the effect of text based math task on dynamic stability control during stair descent abstract stair descent imposes a significant challenge for dynamic stability among young adults the effect of a concurrent text based math task on dynamic stability control remains unclear during stair descent when considering the influence of gait velocity twenty six participants performed three successful stair descent trials under texting or no texting conditions at their preferred speed synchronous kinematics and kinetics were collected by an eight camera vicon infrared motion capture system and two force platforms repeated measures analysis of covariance and wilcoxon signed rank test were used to analyze the differences between the two different task conditions with gait velocity as a covariate the outcomes indicated that under texting condition sagittal margin of stability increased at right foot landing step cadence double support percentage sagittal and frontal joint moment decreased and sagittal and frontal joint angles were also modified it is concluded that concurrent texting impaired sagittal and frontal stability control during stair descent despite slowing down the step cadence knee and ankle joint adjustment strategies were mainly adopted in response to stability control in the sagittal plane with the interference of texting whereas the hip joint adjustment strategy was adopted in the frontal plane in conclusion texting behaviors on mobile phones should be minimized during stair descent

nontrivial periodic solutions for the asymptotically linear hamiltonian systems with resonance at infinity abstract in this paper we are concerned with the existence of nontrivial periodic solutions of an asymptotically linear hamiltonian systems when a kind of resonance condition is satisfied we prove several new existence results via the morse theory the garlerkin methods and the moslov index theory

bifurcation of periodic solutions of delay differential equation with two delays abstract in this paper we develop kaplan yorke s method and consider the existence of periodic solutions for delay differential equations with two delays especially we study hopf and saddle node bifurcations of periodic solutions for the equation with parameters and give conditions under which the bifurcations occur

the monotonicity of the period function for planar hamiltonian vector fields if the hamiltonian system with hamiltonian h x y 12y2 v x has a center at the origin it is shown that the period function for the family of periodic trajectories surrounding the center is monotone when the function v v 2 is convex this theorem is applied to determine existence and uniqueness of solutions for the neumann boundary value problem x a x 2 bx c x 0 x 1 0

femoral strain during walking predicted with muscle forces from static and dynamic optimization mechanical strain plays an important role in skeletal health and the ability to accurately and noninvasively quantify bone strain in vivo may be used to develop preventive measures that improve bone quality and decrease fracture risk a non invasive estimation of bone strain requires combined musculoskeletal finite element modeling for which the applied muscle forces are usually obtained from static optimization so methods in this study we compared finite element predicted femoral strains in walking using muscle forces obtained from so to those obtained from forward dynamics fd simulation the general trends in strain distributions were similar between fd and so derived conditions and both agreed well with previously reported in vivo strain gage measurements on the other hand differences in peak maximum emax and minimum emin principal strain magnitudes were as high as 32 between fd emax emin 945 1271 e and so emax emin 752 859 e these large differences in strain magnitudes were observed during the first half of stance where so predicted lower gluteal muscle forces and virtually no co contraction of the hip adductors compared to fd the importance of these results will likely depend on the purpose application of the modeling procedure if the goal is to obtain a generalized strain distribution for adaptive bone remodeling algorithms then traditional so is likely sufficient in cases were strain magnitudes are critical as is the case with fracture risk assessment bone strain estimation may benefit by including muscle activation and contractile dynamics in so or by using fd when practical

dynamic margins of stability during human walking in destabilizing environments understanding how humans maintain stability when walking particularly when exposed to perturbations is key to preventing falls here we quantified how imposing continuous pseudorandom anterior posterior ap and mediolateral ml oscillations affected the control of dynamic walking stability twelve subjects completed five 3 minute walking trials in the computer assisted rehabilitation environment caren system under each of 5 conditions no perturbation nop ap platform app or visual apv or ml platform mlp or visual mlv oscillations we computed ap and ml margins of stability mos for each trial mean mosml were consistently slightly larger during all perturbation conditions than during nop p 0 038 mean mosap for the app mlp and mlv oscillations were significantly smaller than during nop p 0 0005 variability of both mosap and mosml was significantly greater during the mlp and mlv oscillations than during nop p 0 0005 we also directly quantified how the mos on any given step affected the mos on the following step using first return plots there were significant changes in step to step mosml dynamics between experimental conditions p 0 0005 these changes suggested that subjects may have been trying to control foot placement and consequently stability during the perturbation conditions quantifying step to step changes in margins of dynamic stability may be more useful than mean mos in assessing how individuals control walking stability

reduced knee joint moment in acl deficient patients at a cost of dynamic stability during landing abstract the current study aimed to examine the effect of anterior cruciate ligament deficiency acld on joint kinetics and dynamic stability control after a single leg hop test slht twelve unilateral acld patients and a control subject group n 13 performed a slht over a given distance with both legs the calculation of joint kinetics was done by means of a soft tissue artifact optimized rigid full body model margin of stability mos was quantified by the difference between the base of support and the extrapolated center of mass during landing the acld leg showed lower external knee flexion moments but demonstrated higher moments at the ankle and hip compared to controls p 0 05 the main reason for the joint moment redistribution in the acld leg was a more anterior position of the ground reaction force grf vector which affected the moment arms of the grf acting about the joints p 0 05 for the acld leg trunk angle was more flexed over the entire landing phase compared to controls p 0 05 and we found a significant correlation between moment arms at the knee joint and trunk angle r 2 0 48 p 0 01 the consequence of this altered landing strategy in acld legs was a more anterior position of the center of mass reducing the mos p 0 05 the results illustrate the interaction between trunk angle joint kinetics and dynamic stability during landing maneuvers and provide evidence of a feedforward adaptive adjustment in acld patients i e more flexed trunk angle aimed at reducing knee joint moments at the cost of dynamic stability control

periodic solutions of delay equations with three delays via bi hamiltonian systems in this paper we give sufficient conditions for the existence of periodic solutions of delay differential equations with three delays

a class of hamiltonian systems with increasing periods on considere un systeme hamiltonien de la forme x g y y f x ou h f et h g satisfont certaines hypotheses on montre qu il y a un intervalle maximal 0 a a 0 tel que chaque solution x t y t avec x 0 a 0 a y 0 0 est periodique avec son orbite enfermant 0 0 soit p a la plus petite periode de cette solution alors p 0 a r est differentiable avec p a 0

