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 global optimization method for prediction of muscle forces of human musculoskeletal system

Inverse dynamic optimization is a popular method for predicting muscle and joint reaction forces within human musculoskeletal joints. However, the traditional formulation of the optimization method does not include the joint reaction moment in the moment equilibrium equation, potentially violating the equilibrium conditions of the joint. Consequently, the predicted muscle and joint reaction forces are coordinate system-dependent. This paper presents an improved optimization method for the prediction of muscle forces and joint reaction forces. In this method, the location of the rotation center of the joint is used as an optimization variable, and the moment equilibrium equation is formulated with respect to the joint rotation center to represent an accurate moment constraint condition. The predicted muscle and joint reaction forces are independent of the joint coordinate system. The new optimization method was used to predict muscle forces of an elbow joint. The results demonstrated that the joint rotation center location varied with applied loading conditions. The predicted muscle and joint reaction forces were different from those predicted by using the traditional optimization method. The results further demonstrated that the improved optimization method converged to a minimum for the objective function that is smaller than that reached by using the traditional optimization method. Therefore, the joint rotation center location should be involved as a variable in an inverse dynamic optimization method for predicting muscle and joint reaction forces within human musculoskeletal joints.     

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 low-pass 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 approximately 12 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.     

Lower extremity extension force and electromyography properties as a function of knee angle and their relation to joint torques: implications for strength diagnostics

The purpose of this study was to evaluate whether and how isometric multijoint leg extension strength can be used to assess athletes' muscular capability within the scope of strength diagnosis. External reaction forces (Fext) and kinematics were measured (n = 18) during maximal isometric contractions in a seated leg press at 8 distinct joint angle configurations ranging from 30 to 100° knee flexion. In addition, muscle activation of rectus femoris, vastus medialis, biceps femoris c.l., gastrocnemius medialis, and tibialis anterior was obtained using surface electromyography (EMG). Joint torques for hip, knee, and ankle joints were computed by inverse dynamics. The results showed that unilateral Fext decreased significantly from 3,369 ± 575 N at 30° knee flexion to 1,015 ± 152 N at 100° knee flexion. Despite maximum voluntary effort, excitation of all muscles as measured by EMG root mean square changed with knee flexion angles. Moreover, correlations showed that above-average Fext at low knee flexion is not necessarily associated with above-average Fext at great knee flexion and vice versa. Similarly, it is not possible to deduce high joint torques from high Fext just as above-average joint torques in 1 joint do not signify above-average torques in another joint. From these findings, it is concluded that an evaluation of muscular capability by means of Fext as measured for multijoint leg extension is strongly limited. As practical recommendation, we suggest analyzing multijoint leg extension strength at 3 distinct knee flexion angles or at discipline-specific joint angles. In addition, a careful evaluation of muscular capacity based on measured Fext can be done for knee flexion angles ≥ 80°. For further and detailed analysis of single muscle groups, the use of inverse dynamic modeling is recommended.     

Static optimization underestimates antagonist muscle activity at the glenohumeral joint: A musculoskeletal modeling study

Static optimization is commonly employed in musculoskeletal modeling to estimate muscle and joint loading; however, the ability of this approach to predict antagonist muscle activity at the shoulder is poorly understood. Antagonist muscles, which contribute negatively to a net joint moment, are known to be important for maintaining glenohumeral joint stability. This study aimed to compare muscle and joint force predictions from a subject-specific neuromusculoskeletal model of the shoulder driven entirely by measured muscle electromyography (EMG) data with those from a musculoskeletal model employing static optimization. Four healthy adults performed six sub-maximal upper-limb contractions including shoulder abduction, adduction, flexion, extension, internal rotation and external rotation. EMG data were simultaneously measured from 16 shoulder muscles using surface and intramuscular electrodes, and joint motion evaluated using video motion analysis. Muscle and joint forces were calculated using both a calibrated EMG-driven neuromusculoskeletal modeling framework, and musculoskeletal model simulations that employed static optimization. The EMG-driven model predicted antagonistic muscle function for pectoralis major, latissimus dorsi and teres major during abduction and flexion; supraspinatus during adduction; middle deltoid during extension; and subscapularis, pectoralis major and latissimus dorsi during external rotation. In contrast, static optimization neural solutions showed little or no recruitment of these muscles, and preferentially activated agonistic prime movers with large moment arms. As a consequence, glenohumeral joint force calculations varied substantially between models. The findings suggest that static optimization may under-estimate the activity of muscle antagonists, and therefore, their contribution to glenohumeral joint stability.     

