Inertial sensor-based knee flexion/extension angle estimation

A new method for estimating knee joint flexion/extension angles from segment acceleration and angular velocity data is described. The approach uses a combination of Kalman filters and biomechanical constraints based on anatomical knowledge. In contrast to many recently published methods, the proposed approach does not make use of the earth's magnetic field and hence is insensitive to the complex field distortions commonly found in modern buildings. The method was validated experimentally by calculating knee angle from measurements taken from two IMUs placed on adjacent body segments. In contrast to many previous studies which have validated their approach during relatively slow activities or over short durations, the performance of the algorithm was evaluated during both walking and running over 5 minute periods. Seven healthy subjects were tested at various speeds from 1 to 5 mile/h. Errors were estimated by comparing the results against data obtained simultaneously from a 10 camera motion tracking system (Qualysis). The average measurement error ranged from 0.7 degrees for slow walking (1 mph) to 3.4 degrees for running (5 mph). The joint constraint used in the IMU analysis was derived from the Qualysis data. Limitations of the method, its clinical application and its possible extension are discussed.     

The highest antagonistic coactivation of the vastus intermedius muscle among quadriceps femoris muscles during isometric knee flexion

Although the possibility that the vastus intermedius (VI) muscle contributes to flexion of the knee joint has been suggested previously, the detail of its functional role in knee flexion is not well understood. The purpose of this study was to examine the antagonist coactivation of VI during isometric knee flexion. Thirteen men performed 25–100% of maximal voluntary contraction (MVC) at 90°, 120°, and 150° knee joint angles. Surface electromyography (EMG) of the four individual muscles in the quadriceps femoris (QF) was recorded and normalized by the EMG signals during isometric knee extension at MVC. Cross-talk on VI EMG signal was assessed based on the median frequency response to selective cooling of hamstring muscles. Normalized EMG of the VI was significantly higher than that of the other synergistic QF muscles at each knee joint angle (all P < 0.05) with minimum cross-talk from the hamstrings to VI. There were significant correlations between the EMG signal of the hamstrings and VI (r = 0.55–0.85, P < 0.001). These results suggest that VI acts as a primary antagonistic muscle of QF during knee flexion, and that VI is presumably a main contributor to knee joint stabilization.     

Forces acting on the patella during maximal voluntary contraction of the quadriceps femoris muscle at different knee flexion/extension angles

From knee extension moments measured with a dynamometer, the quadriceps muscle force, the patellar ligament force and the reaction force in the patellofemoral joint at various knee angles (0-90 degrees) were estimated. The information needed to calculate the combined effect of both patellofemoral and tibiofemoral joint on the mechanical advantage of the muscle was obtained from lateral-view radiographs of autopsy knees. The results show that the smallest quadriceps force (2,000 N) is exerted at maximal extension, and the largest force (8,000 N) at about 75 degrees of flexion. The patellar ligament force reaches a maximum (5,000 N) at 60 degrees. The reaction force in the patellofemoral joint is the smallest (1,000 N) at extension and is of the same values as the muscle force in a range from 75 to 90 degrees. Especially at large flexion angles, the value of the estimated forces is considerably larger (by 100%) than reported in the literature. This difference is attributed to the influence of the patellofemoral joint on the mechanical advantage of the muscle, which has not been taken into account in other studies.     

Prediction of pedal forces in bicycling using optimization methods

The bicycle-rider system is modeled as a planar five-bar linkage with pedal forces and pedal dynamics as input. The pedal force profile input is varied, maintaining constant average bicycle power, in order to obtain the optimal pedal force profile that minimizes two cost functions. One cost function is based on joint moments and the other is based on muscle stresses. Predicted (optimal) pedal profiles as well as joint moment time histories are compared to representative real data to examine cost function appropriateness. Both cost functions offer reasonable predictions of pedal forces. The muscle stress cost function, however, better predicts joint moments. Predicted muscle activity also correlates well with myoelectric data. The factors that lead to effective (i.e. low cost) pedalling are examined. Pedalling effectiveness is found to be a complex function of pedal force vector orientation and muscle mechanics.     

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.     

