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

finite time stability of quantum systems governed by schrodinger s equation in this paper we investigate the finite time stability fts and finite time boundedness ftb of quantum systems which are governed by schrodinger s equation we first study the fts and fts at one target state and propose new results for the mentioned quantum systems in the form of sufficient conditions then we present sufficient conditions for the ftb and ftb at one target state in terms of matrix inequalities one numerical simulation is presented to illustrate the effectiveness of the obtained theoretical result

topological properties of reachable sets and the control of quantum bits abstract we consider the problem of controlling the state of a two level quantum system quantum bit via an externally applied electro magnetic field the describing model is a bilinear right invariant system whose state varies on the lie group of 2 2 special unitary matrices we study the topological structure of the reachable sets if two or more independent controls are used then every state can be achieved in arbitrary time however this is no longer true if only one control is available and in this case we give an exact characterization of states reachable in arbitrary time we prove small time local controllability for any state and the existence of a critical time which is the smallest time after which every transfer of state is possible we provide upper and lower bounds for such a time the mathematical development is motivated by the problem of manipulating the state of a quantum bit every transfer of state may be interpreted as a quantum logic operation and not every logic operation can be obtained in arbitrary time the analysis we present provides information about the feasibility of a given operation as well as estimates for the speed of a quantum computer

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

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

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

are recruitment patterns of the trunk musculature compatible with a synergy based on the maximization of endurance abstract to verify that maximization of endurance is important among the functional criteria determining trunk muscle activation patterns symmetric and asymmetric exertions were simulated using a detailed model consisting of 114 muscle slips crossing the lumbosacral junction and employing a cost function which maximizes endurance first the question whether meaningful comparisons can be made between activity predictions for individual muscle slips and surface emg data recorded from larger anatomical entities was addressed this was answered affirmatively since activation patterns predicted by a coarse and a middle version of the model in which activation was constrained to be equal within 14 or 32 groups of muscle slips were similar to those predicted with each muscle slip controlled independently median correlation coefficients between activity vectors predicted by the simplified models and the detailed model were 0 88 and 0 97 respectively the coarse model underestimated the endurance capacity by a median of 21 the middle model by only 0 7 second predicted activities within anatomical entities defined at this level of detail were compared to reference data derived from the literature lavender et al 1992 human factors 34 239 247 1992 journal of orthopaedic research 10 691 700 vink et al 1988 electromyography and clinical neurophysiology 28 517 525 the predicted activity patterns of the crector spinae external oblique and rectus abdominis muscles closely resembled the emg patterns r2 0 48 0 99 furthermore the observed distribution of activity between parts of the crector spinae muscle was adequately predicted

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

subject specific calibration of neuromuscular parameters enables neuromusculoskeletal models to estimate physiologically plausible hip joint contact forces in healthy adults in vivo hip joint contact forces hjcf can be estimated using computational neuromusculoskeletal nms modelling however different neural solutions can result in different hjcf estimations nms model predictions are also influenced by the selection of neuromuscular parameters which are either based on cadaveric data or calibrated to the individual to date the best combination of neural solution and parameter calibration to obtain plausible estimations of hjcf have not been identified the aim of this study was to determine the effect of three electromyography emg informed neural solution modes emg driven emg hybrid and emg assisted and static optimisation each using three different parameter calibrations uncalibrated minimise joint moments error and minimise joint moments error and peak hjcf on the estimation of hjcf in a healthy population n 23 during walking when compared to existing in vivo data the emg assisted mode and static optimisation produced the most physiologically plausible hjcf when using a nms model calibrated to minimise joint moments error and peak hjcf emg assisted mode produced first and second peaks of 3 55 times body weight bw and 3 97 bw during walking static optimisation produced 3 75 bw and 4 19 bw respectively however compared to static optimisation emg assisted mode generated muscle excitations closer to recorded emg signals average across hip muscles r2 0 60 0 37 versus r2 0 12 0 14 findings suggest that the emg assisted mode combined with minimise joint moments error and peak hjcf calibration is preferable for the estimation of hjcf and generation of realistic load distribution across muscles

