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

linear programming in linear time when the dimension is fixed it is demonstrated that the linear programming problem in d variables and n constraints can be solved in o n time when d is fixed this bound follows from a multidimensional search technique which is applicable for quadratic programming as well there is also developed an algorithm that is polynomial in both n and d provided d is bounded by a certain slowly growing function of n

parametric and non parametric unsupervised cluster analysis much work has been published on methods for assessing the probable number of clusters or structures within unknown data sets this paper aims to look in more detail at two methods a broad parametric method based around the assumption of gaussian clusters and the other a non parametric method which utilises methods of scale space filtering to extract robust structures within a data set it is shown that whilst both methods are capable of determining cluster validity for data sets in which clusters tend towards a multivariate gaussian distribution the parametric method inevitably fails for clusters which have a non gaussian structure whilst the scale space method is more robust

grayscale level connectivity theory and applications a novel notion of connectivity for grayscale images is introduced defined by means of a binary connectivity assigned at image level sets in this framework a grayscale image is connected if all level sets below a prespecified threshold are connected the proposed notion is referred to as grayscale level connectivity and includes as special cases other well known notions of grayscale connectivity such as fuzzy grayscale connectivity and grayscale blobs in contrast to those approaches the present framework does not require all image level sets to be connected moreover a connected grayscale object may contain more than one regional maximum grayscale level connectivity is studied in the rigorous framework of connectivity classes the use of grayscale level connectivity in image analysis applications such as object extraction image segmentation object based filtering and hierarchical image representation is discussed and illustrated

the redundant nature of locomotor optimization laws a sagittal plane model of the lower limb which considered the possibility of antagonistic and synergistic muscle action and took account of the load bearing roles of the cruciate ligaments was applied to a dynamic analysis of level walking it was hypothesized that 1 the simple one sided constraints that intra articular contact forces must be compressive and muscle and ligament forces tensile substantially reduce the redundancy of the load transmitting structures of the lower limb 2 many previously proposed optimization laws for muscle selection yield equivalent results when they are applied to a finite set of admissible limiting solutions and 3 the aforementioned optimization laws when applied to a finite set of admissible limiting solutions do not adequately predict the co contraction of antagonistic muscles during gait the problem of indeterminacy was resolved by considering all possible limiting solutions of the system unknowns on the dynamic equations although 498 limiting solutions of nine unknowns could arise at each sampled point on the gait cycle the aforementioned one sided constraints ruled out the large majority of them it was shown that of the 498 possible the minimum number of simultaneous admissible solutions for any subject was as few as three and the maximum number was only 18 the principles of minimal total muscle force squared muscle force muscle stress intra articular contact force and instantaneous muscle power predicted remarkably similar patterns of muscle activity over the gait cycle of the six tested performance criteria the principle of minimal total ligament force was the least successful in terms of selecting solutions that closely matched the emg patterns this result implied that the muscles do not always act to protect the knee ligaments during gait finally each of the above minimum principles failed to predict any antagonistic quadriceps hamstrings action at the knee and hip around the event of heelstrike although such activity was indicated by electromyography

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

flat zones filtering connected operators and filters by reconstruction this correspondence deals with the notion of connected operators starting from the definition for operator acting on sets it is shown how to extend it to operators acting on function typically a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions it is shown that from any connected operator acting on sets one can construct a connected operator for functions however it is not the unique way of generating connected operators for functions moreover the concept of pyramid is introduced in a formal way it is shown that if a pyramid is based on connected operators the flat zones of the functions increase with the level of the pyramid in other words the flat zones are nested filters by reconstruction are defined and their main properties are presented finally some examples of application of connected operators and use of flat zones are described

clustering data by melting we derive a new clustering algorithm based on information theory and statistical mechanics which is the only algorithm that incorporates scale it also introduces a new concept into clustering cluster independence the cluster centers correspond to the local minima of a thermodynamic free energy which are identified as the fixed points of a one parameter nonlinear map the algorithm works by melting the system to produce a tree of clusters in the scale space melting is also insensitive to variability in cluster densities cluster sizes and ellipsoidal shapes and orientations we tested the algorithm successfully on both simulated data and a synthetic aperture radar image of an agricultural site with 12 attributes for crop identification