Contributions of muscle forces and toe-off kinematics to peak knee flexion during the swing phase of normal gait: an induced position analysis

A three-dimensional dynamic simulation of walking was used together with induced position analysis to determine how kinematic conditions at toe-off and muscle forces following toe-off affect peak knee flexion during the swing phase of normal gait. The flexion velocity of the swing-limb knee at toe-off contributed 30 degrees to the peak knee flexion angle; this was larger than any contribution from an individual muscle or joint moment. Swing-limb muscles individually made large contributions to knee angle (i.e., as large as 22 degrees), but their actions tended to balance one another, so that the combined contribution from all swing-limb muscles was small (i.e., less than 3 degrees of flexion). The uniarticular muscles of the swing limb made contributions to knee flexion that were an order of magnitude larger than the biarticular muscles of the swing limb. The results of the induced position analysis make clear the importance of knee flexion velocity at toe-off relative to the effects of muscle forces exerted after toe-off in generating peak knee flexion angle. In addition to improving our understanding of normal gait, this study provides a basis for analyzing stiff-knee gait, a movement abnormality in which knee flexion in swing is diminished.     

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.     

Influence of the knee flexion on muscle activation and transmissibility during whole body vibration

The influence of the knee flexion on muscle activation and transmissibility during whole body vibration is controversially discussed in the literature. In this study, 34 individuals had electromyography activity (EMG) of the vastus lateralis and the acceleration assessed while squatting with 60° and 90° of knee flexion either with or without whole-body vibration (WBV). The conditions were maintained for 10 s with 1 min of rest between each condition. The main findings were (1) the larger the angle of knee flexion (90° vs. 60°), the greater the EMG (p < 0.001), with no difference on acceleration transmissibility; (2) for both angles of knee flexion, the addition of WBV produced no significant difference in EMG and higher acceleration compared to without WBV (p < 0.001). These results suggest that the larger the knee flexion angle (60° vs. 90°), the greater the muscle activation without acceleration modification. However, the addition of WBV increases the transmissibility of acceleration in the lower limbs without modification in EMG of vastus lateralis.     

A dynamic optimization technique for predicting muscle forces in the swing phase of gait

The muscle force sharing problem was solved for the swing phase of gait using a dynamic optimization algorithm. For comparison purposes the problem was also solved using a typical static optimization algorithm. The objective function for the dynamic optimization algorithm was a combination of the tracking error and the metabolic energy consumption. The latter quantity was taken to be the sum of the total work done by the muscles and the enthalpy change during the contraction. The objective function for the static optimization problem was the sum of the cubes of the muscle stresses. To solve the problem using the static approach, the inverse dynamics problem was first solved in order to determine the resultant joint torques required to generate the given hip, knee and ankle trajectories. To this effect the angular velocities and accelerations were obtained by numerical differentiation using a low-pass digital filter. The dynamic optimization problem was solved using the Fletcher-Reeves conjugate gradient algorithm, and the static optimization problem was solved using the Gradient-restoration algorithm. The results show influence of internal muscle dynamics on muscle control histories vis a vis muscle forces. They also illustrate the strong sensitivity of the results to the differentiation procedure used in the static optimization approach.     

Mechanomyogram from the different heads of the quadriceps muscle during incremental knee extension

To investigate the time- and frequency-domain responses of mechanomyograms (MMGs) during the progressive fatigue induced by intermittent incremental contractions, a surface MMG was obtained from the three muscle heads of the quadriceps muscle in seven subjects while they performed isometric knee extensions lasting 7.6 min. Isometric intermittent incremental contractions started at 1% of the maximal voluntary contraction (MVC) for 3 s, with a 3-s relaxation period in between each contraction, and the contraction level was increased by 1% of MVC for every contraction (by 10% of MVC per min) up to exhaustion. Separate contractions with sufficient rest periods were also conducted to serve for the MMG characteristics without fatigue. The integrated MMG (iMMG) was linearly related to force in all of the muscles when fatigue was not involved. With regard to the incremental contractions, the relationship exhibited an ascending-descending shape, but the behavior was not the same for the individual muscle heads, especially for the rectus femoris muscle. A steep increase in the median frequency of MMG from around 60% of MVC corresponded to a decrease in iMMG. These results suggest that analysis of MMG in the time- and frequency-domain during an incremental protocol is a useful way of characterizing the motor unit recruitment strategy and fatigue properties of individual muscles. Accepted: 19 March 1998     

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.     

Agonist-antagonist common drive during fatiguing knee extension efforts using surface electromyography.

AIM: This study examined the electromyographic (EMG) activity of knee extensor agonists and a knee extensor antagonist muscle during fatiguing isometric extensions across a range of force levels. METHODS: Five female subjects performed isometric knee extensions at 25%, 50%, 75% and 100% of their maximal voluntary contraction (MVC) with the knee flexed to 75 degrees. Surface EMG (SEMG) was recorded with bipolar electrodes from the vastus lateralis (VL), vastus medialis (VM), rectus femoris (RF) and biceps femoris (BF) and the root-mean-squared (RMS) amplitude and the percentage frequency compression of these recordings were calculated. Commonality and cross talk between recordings were also examined. RESULTS: Cross talk between recordings was deemed negligible despite significant levels of commonality between the agonist and antagonist SEMG, which was attributed to common drive. SEMG RMS amplitude increased significantly for all muscles during the 25%, 50%, 75% MVC knee extensions until task failure, and decreased significantly for 100% MVC. The frequency spectrum of the SEMG compressed significantly for all muscles and % MVC levels. The VM, VL and BF SEMG recordings responded similarly to fatigue. The RF's frequency spectrum compressed to a significantly higher degree. CONCLUSIONS: The VM, VL, RF, and BF fatigue in parallel, with high similarity between VM, VL and BF, giving support to the concept of a shared agonist-antagonist motoneuron pool.     

Influence of the 3D inverse dynamic method on the joint forces and moments during gait

The joint forces and moments are commonly used in gait analysis. They can be computed by four different 3D inverse dynamic methods proposed in the literature, either based on vectors and Euler angles, wrenches and quaternions, homogeneous matrices, or generalized coordinates and forces. In order to analyze the influence of the inverse dynamic method, the joint forces and moments were computed during gait on nine healthy subjects. A ratio was computed between the relative dispersions (due to the method) and the absolute amplitudes of the gait curves. The influence of the inverse dynamic method was negligible at the ankle (2%) but major at the knee and the hip joints (40%). This influence seems to be due to the dynamic computation rather than the kinematic computation. Compared to the influence of the joint center location, the body segment inertial parameter estimation, and more, the influence of the inverse dynamic method is at least of equivalent importance. This point should be confirmed with other subjects, possibly pathologic, and other movements.     

Peak triceps surae muscle activity is not specific to knee flexion angles during MVIC

There is limited research on peak activity of the separate triceps surae muscles in select knee flexion (KF) positions during a maximum voluntary isometric contraction (MVIC) used to normalize EMG signals. The aim of this study was to determine how frequent peak activity occurred during an MVIC for soleus (SOL), gastrocnemius medialis (GM), and gastrocnemius lateralis (GL) in select KF positions, and if these peaks were recorded in similar KF positions. Forty-eight healthy individuals performed unilateral plantar-flexion MVIC in standing with 0°KF and 45°KF, and in sitting with 90°KF. Surface EMG of SOL, GM, and GL were collected and processed in 250 ms epochs to determine peak root-mean-square amplitude. Peak activity was most frequently captured in standing and rarely in sitting, with no position selective to SOL, GM or GL activity. Peak GM and GL activity was more frequent in 0°KF than 45°KF, and more often in similar KF positions than not. Peak SOL activity was just as likely in 45°KF as 0°KF, and more in positions similar to GM, but not GL. The EMG amplitudes were at least 20% greater in positions that captured peak activity over those that did not. The overall findings support performing an MVIC in more than one KF position to normalize triceps surae EMG. It is emphasized that no KF position is selective to SOL, GM, or GL alone.     

Comparison of erector spinae and hamstring muscle activities and lumbar motion during standing knee flexion in subjects with and without lumbar extension rotation syndrome

The aim of this study was to compare the activity of the erector spinae (ES) and hamstring muscles and the amount and onset of lumbar motion during standing knee flexion between individuals with and without lumbar extension rotation syndrome. Sixteen subjects with lumbar extension rotation syndrome (10 males, 6 females) and 14 healthy subjects (8 males, 6 females) participated in this study. During the standing knee flexion, surface electromyography (EMG) was used to measure muscle activity, and surface EMG electrodes were attached to both the ES and hamstring (medial and lateral) muscles. A three-dimensional motion analysis system was used to measure kinematic data of the lumbar spine. An independent-t test was conducted for the statistical analysis. The group suffering from lumbar extension rotation syndrome exhibited asymmetric muscle activation of the ES and decreased hamstring activity. Additionally, the group with lumbar extension rotation syndrome showed greater and earlier lumbar extension and rotation during standing knee flexion compared to the control group. These data suggest that asymmetric ES muscle activation and a greater amount of and earlier lumbar motion in the sagittal and transverse plane during standing knee flexion may be an important factor contributing to low back pain.     

Influence of knee flexion angle and age on triceps surae muscle fatigue during heel raises

ABSTRACT: Hébert-Losier, K, Schneiders, AG, García, JA, Sullivan, SJ, and Simoneau, GG. Influence of knee flexion angle and age on triceps surae muscle fatigue during heel raises. J Strength Cond Res 26(11): 3134-3147, 2012-The triceps surae (TS) muscle-tendon unit is 1 of the most commonly injured in elite and recreational athletes, with a high prevalence in middle-aged adults. The performance of maximal numbers of unilateral heel raises is used to assess, train, and rehabilitate TS endurance and conventionally prescribed in 0° knee flexion (KF) for the gastrocnemius and 45° for the soleus (SOL). However, the extent of muscle selectivity conferred through the change in the knee angle is lacking for heel raises performed to volitional fatigue. This study investigated the influence of knee angle on TS muscle fatigue during heel raises and determined whether fatigue differed between middle-aged and younger-aged adults. Forty-eight healthy individuals aged 18-25 and 35-45 years performed maximal numbers of unilateral heel raises in 0° and 45° KF. Median frequencies and linear regression slopes were calculated from the SOL, gastrocnemius medialis (GM), and gastrocnemius lateralis (GL) surface electromyographic signals. Stepwise mixed-effect regressions were used for analysis. The subjects completed an average of 45 and 48 heel raises in 0° and 45° KF, respectively. The results indicated that the 3 muscles fatigued during testing as all median frequencies decreased, and regression slopes were negative. Consistent with muscle physiology and fiber typing, fatigue was greater in the GM and GL than in the SOL (p < 0.001). However, knee angle did not influence TS muscle fatigue parameters (p = 0.814), with similar SOL, GM, and GL fatigue in 0° and 45° KF. These findings are in contrast with the traditionally described clinical use of heel raises in select knee angles for the gastrocnemius and the SOL. Furthermore, no difference in TS fatigue between the 2 age groups was able to be determined, despite the reported higher prevalence of injury in middle-aged individuals.     

Influence of knee flexion angle and age on triceps surae muscle activity during heel raises

ABSTRACT: Hébert-Losier, K, Schneiders, AG, García, JA, Sullivan, SJ, and Simoneau, GG. Influence of knee flexion angle and age on triceps surae muscle activity during heel raises. J Strength Cond Res 26(11): 3124-3133, 2012-Triceps surae and Achilles tendon injuries are frequent in sports medicine, particularly in middle-aged adults. Muscle imbalances and weakness are suggested to be involved in the etiology of these conditions, with heel-raise testing often used to assess and treat triceps surae (TS) injuries. Although heel raises are recommended with the knee straight for gastrocnemius and bent for soleus (SOL), the extent of muscle selectivity in these positions is not clear. This study aimed to determine the influence of knee angle and age on TS muscle activity during heel raises. Forty-eight healthy men and women were recruited from a younger-aged (18-25 years) and middle-aged (35-45 years) population. All the subjects performed unilateral heel raises in 0° and 45° knee flexion (KF). Soleus, gastrocnemius medialis (GM) and gastrocnemius lateralis (GL) surface electromyography signals were processed to compute root-mean-square amplitudes, and data were analyzed using mixed-effects models and stepwise regression. The mean TS activity during heel raises was 23% of maximum voluntary isometric contraction when performed in 0° KF and 21% when in 45°. Amplitudes were significantly different between TS muscles (p < 0.001) and KF angles (p < 0.001), with a significant interaction (p < 0.001). However, the age of the population did not influence the results (p = 0.193). The findings demonstrate that SOL activity was 4% greater when tested in 45° compared with 0° KF and 5% lower in the GM and GL. The results are consistent with the recommended use of heel raises in select knee positions for assessing, training, and rehabilitating the SOL and gastrocnemius muscles; however, the 4-5% documented change in activity might not be enough to significantly influence clinical outcome measures or muscle-specific benefits. Contrary to expectations, TS activity did not distinguish between middle-aged and younger-aged adults, despite the higher injury prevalence in middle age.     

A method for determining lower extremity muscle-tendon lengths during flexion/extension movements

A study was conducted to examine the relationship between muscle-tendon lengths of 16 lower extremity muscles and the flexion angle(s) of the joint(s) they cross. Anthropometric data from six subjects were obtained. Various lower extremity joint flexion angle combinations were simulated for each subject using computer software. For each simulated lower extremity position, muscle origin and insertion locations were determined based on averaged cadaveric origin/insertion information and individual anthropometric parameters. Corresponding muscle-tendon lengths were computed and normalized to segment lengths. Regression equations were derived which allow normalized muscle-tendon lengths to be estimated from known joint flexion angles. The regression equations obtained for biarticular muscles fit the data quite well giving correlation coefficients greater than 0.92. The correlation coefficients for the equations describing normalized single joint muscle-tendon lengths range from 0.77 to 0.97. The equations were then validated by comparing predicted lengths to those reported by previous investigations. Confirming the utility of the equations, the comparisons were excellent for both uniarticular and biarticular muscles. Used in conjunction with velocity data (obtained by differentiating the length data) and electromyogram recordings, these equations enable a detailed analysis of muscle function.