A computationally efficient strategy to estimate muscle forces in a finite element musculoskeletal model of the lower limb

Concurrent multiscale simulation strategies are required in computational biomechanics to study the interdependence between body scales. However, detailed finite element models rarely include muscle recruitment due to the computational burden of both the finite element method and the optimization strategies widely used to estimate muscle forces. The aim of this study was twofold: first, to develop a computationally efficient muscle force prediction strategy based on proportional-integral-derivative (PID) controllers to track gait and chair rise experimental joint motion with a finite element musculoskeletal model of the lower limb, including a deformable knee representation with 12 degrees of freedom; and, second, to demonstrate that the inclusion of joint-level deformability affects muscle force estimation by using two different knee models and comparing muscle forces between the two solutions. The PID control strategy tracked experimental hip, knee, and ankle flexion/extension with root mean square errors below 1°, and estimated muscle, contact and ligament forces in good agreement with previous results and electromyography signals. Differences up to 11% and 20% in the vasti and biceps femoris forces, respectively, were observed between the two knee models, which might be attributed to a combination of differing joint contact geometry, ligament behavior, joint kinematics, and muscle moment arms. The tracking strategy developed in this study addressed the inevitable tradeoff between computational cost and model detail in musculoskeletal simulations and can be used with finite element musculoskeletal models to efficiently estimate the interdependence between muscle forces and tissue deformation.     

Gender differences in active musculoskeletal stiffness. Part I. Quantification in controlled measurements of knee joint dynamics.

Active females demonstrate increased risk for musculoskeletal injuries relative to equivalently-trained males. Although gender differences in factors such as passive laxity, skeletal geometry and kinematics have been examined, the effect of gender on active muscle stiffness has not been reported. Stiffness of the active quadriceps and hamstrings musculature were recorded during isometric knee flexion and extension exertions from twelve male and eleven female subjects. A second-order biomechanical model of joint dynamics was used to quantify stiffness from the transient motion response to an angular perturbation of the lower-leg. Female subjects demonstrated reduced active stiffness relative to male subjects at all torque levels, with levels 56-73% of the males. Effective stiffness increased linearly with the torque load, with stiffness increasing at a rate of 3.3 Nm/rad per unit of knee moment in knee flexion exertions (hamstrings) and 6.6 Nm/rad per unit of knee moment extension exertions (quadriceps). To account for gender differences in applied moment associated with leg mass, regressions analyses were completed that demonstrated a gender difference in the slope of stiffness-versus-knee moment relation. Further research is necessary to identify the cause of the observed biomechanical difference and implications for controlling injury.     

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.     

Sensitivity of model predictions of muscle function to changes in moment arms and muscle-tendon properties: a Monte-Carlo analysis

Hill-type muscle models are commonly used in musculoskeletal models to estimate muscle forces during human movement. However, the sensitivity of model predictions of muscle function to changes in muscle moment arms and muscle-tendon properties is not well understood. In the present study, a three-dimensional muscle-actuated model of the body was used to evaluate the sensitivity of the function of the major lower limb muscles in accelerating the whole-body center of mass during gait. Monte-Carlo analyses were used to quantify the effects of entire distributions of perturbations in the moment arms and architectural properties of muscles. In most cases, varying the moment arm and architectural properties of a muscle affected the torque generated by that muscle about the joint(s) it spanned as well as the torques generated by adjacent muscles. Muscle function was most sensitive to changes in tendon slack length and least sensitive to changes in muscle moment arm. However, the sensitivity of muscle function to changes in moment arms and architectural properties was highly muscle-specific; muscle function was most sensitive in the cases of gastrocnemius and rectus femoris and insensitive in the cases of hamstrings and the medial sub-region of gluteus maximus. The sensitivity of a muscle's function was influenced by the magnitude of the muscle's force as well as the operating region of the muscle on its force-length curve. These findings have implications for the development of subject-specific models of the human musculoskeletal system.     

A noninvasive technique for in vivo measurement of joint torques of biarticular muscles.

