Is a joint moment-based cost function associated with preferred cycling cadence?

Eight experienced male cyclists (C), eight well-trained male runners (R), and eight less-trained male noncyclists (LT) were tested under multiple cadence and power output conditions to determine: (1) if the cadence at which lower extremity net joint moments are minimized (cost function cadence) was associated with preferred pedaling cadence (PC), (2) if the cost function cadence increased with increases in power output, and (3) if the association is generalizable across groups differing in cycling experience and aerobic power. Net joint moments at the hip, knee, and ankle were computed from video records and pedal reaction force data using 2-D inverse dynamics. The sum of the average absolute hip, knee, and ankle joint moments defined a cost function at each power output and cadence and provided the basis for prediction of the cadence which minimized net joint moments for each subject at each power output. The cost function cadence was not statistically different from the PC at each power output in all groups. As power output increased, however, the cost function cadence increased for all three subject groups (86 rpm at 100 W, 93 rpm at 150 W, 98 rpm at 200 W, and 96 rpm at 250 W). PC showed little change (R) or a modest decline (C, LT) with increasing power output. Based upon the similarity in the mean data but different trends in the cost function cadence and PC in response to changes in power output as well as the lack of significant correlations between these two variables, it was concluded that minimiking net joint moments is a factor modestly associated with preferred cadence selection.     

Fatigue effects on the coordinative pattern during cycling: Kinetics and kinematics evaluation

The aim of the present study was to analyze the net joint moment distribution, joint forces and kinematics during cycling to exhaustion. Right pedal forces and lower limb kinematics of ten cyclists were measured throughout a fatigue cycling test at 100% of PO_MAX. The absolute net joint moments, resultant force and kinematics were calculated for the hip, knee and ankle joint through inverse dynamics. The contribution of each joint to the total net joint moments was computed. Decreased pedaling cadence was observed followed by a decreased ankle moment contribution to the total joint moments in the end of the test. The total absolute joint moment, and the hip and knee moments has also increased with fatigue. Resultant force was increased, while kinematics has changed in the end of the test for hip, knee and ankle joints. Reduced ankle contribution to the total absolute joint moment combined with higher ankle force and changes in kinematics has indicated a different mechanical function for this joint. Kinetics and kinematics changes observed at hip and knee joint was expected due to their function as power sources. Kinematics changes would be explained as an attempt to overcome decreased contractile properties of muscles during fatigue.     

In vivo hip joint loads and pedal forces during ergometer cycling

The rising prevalence of osteoarthritis and an increase in total hip replacements calls for attention to potential therapeutic activities. Cycling is considered as a low impact exercise for the hip joint and hence recommended. However, there are limited data about hip joint loading to support this claim. The aim of this study was to measure synchronously the in vivo hip joint loads and pedal forces during cycling. The in vivo hip joint loads were measured in 5 patients with instrumented hip implants. Data were collected at several combinations of power and cadence, at two saddle heights.Joint loads and pedal forces showed strong linear correlation with power. So the relationship between the external pedal forces and internal joint forces was shown. While cycling at different cadences the minimum joint loads were acquired at 60 RPM. The lower saddle height configuration results in an approximately 15% increase compared to normal saddle height.The results offered new insights into the actual effects of cycling on the hip joint and can serve as useful tools while developing an optimum cycling regimen for individuals with coxarthrosis or following total hip arthroplasty. Due to the relatively low contact forces, cycling at a moderate power level of 90 W at a normal saddle height is suitable for patients.     

Biomechanics of overground vs. treadmill walking in healthy individuals.

The goal of this study was to compare treadmill walking with overground walking in healthy subjects with no known gait disorders. Nineteen subjects were tested, where each subject walked on a split-belt instrumented treadmill as well as over a smooth, flat surface. Comparisons between walking conditions were made for temporal gait parameters such as step length and cadence, leg kinematics, joint moments and powers, and muscle activity. Overall, very few differences were found in temporal gait parameters or leg kinematics between treadmill and overground walking. Conversely, sagittal plane joint moments were found to be quite different, where during treadmill walking trials, subjects demonstrated less dorsiflexor moments, less knee extensor moments, and greater hip extensor moments. Joint powers in the sagittal plane were found to be similar at the ankle but quite different at the knee and hip joints. Differences in muscle activity were observed between the two walking modalities, particularly in the tibialis anterior throughout stance, and in the hamstrings, vastus medialis and adductor longus during swing. While differences were observed in muscle activation patterns, joint moments and joint powers between the two walking modalities, the overall patterns in these behaviors were quite similar. From a therapeutic perspective, this suggests that training individuals with neurological injuries on a treadmill appears to be justified.     

