an approximation procedure for the zakharov shabat scattering problem for real single humped potentials a procedure is presented for finding simple approximations of the discrete eigenvalues of the zakharov shabat scattering problem corresponding to the nonlinear schrodinger equation the approximation is in the form of an interpolation formula which combines results for small eigenvalues obtained by a direct variational approach and for large eigenvalues obtained by the bohr sommerfeld quantization rule

optimization based differential kinematic modeling exhibits a velocity control strategy for dynamic posture determination in seated reaching movements abstract we proposed a velocity control strategy for dynamic posture determination that underlay an optimization based differential inverse kinematics odik approach for modeling three dimensional 3 d seated reaching movements in this modeling approach a four segment seven dof linkage is employed to represent the torso and right arm kinematic redundancy is resolved efficiently in the velocity domain via a weighted pseudoinverse weights assigned to individual dof describe their relative movement contribution in response to an instantaneous postural change different schemes of posing constraints on the weighting parameters by which various motion apportionment strategies are modeled can be hypothesized and evaluated against empirical measurements a numerical optimization procedure based on simulated annealing estimate the weighting parameter values such that the predicted movement best fits the measurement we applied this approach to modeling 72 seated reaching movements of three distinctive types performed by six subjects results indicated that most of the movements were accurately modeled time averaged rmse

the sensitivity of muscle force predictions to changes in physiologic cross sectional area abstract the mechanical effects of a muscle are related in part to the size of the muscle and to its location relative to the joint it crosses for more than a century researchers have expressed muscle size by its physiological cross sectional area pcsa researchers mathematically calculating muscle and joint forces typically use some expression of a muscle s pcsa to constrain the solution to one which is reasonable i e a solution in which small muscles may not have large forces and large muscles have large forces when expected or when there is significant electromyographic activity it is obvious that muscle mass and therefore any expression of pcsa varies significantly from person to person even in individuals of similar weight and height since it is not practical to predict the pcsa of each muscle in a living subject s limb or trunk it is important to generally understand the sensitivity of muscle force solutions to possible variations in pcsa we used nonlinear optimization techniques to predict 47 muscle forces and hip contact forces in a living subject the pcsa volume muscle fiber length of each of 47 lower limb muscle elements from two cadaver specimens and the 47 pcsa s reported by pierrynowski were input into an optimization algorithm to create three solution sets the three solutions were qualitatively similar but at times a predicted muscle force could vary as much as two to eight times in contrast the joint force solutions were within 11 of each other and therefore much less variable when using optimization techniques to predict muscle forces it must be recognized that the solution is sensitive to many assumptions and variables such as pcsa the muscle force solutions are therefore best used to determine relative values i e trends in parametric studies on the other hand the joint force solutions are less sensitive to such variations and the absolute values are more reliable

variational approach to the zakharov shabat scattering problem it is shown that the zakharov shabat scattering problem associated with the inverse scattering transform technique for solving the nonlinear schr odinger equation can be reformulated as a variational problem this reformulation makes it possible to use direct variational methods for finding the eigenvalues of the scattering problem which determines the speed and amplitude of the solitons emerging from a given initial condition the approach is illustrated by an application to sech shaped initial conditions

sensitivity of dynamic simulations of gait and dynamometer experiments to hill muscle model parameters of knee flexors and extensors we assessed and compared sensitivities of dynamic simulations to musculotendon mt parameters for gait and dynamometer experiments our aim with this comparison was to investigate whether dynamometer experiments could provide information about mt parameters that are important to reliably study mt function during gait this would mean that dynamometer experiments could be used to estimate these parameters muscle contribution to the joint torque mt torque rather than relative mt force primarily affects the resulting gait pattern and torque measured by the dynamometer in contrast to recent studies therefore we assessed the sensitivity of the mt torque rather than the sensitivity of the relative mt force based on sensitivity of the mt torque to a parameter perturbation mt parameters of the knee flexors and extensors were classified in three categories low medium and high for gait classification was based on the average sensitivity during a gait cycle for isometric and isokinetic dynamometer experiments classification was based on the highest sensitivity found in the experiments the calculated muscle contributions to the knee torque during gait and dynamometer experiments had a high sensitivity to only a limited number of mt parameters of the knee flexors and extensors suggesting that not all mt parameters need to be estimated in general the highest sensitivity was found for tendon slack length however for some muscles the sensitivity to the optimal fibre length or the maximal isometric muscle force was also high or medium the classification of the individual mt parameters for gait and dynamometer experiments was largely similar we therefore conclude that dynamometer experiments provide information about mt parameters important to reliably study mt function during gait so that subject specific estimates of mt parameters could be made based on dynamometer experiments