adjustments to zatsiorsky seluyanov s segment inertia parameters zatsiorsky et al in contemporary problems in biomechanics pp 272 291 crc press massachusetts 1990a obtained by means of a gamma ray scanning technique the relative body segment masses center of mass cm positions and radii of gyration for samples of college aged caucasian males and females although these data are the only available and comprehensive set of inertial parameters regarding young adult caucasians they have been rarely utilized for biomechanical analyses of subjects belonging to the same or a similar population the main reason is probably that zatsiorsky et al used bony landmarks as reference points for locating segment cms and defining segment lengths some of these landmarks were markedly distant from the joint centers currently used by most researchers as reference points the purpose of this study was to adjust the mean relative cm positions and radii of gyration reported by zatsiorsky et al in order to reference them to the joint centers or other commonly used landmarks rather than the original landmarks the adjustments were based on a number of carefully selected sources of anthropometric data

the fundamental problem of myoskeletal inverse dynamics and its implications the validity of current inverse dynamics models utilized for motion analysis is investigated it is shown that observables generated by the real biosystem such as ground reaction forces are incompatible with comparable responses of skeletodynamical inverse models currently in use this implies that results obtained with such models are erroneous to varying degrees while a quantification of these errors is difficult or impossible this phenomenon is termed the fundamental myoskeletal inverse dynamics problem a model fidelity indicator is proposed which for a specific inverse dynamics model applied to a particular motion provides a dimensionless numerical measure for the replicative validity of that model and the fidelity of its input data a practical example demonstrates the usefulness of this indicator it is suggested that the development of structurally sufficiently complex and biologically more realistic skeletomechanical models as well as substantial error reductions in data measuring and processing procedures will be necessary to improve the accuracy of inverse dynamics model computations

periodic solutions of delay differential systems via hamiltonian systems abstract with a new definition of the j m index theory developed in liu 2006 we give another application of this index theory in delay differential systems via hamiltonian systems where we do not need the potential function to be c 2 continuous

body weight support impacts lateral stability during treadmill walking body weight support bws systems are a common tool used in gait rehabilitation bws systems may alter the requirements for an individual to actively stabilize by 1 providing lateral restoring forces that reduce the requirements for the nervous system to actively stabilize and 2 decreasing the stabilizing gravitational moment in the frontal plane which could increase the requirements to actively stabilize the goal of the current study was to quantify the interaction between bws and lateral stability we hypothesized that when able bodied people walk with bws 1 the lateral restoring forces provided by bws would reduce the requirements to stabilize in the frontal plane when comparing dynamically similar gaits and 2 increasing bws would decrease the stabilizing gravitational moment in the frontal plane and increase the requirements to stabilize when speed is constrained our findings partly support these hypotheses but indicate a complex interaction between bws and lateral stability with bws subjects significantly decreased step width variability and significantly increased step width p 0 05 for both the dynamically similar and speed matched conditions the decrease in step width variability may be attributable to a combination of lateral restoring forces decreasing the mechanical requirements to stabilize and an enhanced sense of position that could have improved locomotor control increases in step width when walking with high levels of bws could have been due to decreases in the gravitational moment about the stance limb which may challenge the control of stability in multiple planes

gait stability variability and complexity on inclined surfaces this study evaluated the gait stability variability and complexity of healthy young adults on inclined surfaces a total of 49 individuals walked on a treadmill at their preferred speed for 4min at inclinations of 6 8 and 10 in upward up and downward down conditions and in horizontal 0 condition gait variability was assessed using average standard deviation trunk acceleration between strides var gait stability was assessed using margin of stability mos and maximum lyapunov exponent s and gait complexity was assessed using sample entropy sen trunk variability var increased in the medial lateral ml anterior posterior and vertical directions for all inclined conditions the sen values indicated that movement complexity decreased almost linearly from down to up conditions reflecting changes in gait pattern with longer and slower steps as inclination increased the down conditions were associated with the highest variability and lowest stability in the mos ml but not in s stability was lower in up conditions which exhibited the largest s values the overall results support the hypothesis that inclined surfaces decrease gait stability and alter gait variability particularly in up conditions

sherman morrison woodbury formula based algorithms for the surface smoothing problem abstract surface smoothing applied to range elevation data acquired using a variety of sources has been a very active area of research in computational vision over the past decade generalized splines have emerged as the single most popular approximation tool to this end in this paper we present a new and fast algorithm for solving the surface smoothing problem using a membrane a thin plate or a thin plate membrane spline for data containing discontinuities our approach involves imbedding the surface smoothing problem specified on an irregular domain in the sense of discontinuities and boundaries in a rectangular region using the capacitance matrix method based on the sherman morrison woodbury formula of matrix analysis this formula is used in converting the problem of solving the original linear system resulting from a finite element discretization of the variational formulation of the surface smoothing problem to solving a lyapunov matrix equation or a cascade of two lyapunov matrix equations the reduced problem can then be solved very efficiently using the adi method and the bi conjugate gradient technique our solution requires the generation of a dense capacitance matrix for which we propose a practical and efficient method we demonstrate the efficiency of our algorithm via experiments on sparse data surface smoothing making performance comparisons with the conjugate gradient and hierarchical basis preconditioned conjugate gradient algorithms

period function for a class of hamiltonian systems abstract this paper studies the period function of the class of hamiltonian systems x h y y h x where h x y has the special form h x y f x g y and the origin is a non degenerate center more concretely if t h denotes the period of the periodic orbit contained in h x y h we solve the inverse problem of characterizing all systems with a given function t h we also characterize the limiting behaviour of t at infinity when the origin is a global center and apply this result to prove among other results that there are no nonlinear polynomial isochronous centers in this family

center of mass velocity position predictions for balance control the purposes of this analysis were to predict the feasible movements during which balance can be maintained based on environmental contact force anatomical foot geometry and physiological muscle strength constraints and to identify the role of each constraint in limiting movement an inverted pendulum model with a foot segment was used with an optimization algorithm to determine the set of feasible center of mass cm velocity position combinations for movement termination the upper boundary of the resulting feasible region ran from a velocity of 1 1 s 1 normalized to body height at 2 4 foot lengths behind the heel to 0 45 s 1 over the heel to zero over the toe and the lower boundary from a velocity of 0 9 s 1 at 2 7 foot lengths behind the heel to zero over the heel forward falls would be initiated if states exceeded the upper boundary and backward falls would be initiated if the states fell below the lower boundary under normal conditions the constraint on the size of the base of support bos determined the upper and lower boundaries of the feasible region however friction and strength did limit the feasible region when friction levels were less than 0 82 when dorsiflexion was reduced more than 51 or when plantar flexion strength was reduced more than 35 these findings expand the long held concept that balance is based on cm position limits i e the horizontal cm position has to be confined within the bos to guarantee stable standing to a concept based on cm velocity position limits