The effects of sloped surfaces on locomotion: backward walking as a perturbation

The purpose of this study was to examine lower extremity kinetics and muscle activity during backward slope walking to clarify the relationship between joint moments and powers and muscle activity patterns observed in forward slope walking. Nine healthy volunteers walked backward on an instrumented ramp at three grades (-39% (-21 degrees ), 0% (level), +39% (+21 degrees )). EMG activity was recorded from major lower extremity muscles. Joint kinetics were obtained from kinematic and force platform data. The knee joint moment and power generation increased significantly during upslope walking; hip joint moment and power absorption increased significantly during downslope walking. When compared to data from forward slope walking, these backward walking data suggest that power requirements of a task dictate the muscle activity pattern needed to accomplish that movement. During downslope walking tasks, power absorption increased and changes in muscle activity patterns were directly related to the changes in the joint moment patterns. In contrast, during upslope walking tasks, power generation increased and changes in the muscle activity were related to the changes in the joint moments only at the 'primary' joint; at adjacent joints the changes in muscle activity were unrelated to the joint moment pattern. The 'paradoxical' changes in the muscle activity at the adjacent joints are possibly related to the activation of biarticular muscles required by the increased power generation at the primary joint. In total, these data suggest that changing power requirements at a joint impact the control of muscle activity at that and adjacent joints.     

Three-dimensional knee joint loading during seated cycling.

The hypothesis which motivated the work reported in this article was that neglecting pure moments developed between the foot and pedal during cycling leads to a substantial error in computing axial and varus/valgus moments at the knee. To test this hypothesis, a mathematical procedure was developed for computing the three-dimensional knee loads using three-dimensional pedal forces and moments. In addition to data from a six-load-component pedal dynamometer, the model used pedal position and orientation and knee position in the frontal plane to determine the knee joint loads. Experimental data were collected from the right leg of 11 male subjects during steady-state cycling at 90 rpm and 225 W. The mean peak varus knee moment calculated was 15.3 N m and the mean peak valgus knee moment was 11.2 N m. Neglecting the pedal moment about the anterior/posterior axis resulted in an average absolute error of 2.6 N m and a maximum absolute error of 4.0 N m in the varus/valgus knee moment. The mean peak internal and external axial knee moments were 2.8 N m and 2.3 N m, respectively. The average and maximum absolute errors in the axial knee moment for not including the moment about an axis normal to the pedal were found to be 2.6 N m and 5.0 N m, respectively. The results strongly support the use of three-dimensional pedal loads in the computation of knee joint moments out of the sagittal plane.     

Power output and work in different muscle groups during ergometer cycling

The aim of this study was to calculate the magnitude of the instantaneous muscular power output at the hip, knee and ankle joints during ergometer cycling. Six healthy subjects pedalled a weight-braked bicycle ergometer at 120 watts (W) and 60 revolutions per minute (rpm). The subjects were filmed with a cine camera, and pedal reaction forces were recorded from a force transducer mounted in the pedal. The muscular work at the hip, knee and ankle joint was calculated using a model based upon dynamic mechanics described elsewhere. The mean peak concentric power output was, for the hip extensors, 74.4 W, hip flexors, 18.0 W, knee extensors, 110.1 W, knee flexors, 30.0 W and ankle plantar flexors, 59.4 W. At the ankle joint, energy absorption through eccentric plantar flexor action was observed, with a mean peak power of 11.4 W and negative work of 3.4 J for each limb and complete pedal revolution. The energy production relationships between the different major muscle groups were computed and the contributions to the total positive work were: hip extensors, 27%; hip flexors, 4%; knee extensors, 39%; knee flexors, 10%; and ankle plantar flexors 20%.     

