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

a hybrid redesign of newton observers in the absence of an exact discrete time model abstract we study the newton observer design developed by moraal and grizzle when the exact discrete time model of the sampled data plant is not known analytically we eliminate the dependence on this exact model with a hybrid reconstruction that makes use of continuous time filters to produce the numerical value of the exact model we then implement the newton method with finite difference and secant approximations for the jacobian despite the continuous time filters the proposed hybrid redesign preserves the sampled data characteristic of the newton observer because it only employs discrete time measurements of the output it also offers flexibility to be implemented with nonuniform or event driven sampling we finally study how a line search scheme can be incorporated in this hybrid newton observer to enlarge the region of convergence

kinetic analysis of the lower limbs during walking what information can be gained from a three dimensional model kinetic analyses joint moments powers and work of the lower limbs were performed during normal walking to determine what further information can be gained from a three dimensional model over planar models it was to be determined whether characteristic moment and power profiles exist in the frontal and transverse planes across subjects and how much work was performed in these planes kinetic profiles from nine subjects were derived using a three dimensional inverse dynamics model of the lower limbs and power profiles were then calculated by a dot product of the angular velocities and joint moments resolved in a global reference system characteristic joint moment profiles across subjects were found for the hip knee and ankle joints in all planes except for the ankle frontal moment as expected the major portion of work was performed in the plane of progression since the goal of locomotion is to support the body against gravity while generating movements which propel the body forward however the results also showed that substantial work was done in the frontal plane by the hip during walking 23 of the total work at that joint the characteristic joint profiles suggest defined motor patterns and functional roles in the frontal and transverse planes kinetic analysis in three dimensions is necessary particularly if the hip joint is being examined as a substantial amount of work was done in the frontal plane of the hip to control the pelvis and trunk against gravitational forces

on treewidth and minimum fill in of asteroidal triple free graphs we present o n5r n3r3 time algorithms to compute the treewidth pathwidth minimum fill in and minimum interval graph completion of asteroidal triple free graphs where n is the number of vertices and r is the number of minimal separators of the input graph this yields polynomial time algorithms for the four np complete graph problems on any subclass of the asteroidal triple free graphs that has a polynomially bounded number of minimal separators as e g cocomparability graphs of bounded dimension and d trapezoid graphs for any fixed d 1

observer design for nonlinear systems with discrete time measurements this paper focuses on the development of asymptotic observers for nonlinear discrete time systems it is argued that instead of trying to imitate the linear observer theory the problem of constructing a nonlinear observer can be more fruitfully studied in the context of solving simultaneous nonlinear equations in particular it is shown that the discrete newton method properly interpreted yields an asymptotic observer for a large class of discrete time systems while the continuous newton method may be employed to obtain a global observer furthermore it is analyzed how the use of broyden s method in the observer structure affects the observer s performance and its computational complexity an example illustrates some aspects of the proposed methods moreover it serves to show that these methods apply equally well to discrete time systems and to continuous time systems with sampled outputs

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

global optimal attitude estimation using uncertainty ellipsoids a deterministic attitude estimation problem for a rigid body in a potential field with bounded attitude and angular velocity measurement errors is considered an attitude estimation algorithm that globally minimizes the attitude estimation error is obtained assuming that the initial attitude the initial angular velocity and measurement noise lie within given ellipsoidal bounds an uncertainty ellipsoid that bounds the attitude and the angular velocity of the rigid body is obtained the center of the uncertainty ellipsoid provides point estimates and the size of the uncertainty ellipsoid measures the accuracy of the estimates the point estimates and the uncertainty ellipsoids are propagated using a lie group variational integrator and its linearization respectively the attitude and angular velocity estimates are optimal in the sense that the sizes of the uncertainty ellipsoids are minimized

nonlinear h sub spl infin control and its application to rigid spacecraft the problem of h sub spl infin control of a rigid spacecraft with three control torques and disturbances is addressed the hamilton jacobi isaacs inequality for h sub spl infin feedback design is solved an h sub spl infin suboptimal feedback is given and the stability properties of the closed loop system are studied

