prediction of apparent properties with uncertain material parameters using high order fictitious domain methods and pgd model reduction this contribution presents a numerical strategy to evaluate the effective properties of image based microstructures in the case of random material properties the method relies on three points i a high order fictitious domain method ii an accurate spectral stochastic model and iii an efficient model reduction method based on the proper generalized decomposition in order to decrease the computational cost introduced by the stochastic model a feedback procedure is proposed for an automatic estimation of the random effective properties with a given confidence numerical verifications highlight the convergence properties of the method for both deterministic and stochastic models the method is finally applied to a real 3d bone microstructure where the empirical probability density function of the effective behaviour could be obtained

geometrically accurate efficient and flexible quadrature techniques for the tetrahedral finite cell method abstract we illustrate the importance of geometrically accurate volume quadrature for obtaining optimal accuracy with non boundary fitted finite element discretizations when the problem domain is defined by sharp boundaries we consider the tetrahedral finite cell method tetfcm and replace its recursive subdivision based integration approach with geometrically accurate quadrature rules that emanate from higher order geometric parametrizations of cut tetrahedral elements the element wise parametrization procedure relies on the identification of the intersection topology and a series of higher order mappings based on lagrange polynomials we demonstrate with several 3d examples that geometrically faithful local parametrization ensures optimal accuracy while significantly reducing the number of quadrature points with respect to recursive subdivision on the other hand we highlight the strength of subdivision quadrature in the context of a patient specific workflow for the simulation based performance analysis of coupled bone implant configurations in particular we show that accuracy flexibility and computational efficiency of the tetfcm critically depend on flexibly applying the two different quadrature variants for fuzzy imaging data and sharp boundary representations respectively

prediction of the mechanical response of the femur with uncertain elastic properties abstract a mandatory requirement for any reliable prediction of the mechanical response of bones based on quantitative computer tomography is an accurate relationship between material properties usually young s modulus e and bone density many such e relationships are available based on different experiments on femur specimens with a large spread due to uncertainties the first goal of this study is to pool and analyze the relevant available experimental data and develop a stochastic e relationship this analysis highlights that there is no experimental data available to cover the entire density range of the human femur and that some popular e relationships are based on data that contains extreme scatter while others are based on a very limited amount of information the second goal is to use the newly developed stochastic e relationship in high order finite element analyses feas for the computation of strains and displacements in two human proximal femurs mimicking in vitro experiments when compared with the experimental observations the fea predictions using the median of the stochastic e relationship follow the underlying distribution of the stochastic e relationship thus most deviations of the fea predictions from experimental observations can possibly be explained by uncertain elastic properties of the femur

individual density elasticity relationships improve accuracy of subject specific finite element models of human femurs abstract in a previous study on subject specific finite element models we found that appropriate density elasticity relationships to compute the mechanical behavior of femurs seem to be subject specific the purpose of this study was to test the hypothesis that the predictive error of a cohort of subject specific finite element models is lower with subject specific density elasticity relationships than with a cohort specific density elasticity relationship finite element analysis and inverse optimization based on response surface methodology were employed to test the hypothesis subject specific fe models of 17 human femurs and corresponding experimental data from biomechanical tests were taken from a previous study a power function for the relation between radiological bone density and elastic modulus was set up with the optimization variables a and b e mpa a q c t b gk 2 hpo 4 cm 3 the goal of the optimization was to minimize the root mean square error in percent rmse between computational and experimental results a wilcoxon test p 0 05 was performed on all absolute relative errors between the two groups subject specific functions vs cohort specific function the subject specific functions resulted in a 6 lower overall prediction error and a 6 lower rmse than the cohort specific function p e mpa 12486 q c t 1 16 gk 2 hpo 4 cm 3 we conclude that individual density elasticity relationships improve the accuracy of subject specific finite element models future subject specific finite element analyses of bones should include the individuality of the elastic properties by a stochastic density elasticity relationship with mean and standard deviation of a and b

autonomous fes afe a stride toward personalized medicine abstract finite element analysis fea introduced more than half a century ago requires a qualified analyst to generate the necessary input data verify the output and post process the analysis results for a meaningful conclusion the required expertise and labor efforts have precluded the use of fea in daily medical practice by orthopedic surgeons for example patient specific analyses of the mechanical response of human bones may have a tremendous impact in clinical practice should they be easily accessible by orthopedic surgeons recent scientific advancements such as low dose ct scans machine learning and high order fea which facilitates an inherent methodology for assessing numerical accuracy allow a fully autonomous process for assessing bone strength and fracture risk this autonomous process that we shall refer to here as autonomous finite element afe analysis introduces a paradigm shift in the use of fea we shall describe herein a novel process that utilizes afe to produce a patient specific assessment of bone strength the process consists of an automatic segmentation of femurs from ct scans by convolution neural networks an automatic mesh generation and application of boundary conditions based on anatomical points a high order fe analysis with numerical error control and finally an automatic report with a clear assessment of bone fracture risk one specific application of afe is the determination of the risk of fracture for patients with tumors of the femur and whether a prophylactic surgery is needed to the best of our knowledge this is the first ce accredited afe application being used by orthopedic surgeons in clinical practice

multi element generalized polynomial chaos for arbitrary probability measures we develop a multi element generalized polynomial chaos me gpc method for arbitrary probability measures and apply it to solve ordinary and partial differential equations with stochastic inputs given a stochastic input with an arbitrary probability measure its random space is decomposed into smaller elements subsequently in each element a new random variable with respect to a conditional probability density function pdf is defined and a set of orthogonal polynomials in terms of this random variable is constructed numerically then the generalized polynomial chaos gpc method is implemented element by element numerical experiments show that the cost for the construction of orthogonal polynomials is negligible compared to the total time cost efficiency and convergence of me gpc are studied numerically by considering some commonly used random variables me gpc provides an efficient and flexible approach to solving differential equations with random inputs especially for problems related to long term integration large perturbation and stochastic discontinuities

optimality of the cusum procedure in continuous time the optimality of cusum under a lorden type criterion setting is considered we demonstrate the optimality of the cusum test for ito processes in a sense similar to lorden s but with a criterion that replaces expected delays by the corresponding kullback leibler divergence

solving elliptic boundary value problems with uncertain coefficients by the finite element method the stochastic formulation this work studies a linear elliptic problem with uncertainty the introduction gives a survey of different formulations of the uncertainty and resulting numerical approximations the major emphasis

covariance kernel representations of multidimensional second order stochastic processes the dynamics of stationary stochastic processes in space is not exactly analogous to that of stationary stochastic processes in the time domain this is due to the unilateral nature of the time series that is only influenced by past values as opposed to the dependence in all directions of the spatial process in this work we unfold the connection that exits between the covariance kernel of a multi dimensional second order autoregressive random process and its underlying discrete random dynamical system starting from a discrete random dynamical system we show that the random process satisfying that system is governed by the modified helmholtz equation in the continuous limit we establish the dependence of the correlation constant on the grid size of the discretization we also show that the random forcing term in the continuous case turns out to be a white noise process a number of covariance functions are worked out for simple and more complex geometrical domains with various boundary conditions in multi dimensions we use both the discrete and the continuous systems in our computations

quickest detection of parameter changes in stochastic regression nonparametric cusum we consider the problem of detecting abrupt parameter changes in a stochastic regression with unknown noise distribution the process changes at some unknown point of time under general conditions on the regression function and unknown distributions of observations before and after the disruption the paper develops a nonparametric cumulative sum procedure cusum unlike likelihood based cusum algorithms constructed mostly on log likelihood ratio statistics we use a special system of basic statistics in page s procedure by applying a sequential sampling scheme which measures time in terms of accumulated kullback leibler k l divergence we come to a system of statistics with the martingale properties close to those of the log likelihood ratios the proposed approach suggests also an alternative performance criterion in the analysis of the procedure by replacing the expected detection delay by the corresponding k l divergence we show that under the false alarm probability constraint the nonparametric cusum rule is optimal in the sense that it ensures the logarithmic asymptotic for the detection delay

information bounds and quick detection of parameter changes in stochastic systems by using information theoretic bounds and sequential hypothesis testing theory this paper provides a new approach to optimal detection of abrupt changes in stochastic systems this approach not only generalizes previous work in the literature on optimal detection far beyond the relatively simple models treated but also suggests alternative performance criteria which are more tractable and more appropriate for general stochastic systems in addition it leads to detection rules which have manageable computational complexity for on line implementation and yet are nearly optimal under the different performance criteria considered

weakly enforced essential boundary conditions for nurbs embedded and trimmed nurbs geometries on the basis of the finite cell method summary enforcing essential boundary conditions plays a central role in immersed boundary methods nitsche s idea has proven to be a reliable concept to satisfy weakly boundary and interface constraints we formulate an extension of nitsche s method for elasticity problems in the framework of higher order and higher continuity approximation schemes such as the b spline and non uniform rational basis spline version of the finite cell method or isogeometric analysis on trimmed geometries furthermore we illustrate a significant improvement of the flexibility and applicability of this extension in the modeling process of complex 3d geometries with several benchmark problems we demonstrate the overall good convergence behavior of the proposed method and its good accuracy we provide extensive studies on the stability of the method its influence parameters and numerical properties and a rearrangement of the numerical integration concept that in many cases reduces the numerical effort by a factor two a newly composed boundary integration concept further enhances the modeling process and allows a flexible discretization independent introduction of boundary conditions finally we present our strategy in the framework of the modeling and isogeometric analysis process of trimmed non uniform rational basis spline geometries copyright 2013 john wiley sons ltd

numerical solution of the three dimensional ginzburg landau models using artificial boundary for three dimensional simulations of the vortex phenomena in superconductors based on the ginzburg landau gl theory the physical variables must be solved in the whole space in general exact boundary conditions on an artificial boundary are discussed to reformulate the problem in a finite domain approximations of these boundary conditions with high accuracy are given and their convergence properties are examined error estimates are derived for the finite element approximations with the approximate boundary conditions

analysis and approximation of the ginzburg landau model of superconductivity the authors consider the ginzburg landau model for superconductivity first some well known features of superconducting materials are reviewed and then various results concerning the model the resultant differential equations and their solution on bounded domains are derived then finite element approximations of the solutions of the ginzburg landau equations are considered and error estimates of optimal order are derived

optimal stopping times for detecting changes in distributions it is shown that page s stopping time is optimal for the detection of changes in distributions in a well defined sense this work is a generalization of an existing result where it was shown that page s stopping time is optimal asymptotically

stochastic description of the peak hip contact force during walking free and going upstairs abstract uncertainty quantification for the response of a patient specific femur is mandatory when advocating finite element fe models in clinical applications reliable stochastic descriptions of physiological hip contact forces are an essential prerequisite for such an endeavor we therefore analyze the in vivo available data of seven individuals from hip98 and orthoload with the objective of characterizing the variability of the peak hip contact force magnitude and two corresponding spatial angles in sagittal and frontal plane during walking free and going upstairs regression analyses with linear mixed effects models were performed resulting in six normal random variables one for each force component and activity importantly the statistical analysis accounts for the fact that same individuals performed both activities the mean of the peak force magnitude was found to be linearly dependent on the body weight with an additional activity specific intercept and all variances were dominated by the inter patient variability no distinct correlation was found between the two angles and the force magnitude the proposed stochastic description of the peak hip contact force during walking free and going upstairs contributes towards future uncertainty quantification of patient specific fe models

femoral strength is better predicted by finite element models than qct and dxa clinicians and patients would benefit if accurate methods of predicting and monitoring bone strength in vivo were available a group of 51 human femurs age range 21 93 23 females 28 males were evaluated for bone density and geometry using quantitative computed tomography qct and dual energy x ray absorptiometry dxa regional bone density and dimensions obtained from qct and dxa were used to develop statistical models to predict femoral strength ex vivo the qct data also formed the basis of a three dimensional finite element fe models to predict structural stiffness the femurs were separated into two groups a model training set n 25 was used to develop statistical models to predict ultimate load and a test set n 26 was used to validate these models the main goal of this study was to test the ability of dxa qct and fe techniques to predict fracture load non invasively in a simple load configuration which produces predominantly femoral neck fractures the load configuration simulated the single stance phase portion of normal gait in 87 of the specimens clinical appearing sub capital fractures were produced the training test study design provided a tool to validate that the predictive models were reliable when used on specimens with unknown strength characteristics the fe method explained at least 20 more of the variance in strength than the dxa models planned refinements of the fe technique are expected to further improve these results three dimensional fe models are a promising method for predicting fracture load and may be useful in monitoring strength changes in vivo

fixed accuracy estimation of an autoregressive parameter abstract for a first order non explosive autoregressive process with unknown parameter beta epsilon 1 1 it is shown that if data are collected according to a particular stopping rule the least squares estimator of beta is asymptotically normally distributed uniformly in beta in the case of normal residuals the stopping rule may be interpreted as sampling until the observed fisher information reaches a preassigned level the situation is contrasted with the fixed sample size case where the estimator has a non normal limiting distribution when beta 1 author

quickest detection in coupled systems this work considers the problem of quickest detection of signals in a coupled system of n sensors which receive continuous sequential observations from the environment it is assumed that the signals which are modeled by general ito processes are coupled across sensors but that their onset times may differ from sensor to sensor two main cases are considered in the first one signal strengths are the same across sensors while in the second one they differ by a constant the objective is the optimal detection of the first time at which any sensor in the system receives a signal the problem is formulated as a stochastic optimization problem in which an extended minimal kullback leibler divergence criterion is used as a measure of detection delay with a constraint on the mean time to the first false alarm the case in which the sensors employ cumulative sum cusum strategies is considered and it is proved that the minimum of n cusums is asymptotically optimal as the mean time to the first false

a b spline based heterogeneous modeling and analysis of proximal femur with graded element bone is a complex biological tissue and natural heterogeneous object the main objective of this study is to simulate quasi static loading of bio objects like human femur with b spline based modeling and its 3d finite element analysis with graded element b spline surface representation method is extended to represent material composition to develop heterogeneous solid model of proximal femur lagrangian graded element is used to assign inhomogeneous isotropic elastic properties in finite element model to improve the performance convergence study is carried out with finite element model in single leg stance load condition to test the feasibility of the model sensitivity of simulation is investigated to validate the model numerical results are compared with those of an experimental work for the same specimen in simple stance load condition obtained from one of the reference paper good agreement is achieved for vertical displacement and strains in most of the locations

high dimensional integration of smooth functions over cubes we construct a new algorithm for the numerical integration of functions that are defined on a d dimensional cube it is based on the clenshaw curtis rule for d 1 and on smolyak s construction this way we make the best use of the smoothness properties of any nonperiodic function we prove error bounds showing that our algorithm is almost optimal up to logarithmic factors for different classes of functions with bounded mixed derivative numerical results show that the new method is very competitive in particular for smooth integrands and d ge 8

sequential changepoint detection in quality control and dynamical systems after a brief survey of a large variety of sequential detection procedures that are widely scattered in statistical references on quality control and engineering references on fault detection and signal processing we study some open problems concerning these procedures and introduce a unified theory of sequential changepoint detection this theory leads to a class of sequential detection rules which are not too demanding in computational and memory requirements for on line implementation and yet are nearly optimal under several performance criteria

a convergence study of a new partitioned fluid structure interaction algorithm based on fictitious mass and damping we develop analyze and validate a new method for simulating fluid structure interactions fsis which is based on fictitious mass and fictitious damping in the structure equation we employ a partitioned method for the fluid and structure motions in conjunction with sub iteration and aitken relaxation in particular the use of such fictitious parameters requires sub iterations in order to reduce the induced error in addition to the local temporal truncation error to this end proper levels of tolerance for terminating the sub iteration procedure have been obtained in order to recover the formal order of temporal accuracy for the coupled fsi problem these fictitious terms have a significant effect leading to better convergence rate and hence substantially smaller number of sub iterations through analysis we identify the proper range of these parameters which we then verify by corresponding numerical tests we implement the method in the context of spectral element discretization which is more sensitive than low order methods to numerical instabilities arising in the explicit fsi coupling however the method we present here is simple and general and hence applicable to fsi based on any other discretization we demonstrate the effectiveness of the method in applications involving 2d vortex induced vibrations viv and in 3d flexible arteries with structural density close to blood density we also present 3d results for a patient specific aneurysmal flow under pulsatile flow conditions examining in particular the sensitivity of the results on different values of the fictitious parameters

a note on studentizing a test for heteroscedasticity abstract breusch and pagan 1979 have recently proposed a convenient test for heteroscedasticity in general linear models this note derives the asymptotic distribution of their test under sequences of contiguous alternatives to the null hypothesis of homoscedasticity the test is shown to possess asymptotically incorrect size nominal significance level except in the case of strictly gaussian disturbances a slight modification of the test is proposed which corrects this defect

optimal detection of a change in distribution abstract document discusses a stopping rule that is a limit of bayes rules derived then an almost minimax rule is presented

numerical solution of spectral stochastic finite element systems abstract this paper addresses the issues involved in solving systems of linear equations which arise in the context of the spectral stochastic finite element ssfem formulation two efficient solution procedures are presented that dramatically reduce the amount of computations involved in numerically solving these problems a brief review is first provided of the underlying spectral approach which highlights the peculiar structure of the matrices generated and how their properties are related to both the level of approximation involved as well as to the convergence behavior of the proposed solution procedure the differences between these matrices from their deterministic finite element counterparts are illustrated an iterative solution scheme is proposed which utilizes their specific properties for efficient memory management and enhanced convergence behavior results from numerical tests are presented comparisons with standard algorithms illustrate the efficiency of the proposed algorithm the second solution procedure presented in this paper is based on hierarchical basis concepts results from numerical tests are again provided and the limitations of this approach are assessed the performance of both proposed algorithms indicates that the linear algebraic systems from the underlying ssfem formulation can be solved with considerably less effort in memory and computation time than their size suggests furthermore the data structures and the hierarchical concept introduced in this study are found to have great potential for the future development of adaptive procedures in stochastic fem

stochastic finite element analysis of shells with combined random material and geometric properties abstract in this work an extended stochastic formulation of the triangular composite facet shell element tric is presented for the case of combined uncertain material young s modulus poisson s ratio and geometric thickness properties these properties are assumed to be described by uncorrelated two dimensional homogeneous stochastic fields the stochastic finite element analysis of shell structures is performed using the spectral representation method for the description of the random fields in conjunction with monte carlo simulation mcs for the computation of the response variability useful conclusions regarding the influence of each one of the structural parameters on the response variability are derived from the numerical tests examined

the wiener askey polynomial chaos for stochastic differential equations we present a new method for solving stochastic differential equations based on galerkin projections and extensions of wiener s polynomial chaos specifically we represent the stochastic processes with an optimum trial basis from the askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error several continuous and discrete processes are treated and numerical examples show substantial speed up compared to monte carlo simulations for low dimensional stochastic inputs

the tetrahedral finite cell method higher order immersogeometric analysis on adaptive non boundary fitted meshes the finite cell method fcm is an immersed domain finite element method that combines higher order non boundary fitted meshes weak enforcement of dirichlet boundary conditions and adaptive quadrature based on recursive subdivision due to its ability to improve the geometric resolution of intersected elements it can be characterized as an immersogeometric method in this paper we extend the fcm so far only used with cartesian hexahedral elements to higher order non boundary fitted tetrahedral meshes based on a reformulation of the octree based subdivision algorithm for tetrahedral elements we show that the resulting tetfcm scheme is fully accurate in an immersogeometric sense that is the solution fields achieve optimal and exponential rates of convergence for h and p refinement if the immersed geometry is resolved with sufficient accuracy tetfcm can leverage the natural ability of tetrahedral elements for local mesh refinement in three dimensions its suitability for problems with sharp gradients and highly localized features is illustrated by the immersogeometric phase field fracture analysis of a human femur bone

a nonparametric control chart for detecting small disorders we consider sequential observation of independent random variables x 1 cdots x n whose distribution changes from f to g after the first lbrack n theta rbrack variables the object is to detect the unknown change point quickly without too many false alarms a nonparametric control chart based on partial weighted sums of sequential ranks is proposed it is shown that if the change from f to g is small then as n rightarrow infty the appropriately scaled and linearly interpolated graph of partial rank sums converges to a brownian motion on which a drift sets in at time theta using this the asymptotic performance of the one sided control chart is compared with one based on partial sums of the x s location change scale change and contamination are considered it is found that for distributions with heavy tails the control chart based on ranks stops more frequently and faster than the one based on the x s performance of the two procedures are also tested on simulated data and the outcomes are compatible with the theoretical results

a new compact finite difference scheme for solving the complex ginzburg landau equation the complex ginzburg landau equation is often encountered in physics and engineering applications such as nonlinear transmission lines solitons and superconductivity however it remains a challenge to develop simple stable and accurate finite difference schemes for solving the equation because of the nonlinear term most of the existing schemes are obtained based on the crank nicolson method which is fully implicit and must be solved iteratively for each time step in this article we present a fourth order accurate iterative scheme which leads to a tri diagonal linear system in 1d cases we prove that the present scheme is unconditionally stable the scheme is then extended to 2d cases numerical errors and convergence rates of the solutions are tested by several examples

detecting a change in regression first order optimality observations are generated according to a regression with normal error as a function of time when the process is in control the process potentially changes at some unknown point of time and then the ensuing observations are normal with the same mean function plus an arbitrary function under suitable regularity conditions the problem is to obtain a stopping rule that is optimal in the sense that the rule minimizes the expected delay in detecting a change subject to a constraint on the average run length to a false alarm a bound on the expected delay is first obtained it is then shown that the cusum and shiryayev roberts procedures achieve this bound to first order

finite elements for elliptic problems with stochastic coefficients abstract we describe a deterministic finite element fe solution algorithm for a stochastic elliptic boundary value problem sbvp whose coefficients are assumed to be random fields with finite second moments and known piecewise smooth two point spatial correlation function separation of random and deterministic variables parametrization of the uncertainty is achieved via a karhunen loeve kl expansion an o n log n algorithm for the computation of the kl eigenvalues is presented based on a kernel independent fast multipole method fmm truncation of the kl expansion gives an m 1 wiener polynomial chaos pc expansion of the stochastic coefficient and is shown to lead to a high dimensional deterministic boundary value problem dbvp analyticity of its solution in the stochastic variables with sharp bounds for the domain of analyticity are used to prescribe variable stochastic polynomial degree r r1 rm in an m r wiener pc expansion for the approximate solution pointwise error bounds for the fem approximations of kl eigenpairs the truncation of the kl expansion and the fe solution to the dbvp are given numerical examples show that m depends on the spatial correlation length of the random diffusion coefficient the variable polynomial degree r in pc stochastic galerkin fem allows to handle kl expansions with m up to 30 and r1 up to 10 in moderate time

finite dimensional approximation of nonlinear problems in the first two papers of this series 4 5 we have studied a general method of approximation of nonsingular solutions and simple limit points of nonlinear equations in a banach space we derive here general approximation results of the branches of solutions in the neighborhood of a simple bifurcation point the abstract theory is applied to the galerkin approximation of nonlinear variational problems and to a mixed finite element approximation of the von karman equations

formulation of geometrically non linear problems in the spatial reference frame this paper presents a new formulation for geometrically non linear problems and their numerical treatment by the p version of the finite element method the formulation is characterized by a weak form based on the spatial representation of the equilibrium equations a deformed geometry mapped by the displacement field a natural description for non conservative loads that keeps the symmetry of the equations and a direct non incremental iterative algorithm to solve the equations the paper is concerned only with problems for which the solution is unique i e the load displacement curves are single valued and the strains are small examples are presented 1997 by john wiley sons ltd

finite element approximation of a periodic ginzburg landau model for type ii superconductors we consider efficient finite element algorithms for the computational simulation of type ii superconductors the algorithms are based on discretizations of a periodic ginzburg landau model periodicity is defined with respect to a non orthogonal lattice that is not necessarily aligned with the coordinate axes also the primary dependent variables employed in the model satisfy non standard quasi periodic boundary conditions after introducing the model we define finite element schemes derive error estimates of optimal order and present the results of some numerical calculations for a similar quality of simulation the resulting algorithms seem to be significantly less costly than are previously used numerical approximation methods

validation of subject specific automated p fe analysis of the proximal femur abstract background the use of subject specific finite element fe models in clinical practice requires a high level of automation and validation in yosibash et al 2007a reliable simulations of the human proximal femur by high order finite element analysis validated by experimental observations j biomechanics 40 3688 3699 a novel method for generating high order finite element p fe models from ct scans was presented and validated by experimental observations on two fresh frozen femurs harvested from a 30 year old male and 21 year old female herein we substantiate the validation process by enlarging the experimental database 54 year old female femur improving the method and examine its robustness under different ct scan conditions approach a fresh frozen femur of a 54 year old female was scanned under two different environments in air and immersed in water dry and wet ct thereafter the proximal femur was quasi statically loaded in vitro by a 1000 n load the two qct scans were manipulated to generate p fe models that mimic the experimental conditions we compared p fe displacements and strains of the wet ct model to the dry ct model and to the experimental results in addition the material assignment strategy was reinvestigated the inhomogeneous young s modulus was represented in the fe model using two different methods directly extracted from the ct data and using continuous spatial functions as in yosibash et al 2007a reliable simulations of the human proximal femur by high order finite element analysis validated by experimental observations j biomechanics 40 3688 3699 results excellent agreement between dry and wet fe models was found for both displacements and strains i e the method is insensitive to ct conditions and may be used in vivo good agreement was also found between fe results and experimental observations the spatial functions representing young s modulus are local and do not influence strains and displacements prediction finally the p fe results of all three fresh frozen human femurs compare very well to experimental observations exemplifying that the presented method may be in a mature stage to be used in clinical computer aided decision making

discrete gauge invariant approximations of a time dependent ginzburg landau model of superconductivity we present here a mathematical analysis of a nonstandard difference method for the numerical solution of the time dependent ginzburg landau models of superconductivity this type of method has been widely used in numerical simulations of the behavior of superconducting materials we also illustrate some of their nice properties such as the gauge invariance being retained in discrete approximations and the discrete order parameter having physically consistent pointwise bound

accuracy of finite element predictions in sideways load configurations for the proximal human femur abstract in undetermined subject specific finite element models have been used to predict stress state and fracture risk in individual patients while many studies analysed quasi axial loading configurations only few works simulated sideways load configurations such as those arising in a fall the majority among these latter directly predicted bone strength without assessing elastic strain prediction accuracy the aim of the present work was to evaluate if a subject specific finite element modelling technique from ct data that accurately predicted strains in quasi axial loading configurations is suitable to accurately predict strains also when applying low magnitude loads in sideways configurations to this aim a combined numerical experimental study was performed to compare finite element predicted strains with strain gauge measurements from three cadaver proximal femurs instrumented with sixteen strain rosettes and tested non destructively under twelve loading configurations spanning a wide cone 0 30 for both adduction and internal rotation angles of sideways fall scenarios the results of the present study evidenced a satisfactory agreement between experimentally measured and predicted strains r2 greater than 0 9 rmse lower than 10 and displacements the achieved strain prediction accuracy is comparable to those obtained in state of the art studies in quasi axial loading configurations still the presence of the highest strain prediction errors around 30 in the lateral neck aspect would deserve attention in future studies targeting bone failure less

incorporating uncertainty in mechanical properties for finite element based evaluation of bone mechanics finite element fe models of bone developed from computed tomography ct scan data are used to evaluate stresses and strains load transfer and fixation of implants and potential for fracture the experimentally derived relationships used to transform ct scan data in hounsfield unit to modulus and strength contain substantial scatter the scatter in these relationships has potential to impact the results and conclusions of bone studies the objectives of this study were to develop a computationally efficient probabilistic fe based platform capable of incorporating uncertainty in bone property relationships and to apply the model to a representative analysis variability in stresses and fracture risk was predicted in five proximal femurs under stance loading conditions based on published variability in strength and modulus relationships derived in the proximal femur the probabilistic analysis predicted the distributions of stress and risk for the five femurs analyzed the 1 and 99 percentile bounds varied by an average of 17 3 mpa for stress and by 0 28 for risk in each femur the predicted variability in risk was greater than 50 of the mean risk calculated with obvious implications for clinical assessment results using the advanced mean value amv method required only seven analysis trials 1 h and differed by less than 2 when compared to a 1000 trial monte carlo simulation 400 h the probabilistic modeling platform developed has broad applicability to bone studies and can be similarly implemented to investigate other loading conditions structures sources of uncertainty or output measures of interest r 2007 elsevier ltd all rights reserved

comparison of explicit finite element and mechanical simulation of the proximal femur during dynamic drop tower testing abstract current screening techniques based on areal bone mineral density abmd measurements are unable to identify the majority of people who sustain hip fractures biomechanical examination of such events may help determine what predisposes a hip to be susceptible to fracture recently drop tower simulations of in vitro sideways falls have allowed the study of the mechanical response of the proximal human femur at realistic impact speeds this technique has created an opportunity to validate explicit finite element fe models against dynamic test data this study compared the outcomes of 15 human femoral specimens fractured using a drop tower with complementary specimen specific explicit fe analysis correlation coefficient and root mean square error rmse were found to be moderate for whole bone stiffness comparison r2 0 3476 and 22 85 respectively no correlation was found between experimentally and computationally predicted peak force however energy absorption comparison produced moderate correlation and rmse r2 0 4781 and 29 14 respectively by comparing predicted strain maps to high speed video data we demonstrated the ability of the fe models to detect vulnerable portions of the bones based on our observations we conclude that there exists a need to extend the current apparent level material models for bone to cover higher strain rates than previously tested experimentally

a stochastic collocation method for elliptic partial differential equations with random input data in this paper we propose and analyze a stochastic collocation method to solve elliptic partial differential equations with random coefficients and forcing terms input data of the model the input data are assumed to depend on a finite number of random variables the method consists in a galerkin approximation in space and a collocation in the zeros of suitable tensor product orthogonal polynomials gauss points in the probability space and naturally leads to the solution of uncoupled deterministic problems as in the monte carlo approach it can be seen as a generalization of the stochastic galerkin method proposed in i babuscka r tempone and g e zouraris siam j numer anal 42 2004 pp 800 825 and allows one to treat easily a wider range of situations such as input data that depend nonlinearly on the random variables diffusivity coefficients with unbounded second moments and random variables that are correlated or even unbounded we provide a rigorous convergence analysis and demonstrate exponential convergence of the probability error with respect to the number of gauss points in each direction in the probability space under some regularity assumptions on the random input data numerical examples show the effectiveness of the method

stochastic simulation of riser sections with uncertain measured pressure loads and or uncertain material properties abstract we investigate three dimensional problems in solid mechanics with stochastic loading or material properties to solve these problems we use a spectral expansion of the solution and random inputs based on askey type orthogonal polynomials in terms of independent identically distributed i i d random variables a galerkin procedure using these types of expansions the generalized polynomial chaos gpc method is employed to solve linear elasticity problems an analagous spectral collocation formulation is used to study problems in nonlinear elasticity these methods both cast the stochastic problem as a coupled or decoupled high dimensional system of deterministic pdes which is then solved numerically using a deterministic p finite element solver we present algorithms for solving certain coupled systems arising from the stochastic galerkin projection without modifying the original deterministic solver three dimensional riser sections undergoing elastic deformations due to random pressure loads are considered we also model a riser section with stochastic young s modulus undergoing deterministic loads it is demonstrated that the gpc method provides accurate and efficient results at a speed up factor of two and three orders of magnitude compared to traditional monte carlo simulations for nonlinear problems the stochastic collocation method is also shown to be much faster than monte carlo simulation while still rivaling this method in simplicity of implementation

uncertainty quantification for personalized analyses of human proximal femurs 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 relationship and a stochastic hip contact force representing realistic variability of experimental data their influence on the prediction of principal strains 1 and 3 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 1 and 3 are attributable to the uncertainty in the e 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

analysis and convergence of a covolume approximation of the ginzburg landau model of superconductivity in this paper we present the mathematical analysis of a covolume method for the approximations of the ginzburg landau gl model for superconductivity a nice feature of this approach is that the gauge invariance properties are retained in discrete approximations based on triangular grids we also use properties of discrete vector fields to study issues such as the gauge choices and their enforcement