application and validation of a three dimensional mathematical model of the human masticatory system in vivo abstract a previously described three dimensional mathematical model of the human masticatory system predicting maximum possible bite forces in all directions and the recruitment patterns of the masticatory muscles necessary to generate these forces was validated in in vivo experiments the morphological input parameters to the model for individual subjects were collected using mri scanning of the jaw system experimental measurements included recording of maximum voluntary bite force magnitude and direction and surface emg from the temporalis and masseter muscles for bite forces with an angle of 0 10 and 20 relative to the normal to the occlusal plane the predicted maximum possible bite forces were between 0 9 and 1 2 times the measured ones and the average ratio of measured to predicted maximum bite force was close to unity the average measured and predicted muscle recruitment patterns showed no striking differences nevertheless some systematic differences dependent on the bite force direction were found between the predicted and the measured maximum possible bite forces in a second series of simulations the influence of the direction of the joint reaction forces on these errors was studied the results suggest that they were caused primarily by an improper determination of the joint force directions

minimum energy trajectories of the swing ankle when stepping over obstacles of different heights this study was performed to test the hypothesis that the motion of the lower extremities when stepping over obstacles is governed by the criterion of minimum mechanical energy the trajectories of the swing ankle during level walking and when stepping over obstacles of 51 102 153 and 204 mm heights were predicted and measured for eight healthy young adults the predictions were made with a planar seven link linkage model based on the criterion of minimum mechanical energy using the method of dynamic programming when stepping over obstacles the predicted trajectories of the swing ankle were just high enough for the swing toe to clear the obstacles the clearances measured between the obstacle and toe were significantly larger than those predicted when stepping over obstacles the levels of work required to generate the measured trajectories were significantly larger p or 0 002 than those required to produce the predicted trajectories the amount of work necessary to generate the measured or predicted trajectories increased linearly significant at p or 0 022 with obstacle height and except when predicting the trajectory for the lowest obstacle was significantly greater than that required when walking on level ground p 0 02 thus conservation of energy was found to become a less dominant criterion for governing the motion of the body when crossing obstacles than when walking on level ground

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

spectral parameter power series for sturm liouville equations with a potential polynomially dependent on the spectral parameter and zakharov shabat systems a spectral parameter power series spps representation for solutions of sturm liouville equations of the form pu qu u k 1n krk is obtained such equations are known as sturm liouville equations with potentials polynomially dependent on the spectral parameter or sturm liouville pencils slp it allows one to write a general solution of the equation as a power series in terms of the spectral parameter the coefficients of the series are given in terms of recursive integrals involving a particular solution of the equation pu0 qu0 0 the convenient form of the solution of slp provides an efficient numerical method for solving corresponding initial value boundary value and spectral problems a special case of the slp arises in relation with the zakharov shabat system we derive a spps representation for its general solution and consider other applications as the one dimensional dirac system and the equation describing a damped string several numerical examples illustrate the efficiency and the accur