The objective of this work was to develop a noninvasive method to measure the joint torques produced by biarticular muscles at two joints simultaneously. During intramuscular stimulation of the cat medial gastrocnemius (MG) muscle, torques at the ankle and knee joints were calculated from forces measured in two dimensions at the end point of the cat paw under isometric conditions. The method was verified by the known anatomical properties of cat MG muscle and the tibialis anterior (TA) muscle. The MG muscle was shown to produce a significant flexion torque at the knee, besides an extension torque at the ankle. This was in agreement with its anatomical arrangement. The TA muscle produced primarily an ankle flexion torque. The small knee torque, due to measurement errors, yielded an estimate of measurement accuracy of 3.0 +/- 2.1% (n = 52). The coupling ratio of the MG muscle, defined as T(ankle)/T(knee), varied significantly with both knee and ankle angles. The profile of MG mechanical coupling agreed qualitatively with changes in limb configuration. The method can be used to measure recruitment properties of electrically stimulated biarticular muscles, and may potentially be used to study the biomechanics of biarticular coupling.     

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.     

Role of gastrocnemius activation in knee joint biomechanics: gastrocnemius acts as an ACL antagonist

Gastrocnemius is a premier muscle crossing the knee, but its role in knee biomechanics and on the anterior cruciate ligament (ACL) remains less clear when compared to hamstrings and quadriceps. The effect of changes in gastrocnemius force at late stance when it peaks on the knee joint response and ACL force was initially investigated using a lower extremity musculoskeletal model driven by gait kinematics—kinetics. The tibiofemoral joint under isolated isometric contraction of gastrocnemius was subsequently analyzed at different force levels and flexion angles (0°–90°). Changes in gastrocnemius force at late stance markedly influenced hamstrings forces. Gastrocnemius acted as ACL antagonist by substantially increasing its force. Simulations under isolated contraction of gastrocnemius confirmed this role at all flexion angles, in particular, at extreme knee flexion angles (0° and 90°). Constraint on varus/valgus rotations substantially decreased this effect. Although hamstrings and gastrocnemius are both knee joint flexors, they play opposite roles in respectively protecting or loading ACL. Although the quadriceps is also recognized as antagonist of ACL, at larger joint flexion and in contrast to quadriceps, activity in gastrocnemius substantially increased ACL forces (anteromedial bundle). The fact that gastrocnemius is an antagonist of ACL should help in effective prevention and management of ACL injuries.     

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.     

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.     

Functional muscle synergies to support the knee against moment specific loads while weight bearing

ObjectiveExternally applied abduction and rotational loads are major contributors to the knee joint injury mechanism; yet, how muscles work together to stabilize the knee against these loads remains unclear. Our study sought to evaluate lower limb functional muscle synergies in healthy young adults such that muscle activation can be directly related to internal knee joint moments.MethodsConcatenated non-negative matrix factorization extracted muscle and moment synergies of 22 participants from electromyographic signals and joint moments elicited during a weight-bearing force matching protocol.ResultsTwo synergy sets were extracted: Set 1 included four synergies, each corresponding to a general anterior, posterior, medial, or lateral force direction. Frontal and transverse moments were coupled during medial and lateral force directions. Set 2 included six synergies, each corresponding to a moment type (extension/flexion, ab/adduction, internal/external rotation). Hamstrings and quadriceps dominated synergies associated with respective flexion and extension moments while quadriceps-hamstring co-activation was associated with knee abduction. Rotation moments were associated with notable contributions from hamstrings, quadriceps, gastrocnemius, and hip ab/adductors, corresponding to a general co-activation muscle synergy.ConclusionOur results highlight the importance of muscular co-activation of all muscles crossing the knee to support it during injury-inducing loading conditions such as externally applied knee abduction and rotation. Functional muscle synergies can provide new insight into the relationship between neuromuscular control and knee joint stability by directly associating biomechanical variables to muscle activation.     

Knee and ankle joint torque-angle relationships of multi-joint leg extension

The force-length-relation (F-l-r) is an important property of skeletal muscle to characterise its function, whereas for in vivo human muscles, torque-angle relationships (T-a-r) represent the maximum muscular capacity as a function of joint angle. However, since in vivo force/torque-length data is only available for rotational single-joint movements the purpose of the present study was to identify torque-angle-relationships for multi-joint leg extension. Therefore, inverse dynamics served for calculation of ankle and knee joint torques of 18 male subjects when performing maximum voluntary isometric contractions in a seated leg press. Measurements in increments of 10° knee angle from 30° to 100° knee flexion resulted in eight discrete angle configurations of hip, knee and ankle joints. For the knee joint we found an ascending-descending T-a-r with a maximum torque of 289.5° ± 43.3 Nm, which closely matches literature data from rotational knee extension. In comparison to literature we observed a shift of optimum knee angle towards knee extension. In contrast, the T-a-r of the ankle joint vastly differed from relationships obtained for isolated plantar flexion. For the ankle T-a-r derived from multi-joint leg extension subjects operated over different sections of the force-length curve, but the ankle T-a-r derived from isolated joint efforts was over the ascending limb for all subjects. Moreover, mean maximum torque of 234.7 ± 56.6 Nm exceeded maximal strength of isolated plantar flexion (185.7 ± 27.8 Nm). From these findings we conclude that muscle function between isolated and more physiological multi-joint tasks differs. This should be considered for ergonomic and sports optimisation as well as for modelling and simulation of human movement.     

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.     

A Three-Dimensional Musculoskeletal Model of the Human Knee Joint. Part 2: Analysis of Ligament Function

A three-dimensional model of the knee is used to study ligament function during anterior-posterior (a-p) draw, axial rotation, and isometric contractions of the extensor and flexor muscles. The geometry of the model bones is based on cadaver data. The contacting surfaces of the femur and tibia are modeled as deformable; those of the femur and patella are assumed to be rigid. Twelve elastic elements are used to describe the geometry and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by thirteen musculotendinous units, each unit represented as a three-element muscle in series with tendon. The calculations show that the forces applied during a-p draw are substantially different from those applied by the muscles during activity. Principles of knee-ligament function based on the results of in vitro experiments may therefore be overstated. Knee-ligament forces during straight a-p draw are determined solely by the changing geometry of the ligaments relative to the bones: ACL force decreases with increasing flexion during anterior draw because the angle between the ACL and the tibial plateau decreases as knee flexion increases; PCL force increases with increasing flexion during posterior draw because the angle between the PCL and the tibial plateau increases. The pattern of ligament loading during activity is governed by the geometry of the muscles spanning the knee: the resultant force in the ACL during isometric knee extension is determined mainly by the changing orientation of the patellar tendon relative to the tibia in the sagittal plane; the resultant force in the PCL during isometric knee flexion is dominated by the angle at which the hamstrings meet the tibia in the sagittal plane.     

Loading of the knee joint during activities of daily living measured in vivo in five subjects

Detailed knowledge about loading of the knee joint is essential for preclinical testing of implants, validation of musculoskeletal models and biomechanical understanding of the knee joint. The contact forces and moments acting on the tibial component were therefore measured in 5 subjects in vivo by an instrumented knee implant during various activities of daily living.Average peak resultant forces, in percent of body weight, were highest during stair descending (346% BW), followed by stair ascending (316% BW), level walking (261% BW), one legged stance (259% BW), knee bending (253% BW), standing up (246% BW), sitting down (225% BW) and two legged stance (107% BW). Peak shear forces were about 10–20 times smaller than the axial force. Resultant forces acted almost vertically on the tibial plateau even during high flexion. Highest moments acted in the frontal plane with a typical peak to peak range ?2.91% BWm (adduction moment) to 1.61% BWm (abduction moment) throughout all activities. Peak flexion/extension moments ranged between ?0.44% BWm (extension moment) and 3.16% BWm (flexion moment). Peak external/internal torques lay between ?1.1% BWm (internal torque) and 0.53% BWm (external torque).The knee joint is highly loaded during daily life. In general, resultant contact forces during dynamic activities were lower than the ones predicted by many mathematical models, but lay in a similar range as measured in vivo by others. Some of the observed load components were much higher than those currently applied when testing knee implants.     

A Three-Dimensional Musculoskeletal Model of the Human Knee Joint. Part 2: Analysis of Ligament Function

A three-dimensional model of the knee is used to study ligament function during anterior-posterior (a-p) draw, axial rotation, and isometric contractions of the extensor and flexor muscles. The geometry of the model bones is based on cadaver data. The contacting surfaces of the femur and tibia are modeled as deformable; those of the femur and patella are assumed to be rigid. Twelve elastic elements are used to describe the geometry and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by thirteen musculotendinous units, each unit represented as a three-element muscle in series with tendon. The calculations show that the forces applied during a-p draw are substantially different from those applied by the muscles during activity. Principles of knee-ligament function based on the results of in vitro experiments may therefore be overstated. Knee-ligament forces during straight a-p draw are determined solely by the changing geometry of the ligaments relative to the bones: ACL force decreases with increasing flexion during anterior draw because the angle between the ACL and the tibial plateau decreases as knee flexion increases; PCL force increases with increasing flexion during posterior draw because the angle between the PCL and the tibial plateau increases. The pattern of ligament loading during activity is governed by the geometry of the muscles spanning the knee: the resultant force in the ACL during isometric knee extension is determined mainly by the changing orientation of the patellar tendon relative to the tibia in the sagittal plane; the resultant force in the PCL during isometric knee flexion is dominated by the angle at which the hamstrings meet the tibia in the sagittal plane.     

EMG-angle relationship of the hamstring muscles during maximum knee flexion.

The aim of the present study was to investigate the EMG-joint angle relationship during voluntary contraction with maximum effort and the differences in activity among three hamstring muscles during knee flexion. Ten healthy subjects performed maximum voluntary isometric and isokinetic knee flexion. The isometric tests were performed for 5 s at knee angles of 60 and 90 degrees. The isokinetic test, which consisted of knee flexion from 0 to 120 degrees in the prone position, was performed at an angular velocity of 30 degrees /s (0.523 rad/s). The knee flexion torque was measured using a KIN-COM isokinetic dynamometer. The individual EMG activity of the hamstrings, i.e. the semitendinosus, semimembranosus, long head of the biceps femoris and short head of the biceps femoris muscles, was detected using a bipolar fine wire electrode. With isometric testing, the knee flexion torque at 60 degrees knee flexion was greater than that at 90 degrees. The mean peak isokinetic torque occurred from 15 to 30 degrees knee flexion angle and then the torque decreased as the knee angle increased (p<0.01). The EMG activity of the hamstring muscles varied with the change in knee flexion angle except for the short head of the biceps femoris muscle under isometric condition. With isometric contraction, the integrated EMGs of the semitendinosus and semimembranosus muscles at a knee flexion angle of 60 degrees were significantly lower than that at 90 degrees. During maximum isokinetic contraction, the integrated EMGs of the semitendinosus, semimembranosus and short head of the biceps femoris muscles increased significantly as the knee angle increased from 0 to 105 degrees of knee flexion (p<0.05). On the other hand, the integrated EMG of the long head of the biceps femoris muscle at a knee angle of 60 degrees was significantly greater than that at 90 degrees knee flexion with isometric testing (p<0.01). During maximum isokinetic contraction, the integrated EMG was the greatest at a knee angle between 15 and 30 degrees, and then significantly decreased as the knee angle increased from 30 to 120 degrees (p<0.01). These results demonstrate that the EMG activity of hamstring muscles during maximum isometric and isokinetic knee flexion varies with change in muscle length or joint angle, and that the activity of the long head of the biceps femoris muscle differs considerably from the other three heads of hamstrings.     

Kinematic, kinetic and EMG patterns during downward squatting.

The aim of this study was to investigate the kinematic, kinetic, and electromyographic pattern before, during and after downward squatting when the trunk movement is restricted in the sagittal plane. Eight healthy subjects performed downward squatting at two different positions, semisquatting (40 degrees knee flexion) and half squatting (70 degrees knee flexion). Electromyographic responses of the vastus medialis oblique, vastus medialis longus, rectus femoris, vastus lateralis, biceps femoris, semitendineous, gastrocnemius lateralis, and tibialis anterior were recorded. The kinematics of the major joints were reconstructed using an optoelectronic system. The center of pressure (COP) was obtained using data collected from one force plate, and the ankle and knee joint torques were calculated using inverse dynamics. In the upright position there were small changes in the COP and in the knee and ankle joint torques. The tibialis anterior provoked the disruption of this upright position initiating the squat. During the acceleration phase of the squat the COP moved posteriorly, the knee joint torque remained in flexion and there was no measurable muscle activation. As the body went into the deceleration phase, the knee joint torque increased towards extension with major muscle activities being observed in the four heads of the quadriceps. Understanding these kinematic, kinetic and EMG strategies before, during and after the squat is expected to be beneficial to practitioners for utilizing squatting as a task for improving motor function.     

Increasing quadriceps loads affect the lengths of the ligaments and the kinematics of the knee.

The relationships between the lengths of the ligaments and kinematics of the knee and quadriceps load, for low to physiologic levels of quadriceps loads, have not previously been studied. We investigated the effects of increasing levels of quadriceps force, necessary to balance increasing levels of externally applied flexion moments, on the kinematics of the tibiofemoral joint and on the separation distances between insertions of selected fibers of the major ligaments of the knee in twelve cadavera. Static measurements were made using a six-degree-of-freedom digitizer for flexion angles ranging from 0 to 120 deg in 15 deg increments. Quadriceps generated extension of the knee was performed by applying loads to the quadriceps tendon to equilibrate each of four magnitudes of external flexion moments equivalent to 8.33, 16.67, 25.00, and 33.33 percent of values previously reported for maximum isometric extension moments. The magnitude of quadriceps force increased linearly (p < 0.0001) as external flexion moment increased throughout the entire range of flexion. Anterior translation, internal rotation, and abduction of the tibia increased linearly (p < 0.0001, p < 0.001, p < 0.001) as external flexion moment and, hence, quadriceps load increased. For the fibers studied, the anterior cruciate ligament (p < 0.0076), posterior cruciate ligament (p < 0.0001), and medial collateral ligament (p < 0.0383) lengthened linearly while the lateral collateral ligament (p < 0.0124) shortened linearly as quadriceps load increased. Based on these results for low to physiologic levels of quadriceps loads, it is reasonable to assume that the ligament lengths or knee kinematics expected with higher quadriceps loads can be extrapolated.     

Uncertainty of knee joint muscle activity during knee joint torque exertion: the significance of controlling adjacent joint torque.

In the single-joint torque exertion task, which has been widely used to control muscle activity, only the relevant joint torque is specified. However, the neglect of the neighboring joint could make the procedure unreliable, considering our previous result that even monoarticular muscle activity level is indefinite without specifying the adjacent joint torque. Here we examined the amount of hip joint torque generated with knee joint torque and its influence on the activity of the knee joint muscles. Twelve healthy subjects were requested to exert various levels of isometric knee joint torque. The knee and hip joint torques were obtained by using a custom-made device. Because no information about hip joint torque was provided to the subjects, the hip joint torque measured here was a secondary one associated with the task. The amount of hip joint torque varied among subjects, indicating that they adopted various strategies to achieve the task. In some subjects, there was a considerable internal variability in the hip joint torque. Such variability was not negligible, because the knee joint muscle activity level with respect to the knee joint torque, as quantified by surface electromyography (EMG), changed significantly when the subjects were requested to change the strategy. This change occurred in a very systematic manner: in the case of the knee extension, as the hip flexion torque was larger, the activity of mono- and biarticular knee extensors decreased and increased, respectively. These results indicate that the conventional single knee joint torque exertion has the drawback that the intersubject and/or intertrial variability is inevitable in the relative contribution among mono- and biarticular muscles because of the uncertainty of the hip joint torque. We discuss that the viewpoint that both joint torques need to be considered will bring insights into various controversial problems such as the shape of the EMG-force relationship, neural factors that help determine the effect of muscle strength training, and so on.     

Musculo-skeletal modelling of NMES-evoked knee extension in spinal cord injury

The objective of this study was to explore relationships among constants used in musculo-skeletal models predicting torque generated about the knee by the quadriceps muscles. A model was developed and matched to data collected from individuals with spinal cord injury performing quadriceps contractions evoked using neuromuscular electrical stimulation. After fitting tendon slack lengths to the quadriceps muscles, the model was able to accurately match experimentally measured knee extension torques using previously reported values for the moment arm-knee angle and force-velocity relationships. Fitting new constants to these relationships did not improve the match between measured and modelled knee extension torques. There was significant interaction between variables used within the model. Using a narrower active force-length relationship for the muscles required the model to have smaller moment arms about the knee to accurately match measured torque across the full range of motion. Reduced moment arms, however, lowered the model's linear velocity of muscle shortening for each angular velocity of the knee, requiring different constants within the force-velocity relationship to predict the appropriate amount of torque decline. The present study demonstrates that, when a model does not fit the observed data, it is difficult to determine exactly which components are responsible because of the interdependent nature of parameters.