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

sine gordon theory in a semi strip abstract initial boundary value problems for sine gordon and complex sine gordon equations in a semi strip are treated the evolution of the weyl function and a uniqueness result are obtained for the complex sine gordon equation the evolution of the weyl function as well as an existence result and a procedure to recover solution are given for the sine gordon equation it is shown that for a wide class of examples the solutions of the sine gordon equation are unbounded in the quarter plane

boundary value problems for the laplacian in convex and semiconvex domains abstract we study the fully inhomogeneous dirichlet problem for the laplacian in bounded convex domains in r n when the size smoothness of both the data and the solution are measured on scales of besov and triebel lizorkin spaces as a preamble we deal with the dirichlet and regularity problems for harmonic functions in convex domains with optimal nontangential maximal function estimates as a corollary sharp estimates for the green potential are obtained in a variety of contexts including local hardy spaces a substantial part of this analysis applies to bounded semiconvex domains i e lipschitz domains satisfying a uniform exterior ball condition

on a nonlinear boundary value problem modeling corneal shape in this paper we present some results concerning a boundary value problem for a nonlinear ordinary differential equation that was used before in modeling the topography of human cornea these results generalize previously obtained theorems on existence and uniqueness we show that our equation has a unique solution for all parameters and conditions that can arise in physical situation in the second part of the article we derive some new estimates and approximate solutions numerical calculations verify that these approximations are very accurate

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

the canonical symmetry for integrable systems the properties of discrete nonlinear symmetries of integrable equations are investigated these symmetries are shown to be canonical transformations on the basis of the considered examples it is concluded that the densities of the conservation laws are changed under these transformations by spatial divergencies

hp theory on a smooth domain in rn and elliptic boundary value problems in this paper we answer the following two questions question 1 let be an appropriate domain inrn what are the possible natural notions of hp that generalize the usual hardy spaces hp rn we shall see that several versions are possible we concentrate on the two most relevant here which may be considered to be the largest version hpr and the smallest version hpz for the second question consider the dirichlet and neumann problems for the former consists in finding the u g which solves u in and u 0 the latter consists in finding the u g which solves u in and u n 0 question 2 in the context of the relevant hp can one obtain the boundedness of 2g xi xj and g xi xj

weyl titchmarsh m function asymptotics local uniqueness results trace formulas and borg type theorems for dirac operators we explicitly determine the high energy asymptotics for weyl titchmarsh matrices associated with general dirac type operators on half lines and on r we also prove new local uniqueness results for dirac type operators in terms of exponentially small differences of weyl titchmarsh matrices as concrete applications of the asymptotic high energy expansion we derive a trace formula for dirac operators and use it to prove a borg type theorem

sum rules and spectral measures of schrodinger operators with l 2 potentials necessary and sufficient conditions are presented for a positive measure to be the spectral measure of a half line schrodinger operator with square integrable potential

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

the new look on the theory of integrable systems abstract the general properties of canonical discrete transformations of integrable systems are discussed we propose a new group theoretical interpretation for discrete transformation which allows to describe all essential properties of integrable systems as a direct corollary of the theory of representation of the group of discrete transformations

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

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

extension of the discrete kp hierarchy in this paper we discuss possible generalizations of the discrete kp toda lattice hierarchy as a result we introduce the integrable hierarchy which can be considered as the proper extension of the discrete kp hierarchy such extension forces us to introduce an infinite number of additional multi times t n t n 1 x n t n 2 n 2 whereas ordinary discrete kp is relevant to t 1 it is shown that any subsystem of extended discrete kp attached to multi time t n is in fact equivalent to a bi infinite sequence of continuous kp hierarchies whose lax operators are glued together by compatible gauge transformations this paper can be thought of as a natural continuation and generalization of our previous paper svinin a k 2001 j phys a math gen 34 10559 68

nonlinear schrodinger equation in a semi strip evolution of the weyl titchmarsh function and recovery of the initial condition and rectangular matrix solutions from the boundary conditions abstract rectangular matrix solutions of the defocusing nonlinear schrodinger equation dnls are studied in quarter plane and semi strip evolution of the corresponding weyl titchmarsh weyl function is described in terms of the initial weyl function and boundary conditions in the next step the initial weyl function is recovered for the quarter plane case from the long time asymptotics of the wave function considered at the boundary thus it is shown that the evolution of the weyl function is uniquely defined by the boundary conditions moreover a procedure to recover solutions of dnls uniquely defined by the boundary conditions is given in a somewhat different way the same boundary value problem is also dealt with in a semi strip for the case of a quasi analytic initial condition

the development of contact force construction in the dynamic contact task of cycling purposeful movement requires that an individual produce appropriate joint torques to accelerate segments and when environmental contact is involved to develop task appropriate contact forces developmental research has been confined largely to the mastery of unconstrained movement skills pointing kicking the purpose of this study was to study the developmental progression that characterizes the interaction of muscular and non muscular forces in tasks constrained by contact with the environment seven younger children yc 6 8 years 7 older children oc 9 11 years and 7 adults ad pedaled an ergometer 80 rpm at an anthropometrically scaled cycling power resultant forces measured at the pedal s surface were decomposed into muscle inertia and gravity components muscle pedal forces were further examined in terms of the underlying lower extremity joint torques and kinematic weights that constitute the muscular component of the pedal force data showed children applied muscle forces to the pedal in a significantly different manner compared to adults and that this was due to the children s lower segmental mass and inertia the children adjusted the contribution of the proximal joint muscle torques to compensate for reduced contributions to the resultant pedal force by gravitational and inertial components these data show that smaller segmental mass and inertia limit younger children s ability to construct the dynamic contact task of cycling in an adult like form on the basis of these results however the children s response was not immature rather the results show a task appropriate adaptation to lower segmental mass and inertia

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

on the compatibility condition for linear systems and a factorization formula for wave functions the well known compatibility condition for linear systems wx gw and wt fw is considered and new results are obtained in this way a factorization formula for wave functions which is basic in the inverse spectral transform approach to initial boundary value problems is proved in greater generality than before some applications follow

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

hamiltonian properties of the canonical symmetry the properties of the canonical symmetry are investigated the densities of the local conservation laws for the nonlinear schrodinger equation are shown to change under the action of the canonical symmetry by total space derivatives it is also shown how the canonical symmetry can be used to look for the hierarchy of the hamiltonian operators relevant to the system under consideration it appears that only the invariance condition can be used to solve the problem

elbow scattering and inverse scattering applications to lkdv and kdv it is well known that many integrable partial differential equations are consistency conditions of a lax pair of linear differential equations whose variables x t can be considered as coordinates in a plane the standard inverse scattering method and the standard direct linearization methods are related to the scattering problem defined on the x axis in a previous paper the scattering problem defined on the t axis was considered here the scattering on an unbounded line of the plane an elbow is defined and it is shown how it can yield new reconstruction methods for the solutions of the consistency condition the results are neither as complete or as much interesting as the standard ist but their derivation shows that defining the wanted class of solutions is crucial and it helps understanding why the standard ist is so simple

the forced toda lattice an example of an almost integrable system a method for solving forced integrable systems is presented the method requires the knowledge of at least one piece of information about the solution once this is known one may then construct the remainder of the solution in this sense these systems are almost integrable the forced semi infinite toda lattice is used as an example and to illustrate the method

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

on the rigorous foundations of the fokas method for linear elliptic partial differential equations in this paper we address some of the rigorous foundations of the fokas method confining attention to boundary value problems for linear elliptic partial differential equations on bounded convex domains the central object in the method is the global relation which is an integral equation in the spectral fourier space that couples the given boundary data with the unknown boundary values using techniques from complex analysis of several variables we prove that a solution to the global relation provides a solution to the corresponding boundary value problem and that the solution to the global relation is unique the result holds for any number of spatial dimensions and for a variety of boundary value problems

on modified nls kaup and nlbq equations differential transformations and bilinearization new transformations between the nonlinear schrodinger kaup and non local boussinesq equations as well as their modified counterparts are found and analysed the bilinear representations of these equations including an alternative bilinear form of the chen lee liu equation are obtained by a direct method based on the bell s exponential polynomials explicit wronskian solutions to these equations are also presented

inhomogeneous neumann initial boundary value problem for the nonlinear schrodinger equation abstract we consider the inhomogeneous neumann initial boundary value problem for the nonlinear schrodinger equation formulated on a half line we study traditionally important problems of the theory of nonlinear partial differential equations such as global in time existence of solutions to the initial boundary value problem and the asymptotic behavior of solutions for large time

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

a uniqueness theorem for an inverse boundary value problem in two dimensions abstract we consider the inverse problem to determine the potential q entering the schrodinger equation u qu 0 in a bounded smooth domain in r 2 in terms of the boundary measurements dirichlet to neumann map when n 3 the uniqueness for the inverse problem was well established in this paper we prove the uniqueness in two dimensions under the assumption that the lp p 2 norm of q is small this result improves a uniqueness result of sylvester uhlmann under the assumption that the w1 norm of q is small