A model-based study of passive joint properties on muscle effort during static stance

This study examined the impact of lower extremity joint stiffnesses and simulated joint contractures on the muscle effort required to maintain static standing postures after a spinal cord injury (SCI). Static inverse computer simulations were performed with a three-dimensional 15 degree of freedom musculoskeletal model placed in 1600 different standing postures. The required lower extremity muscle forces were calculated through an optimization routine that minimized the sum of the muscle stresses squared, which was used as an index of the muscle effort required for each standing posture. Joint stiffnesses were increased and decreased by 100 percent of their nominal values, and contractures were simulated to determine their effects on the muscle effort for each posture. Nominal muscle and passive properties for an individual with a SCI determined the baseline muscle effort for comparisons. Stiffness changes for the ankle plantar flexion/dorsiflexion, hip flexion/extension, and hip abduction/adduction directions had the largest effect on reducing muscle effort by more than 5 percent, while changes in ankle inversion/eversion and knee flexion/extension had the least effect. For erect standing, muscle effort was reduced by more than 5 percent when stiffness was decreased at the ankle plantar flexion/dorsiflexion joint or hip flexion/extension joint. With simulated joint contractures, the postural workspace area decreased and muscle effort was not reduced by more than 5 percent for any posture. Using this knowledge, methods can be developed through the use of orthoses, physical therapy, surgery or other means to appropriately augment or diminish these passive moments during standing with a neuroprosthesis.     

Dynamic joint and muscle forces during knee isokinetic exercise

Isokinetic exercise has been commonly used in knee rehabilitation, conditioning and research in the past two decades. Although many investigators have used various experimental and theoretical approaches to study the muscle and joint force involved in isokinetic knee extension and flexion exercises, only a few of these studies have actually distinguished between the tibiofemoral joint forces and muscle forces. Therefore, the objective of this study was to specify, via an eletromyography(EMG)-driven muscle force model of the knee, the magnitude of the tibiofemoral joint and muscle forces acting during isokinetic knee extension and flexion exercises. Fifteen subjects ranging from 21 to 36 years of age volunteered to participate in this study. A Kin Com exercise machine (Chattecx Corporation, Chattanooga, TN, U.S.A.) was used as the loading device. An EMG-driven muscle force model was used to predict muscle forces, and a biomechanical model was used to analyze two knee joint constraint forces; compression and shear force. The methods used in this study were shown to be valid and reliable (r > 0.84 andp < 0.05). The effects on the tibiofemoral joint force during knee isokinetic exercises were compared with several functional activities that were investigated by earlier researchers. The muscle forces generated during knee isokinetic exercise were also obtained. Based on the findings obtained in this study, several therapeutic justifications for knee rehabilitation are proposed.     

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.     

Simultaneous prediction of muscle and contact forces in the knee during gait

Musculoskeletal models are currently the primary means for estimating in vivo muscle and contact forces in the knee during gait. These models typically couple a dynamic skeletal model with individual muscle models but rarely include articular contact models due to their high computational cost. This study evaluates a novel method for predicting muscle and contact forces simultaneously in the knee during gait. The method utilizes a 12 degree-of-freedom knee model (femur, tibia, and patella) combining muscle, articular contact, and dynamic skeletal models. Eight static optimization problems were formulated using two cost functions (one based on muscle activations and one based on contact forces) and four constraints sets (each composed of different combinations of inverse dynamic loads). The estimated muscle and contact forces were evaluated using in vivo tibial contact force data collected from a patient with a force-measuring knee implant. When the eight optimization problems were solved with added constraints to match the in vivo contact force measurements, root-mean-square errors in predicted contact forces were less than 10 N. Furthermore, muscle and patellar contact forces predicted by the two cost functions became more similar as more inverse dynamic loads were used as constraints. When the contact force constraints were removed, estimated medial contact forces were similar and lateral contact forces lower in magnitude compared to measured contact forces, with estimated muscle forces being sensitive and estimated patellar contact forces relatively insensitive to the choice of cost function and constraint set. These results suggest that optimization problem formulation coupled with knee model complexity can significantly affect predicted muscle and contact forces in the knee during gait. Further research using a complete lower limb model is needed to assess the importance of this finding to the muscle and contact force estimation process.     