adaptive compensation of gyro bias in rigid body attitude estimation using a single vector measurement the presence of bias in measurement of rate gyros is a performance limiting factor for satellite attitude determination systems gyro bias is usually handled by kalman filtering methods which are mostly based on linearization approaches and lack global convergence properties on the other hand the existing asymptotically convergent nonlinear observers take into account the gyro bias only when multiple vector measurements are available we present an asymptotically convergent attitude estimator which uses only one vector measurement and a rate gyro whose output is contaminated with an unknown and constant bias the effect of unknown bias is compensated by means of a parameter adaptation law an explicit condition on the reference vectors for ensuring observability of the system is introduced a realistic simulation is presented to illustrate the performance of the proposed attitude estimator in face of significant bias in gyro measurement and when a magnetometer is used to provide the single vector measurement

a framework for nonlinear sampled data observer design via approximate discrete time models and emulation we study observer design for sampled data nonlinear systems using two approaches i the observer is designed via an approximate discrete time model of the plant ii the observer is designed based on the continuous time plant model and then discretized for sampled data implementation emulation we investigate under what conditions and in what sense these designs achieve convergence for the unknown exact discrete time model we present examples which show that designs that violate our conditions may indeed lead to instability when implemented on the exact model

global attitude estimation using single delayed vector measurement and biased gyro time delay in attitude determination systems is unavoidable and it is usually caused by low quality data sampling poor sensor synchronization momentary sensor outage or operational restrictions of sensors despite its performance degrading effect time delay has been widely neglected in the existing attitude estimation methods this paper presents a general framework for design of attitude estimators with and without so 3 manifold restriction by assuming that measurement of a single vector measurement is available with time delay also measurement of rigid body angular velocity is considered available with an unknown bias the proposed estimator guarantees global and asymptotic convergence of attitude estimate to its true value the observer gain is calculated by solving a delay dependent matrix differential equation solvability of the differential equation depends on an observability condition related to the reference vectors to illustrate performance of the proposed observer we present simulation of a satellite system where the single delayed vector measurement is provided by a magnetometer

lumbar spinal muscle activation synergies predicted by multi criteria cost function the hypothesis that control of lumbar spinal muscle synergies is biomechanically optimized was studied by comparing emg data with an analytical model with a multi component cost function that could include 1 trunk displacements 2 intervertebral displacements 3 intervertebral forces 4 sum of cubed muscle stresses and 5 eigenvalues for the first two spinal buckling modes the model s independent variables were 180 muscle forces the 36 displacements of 6 vertebrae were calculated from muscle forces and the spinal stiffness calculated muscle activation was compared with emg data from 14 healthy human subjects who performed isometric voluntary ramped maximum efforts at angles of 0 degrees 45 degrees 90 degrees 135 degrees and 180 degrees to the right from the anterior direction muscle activation at each angle was quantified as the linear regression slope of the rms emg versus external force relationship normalized by the maximum observed emg there was good agreement between the analytical model and emg data for the dorsal muscles when the model included either minimization of intervertebral displacements or minimization of intervertebral forces in its cost function but the model did not predict a realistic level of abdominal muscles activation agreement with emg data was improved with the sum of the cubed muscle stresses added to the cost function addition of a cost function component to maximize the trunk stability produced higher levels of antagonistic muscle activation at low efforts than at greater efforts it was concluded that the muscle activation strategy efficiently limits intervertebral forces and displacements and that costs of higher muscle stresses are taken into account but stability does not appear to be maximized trunk muscles are apparently not controlled solely to optimize any one of the biomechanical costs considered here