quantum measurement based feedback control a nonsmooth time delay control approach this paper addresses the problem of measurement based feedback control for quantum systems in which the time to compute the filter based control input is taken into account by considering the input delay it starts with a new lyapunov lasalle like theorem for delay dependent stochastic stability of a class of time delay stochastic nonlinear systems nonsmooth time delay control is then constructed to compensate for the control computation time which is known but arbitrarily long while globally stabilizing the quantum filters almost surely the nonsmooth property enables the control to deal with the symmetric topology of filter state space the effectiveness of the proposed control is illustrated through the global stabilization of the spin 1 2 systems simulation results are presented and discussed to show the effectiveness of the proposed control

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

optimal control of multi level quantum system with energy cost functional in this paper we have synthesized optimal control of multi level quantum system by representing unitary operator in terms of the projection operators of the hamiltonian of the system we have solved the steering problem for multi level quantum systems minimizing energy cost functional of the control the optimal control problem of the time evolution of quantum spin of pauli two level system subjected to an external field with the minimum energy function is also illustrated and formulated in terms of the quantum spin up and spin down states of the pauli two level system

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

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

an emg driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo this paper examined if an electromyography emg driven musculoskeletal model of the human knee could be used to predict knee moments calculated using inverse dynamics across a varied range of dynamic contractile conditions muscle tendon lengths and moment arms of 13 muscles crossing the knee joint were determined from joint kinematics using a three dimensional anatomical model of the lower limb muscle activation was determined using a second order discrete non linear model using rectified and lowpass filtered emg as input a modified hill type muscle model was used to calculate individual muscle forces using activation and muscle tendon lengths as inputs the model was calibrated to six individuals by altering a set of physiologically based parameters using mathematical optimisation to match the net flexion extension fe muscle moment with those measured by inverse dynamics the model was calibrated for each subject using 5 different tasks including passive and active fe in an isokinetic dynamometer running and cutting manoeuvres recorded using three dimensional motion analysis once calibrated the model was used to predict the fe moments estimated via inverse dynamics from over 200 isokinetic dynamometer running and sidestepping tasks the inverse dynamics joint moments were predicted with an average r 2 of 0 91 and mean residual error of b12 nm a re calibration of only the emg to activation parameters revealed fe moments prediction across weeks of similar accuracy changing the muscle model to one that is more physiologically correct produced better predictions the modelling method presented represents a good way to estimate in vivo muscle forces during movement tasks r 2003 elsevier science ltd all rights reserved

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

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

femoral strength is better predicted by finite element models than qct and dxa clinicians and patients would benefit if accurate methods of predicting and monitoring bone strength in vivo were available a group of 51 human femurs age range 21 93 23 females 28 males were evaluated for bone density and geometry using quantitative computed tomography qct and dual energy x ray absorptiometry dxa regional bone density and dimensions obtained from qct and dxa were used to develop statistical models to predict femoral strength ex vivo the qct data also formed the basis of a three dimensional finite element fe models to predict structural stiffness the femurs were separated into two groups a model training set n 25 was used to develop statistical models to predict ultimate load and a test set n 26 was used to validate these models the main goal of this study was to test the ability of dxa qct and fe techniques to predict fracture load non invasively in a simple load configuration which produces predominantly femoral neck fractures the load configuration simulated the single stance phase portion of normal gait in 87 of the specimens clinical appearing sub capital fractures were produced the training test study design provided a tool to validate that the predictive models were reliable when used on specimens with unknown strength characteristics the fe method explained at least 20 more of the variance in strength than the dxa models planned refinements of the fe technique are expected to further improve these results three dimensional fe models are a promising method for predicting fracture load and may be useful in monitoring strength changes in vivo

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

scanner influence on the mechanical response of qct based finite element analysis of long bones abstract patient specific qct based finite element qctfe analyses enable highly accurate quantification of bone strength we evaluated ct scanner influence on qctfe models of long bones a femur humerus and proximal femur without the head were scanned with k2hpo4 phantoms by seven ct scanners four models using typical clinical protocols qctfe models were constructed the geometrical dimensions as well as the qct values expressed in hounsfield unit hu distribution was compared principal strains at representative regions of interest rois and maximum principal strains associated with fracture risk were compared intraclass correlation coefficients iccs were calculated to evaluate strain prediction reliability for different scanners repeatability was examined by scanning the femur twice and comparing resulting qctfe models maximum difference in geometry was 2 3 hu histograms before phantom calibration showed wide variation between qct scans however bone density histogram variability was reduced after calibration and algorithmic manipulation relative standard deviation rsd in principal strains at rois was 0 9 fracture associated strain had 6 7 8 1 and 13 3 maximum rsd for the femur humerus and proximal femur respectively the difference in maximum strain location was quantification of strain differences showed mean rsd bounded by 6 in rois fracture associated strains in regular bones showed a mean rsd bounded by 8 strains were obtained within a 10 difference relative to the mean thus in a longitudinal study only changes larger than 20 in the principal strains may be significant iccs indicated high reliability of qctfe models derived from different scanners

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

elliptic curve cryptosystems we discuss analogs based on elliptic curves over finite fields of public key cryptosystems which use the multiplicative group of a finite field these elliptic curve cryptosystems may be more secure because the analog of the discrete logarithm problem on elliptic curves is likely to be harder than the classical discrete logarithm problem especially over gf 2 we discuss the question of primitive points on an elliptic curve modulo p and give a theorem on nonsmoothness of the order of the cyclic subgroup generated by a global point

optimal control of two level quantum systems we study the manipulation of two level quantum systems this research is motivated by the design of quantum mechanical logic gates which perform prescribed logic operations on a two level quantum system a quantum bit we consider the problem of driving the evolution operator to a desired state while minimizing an energy type cost mathematically this problem translates into an optimal control problem for systems varying on the lie group of special unitary matrices of dimension two with cost that is quadratic in the control we develop a comprehensive theory of optimal control for two level quantum systems this includes in particular a classification of normal and abnormal extremals and a proof of regularity of the optimal control functions the impact of the results of the paper on nuclear magnetic resonance experiments and quantum computation is discussed

to what extent is joint and muscle mechanics predicted by musculoskeletal models sensitive to soft tissue artefacts musculoskeletal models are widely used to estimate joint kinematics intersegmental loads and muscle and joint contact forces during movement these estimates can be heavily affected by the soft tissue artefact sta when input positional data are obtained using stereophotogrammetry but this aspect has not yet been fully characterised for muscle and joint forces this study aims to assess the sensitivity to the sta of three open source musculoskeletal models implemented in opensim a baseline dataset of marker trajectories was created for each model from experimental data of one healthy volunteer five hundred sta realizations were then statistically generated using a marker dependent model of the pelvis and lower limb artefact and added to the baseline data the sta s impact on the musculoskeletal model estimates was finally quantified using a monte carlo analysis the modelled sta distributions were in line with the literature observed output variations were comparable across the three models and sensitivity to the sta was evident for most investigated quantities shape magnitude and timing of the joint angle and moment time histories were not significantly affected throughout the entire gait cycle whereas magnitude variations were observed for muscle and joint forces ranges of contact force variations differed between joints with hip variations up to 1 8 times body weight observed variations of more than 30 were observed for some of the muscle forces in conclusion musculoskeletal simulations using stereophotogrammetry may be safely run when only interested in overall output patterns caution should be paid when more accurate estimated values are needed

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

to what extent can linear finite element models of human femora predict failure under stance and fall loading configurations proximal femur strength estimates from computed tomography ct based finite element fe models are finding clinical application published models reached a high in vitro accuracy yet many of them rely on nonlinear methodologies or internal best fitting of parameters the aim of the present study is to verify to what extent a linear fe modelling procedure fully based on independently determined parameters can predict the failure characteristics of the proximal femur in stance and sideways fall loading configurations fourteen fresh frozen cadaver femora were ct scanned seven femora were tested to failure in stance loading conditions and seven in fall fracture was monitored with high speed videos linear fe models were built from ct images according to a procedure already validated in the prediction of strains an asymmetric maximum principal strain criterion 0 73 tensile 1 04 compressive limit was used to define a node based risk factor rf fe predicted failure load mode tensile compressive and location were determined from the first node reaching rf 1 fe predicted and measured failure loads were highly correlated r 2 0 89 see 814n in all specimens fe models correctly identified the failure mode tensile in stance compressive in fall and the femoral region where fracture started supero lateral neck aspect the location of failure onset was accurately predicted in eight specimens in summary a simple fe model adaptable in the future to multiple loads e g including muscles was highly correlated with experimental failure in two loading conditions on specimens ranging from normal to osteoporotic thus it can be suitable for use in clinical studies

application of a falsification strategy to a musculoskeletal model of the lower limb and accuracy of the predicted hip contact force vector in the literature lower limb musculoskeletal models validated against in vivo measured hip contact forces hcfs exhibit a tendency to overestimate the hcfs magnitude and predict inaccurate components of the hcf vector in the transverse plane in order to investigate this issue a musculoskeletal model was forced to produce hcfs identical to those measured and the resulting joint equilibrium equations were studied through both a general approach and a static optimization framework in the former case the existence of solutions to the equilibrium equations was investigated and the effect of varying the intersegmental moments and the muscle tetanic stress assessed for a value of 100 n cm 2 and moments calculated from an inverse dynamics analysis on average only 62 of analyzed frames were solvable for level walking and 70 for stair climbing in the static optimization study the model could reproduce the experimental hcfs but the recruited muscles were unable to simultaneously equilibrate the hip intersegmental moments without the contribution of reserve moment actuators without constraints imposed on the hcfs the predicted hcf vectors presented maximum angle deviations up to 22 for level walking and 33 for stair climbing during the gait stance phase the influence of the medio lateral hcf component on the solvability of the equilibrium equations and the muscle recruitment alteration when the model was forced to produce the experimental hcfs suggest that a more accurate geometrical representation of the gluteal muscles is mandatory to improve predictions of the hcf vector yielded by the static optimization technique

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

a novel method to estimate the stiffness of the equine back diagnosis of back problems in equine orthopedics can be a difficult task the aim of our study was to develop a new method for estimating the stiffness of the equine back in vivo we measured the activity of the long back muscle at two locations on both sides at thoracic vertebrae t12 and t16 of 15 horses flexing and extending their back at stance using telemetric surface electromyography while simultaneously recording the motion of the back with a video camera system out of these paired data sets we computed a transfer function in the frequency domain and evaluated its capability of capturing the biomechanical behavior the transfer function was evaluated via correlation between calculated and actual motion resulting in correlation coefficients of 0 89 for lateral flexion and 0 83 for ventral extension at t16 and 0 82 for lateral flexion and 0 83 for ventral extension at t12 the transfer function was fitted to a filter polynomial of second order and related to the motion equation by comparison of coefficients we gained an estimate for the stiffness of the back resulting in a mean value of approximately 6100 n m for lateral flexion and 650 n m for ventral extension this new method enables clinicians in equine orthopedics to estimate back stiffness in horses and it also provides reality grounded values for biomechanical models of the equine back

a novel training free method for real time prediction of femoral strain surrogate methods for rapid calculation of femoral strain are limited by the scope of the training data we compared a newly developed training free method based on the superposition principle superposition principle method spm and popular surrogate methods for calculating femoral strain during activity finite element calculations of femoral strain muscle and joint forces for five different activity types were obtained previously multi linear regression multivariate adaptive regression splines and gaussian process were trained for 50 100 200 and 300 random samples generated using latin hypercube lh and design of experiment doe sampling the spm method used weighted linear combinations of 173 activity independent finite element analyses accounting for each muscle and hip contact force across the surrogate methods we found that 200 doe samples consistently provided low error rmse 100 e with model construction time ranging from 3 8 to 63 3 h and prediction time ranging from 6 to 1236 s per activity the spm method provided the lowest error rmse 40 e the fastest model construction time 3 2 h and the second fastest prediction time per activity 36 s after multi linear regression 6 s the spm method will enable large numerical studies of femoral strain and will narrow the gap between bone strain prediction and real time clinical applications