Feasibility of using EMG driven neuromusculoskeletal model for prediction of dynamic movement of the elbow.

Neuromusculoskeletal (NMS) modeling is a valuable tool in orthopaedic biomechanics and motor control research. To evaluate the feasibility of using electromyographic (EMG) signals with NMS modeling to estimate individual muscle force during dynamic movement, an EMG driven NMS model of the elbow was developed. The model incorporates dynamical equation of motion of the forearm, musculoskeletal geometry and musculotendon modeling of four prime elbow flexors and three prime elbow extensors. It was first calibrated to two normal subjects by determining the subject-specific musculotendon parameters using computational optimization to minimize the root mean square difference between the predicted and measured maximum isometric flexion and extension torque at nine elbow positions (0-120 degrees of flexion with an increment of 15 degrees ). Once calibrated, the model was used to predict the elbow joint trajectories for three flexion/extension tasks by processing the EMG signals picked up by both surface and fine electrodes using two different EMG-to-activation processing schemes reported in the literature without involving any trajectory fitting procedures. It appeared that both schemes interpreted the EMG somewhat consistently but their prediction accuracy varied among testing protocols. In general, the model succeeded in predicting the elbow flexion trajectory in the moderate loading condition but over-drove the flexion trajectory under unloaded condition. The predicted trajectories of the elbow extension were noted to be continuous but the general shape did not fit very well with the measured one. Estimation of muscle activation based on EMG was believed to be the major source of uncertainty within the EMG driven model. It was especially so apparently when fine wire EMG signal is involved primarily. In spite of such limitation, we demonstrated the potential of using EMG driven neuromusculoskeletal modeling for non-invasive prediction of individual muscle forces during dynamic movement under certain conditions.     

Maximum voluntary joint torque as a function of joint angle and angular velocity: model development and application to the lower limb

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

Estimation of muscle response using three-dimensional musculoskeletal models before impact situation: a simulation study

When car crash experiments are performed using cadavers or dummies, the active muscles' reaction on crash situations cannot be observed. The aim of this study is to estimate muscles' response of the major muscle groups using three-dimensional musculoskeletal model by dynamic simulations of low-speed sled-impact. The three-dimensional musculoskeletal models of eight subjects were developed, including 241 degrees of freedom and 86 muscles. The muscle parameters considering limb lengths and the force-generating properties of the muscles were redefined by optimization to fit for each subject. Kinematic data and external forces measured by motion tracking system and dynamometer were then input as boundary conditions. Through a least-squares optimization algorithm, active muscles' responses were calculated during inverse dynamic analysis tracking the motion of each subject. Electromyography for major muscles at elbow, knee, and ankle joints was measured to validate each model. For low-speed sled-impact crash, experiment and simulation with optimized and unoptimized muscle parameters were performed at 9.4 m/h and 10 m/h and muscle activities were compared among them. The muscle activities with optimized parameters were closer to experimental measurements than the results without optimization. In addition, the extensor muscle activities at knee, ankle, and elbow joint were found considerably at impact time, unlike previous studies using cadaver or dummies. This study demonstrated the need to optimize the muscle parameters to predict impact situation correctly in computational studies using musculoskeletal models. And to improve accuracy of analysis for car crash injury using humanlike dummies, muscle reflex function, major extensor muscles' response at elbow, knee, and ankle joints, should be considered.     

In vivo changes in the human patellar tendon moment arm length with different modes and intensities of muscle contraction

The purpose of this study was to examine the effect of different muscle contraction modes and intensities on patellar tendon moment arm length (d(PT)). Five men performed isokinetic concentric, eccentric and passive knee extensions at an angular velocity of 60 deg/s and six men performed gradually increasing to maximum effort isometric muscle contractions at 90( composite function) and 20( composite function) of knee flexion. During the tests, lateral X-ray fluoroscopy imaging was used to scan the knee joint. The d(PT) differences between the passive state and the isokinetic concentric and extension were quantified at 15( composite function) intervals of knee joint flexion angle. Furthermore, the changes of the d(PT) as a function of the isometric muscle contraction intensities were determined during the isometric knee extension at 90( composite function) and 20( composite function) of knee joint flexion. Muscle contraction-induced changes in knee joint flexion angle during the isometric muscle contraction were also taken into account for the d(PT) measurements. During the two isometric knee extensions, d(PT) increased from rest to maximum voluntary muscle contraction (MVC) by 14-15%. However, when changes in knee joint flexion angle induced by the muscle contraction were taken into account, d(PT) during MVC increased by 6-26% compared with rest. Moreover, d(PT) increased during concentric and eccentric knee extension by 3-15%, depending on knee flexion angle, compared with passive knee extension. These findings have important implications for estimating musculoskeletal loads using modelling under static and dynamic conditions.     