forces of individual cat ankle extensor muscles during locomotion predicted using static optimization abstract in order to test the principles of the control of synergistie muscles that were proposed in the literature forces of cat soleus so gastrocnemius ga and plantaris pl measured during locomotion were compared with the corresponding forces predicted using different optimization criteria forces of cat so ga and pl and the corresponding cat kinematics were recorded simultaneously using e shaped force transducers and high speed video respectively measurements were obtained from three cats walking and trotting on a treadmill at five nominal speeds ranging from 0 4 to 1 8 ms 1 muscle forces were predicted using static optimization and a musculoskeletal model of the cat hindlimb consisting of three segments foot shank and thigh and three muscles so ga and pl six optimization criteria which had been proposed in the literature were tested linear criteria based on the principles of minimum muscle force and stress predicted forces during the stance phase with an average normalized error of 59 322 three other criteria minimization of the sum of the relative muscle forces squared minimization of the sum of the muscle stresses cubed and minimization of the upper bound for all of the muscle stresses showed a better performance i the average error was 43 119 and ii the correlation coefficient calculated between the predicted and actual forces exceeded 0 9 for all three muscles a criterion that was based on the principle of minimum fatigue and accounted for the percentage of slow twitch fibers in the muscles had the lowest average error 26 52 the high correlation 0 97 0 99 between the measured forces and forces predicted by using the minimum fatigue criterion suggested that force sharing among so ga and pl during cat locomotion may be the same for a given set of joint moments and muscle moment arms it was concluded that static optimization with the appropriate criterion can predict muscle forces adequately for specific movement conditions

muscular synergism ii a minimum fatigue criterion for load sharing between synergistic muscles a new physiological criterion for muscular load sharing is developed the criterion is based on the assumption that the endurance time of muscular contractions is maximized hence muscular fatigue is minimized the optimization problem is cast in the form of a linearly constrained non linear minimax optimization the new method predicts that 1 there is synergistic muscle action 2 muscle force increases non linearly with external force load 3 relatively more force is allocated to muscles that have a large maximum force large muscles 4 relatively more force is allocated to muscles with a high percentage of slow twitch fibers muscles that are fatigue resistant 5 the load sharing does not depend on the moment arm of the muscles although the absolute force levels do depend on this variable the predicted load sharing between two cat muscles during standing and walking is in good agreement with direct force measurement data from the literature

effect of foot progression angle on hip joint moments during gait loosening has emerged as the most serious long term complication of total hip replacement and torsional loading of the femoral implant has been implicated as a possible cause in an effort to explore a strategy for minimizing this risk the following hypothesis was tested the foot progression angle has a significant effect on the resultant hip moments and particularly the internal external rotation moment during level walking twelve normal subjects performed a total of nine trials three in which they walked normally with the right foot pointing approximately straight ahead three in which they were told to walk with the foot internally rotated approximately 30 degrees and three in which the foot was externally rotated about 30 degrees the inverse dynamics approach was used to integrate the body segment parameter kinematic and force plate data and to solve for the resultant moment at the right hip joint in all three conditions foot straight foot in and foot out the subjects walked at the same average speed of 1 5 0 3 ms 1 for the flexion extension moment where the maximum flexion moment of 95 nm was in good agreement with other published data there was no significant difference between the three foot orientation conditions for the abduction adduction moment the foot straight condition exhibited the classic double peak pattern with a maximum abductor moment of 57 nm and there was no statistically significant difference between the three curves abstract truncated at 250 words

analytic analysis of the force sharing among synergistic muscles in one and two degree of freedom models abstract mathematical optimization of specific cost functions has been used in theoretical models to calculate individual muscle forces measurements of individual muscle forces and force sharing among individual muscles show an intensity dependent non linear behavior it has been demonstrated that the force sharing between the cat gastrocnemius plantaris and soleus shows distinct loops that change orientation systematically depending on the intensity of the movement the purpose of this study was to prove whether or not static non linear optimization could inherently predict force sharing loops between agonistic muscles using joint moment data from a step cycle of cat locomotion the forces in three cat ankle plantar flexors gastrocnemius plantaris and soleus were calculated using two popular optimization algorithms and two musculo skeletal models the two musculo skeletal models included a one degree of freedom model that considered the ankle joint exclusively and a two degree of freedom model that included the ankle and the knee joint the main conclusion of this study was that solutions of the one degree of freedom model do not guarantee force sharing loops but the two degree of freedom model predicts force sharing loops independent of the specific values of the input parameters for the muscles and the musculo skeletal geometry the predicted force sharing loops were found to be a direct result of the loops formed by the knee and ankle moments in a moment moment graph