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

accuracy of the tibiofemoral contact forces estimated by a subject specific musculoskeletal model with fluoroscopy based contact point trajectories abstract accurate estimation of the tibiofemoral contact forces relies on exact kinematics and joint geometry subject specific kinematic constraints representing contact point trajectories derived from fluoroscopic measurements during lunge are introduced in a musculoskeletal model of the lower limb and compared to generic kinematic constraints the medial lateral and total contact forces during gait and squat are validated using the data of four patients with an instrumented prosthesis the accuracy of the estimated contact forces both with subject specific and generic kinematic constraints remains close to the level reported in the literature the mean root mean square errors range from 0 32 to 0 52 body weights for gait and from 0 27 to 0 72 body weights for squat the impact of the subject specific contact point trajectories is not found substantial or consistent between patients and tasks indeed the kinematics of the total knee prostheses remains close to the kinematics of a hinge joint and the contact point locations remain generally centred at 20 mm from the tibia centreline close to the constant value defined in the generic constraints the contact point trajectories are also suspected to differ between tasks lunge vs gait and squat while the contact point trajectories have been reported to be sensitive model parameters no clear improvement of the contact force accuracy is demonstrated on patients with instrumented prosthesis the introduction as kinematic constraints of fluoroscopy based contact point trajectories may be considered in cases where these trajectories are significantly altered as reported for osteoarthritis patients

identification of dynamic myoelectric signal to force models during isometric lumbar muscle contractions a 14 muscle myoelectric signal mes driven muscle force prediction model of the l3 l4 cross section is developed which includes a dynamic mes force relationship and allows for cocontraction model parameters are estimated from mes and moments data recorded during rapid exertions in trunk flexion extension lateral bending and axial twist nine young healthy males participated in the experimental testing the model used in the parameter estimation is of the output error type consistent and physically feasible parameter estimates were obtained by normalizing the rms mes to maximum exertion levels and using nonlinear constrained optimization to minimize a cost function consisting of the trace of the output error covariance matrix model performance was evaluated by comparing measured and mes predicted moments over a series of slow and rapid exertions moment prediction errors were on the order of 25 30 and 40 during attempted trunk flexion extensions lateral bends and axial twists respectively the model and parameter estimation methods developed provide a means to estimate lumbar muscle and spine loads as well as to empirically investigate the use and effects of cocontraction during physical task performances

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

flatness based control of a single qubit gate this work considers the open loop control problem of steering a two level quantum system from any initial to any final condition the model of this system evolves on the state space having two inputs that correspond to the complex amplitude of a resonant laser field a symmetry preserving flat output is constructed using a fully geometric construction and quaternion computations simulation results of this flatness based open loop control are provided

robust incoherent control of qubit systems via switching and optimisation a robust incoherent quantum control scheme via projective measurements plus unitary transformations is proposed for driving a qubit system from an unknown initial mixed state to an arbitrary target pure state this scheme consists of two main steps projective measurement on the initial mixed state and optimal control between two pure states the first step projects the initial state into an eigenstate of the qubit system by projective measurement and guarantees that the proposed scheme is robust to different initial mixed states the second step finds a set of suitable optimal controls to drive the qubit system from the conditional eigenstate to the target pure state the connection between the two steps is accomplished by a switching strategy to accomplish the second step two approaches are presented in detail these approaches are time optimal transition with unbounded control and bang bang control with minimal switches the minimal time and minimal number of switches in these approaches can be calcu