multivariable optimization of cycling biomechanics relying on a biomechanical model of the lower limb which treats the leg bicycle system as a five bar linkage constrained to plane motion a cost function derived from the joint moments developed during cycling is computed at constant average power of 200 w the effect of five variables on the cost function is studied the five variables are pedalling rate crank arm length seat tube angle seat height and longitudinal foot position on the pedal a sensitivity analysis of each of the five variables shows that pedalling rate is the most sensitive followed by the crank arm length seat tube angle seat height and longitudinal foot position on the pedal the least sensitive based on powell s method a multivariable optimization search is made for the combination of variable values which minimize the cost function for a rider of average anthropometry height 1 78 m weight 72 5 kg a pedalling rate of 115 rev min 1 crank arm length of 0 140 m seat tube angle of 76 seat height plus crank arm length equal to 97 of trochanteric leg length and longitudinal foot position on the pedal equal to 54 of foot length correspond to the cost function global minimum the effect of anthropometric parameter variations is also examined and these variations influence the results significantly the optimal crank arm length seat height and longitudinal foot position on the pedal increase as the size of rider increases whereas the optimal cadence and seat tube angle decrease as the rider s size increases the dependence of optimization results on anthropometric parameters emphasizes the importance of tailoring bicycle equipment to the anthropometry of the individual

muscle activities of the lower limb during level and uphill running this study aimed to compare the muscle activities of the lower limb during overground level running lr and uphill running ur by using a musculoskeletal model six male distance runners ran at three running speeds slow 3 3 m s medium 4 2 m s and high 5 0 m s on a level runway and a slope of 9 1 grade in which force platforms were mounted a musculoskeletal leg model and optimization were used to estimate the muscle activation and muscle torque from the joint torque of the lower limb calculated by the inverse dynamics approach at high speed the activation and muscle torque of the muscle groups surrounding the hip joints such as the hamstrings and iliopsoas during the recovery phase were significantly greater during ur than during lr at all the running speeds the knee extension torque by the vasti during the support phase was significantly smaller during ur further the hip flexion and knee extension torques by the rectus femoris during ur were significantly greater than those during lr at all the speeds this would play a role in compensating for the decrease in the knee extension torque by the vasti and in maintaining the trunk in a forward leaning position these results revealed that the activation and muscle torque of the hip extensors and flexors were augmented during ur at the high speed

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

are the maximum shortening velocity and the shape parameter in a hill type model of whole muscle related to activation abstract mathematical models of the inter relationship of muscle force velocity and activation are useful in forward dynamic simulations of human movement tasks the objective of this work was to determine whether the parameters maximum shortening velocity v max and shape parameter k of a hill type muscle model interrelating muscle force velocity and activation are themselves dependent on the activation to fulfill this objective surface emg signals from four muscles as well as the kinematics and kinetics of the arm were recorded from 14 subjects who performed rapid release elbow extension tasks at 25 50 75 and 100 activation mvc the experimental elbow flexion angle was tracked by a forward dynamic simulation of the task in which v max and k of the triceps brachii were varied at each activation level to minimize the difference between the simulated and experimental elbow flexion angle because a preliminary analysis demonstrated no dependency of k on activation additional simulations were performed with constant k values of 0 15 0 20 and 0 25 the optimized values of v max normalized to the average value within a subject were then regressed onto the activation normalized v max depended significantly on the activation p k furthermore the estimated v max values were not sensitive to the selected k value the results support the use of hill type models in which v max depends on activation in forward dynamic simulations modeling muscles with mixed fiber type composition recruited in the range of 25 100 activation the use of more accurate models will lend greater confidence to the results of forward dynamic simulations

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

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

a non invasive protocol to determine the personalized moment arms of knee and ankle muscles one difficulty that comes with predicting muscular forces is the accuracy of experimental data particularly the assessment of muscle moment arms with respect to each joint rotation axis this paper presents a non invasive experimental protocol to obtain the personalized muscle moment arms with respect to the ankle and knee joints a specific pointer is used by a specialist of lower limb anatomy in order to define the local portion of the line of action of the different muscles closed to the joint on the standing subject s lower limb with this pointer the three dimensional coordinates of several points representing the line of action of 12 ankle and knee muscles are collected by a motion analysis system the collection is done five times by the same operator and one time by two different operators from this data the intra and inter operator repeatabilities are tested relative icc and absolute sem reliabilities are determined in order to evaluate the intra operator repeatability of this non invasive protocol the icc values obtained are higher than 0 91 for 10 among 12 muscles the intra operator repeatability is thus confirmed from the records realized by the two operators the differences are negligible thus the inter operator repeatability is also confirmed the moments arms obtained using this non invasive experimental protocol are compared with those calculated from origin and insertion points reported in the literature according to the work of whites pierrynowskis and kepples respectively the estimations obtained using the non invasive experimental protocol are found for some muscles more realistic than those calculated using the literature data and are always coherent with the role of the muscles described in anatomical books