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

validation of optimization models that estimate the forces exerted by synergistic muscles the purpose of this study was to validate the mathematical predictions of individual muscle forces obtained using optimization models mathematical muscle force predictions were made using linear and nonlinear optimization models proposed in the literature actual muscle forces were measured experimentally from soleus gastrocnemius and plantaris muscles of an adult male cat during a variety of locomotor tasks mathematically predicted muscle forces did not agree well with the experimentally determined muscle forces because changes in force sharing during given step cycles and for different locomotor speeds were largely ignored in the theoretical models tested it is suggested that changes in force sharing during given step cycles may be caused by differences in force velocity characteristics or small time delays of onset of activation between muscles whereas changes in force sharing associated with different speeds of locomotion may be caused by corresponding changes in the magnitude of centrally controlled activation theoretical simulations testing the feasibility of these suggestions were encouraging in view of the findings of this study it is suggested that future models should be developed and validated based on experimental findings

sufficient conditions for stabilization of sampled data nonlinear systems via discrete time approximations given a parameterized by sampling period t family of approximate discrete time models of a sampled nonlinear plant and given a family of controllers stabilizing the family of plant models for all t sufficiently small we present conditions which guarantee that the same family of controllers semi globally practically stabilizes the exact discrete time model of the plant for sufficiently small sampling periods when the family of controllers is locally bounded uniformly in the sampling period the inter sample behavior can also be uniformly bounded so that the time varying sampled data model of the plant is uniformly semi globally practically stabilized the result justifies controller design for sampled data nonlinear systems based on the approximate discrete time model of the system when sampling is sufficiently fast and the conditions we propose are satisfied our analysis is applicable to a wide range of time discretization schemes and general plant models

comparison of global and joint to joint methods for estimating the hip joint load and the muscle forces during walking a three dimensional musculoskeletal model of the lower limb was developed to study the influence of biarticular muscles on the muscle force distribution and joint loads during walking a complete walking cycle was recorded for 9 healthy subjects using the standard optoelectronic motion tracking system ground contact forces were also measured using a 6 axes force plate inverse dynamics was used to compute net joint reactions forces and torques in the lower limb a static optimization method was then used to estimate muscle forces two different approaches were used in the first one named global method the biarticular muscles exerted a torque on the two joints they spanned at the same time and in the second one called joint by joint method these biarticular muscles were divided into two mono articular muscles with geometrical insertion origin via points and physiological properties remained unchanged the hip joint load during the gait cycle was then calculated taking into account the effect of muscle contractions the two approaches resulted in different muscle force repartition the biarticular muscles were favoured over any set of single joint muscles with the same physiological function when using the global method while the two approaches yielded only little difference in the resultant hip load the examination of muscle power showed that biarticular muscles could produce positive work at one joint and negative work at the other transferring energy between body segments and thus decreasing the metabolic cost of movement

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

sensitivity of predicted muscle forces to parameters of the optimization based human leg model revealed by analytical and numerical analyses there are different opinions in the literature on whether the cost functions the sum of muscle stresses squared and the sum of muscle stresses cubed can reasonably predict muscle forces in humans one potential reason for the discrepancy in the results could be that different authors use different sets of model parameters which could substantially affect forces predicted by optimization based models in this study the sensitivity of the optimal solution obtained by minimizing the above cost functions for a planar three degrees of freedom dof model of the leg with nine muscles was investigated analytically for the quadratic function and numerically for the cubic function analytical results revealed that generally the non zero optimal force of each muscle depends in a very complex non linear way on moments at all three joints and moment arms and physiological cross sectional areas pcsas of all muscles deviations of the model parameters moment arms and pcsas from their nominal values within a physiologically feasible range affected not only the magnitude of the forces predicted by both criteria but also the number of non zero forces in the optimal solution and the combination of muscles with non zero predicted forces muscle force magnitudes calculated by both criteria were similar they could change several times as model parameters changed whereas patterns of muscle forces were typically not as sensitive it is concluded that different opinions in the literature about the behavior of optimization based models can be potentially explained by differences in employed model parameters

a new parametric approach for modeling hip forces during gait an analytical parametric model was developed to estimate the natural biological variations in muscle forces and their effect on the hip forces subject only to physiological constraints and not predefined optimization criterion force predictions are based on the joint kinematics and kinetics of each subject a previously published muscle model and physiological constraints on the muscle force distributions the model was used to determine the hip contact forces throughout the stance phase of gait of a subject with a total hip replacement thr the parametrically modeled peak hip force without antagonistic muscle activity varied from 2 7 to 3 2 body weights mean 2 9 body weights which agreed well with published in vivo measurements from instrumented thrs in other subjects for every 10 increase in antagonistic activity the mean peak hip force increased by 0 2 body weights the parametric model allows one to examine the effect of specific muscle weaknesses or increased antagonistic muscle activity on the hip forces the model also provides a tool for studying the effect of gait adaptations on hip forces as predictions are based on each individual s gait data differences in peak forces between subjects can then be evaluated relative to the uncertainty in not knowing the precise muscle force distributions

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

about weight factors in the non linear objective functions used for solving indeterminate problems in biomechanics a lot of non linear objective criteria are applied for solving the indeterminate problems formulated for di erent biomechanical models most of them can be covered by the expression c i dfo i dn it might be noted however that most of the suggested criteria are not applicable if considerable antagonistic co contractions exist this could be an e ect of treating the agonistic muscles and their respective antagonists in one and the same manner in the objective function using a completely inverse approach the muscle forces are supposed to be known quantities and a simple 1dof model actuated by three agonistic muscles and one corresponding antagonist it has been shown which values of the weight factors c i may predict di erent levels of muscle forces from the two antagonistic groups three hypothetical border variants for magnitudes of the muscle forces are considered exor muscles are only active extensor muscles are only active considerable co contraction of exors and extensors exists the main conclusions are the signs of c i at agonistic muscles have to be opposite to the c i signs at their antagonists the signs of the weight factors depend on the direction of the net external joint moment the closer c i to zero the bigger force will be predicted in the ith muscle 1999 elsevier science ltd all rights reserved

listing all potential maximal cliques of a graph a potential maximal clique of a graph is a vertex set that induces a maximal clique in some minimal triangulation of that graph it is known that if these objects can be listed in polynomial time for a class of graphs the treewidth and the minimum fill in are polynomially tractable for these graphs we show here that the potential maximal cliques of a graph can be generated in polynomial time in the number of minimal separators of the graph thus the treewidth and the minimum fill in are polynomially tractable for all classes of graphs with a polynomial number of minimal separators

brief paper a discrete time observer design for spacecraft attitude determination using an orthogonality preserving algorithm this paper studies a nonlinear discrete time partial state observer design problem for rigid spacecraft systems particularly for spacecraft attitude estimation the construction is inspired by an orthogonality preserving numerical algorithm and it yields a semiglobal practical asymptotic observer we show that the separation principle holds and hence stabilization using output feedback is possible an example is provided to illustrate the usefulness of our results in a sampled data implementation of an attitude control for a rigid spacecraft using output feedback and to illustrate the advantages of the proposed observer design especially compared to a sample and hold version of a similar type observer designed in continuous time

treewidth and minimum fill in on permutation graphs in linear time permutation graphs form a well studied subclass of cocomparability graphs permutation graphs are the cocomparability graphs whose complements are also cocomparability graphs a triangulation of a graph g is a graph h that is obtained by adding edges to g to make it chordal if no triangulation of g is a proper subgraph of h then h is called a minimal triangulation the main theoretical result of the paper is a characterisation of the minimal triangulations of a permutation graph that also leads to a succinct and linear time computable representation of the set of minimal triangulations we apply this representation to devise linear time algorithms for various minimal triangulation problems on permutation graphs in particular we give linear time algorithms for computing treewidth and minimum fill in on permutation graphs

formulas relating kl stability estimates of discrete time and sampled data nonlinear systems abstract we provide an explicit kl stability or input to state stability iss estimate for a sampled data nonlinear system in terms of the kl estimate for the corresponding discrete time system and a k function describing inter sample growth it is quite obvious that a uniform inter sample growth condition plus an iss property for the exact discrete time model of a closed loop system implies uniform iss of the sampled data nonlinear system our results serve to quantify these facts by means of comparison functions our results can be used as an alternative to prove and extend results in 1 or extend some results in 4 to a class of nonlinear systems finally the formulas we establish can be used as a tool for some other problems which we indicate

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

treewidth and minimum fill in grouping the minimal separators we use the notion of potential maximal clique to characterize the maximal cliques appearing in minimal triangulations of a graph we show that if these objects can be listed in polynomial time for a class of graphs the treewidth and the minimum fill in are polynomially tractable for these graphs we prove that for all classes of graphs for which polynomial algorithms computing the treewidth and the minimum fill in exist we can list their potential maximal cliques in polynomial time our approach unifies these algorithms finally we show how to compute in polynomial time the potential maximal cliques of weakly triangulated graphs for which the treewidth and the minimum fill in problems were open

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

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

velocity dependent cost function for the prediction of force sharing among synergistic muscles in a one degree of freedom model prediction of accurate and meaningful force sharing among synergistic muscles is a major problem in biomechanics research given a resultant joint moment a unique set of muscle forces can be obtained from this mathematically redundant system using nonlinear optimization the classical cost functions for optimization involve a normalization of the muscle forces to the absolute force capacity of the target muscles usually by the cross sectional area or the maximal isometric force in a one degree of freedom model this leads to a functional relationship between moment arms and the predicted muscle forces such that for constant moment arms or constant ratios of moment arms agonistic muscle forces increase or decrease in unison experimental studies have shown however that the relationship between muscle forces is highly task dependent often causing forces to increase in one muscle while decreasing in a functional agonist likely because of the contractile conditions and contractile properties of the involved muscles we therefore suggest a modified cost function that accounts for the instantaneous contraction velocity of the muscles and its effect on the instantaneous maximal force with this novel objective function a task dependent prediction of muscle force distribution is obtained that allows even in a one degree of freedom system the prediction of force sharing loops and simultaneously increasing and decreasing forces for agonist pairs of muscles

dynamic coordinate data for describing muscle tendon paths a mathematical approach when modelling the musculoskeletal system over a range of joint angles the use of fixed points to describe muscle tendon paths has inherent limitations these result in fewer deflection points and the use of effective insertions to accommodate both relative marker movement and avoid muscle paths contacting bony structures model performance is dependent on the joint angle relative to the anatomical position where the muscle tendon paths were defined the present study proposes a scheme for the implementation of dynamic coordinates for describing muscle tendon paths for each muscle tendon element a plane is defined in which the muscle tendon complex acts when crossing a given joint the muscle tendon plane is dependent on 3d segment orientations and describes one degree of freedom while the remaining two degrees of freedom are described by polar coordinates and locate the dynamic point in the muscle tendon plane the dynamic approach is implemented on four muscles of the lower limb in modelled and simulated joint movements and offers a significant improvement on previous approaches based on fixed deflection points the scheme accommodates compound 3d rotations about joint axes is not computationally difficult or require large data sets and does not impose limitations on the number of points that may be defined along a muscle tendon path

a globally convergent angular velocity observer for rigid body motion the problem of obtaining the angular velocity of a rigid body from orientation and torque measurements only without noisy numerical differentiation is considered a novel angular velocity angular momentum observer for rigid body motion is presented using euler quaternions and a mechanical energy function approach it is shown that the observer estimates converge globally and that the convergence is eventually exponential it is hoped that a mechanical energy function approach to rigid body control can be combined with the observer presented to lead to a globally stable nonlinear observer based rigid body controller in which the observer and controller errors can be separated in much the same way as one can separate controller and observer poles in the output feedback controllers of linear system theory