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

sensitivity of femoral strain calculations to anatomical scaling errors in musculoskeletal models of movement the determination of femoral strain in post menopausal women is important for studying bone fragility femoral strain can be calculated using a reference musculoskeletal model scaled to participant anatomies referred to as scaled generic combined with finite element models however anthropometric errors committed while scaling affect the calculation of femoral strains we assessed the sensitivity of femoral strain calculations to scaled generic anthropometric errors we obtained ct images of the pelves and femora of 10 healthy post menopausal women and collected gait data from each participant during six weight bearing tasks scaled generic musculoskeletal models were generated using skin mounted marker distances image based models were created by modifying the scaled generic models using muscle and joint parameters obtained from the ct data scaled generic and image based muscle and hip joint forces were determined by optimisation a finite element model of each femur was generated from the ct images and both image based and scaled generic principal strains were computed in 32 regions throughout the femur the intra participant regional rms error increased from 380 e r2 0 92 p 0 001 to 4064 e r2 0 48 p 0 001 representing 5 2 and 55 6 of the tensile yield strain in bone respectively the peak strain difference increased from 2821 e in the proximal region to 34 166 e at the distal end of the femur the inter participant rms error throughout the 32 femoral regions was 430 e r2 0 95 p 0 001 representing 5 9 of bone tensile yield strain we conclude that scaled generic models can be used for determining cohort based averages of femoral strain whereas image based models are better suited for calculating participant specific strains throughout the femur

identity based encryption from the weil pairing we propose a fully functional identity based encryption ibe scheme the scheme has chosen ciphertext security in the random oracle model assuming a variant of the computational diffie hellman problem our system is based on bilinear maps between groups the weil pairing on elliptic curves is an example of such a map we give precise definitions for secure ibe schemes and give several applications for such systems

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

proximal femur bone strength estimated by a computationally fast finite element analysis in a sideways fall configuration finite element fe analysis based on quantitative computed tomography qct images is an emerging tool to estimate bone strength in a specific patient or specimen however it is limited by the computational power required and the associated time required to generate and solve the models thus our objective was to develop a fast validated method to estimate whole bone structural stiffness and failure load in addition to a sensitivity analysis of varying boundary conditions we performed qct scans on twenty fresh frozen proximal femurs age 77 13 years and mechanically tested the femurs in a configuration that simulated a sideways fall on the hip we used custom software to generate the fe models with boundary conditions corresponding to the mechanical tests and solved the linear models to estimate bone structural stiffness and estimated failure load for the sensitivity analysis we varied the internal rotation angle of the femoral neck from 30 to 45 at 15 intervals and estimated structural stiffness at each angle we found both the fe estimates of structural stiffness r 2 0 89 p 0 01 and failure load r 2 0 81 p 0 01 to be in high agreement with the values found by mechanical testing an important advantage of these methods was that the models of approximately 500 000 elements took less than 11 min to solve using a standard desktop workstation in this study we developed and validated a method to quickly and accurately estimate proximal femur structural stiffness and failure load using qct driven fe methods

modular polynomials via isogeny volcanoes we present a new algorithm to compute the classical modular polynomial l in the rings z x y and z mz x y for a prime l and any positive integer m our approach uses the graph of l isogenies to eciently compute l mod p for many primes p of a suitable form and then applies the chinese remainder theorem crt under the generalized riemann hypoth esis grh we achieve an expected running time of o l 3 logl 3 log logl and compute l mod m using o l 2 logl 2 l 2 logm space we have used the new algorithm to compute l with l over 5000 and l mod m with l over 20000 we also consider several modular functions g for which g is smaller than l allowing us to handle l over 60000

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

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

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

validation of a functional method for the estimation of hip joint centre location the present study assesses the accuracy with which the subject specific coordinates of the hip joint centre hjc in a pelvic anatomical frame can be estimated using different methods the functional method was applied by calculating the centre of the best sphere described by the trajectory of markers placed on the thigh during several trials of hip rotations different prediction methods proposed in the literature and in the present investigation which estimate the hjc of adult subjects using regression equations and anthropometric measurements were also assessed the accuracy of each of the above mentioned methods was investigated by comparing their predictions with measurements obtained on a sample of 11 male adult able bodied volunteers using roentgen stereophotogrammetric analysis rsa assumed to provide the true hjc locations prediction methods estimated the hjc location at an average rms distance of 25 30 mm the functional method performed significantly better and estimated hjcs within a rms distance of 13 mm on average this result may be confidently generalised if the photogrammetric experiment is carefully conducted and an optimal analytical approach used the method is therefore suggested for use in motion analysis when the subject s hip range of motion is not limited in addition the facts that it is not an invasive technique and that it has relatively small and un biased errors make it suitable for regression equations identification with no limit to sample size and population typology

elliptic curves over finite fields and the computation of square roots mod p in this paper we present a deterministic algorithm to compute the number of f points of an elliptic curve that is defined over a finite field fv and which is given by a weierstrass equation the algorithm takes 0 log9 q elementary operations as an application wc give an algorithm to compute square roots mod p for fixed i e z it takes 0 log9p elementary operations to compute fx mod p 1 introduction in this paper we present an algorithm to compute the number of f points of an elliptic curve defined over a finite field f which is given by a weierstrass equation we restrict ourselves to the case where the characteristic of f is not 2 or 3 the algorithm is deterministic does not depend on any unproved hypotheses and takes 0 log9 0 if one applies fast multiplication techniques the algorithm will take 0 x 1 2log p 6 f elementary operations for any e 0 let be an elliptic curve defined over the prime field fp and let an affine model of it be given by a weierstrass equation y2 x3 ax b a befp an explicit formula for the number of f points on is given by

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

notions of controllability for bilinear multilevel quantum systems in this note we define four different notions of controllability of physical interest for multilevel quantum mechanical systems these notions involve the possibility of driving the evolution operator as well as the state of the system we establish the connections among these different notions as well as methods to verify controllability

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

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

computing l l isogenies in polynomial time on jacobians of genus 2 curves in this paper we compute l isogenies between abelian varieties over a field of characteristic different from 2 in polynomial time in l when l is an odd prime which is coprime to the characteristic we use level n symmetric theta structure where n 2 or n 4 in a second part of this paper we explain how to convert between mumford coordinates of jacobians of genus 2 hyperelliptic curves to theta coordinates of level 2 or 4 combined with the preceding algorithm this gives a method to compute l l isogenies in polynomial time on jacobians of genus 2 curves

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

accuracy of finite element predictions in sideways load configurations for the proximal human femur abstract in undetermined subject specific finite element models have been used to predict stress state and fracture risk in individual patients while many studies analysed quasi axial loading configurations only few works simulated sideways load configurations such as those arising in a fall the majority among these latter directly predicted bone strength without assessing elastic strain prediction accuracy the aim of the present work was to evaluate if a subject specific finite element modelling technique from ct data that accurately predicted strains in quasi axial loading configurations is suitable to accurately predict strains also when applying low magnitude loads in sideways configurations to this aim a combined numerical experimental study was performed to compare finite element predicted strains with strain gauge measurements from three cadaver proximal femurs instrumented with sixteen strain rosettes and tested non destructively under twelve loading configurations spanning a wide cone 0 30 for both adduction and internal rotation angles of sideways fall scenarios the results of the present study evidenced a satisfactory agreement between experimentally measured and predicted strains r2 greater than 0 9 rmse lower than 10 and displacements the achieved strain prediction accuracy is comparable to those obtained in state of the art studies in quasi axial loading configurations still the presence of the highest strain prediction errors around 30 in the lateral neck aspect would deserve attention in future studies targeting bone failure less

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

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

notes on sliding mode control of two level quantum systems in dong d and petersen i r 2012 sliding mode control of two level quantum systems automatica 48 725 735 a sliding mode control approach has been proposed for two level quantum systems to deal with bounded uncertainties in the system hamiltonian this paper further extends these results in two directions one extension is to consider the effect of uncertainties during the process of driving the system s state back to the sliding mode domain from outside and we propose two approaches to accomplish this control task the other extension generalizes the previous design approach to consider uncertainties described as perturbations in the free hamiltonian

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

the mechanics of back extensor torque production about the lumbar spine the purpose of this study was to develop and evaluate a biomechanical model of lumbar back extension over a wide range of positions for the lumbar spine incorporating the latest information on muscle geometry and intra abdominal pressure iap analysis of the visible human data was utilised in order to obtain anatomical information unavailable from the literature and magnetic resonance imaging was used to generate subject specific anatomical descriptions the model was evaluated by comparisons with measured maximal voluntary static back extension torques predicted maximal specific muscle tensions agreed well with in vitro measurements from the literature when modelling the maximal static back extension torque production it was possible to come fairly close to simultaneous equilibrium about all the lumbar discs simply by a uniform muscle activation of all back extensor muscles the caudal part showed however less agreement this indicates that equilibrium in the lumbar spine is mainly regulated by passive mechanical properties e g muscle length changes due to postural changes rather than due to complex muscle coordination as earlier proposed the model showed that iap measured during torque exertions contributes about 10 of the total maximal voluntary back extensor torque and that it can unload the spine from compression the spinal unloading effect from the iap was greatest with the spine held in a flexed position this is in opposition to the effects of changed muscle lever arm lengths which for a given load would give the largest spinal unloading in the extended position these findings have implications for the evaluation of optimal lifting techniques

computing modular correspondences for abelian varieties the aim of this paper is to give a higher dimensional equivalent of the classical modular polynomials phi ell x y if j is the j invariant associated to an elliptic curve e k over a field k then the roots of phi ell j x correspond to the j invariants of the curves which are ell isogeneous to e k denote by x 0 n the modular curve which parametrizes the set of elliptic curves together with a n torsion subgroup it is possible to interpret phi ell x y as an equation cutting out the image of a certain modular correspondence x 0 ell rightarrow x 0 1 times x 0 1 in the product x 0 1 times x 0 1 let g be a positive integer and overn in n g we are interested in the moduli space that we denote by mn of abelian varieties of dimension g over a field k together with an ample symmetric line bundle pol and a symmetric theta structure of type overn if ell is a prime and let overl ell ldots ell there exists a modular correspondence mln rightarrow mn times mn we give a system of algebraic equations defining the image of this modular correspondence we describe an algorithm to solve this system of algebraic equations which is much more efficient than a general purpose gr obner basis algorithm as an application we explain how this algorithm can be used to speed up the initialisation phase of a point counting algorithm

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

uncertainty quantification for personalized analyses of human proximal femurs computational models for the personalized analysis of human femurs contain uncertainties in bone material properties and loads which affect the simulation results to quantify the influence we developed a probabilistic framework based on polynomial chaos pc that propagates stochastic input variables through any computational model we considered a stochastic e relationship and a stochastic hip contact force representing realistic variability of experimental data their influence on the prediction of principal strains 1 and 3 was quantified for one human proximal femur including sensitivity and reliability analysis large variabilities in the principal strain predictions were found in the cortical shell of the femoral neck with coefficients of variation of 40 between 60 and 80 of the variance in 1 and 3 are attributable to the uncertainty in the e relationship while 10 are caused by the load magnitude and 5 30 by the load direction principal strain directions were unaffected by material and loading uncertainties the antero superior and medial inferior sides of the neck exhibited the largest probabilities for tensile and compression failure however all were very small pf 0 001 in summary uncertainty quantification with pc has been demonstrated to efficiently and accurately describe the influence of very different stochastic inputs which increases the credibility and explanatory power of personalized analyses of human proximal femurs

computing hilbert class polynomials with the chinese remainder theorem we present a space efficient algorithm to compute the hilbert class polynomial h d x modulo a positive integer p based on an explicit form of the chinese remainder theorem under the generalized riemann hypothesis the algorithm uses o d 1 2 e log p space and has an expected running time of o d 1 e we describe practical optimizations that allow us to handle larger discriminants than other methods with d as large as 10 13 and h d up to 10 6 we apply these results to construct pairing friendly elliptic curves of prime order using the cm method