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

subject specific knee joint geometry improves predictions of medial tibiofemoral contact forces estimating tibiofemoral joint contact forces is important for understanding the initiation and progression of knee osteoarthritis however tibiofemoral contact force predictions are influenced by many factors including muscle forces and anatomical representations of the knee joint this study aimed to investigate the influence of subject specific geometry and knee joint kinematics on the prediction of tibiofemoral contact forces using a calibrated emg driven neuromusculoskeletal model of the knee one participant fitted with an instrumented total knee replacement walked at a self selected speed while medial and lateral tibiofemoral contact forces ground reaction forces whole body kinematics and lower limb muscle activity were simultaneously measured the combination of generic and subject specific knee joint geometry and kinematics resulted in four different opensim models used to estimate muscle tendon lengths and moment arms the subject specific geometric model was created from ct scans and the subject specific knee joint kinematics representing the translation of the tibia relative to the femur was obtained from fluoroscopy the emg driven model was calibrated using one walking trial but with three different cost functions that tracked the knee flexion extension moments with and without constraint over the estimated joint contact forces the calibrated models then predicted the medial and lateral tibiofemoral contact forces for five other different walking trials the use of subject specific models with minimization of the peak tibiofemoral contact forces improved the accuracy of medial contact forces by 47 and lateral contact forces by 7 respectively compared with the use of generic musculoskeletal model

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

functional muscle synergies constrain force production during postural tasks abstract we recently demonstrated that a set of five functional muscle synergies were sufficient to characterize both hindlimb muscle activity and active forces during automatic postural responses in cats standing at multiple postural configurations this characterization depended critically upon the assumption that the endpoint force vector synergy force vector produced by the activation of each muscle synergy rotated with the limb axis as the hindlimb posture varied in the sagittal plane here we used a detailed 3d static model of the hindlimb to confirm that this assumption is biomechanically plausible as we varied the model posture simulated synergy force vectors rotated monotonically with the limb axis in the parasagittal plane r 2 0 94 0 08 we then tested whether a neural strategy of using these five functional muscle synergies provides the same force generating capability as controlling each of the 31 muscles individually we compared feasible force sets ffss from the model with and without a muscle synergy organization ffs volumes were significantly reduced with the muscle synergy organization f 1556 01 p 0 01 and as posture varied the synergy limited ffss changed in shape consistent with changes in experimentally measured active forces in contrast nominal ffs shapes were invariant with posture reinforcing prior findings that postural forces cannot be predicted by hindlimb biomechanics alone we propose that an internal model for postural force generation may coordinate functional muscle synergies that are invariant in intrinsic limb coordinates and this reduced dimension control scheme reduces the set of forces available for postural control

determination of subject specific model parameters for visco elastic elements the determination of subject specific model parameter values is necessary in order for a computer simulation model of human motion to be evaluated quantitatively this study used an optimisation procedure along with a kinematically driven simulation model of the contact phase in running jumps to determine the elastic parameters of segmental wobbling masses and the foot ground interface kinetic and kinematic data were obtained on running jumps for height and distance performed by an elite male high jumper stiffness and damping coefficients of the visco elastic elements in the model were varied until the difference between simulation and performance was minimised percentage differences of 6 and 9 between the simulated and recorded performances were obtained in the jumps for height and distance respectively when the parameters obtained from the jump for height were used in a simulation of the jump for distance and vice versa there was poor agreement with the recorded jump on the other hand a common set of visco elastic parameters were obtained using the data from both recorded jumps resulting in a mean difference of only 8 made up of 7 and 10 between simulation and performance that was almost as good as the individual matches simulations were not overly sensitive to perturbations of the common set of visco elastic parameters it is concluded that subject specific elastic parameters should be calculated from more than a single jump in order to provide a robust set of values that can be used in different simulations

theoretical considerations on cocontraction of sets of agonistic and antagonistic muscles it is well known that static non linear minimization of the sum of the stress in muscles to a certain power cannot predict cocontraction of pairs of one joint antagonistic muscles in this report we prove that for a single joint either all agonistic muscles cocontract or all are silent for two joint muscles we show that lengthening and shortening of muscles corresponds closely to zero force and non zero force states respectively this gives a new physiological interpretation of situations in which cocontraction of pairs of two joint antagonistic muscles is predicted by these static non linear optimization approaches

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

variational principle for zakharov shabat equations in two dimensions we study the corresponding scattering problem for zakharov and shabat compatible differential equations in two dimensions the representation for a solution of the nonlinear schrodinger equation is formulated as a variational problem in two dimensions we extend the derivation to the variational principle for the zakharov and shabat equations in one dimension we also developed an approximate analytical technique for finding discrete eigenvalues of the complex spectral parameters in zakharov and shabat equations for a given pulse shaped potential which is equivalent to the physically important problem of finding the soliton content of the given initial pulse using a trial function in a rectangular box we find the functional integral the general case for the two box potential can be obtained on the basis of a different ansatz where we approximate the jost function by polynomials of order n instead of a piecewise linear function we also demonstrated that the simplest version of the variational approximation based on trial functions with one two and n free parameters respectively and treated analytically

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

hip joint contact loads in older adults during recovery from forward loss of balance by stepping hip joint contact loads during activities of daily living are not generally considered high enough to cause acute bone or joint injury however there is some evidence that hip joint loads may be higher in stumble recovery from loss of balance a common laboratory method used to evaluate balance recovery performance involves suddenly releasing participants from various static forward lean magnitudes perturbation intensities prior studies have shown that when released from the same perturbation intensity some older adults are able to recover with a single step whereas others require multiple steps the main purpose of this study was to use a musculoskeletal model to determine the effect of three balance perturbation intensities and the use of single versus multiple recovery steps on hip joint contact loads during recovery from forward loss of balance in community dwelling older adults n 76 we also evaluated the association of peak hip contact loads with perturbation intensity step length and trunk flexion angle at foot contact at each participant s maximum recoverable lean angle mrla peak hip joint contact loads were computed using muscle force estimates obtained using static optimisation and increased as lean magnitude was increased and were on average 32 higher for single steppers compared to multiple steppers at the mrla peak hip contact loads ranged from 4 3 to 12 7 body weights and multiple linear stepwise regression further revealed that initial lean angle step length and trunk angle at foot contact together explained 27 of the total variance in hip joint contact load overall findings indicated that older adults experience peak hip joint contact loads during maximal balance recovery by stepping that in some cases exceeded loads reported to cause mechanical failure of cadaver femurs while step length and trunk flexion angle are strong predictors of step recovery performance they are at best moderate predictors of peak hip joint loading

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

in response to sensitivity of predicted muscle forces to parameters of the optimization based human leg model revealed by analytical and numerical analysis by r t raikova and b i prilutsky and a physiologically based criterion of muscle force prediction in locomotion by r d crowninsheild and r a brand

comparison meaningful operators and ordinal invariant preferences this work has been partially supported by the research projects eco2012 34828 mtm2012 37894 c02 02 and tin2013 40765 p spain

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

the effect of strict muscle stress limits on abdominal muscle force predictions for combined torsion and extension loadings the objective of this study was to determine to what extent the central nervous system activates torso muscles so as to equalize the largest muscle stresses two optimization models that treat large muscle stresses differently were formulated one model minimized spinal compression force subject to the lowest possible muscle stress limit and the other model minimized the sum of cubed muscle stresses experimental conditions were determined for which the two models made different muscle force predictions specifically the models predicted different rectus abdominis activity levels for tasks involving torsion and extension moment loadings surface electromyography was used to evaluate the model predictions applied loads were chosen to assure that the rectus abdominis emg exceeded 30 mvc analysis of variance indicated that rectus abdominis activity was not affected by torsion loading at the p 0 05 level of significance in a statistical design having 90 power which was consistent with the predictions of the model that minimized the sum of cubed muscle stresses thus it was concluded that equalization of the largest muscles stress was not the paramount objective of the central nervous system in the tasks studied