Mechanical muscular power output and work during ergometer cycling at different work loads and speeds

The aim of the study was to calculate the magnitude of the instantaneous muscular power output at the hip, knee and ankle joints during ergometer cycling at different work loads and speeds. Six healthy subjects pedalled a weight-braked cycle ergometer at 0, 120 and 240 W at a constant speed of 60 rpm. The subjects also pedalled at 40, 60, 80 and 100 rpm against the same resistance, giving power outputs of 80, 120, 160 and 200 W respectively. The subjects were filmed with a cine-film camera, and pedal reaction forces were recorded from a force transducer mounted in the pedal. The muscular work for the hip, knee and ankle joint muscles was calculated using a model based upon dynamic mechanics and described elsewhere. The total work during one pedal revolution significantly increased with increased work load but did not increase with increased pedalling rate at the same braking force. The relative proportions of total positive work at the hip, knee and ankle joints were also calculated. Hip and ankle extension work proportionally decreased with increased work load. Pedalling rate did not change the relative proportion of total work at the different joints.     

Biomechanical model and evaluation of a linear motion squat type exercise

A biomechanical model of a squat exercise performed on a device using a bar that is restricted to a linear motion was developed. Hip and knee moments were evaluated at varying foot positions. The range of motion of the exercise was limited by the knee joint angle beginning at an 80 degrees angle (flexed) to a 179 degrees joint angle (extended). Variations in foot placement were evaluated for differences in torque applied about the transverse axes of the user's knee and hip joints. Because the user's feet were positioned farther forward (anterior), the moment about the knee decreased whereas the moment about the hip increased. Positive moments were those that resulted in forces to flex the knee and hip joints. Positive knee moments were determined in all conditions when the knee was flexed and became negative when the knee was at or near full extension. The model always produced positive moments about the hip. Thus, foot position is a critical factor in hip and knee moments, and therefore in the muscle groups stressed, in a linear motion squat type exercise.     

Effect of landing height on frontal plane kinematics, kinetics and energy dissipation at lower extremity joints

Lack of the necessary magnitude of energy dissipation by lower extremity joint muscles may be implicated in elevated impact stresses present during landing from greater heights. These increased stresses are experienced by supporting tissues like cartilage, ligaments and bones, thus aggravating injury risk. This study sought to investigate frontal plane kinematics, kinetics and energetics of lower extremity joints during landing from different heights. Eighteen male recreational athletes were instructed to perform drop-landing tasks from 0.3- to 0.6-m heights. Force plates and motion-capture system were used to capture ground reaction force and kinematics data, respectively. Joint moment was calculated using inverse dynamics. Joint power was computed as a product of joint moment and angular velocity. Work was defined as joint power integrated over time. Hip and knee joints delivered significantly greater joint power and eccentric work (p<0.05) than the ankle joint at both landing heights. Substantial increase (p<0.05) in eccentric work was noted at the hip joint in response to increasing landing height. Knee and hip joints acted as key contributors to total energy dissipation in the frontal plane with increase in peak ground reaction force (GRF). The hip joint was the top contributor to energy absorption, which indicated a hip-dominant strategy in the frontal plane in response to peak GRF during landing. Future studies should investigate joint motions that can maximize energy dissipation or reduce the need for energy dissipation in the frontal plane at the various joints, and to evaluate their effects on the attenuation of lower extremity injury risk during landing.     

Expressing the joint moments of drop jumps and sidestep cutting in different reference frames – does it matter?

Joint moments help us understand joint loading and muscle function during movement. However, the interpretation depends on the choice of reference frame, but the different reference frames have not been compared in dynamic, high-impact sporting movements. We have compared the magnitude and the resulting ranking of hip and knee joint moments expressed in the laboratory coordinate system, the local system of the distal segment and projected or decomposed to the Joint Coordinate System (JCS) axes. Hip and knee joint moments of drop jumps and sidestep cutting in 70 elite female handball players were calculated based on recordings from an eight-camera 240 Hz system and two force platforms and expressed with the four methods. The greatest variations in magnitude between conditions were seen for drop jump hip internal rotation (range: 0.31–0.71 Nm/kg) and sidestep cutting knee flexion (2.87–3.39 Nm/kg) and hip internal rotation (0.87–2.36 Nm/kg) and knee internal rotation (0.10–0.40 Nm/kg) moments. The rank correlations were highest between conditions for flexion moments (0.88–1.00) and sidestep cutting abduction moments (0.71–0.98). The rank correlations ranged from 0.64 to 0.73 for drop jump knee abduction moments and between −0.17 and 0.67 for hip and knee internal rotation moments. Expression of joint moments in different reference systems affects the magnitude and ranking of athletes. This lack of consistency may complicate the comparison and combination of results. Projection to the JCS is the only method where joint moments correspond to muscle and ligament loading. More widespread adoption of this convention could facilitate comparison of studies and ease the interpretation of results.     

The effects of cycling cadence on the phases of joint power,crank power,force and force effectiveness

We examined the influence of cadence in cycling technique by quantifying phase relationships for a number of important variables at the crank and lower extremity joints. Any difference in the effect of cadence on force, effectiveness, and power phases would indicate an essential change in coordination pattern. Cycle kinetics was recorded for 10 male competitive cyclists at five cadences (60–100 rpm) at submaximal load (260 W). Joint powers were calculated using inverse dynamics methods. All data were expressed as a function of crank position. The phase of the crank mechanical profiles (total force, crank and joint power, and effectiveness) was calculated using four methods: crank angle of maximum (MA) and minimum (MI), fitting a sine wave (SI) and by cross-correlation (XC). These methods, apart from the MA method, showed the same relative phase. The variables, however, showed different phases being expressed as time lag: force effectiveness: 0.131 (±0.034) s; total force: 0.149 (±0.021) s; power: 0.098 (±0.027) s. The phases in joint powers hip 0.071 (±0.008), knee 0.082 (±0.009), and hip 0.077 (±0.012) were only well described by XC, and were somewhat lower than the crank power phase. These differences indicate the potential effect of inertia of the lower limb in phase shifts from joints to crank. Furthermore, the differences between the various crank variables indicate a change of technique with cadence.     

Multivariable optimization of cycling biomechanics

Relying on a biomechanical model of the lower limb which treats the leg-bicycle system as a five-bar linkage constrained to plane motion, a cost function derived from the joint moments developed during cycling is computed. At constant average power of 200 W, the effect of five variables on the cost function is studied. The five variables are pedalling rate, crank arm length, seat tube angle, seat height, and longitudinal foot position on the pedal. A sensitivity analysis of each of the five variables shows that pedalling rate is the most sensitive, followed by the crank arm length, seat tube angle, seat height, and longitudinal foot position on the pedal (the least sensitive). Based on Powell's method, a multivariable optimization search is made for the combination of variable values which minimize the cost function. For a rider of average anthropometry (height 1.78 m, weight 72.5 kg), a pedalling rate of 115 rev min-1, crank arm length of 0.140 m, seat tube angle of 76 degrees, seat height plus crank arm length equal to 97% of trochanteric leg length, and longitudinal foot position on the pedal equal to 54% of foot length correspond to the cost function global minimum. The effect of anthropometric parameter variations is also examined and these variations influence the results significantly. The optimal crank arm length, seat height, and longitudinal foot position on the pedal increase as the size of rider increases whereas the optimal cadence and seat tube angle decrease as the rider's size increases. The dependence of optimization results on anthropometric parameters emphasizes the importance of tailoring bicycle equipment to the anthropometry of the individual.     

Crank inertial load has little effect on steady-state pedaling coordination

Inertial load can affect the control of a dynamic system whenever parts of the system are accelerated ordeclerated. During steady-state pedating, because within-cycle variations in crank angular acceleration still exist, the amount of crank inertia present (which varies widely with road-riding gear ratio) may affect the within-cycle coordination of muscles. However, the effect of inertial load on steady-state pedaling coordination is almos always assumed to be negligible, since the net mechanical energy per cycle developed by muscles only depends on the constant cadence and workload. This study tests the hypothesis that under steady-state conditions, the net joint torques produced by muscles at the hip, knee, and ankle are unaffected by crank inertial load. To perform the investigation, we constructed a pedaling apparatus which could emulate the low inertial load of a standard ergometer or the high inertial load of a road bicycle in high gear. Crank angle and bilateral pedal force and angle data were collected from ten subjects instructed to pedal steadily (i.e. constant speed across cycles) and smoothly (i.e. constant speed within a cycle) against both inertias at a constant workload. Virtually no statistically significant changes were found in the net hip and knee muscle joint torques calculated from an inverse dynamics analysis. Though the net ankle muscle joint torque, as well as the one- and two-legged crank torque, showed statistically significant increases at the higher inertia, the changes were small. In contrast, large statistically significant reductions were found in crank kinematic variability both within a cycle and between cycles (i.e. cadence), primarily because a larger inertial load means a slower crank dynamic response. Nonetheless, the reduction in cadence variability was somewhat attenuated by a large statistically significant increase in one-legged crank torque variability. We suggest, therefore, that muscle coordination during steady-state pedaling is largely unaffected, though less well regulated, when crank inertial load is increased.     

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.     

The effect of direct measurement versus cadaver estimates of anthropometry in the calculation of joint moments during above-knee prosthetic gait in pediatrics

Joint reaction forces, moments and powers are important in interpreting gait mechanics and compensatory strategies used by patients walking with above-knee prostheses. Segmental anthropometrics, required to calculate joint moments, are often estimated using data from cadaver studies. However, these values may not be accurate for patients following amputation as prostheses are composed of non-biologic material. The purpose of this study was to compare joint moments using anthropometrics calculated from cadaver studies versus direct measurements of the residual limb and prosthesis for children with an above-knee amputation. Gait data were collected for four subjects with above-knee prostheses walking at preferred and fast speeds. Joint moments were computed using anthropometrics from cadaver studies and direct measurements for each subject. The difference between these two methods primarily affected the inertia couple (Ialpha term) and the inertial effect due to gravity, which comprised a greater percentage of the total joint moment during swing as compared to stance. Peak hip and knee flexor and extensor moments during swing were significantly greater when calculated using cadaver data (p<0.05). These differences were greater while walking fast as compared to slow speeds. A significant difference was not found between these two methods for peak hip and knee moments during stance. A significant difference was found for peak ankle joint moments during stance, but the magnitude was not clinically important. These results support the use of direct measurements of anthropometry when examining above-knee prosthetic gait, particularly during swing.     

Modeling the stance leg in two-dimensional analyses of sprinting: inclusion of the MTP joint affects joint kinetics

Two-dimensional analyses of sprint kinetics are commonly undertaken but often ignore the metatarsalphalangeal (MTP) joint and model the foot as a single segment. Due to the linked-segment nature of inverse dynamics analyses, the aim of this study was to investigate the effect of ignoring the MTP joint on the calculated joint kinetics at the other stance leg joints during sprinting. High-speed video and force platform data were collected from four to five trials for each of three international athletes. Resultant joint moments, powers, and net work at the stance leg joints during the first stance phase after block clearance were calculated using three different foot models. By ignoring the MTP joint, peak extensor moments at the ankle, knee, and hip were on average 35% higher (p < .05 for each athlete), 40% lower (p < .05), and 9% higher (p > .05), respectively, than those calculated with the MTP joint included. Peak ankle and knee joint powers and net work at all joints were also significantly (p < .05) different. By ignoring a genuine MTP joint plantar flexor moment, artificially high peak ankle joint moments are calculated, and these also affect the calculated joint kinetics at the knee.     

Mechanical analysis of the landing phase in heel-toe running.

Results of mechanical analyses of running may be helpful in the search for the etiology of running injuries. In this study a mechanical analysis was made of the landing phase of three trained heel-toe runners, running at their preferred speed and style. The body was modeled as a system of seven linked rigid segments, and the positions of markers defining these segments were monitored using 200 Hz video analysis. Information about the ground reaction force vector was collected using a force plate. Segment kinematics were combined with ground reaction force data for calculation of the net intersegmental forces and moments. The vertical component of the ground reaction force vector Fz was found to reach a first peak approximately 25 ms after touch-down. This peak occurs because, in the support leg, the vertical acceleration of the knee joint is not reduced relative to that of the ankle joint by rotation of the lower leg, so that the support leg segments collide with the floor. Rotation of the support upper leg, however, reduces the vertical acceleration of the hip joint relative to that of the knee joint, and thereby plays an important role in limiting the vertical forces during the first 40 ms. