wille@tum.de.
authors.forename: Hagen
authors.initials: H
authors.lastname: Wille
authors.affiliation: Faculty of Aerospace Engineering, Delft University of Technology, Delft, Netherlands. Electronic address: m.ruess@tudelft.nl.
authors.forename: Martin
authors.initials: M
authors.lastname: Ruess
authors.affiliation: Chair for Computation in Engineering, Technische Universität München, Munich, Germany; Institute for Advanced Study, Technische Universität München, Munich, Germany. Electronic address: ernst.rank@tum.de.
authors.forename: Ernst
authors.initials: E
authors.lastname: Rank
authors.affiliation: Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel. Electronic address: zohary@bgu.ac.il.
authors.forename: Zohar
authors.initials: Z
authors.lastname: Yosibash
mesh_terms: D000368:Aged; D000369:Aged, 80 and over; D001696:Biomechanical Phenomena; D005260:Female; D005269:Femur; D006801:Humans; D008297:Male; D055595:Mechanical Phenomena; D008875:Middle Aged; D066230:Patient-Specific Modeling; D015203:Reproducibility of Results; D013269:Stochastic Processes; D013314:Stress, Mechanical; D035501:Uncertainty
keywords: Femur; Finite cell method; Personalized medicine; Polynomial chaos; Uncertainty quantification