homothetic and translatable preferences utility representation and functional equations involved abstract i provide a full characterization of those preferences total preorders defined on r n that admit a representation by means of a continuous homogeneous of degree one and translative utility order preserving function in addition i pay attention to the functional form of the kind of representation obtained including some qualifications such as being continuous and or monotonic in particular a full description of the functions f r 3 r that are continuous homogeneous of degree one translative and monotonic is presented further applications to utility theory and social choice theory are also provided

variational principle of the zakharov shabat equations abstract we put forth a variational principle for the zakharov shabat zs equations which is the basis of the inverse scattering transform of a number of important nonlinear pde s using the variational representation of the zs equations we develop an approximate analytical technique for finding discrete eigenvalues of the complex spectral parameter in the zs equations for a given pulse shaped potential which is equivalent to the physically important problem of finding the soliton content of the given initial pulse we apply the technique to several particular shapes of the pulse and demonstrate that the simplest version of the variational approximation based on trial functions with one or two free parameters proves to be fully analytically tractable and it yields threshold conditions for the appearance of the first soliton or of the first soliton pair which are in a fairly good agreement with available numerical results however more free parameters are necessary to allow prediction of additional solitons produced by the given pulse

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

variation of muscle moment arms with elbow and forearm position we hypothesized that the moment arms of muscles crossing the elbow vary substantially with forearm and elbow position and that these variations could be represented using a three dimensional computer model flexion extension and pronation supination moment arms of the brachioradialis biceps brachialis pronator teres and triceps were calculated from measurements of tendon displacement and joint angle in two anatomic specimens and were estimated using a computer model of the elbow joint the anatomical measurements revealed that the flexion extension moment arms varied by at least 30 over a 95 degrees range of motion the changes in flexion extension moment arm magnitudes with elbow flexion angle were represented well by the computer model the anatomical studies and the computer model demonstrate that the biceps flexion moment arm peaks in a more extended elbow position and has a larger peak when the forearm is supinated also the peak biceps supination moment arm decreases as the elbow is extended these results emphasize the need to account for the variation of muscle moment arms with elbow flexion and forearm position

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

sensitivity of subject specific models to errors in musculo skeletal geometry subject specific musculo skeletal models of the lower extremity are an important tool for investigating various biomechanical problems for instance the results of surgery such as joint replacements and tendon transfers the aim of this study was to assess the potential effects of errors in musculo skeletal geometry on subject specific model results we performed an extensive sensitivity analysis to quantify the effect of the perturbation of origin insertion and via points of each of the 56 musculo tendon parts contained in the model we used two metrics namely a local sensitivity index lsi and an overall sensitivity index osi to distinguish the effect of the perturbation on the predicted force produced by only the perturbed musculo tendon parts and by all the remaining musculo tendon parts respectively during a simulated gait cycle results indicated that for each musculo tendon part only two points show a significant sensitivity its origin or pseudo origin point and its insertion or pseudo insertion point the most sensitive points belong to those musculo tendon parts that act as prime movers in the walking movement insertion point of the achilles tendon lsi 15 56 osi 7 17 origin points of the rectus femoris lsi 13 89 osi 2 44 and as hip stabilizers insertion points of the gluteus medius anterior lsi 17 92 osi 2 79 insertion point of the gluteus minimus lsi 21 71 osi 2 41 the proposed priority list provides quantitative information to improve the predictive accuracy of subject specific musculo skeletal models

is a joint moment based cost function associated with preferred cycling cadence eight experienced male cyclists c eight well trained male runners r and eight less trained male noncyclists lt were tested under multiple cadence and power output conditions to determine 1 if the cadence at which lower extremity net joint moments are minimized cost function cadence was associated with preferred pedaling cadence pc 2 if the cost function cadence increased with increases in power output and 3 if the association is generalizable across groups di ering in cycling experience and aerobic power net joint moments at the hip knee and ankle were computed from video records and pedal reaction force data using 2 d inverse dynamics the sum of the average absolute hip knee and ankle joint moments de ned a cost function at each power output and cadence and provided the basis for prediction of the cadence which minimized net joint moments for each subject at each power output the cost function cadence was not statistically di erent from the pc at each power output in all groups as power output increased however the cost function cadence increased for all three subject groups 86 rpm at 100 w 93 rpm at 150 w 98 rpm at 200 w and 96 rpm at 250 w pc showed little change r or a modest decline c lt with increasing power output based upon the similarity in the mean data but di erent trends in the cost function cadence and pc in response to changes in power output as well as the lack of signi cant correlations between these two variables it was concluded that minimizing net joint moments is a factor modestly associated with preferred cadence selection 2000 elsevier science ltd all rights reserved

evaluating the effect of co contraction in optimization models the effect of co contraction of antagonist muscles on spinal compression force is estimated using karush kuhn tucker k k t multipliers co contraction is modelled as an incremental increase in the lower bounds on the allowable muscle forces in an optimization model formation the k k t multipliers associated with each lower bound provide an estimate of the partial derivate of the optimal objective function value with respect to a change in the lower bound a model whose objective function is spinal compression force is analyzed to estimate the effect of co contraction on spinal compression force while the effect depends on the specific muscle and task under consideration the marginal effect of co contraction on spinal compression force can be as high as 5 52 n additional spinal compression force for every additional n of muscle force paradoxically the co contraction may slightly decrease predicted spinal compression in special circumstances

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

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

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

a general approach for modelling and mathematical investigation of the human upper limb this paper is an attempt to systematize and solve the problems connected with biomechanical modelling and mathematical investigation of the upper limb when all muscles acting on the shoulder elbow and wrist joint are included the basic problem is the assumption of a hypothesis for the unit vectors collinear with muscle forces the so called segment lines modelling of the muscle force direction is proposed for solving this problem this approach combines the simplicity of the straight line joining the muscle tendon origin to the insertion point its application for the analytical description of the model and the real description of the muscle anatomical functions the principle of the anatomically adequate moment is the general criterion for choosing the segments straight and curvilinear sections by which the direction of the muscle action is replaced the different optimization techniques which are used for solving the statically indeterminate problem formulated for musculoskeletal biomechanical models are considered aiming to obtain strictly positive and continuous solutions for the muscle forces moduli the application of the lagrange multipliers method is proposed the possibility of applying different optimization criteria is explored a general conclusion may be formulated if there exists any criterion which is independent of the joint angles it follows than that it must be dependent on the joint reactions and in addition it must be nonlinearly dependent on the muscle forces moduli

extension of a state of the art optimization criterion to predict co contraction most studies concerned with the prediction of muscle forces have tried to predict a physiologically reasonable synergistic muscle behavior in addition to the load sharing of synergistic muscles co contraction of antagonistic muscles also occurs an extension to a standard quadratic criterion for the calculation of muscle forces is presented in this study this extension however is not limited to quadratic optimization the extension is applied to a planar one degree of freedom model of the human knee for this model an analytical solution is presented with the extended criterion it was possible to predict and control the amount of co contraction for the knee model the enforced antagonistic muscle activity led to higher agonistic muscle activity in the absence of an external load flexor and extensor muscles were activated as a consequence the knee joint was preloaded this might indicate that antagonistic muscle activity is generated to maintain or improve joint stability in conclusion this study presents a novel approach to predict co contraction when using optimization techniques to determine muscle forces by introducing a shift parameter for the optimization criterion

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

moment distribution among human elbow extensor muscles during isometric and submaximal extension to understand better how the central nervous system cns distributes a joint moment among muscles moment distribution among the three heads of the triceps and the anconeus muscles during isometric elbow extension was quantified in vivo and noninvasively electrical stimulation was used to activate an individual muscle selectively at various contraction levels and the relationship between the peak m wave amplitude and peak elbow extension moment was established across various contraction levels for each muscle the relationship was then used to calibrate the corresponding emg signal and determine moment distribution among the muscles during voluntary isometric elbow extension results showed that moment distribution among muscles was not proportional to the muscles physiological cross sectional areas pcsa and the cns favored uniarticular muscles for the isometric task performed the uniarticular lateral and medial heads of the triceps were dominant contributing approximately 70 90 of the total elbow extension moment and the anconeus contributed significantly especially at the lower levels of elbow extension moment up to approximately 15 of the extension moment in contrast the two joint long head of the triceps contributed significantly less than the uniarticular heads of the triceps while the absolute contributions of all the muscles increased with the total elbow extension moment the relative contributions of the muscles may increase or decrease with the elbow extension moment cross validation using fresh data not used in determining the moment distribution showed close match between the measured and predicted elbow extension moment except for trials in which fatigue became significant

a theoretical analysis of preferred pedaling rate selection in endurance cycling one objective of this study was to investigate whether neuromuscular quantities were associated with preferred pedaling rate selection during submaximal steady state cycling from a theoretical perspective using a musculoskeletal model with an optimal control analysis specific neuromuscular quantities of interest were the individual muscle activation force stress and endurance to achieve this objective a forward dynamic model of cycling and optimization framework were used to simulate pedaling at three different rates of 75 90 and 105 rpm at 265 w the pedaling simulations were produced by optimizing the individual muscle excitation timing and magnitude to reproduce experimentally collected data the results from these pedaling simulations indicated that all neuromuscular quantities were minimized at 90 rpm when summed across muscles in the context of endurance cycling these results suggest that minimizing neuromuscular fatigue is an important mechanism in pedaling rate selection a second objective was to determine whether any of these quantities could be used to predict the preferred pedaling rate by using the quantities with the strongest quadratic trends as the performance criterion to be minimized in an optimal control analysis these quantities were analyzed to assess whether they could be further minimized at 90 rpm and produce normal pedaling mechanics the results showed that both the integrated muscle activation and average endurance summed across all muscles could be further minimized at 90 rpm indicating that these quantities cannot be used individually to predict preferred pedaling rates

a biomechanical analysis of muscle strength as a limiting factor in standing posture we developed a method for studying muscular coordination and strength in multijoint movements and have applied it to standing posture the method is based on a musculoskeletal model of the human lower extremity in the sagittal plane and a technique to visualize geometrically how constraints internal and external to the body affect movement we developed an algorithm to calculate the set of all feasible accelerations i e the feasible acceleration set or fas that muscles can induce for the ankle knee and hip joints in the sagittal plane this set is a polyhedron in three dimensions using the volume of the fas as an indicator of overall mobility we found that strengthening muscles on the posterior side as opposed to the anterior of the body would cause greater increases in mobility employing the experimental observations of others we also found that acceleration constraints greatly reduce the range of feasible accelerations we then defined a set of four basic acceleration vectors which when used in various combinations can produce the repertoire of postural movements we used linear programming to find the maximum magnitudes of these vectors and the sensitivity of these magnitudes to muscle strength thereby delineating those muscles which if strengthened would cause the greatest increase in the body s ability to generate the basic acceleration vectors for our particular model those muscle groups were found to be hamstrings tibialis anterior rectus femoris and gastrocnemius these muscle groups would be of great importance in cases involving severely reduced muscle strength this methodology may therefore be useful for purposes such as design of functional electrical stimulation controllers or exercises for persons at risk for falling

bivariate optimization of pedalling rate and crank arm length in cycling the contribution of this paper is a bivariate optimization of cycling performance relying on a biomechanical model of the lower limb a cost function derived from the joint moments developed during cycling is computed at constant average power both pedalling rate i e rpm and crank arm length are systematically varied to explore the relation between these variables and the cost function a crank arm length of 170 mm and pedalling rate of 100 rpm correspond closely to the cost function minimum in cycling situations where the rpm deviates from 100 rpm however crank arms of length other than 170 mm yield minimum cost function values in addition the sensitivity of optimization results to both increased power and anthropometric parameter variations is examined at increased power the cost function minimum is more strongly related to the pedalling rate with higher pedalling rates corresponding to the minimum anthropometric parameter variations influence the results significantly in general it is found that the cost function minimum for tall people occurs at longer crank arm lengths and lower pedalling rates than the length and rate for short people

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