associations between trunk postural control in walking and unstable sitting at various levels of task demand abstract trunk postural control tpc has been investigated in several populations and tasks previous work observed targeted training of tpc via isolated trunk control tasks may improve performance in other activities e g walking however the nature of this relationship remains unknown we therefore investigated the relationship between tpc at both the global i e response to finite perturbations and local i e resistance to continuous perturbations levels during walking and unstable sitting both at varying levels of task demand thirteen individuals 11 male 2 female with no recent history past 12 months of illness injury or musculoskeletal disorders walked on a dual belt treadmill at four speeds 20 10 10 and 20 of self selected walking speed and completed an unstable sitting task at four levels of chair instability 100 75 60 and 45 of an individual s neutral stability as defined by the gravitational gradient three dimensional trunk and pelvic kinematics were collected tri planar lyapunov exponents and sample entropy characterized local tpc global tpc was characterized by ranges of motion and for seated trials metrics derived from center of pressure time series i e path length 95 confidence ellipse area mean velocity and rms position no strong or significant correlations 0 057

is slow walking more stable several efforts have been made to study gait stability using measures derived from nonlinear timeseries analysis the maximum finite time lyapunov exponent lmax quantifies how a system responds to an infinitesimally small perturbation recent studies suggested that slow walking leads to lower lmax values and thus is more stable than fast walking but these studies suffer from methodological limitations we studied the effects of walking speed on the amount of kinematic variability and stability in human walking trunk motions of 15 healthy volunteers were recorded in 3d during 2 min of treadmill walking at different speeds from those time series maximum lyapunov exponents indicating short term and long term divergence ls stride and ll stride and mean standard deviation meansd were calculated ls stride showed a linear decrease with increasing speed for forward backward ap movements and quadratic effects inverted u shaped for medio lateral ml and up down vt movements ll stride showed a quadratic effect inverted u shaped of walking speed for ap movements a linear decrease for ml movements and a linear increase for vt movements moreover positive correlations between ls and meansd were found for all directions while ll stride and meansd were correlated negatively in the ap direction the different effects of walking speed on ls stride and ll stride for the different planes suggest that slow walking is not necessarily more stable than fast walking the absence of a consistent pattern of correlations between ll stride and meansd over the three directions suggests that variability and stability reflect at least to a degree different properties of the dynamics of walking

local dynamic stability in turning and straight line gait successful community and household ambulation require the ability to navigate corners and maneuver around obstacles posing unique challenges compared to straight line walking the challenges associated with turning may contribute to an increased incidence of falling and the occurrence of fall related injuries a measure of stability applied to turning gait may be able to quantify a system s response to naturally occurring disturbances associated with turning and identify subjects at greater risk of falling an index of stability has been used previously to assess the rate of kinematic separation local dynamic stability during straight line gait the purpose of this study was to determine if local dynamic stability during constant speed turning is reduced compared to straight line treadmill walking maximum finite time lyapunov exponents lambda were used to estimate the local stability of able bodied subjects n 19 sagittal plane hip knee and ankle trajectories for turning compared to straight line walking at two different walking speeds turning lambda was greater than straight lambda for the hip right knee and ankle p 0 05 turning lambda for the left knee angle was similar to straight lambda there were no differences in lambda between left and right limbs for the hip and ankle and also no differences between the inside and outside limbs during turning for all joints these findings indicate able bodied subjects hip right knee and ankle kinematics are less locally stable while turning than walking in a straight line and may be used as a comparative tool for determining the efficacy of therapeutic interventions for mobility impaired populations

comparison of different state space definitions for local dynamic stability analyses abstract measures of local dynamic stability such as the local divergence exponent s quantify how quickly small perturbations deviate from an attractor that defines the motion when the governing equations of motion are unknown an attractor can be reconstructed by defining an appropriate state space however state space definitions are not unique and accepted methods for defining state spaces have not been established for biomechanical studies this study first determined how different state space definitions affected s for the lorenz attractor since exact theoretical values were known a priori values of s exhibited errors s decreased post fatigue for all 6 state spaces differences were statistically significant for 3 of these state spaces for state spaces defined using delay embedding increasing the embedding dimension decreased s in both the lorenz and experimental data overall our findings suggest that direct numerical comparisons between studies that use different state space definitions should be made with caution however trends across experimental comparisons appear to persist biomechanical state spaces constructed using positions and velocities or delay reconstruction of individual states are likely to provide consistent results