The interaction of muscle moment arm,knee laxity,and torque in a multi-scale musculoskeletal model of the lower limb

IntroductionMusculoskeletal modeling allows insight into the interaction of muscle force and knee joint kinematics that cannot be measured in the laboratory. However, musculoskeletal models of the lower extremity commonly use simplified representations of the knee that may limit analyses of the interaction between muscle forces and joint kinematics. The goal of this research was to demonstrate how muscle forces alter knee kinematics and consequently muscle moment arms and joint torque in a musculoskeletal model of the lower limb that includes a deformable representation of the knee.MethodsTwo musculoskeletal models of the lower limb including specimen-specific articular geometries and ligament deformability at the knee were built in a finite element framework and calibrated to match mean isometric torque data collected from 12 healthy subjects. Muscle moment arms were compared between simulations of passive knee flexion and maximum isometric knee extension and flexion. In addition, isometric torque results were compared with predictions using simplified knee models in which the deformability of the knee was removed and the kinematics at the joint were prescribed for all degrees of freedom.ResultsPeak isometric torque estimated with a deformable knee representation occurred between 45° and 60° in extension, and 45° in flexion. The maximum isometric flexion torques generated by the models with deformable ligaments were 14.6% and 17.9% larger than those generated by the models with prescribed kinematics; by contrast, the maximum isometric extension torques generated by the models were similar. The change in hamstrings moment arms during isometric flexion was greater than that of the quadriceps during isometric extension (a mean RMS difference of 9.8 mm compared to 2.9 mm, respectively).DiscussionThe large changes in the moment arms of the hamstrings, when activated in a model with deformable ligaments, resulted in changes to flexion torque. When simulating human motion, the inclusion of a deformable joint in a multi-scale musculoskeletal finite element model of the lower limb may preserve the realistic interaction of muscle force with knee kinematics and torque.     

The importance of quadriceps and hamstring muscle loading on knee kinematics and in-situ forces in the ACL

This study investigated the effect of hamstring co-contraction with quadriceps on the kinematics of the human knee joint and the in-situ forces in the anterior cruciate ligament (ACL) during a simulated isometric extension motion of the knee. Cadaveric human knee specimens (n = 10) were tested using the robotic universal force moment sensor (UFS) system and measurements of knee kinematics and in-situ forces in the ACL were based on reference positions on the path of passive flexion/extension motion of the knee. With an isolated 200 N quadriceps load, the knee underwent anterior and lateral tibial translation as well as internal tibial rotation with respect to the femur. Both translation and rotation increased when the knee was flexed from full extension to 30 of flexion; with further flexion, these motion decreased. The addition of 80 N antagonistic hamstrings load significantly reduced both anterior and lateral tibial translation as well as internal tibial rotation at knee flexion angles tested except at full extension. At 30 of flexion, the anterior tibial translation, lateral tibial translation, and internal tibial rotation were significantly reduced by 18, 46, and 30%, respectively (p<0.05). The in-situ forces in the ACL under the quadriceps load were found to increase from 27.8+/-9.3 N at full extension to a maximum of 44.9+/-13.8 N at 15 of flexion and then decrease to 10 N beyond 60 of flexion. The in-situ force at 15 was significantly higher than that at other flexion angles (p<0.05). The addition of the hamstring load of 80 N significantly reduced the in-situ forces in the ACL at 15, 30 and 60 of flexion by 30, 43, and 44%, respectively (p<0.05). These data demonstrate that maximum knee motion may not necessarily correspond to the highest in-situ forces in the ACL. The data also suggest that hamstring co-contraction with quadriceps is effective in reducing excessive forces in the ACL particularly between 15 and 60 of knee flexion.     

The effects of the antagonist muscle force on intersegmental loading during isokinetic efforts of the knee extensors

Hamstrings activation when acting as antagonists is considered very important for knee joint stability. However, the effect of hamstring antagonist activity on knee joint loading in vivo is not clear. Therefore, the purpose of this study was to examine the differences in antagonistic muscle force and their effect on agonist muscle and intersegmental forces during isokinetic eccentric and concentric efforts of the knee extensors. Ten males performed maximum isokinetic eccentric and concentric efforts of the knee extensors at 30 degrees s(-1). The muscular and tibiofemoral joint forces were then estimated using a two-dimensional model with and without including the antagonist muscle forces. The antagonist moment was predicted using an IEMG-moment model. The predicted antagonist force reached a maximum of 2.55 times body weight (BW) and 1.16 BW under concentric and eccentric conditions respectively. Paired t-tests indicated that these were significantly different (p<0.05). A one-way analysis of variance indicated that when antagonist forces are included in the calculations the patella tendon, compressive and posterior shear joint forces are significantly higher compared to those calculated without including the antagonist forces. The anterior shear force was not affected by antagonist activity. The antagonists produce considerable force throughout the range of motion and affect the joint forces exerted at the knee joint. Further, it appears that the antagonist effect depends on the type of muscle action examined as it is higher during concentric compared to eccentric efforts of the knee extensors.     

A comparison of optimisation methods and knee joint degrees of freedom on muscle force predictions during single-leg hop landings

The aim of this paper was to compare the effect of different optimisation methods and different knee joint degrees of freedom (DOF) on muscle force predictions during a single legged hop. Nineteen subjects performed single-legged hopping manoeuvres and subject-specific musculoskeletal models were developed to predict muscle forces during the movement. Muscle forces were predicted using static optimisation (SO) and computed muscle control (CMC) methods using either 1 or 3 DOF knee joint models. All sagittal and transverse plane joint angles calculated using inverse kinematics or CMC in a 1 DOF or 3 DOF knee were well-matched (RMS error<3°). Biarticular muscles (hamstrings, rectus femoris and gastrocnemius) showed more differences in muscle force profiles when comparing between the different muscle prediction approaches where these muscles showed larger time delays for many of the comparisons. The muscle force magnitudes of vasti, gluteus maximus and gluteus medius were not greatly influenced by the choice of muscle force prediction method with low normalised root mean squared errors (<48%) observed in most comparisons. We conclude that SO and CMC can be used to predict lower-limb muscle co-contraction during hopping movements. However, care must be taken in interpreting the magnitude of force predicted in the biarticular muscles and the soleus, especially when using a 1 DOF knee. Despite this limitation, given that SO is a more robust and computationally efficient method for predicting muscle forces than CMC, we suggest that SO can be used in conjunction with musculoskeletal models that have a 1 or 3 DOF knee joint to study the relative differences and the role of muscles during hopping activities in future studies.     

A lower extremity model for muscle-driven simulation of activity using explicit finite element modeling

A key strength of computational modeling is that it can provide estimates of muscle, ligament, and joint loads, stresses, and strains through non-invasive means. However, simulations that can predict the forces in the muscles during activity while maintaining sufficient complexity to realistically represent the muscles and joint structures can be computationally challenging. For this reason, the current state of the art is to apply separate rigid-body dynamic and finite-element (FE) analyses in series. However, the use of two or more disconnected models often fails to capture key interactions between the joint-level and whole-body scales. Single framework MSFE models have the potential to overcome the limitations associated with disconnected models in series. The objectives of the current study were to create a multi-scale FE model of the human lower extremity that combines optimization, dynamic muscle modeling, and structural FE analysis in a single framework and to apply this framework to evaluate the mechanics of healthy knee specimens during two activities. Two subject-specific FE models (Model 1, Model 2) of the lower extremity were developed in ABAQUS/Explicit including detailed representations of the muscles. Muscle forces, knee joint loading, and articular contact were calculated for two activities using an inverse dynamics approach and static optimization. Quadriceps muscle forces peaked at the onset of chair rise (2174 N, 1962 N) and in early stance phase (510 N, 525 N), while gait saw peak forces in the hamstrings (851 N, 868 N) in midstance. Joint forces were similar in magnitude to available telemetric patient data. This study demonstrates the feasibility of detailed quasi-static, muscle-driven simulations in an FE framework.     

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.     

Analytic analysis of the force sharing among synergistic muscles in one- and two-degree-of-freedom models

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.