modelling the dynamic margins of stability for use in evaluations of balance following a support surface perturbation the dynamic margin of stability provides a method that captures the center of mass com state position velocity in relation to the base of support bos however the model upon which this concept was derived does not consider how the inertial characteristics of forced support surface perturbations would influence balance control within the current article the inverted pendulum model was restructured to account for fixed piecewise accelerations of the bos from this logic two variations of the adjusted margin of stability each maintaining a similar definition of extrapolated com are proposed one ignoring horizontal ground contact and inertial forces applied to the bos the other incorporating these forces unique within the proposed models is the time variant bos boundaries that depend on the perturbation applied verification of the solution for each model is provided along with a comparison of obtained values to previous methods of defining com position velocity stability metrics using a computational model and optimal control for the simpler model variation ignoring forces we also assessed how com position and perturbation parameter selection over underestimate the predicted maximal permissible velocity the results of these analyses suggest that factors which increase the acceleration impulse decrease the difference between the two models the opposite was observed for factors increasing displacements between the com and bos boundary lastly use of the proposed adjusted margin of stability within an experimental data set highlights the ability of our model to predict instability stepping strategies negative margin of stability relative to the use of the extrapolated com alone

the poincare bendixson theorem for monotone cyclic feedback systems with delay abstract we consider cyclic nearest neighbor systems of differential delay equations in which the coupling between neighbors possesses a monotonicity property using a discrete integer valued lyapunov function we prove that the poincare bendixson theorem holds for such systems we also obtain results on piecewise monotonicity and stability of periodic solutions of such systems

an actuated dissipative spring mass walking model predicting human like ground reaction forces and the effects of model parameters abstract simple models are widely used to understand the mechanics of human walking the optimization based minimal biped model and spring loaded inverted pendulum slip model are two popular models that can achieve human like walking patterns however ground reaction forces grf from these two models still deviate from experimental data in this paper we proposed an actuated dissipative spring mass model by integrating these two models to realize more human like grf patterns we first explored the function of stiffness damping and weights of both energy cost and force cost in the objective function and found that these parameters have distinctly different influences on the optimized gait and grf profiles the stiffness and objective weight affect the number and size of peaks in the vertical grf and stance time the damping changes the relative size of the peaks but has little influence on stance time based on these observations these parameters were manually tuned at three different speeds to approach experimentally measured vertical grf and the highest correlation coefficient can reach 0 983 these results indicate that the stiffness damping and proper objective functions are all important factors in achieving human like motion for this simple walking model these findings can facilitate the understanding of human walking dynamics and may be applied in future biped models

on the periodic oscillations of x g x abstract in this paper we introduce certain generalized concepts of isochronism for the periodic oscillations of the scalar equation x g x we give characterizations of these concepts we also study two such characterizations as well as some related topics in more depth each one of these two last concepts is equivalent to the stability of the equilibrium for some related system of differential equations

nontrivial periodic solutions for delay differential systems via morse theory abstract the existence of the nontrivial periodic solutions to the system of delay differential equations 1 1 x t f x t is investigated where x r n f c r n r n we prove several new existence results via morse theory and the galerkin methods

the discriminant capabilities of stability measures trunk kinematics and step kinematics in classifying successful and failed compensatory stepping responses by young adults abstract this study evaluated the discriminant capability of stability measures trunk kinematics and step kinematics to classify successful and failed compensatory stepping responses in addition the shared variance between stability measures step kinematics and trunk kinematics is reported the stability measures included the anteroposterior distance d between the body center of mass and the stepping limb toe the margin of stability mos as well as time to boundary considering velocity ttb v velocity and acceleration ttb a and mos ttb mos kinematic measures included trunk flexion angle and angular velocity step length and the time after disturbance onset of recovery step completion fourteen young adults stood on a treadmill that delivered surface accelerations necessitating multiple forward compensatory steps thirteen subjects fell from an initial disturbance but recovered from a second identical disturbance trunk flexion velocity at completion of the first recovery step and trunk flexion angle at completion of the second step had the greatest overall classification of all measures 92 3 ttb v and ttb a at completion of both steps had the greatest classification accuracy of all stability measures 80 8 the length of the first recovery step r 0 70 and trunk flexion angle at completion of the second recovery step r 0 54 had the largest correlations with stability measures although ttb v and ttb a demonstrated somewhat smaller discriminant capabilities than trunk kinematics the small correlations between these stability measures and trunk kinematics r 0 52 suggest that they reflect two important yet different aspects of a compensatory stepping response

moving beyond quiet stance applicability of the inverted pendulum model to stooping and crouching postures background currently it is unknown whether the inverted pendulum model is applicable to stooping or crouching postures therefore the aim of this study was to determine the degree of applicability of the inverted pendulum model to these postures via examination of the relationship between the centre of mass com acceleration and centre of pressure cop com difference methods ten young adults held static standing stooping and crouching postures each for 20 s for both the anterior posterior ap and medio lateral ml directions the time varying com acceleration and the cop com were computed and the relationship between these two variables was determined using pearson s correlation coefficients additionally in both directions the average absolute com acceleration average absolute cop com signal and the inertial component i e i wh were compared across postures results pearson correlation coefficients revealed a significant negative relationship between the com acceleration and cop com signal for all comparisons regardless of the direction p 0 001 while no effect of posture was observed in the ap direction p 0 463 in the ml direction the correlation coefficients for stooping were different i e stronger than standing p 0 008 regardless of direction the average absolute com acceleration for both the stooping and crouching postures was greater than standing p 0 002 conclusion the high correlations indicate that the inverted pendulum model is applicable to stooping and crouching postures due to their importance in completing activities of daily living there is merit in determining what type of motor strategies are used to control such postures and whether these strategies change with age

an algorithm for determining gravity line location from posturographic recordings abstract in posturographic recordings the center of pressure cop displacement does not accurately reflect migration of the gravity line gl the vertical line passing through the body s center of gravity cog since the horizontal ground reaction force f x is proportional to the horizontal acceleration of the cog its second integral does represent the horizontal position of the gravity line glp however the initial constants of integration initial velocity and position are not known in this note a technique for estimating these integration constants is suggested zero point to zero point integration this method is based on a postulation that when f x 0 the glp and cop coincide by integrating f x from one zero point to another zero point both the instantaneous glp and its velocity are determined a validation of the suggested algorithm was performed using optical methods to determine the glp during a one legged standing tasks cross correlation values of glp determined via videography and the suggested algorithm ranged from 0 79 to 0 96 these results suggest that the zero point to zero point integration is an acceptable technique for determining glp from posturographic recordings

compliant bipedal model with the center of pressure excursion associated with oscillatory behavior of the center of mass reproduces the human gait dynamics although the compliant bipedal model could reproduce qualitative ground reaction force grf of human walking the model with a fixed pivot showed overestimations in stance leg rotation and the ratio of horizontal to vertical grf the human walking data showed a continuous forward progression of the center of pressure cop during the stance phase and the suspension of the cop near the forefoot before the onset of step transition to better describe human gait dynamics with a minimal expense of model complexity we proposed a compliant bipedal model with the accelerated pivot which associated the cop excursion with the oscillatory behavior of the center of mass com with the existing simulation parameter and leg stiffness owing to the pivot acceleration defined to emulate human cop profile the arrival of the cop at the limit of the stance foot over the single stance duration initiated the step to step transition the proposed model showed an improved match of walking data as the forward motion of com during single stance was partly accounted by forward pivot translation the previously overestimated rotation of the stance leg was reduced and the corresponding horizontal grf became closer to human data the walking solutions of the model ranged over higher speed ranges 1 7 m s than those of the fixed pivoted compliant bipedal model 1 5m s and exhibited other gait parameters such as touchdown angle step length and step frequency comparable to the experimental observations the good matches between the model and experimental grf data imply that the continuous pivot acceleration associated with com oscillatory behavior could serve as a useful framework of bipedal model

preconditioning capacitance matrix problems in domain imbedding various preconditioners for the capacitance matrix problems in domain imbedding di are studied such preconditioners can be viewed as inverses of the preconditioners for the schur complement domain decomposition dd methods preconditioning techniques based on the hierarchical basis hb the square root of d 2 ds 2 and on the vector probing for solving the capacitance matrix problems using preconditioned conjugate gradient iterations are analyzed and tested numerically

the monotonicity of period function for codimension four quadratic system q4 abstract in this paper we study the codimension four quadratic system q 4 z iz 4 z 2 2 z 2 b ic z 2 where b and c are real constants i 2 1 z x iy b ic 2 it is proved that the period function of periodic trajectories for q 4 is monotone the content of this paper can be viewed as a contribution to the proof of chicone s conjecture cf mr 94h 58072

on critical point theory for indefinite functionals in the presence of symmetries we consider functionals which are not bounded from above or from below even modulo compact perturbations and which exhibit certain symmetries with respect to the action of a compact lie group we develop a method which permits us to prove the existence of multiple critical points for such functionals the proofs are carried out directly in an infinite dimensional hilbert space and they are based on minimax arguments the applications given here are to hamiltonian systems of ordinary differential equations where the existence of multiple time periodic solutions is established for several classes of hamiltonians symmetry properties of these hamiltonians such as time translation invariancy or evenness are exploited introduction many variational problems which arise from physics or mathematical physics are indefinite in the sense that the functionals involved are not bounded from below or from above however some of these functionals defined in an appropriate function space are semidefinite in the sense that they are bounded from below or from above if perturbed with a weakly continuous functional this paper deals with functionals which are not semidefinite usually problems involving indefinite functionals are more difficult to handle and only very recently a method has been developed which permits us to treat such problems directly in an infinite dimensional function space 7 in 7 some theorems have been proved which establish the existence of at least one nontrivial critical point for such functionals in many physical situations there are problems which have symmetries with respect to the action of some lie group in this case we expect the existence of many critical points this has been established for semidefinite functionals cf e g 8 and 3 for even functionals 9 for a zp action with p prime numbers 15 16 10 and 6 for an s action in this paper we develop a method which allows us to estimate the number of critical points of indefinite functionals in the presence of symmetries more precisely received by the editors july 16 1980 and in revised form june 26 1981 1980 mathematics subject classification primary 58e05 70h05 secondary 34c25

influence of gait speed on the control of mediolateral dynamic stability during gait initiation this study investigated the influence of gait speed on the control of mediolateral dynamic stability during gait initiation thirteen healthy young adults initiated gait at three self selected speeds slow normal and fast the results indicated that the duration of anticipatory postural adjustments apa decreased from slow to fast i e the time allocated to propel the centre of mass com towards the stance leg side was shortened likely as an attempt at compensation the peak of the anticipatory centre of pressure cop shift increased however cop compensation was not fully efficient since the results indicated that the mediolateral com shift towards the stance leg side at swing foot off decreased with gait speed consequently the com shift towards the swing leg side at swing heel contact increased from slow to fast indicating that the mediolateral com fall during step execution increased as gait speed rose however this increased com fall was compensated by greater step width so that the margin of stability the distance between the base of support boundary and the mediolateral component of the extrapolated centre of mass at heel contact remained unchanged across the speed conditions furthermore a positive correlation between the mediolateral extrapolated com position at heel contact and step width was found indicating that the greater the mediolateral com fall the greater the step width globally these results suggest that mediolateral apa and step width are modulated with gait speed so as to maintain equivalent mediolateral dynamical stability at the time of swing heel contact

spectral domain embedding for elliptic pdes in complex domains spectral methods are a class of methods for solving partial differential equations pdes when the solution of the pde is analytic it is known that the spectral solutions converge exponentially as a function of the number of modes used the basic spectral method works only for regular domains such as rectangles or disks domain decomposition methods spectral element methods extend the applicability of spectral methods to more complex geometries an alternative is to embed the irregular domain into a regular one this paper uses the spectral method with domain embedding to solve pdes on complex geometry the running time of the new algorithm has the same order as that for the usual spectral collocation method for pdes on regular geometry the algorithm is extremely simple and can handle dirichlet neumann boundary conditions as well as nonlinear equations

stability normalised walking speed a new approach for human gait perturbation research 2019 in gait stability research neither self selected walking speeds nor the same prescribed walking speed for all participants guarantee equivalent gait stability among participants furthermore these options may differentially affect the response to different gait perturbations which is problematic when comparing groups with different capacities we present a method for decreasing inter individual differences in gait stability by adjusting walking speed to equivalent margins of stability mos eighteen healthy adults walked on a split belt treadmill for two minute bouts at 0 4 m s up to 1 8 m s in 0 2 m s intervals the stability normalised walking speed mos 0 05 m was calculated using the mean mos at touchdown of the final 10 steps of each speed participants then walked for three minutes at this speed and were subsequently exposed to a treadmill belt acceleration perturbation a further 12 healthy adults were exposed to the same perturbation while walking at 1 3 m s the average of the previous group large ranges in mos were observed during the prescribed speeds 6 10 cm across speeds and walking speed significantly p 0 001 affected mos the stability normalised walking speeds resulted in mos equal or very close to the desired 0 05 m and reduced between participant variability in mos the second group of participants walking at 1 3 m s had greater inter individual variation in mos during both unperturbed and perturbed walking compared to 12 sex height and leg length matched participants from the stability normalised walking speed group the current method decreases inter individual differences in gait stability which may benefit gait perturbation and stability research in particular studies on populations with different locomotor capacities preprint https doi org 10 1101 314757