local dynamic stability of treadmill walking intrasession and week to week repeatability abstract repetitive falls degrade the quality of life of elderly people and of patients suffering of various neurological disorders in order to prevent falls while walking one should rely on relevant early indicators of impaired dynamic balance the local dynamic stability lds represents the sensitivity of gait to small perturbations divergence exponents maximal lyapunov exponents assess how fast a dynamical system diverges from neighbor points although numerous findings attest the validity of lds as a fall risk index reliability results are still sparse the present study explores the intrasession and intersession repeatability of gait lds using intraclass correlation coefficients icc and standard error of measurement sem ninety five healthy individuals performed 5 min treadmill walking in two sessions separated by 9 days trunk acceleration was measured with a 3d accelerometer three time scales were used to estimate lds over 4 10 strides 4 10 over one stride 1 and over one step 0 5 the intrasession repeatability was assessed from three repetitions of either 35 strides or 70 strides taken within the 5 min tests the intersession repeatability compared the two sessions which totalized 210 strides the intrasession iccs 70 strides estimates 35 strides estimates were 0 52 0 18 for 4 10 and 0 84 0 77 for 1 and 0 5 the intersession iccs were around 0 60 the sem results revealed that 0 5 measured in medio lateral direction exhibited the best reliability sufficient to detect moderate changes at individual level 20 however due to the low intersession repeatability one should average several measurements taken on different days in order to better approximate the true lds

when human walking becomes random walking fractal analysis and modeling of gait rhythm fluctuations abstract we present a random walk fractal analysis of the stride to stride fluctuations in the human gait rhythm the gait of healthy young adults is scale free with long range correlations extending over hundreds of strides this fractal scaling changes characteristically with maturation in children and older adults and becomes almost completely uncorrelated with certain neurologic diseases stochastic modeling of the gait rhythm dynamics based on transitions between different neural centers reproduces distinctive statistical properties of the gait pattern by tuning one model parameter the hopping transition range the model can describe alterations in gait dynamics from childhood to adulthood including a decrease in the correlation and volatility exponents with maturation

step width variability but not step length variability or step time variability discriminates gait of healthy young and older adults during treadmill locomotion the variability of spatial and temporal step kinematics have separately been shown to prospectively predict falls by older adults however the published literature has not addressed the relative importance of the information related to locomotion control contributed by variability of spatial variables temporal variables or both we conducted a post hoc analysis to determine the extent to which the variability of spatial and temporal step kinematics are independent descriptors of locomotion control in healthy young and older adults a second purpose of the analysis was to establish the extent to which treadmill walking mimics overground walking using a benchmark for step kinematics eighteen young adults and 12 older adults walked at a self selected velocity on an instrumented treadmill from which step length variability step width variability and step time variability were computed stepwise discriminant analysis correctly classified group membership of 70 percent of the 30 subjects i e young or older adult using only step width variability p 0 037 wilk s lamda 0 854 step width variability was 70 57 percent larger than step length variability p 0 001 this relationship was similar to that of the benchmark established for overground locomotion the results suggest that for healthy younger and older adults step width variability is a more meaningful descriptor of locomotion control than step length variability and step time variability given the potential clinical impact further systematic study and improvement of the methods and technology for acquiring step kinematic data are warranted

general variational approach to the interpolation problem abstract the talmi and gilat variational approach to the interpolation problem in arbitrary dimension is presented together with the corresponding physical model the connection of this approach to some known spline methods is demonstrated and new interpolation functions are derived for one two and three dimensional cases they are designed to be flexible through the use of meaningful parameters and to give good approximations of both the function itself and its derivatives as well

overcoming the limitations of the harmonic ratio for the reliable assessment of gait symmetry the harmonic ratio hr is an index based on the spectral analysis of lower trunk accelerations that is commonly used to assess the quality of gait however it presents several issues concerning reliability and interpretability as a consequence the literature provides very different values albeit corresponding to the same populations in the present work an improved harmonic ratio ihr was defined relating the power of the intrinsic harmonics i e associated with the symmetric component of gait to the total power of the signal for each stride leading to a normalised index ranging from 0 to 100 the effect of the considered number of harmonics and strides on the estimate of both hr and ihr was assessed the gait of three groups of volunteers was investigated young healthy adults elderly women and male trans femoral amputees both hr and ihr were able to discriminate gait deviations from the gait of young healthy adults moreover ihr proved to be more robust with respect to the number of considered harmonics and strides and to exhibit a lower inter stride variability additionally using a normalised index as ihr led to a more straightforward interpretation and improved comparability the importance of standardised conditions for the index evaluation was unveiled and in order to enhance the future comparability of the index the following guidelines were presented considering at least 20 harmonics and 20 strides expressing the acceleration components in a repeatable anatomical local system of reference and evaluating the ihr index rather than the traditional hr

a minimal integrity basis for the elasticity tensor we definitively solve the old problem of finding a minimal integrity basis of polynomial invariants of the fourth order elasticity tensor c decomposing c into its so 3 irreducible components we reduce this problem to finding joint invariants of a triplet a b d where a and b are second order harmonic tensors and d is a fourth order harmonic tensor combining theorems of classical invariant theory and formal computations a minimal integrity basis of 297 polynomial invariants for the elasticity tensor is obtained for the first time

effect of noise and filtering on largest lyapunov exponent of time series associated with human walking this study aimed to determine the effect of added noise filtering and time series length on the largest lyapunov exponent lye value calculated for time series obtained from a passive dynamic walker the simplest passive dynamic walker model comprising of two massless legs connected by a frictionless hinge joint at the hip was adopted to generate walking time series the generated time series was used to construct a state space with the embedding dimension of 3 and time delay of 100 samples the lye was calculated as the exponential rate of divergence of neighboring trajectories of the state space using rosenstein s algorithm to determine the effect of noise on lye values seven levels of gaussian white noise snr 55 25db with 5db steps were added to the time series in addition the filtering was performed using a range of cutoff frequencies from 3hz to 19hz with 2hz steps the lye was calculated for both noise free and noisy time series with different lengths of 6 50 100 and 150 strides results demonstrated a high percent error in the presence of noise for lye therefore these observations suggest that rosenstein s algorithm might not perform well in the presence of added experimental noise furthermore findings indicated that at least 50 walking strides are required to calculate lye to account for the effect of noise finally observations support that a conservative filtering of the time series with a high cutoff frequency might be more appropriate prior to calculating lye

some splines produced by smooth interpolation the spline theory can be derived from two sources the algebraic one where splines are understood as piecewise smooth functions satisfying some continuity conditions and the variational one where splines are obtained via minimization of some quadratic functionals with constraints we show that the general variational approach called smooth interpolation introduced by talmi and gilat covers not only the cubic spline but also the tension spline called also spline in tension or spline with tension in one or more dimensions we show the results of a 1d numerical example that present the advantages and drawbacks of the tension spline

determination of the size of the representative volume element for random composites statistical and numerical approach the representative volume element rve plays a central role in the mechanics and physics of random heterogeneous materials with a view to predicting their effective properties a quantitative definition of its size is proposed in this work a rve size can be associated with a given precision of the estimation of the wanted overall property and the number of realizations of a given volume v of microstructure that one is able to consider it is shown to depend on the investigated morphological or physical property the contrast in the properties of the constituents and their volume fractions the methodology is applied to a specific random microstructure namely a two phase three dimensional voronoi mosaic finite element simulations of volumes of different sizes are performed in the case of linear elasticity and thermal conductivity the volumes are subjected to homogeneous strain stress or periodic boundary conditions the effective properties can be determined for large volumes and a small number of realizations conversely smaller volumes can be used providing that a sufficient number of realizations are considered a bias in the estimation of the effective properties is observed for too small volumes for all types of boundary conditions the variance of computed apparent properties for each volume size is used to define the precision of the estimation the key notion of integral range is introduced to relate this error estimation and the definition of the rve size for given wanted precision and number of realizations one is able to provide a minimal volume size for the computation of effective properties the results can also be used to predict the minimal number of realizations that must be considered for a given volume size in order to estimate the effective property for a given precision the rve sizes found for elastic and thermal properties but also for a geometrical property like volume fraction are compared

derivation of anisotropic matrix for bi dimensional strain gradient elasticity behavior the different forms of second order elasticity operators in mindlin s strain gradient elasticity are given for a bi dimensional physical space these different forms are obtained according to the different symmetry classes of a material media dimensional aspects are discussed together with observations made on the physical behavior of such a media

the effects of general fatigue induced by incremental exercise test and active recovery modes on energy cost gait variability and stability in male soccer players abstract the aerobic endurance is considered an important physiological capacity of soccer players which is examined by incremental exercise test iet however it is not clear how general fatigue induced by iet influences physiological and biomechanical gait features in soccer players and how players recover optimally at post iet here the effect of general fatigue induced by iet on energy cost gait variability and stability in soccer players was investigated to identify an optimal recovery mode the effect of walking at preferred walking speed pws running at individual ventilation threshold ivt two active recovery modes and rest a passive recovery mode on aforementioned features were studied nine male players walked 4 min at pws on a treadmill prior iet pret which was followed by four 4 min walking trials post 0 1 2 and 3 with three 4 min recovery intervals pws ivt or rest between them in three sessions one for each recovery mode in a random order energy cost gait variability and stability were examined at pret baseline and at post 0 1 2 and 3 intervals of respectively 0 4 8 12 16 20 24 28 min at post iet gait variability was assessed by the standard deviation of trunk angle and gait stability was assessed by the local dynamic stability of trunk angular velocity gait stability was not affected by iet despite increases in gait variability and energy cost different from ivt pws and rest recovery modes reduced energy cost at post iet gait variability and energy cost recovered at post 1 and post 2 suggesting that 8 12 and 16 20 min recovery intervals respectively were required for returning to their baselines no preference for active over passive recovery was found in terms of gait variability and energy cost

invariant based reconstruction of bidimensional elasticity tensors in the present paper a method to reconstruct the 2d elasticity tensor from observations is proposed the novelty of the method compared to other ones is that this approach is based on the identification of the invariants rather than the components of the elasticity tensor the main advantage is that all the information concerning the material such as its symmetry class and the orientation of the tested sample are obtained during the reconstruction process we believe that such an approach based on intrinsic quantities may find interesting applications for the identification of mechanical parameters based on full field measurements

amplitude effects of medio lateral mechanical and visual perturbations on gait falls during walking are a major contributor to accidental deaths and injuries that can result in debilitating hospitalization costs lost productivity and diminished quality of life to reduce these losses we must develop a more profound understanding of the characteristic responses to perturbations similar to those encountered in daily life this study addresses this issue by building on our earlier studies that examined mechanical and visual perturbations in the same environment by applying the same continuous pseudo random perturbations at multiple 3 mechanical 5 visual amplitudes walking variability during mechanical perturbations increased significantly with amplitude for all subjects and differences as measured by variabilities of step width com position and com velocity these parameters were the only ones sensitive to the presence of visual perturbations but none of them changed significantly with perturbation amplitude additionally visual perturbation effects were far less consistent across participants with several who were essentially unaffected by visual perturbations at any level the homogeneity of the mechanical perturbation effects demonstrates that human responses to mechanical perturbations are similar because they are driven by kinetics that require similar corrections that must be made in order to maintain balance conversely responses to visual perturbations are driven by the perceived need to make corrections and this perception is not accurate enough to produce amplitude related corrections even for a single participant nor is this perception consistent across individuals this latter finding is likely to be relevant to future visual perturbation studies and the diagnosis and rehabilitation of gait and balance disorders

effects of perturbation magnitude on dynamic stability when walking in destabilizing environments external perturbations applied to the walking surface or visual field can challenge an individual s ability to maintain stability during walking accurately quantifying and predicting changes in stability during walking will further our understanding of how individuals respond to challenges encountered during daily life and guide the development of assessments and rehabilitation interventions for individuals at increased risk of falling this study is the first to determine how orbital and local dynamic stability metrics including maximum floquet multipliers and local divergence exponents change in response to continuous mediolateral visual and surface perturbations of different amplitudes eleven healthy individuals walked in a fully immersive virtual environment participants completed two 3 min walking trials each under the following nine conditions no perturbations surface perturbations at each of 3 amplitudes and visual perturbations at each of 5 amplitudes all perturbations were applied as continuous pseudo random oscillations during both surface and visual perturbations individuals were significantly more orbitally and locally unstable compared to un perturbed walking as walking surface perturbation amplitudes increased individuals were more orbitally but not locally unstable as visual perturbation amplitudes increased individuals were more locally but not orbitally unstable between lower and higher amplitudes overall these dynamic stability metrics were much less sensitive to changes in perturbation amplitudes than to differences between un perturbed and perturbed walking or to differences between mechanical and visual perturbations this suggests that the type of perturbation s applied has a far greater impact than the magnitude of those perturbations in determining the response that will be elicited

walking variability during continuous pseudo random oscillations of the support surface and visual field abstract walking on uneven surfaces or while undergoing perturbations has been associated with increased gait variability in both modeling and human studies previous gait research involving continuous perturbations has focused on sinusoidal oscillations which can result in individuals predicting the perturbation and or entraining to it therefore we examined the effects of continuous pseudo random support surface and visual field oscillations on 12 healthy young participants participants walked in a virtual reality environment under no perturbation nop anterior posterior ap walking surface and visual oscillation and mediolateral ml walking surface and visual oscillation conditions participants exhibited shorter p 0 005 wider p

a complete description of bi dimensional anisotropic strain gradient elasticity in the present paper spaces of fifth order tensors involved in bidimensional strain gradient elasticity are studied as a result complete sets of matrices representing these tensors in each one of their anisotropic system are provided this paper completes and ends some previous studies on the subject providing a complete description of the anisotropic bidimensional strain gradient elasticity it is proved that this behavior is divided into 14 non equivalent anisotropic classes 8 of them being isotropic for classical elasticity the classification and matrix representations of the acoustical gyrotropic tensor are also provided these results may find interesting applications to the study of waves propagation in dispersive micro structured media

a practical method for calculating largest lyapunov exponents from small data sets detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the largest lyapunov exponent lyapunov exponents quantify the exponential divergence of initially close state space trajectories and estimate the amount of chaos in a system we present a new method for calculating the largest lyapunov exponent from an experimental time series the method follows directly from the definition of the largest lyapunov exponent and is accurate because it takes advantage of all the available data we show that the algorithm is fast easy to implement and robust to changes in the following quantities embedding dimension size of data set reconstruction delay and noise level furthermore one may use the algorithm to calculate simultaneously the correlation dimension thus one sequence of computations will yield an estimate of both the level of chaos and the system complexity

active control of lateral balance in human walking we measured variability of foot placement during gait to test whether lateral balance must be actively controlled against dynamic instability the hypothesis was developed using a simple dynamical model that can walk down a slight incline with a periodic gait resembling that of humans this gait is entirely passive except that it requires active control for a single unstable mode con ned mainly to lateral motion an especially e cient means of controlling this instability is to adjust lateral foot placement we hypothesized that similar active feedback control is performed by humans with fore aft dynamics stabilized either passively or by very low level control the model predicts that uncertainty within the active feedback loop should result in variability in foot placement that is larger laterally than fore aft in addition loss of sensory information such as by closing the eyes should result in larger increases in lateral variability the control model also predicts a slight coupling between step width and length we tested 15 young normal human subjects and found that lateral variability was 79 larger than fore aft variability with eyes open and a larger increase in lateral variability 53 vs 21 with eyes closed consistent with the model s predictions we also found that the coupling between lateral and fore aft foot placements was consistent with a value of 0 13 predicted by the control model our results imply that humans may harness passive dynamic properties of the limbs in the sagittal plane but must provide signi cant active control in order to stabilize lateral motion 2000 elsevier science ltd all rights reserved

elasticity and symmetry of triangular lattice materials the elastic tensor of any triangular 2d lattice material is given with re spect to the geometry and the mechanical properties of the links between the nodes the links can bear central forces tensional material for example with hinged joints momentums flexural materials or a combination of the two the symmetry class of the stiffness tensor is detailed in any case by using the invariants of forte and vianello a distinction is made between the trivial cases where the elasticity symmetry group corresponds to the mi crostructure s symmetry group and the non trivial cases in the opposite case interesting examples of isotropic auxetic materials with negative poisson s ratio and non trivial materials with isotropic elasticity but anisotropic frac turation weak direction are shown the proposed set of equations can be used in a engineering process to create a 2d triangular lattice material of the desired elasticity

harmonic ratios a quantification of step to step symmetry the harmonic ratio hr derived from the fourier analysis of trunk accelerations has been described in various ways as a measure of walking smoothness walking rhythmicity or dynamic stability there is an increasing interest in applying the hr technique to investigate the impact of various pathologies on locomotion however explanation of the method has been limited the aim here is to present a clear description of the mathematical basis of hrs and an understanding of their interpretation we present harmonic theory the interpretation of the hr using sinusoidal signals and an example using actual trunk accelerations and harmonic analyses during limb loading conditions we suggest that the hr method may be better defined not as a measure of rhythmicity or stability but as a measure of step to step symmetry within a stride

polyharmonic splines generated by multivariate smooth interpolation abstract polyharmonic splines of order m satisfy the polyharmonic equation of order m in n variables moreover if employed as basis functions for interpolation they are radial functions we are concerned with the problem of construction of the smooth interpolation formula presented as the minimizer of suitable functionals subject to interpolation constraints for n 1 this is the principal motivation of the paper we show a particular procedure for determining the interpolation formula that in a natural way leads to a linear combination of polyharmonic splines of a fixed order possibly complemented with lower order polynomial terms if it is advantageous for the interpolant in the problem solved to be a polyharmonic spline we can construct such an interpolant directly using the multivariate smooth approximation technique the smoothness of the spline can be a priori chosen smooth interpolation can be very useful e g in signal processing computer aided geometric design or construction of geographic information systems a 1d computational example is presented

on the direct determination of invariant parameters governing anisotropic plate bending problems abstract many papers deal with the determination of flexural rigidities of anisotropic plates from only one specimen subjected to one or several loading conditions in such a problem one of the main questions is the best identification of the unknown parameters according to the type of material the shape of the specimen and the loading conditions it seems that no general rule giving the best configuration leading to an accurate determination has been established one of the main reasons is the anisotropic nature of the tested plates which leads the mechanical configuration to be dependent on the material itself this problem would be avoided by the direct measurement of invariant parameters from which the rigidities are easily deduced these invariant parameters reveal the intrinsic elastic behavior of the tested plate contrary to the rigidities usually considered which are directional quantities this paper describes a procedure for the identification of invariant parameters governing the bending of anisotropic plates it is shown that the whole displacement field processing of the surface strain fields obtained in two particular loading cases directly provides those parameters a numerical simulation shows the stability of the present method

a direct comparison of spine rotational stiffness and dynamic spine stability during repetitive lifting tasks stability of the spinal column is critical to bear loads allow movement and at the same time avoid injury and pain however there has been a debate in recent years as to how best to define and quantify spine stability with the outcome being that different methods are used without a clear understanding of how they relate to one another therefore the goal of the present study was to directly compare lumbar spine rotational stiffness calculated with an emg driven biomechanical model to local dynamic spine stability calculated using lyapunov analyses of kinematic data during a series of continuous dynamic lifting challenges twelve healthy male subjects performed 30 repetitive lifts under three varying load and three varying rate conditions with an increase in the load lifted constant rate there was a significant increase in mean maximum and minimum spine rotational stiffness po 0 001 and a significant increase in local dynamic stability po 0 05 both stability measures were moderately to strongly related to one another r 0 55 to 0 71 with an increase in lifting rate constant load there was also a significant increase in mean and maximum spine rotational stiffness po 0 01 however there was a non significant decrease in the minimum rotational stiffness and a non significant decrease in local dynamic stability p40 05 weak linear relationships were found for the varying rate conditions r 0 02 to 0 27 the results suggest that spine rotational stiffness and local dynamic stability are closely related to one another as they provided similar information when movement rate was controlled however based on the results from the changing lifting rate conditions it is evident that both models provide unique information and that future research is required to completely understand the relationship between the two models using both techniques concurrently may provide the best information regarding the true effects of in stability under different loading and movement scenarios and in comparing healthy and clinical populations

quaternions and joint angles in an analysis of local stability of gait for different variants of walking speed and treadmill slope the authors describe an example of application of a nonlinear time series analysis directed at identifying the presence of deterministic chaos in human gait kinematic data by means of the largest lyapunov exponent lle a positive lle value is interpreted as an indicator of local instability the research was aimed at assessment of the influence of both walking speed and ground slope on the resilience of gait control to infinitesimally small perturbations that occur naturally during walking the analysis of treadmill gait data was carried out twofold 1 for the time series representing the following joint angles hip flexion extension knee flexion extension and dorsiflexion plantarflexion of the ankle and 2 for the time series representing rotations of foot tibia and femur segments through euler angles converted to a quaternion representation a comparison between both approaches as well as a dependency between treadmill inclination and lle values constitute the original aspects of this study the lle value was estimated threefold for every time series as the short term lle for both the first step and the first stride and as the long term lle over a fixed interval between the fourth and the tenth stride it was confirmed that all considered movements are characterized by positive lle values which quantify a local instability moreover a tendency to attenuate the perturbation consequences is evident in all variants of walking speed and treadmill slope

the effect of walking speed on local dynamic stability is sensitive to calculation methods local dynamic stability has been assessed by the short term local divergence exponent s which quantifies the average rate of logarithmic divergence of infinitesimally close trajectories in state space both increased and decreased local dynamic stability at faster walking speeds have been reported this might pertain to methodological differences in calculating s therefore the aim was to test if different calculation methods would induce different effects of walking speed on local dynamic stability ten young healthy participants walked on a treadmill at five speeds 60 80 100 120 and 140 of preferred walking speed for 3min each while upper body accelerations in three directions were sampled from these time series s was calculated by three different methods using a a fixed time interval and expressed as logarithmic divergence per stride time s a b a fixed number of strides and expressed as logarithmic divergence per time s b and c a fixed number of strides and expressed as logarithmic divergence per stride time s c mean preferred walking speed was 1 16 0 09m s there was only a minor effect of walking speed on s a s b increased with increasing walking speed indicating decreased local dynamic stability at faster walking speeds whereas s c decreased with increasing walking speed indicating increased local dynamic stability at faster walking speeds thus the effect of walking speed on calculated local dynamic stability was significantly different between methods used to calculate local dynamic stability therefore inferences and comparisons of studies employing s should be made with careful consideration of the calculation method language en

isotropic invariants of a completely symmetric third order tensor in both theoretical and applied mechanics the modeling of nonlinear constitutive relations of materials is a topic of prime importance to properly formulate consistent constitutive laws some restrictions need to be imposed on tensor functions to that aim representations theorems for both isotropic and anisotropic functions have been extensively investigated since the middle of the 20th century nevertheless in three dimensional physical space most of the results are restricted to sets of tensors up to second order the purpose of the present paper is thus to get one step further and to provide an integrity basis for isotropic polynomial functions of a completely symmetric third order tensor we exploit the link between the o 3 action on harmonic tensors and the sl 2 c action on the space of binary forms to explicitly construct this basis we believe that such an integrity basis may found interesting applications both in continuum mechanics and in other fields of theoretical physics

can stability really predict an impending slip related fall among older adults the primary purpose of this study was to systematically evaluate and compare the predictive power of falls for a battery of stability indices obtained during normal walking among community dwelling older adults one hundred and eighty seven community dwelling older adults participated in the study after walking regularly for 20 strides on a walkway participants were subjected to an unannounced slip during gait under the protection of a safety harness full body kinematics and kinetics were monitored during walking using a motion capture system synchronized with force plates stability variables including feasible stability region measurement margin of stability the maximum floquet multiplier the lyapunov exponents short and long term and the variability of gait parameters including the step length step width and step time were calculated for each subject sensitivity of predicting slip outcome fall vs recovery was examined for each stability variable using logistic regression results showed that the feasible stability region measurement predicted fall incidence among these subjects with the highest sensitivity 68 4 except for the step width with an sensitivity of 60 2 no other stability variables could differentiate fallers from those who did not fall for the sample included in this study the findings from the present study could provide guidance to identify individuals at increased risk of falling using the feasible stability region measurement or variability of the step width

a periodic basis system of the smooth approximation space the paper is primarily devoted to the problem of smooth interpolation of data in 1d in addition to the exact interpolation of data at nodes we are also concerned with the smoothness of the interpolating curve and its derivatives the interpolating curve is defined as the solution of a variational problem with constraints the system of functions exp i kx k being an integer is taken for the basis of the space where we measure the smoothness of the result it also generates the functions used for the interpolation itself choosing different norms when measuring the smoothness we arrive at different interpolating functions we also mention the problem of smooth curve fitting data smoothing we discuss the proper choice of different norms for this way of approximation and present the results of several 1d numerical examples that show the advantages and drawbacks of smooth interpolation

kinematic variability and local dynamic stability of upper body motions when walking at different speeds a ubiquitous characteristic of elderly and patients with gait disabilities is that they walk slower than healthy controls many clinicians assume these patients walk slower to improve their stability just as healthy people slow down when walking across ice however walking slower also leads to greater variability which is often assumed to imply deteriorated stability if this were true then slowing down would be completely antithetical to the goal of maintaining stability this study sought to resolve this paradox by directly quantifying the sensitivity of the locomotor system to local perturbations that are manifested as natural kinematic variability eleven young healthy subjects walked on a motorized treadmill at five different speeds three dimensional movements of a single marker placed over the first thoracic vertebra were recorded during continuous walking mean stride to stride standard deviations and maximum finite time lyapunov exponents were computed for each time series to quantify the variability and local dynamic stability respectively of these movements quadratic regression analyses of the dependent measures vs walking speed revealed highly significant u shaped trends for all three mean standard deviations but highly significant linear trends with significant or nearly significant quadratic terms for five of the six finite time lyapunov exponents subjects exhibited consistently better local dynamic stability at slower speeds for these five measures these results support the clinically based intuition that people who are at increased risk of falling walk slower to improve their stability even at the cost of increased variability

dangers of geometric filtering abstract we argue that there are unrecognised dangers in the popular and powerful geometric filtering method carelessly applied geometric filtering can produce apparent structure in data which is pure noise or can cause severe distortions in clean deterministic data the explanations for these effects are straightforward and the dangers are easily avoided by taking simple precautions in the filtering process

dynamic stability of human walking in visually and mechanically destabilizing environments abstract understanding how humans remain stable during challenging locomotor activities is critical to developing effective tests to diagnose patients with increased fall risk this study determined if different continuous low amplitude perturbations would induce specific measureable changes in measures of dynamic stability during walking we applied continuous pseudo random oscillations of either the visual scene or support surface in either the anterior posterior or mediolateral directions to subjects walking in a virtual environment with speed matched optic flow floquet multipliers and short term local divergence exponents both increased indicating greater instability during perturbed walking these responses were generally much stronger for body movements occurring in the same directions as the applied perturbations likewise subjects were more sensitive to both visual and mechanical perturbations applied in the mediolateral direction than to those applied in the anterior posterior direction consistent with previous experiments and theoretical predictions these responses were likewise consistent with subjects anecdotal perceptions of which perturbation conditions were most challenging contrary to the floquet multipliers and short term local divergence exponents which both increased long term local divergence exponenets decreased during perturbed walking however this was consistent with specific changes in the mean log divergence curves which indicated that subjects movements reached their maximum local divergence limits more quickly during perturbed walking overall the floquet multipliers were less sensitive but reflected greater specificity in their responses to the different perturbation conditions conversely the short term local divergence exponents exhibited less specificity in their responses but were more sensitive measures of instability in general

walking at the preferred stride frequency maximizes local dynamic stability of knee motion healthy humans display a preference for walking at a stride frequency dependent on the inertial properties of their legs walking at preferred stride frequency psf is predicted to maximize local dynamic stability whereby sensitivity to intrinsic perturbations arising from natural variability inherent in biological motion is minimized previous studies testing this prediction have employed different variability measures but none have directly quantified local dynamic stability by computing maximum finite time lyapunov exponent max which quantifies the rate of divergence of nearby trajectories in state space here ten healthy adults walked 45 m overground while sagittal motion of both knees was recorded via electrogoniometers an auditory metronome prescribed 7 different frequencies relative to each individual s psf psf 5 10 15 strides min stride frequencies were performed under both freely adopted speed fs and controlled speed cs set at the speed of psf trials conditions local dynamic stability was maximal max was minimal at the psf becoming less stable for higher and lower stride frequencies this occurred under both fs and cs conditions although controlling speed further reduced local dynamic stability at non preferred stride frequencies in contrast measures of variability revealed effects of stride frequency and speed conditions that were distinct from max in particular movement regularity computed by approximate entropy apen increased for slower walking speeds appearing to depend on speed rather than stride frequency the cadence freely adopted by humans has the benefit of maximizing local dynamic stability which can be interpreted as humans tuning to their resonant frequency of walking

influence of simulated neuromuscular noise on movement variability and fall risk in a 3d dynamic walking model people at risk of falling exhibit increased gait variability which may predict future falls however the causal mechanisms underlying these correlations are not well known increased neuronal noise associated with aging likely leads to increased gait variability which could in turn lead to increased fall risk this paper presents a model of how changes in neuromuscular noise independently affect gait variability and probability of falling and aims to determine the extent to which changes in gait variability directly predict fall risk we used a dynamic walking model that incorporates a lateral step controller to maintain lateral stability noise was applied to this controller to approximate neuromuscular noise in humans noise amplitude was varied between low amplitudes that did not induce falls and high amplitudes for which the model always fell with increases in noise amplitude the model fell more often and after fewer steps gait variability increased with noise amplitude and predicted increased probability of falling importantly these relationships were not linear at either low gait variability or very high gait variability small increases in noise and variability affected probability of falling very little conversely at intermediate noise and or variability levels the same small increases resulted in large increases in probability of falling our results validate the idea that age related increases in neuromuscular noise likely play a direct contributing role in increasing fall risk however neuromuscular noise remains only one of many important factors that need to be considered these findings have important implications for fall prevention research and practice

does the personal lift assist device affect the local dynamic stability of the spine during lifting abstract the personal lift assist device plad is an on body ergonomic aid that reduces low back physical demands through the restorative moment of an external spring element which possesses a mechanical advantage over the erector spinae although the plad has proven effective at reducing low back muscular demand spinal moments and localized muscular fatigue during laboratory and industrial tasks the effects of the device on the neuromuscular control of spinal stability during lifting have yet to be assessed thirty healthy subjects 15m 15f performed repetitive lifting for three minutes at a rate of 10 lifts per minute with and without the plad maximum finite time lyapunov exponents representing short term max s and long term max l divergence were calculated from the measured trunk kinematics to estimate the local dynamic stability of the lumbar spine using a mixed design repeated measures anova it was determined that wearing the plad did not significantly change max s np 0 335 p 0 321 p 0 225 but did significantly reduce max l np 0 0024 p 0 0011 p 0 014 2 0 197 there were no between subject effects of sex or significant interactions p 0 720 the present results indicated that max s was not statistically different between the device conditions but that the plad significantly reduced max l to a negative stable value this shows that subjects neuromuscular systems were able to respond to local perturbations more effectively when wearing the device reflecting a more stable control of spinal movements these findings are important when recommending the plad for long term industrial or clinical use