morphologically constrained grfs applications to texture synthesis and analysis a new class of gibbs random fields grfs is proposed capable of modeling geometrical constraints in images by means of mathematical morphology the proposed approach known as morphologically constrained grfs models images by means of their size density since the size density is a multiresolution statistical summary morphologically constrained grfs explicitly incorporate multiresolution information into image modeling important properties are studied and their implication to texture synthesis and analysis is discussed statistical inference can be easily implemented by means of mathematical morphology this allows the design of a computationally simple morphological bayes classifier which produces excellent results in classifying natural textures

evolution equations for continuous scale morphological filtering multiscale signal analysis has emerged as a useful framework for many computer vision and signal processing tasks morphological filters can be used to develop nonlinear multiscale operations that have certain advantages over linear multiscale approaches in that they preserve important signal features such as edges the authors discuss several nonlinear partial differential equations that model the scale evolution associated with continuous space multiscale morphological erosions dilations openings and closings these equations relate the rate of change of the multiscale signal ensemble as scale increases to a nonlinear operator acting on the space of signals the nonlinear operator is characterized by the shape and dimensionality of the structuring element used by the morphological operators generally taking the form of a nonlinear function of certain partial differential operators

pattern spectrum and multiscale shape representation the results of a study on multiscale shape description smoothing and representation are reported multiscale nonlinear smoothing filters are first developed using morphological opening and closings g matheron 1975 used openings and closings to obtain probabilistic size distributions of euclidean space sets continuous binary images these distributions are used to develop a concept of pattern spectrum a shape size descriptor a pattern spectrum is introduced for continuous graytone images and arbitrary multilevel signals as well as for discrete images by developing a discrete size family of patterns large jumps in the pattern spectrum at a certain scale indicate the existence of major protruding or intruding substructures of the signal at the scale an entropy like shape size complexity measure is also developed based on the pattern spectrum for shape representation a reduced morphological skeleton transform is introduced for discrete binary and graytone images this transform is a sequence of skeleton components sparse images which represent the original shape at various scales it is shown that the partially reconstructed images from the inverse transform on subsequences of skeleton components are the openings of the image at a scale determined by the number of eliminated components in addition two way correspondences are established among the degree of shape smoothing via multiscale openings or closings the pattern spectrum zero values and the elimination or nonexistence of skeleton components at certain scales

object based image analysis using multiscale connectivity this paper introduces a novel approach for image analysis based on the notion of multiscale connectivity we use the proposed approach to design several novel tools for object based image representation and analysis which exploit the connectivity structure of images in a multiscale fashion more specifically we propose a nonlinear pyramidal image representation scheme which decomposes an image at different scales by means of multiscale grain filters these filters gradually remove connected components from an image that fail to satisfy a given criterion we also use the concept of multiscale connectivity to design a hierarchical data partitioning tool we employ this tool to construct another image representation scheme based on the concept of component trees which organizes partitions of an image in a hierarchical multiscale fashion in addition we propose a geometrically oriented hierarchical clustering algorithm which generalizes the classical single linkage algorithm finally we propose two object based multiscale image summaries reminiscent of the well known morphological pattern spectrum which can be useful in image analysis and image understanding applications

the morphological structure of images the differential equations of morphological scale space we introduce a class of nonlinear differential equations that are solved using morphological operations the erosion and dilation act as morphological propagators propagating the initial condition into the scale space much like the gaussian convolution is the propagator for the linear diffusion equation the analysis starts in the set domain resulting in the description of erosions and dilations in terms of contour propagation we show that the structuring elements to be used must have the property that at each point of the contour there is a well defined and unique normal vector then given the normal at a point of the dilated contour we can find the corresponding point point of contact on the original contour in some situations we can even link the normal of the dilated contour with the normal in the point of contact of the original contour the results of the set domain are then generalized to grey value images the role of the normal is replaced with the function gradient the same analysis also holds for the erosion using a family of increasingly larger structuring functions we are then able to link infinitesimal changes in grey value with the gradient in the image

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 scale based connected coherence tree algorithm for image segmentation this paper presents a connected coherence tree algorithm ccta for image segmentation with no prior knowledge it aims to find regions of semantic coherence based on the proposed epsiv neighbor coherence segmentation criterion more specifically with an adaptive spatial scale and an appropriate intensity difference scale ccta often achieves several sets of coherent neighboring pixels which maximize the probability of being a single image content including kinds of complex backgrounds in practice each set of coherent neighboring pixels corresponds to a coherence class cc the fact that each cc just contains a single equivalence class ec ensures the separability of an arbitrary image theoretically in addition the resultant ccs are represented by tree based data structures named connected coherence tree cct s in this sense ccta is a graph based image analysis algorithm which expresses three advantages 1 its fundamental idea epsiv neighbor coherence segmentation criterion is easy to interpret and comprehend 2 it is efficient due to a linear computational complexity in the number of image pixels 3 both subjective comparisons and objective evaluation have shown that it is effective for the tasks of semantic object segmentation and figure ground separation in a wide variety of images those images either contain tiny long and thin objects or are severely degraded by noise uneven lighting occlusion poor illumination and shadow

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

size density spectra and their application to image classification we develop a density opening operator that is shown to satisfy the properties of an algebraic opening this density opening enables the development of a number of variants of pattern spectra which quantify the size or density information of a blob arrangement within the image in contrast to regular morphological pattern size spectra the proposed pattern spectra are spatially sensitive and robust to noise distortions a pattern size density spectrum or 2d signature was introduced and used for solving image classification tasks its application to the classification of real world medical images is illustrated

scanner influence on the mechanical response of qct based finite element analysis of long bones abstract patient specific qct based finite element qctfe analyses enable highly accurate quantification of bone strength we evaluated ct scanner influence on qctfe models of long bones a femur humerus and proximal femur without the head were scanned with k2hpo4 phantoms by seven ct scanners four models using typical clinical protocols qctfe models were constructed the geometrical dimensions as well as the qct values expressed in hounsfield unit hu distribution was compared principal strains at representative regions of interest rois and maximum principal strains associated with fracture risk were compared intraclass correlation coefficients iccs were calculated to evaluate strain prediction reliability for different scanners repeatability was examined by scanning the femur twice and comparing resulting qctfe models maximum difference in geometry was 2 3 hu histograms before phantom calibration showed wide variation between qct scans however bone density histogram variability was reduced after calibration and algorithmic manipulation relative standard deviation rsd in principal strains at rois was 0 9 fracture associated strain had 6 7 8 1 and 13 3 maximum rsd for the femur humerus and proximal femur respectively the difference in maximum strain location was quantification of strain differences showed mean rsd bounded by 6 in rois fracture associated strains in regular bones showed a mean rsd bounded by 8 strains were obtained within a 10 difference relative to the mean thus in a longitudinal study only changes larger than 20 in the principal strains may be significant iccs indicated high reliability of qctfe models derived from different scanners

a novel training free method for real time prediction of femoral strain surrogate methods for rapid calculation of femoral strain are limited by the scope of the training data we compared a newly developed training free method based on the superposition principle superposition principle method spm and popular surrogate methods for calculating femoral strain during activity finite element calculations of femoral strain muscle and joint forces for five different activity types were obtained previously multi linear regression multivariate adaptive regression splines and gaussian process were trained for 50 100 200 and 300 random samples generated using latin hypercube lh and design of experiment doe sampling the spm method used weighted linear combinations of 173 activity independent finite element analyses accounting for each muscle and hip contact force across the surrogate methods we found that 200 doe samples consistently provided low error rmse 100 e with model construction time ranging from 3 8 to 63 3 h and prediction time ranging from 6 to 1236 s per activity the spm method provided the lowest error rmse 40 e the fastest model construction time 3 2 h and the second fastest prediction time per activity 36 s after multi linear regression 6 s the spm method will enable large numerical studies of femoral strain and will narrow the gap between bone strain prediction and real time clinical applications

an adaptive morphological filter for image processing novel types of opening operator nop and closing operator ncp are proposed an adaptive morphological filter is then constructed on the basis of the nop and ncp the filter can remove any details consisting of fewer pixels than a given number n while preserving the other details efficient algorithms are also developed for the implementation of the nop and ncp

a multiscanning approach based on morphological filtering it is argued that the mathematical morphology method seems to be more reasonable and powerful in studying certain multiscaling vision problems than the approach that uses derivatives of gaussian shaped filters of different sizes to show the validity of this method the authors concentrated on an application that involves forming scale space image of a 2 d shape using morphological opening filtering a proof is given to show that morphological opening filtering has a property of not introducing additional zero crossings as one moves to a coarser scale this is a different result from the conclusion by a l yuille and t a poggio ibid vol pami 8 jan 1986 that the gaussian filter is the only filter with this property in addition opening filtering is computationaly simpler than the gaussian filter

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

to what extent can linear finite element models of human femora predict failure under stance and fall loading configurations proximal femur strength estimates from computed tomography ct based finite element fe models are finding clinical application published models reached a high in vitro accuracy yet many of them rely on nonlinear methodologies or internal best fitting of parameters the aim of the present study is to verify to what extent a linear fe modelling procedure fully based on independently determined parameters can predict the failure characteristics of the proximal femur in stance and sideways fall loading configurations fourteen fresh frozen cadaver femora were ct scanned seven femora were tested to failure in stance loading conditions and seven in fall fracture was monitored with high speed videos linear fe models were built from ct images according to a procedure already validated in the prediction of strains an asymmetric maximum principal strain criterion 0 73 tensile 1 04 compressive limit was used to define a node based risk factor rf fe predicted failure load mode tensile compressive and location were determined from the first node reaching rf 1 fe predicted and measured failure loads were highly correlated r 2 0 89 see 814n in all specimens fe models correctly identified the failure mode tensile in stance compressive in fall and the femoral region where fracture started supero lateral neck aspect the location of failure onset was accurately predicted in eight specimens in summary a simple fe model adaptable in the future to multiple loads e g including muscles was highly correlated with experimental failure in two loading conditions on specimens ranging from normal to osteoporotic thus it can be suitable for use in clinical studies

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

antiextensive connected operators for image and sequence processing this paper deals with a class of morphological operators called connected operators these operators filter the signal by merging its flat zones as a result they do not create any new contours and are very attractive for filtering tasks where the contour information has to be preserved this paper shows that connected operators work implicitly on a structured representation of the image made of flat zones the max tree is proposed as a suitable and efficient structure to deal with the processing steps involved in antiextensive connected operators a formal definition of the various processing steps involved in the operator is proposed and as a result several lines of generalization are developed first the notion of connectivity and its definition are analyzed several modifications of the traditional approach are presented they lead to connected operators that are able to deal with texture they also allow the definition of connected operators with less leakage than the classical ones second a set of simplification criteria are proposed and discussed they lead to simplicity entropy and motion oriented operators the problem of using a nonincreasing criterion is analyzed its solution is formulated as an optimization problem that can be very efficiently solved by a viterbi 1979 algorithm finally several implementation issues are discussed showing that these operators can be very efficiently implemented

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

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

sensitivity of femoral strain calculations to anatomical scaling errors in musculoskeletal models of movement the determination of femoral strain in post menopausal women is important for studying bone fragility femoral strain can be calculated using a reference musculoskeletal model scaled to participant anatomies referred to as scaled generic combined with finite element models however anthropometric errors committed while scaling affect the calculation of femoral strains we assessed the sensitivity of femoral strain calculations to scaled generic anthropometric errors we obtained ct images of the pelves and femora of 10 healthy post menopausal women and collected gait data from each participant during six weight bearing tasks scaled generic musculoskeletal models were generated using skin mounted marker distances image based models were created by modifying the scaled generic models using muscle and joint parameters obtained from the ct data scaled generic and image based muscle and hip joint forces were determined by optimisation a finite element model of each femur was generated from the ct images and both image based and scaled generic principal strains were computed in 32 regions throughout the femur the intra participant regional rms error increased from 380 e r2 0 92 p 0 001 to 4064 e r2 0 48 p 0 001 representing 5 2 and 55 6 of the tensile yield strain in bone respectively the peak strain difference increased from 2821 e in the proximal region to 34 166 e at the distal end of the femur the inter participant rms error throughout the 32 femoral regions was 430 e r2 0 95 p 0 001 representing 5 9 of bone tensile yield strain we conclude that scaled generic models can be used for determining cohort based averages of femoral strain whereas image based models are better suited for calculating participant specific strains throughout the femur

self validated labeling of markov random fields for image segmentation this paper addresses the problem of self validated labeling of markov random fields mrfs namely to optimize an mrf with unknown number of labels we present graduated graph cuts ggc a new technique that extends the binary s t graph cut for self validated labeling specifically we use the split and merge strategy to decompose the complex problem to a series of tractable subproblems in terms of gibbs energy minimization a suboptimal labeling is gradually obtained based upon a set of cluster level operations by using different optimization structures we propose three practical algorithms tree structured graph cuts tsgc net structured graph cuts nsgc and hierarchical graph cuts hgc in contrast to previous methods the proposed algorithms can automatically determine the number of labels properly balance the labeling accuracy spatial coherence and the labeling cost i e the number of labels and are computationally efficient independent to initialization and able to converge to good local minima of the objective energy function we apply the proposed algorithms to natural image segmentation experimental results show that our algorithms produce generally feasible segmentations for benchmark data sets and outperform alternative methods in terms of robustness to noise speed and preservation of soft boundaries

morphological pattern spectrum classification of noisy shapes exterior granulometries abstract moments of morphological granulometric pattern spectra have been used for classification of both texture and patterns the present paper concerns shape classification in the presence of edge noise when using granulometries generated by linear structuring elements although these have been shown to provide excellent texture classification it is shown here that they cannot successfully discriminate between close convex shapes when there is even modest edge noise by redefining a linear granulometry so that it operates on the linear convex hull in the direction of the generating structuring element excellent shape recognition is achieved even for edge noise exceeding that typically encountered in practice these newly proposed granulometries are called exterior granulometries and for a given shape class optimal feature sets from amongst their first three pattern spectrum moments are obtained their superior performance is demonstrated by a probabilistic comparison between the stability of the pattern spectrum means for both ordinary and exterior linear granulometries

the efficiency of the simplex method a survey the linear programming problem is by far the most widely used optimization model its impact on economic and government modeling is immense the simplex method for solving the linear programming lp problem due to george dantzig has been an extremely efficient computational tool for almost four decades the method has been the subject of intense investigations for many years but some major aspects of its behavior are not fully understood yet the purpose of this paper is to survey the body of knowledge on the efficiency of the simplex method from both practical and theoretical points of view adopting the number of iterations pivot steps as the yardstick for efficiency we survey four aspects of the issue 1 reports on practical experience of the method s performance on real life lp problems 2 results on controlled monte carlo experiments solving lp problems which were randomly generated according to some predetermined distributions 3 complexity results including theoretical analyses on both upper and lower bounds for the performance of the simplex as well as non simplex algorithms for lp 4 results of recent theoretical studies using probabilistic analysis to derive bounds on the average behavior of the simplex method we discuss the consequences and limitations of the various studies special emphasis is given to open questions

morphological grayscale reconstruction in image analysis applications and efficient algorithms two different formal definitions of gray scale reconstruction are presented the use of gray scale reconstruction in various image processing applications discussed to illustrate the usefulness of this transformation for image filtering and segmentation tasks the standard parallel and sequential approaches to reconstruction are reviewed it is shown that their common drawback is their inefficiency on conventional computers to improve this situation an algorithm that is based on the notion of regional maxima and makes use of breadth first image scannings implemented using a queue of pixels is introduced its combination with the sequential technique results in a hybrid gray scale reconstruction algorithm which is an order of magnitude faster than any previously known algorithm

is binary encoding appropriate for the problem language relationship abstract it is proved that there exist encoding schemes which are arbitrarily as efficient as the binary encoding in terms of compactness and arithmetic operations with respect to which khachiyan s algorithm for linear programming is exponential this constitutes an objection to the standard translation of problems into languages via the binary encoding

proximal femur bone strength estimated by a computationally fast finite element analysis in a sideways fall configuration finite element fe analysis based on quantitative computed tomography qct images is an emerging tool to estimate bone strength in a specific patient or specimen however it is limited by the computational power required and the associated time required to generate and solve the models thus our objective was to develop a fast validated method to estimate whole bone structural stiffness and failure load in addition to a sensitivity analysis of varying boundary conditions we performed qct scans on twenty fresh frozen proximal femurs age 77 13 years and mechanically tested the femurs in a configuration that simulated a sideways fall on the hip we used custom software to generate the fe models with boundary conditions corresponding to the mechanical tests and solved the linear models to estimate bone structural stiffness and estimated failure load for the sensitivity analysis we varied the internal rotation angle of the femoral neck from 30 to 45 at 15 intervals and estimated structural stiffness at each angle we found both the fe estimates of structural stiffness r 2 0 89 p 0 01 and failure load r 2 0 81 p 0 01 to be in high agreement with the values found by mechanical testing an important advantage of these methods was that the models of approximately 500 000 elements took less than 11 min to solve using a standard desktop workstation in this study we developed and validated a method to quickly and accurately estimate proximal femur structural stiffness and failure load using qct driven fe methods

validation of a functional method for the estimation of hip joint centre location the present study assesses the accuracy with which the subject specific coordinates of the hip joint centre hjc in a pelvic anatomical frame can be estimated using different methods the functional method was applied by calculating the centre of the best sphere described by the trajectory of markers placed on the thigh during several trials of hip rotations different prediction methods proposed in the literature and in the present investigation which estimate the hjc of adult subjects using regression equations and anthropometric measurements were also assessed the accuracy of each of the above mentioned methods was investigated by comparing their predictions with measurements obtained on a sample of 11 male adult able bodied volunteers using roentgen stereophotogrammetric analysis rsa assumed to provide the true hjc locations prediction methods estimated the hjc location at an average rms distance of 25 30 mm the functional method performed significantly better and estimated hjcs within a rms distance of 13 mm on average this result may be confidently generalised if the photogrammetric experiment is carefully conducted and an optimal analytical approach used the method is therefore suggested for use in motion analysis when the subject s hip range of motion is not limited in addition the facts that it is not an invasive technique and that it has relatively small and un biased errors make it suitable for regression equations identification with no limit to sample size and population typology

nonlinear multiresolution signal decomposition schemes ii morphological wavelets interest in multiresolution techniques for signal processing and analysis is increasing steadily an important instance of such a technique is the so called pyramid decomposition scheme this paper presents a general theory for constructing linear as well as nonlinear pyramid decomposition schemes for signal analysis and synthesis the proposed theory is based on the following ingredients 1 the pyramid consists of a finite or infinite number of levels such that the information content decreases toward higher levels and 2 each step toward a higher level is implemented by an information reducing analysis operator whereas each step toward a lower level is implemented by an information preserving synthesis operator one basic assumption is necessary synthesis followed by analysis yields the identity operator meaning that no information is lost by these two consecutive steps several examples of pyramid decomposition schemes are shown to be instances of the proposed theory a particular class of linear pyramids morphological skeleton decompositions the morphological haar pyramid median pyramids etc furthermore the paper makes a distinction between single scale and multiscale decomposition schemes i e schemes without or with sample reduction finally the proposed theory provides the foundation of a general approach to constructing nonlinear wavelet decomposition schemes and filter banks

the d step conjecture and its relatives the d step conjecture arose from an attempt to understand the computational complexity of edge following algorithms for linear programming such as the simplex algorithm it can be stated in terms of diameters of graphs of convex polytopes in terms of the existence of nonrevisiting paths in such graphs in terms of an exchange process for simplicial bases of a vector space and in terms of matrix pivot operations first formulated by w m hirsch in 1957 the conjecture remains unsettled though it has been proved in many special cases and counterexamples have been found for slightly stronger conjectures if the conjecture is false as we believe to be the case then finding a counterexample will be merely a small first step in the line of investigation related to the conjecture this report summarizes what is known about the d step conjecture and its relatives a considerable amount of new material is included but it does not seem to come close to settling the conjecture of special interest is the first example of a polytope that is not vertex decomposable showing that a certain natural approach to the conjecture will not work also significant are the quantitative relations among the lengths of paths associated with various forms of the conjecture

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

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

effect of sub optimal neuromotor control on the hip joint load during level walking skeletal forces are fundamental information in predicting the risk of bone fracture the neuromotor control system can drive muscle forces with various task and health dependent strategies but current modelling techniques provide a single optimal solution of the muscle load sharing problem the aim of the present work was to study the variability of the hip load magnitude due to sub optimal neuromotor control strategies using a subject specific musculoskeletal model the model was generated from computed tomography ct and dissection data from a single cadaver gait kinematics ground forces and electromyographic emg signals were recorded on a body matched volunteer model results were validated by comparing the traditional optimisation solution with the published hip load measurements and the recorded emg signals the solution space of the instantaneous equilibrium problem during the first hip load peak resulted in 105 dynamically equivalent configurations of the neuromotor control the hip load magnitude was computed and expressed in multiples of the body weight bw sensitivity of the hip load boundaries to the uncertainty on the muscle tetanic stress tms was also addressed the optimal neuromotor control induced a hip load magnitude of 3 3 bw sub optimal neuromotor controls induced a hip load magnitude up to 8 93 bw reducing tms from the maximum to the minimum the lower boundary of the hip load magnitude varied moderately whereas the upper boundary varied considerably from 4 26 to 8 93 bw further studies are necessary to assess how far the neuromotor control can degrade from the optimal activation pattern and to understand which sub optimal controls are clinically plausible however we can consider the possibility that sub optimal activations of the muscular system play a role in spontaneous fractures not associated with falls

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

3 is a more promising algorithmic parameter than 2 abstract in this paper we have observed and shown that ternary systems are more promising than the more traditional binary systems used in computers in particular ternary number system heaps on ternary trees and quicksort with three partitions do indicate some theoretical advantages over the more established binary systems the magic napierian e plays the crucial role to establish the results the experimental data supporting the analysis have also been presented

the mechanics of back extensor torque production about the lumbar spine the purpose of this study was to develop and evaluate a biomechanical model of lumbar back extension over a wide range of positions for the lumbar spine incorporating the latest information on muscle geometry and intra abdominal pressure iap analysis of the visible human data was utilised in order to obtain anatomical information unavailable from the literature and magnetic resonance imaging was used to generate subject specific anatomical descriptions the model was evaluated by comparisons with measured maximal voluntary static back extension torques predicted maximal specific muscle tensions agreed well with in vitro measurements from the literature when modelling the maximal static back extension torque production it was possible to come fairly close to simultaneous equilibrium about all the lumbar discs simply by a uniform muscle activation of all back extensor muscles the caudal part showed however less agreement this indicates that equilibrium in the lumbar spine is mainly regulated by passive mechanical properties e g muscle length changes due to postural changes rather than due to complex muscle coordination as earlier proposed the model showed that iap measured during torque exertions contributes about 10 of the total maximal voluntary back extensor torque and that it can unload the spine from compression the spinal unloading effect from the iap was greatest with the spine held in a flexed position this is in opposition to the effects of changed muscle lever arm lengths which for a given load would give the largest spinal unloading in the extended position these findings have implications for the evaluation of optimal lifting techniques

constrained connectivity for hierarchical image partitioning and simplification this paper introduces an image partitioning and simplification method based on the constrained connectivity paradigm according to this paradigm two pixels are said to be connected if they satisfy a series of constraints defined in terms of simple measures such as the maximum gray level differences over well defined pixel paths and regions the resulting connectivity relation generates a unique partition of the image definition domain the simplification of the image is then achieved by setting each segment of the partition to the mean value of the pixels falling within this segment fine to coarse partition hierarchies and therefore images of increasing degree of simplification are produced by varying the threshold value associated with each connectivity constraint the paper also includes a generalization to multichannel images application examples a review of related image segmentation techniques and pseudocode for an implementation based on queue and stack data structures

the relationship between two different mechanical cost functions and muscle oxygen consumption abstract inverse dynamic models often use cost functions to solve the load sharing problem although it is often assumed that energy is minimised most cost functions are based on mechanically related measures like muscle force or stress the aim of this study was to analyse the relationships of two cost functions with experimentally determined data on muscle energy consumption four subjects performed isometric contractions generating combinations of elbow flexion extension and pro supination moments muscle oxygen consumption v o 2 of the m biceps breve m biceps longum m brachioradialis and m triceps laterale was measured with near infrared spectroscopy both cost functions were implemented into an existing inverse dynamic shoulder and elbow model and the individual cost values per muscle were calculated normalised and subsequently compared to experimental v o 2 values the minimum stress cost function led to a good correspondence between v o 2 and cost for the m triceps laterale but for the flexor muscles cost was significantly lower a newly proposed energy related cost function showed however a far better correspondence the inclusion of a linear term and muscle mass in the new criterion led model results to correspond better to experimental results the energy related cost function appeared to be a better measure for muscle energy consumption than the stress cost function and led to more realistic predictions of muscle activation

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

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed