instantaneous helical axis estimation from 3 d video data in neck kinematics for whiplash diagnostics to date the diagnosis of whiplash injuries has been very difficult and largely based on subjective clinical assessment the work by winters and peles multiple muscle systems biomechanics and movement organization springer new york 1990 suggests that the use of finite helical axes fhas in the neck may provide an objective assessment tool for neck mobility thus the position of the fha describing head trunk motion may allow discrimination between normal and pathological cases such as decreased mobility in particular cervical joints for noisy unsmoothed data the fhas must be taken over rather large angular intervals if the fhas are to be reconstructed with sufficient accuracy in the winters and peles study these intervals were approximately 10 in order to study the movements microstructure the present investigation uses instantaneous helical axes ihas estimated from low pass smoothed video data here the small step noise sensitivity of the fha no longer applies and proper low pass filtering allows estimation of the iha even for small rotation velocity of the moving neck for marker clusters mounted on the head and trunk technical system validation showed that the ihas direction dispersions were on the order of one degree while their position dispersions were on the order of 1 mm for low pass cut off frequencies of a few hz the dispersions were calculated from weighted errors in order to account for the adverse effects of vanishing various simple planar models relating the instantaneous 2 d centre of rotation with the geometry and kinematics of a multi joint neck model are derived in order to gauge the utility of the fha and iha approaches some preliminary results on asymptomatic and pathological subjects are provided in terms of the ruled surface formed by sampled ihas and of their piercing points through the mid sagittal plane during a prescribed flexion extension movement of the neck

optimal digital filtering requires a different cut off frequency strategy for the determination of the higher derivatives the present study investigated four different filtering and differentiation sequences for the calculation of the higher derivatives from noisy displacement data when using a second order butterworth filter and first order finite differences these were 1 the conventional sequence i e filtering the displacement data and then differentiating 2 filtering the displacement with a different cut off frequency depending upon optimal 0th 1st and 2nd derivatives 3 double filtering and differentiation only for acceleration and 4 differentiation and then filtering separately in each derivative domain i e treating the noisy higher derivatives as individual signals thirty levels of time domain and 30 levels of frequency domain computer generated pure noise signals were superimposed on 24 reference signals which simulated the medial lateral anterior posterior and vertical displacement patterns of eight markers attached to the lower extremity segments during walking the optimum cut off frequency for the displacement velocity and acceleration data was calculated as the one that produced the minimum root mean square error between the reference and noisy data in each derivative domain the results indicated that the conventional strategy has to be reconsidered and modified as the best results were obtained by the second strategy the optimum cut off frequency for acceleration was lower than that required for the velocity which in turn was lower than the optimum cut off frequency for displacement the findings of the present study will contribute to the development of existing and future automatic filtering techniques based on digital filtering

bayesian predictive inference for time series count data summary correlated count data arise often in practice especially in repeated measures situations or instances in which observations are collected over time in this paper we consider a parametric model for a time series of counts by constructing a likelihood based version of a model similar to that of zeger 1988 biometrika75 621 629 the model has the advantage of incorporating both over dispersion and autocorrelation we consider a bayesian approach and propose a class of informative prior distributions for the model parameters that are useful for prediction the prior specification is motivated from the notion of the existence of data from similar previous studies called historical data which is then quantified into a prior distribution for the current study we derive the bayesian predictive distribution and use a bayesian criterion called the predictive l measure for assessing the predictions for a given time series model the distribution of the predictive l measure is also derived which will enable us to compare the predictive ability for each model under consideration our methodology is motivated by a real data set involving yearly pollen counts which is examined in some detail

3 d attitude representation of human joints a standardization proposal abstract in view of the singularities asymmetries and other adverse properties of existing three dimensional definitions for joint and segment angles the present paper proposes a new convention for unambiguous and easily interpretable 3 d joint angles based on the concept of the attitude vector as derived from euler s theorem the suggested standard can be easily explained to non mathematically trained clinicians is readily implemented in software and can be simply related to classical cardanic eulerian angles for planar rotations about a coordinate system s axes the proposed convention coincides with the cardanic convention the attitude vector dispenses with the gimbal lock and non orthogonality disadvantages of cardanic eulerian conventions therefore its components have better metrical properties and they are less sensitive to measurement errors and to coordinate system uncertainties than cardanic eulerian angles a sensitivity analysis and a physical interpretation of the proposed standard are given and some experimental results that demonstrate its advantages

comparison of different calculations of three dimensional joint kinematics from video based system data when skin fixed marker trajectories are used to calculate 3d joint kinematics the measurement errors i e the difference between the trajectories of the external markers and those of the skeleton influence to some extent the accuracy of the results depending both on the calculation method and on the axes about which the rotations are expressed the purpose of this paper is to compare several expressions of joint angular variations two kinematic concepts are used to calculate the changes in the orientation of the distal segment versus the proximal one the first method consists of computing the components of the spatial attitude vector the second one deals with the determination of elementary rotations about successive axes for each of these methods two sets of three axes are tested to express the results the axes forming the reference frame affixed to the body segment adjacent to the joint named fixed axes and a set consisting of a first axis belonging to the proximal segment a third axis belonging to the distal segment and a second floating axis defined as the cross product between the two other ones named mobile axes to compare these four distinct expressions on the knee joint numerical simulations of perturbed skin marker trajectories are performed based on experimental data recorded by a motion analysis system during a normal gait cycle a significant difference is pointed out only for the internal external rotation angle for which the best expression from the viewpoint of sensitivity to experimental errors is obtained using the components of the attitude vector in a segment embedded reference frame

generalized linear models with random effects salamander mating revisited in recent years much effort has been devoted to extending regression methodology to non gaussian data where responses are not independent these methods for dependent responses are suitable for data from longitudinal studies or nested designs however use of these methods for crossed designs seems to have serious limitations due to the intensive computations involved because of the intractable nature of the joint distribution in this paper we cast the problem in a bayesian framework and use a monte carlo method the gibbs sampler to avoid current computational limitations the flexibility of this approach is illustrated by analyzing the interesting salamander mating data reported by mccullagh and nelder 1989 generalized linear models 2nd edition london chapman and hall

optimal differentiation based on stochastic signal models the problem of estimating the time derivative of a signal from sampled measurements is addressed the measurements may be corrupted by colored noise a key idea is to use stochastic models of the signal to be differentiated and of the measurement noise two approaches are suggested the first is based on a continuous time stochastic process as a model of the signal the second uses a discrete time arma model of the signal and a discrete time approximation of the derivative operator digital differentiators are presented in a shift operator polynomial form they minimize the mean square estimation error and are calculated from a linear polynomial equation and a polynomial spectral factorization the three obstacles to perfect differentiation namely a finite smoothing lag measurement noise and aliasing effects due to sampling are discussed

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

estimation of the centre of rotation a methodological contribution the location of the centre of rotation of human joints that can be modelled as a spherical hinge can be estimated using kinematics information about the two adjacent bony segments involved recorded while the subject makes them move one relative to the other functional method in order to solve the relevant analytical problem several algorithms have been proposed most recently two methods one based on a spherical best fit approach and another based on the reuleaux construction have been presented as being different and submitted to comparative evaluation this paper modifies the second method taking all information in the data set into account and shows that having done this the two methods coincide analytically

self modelling with random shift and scale parameters and a free knot spline shape function the shape invariant model is a semi parametric approach to estimating a function relationship from clustered data multiple observations on each of a number of individuals the common response curve shape over individuals is estimated by adjusting for individual scaling differences while pooling shape information in practice the common response curve is restricted to some flexible family of functions this paper introduces the use of a free knot spline shape function and reduces the number of parameters in the shape invariant model by assuming a random distribution on the parameters that control the individual scaling of the shape function new graphical diagnostics are presented parameter identifiability and estimation are discussed and an example is presented

markov chain monte carlo convergence diagnostics a comparative review abstract a critical issue for users of markov chain monte carlo mcmc methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest research into methods of computing theoretical convergence bounds holds promise for the future but to date has yielded relatively little of practical use in applied work consequently most mcmc users address the convergence problem by applying diagnostic tools to the output produced by running their samplers after giving a brief overview of the area we provide an expository review of 13 convergence diagnostics describing the theoretical basis and practical implementation of each we then compare their performance in two simple models and conclude that all of the methods can fail to detect the sorts of convergence failure that they were designed to identify we thus recommend a combination of strategies aimed at evaluating and accelerating mcmc sampler convergence including ap

shape invariant modeling of circadian rhythms with random effects and smoothing spline anova decompositions medical studies often collect physiological and or psychological measurements over time from multiple subjects to study dynamics such as circadian rhythms under the assumption that the expected response functions of all subjects are the same after shift and scale transformations shape invariant models have been applied to analyze this kind of data the shift and scale parameters provide efficient and interpretable data summaries while the common shape function is usually modeled nonparametrically to provide flexibility however due to the deterministic nature of the shift and scale parameters potential correlations within a subject are ignored furthermore the shape of the common function may depend on other factors such as disease in this article we propose shape invariant mixed effects models a second stage model with fixed and random effects is used to model individual shift and scale parameters a second stage smoothing spline anova model is used to study potential covariate effects on the common shape function we apply our methods to a real data set to investigate disease effects on circadian rhythms of cortisol a hormone that is affected by stress we find that patients with cushing s syndrome lost circadian rhythms and their 24 hour means were elevated to very high levels patients with major depression had the same circadian shape and phases as normal subjects however their 24 hour mean levels were elevated and amplitudes were dampened for some patients

global existence for coupled reaction diffusion systems abstract we prove here global existence in time of classical solutions for reaction diffusion systems with strong coupling in the diffusion and with natural structure conditions on the nonlinear reactive terms this extends some similar results in the case of a diagonal diffusion operator associated with nonlinearities preserving the positivity and the total mass of the solutions or for which the total mass is a priori bounded here however no positivity assumption is made since nondiagonal systems do not preserve it

minimization of the gliding index criterion for the generation of the surfaces of a knee endoprosthesis previous studies on removed failed artificial knees revealed significant degradation of the articular surfaces including pitting and shredding as well as burnishing accompanied by score marks and scratches the latter damage group being related to the gliding motion of the joint in an attempt to introduce an improved version of an artificial knee joint we have proposed a general model by which the opposing surfaces of the prosthesis components can be synthesized the criterion applied was that of minimization of a defined gliding index the femoral condyles in this model were expressed in terms of torus geometry and the kinematics of motion fed into the model was that of normal motion in the sagittal plane including angles as well as the displacement vector in the knee joint geometry of the tibial component was obtained from the tangents of the femoral surface in subsequent positions of motion the optimal surfaces were those for which the gliding index assumed a minimal value the solutions obtained for various input motions are presented and discussed

a comparison of two non invasive methods for measuring scapular orientation in functional positions identification of scapular dyskinesis and evaluation of interventions depend on the ability to properly measure scapulothoracic st motion the most widely used measurement approach is the acromion marker cluster amc which can yield large errors in extreme humeral elevation and can be inaccurate in children and patient populations recently an individualized regression approach has been proposed as an alternative to the amc this technique utilizes the relationship between st orientation humerothoracic orientation and acromion process position derived from calibration positions to predict dynamic st orientations from humerothoracic and acromion process measures during motion these individualized regressions demonstrated promising results for healthy adults however this method had not yet been compared to the more conventional amc this study compared st orientation estimates by the amc and regression approaches to static st angles determined by surface markers placed on palpated landmarks in typically developing adolescents performing functional tasks both approaches produced errors within the range reported in the literature for skin based scapular measurement techniques the performance of the regression approach suffered when applied to positions outside of the range of motion in the set of calibration positions the amc significantly underestimated st internal rotation across all positions and overestimated posterior tilt in some positions overall root mean square errors for the regression approach were smaller than the amc for every position across all axes of st motion accordingly we recommend the regression approach as a suitable technique for measuring st kinematics in functional motion

point of optimal kinematic error improvement of the instantaneous helical pivot method for locating centers of rotation this paper proposes a variation of the instantaneous helical pivot technique for locating centers of rotation the point of optimal kinematic error poke which minimizes the velocity at the center of rotation may be obtained by just adding a weighting factor equal to the square of angular velocity in woltring s equation of the pivot of instantaneous helical axes piha calculations are simplified with respect to the original method since it is not necessary to make explicit calculations of the helical axis and the effect of accidental errors is reduced the improved performance of this method was validated by simulations based on a functional calibration task for the gleno humeral joint center noisy data caused a systematic dislocation of the calculated center of rotation towards the center of the arm marker cluster this error in piha could even exceed the effect of soft tissue artifacts associated to small and medium deformations but it was successfully reduced by the poke estimation

a model of the soft tissue artefact rigid component when using stereophotogrammetry and skin markers the reconstruction of skeletal movement is affected by soft tissue artefact sta this may be described by considering a marker cluster as a deformable shape undergoing a geometric transformation formed by a non rigid change in size and shape and a rigid component translation and rotation displacements a modal decomposition of the sta relative to an appropriately identified basis allows the separation of these components this study proposes a mathematical model of the sta that embeds only its rigid component and estimates the relevant six mode amplitudes as linear functions of selected proximal and distal joint rotations during the analysed task this model was successfully calibrated for thigh and shank using simultaneously recorded pin and skin marker data of running volunteers the root mean square difference between measured and model estimated sta rigid component was 1 1 0 8 mm median inter quartile range over 3 subjects 5 trials 33 markers coordinates and it was mostly due to the wobbling not included in the model knee joint kinematics was estimated using reference pin marker data and skin marker data both raw and compensated with the model estimated sta sta compensation decreased inaccuracy on average from 6 to 1 for flexion extension from 43 to 18 for the other two rotations and from 69 to 25 for the linear displacements thus the proposed mathematical model provides an sta estimate which can be effectively used within optimal bone pose and joint kinematics estimators for artefact compensation and for simulations aimed at their comparative assessments

a survey of formal methods for determining the centre of rotation of ball joints abstract the determination of an accurate centre of rotation cor from segment marker positions is of interest across a wide range of applications but particularly for clinical gait analysis and for estimating the hip joint centre during surgical intervention of the knee for limb alignment purposes for the first time in this survey of formal methods we classify analyse and compare different methods geometric algebraic bias compensated algebraic and pratt sphere fit methods as well as the centre transformation technique the holzreiter approach the helical pivot technique the schwartz transformation techniques the minimal amplitude point method and the stoddart approach for the determination of spherical joint centres from marker position data in addition we propose a new method the symmetrical cor estimation or score in which the coordinates of the joint centre must only remain constant relative to each segment thus not requiring the assumption that one segment should remain at rest for each method 1000 cor estimations were analysed with the application of isotropic independent and identically distributed gaussian noise standard deviation 0 1 cm to each of the marker positions to all markers on the segment simultaneously and the two in combination for the test conditions used here most techniques were capable of determining the cor to within 0 3 cm as long as the spherical range of motion rom of the joint was 45 or more under the most stringent conditions tested however the score was capable of best determining the cor to within approximately 1 2 mm with a rom of 20 the correct selection and application of these methodologies should help improve the accuracy of surgical navigation and clinical kinematic measurement

instantaneous moment arm determination of the cat knee the moment arm is an important parameter for calculating forces and pressures at a joint present techniques described in the literature are limited for joint studies in animals because of the invasive procedures required which destroy the joint integrity this paper describes a new application of the instantaneous helical axis iha for determination of the moment arm of the knee joint without compromising its integrity measurements based on the iha technique are compared to an established technique using six cadaveric cat hind limbs one experiment using the iha technique was performed to demonstrate its application in situ it was found that the moment arm determined by both techniques resulted in continuous estimations of similar magnitudes over the expected range of motion of the knee joint although the iha technique is sensitive to smoothing a trend toward increasing moment arm as a function of increasing knee angle was observed in four of six specimens the in situ experiment demonstrated the ability to use the iha technique without compromising the integrity of the knee joint so that further histological morphological or topological information could be investigated

latent variable poisson models for assessing the regularity of circadian patterns over time abstractmany researchers in biology and medicine have focused on trying to understand biological rhythms and their potential impact on disease a common biological rhythm is circadian where the cycle repeats itself every 24 hours however a disturbance of the circadian pattern may be indicative of future disease in this article we develop new statistical methodology for assessing the degree of disturbance or irregularity in a circadian pattern for count sequences that are observed over time in a population of individuals we develop a latent variable poisson modeling approach with both circadian and stochastic short term trend autoregressive latent process components that allow for individual variation in the degree of each component a parameterization is proposed for modeling covariate dependence on the proportion of these two model components across individuals in addition we incorporate covariate dependence in the overall mean the magnitude of the trend and the phase shift of the circadian p

estimation of the axis of a screw motion from noisy data a new method based on plucker lines the problems of estimating the motion and orientation parameters of a body segment from two n point set patterns are analyzed using the plucker coordinates of a line plucker lines the aim is to find algorithms less complex than those in conventional use and thus facilitating more accurate computation of the unknown parameters all conventional techniques use point transformation to calculate the screw axis in this paper we present a novel technique that directly estimates the axis of a screw motion as a plucker line the plucker line can be transformed via the dual number coordinate transformation matrix this method is compared with schwartz and rozumalski 2005 a new method for estimating joint parameters from motion data journal of biomechanics 38 107 116 in simulations of random measurement errors and systematic skin movements simulation results indicate that the methods based on plucker lines plucker line method are superior in terms of extremely good results in the determination of the screw axis direction and position as well as a concise derivation of mathematical statements this investigation yielded practical results which can be used to locate the axis of a screw motion in a noisy environment developing the dual transformation matrix dtm from noisy data and determining the screw axis from a given dtm is done in a manner analogous to that for handling simple rotations a more robust approach to solve for the dual vector associated with dtm is also addressed by using the eigenvector and the singular value decomposition

a flexible model for human circadian rhythms many hormones and other physiological processes vary in a circadian pattern although a sine cosine function can be used to model these patterns this functional form is not appropriate when there is asymmetry between the peak and nadir phases in this paper we describe a semiparametric periodic spline function that can be fit to circadian rhythms the model includes both phase and amplitude so that the time and the magnitude of the peak or nadir can be estimated we also describe tests of fit for components in the model data from an experiment to study immunological responses in humans are used to demonstrate the methods

semiparametric models for longitudinal data with application to cd4 cell numbers in hiv seroconverters summary the paper describes a semiparametric model for longitudinal data which is illustrated by its application to data on the time evolution of cd4 cell numbers in hiv seroconverters the essential ingredients of the model are a parametric linear model for covariate adjustment a nonparametric estimation of a smooth time trend serial correlation between measurements on an individual subject and random measurement error a back fitting algorithm is used in conjunction with a cross validation prescription to fit the model a notable feature in the application is that the onset of hiv infection is associated with a sudden drop in cd4 cells followed by a longer term slower decay the model is also used to estimate an individual s curve by combining his data with the population curve shrinkage toward the population mean trajectory is controlled in a natural way by the estimated covariance structure of the data

relevance of mandibular helical axis analysis in functional and dysfunctional tmjs the helical axis ha or motion screw yields a comprehensive description of joint motion the perspective representation of this axis clearly visualizes the regularity of mandibular functional movements yatabe et al 1997 journal of dentist research 76 714 719 and gallo et al 2000 journal of dental research 79 1566 1572 in this study the sensitivity of the ha representation was investigated relative to a irregularities in pathologic motion of clicking temporomandibular joints tmjs for jaw opening closing and b differences in food bolus size and consistency for unilateral mastication in subjects with normal tmjs mandibular motion relative to the head was acquired using a jaw tracker with six degrees of freedom with a sampling frequency of 70 hz the ha was calculated according to an eigenvalue method spoor and veldpaus 1980 journal of biomechanics 13 391 393 and parameters were defined describing its position and orientation relative to the anatomy we analyzed 39 subjects with unilateral or bilateral reciprocal tmj clicking during jaw opening closing and seven asymptomatic subjects during unilateral mastication of five different types of soft and hard food in two different bolus sizes the results showed a greater variability of the ha parameters in the group of clicking joints than in the asymptomatic group in particular the area in which the ha moved was wider in clicking joints than in normal ones and the ha in clicking tmjs had a much greater fluctuation than in normal ones during unilateral mastication for more consistent food or a bigger bolus the ha showed a significantly greater excursion of the orientation parameters furthermore a significantly greater excursion of the dorsoventral and of the craniocaudal component of the distance vector from the ha to the condyle were found the helical axis analysis of mandibular movements was sensitive to kinematic irregularities of the mandible due to an internal joint derangement as well as to differences in food bolus size and consistency

robust estimation of dominant axis of rotation a simple method is developed for robustly estimating a fixed dominant axis of rotation aor of anatomical joints from surface marker data previous approaches which assume a model of circular marker trajectories use plane fitting to estimate the direction of the aor however when there is limited joint range of motion and rotation due to a second degree of freedom minimizing only the planar error can give poor estimates of the aor direction optimizing a cost function which includes the error component within a plane instead of only the component orthogonal to a plane leads to improved estimates of the aor direction for joints which exhibit additional rotational motion from a second degree of freedom results from synthetic data validation show the ranges of motion where the new method has lower estimation error compared to plane fitting techniques estimates of the flexion extension aor from empirical motion capture data of the knee and index finger joints were also more anatomically plausible

the centre of rotation of the shoulder complex and the effect of normalisation shoulder motions consist of a composite movement of three joints and one pseudo joint which together dictate the humerothoracic motion the purpose of this work was to quantify the location of the centre of rotation cor of the shoulder complex as a whole dynamic motion of 12 participants was recorded using optical motion tracking during coronal scapular and sagittal plane elevation the instantaneous cor was found for each angle of elevation using helical axes projected onto the three planes of motion the location of an average cor for each plane was evaluated using digitised and anthropometric measures for normalisation when conducting motion in the coronal scapular and sagittal planes respectively the coefficients for locating the cors of the shoulder complex are 61 61 and 65 of the anterior posterior dimension the vector between the midpoint of the incisura jugularis and the xiphoid process and the midpoint of the seventh cervical vertebra and the eighth thoracic vertebra 0 1 and 2 of the superior inferior dimension the vector between the midpoint of the acromioclavicular joints and the midpoint of the anterior superior iliac spines and 57 57 and 78 of the medial lateral dimension 0 129 times the height of the participant knowing the location of the cor of the shoulder complex as a whole enables improved participant positioning for evaluation and rehabilitation activities that involve movement of the hand with a fixed radius such as those that employ isokinetic dynamometers

two dimensional rigid body kinematics using image contour registration a method for calculating two dimensional rigid body kinematic parameters using shape features is presented proposed applications include the noninvasive quantification of planar joint motion in vivo by using digitized images computed tomographs radiographs etc of a bone contour at two positions the contour curvatures can be best fit to obtain a one to one mapping or registration of the bone images this produces a dense field of displacement vectors from which planar rigid body kinematic parameters can be estimated accuracy was studied using radiographic images of cadaveric femoral bone the two motions of pure rotation with a fixed center of rotation and of pure translation were simulated for pure rotation error in rotation was independent of the rotation magnitude with an average n 10 error of 0 3 0 8 degrees the translation error averaged 0 9 0 5 mm for pure translation the error in rotation was 0 01 0 69 degrees and the error in translation was 0 62 0 98 mm n 10 this novel method has broad applications in the field of planar kinematics especially in cases for which marker fixation is neither possible nor practical

soft tissue artifact compensation by linear 3d interpolation and approximation methods several compensation methods estimate bone pose from a cluster of skin mounted makers each influenced by soft tissue artifact sta in this study linear 3d interpolation and approximation methods affine mapping kriging and radial basis function rbf and the conventional singular value decomposition svd method were examined to determine their suitability for sta compensation the ability of these four methods to estimate knee angles and displacements was compared using simulated gait data with and without added sta the knee angle and the displacement estimates of all four methods were similar with root mean square errors rmses near 1 5 degrees and 4mm respectively the 3d interpolation and approximation methods were more complicated to implement than the conventional svd method however these non standard methods provided additional geometric homothety stretch and time functions that model the deformation of the cluster of markers this additional information may be useful to model and compensate the sta

global nonexistence for the cauchy problem of some nonlinear reaction diffusion systems we first consider the parabolic equationut 2um a x uq f t x u p w t x t 0 x rn where 2 is the 2 fractional power of the laplacian which for 0 2 stands for impurities and f t x and w t x are given nonnegative functions and find its critical exponent then we consider the criticality for five systems of strongly coupled parabolic equations two of them with nonlinear convective terms our results answer positively some open problems raised recently by bandle deng levine and zhang

bayesian vs least squares inverse kinematics simulation experiments with models of 3d rigid body motion and 2d models including soft tissue artefacts abstract two simulation experiments are presented to gauge the accuracy of a new inverse kinematics method based on bayesian inference bik pataky et al 2019 j biomech in more realistic models than were considered previously the first application concerns planar kinematics in the presence of soft tissue artefacts and the second application concerns rigid body kinematics in 3d with finite helical axes fha the percentage of simulations in which bik was more accurate than least squares based methods was only high in cases of relatively large noise magnitudes noise sd 5 mm or when the rotation magnitude was very small 5 deg in the 3d fha model correlated parameters are the likely culprit of the low performance of bik also computation time is a major deficit of the bik approach 20 s for the movement between two time frames these results indicate that more research will be necessary to improve the accuracy of bik for complex biomechanical models at realistic noise levels and to reduce computation time

assessment of anatomical frame variation effect on joint angles a linear perturbation approach although the interpretability and reliability of joint kinematics depends strongly on the accuracy and precision of determining the anatomical frame af orientation the exact dependency of joint angle error on af misalignment is still not clear to fully understand the behavior this study uses linear perturbations to quantify joint angle error due to known modifications of the afs where the joint angles are calculated according to the cardanic convention the result is a functional representation of joint angle error with dependence on nominal joint angles and on the orientations of the alternative afs relative to the nominal afs the results are validated using numerical analysis on knee joint angle data during walking the derived relationship elucidates results from previous work studying this effect and allows af differences to be inferred by joint angle curves when multiple sets of joint angle curves are collected simultaneously

on precision limits for derivatives numerically calculated from noisy data abstract this paper has three purposes 1 1 to verify an error formula from which the maximal precision in derivatives obtained from noisy measurement data can be calculated the formula is verified by comparison with the resulting noise in derivatives obtained by local least squares polynomial fitting it is also verified that differentiation by fourier series expansion gives noise exceeding the minimum value according to the error formula 2 2 an index called the relative noise amplification rna is introduced for an arbitrary differentiating filter it is defined as the noise transmission of the filter divided by the minimal noise transmission according to the above mentioned error formula when the filter produces unbiased estimates the value of the rna always exceeds one the rna can be used as a quality index for differentiating filters the filter with the smallest value on the rna also has the smallest amount of noise superimposed on the calculated derivatives provided the input noise is white and additive 3 3 the bandwidth and the relative noise amplification of differentiating filters obtained by local least squares polynomial fitting are presented the 0th 1st and 2nd order derivatives have been investigated for polynomials up to 8th order these results can be used for the determination of suitable filter parameters in various applications

fitting nonlinear models with arma errors to biological rhythm data many behavioural and physiological processes are periodic with a period of approximately 24 hours for descriptive purposes linear regression using a simple sinusoid with a fixed 24 hour period is sometimes an adequate tool for analysing data from such processes inference based on regression models under the assumption of independent and identically distributed errors however can often mislead seriously in this paper we present a general class of models for fitting biological rhythms with use of higher order harmonic terms of one or more unknown fundamentals and arma processes for the errors we describe the procedures for model specification and estimation and give the theoretical justification for these procedures analysis of a series of human core body temperature illustrates the methodology

a new method for estimating joint parameters from motion data joint centers and axes of rotation joint parameters are central to all branches of movement analysis in gait analysis the standard protocol used to determine hip and knee joint parameters is prone to errors arising from palpation anthropometric regression equations and misplaced alignment devices several alternative methods have been proposed but to date none have been shown to be accurate and reliable enough for use in the clinical setting this article describes a new method for joint parameter estimation the new method can be summarized as follows i the motions of two adjacent segments spanning a single joint are tracked ii the axis of rotation between every pair of observed segment configurations is computed iii the most likely intersection of all axes effective joint center and most likely orientation of the axes effective joint axis is found initial validation of the method was conducted on a hinged mechanical analog and a single healthy adult subject for the analog the center was found to be within 3 8 mm of the geometric center and 2 0 degrees of the geometric axis standard deviation for the adult subject hip centers varied on the order of 1 3 mm knee centers by 3 9 mm and knee axes by 2 0 degrees the results suggest that the new method is an objective precise and practical alternative to the standard clinical approach

finite centroid and helical axis estimation from noisy landmark measurements in the study of human joint kinematics abstract recent work on joint kinematics indicates that the finite centroid centre of rotation and the finite helical axis axis of rotation screw axis twist axis are highly susceptible to measurement errors when they are experimentally determined from landmark position data this paper presents an analytical model to describe these effects under isotropic conditions for the measurement errors and for the spatial landmark distribution it appears that the position and direction errors are inversely proportional to the rotation magnitude and that they are much more error prone than the relatively well determined rotation and translation magnitudes furthermore the direction and rotation magnitude errors are inversely proportional to the landmark distribution radius and the position and translation magnitude errors are minimal if the mean position of the landmarks coincides with the centroid or helical axis for the planar centroid the use of rigid body constraints results in considerable precision improvement relative to the classical finite reuleaux method for centroid reconstruction these analytical results can be used to define suitable measurement configurations and they are used in this paper to explain experimental results on rontgenphotogrammetrically acquired in vitro wrist joint movement

accuracy of a ct based bone contour registration method to measure relative bone motions in the hindfoot abstract for measuring the in vivo range of motion of the hindfoot a ct based bone contour registration method ct bcm was developed to determine the three dimensional position and orientation of bones to validate this technique we hypothesized that the range of motion in the hindfoot is equally accurately measured by roentgen stereophotogrammetric analysis rsa as by the ct bcm technique tantalum bone markers were placed in the distal tibia talus and calcaneus of one cadaver specimen with a fixed lower leg the cadaveric foot was held in neutral and subsequently loaded in eight extreme positions immediately after acquiring a ct scan with the foot in a position rsa radiographs were made bone contour registration and rsa was performed helical axis parameters were calculated for talocrural and subtalar joint motion from neutral to extreme positions and between opposite extreme positions differences between ct bcm and rsa were calculated compared with rsa the ct bcm data registered an overall root mean square difference rmsd of 0 21 for rotation about the helical axis and 0 20 mm translation along the helical axis for the talocrural and subtalar joint and for all motions combined the rmsd of the position and direction of the helical axes was 3 3 mm and 2 4 respectively the latter errors were larger with smaller helical rotations the differences are similar to those reported for validated rsa and thus are not clinically relevant concluding ct bcm is an accurate and accessible alternative for studying joint motion as it does not have the risk of infection and overlapping bone markers

the collapsed gibbs sampler in bayesian computations with applications to a gene regulation problem abstract this article describes a method of grouping and collapsing in using the gibbs sampler and proves from an operator theory viewpoint that the method is in general beneficial the norms of the forward operators associated with the corresponding nonreversible markov chains are used to discriminate among different simulation schemes when applied to bayesian missing data problems the idea of collapsing suggests skipping the steps of sampling parameter s values in standard data augmentation by doing this we obtain a predictive update version of the gibbs sampler a procedure of calculating the posterior odds ratio via the collapsed gibbs sampler when incomplete observations are involved is presented as an illustration of possible applications three examples along with a bayesian treatment for identifying common protein binding sites in unaligned dna sequences are provided

global solutions of reaction diffusion systems with a balance law and nonlinearities of exponential growth abstract we consider the initial boundary value problem of the form u t a u f u v v t c u d v f u v x r n n 1 t r where f u v 0 f 0 v 0 v r f u v k u e v k and are positive constants is any continuous nonnegative locally lipschitzian function on r such that 0 0 d a and c d a with bounded continuous nonegative initial data this system contains in particular the frank kamenetskii approximation to an n th order exothermic chemical reaction of arrhenius type and non systemically autocatalysed reaction diffusion systems we prove the existence of global classical solutions and study their large time behaviour our main tools are estimates of the neumann function for the heat equation and local l p a priori estimates independent of time

calculating the 2d motion of lumbar vertebrae using splines in this study we investigate the use of splines and the icp method besl p mckay n 1992 a method for registration of 3d shapes ieee transactions on pattern analysis and machine intelligence 14 239 256 for calculating the transformation parameters for a rigid body undergoing planar motion parallel to the image plane we demonstrate the efficacy of the method by estimating the finite centre of rotation and angle of rotation from lateral flexion extension radiographs of the lumbar spine in an in vitro error study the method displayed an average error of rotation of 0 44 0 45 degrees and an average error in fcr calculation of 7 6 8 5 mm the method was shown to be superior to that of crisco et al two dimensional rigid body kinematics using image contour registration journal of biomechanics 28 1 119 124 and brinckmann et al quantification of overload injuries of the thoracolumbar spine in persons exposed to heavy physical exertions or vibration at the workplace part i the shape of vertebrae and intervertebral discs study of a yound healthy population and a middle aged control group clinical biomechanics supplement 1 s5 s83 for the tests performed here in general we believe the use of splines to represent planar shapes to be superior to using digitised curves or landmarks for several reasons first with appropriate software splines require less effort to define and are a compact representation with most vertebra outlines using less than 30 control points second splines are inherently sub pixel representations of curves even if the control points are limited to pixel resolutions third there is a well defined method the icp algorithm for registering shapes represented as splines finally like digitised curves splines are able to represent a large class of shapes with little effort but reduce potential segmentation errors from two dimensions parallel and perpendicular to the image gradient to just one parallel to the image gradient we have developed an application for performing all the necessary computations which can be downloaded from http www claritysmart com

on intrinsic equivalences of the finite helical axis the instantaneous helical axis and the sara approach a mathematical perspective accurate determination of joint axes is essential for understanding musculoskeletal function whilst numerous algorithms to compute such axes exist the conditions under which each of the methods performs best remain largely unknown typically algorithms are evaluated for specific conditions only limiting the external validity of conclusions regarding their performance we derive exact mathematical relationships between three commonly used algorithms for computing joint axes from motion data finite helical axes fha instantaneous helical axes iha and sara symmetrical axis of rotation approach including relationships for an extension to the mean helical axes methods that facilitate determining joint centres and axes through the derivation of a sound mathematical framework to objectively compare the algorithms we demonstrate that the fha and sara approach are equivalent for the analysis of two time frames moreover we show that the position of a helical axis derived from the iha using positional data is affected by a systematic error perpendicular to the true axis direction whereas the axis direction is identical to those computed with either the fha or sara approach true direction finally with an appropriate choice of weighting factors the mean fha mfha method is equivalent to the symmetrical centre of rotation estimation score algorithm for determination of a centre of rotation cor and similarly equivalent to the sara algorithm for determination of an axis of rotation aor the deep understanding of the equivalences between methods presented here enables readers to choose numerically efficient robust methods for determining aors and cors with confidence

in vivo determination of the anatomical axes of the ankle joint complex an optimization approach this study investigates the feasibility of a subject specific three dimensional model of the ankle joint complex for kinematic and dynamic analysis of movement the ankle joint complex was modelled as a three segment system connected by two ideal highe joints the talocrural and the subtalar joint a mathematical formulation was developed to express the three dimensional translation and rotation between the foot and shank segments as a function of the two joint angles and 12 model parameters describing the locations of the joint axes an optimization method was used to fit the model parameters to three dimensional kinematic data of foot and shank markers obtained during test movements throughout the entire physiological range of motion of the ankle joint the movement of the talus segment which cannot be measured non invasively is not necessary for the analysis this optimization method was used to determine the position and orientation of the joint axes in 14 normal subjects after optimization the discrepancy between the best fitting model and actual marker kinematics was between 1 and 3 mm for all subjects the predicted inclination of the subtalar joint axis from the horizontal plane was 37 4 2 7 and the medial deviation was 18 0 16 2 the lateral side of the talucrural axis was directed slightly posteriorly 6 8 8 1 and inclined downward by 7 0 5 4 these results are similar to previously reported typical results from anatomical in vitro studies reproducibility was evaluated by repeated testing of one subject which resulted in variations of about one fifth of the standard deviation within the group the inclination of the subtalar joint axis was significantly correlated to the arch height and a radiographic tarsal index it is concluded that this optimization method provides the opportunity to incorporate inter individual anatomical differences into kinematic and dynamic analysis of the ankle joint complex this allows a more functional interpretation of kinematic data and more realistic estimates of internal forces

a directional model for the estimation of the rotation axes of the ankle joint this article is motivated by the estimation of the directions of the two rotation axes of the ankle these axes carry information on individual ankles they are useful in the construction of biomechanical models and the treatment of orthopedic problems in biomechanics the rotation axes of the ankle often are estimated using optimization techniques this work investigates a statistical model for carrying out the estimation the data set for analysis is a time ordered sequence of 3 3 rotation matrixes giving the ankle s orientations as the foot moves with respect to the lower leg these rotation matrixes are assumed to follow fisher von mises distributions the predicted values for the observed rotations feature four angles for the orientation of two rotation axes and two series of time varying rotation angles about the two axes maximum likelihood estimators of the parameters are derived approximations to their sampling distributions are obtained when the errors are clustered around the identity matrix

comparison of the score and ha methods for locating in vivo the glenohumeral joint centre a recent paper has described a new functional method the symmetrical centre of rotation score for locating joint centre position ehrig r m taylor w r duda g n heller m o 2006 a survey of formal methods for determining the centre of rotation of ball joints journal of biomechanics 39 15 2798 2809 for in vitro analyses the score method showed better precision than helical axis ha or sphere fitting methods despites ha determination is very sensitive to small angular velocity the international society of biomechanics has recommended to use ha for locating the glenohumeral joint centre this paper aims at comparing the score method with the ha method for locating in vivo the glenohumeral joint centre according to the movement characteristics nine subjects performed 10 cycles of three different movements at two different velocities for each test combination of movements the location of the centre of rotation was estimated with both methods score and ha analyses focused on the 3d location of the glenohumeral joint centre and on the repeatability of location standard deviation this study showed that score and ha methods yielded the same gh location nevertheless with score method the location of the glenohumeral joint centre was different according to the test this study evidenced that the score method was more precise than ha method error of 3 mm versus 4 6 mm and that the gh location with the score method was not affected by movements with slow velocities

the score residual a quality index to assess the accuracy of joint estimations abstract the determination of an accurate centre of rotation cor from skin markers is essential for the assessment of abnormal gait patterns in clinical gait analysis despite the many functional approaches to estimate cors no non invasive analytical determination of the error in the reconstructed joint location is currently available the purpose of this study was therefore to verify the residual of the symmetrical centre of rotation estimation score as a reliable indirect measure of the error of the computed joint centre to evaluate the score residual numerical simulations were performed to evaluate cor estimations at different ranges of joint motion a statistical model was developed and used to determine the theoretical relationships among the score residual the magnitude of the skin marker artefact the corrections to the marker positions and the error of the cor estimations to the known centre of rotation we found that the equation err 0 5rs provides a reliable relationship among the cor error err and the scaled score residual rs providing that any skin marker artefact is first minimised using the optimal common shape technique ocst measurements on six healthy volunteers showed a reduction of score residual from 11 to below 6 mm and therefore demonstrated consistency of the theoretical considerations and numerical simulations with the in vivo data this study also demonstrates the significant benefit of the ocst for reducing skin marker artefact and thus for predicting the accuracy of determining joint centre positions in functional gait analysis for the first time this understanding of the score residual allows a measure of error in the non invasive assessment of joint centres this measure now enables a rapid assessment of the accuracy of the cor as well as an estimation of the reproducibility and repeatability of skeletal motion patterns

ground reaction intrinsic and extrinsic variability assessment and related method for artefact treatment ground reaction gr components measured by a dynamometric platform represent the dynamic interaction of the moving human body with the ground and depend on the subject platform relative position and orientation the observed variability among the gr measurements of the walking trials of an individual is either due to variability in the motor performance intrinsic variability or due to changes in the direction of walking and in the position and orientation of the striking foot relative to the platform extrinsic variability a method based on the median operator is presented here which lets us quantify the two components of variability the application of the method to a large data set of normal subjects evidenced changes in progression direction foot orientation 95th percentile value is 6 9 degrees which can dramatically change the patterns of gr components this result warns about improper analysis of ground reaction measurement an algorithm for restoring gr measurements affected by artefact was derived from the above method this tool can be of valuable aid in clinical practice where patients conditions suggest to not insist on repetition of trials even if the required number of correct foot placements has not been achieved the artefact correction algorithm has been applied to a large data set artificially corrupted to evaluate its robustness

bayesian analysis for generalized linear models with nonignorably missing covariates we propose bayesian methods for estimating parameters in generalized linear models glms with nonignorably missing covariate data we show that when improper uniform priors are used for the regression coefficients phi of the multinomial selection model for the missing data mechanism the resulting joint posterior will always be improper if i all missing covariates are discrete and an intercept is included in the selection model for the missing data mechanism or ii at least one of the covariates is continuous and unbounded this impropriety will result regardless of whether proper or improper priors are specified for the regression parameters beta of the glm or the parameters alpha of the covariate distribution to overcome this problem we propose a novel class of proper priors for the regression coefficients phi in the selection model for the missing data mechanism these priors are robust and computationally attractive in the sense that inferences about beta are not sensitive to the choice of the hyperparameters of the prior for phi and they facilitate a gibbs sampling scheme that leads to accelerated convergence in addition we extend the model assessment criterion of chen dey and ibrahim 2004a biometrika 91 45 63 called the weighted l measure to glms and missing data problems as well as extend the deviance information criterion dic of spiegelhalter et al 2002 journal of the royal statistical society b 64 583 639 for assessing whether the missing data mechanism is ignorable or nonignorable a novel markov chain monte carlo sampling algorithm is also developed for carrying out posterior computation several simulations are given to investigate the performance of the proposed bayesian criteria as well as the sensitivity of the prior specification real datasets from a melanoma cancer clinical trial and a liver cancer study are presented to further illustrate the proposed methods

bone orientation and position estimation errors using cosserat point elements and least squares methods application to gait the aim of this study was to analyze the accuracy of bone pose estimation based on sub clusters of three skin markers characterized by triangular cosserat point elements tcpes and to evaluate the capability of four instantaneous physical parameters which can be measured non invasively in vivo to identify the most accurate tcpes moreover tcpe pose estimations were compared with the estimations of two least squares minimization methods applied to the cluster of all markers using rigid body rbls and homogeneous deformation hdls assumptions analysis was performed on previously collected in vivo treadmill gait data composed of simultaneous measurements of the gold standard bone pose by bi plane fluoroscopy tracking the subjects knee prosthesis and a stereophotogrammetric system tracking skin markers affected by soft tissue artifact femur orientation and position errors estimated from skin marker clusters were computed for 18 subjects using clusters of up to 35 markers results based on gold standard data revealed that instantaneous subsets of tcpes exist which estimate the femur pose with reasonable accuracy median root mean square error during stance swing 1 4 2 8deg for orientation 1 5 4 2mm for position a non invasive and instantaneous criteria to select accurate tcpes for pose estimation 4 8 7 3deg 5 8 12 3mm was compared with rbls 4 3 6 6deg 6 9 16 6mm and hdls 4 6 7 6deg 6 7 12 5mm accounting for homogeneous deformation using hdls or selected tcpes yielded more accurate position estimations than rbls method which conversely yielded more accurate orientation estimations further investigation is required to devise effective criteria for cluster selection that could represent a significant improvement in bone pose estimation accuracy

error propagation from kinematic data to modeled muscle tendon lengths during walking kinematic data from 3d gait analysis together with musculoskeletal modeling techniques allow the derivation of muscle tendon lengths during walking however kinematic data are subject to soft tissue artifacts sta referring to skin marker displacements during movement sta are known to significantly affect the computation of joint kinematics and would therefore also have an effect on muscle tendon lengths which are derived from the segmental positions the present study aimed to introduce an analytical approach to calculate the error propagation from sta to modeled muscle tendon lengths skin marker coordinates were assigned uncorrelated isotropic error functions with given standard deviations accounting for sta two different musculoskeletal models were specified one with the joints moving freely in all directions and one with the joints constrained to rotation but no translation using reference kinematic data from two healthy boys mean age 9 y 5 m the propagation of sta to muscle tendon lengths was quantified for semimembranosus gastrocnemius and soleus the resulting average sd ranged from 6 to 50 of the normalized muscle tendon lengths during gait depending on the muscle the sta magnitudes and the musculoskeletal model these results highlight the potential impact sta has on the biomechanical analysis of modeled muscle tendon lengths during walking and suggest the need for caution in the clinical interpretation of muscle tendon lengths derived from joint kinematics

global bounds and asymptotics for a system of reaction diffusion equations on etudie le probleme aux valeurs limites non lineaire u t a u u v dans r v t c u d v u v dans r avec les conditions u v 0 sur r et u 0 x u 0 x v 0 x v 0 x dans on etablit l existence de solutions globales fortes et on etudie leur comportement quand t

on systems of reaction diffusion equations with a balance law the sequel abstract this paper is a sequel of the review paper on reaction diffusion systems with a balance law by martin and pierre 1990 here we present the results obtained after martin and pierre 1990 not only for classical systems but also for systems with either time fractional derivatives or space fractional derivatives accounting for anomalous diffusions

on analyzing circadian rhythms data using nonlinear mixed models with harmonic terms summarywang ke and brown 2003 biometrics59 804 812 developed a smoothing based approach for modeling circadian rhythms with random effects their approach is flexible in that fixed and random covariates can affect both the amplitude and phase shift of a nonparametrically smoothed periodic function in motivating their approach wang et al stated that a simple sinusoidal function is too restrictive in addition they stated that although adding harmonics can improve the fit it is difficult to decide how many harmonics to include in the model and the results are difficult to interpret we disagree with the notion that harmonic models cannot be a useful tool in modeling longitudinal circadian rhythm data in this note we show how nonlinear mixed models with harmonic terms allow for a simple and flexible alternative to wang et al s approach we show how to choose the number of harmonics using penalized likelihood to flexibly model circadian rhythms and to estimate the effect of covariates on the rhythms we fit harmonic models to the cortisol circadian rhythm data presented by wang et al to illustrate our approach furthermore we evaluate the properties of our procedure with a small simulation study the proposed parametric approach provides an alternative to wang et al s semiparametric approach and has the added advantage of being easy to implement in most statistical software packages

a solidification procedure to facilitate kinematic analyses based on video system data abstract when video based motion analysis systems are used to measure segmental kinematics the major source of error is the displacement of skin fixed markers relative to the underlying skeletal structure such displacements cause the marker representation of the segment to deform thereby decreasing the accuracy of subsequent three dimensional kinematic calculations we have developed a two step solidification procedure to address this problem first the mean rigid shape is computed which best represents the time varying marker configuration of each segment second a least squares minimization is used to replace the measured marker coordinates with those corresponding to the best fit mean rigid shape rigid body theory can then be applied unambiguously to perform kinematic analyses to evaluate this approach we defined an unperturbed three dimensional reference movement using kinematic data from the swing phase of gait after perturbing the marker coordinates with artificial noise the rotation matrix and translation vector absolute and relative movement between each pair of successive images were computed using 1 reference frames fixed directly to the perturbed marker coordinates 2 a least squares minimization procedure found in the literature and 3 the proposed solidification procedure the least squares and solidification procedures produced extremely similar results which relative to the direct calculation reduced kinematic errors on average by 20 25 when the maximum distance between markers was small e g

the use of optimally regularized fourier series for estimating higher order derivatives of noisy biomechanical data abstract optimally regularized filtered fourier series can be used most effectively for estimating higher order derivatives of noisy data sequences such as occur in biomechanical investigations as the optimal filtering process takes place in the derivative domain use being made of the statistical information contained in the periodogram of the data sequence no numerical differentiation as such takes place and all the problems known to be associated with such a procedure are avoided the optimally filtered approximation to the function itself is obtained by the same technique the algorithm is based on known results from time series and approximation theory and offers several advantages when compared with other techniques the optimally filtered approximations of the function and all its required derivatives are obtained in a single run compact analytical fourier representations of the filtered function and the derivatives are available allowing interpolation between data points and further analytical treatment of the function all the desirable properties of fourier approximations such as periodicity end point continuity etc can be utilized if fast fourier transforms are used the algorithm is computationally far more efficient than other techniques

in vivo estimation of the glenohumeral joint centre by functional methods accuracy and repeatability assessment abstract several algorithms have been proposed for determining the centre of rotation of ball joints these algorithms are used rather to locate the hip joint centre few studies have focused on the determination of the glenohumeral joint centre however no studies have assessed the accuracy and repeatability of functional methods for glenohumeral joint centre this paper aims at evaluating the accuracy and the repeatability with which the glenohumeral joint rotation centre ghrc can be estimated in vivo by functional methods the reference joint centre is the glenohumeral anatomical centre obtained by medical imaging five functional methods were tested the algorithm of gamage and lasenby 2002 bias compensated halvorsen 2003 symmetrical centre of rotation estimation ehrig et al 2006 normalization method chang and pollard 2007 helical axis woltring et al 1985 the glenohumeral anatomical centre ghac was deduced from the fitting of the humeral head four subjects performed three cycles of three different movements flexion extension abduction adduction and circumduction for each test the location of the glenohumeral joint centre was estimated by the five methods analyses focused on the 3d location on the repeatability of location and on the accuracy by computing the euclidian distance between the estimated ghrc and the ghac for all the methods the error repeatability was inferior to 8 25 mm this study showed that there are significant differences between the five functional methods the smallest distance between the estimated joint centre and the centre of the humeral head was obtained with the method of gamage and lasenby 2002

influence of geometrical distribution of common points on the accuracy of coordinate transformation geometrical distribution of common points is of significance for coordinate transformation as the transformation parameters are computed through common points whose coordinates are known common points can be divided into a calculating set and a testing set whose geometrical distribution can be described by internal and external distribution parameters the former contains the number of points the reference coordinate and the coordinate difference the latter is defined as the overlapping degree between both sets both a rotation matrix and a translation vector are involved in the transformation parameters and could be evaluated by 3 approaches i e the coordinate error method the rms error method and the error method of relative euclidean distance an invalidation of the third method has been proven that evaluating indexes will remain invariant for a fixed testing set regardless of variation in the calculating set according to the classification of geometrical distribution of common points the influences of internal and external distribution parameters on the accuracy of coordinate transformation are related to the number of points symmetrical distribution and the overlapping degree which will be formulated and summarized in detail finally the above conclusions can be verified and proven by computer simulation and practical experiment respectively

a least squares algorithm for the equiform transformation from spatial marker co ordinates the present paper describes an algorithm for estimating the translation vector and the rotation matrix of a moving body from noisy measurements on the spatial co ordinates of at least three non collinear markers a sensitivity analysis of the estimated parameters and of the helical axis is presented in terms of characteristics of the marker distribution the implementation of the proposed algorithm in a fortran subroutine is appended

optimal marker placement for calculating the instantaneous center of rotation abstract a computer simulation with error propagation was performed to determine the optimal placement of marker points for calculating the instantaneous center of rotation cri the authors assume that planar rigid body motion occurs between two positions each defined by marker points noisy marker points were generated by perturbing their coordinates with random values from a normal population of errors the effects of these errors on the range of errors in calculating cri location were investigated parametric analysis determined that marker point placement had important effects on cri error marker placement was optimal when the estimated cri was located at the midpoint between the marker points while increasing the distance between marker points increased accuracy there is a critical distance above which no additional increase in accuracy was noted when using this placement the farther the marker midpoint was from the cri the greater was the error at these placements increasing the distance between the marker points continually decreased cri error the methodologies presented here help to improve the accuracy with which the location of the cri can be calculated however it is emphasized that the cri remains sensitive to noise and investigators should apply this kinematic parameter knowingly

determination of rigid body registration marker error from edge error registration markers affixed to rigid bodies fixed to bone as opposed to skin are commonly used when tracking 3d rigid body motion the measured positions of registration markers are subject to unavoidable errors both systematic and non systematic prior studies have investigated the error propagated to such derived properties as rigid body positions and helical axes while others have focused on the error associated with a specific position tracking system under restricted conditions theoretical and simulation based error propagation requires knowledge of the variation due to individual registration markers however the variation in registration marker position measurement has previously been either assumed or determined from static cases the objective of this paper is the introduction of a method for determining individual marker variation irrespective of change in rigid body position or motion by utilizing the distances between the markers edge lengths which are invariant under rotation and translation simulations were used to validate and characterize the introduced technique demonstrating that the predictions improve with greater edge length and additional markers converge on reference values where the edge length is at least 4 times the magnitude of the maximum vertex variation and that under ideal conditions the confidence interval about the predicted variation is within 7 of the maximum variation associated with that marker set the introduced technique was tested on the results of a motion tracking experiment to demonstrate the wide disparity in vertex variation between static and non static measurements of the same registration markers where the non static variation exceeded the static variation by an average factor of 12 7

a regression model for time series of counts summary this paper discusses a model for regression analysis with a time series of counts correlation is assumed to arise from an unobservable process added to the linear predictor in a log linear model an estimating equation approach used for parameter estimation leads to an iterative weighted and filtered least squares algorithm asymptotic properties for the regression coefficients are presented we illustrate the technique with an analysis of trends in u s polio incidence since 1970

semiparametric stochastic mixed models for longitudinal data abstract we consider inference for a semiparametric stochastic mixed model for longitudinal data this model uses parametric fixed effects to represent the covariate effects and an arbitrary smooth function to model the time effect and accounts for the within subject correlation using random effects and a stationary or nonstationary stochastic process we derive maximum penalized likelihood estimators of the regression coefficients and the nonparametric function the resulting estimator of the nonparametric function is a smoothing spline we propose and compare frequentist inference and bayesian inference on these model components we use restricted maximum likelihood to estimate the smoothing parameter and the variance components simultaneously we show that estimation of all model components of interest can proceed by fitting a modified linear mixed model we illustrate the proposed method by analyzing a hormone dataset and evaluate its performance through simulations

rigid and non rigid geometrical transformations of a marker cluster and their impact on bone pose estimation when stereophotogrammetry and skin markers are used bone pose estimation is jeopardised by the soft tissue artefact sta at marker cluster level this can be represented using a modal series of rigid rt translation and rotation and non rigid nrt homothety and scaling geometrical transformations the nrt has been found to be smaller than the rt and claimed to have a limited impact on bone pose estimation this study aims to investigate this matter and comparatively assessing the propagation of both sta components to bone pose estimate using different numbers of markers twelve skin markers distributed over the anterior aspect of a thigh were considered and sta time functions were generated for each of them as plausibly occurs during walking using an ad hoc model and represented through the geometrical transformations using marker clusters made of four to 12 markers affected by these stas and a procrustes superimposition approach bone pose and the relevant accuracy were estimated this was done also for a selected four marker cluster affected by stas randomly simulated by modifying the original sta nrt component so that its energy fell in the range 30 90 of total sta energy the pose error which slightly decreased while increasing the number of markers in the marker cluster was independent from the nrt amplitude and was always null when the rt component was removed it was thus demonstrated that only the rt component impacts pose estimation accuracy and should thus be accounted for when designing algorithms aimed at compensating for sta