the sensitivity of muscle force predictions to changes in physiologic cross sectional area abstract the mechanical effects of a muscle are related in part to the size of the muscle and to its location relative to the joint it crosses for more than a century researchers have expressed muscle size by its physiological cross sectional area pcsa researchers mathematically calculating muscle and joint forces typically use some expression of a muscle s pcsa to constrain the solution to one which is reasonable i e a solution in which small muscles may not have large forces and large muscles have large forces when expected or when there is significant electromyographic activity it is obvious that muscle mass and therefore any expression of pcsa varies significantly from person to person even in individuals of similar weight and height since it is not practical to predict the pcsa of each muscle in a living subject s limb or trunk it is important to generally understand the sensitivity of muscle force solutions to possible variations in pcsa we used nonlinear optimization techniques to predict 47 muscle forces and hip contact forces in a living subject the pcsa volume muscle fiber length of each of 47 lower limb muscle elements from two cadaver specimens and the 47 pcsa s reported by pierrynowski were input into an optimization algorithm to create three solution sets the three solutions were qualitatively similar but at times a predicted muscle force could vary as much as two to eight times in contrast the joint force solutions were within 11 of each other and therefore much less variable when using optimization techniques to predict muscle forces it must be recognized that the solution is sensitive to many assumptions and variables such as pcsa the muscle force solutions are therefore best used to determine relative values i e trends in parametric studies on the other hand the joint force solutions are less sensitive to such variations and the absolute values are more reliable

approximation of a laminated microstructure for a rotationally invariant double well energy density we give error estimates for the approximation of a laminated microstructure which minimizes the energy int omega phi nabla v x dx for a rotationally invariant double well energy density phi a we present error estimates for the convergence of the deformation in l 2 the convergence of directional derivatives of the deformation in the twin planes the weak convergence of the deformation gradient the convergence of the microstructure or young measure of the deformation gradients and the convergence of nonlinear integrals of the deformation gradient

a level set approach to the computation of twinning and phase transition dynamics a computational method is proposed for the dynamics of solids capable of twinning and phase transitions in a two dimensional sharp interface model of twinning the stored energy function is a nonconvex potential with multiple wells the evolution of twin interfaces is governed by field equations and jump conditions of momentum balance and by a kinetic relation expressing the interface velocity as a function of the local driving traction and interfacial orientation a regularized version of the model is constructed based on the level set method a level set function which changes signs across the interface is introduced the evolution of this function is described by a hamilton jacobi equation whose velocity coefficient is determined by the kinetic relation jump conditions are thereby eliminated allowing finite difference discretization numerical simulations exhibit complex evolution of the interface including cusp formation needle growth spontaneous tip splitting and topological changes that result in microstructure refinement the results capture experimentally observed phenomena in martensitic crystals

construction of hadamard states by pseudo differential calculus we give a new construction based on pseudo differential calculus of quasi free hadamard states for klein gordon equations on a class of space times whose metric is well behaved at spatial infinity in particular on this class of space times we construct all pure hadamard states whose two point function expressed in terms of cauchy data on a cauchy surface is a matrix of pseudo differential operators we also study their covariance under symplectic transformations

dynamic solid solid transitions with phase characterized by an order parameter abstract we develop a thermodynamically consistent continuum theory for the study of solid solid phase transitions where deformation dominates heat and mass transfer we use an order parameter to characterize the notion of phase and identify phase interfaces with thin transition zones within which the strain and order parameter exhibit large gradients to model the growth of one phase at the expense of another we introduce configurational forces subject to their own balance that work against changes in the order parameter by studying traveling waves and the asymptotics of a transition layer we establish connections between our theory and more standard approaches that identify phase interfaces with surfaces of strain discontinuity

kinetic relations and the propagation of phase boundaries in solids this paper treats the dynamics of phase transformations in elastic bars the specific issue studied is the compatibility of the field equations and jump conditions of the one dimensional theory of such bars with two additional constitutive requirements a kinetic relation controlling the rate at which the phase transition takes place and a nucleation criterion for the initiation of the phase transition a special elastic material with a piecewise linear non monotonic stress strain relation is considered and the riemann problem for this material is analyzed for a large class of initial data it is found that the kinetic relation and the nucleation criterion together single out a unique solution to this problem from among the infinitely many solutions that satisfy the entropy jump condition at all strain discontinuities

statistical shape modelling versus linear scaling effects on predictions of hip joint centre location and muscle moment arms in people with hip osteoarthritis abstract marker based dynamic functional or regression methods are used to compute joint centre locations that can be used to improve linear scaling of the pelvis in musculoskeletal models although large errors have been reported using these methods this study aimed to investigate if statistical shape models could improve prediction of the hip joint centre hjc location the inclusion of complete pelvis imaging data from computed tomography ct was also explored to determine if free form deformation techniques could further improve hjc estimates mean euclidean distance errors were calculated between hjc from ct and estimates from shape modelling methods and functional and regression based linear scaling approaches the hjc of a generic musculoskeletal model was also perturbed to compute the root mean squared error rmse of the hip muscle moment arms between the reference hjc obtained from ct and the different scaling methods shape modelling without medical imaging data significantly reduced hjc location error estimates 11 4 3 3 mm compared to functional 36 9 17 5 mm p

one dimensional front tracking based on high resolution wave propagation methods a simple approach to shock tracking is presented in conjunction with conservative high resolution shock capturing methods in one space dimension an underlying uniform grid is used with additional grid interfaces introduced at appropriate points for tracked shocks conservative high resolution methods based on the large time step wave propagation approach are used on the resulting nonuniform grid this method is stable even if some of the small cells created by the tracked interface are orders of magnitude smaller than the regular cells used to determine the time step a fractional step method is used to handle source terms several calculations are presented to demonstrate the effectiveness of the method including an unstable detonation wave calculation where mesh refinement in the reaction zone is required in addition to shock tracking stability and accuracy results of the method are also shown for some sample problems the basic ideas described here can be extended to two space dimensions as will be

subject specific calibration of neuromuscular parameters enables neuromusculoskeletal models to estimate physiologically plausible hip joint contact forces in healthy adults in vivo hip joint contact forces hjcf can be estimated using computational neuromusculoskeletal nms modelling however different neural solutions can result in different hjcf estimations nms model predictions are also influenced by the selection of neuromuscular parameters which are either based on cadaveric data or calibrated to the individual to date the best combination of neural solution and parameter calibration to obtain plausible estimations of hjcf have not been identified the aim of this study was to determine the effect of three electromyography emg informed neural solution modes emg driven emg hybrid and emg assisted and static optimisation each using three different parameter calibrations uncalibrated minimise joint moments error and minimise joint moments error and peak hjcf on the estimation of hjcf in a healthy population n 23 during walking when compared to existing in vivo data the emg assisted mode and static optimisation produced the most physiologically plausible hjcf when using a nms model calibrated to minimise joint moments error and peak hjcf emg assisted mode produced first and second peaks of 3 55 times body weight bw and 3 97 bw during walking static optimisation produced 3 75 bw and 4 19 bw respectively however compared to static optimisation emg assisted mode generated muscle excitations closer to recorded emg signals average across hip muscles r2 0 60 0 37 versus r2 0 12 0 14 findings suggest that the emg assisted mode combined with minimise joint moments error and peak hjcf calibration is preferable for the estimation of hjcf and generation of realistic load distribution across muscles

coupling of general lagrangian systems this work is devoted to the coupling of two fluid models such a s two euler systems in lagrangian coordinates at a fixed interface we define coupling conditi ons which can be expressed in terms of continuity of some well chosen variables and then solve the coupled riemann problem in the present setting where the interface is characteristic a particula r choice of dependent variables which are transmitted ensures the overall conservativity

the generally covariant locality principle a new paradigm for local quantum field theory a new approach to the model independent description of quantum field theories will be introduced in the present work the main feature of this new approach is to incorporate in a local sense the principle of general covariance of general relativity thus giving rise to the concept of a locally covariant quantum field theory such locally covariant quantum field theories will be described mathematically in terms of covariant functors between the categories on one side of globally hyperbolic spacetimes with isometric embeddings as morphisms and on the other side of algebras with unital injective monomorphisms as morphisms moreover locally covariant quantum fields can be described in this framework as natural transformations between certain functors the usual haag kastler framework of nets of operator algebras over a fixed spacetime background manifold together with covariant automorphic actions of the isometry group of the background spacetime can be re gained from this new approach as a special case examples of this new approach are also outlined in case that a locally covariant quantum field theory obeys the time slice axiom one can naturally associate to it certain automorphic actions called relative cauchy evolutions which describe the dynamical reaction of the quantum field theory to a local change of spacetime background metrics the functional derivative of a relative cauchy evolution with respect to the spacetime metric is found to be a divergence free quantity which has as will be demonstrated in an example the significance of an energy momentum tensor up to addition of scalar functions for the locally covariant quantum field theory furthermore we discuss the functorial properties of state spaces of locally covariant quantum field theories that entail the validity of the principle of local definiteness

the massive feynman propagator on asymptotically minkowski spacetimes we consider the massive klein gordon equation on asymptoti cally minkowski spacetimes in the sense that the manifold is r 1 d and the metric approaches that of minkowski space at infinity in a short range way jointly in time and space variables in this setup we define feynman and anti feynman scattering data and prove the fredholm property of the klein gordon operator with the associated atiyah patodi singer type boundary conditions at infinite times we then construct a parametrix with compact remainder terms for the fredholm problem and prove that it is also a feynman parametrix in the sense of duistermaat and hormander

a level set approach to domain wall kinetics and domain patterning in elastic ferroelectrics the level set method is a powerful tool for tracking a moving interface in ferroelectric materials the boundaries between domains of uniform polarization referred to as domain walls are viewed as interfaces in this work a variational level set method is used to formulate a model for the behavior of elastic ferroelectrics and more particularly to describe the domain formation and the domain wall kinetics a regularized version of the sharp interface theory is introduced by substitution of the singular surfaces with thin transition layers inserting so inhomogeneities into the energy density function it is proved that the forces driving domain wall motion are in fact inhomogeneity forces with this description the level set method becomes an appropriate framework to insert and exploit material forces the proposed model may interpret typical microstructures in 2 d elastic ferroelectrics with tetragonal crystal symmetry comparisons with phase field models and experiments show good agreement

a level set approach for computing solutions to incompressible two phase flow a level set approach for computing solutions to incompressible two phase flow is presented the interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function a new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface we never have to explicitly reconstruct or find the zero level set consequently we are able to handle arbitrarily complex topologies large density and viscosity ratios and surface tension on relatively coarse grids we use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations we consider the motion of air bubbles and water drops we also compute flows with multiple fluids such as air oil and water

on nonlinear stability of general undercompressive viscous shock waves we study the nonlinear stability of general undercompressive viscous shock waves previously the authors showed stability in a special case when the shock phase shift can be determined a priori from the total mass of the perturbation using new pointwise methods by examining time invariants associated with the linearized equations we can now overcome a new difficulty in the general case namely nonlinear movement of the shock we introduce a coordinate transformation suitable to treat this new aspect and demonstrate our method by analyzing a model system of generic type we obtain sharp pointwise bounds andlp behavior of the solution for allp 1 p

high order schemes entropy inequalities and nonclassical shocks we are concerned with the approximation of undercompressive regularization sensitive nonclassical solutions of hyperbolic systems of conservation laws by high order accurate conservative and semidiscrete finite difference schemes nonclassical shock waves can be generated by diffusive and dispersive terms kept in balance particular attention is given here to a class of systems of conservation laws including the scalar equations and the system of nonlinear elasticity and to linear diffusion and dispersion in either the conservative or the entropy variables first we investigate the existence and the properties of entropy conservative schemes a notion due to tadmor math comp 49 1987 pp 91 103 in particular we exhibit a new five point scheme which is third order accurate at least second we study a class of entropy stable and high order accurate schemes satisfying a single cell entropy inequality they are built from any high order entropy conservative scheme by adding to it a mesh independent numerical viscosity which preserves the order of accuracy of the base scheme these schemes can only converge to solutions of the system of conservation laws satisfying the entropy inequality these entropy stable schemes exhibit mild oscillations near shocks and interestingly may converge to classical or nonclassical entropy solutions depending on the sign of their dispersion coefficient then based on a third order entropy conservative scheme we propose a general scheme for the numerical computation of nonclassical shocks importantly our scheme satisfies a cell entropy inequality following hayes and lefloch siam j numer anal 35 1998 pp 2169 2194 we determine numerically the kinetic function which uniquely characterizes the dynamics of nonclassical shocks for each regularization of the conservation laws our results compare favorably with previous analytical and numerical results finally we prove that there exists no fully discrete and entropy conservative scheme and we investigate the entropy stability of a class of fully discrete lax wendroff type schemes

an emg driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo this paper examined if an electromyography emg driven musculoskeletal model of the human knee could be used to predict knee moments calculated using inverse dynamics across a varied range of dynamic contractile conditions muscle tendon lengths and moment arms of 13 muscles crossing the knee joint were determined from joint kinematics using a three dimensional anatomical model of the lower limb muscle activation was determined using a second order discrete non linear model using rectified and lowpass filtered emg as input a modified hill type muscle model was used to calculate individual muscle forces using activation and muscle tendon lengths as inputs the model was calibrated to six individuals by altering a set of physiologically based parameters using mathematical optimisation to match the net flexion extension fe muscle moment with those measured by inverse dynamics the model was calibrated for each subject using 5 different tasks including passive and active fe in an isokinetic dynamometer running and cutting manoeuvres recorded using three dimensional motion analysis once calibrated the model was used to predict the fe moments estimated via inverse dynamics from over 200 isokinetic dynamometer running and sidestepping tasks the inverse dynamics joint moments were predicted with an average r 2 of 0 91 and mean residual error of b12 nm a re calibration of only the emg to activation parameters revealed fe moments prediction across weeks of similar accuracy changing the muscle model to one that is more physiologically correct produced better predictions the modelling method presented represents a good way to estimate in vivo muscle forces during movement tasks r 2003 elsevier science ltd all rights reserved

a conservative and convergent scheme for undercompressive shock waves undercompressive shock waves arise in numerous physical applications we propose a class of conservative finite volume type schemes to approximate weak solutions of conservation laws that contain undercompressive shock waves we prove the convergence of a subsequence of approximate solutions towards a generalized entropy solution if the mesh width tends to zero the proof relies on a refined bv compactness analysis which accounts for the effect of the kinetic relation that drives the undercompressive wave at the same time we establish a new proof for the existence of solutions to the underlying model numerical experiments supplement the analytical results

the three dimensional determination of internal loads in the lower extremity a three dimensional model of the lower limb containing 47 muscles was developed to study the differences between a two and three dimensional approach for determining internal loads the role of the dynamic joint representation and the behavior of different load bearing criteria in walking and running the problem of redundancy of the musculo skeletal system was resolved by applying inverse dynamics and static optimization methods different hypothetical load bearing capabilities of hinge spherical and intermediate joint types for the knee and the ankle joints were tested it was found that even almost planar movements such as walking and running are associated with significant three dimensional intersegment moments especially in the frontal plane thus a two dimensional approach may underestimate internal loads up to 60 it is shown that pure hinge joints are inappropriate for modeling the dynamical joint function of the knee and ankle joints a more flexible joint representation in combination with a squared muscle stress minimization criterion predicted a lot of synergistic as well as antagonistic muscle activation which was also found in the emg patterns the results indicate the importance of muscular joint stabilization in natural human movements compared to in vivo measurements it is speculated that the predicted force magnitudes are considerably overestimated due to error propagation and still insufficient anatomical models thus increased efforts to improve further the reliability of internal load calculations should be made in the future

a one parameter neural activation to muscle activation model estimating isometric joint moments from electromyograms nonlinearities have been observed in the isometric emg force relationship however these are generally not included when using emg driven hill type muscle models that account for muscle activation dynamics in this paper we present a formulation for a one parameter transformation model i e a model that accounts for the type of physiological nonlinearities observed at low levels of force the general shape for the curvilinear portion of the curve was based on phenomenological data reported by woods and bigland ritchie the one parameter a model is easy to implement and when used with an emg driven hill type model was shown to provide a better fit of the measured joint moment optimization methods were used to determine the appropriate curvature of the relationship for each muscle and thus introduced a degree of tuning to each subject

subject specific knee joint geometry improves predictions of medial tibiofemoral contact forces estimating tibiofemoral joint contact forces is important for understanding the initiation and progression of knee osteoarthritis however tibiofemoral contact force predictions are influenced by many factors including muscle forces and anatomical representations of the knee joint this study aimed to investigate the influence of subject specific geometry and knee joint kinematics on the prediction of tibiofemoral contact forces using a calibrated emg driven neuromusculoskeletal model of the knee one participant fitted with an instrumented total knee replacement walked at a self selected speed while medial and lateral tibiofemoral contact forces ground reaction forces whole body kinematics and lower limb muscle activity were simultaneously measured the combination of generic and subject specific knee joint geometry and kinematics resulted in four different opensim models used to estimate muscle tendon lengths and moment arms the subject specific geometric model was created from ct scans and the subject specific knee joint kinematics representing the translation of the tibia relative to the femur was obtained from fluoroscopy the emg driven model was calibrated using one walking trial but with three different cost functions that tracked the knee flexion extension moments with and without constraint over the estimated joint contact forces the calibrated models then predicted the medial and lateral tibiofemoral contact forces for five other different walking trials the use of subject specific models with minimization of the peak tibiofemoral contact forces improved the accuracy of medial contact forces by 47 and lateral contact forces by 7 respectively compared with the use of generic musculoskeletal model

the computational modelling of branching fine structures in constrained crystals we introduce a finite element method which is piecewise continuous on the microscopic scale of the spatial resolution h but discontinuous on the mesoscopic scale h 0 1 the method is designed to capture the morphology of needle twin structures frequently found in ferric and pseudo elastic crystals namely in uniaxial ferromagnets and au milieu of the austenite martensite interfaces the approach is based on a domain decomposition method that interpolates between the scale on order of the size of crystal and the microscopic scale of finite element approximation h the scale interpolation is enabled by incorporating frequency adaptivity the visualization and analysis of the computational results presented disclose microstructures corresponding to complex scaling laws we document that the fine structures obtained by the presented method are not visible using classical formulation of the underlying variational problem and using conforming approximation of admissible sets the proposed method is suitable for non smooth relaxation and optimization when the minimizers lack the often required c1 regularity and when they exhibit fractal behavior

propagating phase boundaries formulation of the problem and existence via the glimm method this paper treats the hyperbolic elliptic system of two conservation laws which describes the dynamics of an elastic material having a non monotone strain stress function followingabeyaratne knowles we propose a notion of admissible weak solution for this system in the class of functions of bounded variation the formulation includes an entropy inequality a kinetic relation imposed along any subsonic phase boundary and an initiation criterion for the appearance of new phase boundaries we prove thel1 continuous dependence of the solution to the riemann problem our main result yields the existence and the stability of propagating phase boundaries the proofs are based onglimm s scheme and in particular on the techniques ofglimm andlax in order to deal with the kinetic relation we prove a result of pointwise convergence of the phase boundary

computational methods for propagating phase boundaries this paper considers numerical methods for computing propagating phase boundaries in solids described by the physical model introduced by abeyaratne and knowles the model under consideration consists of a set of conservation laws supplemented with a kinetic relation and a nucleation criterion discontinuities between two different phases are undercompressive crossing waves in the general terminology of nonstrictly hyperbolic systems of conservation laws this paper studies numerical methods designed for the computation of such crossing waves we propose a godunov type method combining front tracking with a capturing method we also consider glimm s random choice scheme both methods share the property that the phase boundaries are sharply computed in the sense that there are no numerical interior points for the description of a phase boundary this property is well known for the glimm s scheme on the other hand our front tracking algorithm is designed so that it tracks phase boundaries but captures shock waves phase boundaries are sensitive to numerical dissipation effects so the above property is essential to ensure convergence toward the correct entropy weak solution convergence of the godnuov type method is demonstrated numerically extensive numerical experiments show the practical interest of both approaches for computations of undercompressive crossing waves

to what extent is joint and muscle mechanics predicted by musculoskeletal models sensitive to soft tissue artefacts musculoskeletal models are widely used to estimate joint kinematics intersegmental loads and muscle and joint contact forces during movement these estimates can be heavily affected by the soft tissue artefact sta when input positional data are obtained using stereophotogrammetry but this aspect has not yet been fully characterised for muscle and joint forces this study aims to assess the sensitivity to the sta of three open source musculoskeletal models implemented in opensim a baseline dataset of marker trajectories was created for each model from experimental data of one healthy volunteer five hundred sta realizations were then statistically generated using a marker dependent model of the pelvis and lower limb artefact and added to the baseline data the sta s impact on the musculoskeletal model estimates was finally quantified using a monte carlo analysis the modelled sta distributions were in line with the literature observed output variations were comparable across the three models and sensitivity to the sta was evident for most investigated quantities shape magnitude and timing of the joint angle and moment time histories were not significantly affected throughout the entire gait cycle whereas magnitude variations were observed for muscle and joint forces ranges of contact force variations differed between joints with hip variations up to 1 8 times body weight observed variations of more than 30 were observed for some of the muscle forces in conclusion musculoskeletal simulations using stereophotogrammetry may be safely run when only interested in overall output patterns caution should be paid when more accurate estimated values are needed

application of a falsification strategy to a musculoskeletal model of the lower limb and accuracy of the predicted hip contact force vector in the literature lower limb musculoskeletal models validated against in vivo measured hip contact forces hcfs exhibit a tendency to overestimate the hcfs magnitude and predict inaccurate components of the hcf vector in the transverse plane in order to investigate this issue a musculoskeletal model was forced to produce hcfs identical to those measured and the resulting joint equilibrium equations were studied through both a general approach and a static optimization framework in the former case the existence of solutions to the equilibrium equations was investigated and the effect of varying the intersegmental moments and the muscle tetanic stress assessed for a value of 100 n cm 2 and moments calculated from an inverse dynamics analysis on average only 62 of analyzed frames were solvable for level walking and 70 for stair climbing in the static optimization study the model could reproduce the experimental hcfs but the recruited muscles were unable to simultaneously equilibrate the hip intersegmental moments without the contribution of reserve moment actuators without constraints imposed on the hcfs the predicted hcf vectors presented maximum angle deviations up to 22 for level walking and 33 for stair climbing during the gait stance phase the influence of the medio lateral hcf component on the solvability of the equilibrium equations and the muscle recruitment alteration when the model was forced to produce the experimental hcfs suggest that a more accurate geometrical representation of the gluteal muscles is mandatory to improve predictions of the hcf vector yielded by the static optimization technique

muscle recruitment by the min max criterion a comparative numerical study this paper introduces the min max criterion for simulation of muscle recruitment in multiple muscle systems the criterion is introduced and justified by comparison to two known criterion types the polynomial criterion and the soft saturation criterion the comparison is performed on a planar three muscle elbow model performing a dumbbell curl a generalized form of the soft saturation criterion is introduced and it is shown that the min max criterion can be interpreted as the limit of the classical criteria when the exponents in their mathematical expressions approach infinity we finally show how the min max criterion can be cast into a form that allows for efficient and robust numerical solution by linear programming it is concluded that the min max criterion possesses a number of attractive physiological as well as algorithmic advantages

hip joint contact loads in older adults during recovery from forward loss of balance by stepping hip joint contact loads during activities of daily living are not generally considered high enough to cause acute bone or joint injury however there is some evidence that hip joint loads may be higher in stumble recovery from loss of balance a common laboratory method used to evaluate balance recovery performance involves suddenly releasing participants from various static forward lean magnitudes perturbation intensities prior studies have shown that when released from the same perturbation intensity some older adults are able to recover with a single step whereas others require multiple steps the main purpose of this study was to use a musculoskeletal model to determine the effect of three balance perturbation intensities and the use of single versus multiple recovery steps on hip joint contact loads during recovery from forward loss of balance in community dwelling older adults n 76 we also evaluated the association of peak hip contact loads with perturbation intensity step length and trunk flexion angle at foot contact at each participant s maximum recoverable lean angle mrla peak hip joint contact loads were computed using muscle force estimates obtained using static optimisation and increased as lean magnitude was increased and were on average 32 higher for single steppers compared to multiple steppers at the mrla peak hip contact loads ranged from 4 3 to 12 7 body weights and multiple linear stepwise regression further revealed that initial lean angle step length and trunk angle at foot contact together explained 27 of the total variance in hip joint contact load overall findings indicated that older adults experience peak hip joint contact loads during maximal balance recovery by stepping that in some cases exceeded loads reported to cause mechanical failure of cadaver femurs while step length and trunk flexion angle are strong predictors of step recovery performance they are at best moderate predictors of peak hip joint loading

accuracy of the tibiofemoral contact forces estimated by a subject specific musculoskeletal model with fluoroscopy based contact point trajectories abstract accurate estimation of the tibiofemoral contact forces relies on exact kinematics and joint geometry subject specific kinematic constraints representing contact point trajectories derived from fluoroscopic measurements during lunge are introduced in a musculoskeletal model of the lower limb and compared to generic kinematic constraints the medial lateral and total contact forces during gait and squat are validated using the data of four patients with an instrumented prosthesis the accuracy of the estimated contact forces both with subject specific and generic kinematic constraints remains close to the level reported in the literature the mean root mean square errors range from 0 32 to 0 52 body weights for gait and from 0 27 to 0 72 body weights for squat the impact of the subject specific contact point trajectories is not found substantial or consistent between patients and tasks indeed the kinematics of the total knee prostheses remains close to the kinematics of a hinge joint and the contact point locations remain generally centred at 20 mm from the tibia centreline close to the constant value defined in the generic constraints the contact point trajectories are also suspected to differ between tasks lunge vs gait and squat while the contact point trajectories have been reported to be sensitive model parameters no clear improvement of the contact force accuracy is demonstrated on patients with instrumented prosthesis the introduction as kinematic constraints of fluoroscopy based contact point trajectories may be considered in cases where these trajectories are significantly altered as reported for osteoarthritis patients

image based weighted center of proximity versus directly measured knee contact location during simulated gait abstract to understand the mechanical consequences of knee injury requires a detailed analysis of the effect of that injury on joint contact mechanics during activities of daily living three dimensional 3d knee joint geometric models have been combined with knee joint kinematics to dynamically estimate the location of joint contact during physiological activities using a weighted center of proximity wcop method however the relationship between the estimated wcop and the actual location of contact has not been defined the objective of this study was to assess the relationship between knee joint contact location as estimated using the image based wcop method and a directly measured weighted center of contact wcoc method during simulated walking to achieve this goal we created knee specific models of six human cadaveric knees from magnetic resonance imaging all knees were then subjected to physiological loads on a knee simulator intended to mimic gait knee joint motion was captured using a motion capture system knee joint contact stresses were synchronously recorded using a thin electronic sensor throughout gait and used to compute wcoc for the medial and lateral plateaus of each knee wcop was calculated by combining knee kinematics with the mri based knee specific model both metrics were compared throughout gait using linear regression the anteroposterior ap location of wcop was significantly correlated with that of wcoc on both tibial plateaus in all specimens p r 0 but the correlation was not significant in the mediolateral ml direction for 4 6 knees p 0 05 our study demonstrates that while the location of joint contact obtained from 3d knee joint contact model using the wcop method is significantly correlated with the location of actual contact stresses in the ap direction that relationship is less certain in the ml direction

nonclassical shocks and kinetic relations finite difference schemes we consider hyperbolic systems of conservation laws that are not genuinely nonlinear the solutions generated by diffusive dispersive regularizations may include nonclassical n c shock waves that do not satisfy the classical liu entropy criterion we investigate the numerical approximation of n c shocks via conservative difference schemes constrained only by a single entropy inequality the schemes are designed by comparing their equivalent equations with the continuous model and include discretizations of the diffusive and dispersive terms limits of these schemes are characterized via the kinetic relation introduced earlier by the authors we determine the kinetic function numerically for several examples of systems and schemes this study demonstrates that the kinetic relation is a suitable tool for the selection of unique n c solutions and for the study of their sensitive dependence on the critical parameters the ratios of diffusion dispersion and diffusion mesh size the shock strength and the order of discretization of the flux

sensitivity of tibio menisco femoral joint contact behavior to variations in knee kinematics abstract use of computational models with kinematic boundary conditions to study the knee joint contact behavior for normal and pathologic knee joints depends on an understanding of the impacts of kinematic uncertainty we studied the sensitivities of tibio menisco femoral joint contact behavior to variations in knee kinematics using a finite element model fem with geometry and kinematic boundary conditions derived from sequences of magnetic resonance mr images the mr images were taken before and after axial compression was applied to the knee joint of a healthy subject a design of experiments approach was used to study the impact of the variation in knee kinematics on the contact outputs we also explored the feasibility of using supplementary hip images to improve the accuracy of knee kinematics variations in knee kinematics 0 25 mm in medial lateral 0 1 mm in anterior posterior and superior inferior translations and 0 1 in flexion extension and varus valgus 0 25 in external internal rotations caused large variations in joint contact behavior when kinematic boundary conditions resulted in close approximations of the model predicted joint contact force to the applied force variations in predictions of contact parameters were also reduced the combination of inferior superior and medial lateral translations accounted for over 70 of variations for all the contact parameters examined the inclusion of hip images in kinematic calculations improved knee kinematics by matching the femoral head position our findings demonstrate the importance of improving the accuracy and precision of knee kinematic measurements especially when utilized as an input for finite element models

knee medial and lateral contact forces in a musculoskeletal model with subject specific contact point trajectories abstract contact point cp trajectory is a crucial parameter in estimating medial lateral tibio femoral contact forces from the musculoskeletal msk models the objective of the present study was to develop a method to incorporate the subject specific cp trajectories into the msk model ten healthy subjects performed 45 s treadmill gait trials the subject specific cp trajectories were constructed on the tibia and femur as a function of extension flexion using low dose bi plane x ray images during a quasi static squat at each extension flexion position the tibia and femur cps were superimposed in the three directions on the medial side and in the anterior posterior and proximal distal directions on the lateral side to form the five kinematic constraints of the knee joint the lagrange multipliers associated to these constraints directly yielded the medial lateral contact forces the results from the personalized cp trajectory model were compared against the linear cp trajectory and sphere on plane cp trajectory models which were adapted from the commonly used msk models changing the cp trajectory had a remarkable impact on the knee kinematics and changed the medial and lateral contact forces by 1 03 bw and 0 65 bw respectively in certain subjects the direction and magnitude of the medial lateral contact force were highly variable among the subjects and the medial lateral shift of the cps alone could not determine the increase decrease pattern of the contact forces the suggested kinematic constraints are adaptable to the cp trajectories derived from a variety of joint models and those experimentally measured from the 3d imaging techniques

a physiologically based criterion of muscle force prediction in locomotion abstract the inversely nonlinear relationship of muscle contraction force and the possible contraction duration i e endurance is utilized in a method to mathematically predict individual muscle forces the method uses a nonlinear optimization scheme to solve the redundant distribution problem at the joints of interest the method is demonstrated at the elbow during isometric contraction and in the lower extremity during locomotion during gait the observed muscle activity pattern in the lower extremity as determined by emg shows substantial agreement with that activity pattern predicted when endurance is used as the optimization criterion the importance of selecting muscle prediction criteria based on sound physiological bases rather than on an arbitrary or mathematically convenient basis is emphasized

a level set formulation of eulerian interface capturing methods for incompressible fluid flows a level set formulation is derived for incompressible immiscible navier stokes equations separated by a free surface the interface is identified as the zero level set of a smooth function eulerian finite difference methods based on this level set formulation are proposed these methods are robust and efficient and are capable of computing interface singularities such as merging and reconnection numerical experiments are presented to demonstrate the effectiveness of the methods

micro local approach to the hadamard condition in quantum field theory on curved space time for the two point distribution of a quasi free klein gordon neutral scalar quantum field on an arbitrary four dimensional globally hyperbolic curved space time we prove the equivalence of 1 the global hadamard condition 2 the property that the feynman propagator is a distinguished parametrix in the sense of duistermaat and hormander and 3 a new property referred to as the wave front set spectral condition wfssc because it is reminiscent of the spectral condition in axiomatic quantum field theory on minkowski space results in micro local analysis such as the propagation of singularities theorem and the uniqueness up toc of distinguished parametrices are employed in the proof we include a review of kay and wald s rigorous definition of the global hadamard condition and the theory of distinguished parametrices specializing to the case of the klein gordon operator on a globally hyperbolic space time as an alternative to a recent computation of the wave front set of a globally hadamard two point distribution on a globally hyperbolic curved space time given elsewhere by kohler to correct an incomplete computation in 32 we present a version of this computation that does not use a deformation argument such as that used in fulling narcowich and wald and is independent of the cauchy evolution argument of fulling sweeny and wald both of which are relied upon in kohler s proof this leads to a simple micro local proof of the preservation of hadamard form under cauchy evolution first shown by fulling sweeny and wald relying only on the propagation of singularities theorem in another paper 33 the equivalence theorem is used to prove a conjecture by kay that a locally hadamard quasi free klein gordon state on any globally hyperbolic curved space time must be globally hadamard

sensitivity of medial and lateral knee contact force predictions to frontal plane alignment and contact locations musculoskeletal models are increasingly used to estimate medial and lateral knee contact forces which are difficult to measure in vivo the sensitivity of contact force predictions to modeling parameters is important to the interpretation and implication of results generated by the model the purpose of this study was to quantify the sensitivity of knee contact force predictions to simultaneous errors in frontal plane knee alignment and contact locations under different dynamic conditions we scaled a generic musculoskeletal model for n 23 subjects stature and radiographic knee alignment then perturbed frontal plane alignment and mediolateral contact locations within experimentally possible ranges of 10 to 10 and 10 to 10mm respectively the sensitivity of first peak second peak and mean medial and lateral knee contact forces to knee adduction angle and contact locations was modeled using linear regression medial loads increased and lateral loads decreased by between 3 and 6 bodyweight for each degree of varus perturbation shifting the medial contact point medially increased medial loads and decreased lateral loads by between 1 and 4 bodyweight per millimeter this study demonstrates that realistic measurement errors of 5mm contact distance or 5 frontal plane alignment could result in a combined 50 bw error in subject specific contact force estimates we also show that model sensitivity varies between subjects as a result of differences in gait dynamics these results demonstrate that predicted knee joint contact forces should be considered as a range of possible values determined by model uncertainty

subject specific regression equations to estimate lower spinal loads during symmetric and asymmetric static lifting abstract workplace safety assessment personalized treatment design and back pain prevention programs require accurate subject specific estimation of spinal loads since no noninvasive method can directly estimate spinal loads easy to use regression equations that are constructed based on the results of complex musculoskeletal models appear as viable alternatives thus we aim to develop subject specific regression equations of l4 l5 and l5 s1 shear and compression forces during various symmetric asymmetric tasks using a nonlinear personalized finite element musculoskeletal trunk model kinematics and electromyography emg activities of 19 young healthy subjects were collected during 64 different symmetric asymmetric tasks to investigate the reliability and accuracy of the musculoskeletal model and regression equations we compared estimated trunk muscle activities and l4 l5 intradiscal pressures idps respectively with our own electromyography data emgs and reported in vivo pressure measurements although in general six independent rotation components three trunk t11 rotations and three pelvic s1 rotations are required to determine kinematics along the spine only two surrogate variables trunk flexion and its asymmetric angles satisfactorily predicted all six rotation components r2 0 94 regression equations developed based on subject specific inputs predicted spinal loads in satisfactory agreement with idp measurements r2 0 85 predicted muscle activities in the personalized musculoskeletal models were in moderate to weak agreements with our measured emgs in 19 participants based on dominance analysis trunk flexion and its asymmetry angle hand load weight hand load lever arm and body weight were the most important variables while the effects of body height and sex on spinal loads remained small

hadamard states for the linearized yang mills equation on curved spacetime we construct hadamard states for the yang mills equation linearized around a smooth space compact background solution we assume the spacetime is globally hyperbolic and its cauchy surface is compact or equal mathbb r d

level of subject specific detail in musculoskeletal models affects hip moment arm length calculation during gait in pediatric subjects with increased femoral anteversion biomechanical parameters of gait such as muscle s moment arm length mal and muscle tendon length are known to be sensitive to anatomical variability nevertheless most studies rely on rescaled generic models rgmo constructed from averaged data of cadaveric measurements in a healthy adult population as an alternative deformable generic models dgmo have been proposed these models integrate a higher level of subject specific detail by applying characteristic deformations to the musculoskeletal geometry in contrast musculoskeletal models based on magnetic resonance mr images mrmo reflect the involved subject s characteristics in every level of the model this study investigated the effect of the varying levels of subject specific detail in these three model types on the calculated hip mal during gait in a pediatric population of seven cerebral palsy subjects presenting aberrant femoral geometry our results show large percentage differences in calculated mal between rgmo and mrmo furthermore the use of dgmo did not uniformly reduce inter model differences in calculated mal the magnitude of these percentage differences stresses the need to take these effects into account when selecting the level of subject specific detail one wants to integrate in musculoskeletal furthermore the variability of these differences between subjects and between muscles makes it very difficult to a priori estimate their importance for a biomechanical analysis of a certain muscle in a given subject

an open source lower limb model hip joint validation musculoskeletal lower limb models have been shown to be able to predict hip contact forces hcfs that are comparable to in vivo measurements obtained from instrumented prostheses however the muscle recruitment predicted by these models does not necessarily compare well to measured electromyographic emg signals in order to verify if it is possible to accurately estimate hcfs from muscle force patterns consistent with emg measurements a lower limb model based on a published anatomical dataset klein horsman et al 2007 clinical biomechanics 22 239 247 has been implemented in the open source software opensim a cycle to cycle hip joint validation was conducted against hcfs recorded during gait and stair climbing trials of four arthroplasty patients bergmann et al 2001 journal of biomechanics 34 859 871 hip joint muscle tensions were estimated by minimizing a polynomial function of the muscle forces the resulting muscle activation patterns obtained by assessing multiple powers of the objective function were compared against emg profiles from the literature calculated hcfs denoted a tendency to monotonically increase their magnitude when raising the power of the objective function the best estimation obtained from muscle forces consistent with experimental emg profiles was found when a quadratic objective function was minimized average overestimation at experimental peak frame 10 1 for walking 7 8 for stair climbing the lower limb model can produce appropriate balanced sets of muscle forces and joint contact forces that can be used in a range of applications requiring accurate quantification of both the developed model is available at the website https simtk org home low limb london

a local to global singularity theorem for quantum field theory on curved space time we prove that if a reference two point distribution of positive type on a time orientable curved space time cst satisfies a certain condition on its wave front set the classp m g condition and if any other two point distribution i is of positive type ii has the same antisymmetric part as the reference modulo smooth function and iii has the same local singularity structure then it has the same global singularity structure in the proof we use a smoothing positivity preserving pseudo differential operator the support of whose symbol is restricted to a certain conic region which depends on the wave front set of the reference state this local to global theorem together with results published elsewhere leads to a verification of a conjecture by kay that for quasi free states of the klein gordon quantum field on a globally hyperbolic cst the local hadamard condition implies the global hadamard condition a counterexample to the local to global theorem on a strip in minkowski space is given when the classp m g condition is not assumed

muscular synergism i on criteria for load sharing between synergistic muscles the use of optimization techniques to predict individual muscle forces in redundant biomechanical systems implies the formulation of a criterion for load sharing between the muscles in part i of this paper the characteristics and performance of several linear and non linear criteria reported in the literature have been compared for static isometric knee flexion the results show that linear criteria inherently predict discrete muscle action orderly recruitment of muscles whereas non linear criteria can predict synergistic action all criteria predict that relatively more force is allocated to muscles with large moment arms when muscle stresses or ratios of muscle force to maximum muscle force are used as the decision variables in the objective function then relatively more force is allocated to muscles with large maximum possible force as well future formulations of the optimization should consider the differences in fiber type composition among the muscles such an approach is presented in part ii of the paper

on the derivation of a tensor to calculate six degree of freedom musculotendon joint stiffness implications for stability and impedance analyses major joints such as the knee shoulder and spine can buckle along the translational degrees of freedom dof causing injury to ligaments and other passive tissues despite this stability and impedance analyses have focused primarily on the rotational dof as such mathematical models quantifying musculotendon translational stiffnesses remain limited and to our knowledge there are no published works that explicitly describes the interactions between dof using an energy approach we derived a six dof stiffness tensor and provided the necessary equations needed to quantify the musculotendon stiffness of any joint using a knee model we then compared the derived stiffness tensor against two commonly used measures one that excludes translational dof and another that excludes interactions between dof we found that both of these measures had large over estimations of stiffness particularly for the rotational dof compared to our derived tensor these findings indicate that previous analyses may have found rotational dof to be stable when they were unstable

analytic hadamard states calderon projectors and wick rotation near analytic cauchy surfaces we consider the klein gordon equation on analytic spacetimes with an analytic cauchy surface in this setting we prove the existence of pure analytic hadamard states the proof is based on considering an elliptic operator obtained by wick rotating the klein gordon operator in a neighborhood of a cauchy hypersurface the cauchy data of hadamard two point functions are constructed as calderon projectors suitably generalized if the hypersurface is non compact for the elliptic operator

hadamard states for the klein gordon equation on lorentzian manifolds of bounded geometry we consider the klein gordon equation on a class of lorentzian manifolds with cauchy surface of bounded geometry which is shown to include examples such as exterior kerr kerr de sitter spacetime and the maximal globally hyperbolic extension of the kerr outer region in this setup we give an approximate diagonalization and a microlocal decomposition of the cauchy evolution using a time dependent version of the pseudodifferential calculus on riemannian manifolds of bounded geometry we apply this result to construct all pure regular hadamard states and associated feynman inverses where regular refers to the state s two point function having cauchy data given by pseudodifferential operators this allows us to conclude that there is a one parameter family of elliptic pseudodifferential operators that encodes both the choice of pure regular hadamard state and the underlying spacetime metric

smooth approximation of lipschitz functions on riemannian manifolds abstract we show that for every lipschitz function f defined on a separable riemannian manifold m possibly of infinite dimension for every continuous e m 0 and for every positive number r 0 there exists a c smooth lipschitz function g m r such that f p g p e p for every p m and lip g lip f r consequently every separable riemannian manifold is uniformly bumpable we also present some applications of this result such as a general version for separable riemannian manifolds of deville godefroy zizler s smooth variational principle

a method for concise reporting of joint reaction forces orientation during gait estimation of joint reaction forces jrf is critical for the understanding of load related pathologies such as osteoarthritis oa typically singular components at discrete time points are presented without knowledge of their orientation over time the aim of this study was to develop and demonstrate the utility of a method for the concise and intuitive representation of jrf orientation a scaled musculoskeletal model of the lower limbs was informed by walking gait data from adults with knee oa n 10 and healthy controls c n 10 muscle forces and subsequently jrf were computed the intersections of the jrf vector and a transverse plane proximal to the joint were computed the 95 confidence ellipse was computed for these points this allowed the following metrics to be calculated the normalised area of the ellipse a the ratio of the long and short axes r the angle between the long axis of the ellipse and the anterior posterior axis of the distal segment and the position of the centre of the ellipse relative to the origin of the segment xc zc at the knee the oa group displayed a more ap oriented jrf oa 3 0 28 2 c 15 3 37 1 p 0 03 less overall variation in the jrf orientation oa a 0 04 0 03c a 0 07 0 03 p 0 001 and less ml fluctuations of the jrf oa r 4 17 3 48c r 2 41 0 76 p 0 01 significant effects were also observed at the hip and ankle the method presented has the potential to allow better visualisation and insight into the behaviour of joint contact forces in clinically relevant pathologies

a constraint based approach to modelling the mobility of the human knee joint a model of knee mobility able to predict the range and pattern of movement in the unloaded joint was proposed by wilson et al j biomech 31 1998 1127 1136 the articular surfaces in the lateral and medial compartments and isometric fascicles in three of the knee ligaments were represented as five constraints on motion between the femur and tibia in a single degree of freedom parallel spatial mechanism the path of movement of the bones during passive flexion was found by solving the forward kinematics of the mechanism using an iterative method the present paper shows that such a mechanism based solution approach can lead to an underestimation of the flexion range this is due to the mechanism reaching a stationary configuration and locking a new constraint based approach to the solution of the model joint displacement is proposed it avoids the representation of ligaments and articular surfaces by kinematically equivalent chains of one degree of freedom pairs which are prone to singularities it relies instead on a numerical solution of five non linear constraint equations to find the relative positions of the bones at a series of flexion angles the method is successful both in its ability to predict motion through a physiological range and in its efficiency with a solution rate forty times faster than the original algorithm the new approach may be extended to include more complex joint surface geometry allowing a study of the effects of articular surface shape and ligament arrangement on joint kinematics

non classical shocks and kinetic relations scalar conservation laws this paper analyzes the non classical shock waves which arise as limits of certain diffusive dispersive approximations to hyperbolic conservation laws such shocks occur for non convex fluxes and connect regions of different convexity they have negative entropy dissipation for a single convex entropy function but not all convex entropies and do not obey the classical oleinik entropy criterion we derive necessary conditions for the existence of non classical shock waves and construct them as limits of traveling wave solutions for several diffusive dispersive approximations

the microlocal spectrum condition and wick polynomials of free fields on curved spacetimes quantum fields propagating on a curved spacetime are investigated in terms of microlocal analysis we discuss a condition on the wave front set for the correspondingn point distributions called microlocal spectrum condition sc on minkowski space this condition is satisfied as a consequence of the usual spectrum condition based on radzikowski s determination of the wave front set of the two point function of a free scalar field satisfying the hadamard condition in the kay and wald sense we construct in the second part of this paper all wick polynomials including the energy momentum tensor for this field as operator valued distributions on the manifold and prove that they satisfy our microlocal spectrum condition