properties of the period function for some hamiltonian systems and homogeneous solutions of a semilinear elliptic equation abstract in this work we study the period function t of solutions to the conservative equation x t f x t 0 we present conditions on f that imply the monotonicity and convexity of t as a consequence we obtain the criterium established by c chicone and find conditions easier to apply we also get a condition obtained by cima gasull and manosas about monotonicity and following some of their calculations present results on the period function of hamiltonian systems where h x y f x n 1 y n using the monotonicity of t we count the homogeneous solutions to the semilinear elliptic equation u u 1 in two dimensions

center of pressure control for balance maintenance during lateral waist pull perturbations in older adults when balance is disturbed location of the center of pressure cop contributes to a person s ability to recover from a perturbation this study investigated cop control prior to first step lift off fslo during lateral perturbations in older non fallers and fallers 38 non fallers and 16 fallers received lateral waist pulls at 5 different intensities crossover stepping responses at the intensity level where the largest number of subjects responded with crossover steps were analyzed whole body center of mass com and cop positions in the medio lateral ml direction with respect to the base of support bos and cop velocity were calculated an inverted pendulum model was used to define the bos stability boundary at fslo which was also adjusted using the cop position at fslo functional boundary no significant differences were found in the cop velocities between fallers and non fallers p 093 however the cop positions for fallers were located significantly more medial at fslo p 01 resulting in a significantly reduced functional boundary although the stability margins measures of stability based on the bos were significantly larger than zero for fallers p 004 they were not significantly different from zero for the functional boundary i e reaching the functional stability limit fallers had reduced functional limits of stability in the ml direction which would predispose them to more precarious stability conditions than non fallers this could be a cause for taking more steps than non fallers for balance recovery as we observed the functional boundary estimation may be a more sensitive marker of balance instability than the bos boundary

applications of a zp index theory to periodic solutions for a class of functional differential equations abstract by means of a new geometrical index with z p group actions multiplicity results for a certain class of nonautonomous time periodic functional differential systems are obtained

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

isochronicity for several classes of hamiltonian systems abstract in this paper we study isochronous centers of analytic hamiltonian systems giving special attention to the polynomial case we first revisit the potential systems and we show the connection between isochronicity and involutions we then study a more general system namely the ones associated to hamiltonians of the form h x y a x b x y c x y 2 as an application we classify the cubic polynomial hamiltonian isochronous centers and we give examples of nontrivial and nonglobal polynomial hamiltonian isochronous centers

multiplicity results for periodic solutions to delay differential equations via critical point theory abstract by the critical point theory we study the existence and multiplicity of periodic solutions to the following system of delay differential equations x t f x t r where x r n f c r n r n and r 0 is a given constant a sufficient condition on the existence and multiplicity of periodic solutions for eq is obtained to the authors knowledge this is the first time the existence of periodic solutions to systems of delay differential equations is dealt with by using variational approaches directly

simulation of quadrupedal locomotion using a rigid body model locomotion of the horse is simulated using a mathematical model based on rigid body dynamics a general method to generate the equations of motion for a two dimensional rigid body model with an arbitrary number of hinge joints is presented and a numerical solution method restricted to tree structured models is described joint movements originating from muscular forces or moments are simulated but the method also allows that parts of the model follow strictly the pattern of kinematic data moment generators with first order linear feedback were used as a rotational muscle equivalent ground hoof interaction forces are approximated by a viscoelastic model and pseudo coulomb friction in vertical and horizontal directions respectively results of model simulations are compared to experimentally recorded data subsequently adjustments are made to improve the agreement between simulation and experimental results

a comparison of muscle energy models for simulating human walking in three dimensions the popular hill model for muscle activation and contractile dynamics has been extended with several different formulations for predicting the metabolic energy expenditure of human muscle actions these extended models differ considerably in their approach to computing energy expenditure particularly in their treatment of active lengthening and eccentric work but their predictive abilities have never been compared in this study we compared the predictions of five different hill based muscle energy models in 3d forward dynamics simulations of normal human walking in a data tracking simulation that minimized muscle fatigue the energy models predicted metabolic costs that varied over a three fold range 2 45 7 15 j m kg with the distinction arising from whether or not eccentric work was subtracted from the net heat rate in the calculation of the muscle metabolic rate in predictive simulations that optimized neuromuscular control to minimize the metabolic cost all five models predicted similar speeds step lengths and stance phase durations however some of the models predicted a hip circumduction strategy to minimize metabolic cost while others did not and the accuracy of the predicted knee and ankle angles and ground reaction forces also depended on the energy model used the results highlights the need to clarify how eccentric work should be treated when calculating muscle energy expenditure the difficulty in predicting realistic metabolic costs in simulated walking even with a detailed 3d musculoskeletal model the potential for using such models to predict energetically optimal gait modifications and the room for improvement in existing muscle energy models and locomotion simulation frameworks

phase portraits of separable hamiltonian systems abstract we study a generalization of potential hamiltonian systems h x y y 2 f x with one degree of freedom namely those with hamiltonian functions of type h x y f x g y which will be denoted by x h we present an algorithm to obtain the phase portrait including the behaviour at infinity of x h when f and g are arbitrary polynomials indeed from the graphs of the one variable functions f and g we are able to give the full description on the poincare disk therefore extending the well known method to obtain the phase portrait of potential systems in the finite plane the fact that the phase portraits can be fully described in terms of the two one variable real functions f and g allows as well a complete study of the bifurcation diagrams in complete families of vector fields the algorithm can be applied to study separable hamiltonian systems with one degree of freedom which include a vast amount of examples in physical applications

predicting dynamic postural instability using center of mass time to contact information our purpose was to determine whether spatiotemporal measures of center of mass motion relative to the base of support boundary could predict stepping strategies after upper body postural perturbations in humans we expected that inclusion of center of mass acceleration in such time to contact ttc calculations would give better predictions and more advanced warning of perturbation severity ttc measures were compared with traditional postural variables which do not consider support boundaries and with an inverted pendulum model of dynamic stability developed by hof et al 2005 the condition for dynamic stability journal of biomechanics 38 1 8 a pendulum was used to deliver sequentially increasing perturbations to 10 young adults who were strapped to a wooden backboard that constrained motion to sagittal plane rotation about the ankle joint subjects were instructed to resist the perturbations stepping only if necessary to prevent a fall peak center of mass and center of pressure velocity and acceleration demonstrated linear increases with postural challenge in contrast boundary relevant minimum ttc values decreased nonlinearly with postural challenge enabling prediction of stepping responses using quadratic equations when ttc calculations incorporated center of mass acceleration the quadratic fits were better and gave more accurate predictions of the ttc values that would trigger stepping responses in addition ttc minima occurred earlier with acceleration inclusion giving more advanced warning of perturbation severity our results were in agreement with ttc predictions based on hof s model and suggest that ttc may function as a control parameter influencing the postural control system s decision to transition from a stationary base of support to a stepping strategy

stepping boundary of external force controlled perturbations of varying durations comparison of experimental data and model simulations abstract this study investigated the stepping boundary the force that can be resisted without stepping for force controlled perturbations of different durations twenty two healthy young adults 19 37 years old were instructed to try not to step in response to 86 different force time combinations of forward waist pulls the forces at which 50 of subjects stepped f50 were identified for each tested perturbation durations results showed that f50 decreased hyperbolically when the perturbation s duration increased and converged toward a constant value about 10 bw for longer perturbations over 1500 ms the effect of perturbation duration was critical for the shortest perturbations less than 1 s in parallel a simple function was proposed to estimate this stepping boundary considering the dynamics of a linear inverted pendulum foot model and simple balance recovery reactions we could express the maximum pulling force that can be withstood without stepping as a simple function of the perturbation duration when used with values of the main model parameters determined experimentally this function replicated adequately the experimental results this study demonstrates for the first time that perturbation duration has a major influence on the outcomes of compliant perturbations such as force controlled pulls the stepping boundary corresponds to a constant perturbation force duration product and is largely explained by only two parameters the reaction time and the displacement of the center of pressure within the functional base of support future work should investigate pathological populations and additional parameters characterizing the perturbation time profile such as the time derivative of the perturbation

adaptational responses in dynamic stability during disturbed walking in the elderly the purpose of this study was to examine the age related predictive and feedback adaptive locomotor improvements in the components of dynamic stability control during disturbed walking thirteen old 62 74 yrs and ten young 23 30 yrs male subjects performed a gait protocol on a gangway which included one covered element by exchanging this element the subjects walked either solely over hard surface or experienced a perturbation of the gait on the soft surface element the gait protocol consisted of a baseline on hard surface and an adaptation phase with 19 trials on soft or hard 2nd 8th and 19th surface the investigation of dynamic stability was made by using the margin of stability ms which was calculated as the difference between the base of support and the extrapolated center of mass cm horizontal velocity of cm and its vertical projection in anterior posterior direction as well as the eigenfrequency of an inverted pendulum generate the extrapolated cm as a result of the first unexpected disturbance ms was decreased in the step following the perturbation compared to baselines in both age groups this decrease was higher for the old participants compared to the young ones indicating a more unstable position in the step after the perturbation for the elderly in the following adaptation phase ms returned to baseline values in both age groups in the hard trial after the first unexpected perturbation both age groups increased ms at touchdown of the disturbed leg compared to baseline reflecting fast predictive adjustments our findings show that the well known age related biological impairments did not inhibit the adaptive improvements in the components of dynamic stability in the elderly however the feedback corrections after the first unexpected perturbation were less effective for the elderly this may increase the risk of falling

the condition for dynamic stability the well known condition for standing stability in static situations is that the vertical projection of the centre of mass com should be within the base of support bos on the basis of a simple inverted pendulum model an extension of this rule is proposed for dynamical situations the position of the vertical projection of the com plus its velocity times a factor rootl g should be within the bos l being leg length and g the acceleration of gravity it is proposed to name this vector quantity extrapolated centre of mass position xcom the definition suggests as a measure of stability the margin of stability b the minimum distance from xcom to the boundaries of the bos an alternative measure is the temporal stability margin tau the time in which the boundary of the bos would be reached without intervention some experimental data of subjects standing on one or two feet flatfoot and tiptoe are presented to give an idea of the usual ranges of these margins of stability example data on walking are also presented c 2004 elsevier ltd all rights reserved

active arm swing and asymmetric walking leads to increased variability in trunk kinematics in young adults abstract fall induced injuries are a leading cause for occupational injuries with the majority originating from challenging same level walking surfaces despite current perturbation and fall prevention paradigms occupational fall prevalence remains stable typically these paradigms do not account for arm swing which has been demonstrated to affect the center of mass movement during walking this study examined the effect of different arm swing on postural control during symmetric and asymmetric walking fifteen healthy young adults age 23 4 2 8 walked symmetrically and asymmetrically with three arm motions normal held and active on a split belt treadmill caren extended system motek medical amsterdam nl mean standard deviation and maximal values of trunk linear and angular velocity and whole body angular momentum were calculated in all three axes additionally step length time and width mean and coefficient of variation margin of stability and harmonic ratios were calculated compared to normal and held conditions active arm increased trunk linear and angular velocity standard deviation max velocity values mean step length and time as well as the coefficient of variation for step length time and width furthermore whole body angular momentum increased as a function of arm swing amplitude active arm swing further reduced harmonic ratios in the mediolateral and anteroposterior directions asymmetric walking increased average step time and width as well as increased the coefficient of variation for step length and time but reduced left average step length and step width coefficient of variation further asymmetric walking increased mediolateral margin of stability and reduced anteroposterior and mediolateral harmonic ratios finally results demonstrated that actively increasing arm swing increases trunk linear and angular velocity variability in healthy young adults during symmetric and asymmetric treadmill walking findings may be due to active arm swing and asymmetric walking causing a disproportional contribution to trunk and center of mass movement causing participants to modify their base of support to maintain stability

the period function for quadratic integrable systems with cubic orbits this paper is concerned with the monotonicity of the period function for families of quadratic systems with centers whose orbits lie on cubic planar curves it is proved that each such system has a period function with at most one critical point

bifurcation of critical periods for plane vector fields on etudie un probleme de bifurcation dans des familles de champs de vecteurs analytiques plans qui ont un centre non degenere a l origine pour toutes les valeurs d un parametre r n on definit la fonction periode p on determine les points critiques de cette fonction pres du centre avec comme parametre de bifurcation

global optimization of statistical functions with simulated annealing abstract many statistical methods rely on numerical optimization to estimate a model s parameters unfortunately conventional algorithms sometimes fail even when they do converge there is no assurance that they have found the global rather than a local optimum we test a new optimization algorithm simulated annealing on four econometric problems and compare it to three common conventional algorithms not only can simulated annealing find the global optimum it is also less likely to fail on difficult functions because it is a very robust algorithm the promise of simulated annealing is demonstrated on the four econometric problems

generalized capacitance matrix theorems and algorithm for solving linear systems the capacitance matrix method has been widely used as an efficient numerical tool for solving the boundary value problems on irregular regions initially this method was based on the sherman morrison woodbury formula an expression for the inverse of the matrix a uvt with bf a in re n times n and bf u v in re n times p extensions of this method reported in literature have made restrictive assumptions on the matrices a and a uvt in this paper we present several theorems which are generalizations of the capacitance matrix theorem in cite buzbee and are suited for very general matrices a and a uvt a generalized capacitance matrix algorithm is developed from these theorems and holds the promise of being applicable to more general problems in addition it gives ample freedom to choose the matrix a for developing very efficient numerical algorithms we demonstrate the usefulness of our generalized capacitance matrix algorithm by applying it to efficiently solve large sparse linear systems in several computer vision problems namely the surface reconstruction and interpolation and the shape from orientation problem

bifurcations of periodic solutions of delay differential equations abstract in this paper we develop kaplan yorke s method and consider the existence of periodic solutions for some delay differential equations we especially study hopf and saddle node bifurcations of periodic solutions with certain periods for these equations with parameters and give conditions under which the bifurcations occur we also give application examples and find that hopf and saddle node bifurcations often occur infinitely many times

muscle oxygen consumption determined by nirs in relation to external force and emg local oxygen consumption in a muscle vo 2 can be determined by near infrared spectroscopy nirs in principle it should be possible to use this measure to validate musculoskeletal models however the relationship between vo 2 and external force or between vo 2 and surface emg as a measure for muscle activity is hardly known the aim of this study was 1 to evaluate the characteristics of the relationship between vo 2 and external moments and 2 to determine whether differences exist between the emg moment relationship and the vo 2 moment relationship subjects n 5 were asked to perform isometric contractions exerting combinations of elbow flexion and pro supination moments at force levels up to 70 of their maximum simultaneous surface emg and nirs measurements were performed on the m biceps breve bb and the m brachioradialis br a linear relationship was found between emg and vo 2 for the bb vo 2 and emg were linearly related to both the flexion moment and the pro supination moment however for the br only a linear relationship with flexion moment was found as expected based on the findings above the relationship between vo 2 and elbow flexion moment can be described by a linear equation under the conditions of this study isometric and force levels up to 70 these findings suggest that load sharing is independent of force level and that next to emg vo 2 can be used for the validation of musculoskeletal models

spring like gait mechanics observed during walking in both young and older adults a spring loaded inverted pendulum model successfully demonstrated the oscillatory behavior of the center of mass com and corresponding ground reaction forces grfs of young healthy subjects this study questioned whether spring like leg walking dynamics are consistently observed in the walking of older adults that exhibit different gait characteristics such as slower gait speed from the young eight young and eight older adult subjects participated in overground walking experiments performed at four different gait speeds ranging from their self selected speed to a maximum walking speed to calculate the effective leg stiffness the damped compliant leg model with a curved foot was used the model parameters of leg stiffness and damping constant were optimized to achieve the best fit between model and human grfs data we observed that the grfs data from both age groups were reasonably well fitted by spring like leg dynamics throughout the broad range of gait speeds the leg stiffness and damping constant consistently increased as a function of the walking speed in both age groups but slightly greater variations of the model parameters were observed for the older adults trials the results imply that human walking dynamics and the variation with respect to age can be well captured by spring like leg dynamics

the correlation between metabolic and individual leg mechanical power during walking at different slopes and velocities during level ground walking mechanical work from each leg is required to redirect and accelerate the center of mass previous studies show a linear correlation between net metabolic power and the rate of step to step transition work during level ground walking with changing step lengths however correlations between metabolic power and individual leg power during step to step transitions while walking on uphill downhill slopes and at different velocities are not known this basic understanding of these relationships between metabolic demands and biomechanical tasks can provide important information for design and control of biomimetic assistive devices such as leg prostheses and orthoses thus we compared changes in metabolic power and mechanical power during step to step transitions while 19 subjects walked at seven slopes 0 3 6 and 9 and three velocities 1 00 1 25 and 1 50 m s a quadratic model explained more of the variance r2 0 58 0 61 than a linear model r2 0 37 0 52 between metabolic power and individual leg mechanical power during step to step transitions across all velocities a quadratic model explained more of the variance r2 0 57 0 76 than a linear model r2 0 52 0 59 between metabolic power and individual leg mechanical power during step to step transitions at each velocity for all slopes and explained more of the variance r2 0 12 0 54 than a linear model r2 0 07 0 49 at each slope for all velocities our results suggest that it is important to consider the mechanical function of each leg in the design of biomimetic assistive devices aimed at reducing metabolic costs when walking at different slopes and velocities

effects of walking speed on the step by step control of step width abstract young healthy adults walking at typical preferred speeds use step by step adjustments of step width to appropriately redirect their center of mass motion and ensure mediolateral stability however it is presently unclear whether this control strategy is retained when walking at the slower speeds preferred by many clinical populations we investigated whether the typical stabilization strategy is influenced by walking speed twelve young neurologically intact participants walked on a treadmill at a range of prescribed speeds 0 2 1 2 m s the mediolateral stabilization strategy was quantified as the proportion of step width variance predicted by the mechanical state of the pelvis throughout a step calculated as r2 magnitude from a multiple linear regression our ability to accurately predict the upcoming step width increased over the course of a step the strength of the relationship between step width and pelvis mechanics at the start of a step was reduced at slower speeds however these speed dependent differences largely disappeared by the end of a step other than at the slowest walking speed 0 2 m s these results suggest that mechanics dependent adjustments in step width are a consistent component of healthy gait across speeds and contexts however slower walking speeds may ease this control by allowing mediolateral repositioning of the swing leg to occur later in a step thus encouraging slower walking among clinical populations with limited sensorimotor control

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

linearization of isochronous centers abstract in this paper we study isochronous centers of polynomial systems we first discuss isochronous centers of quadratic systems cubic symmetric systems and reduced kukles system all these systems have rational first integrals we give a unified proof of the isochronicity of these systems by constructing algebraic linearizing changes of coordinates we then study two other classes of systems with isochronous centers namely the class of complex systems z ip z and the class of cubic systems symmetric with respect to a line and satisfying 1 both classes consist of darboux integrable systems we discuss their geometric properties and construct the linearizing changes of coordinates we show that the class of polynomial isochronous systems carries a very rich geometry finally we discuss the geometry of the linearizing changes of coordinates in the complex plane

isochronicity and linearizability of planar polynomial hamiltonian systems in this paper we study isochronicity and linearizability of planar polynomial hamiltonian systems first we prove a theorem which supports a negative answer to the following open question stated by jarque and villadelprat in 15 do there exist planar polynomial hamiltonian systems of even degree having an isochronous center additionally we obtain some conditions for linearizability of complex cubic hamiltonian systems

circulant matrices and differential delay equations on etudie les solutions periodiques non triviales de familles parametrisees d equations differentielles a retard

characteristic multipliers and stability of symmetric periodic solutions of x t g x t 1 on etudie l equation differentielle scalaire a retard x t g x t 1 a retroaction negative on suppose que la fonction non lineaire g est impaire et monotone on demontre que des solutions periodiques x t de type legerement oscillant satisfaisant la condition de symetrie x t x t 2 t r sont non degenerees et ont toutes des multiplicateurs de floquet non triviaux dans le cercle unite

two inverse problems for analytic potential systems in this paper we solve a basic problem about the existence of an analytic potential with a prescribed period function as an application it is shown how to extend to the whole phase plane an arbitrary potential defined on a semiplane in order to get isochronicity

predicted threshold against backward balance loss in gait the purpose of this study was to determine the minimum forward center of mass com velocity required to prevent backward loss of balance in gait as function of the initial com position we hypothesized that these threshold values would be different from those previously published for standing because of the postural differences between gait and standing to investigate this issue we constructed a seven link nine degree of freedom biomechanical model and employed dynamic optimization to estimate these threshold values under two initial postural conditions 1 the posture at the beginning of swing phase i e at toe off and 2 symmetric bipedal standing in particular for a range of possible com positions posterior to the base of support bos simulated annealing was used to search for the minimum velocity that could carry the com into the bos and avoid backward loss of balance we found that the stability boundary against backward balance loss in walking had a similar overall trend as that previously published for standing in general the minimal com velocity necessary to prevent a backward loss of balance in walking was greater than that in symmetric bipedal standing and the difference could approach 30 or more when the com started 0 5 and 1 0 foot lengths behind the bos these discrepancies suggest that simpler biomechanical models while being more efficient and easier to employ may not always be adequate for exploring stability limits of humans

moment arms and musculotendon lengths estimation for a three dimensional lower limb model this paper presents a set of polynomial expressions that can be used as regression equations to estimate length and three dimensional moment arms of 43 lower limb musculotendon actuators these equations allow one to find at a low computational cost the musculotendon geometric parameters required for numerical simulation of large musculoskeletal models nominal values for these biomechanical parameters were established using a public domain musculoskeletal model of the lower limb ieee trans biomed eng 37 1990 757 to fit these nominal values regression equations with different levels of complexity were generated based on the number of generalized coordinates of the joints spanned by each musculotendon actuator least squares fitting was used to identify regression equation coefficients the goodness of the fit and confidence intervals were assessed and the best fitting equations selected

single and multiple step balance recovery responses can be different at first step lift off following lateral waist pull perturbations in older adults abstract an inability to recover lateral balance with a single step is predictive of future falls in older adults this study investigated if balance stability at first step lift off fslo would be different between multiple and single stepping responses to lateral perturbations 54 healthy older adults received left and right waist pulls at 5 different intensities levels 1 5 crossover stepping responses at and above intensity level 3 that induced both single and multiple steps were analyzed whole body center of mass com and center of pressure cop positions in the medio lateral direction with respect to the base of support were calculated an inverted pendulum model was used to define the lateral stability boundary which was also adjusted using the cop position at fslo functional boundary no significant differences were detected in the cop positions between the responses at fslo p 0 075 indicating no difference in the functional boundaries between the responses significantly smaller stability margins were observed at first step landing for multiple steps at all levels p 0 024 while stability margins were also significantly smaller at fslo for level 3 and 4 p 0 048 these findings indicate that although reduced stability at first foot contact would be associated with taking additional steps stepping responses could also be attributable to the com motion state as early as first step lift off preceding foot contact perturbation based training interventions aimed at improving the reactive control of stability would reduce initial balance instability at first step lift off and possibly the consequent need for multiple steps in response to balance perturbations

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

simultaneous positive and negative external mechanical work in human walking in human walking the center of mass motion is similar to an inverted pendulum viewing double support as a transition from one inverted pendulum to the next we hypothesized that the leading leg performs negative work to redirect the center of mass velocity while simultaneously the trailing leg performs positive work to replace the lost energy to test this hypothesis we developed a method to quantify the external mechanical work performed by each limb individual limbs method traditional measures of external mechanical work use the sum of the ground reaction forces acting on the limbs combined limbs method allowing for the mathematical cancellation of simultaneous positive and negative work during multiple support periods we expected to find that the traditional combined limbs method underestimates external mechanical work by a substantial amount we used both methods to measure the external mechanical work performed by humans walking over a range of speeds we found that during double support the legs perform a substantial amount of positive and negative external work simultaneously the combined limbs measures of positive and negative external work were approximately 33 less than those calculated using the individual limbs method at all speeds the trailing leg performs greater than 97 of the double support positive work while the leading leg performs greater than 94 of the double support negative work

maximum voluntary joint torque as a function of joint angle and angular velocity model development and application to the lower limb measurements of human strength can be important during analyses of physical activities such measurements have often taken the form of the maximum voluntary torque at a single joint angle and angular velocity however the available strength varies substantially with joint position and velocity when examining dynamic activities strength measurements should account for these variations a model is presented of maximum voluntary joint torque as a function of joint angle and angular velocity the model is based on well known physiological relationships between muscle force and length and between muscle force and velocity and was tested by fitting it to maximum voluntary joint torque data from six different exertions in the lower limb isometric concentric and eccentric maximum voluntary contractions were collected during hip extension hip flexion knee extension knee flexion ankle plantar flexion and dorsiflexion model parameters are reported for each of these exertion directions by gender and age group this model provides an efficient method by which strength variations with joint angle and angular velocity may be incorporated into comparisons between joint torques calculated by inverse dynamics and the maximum available joint torques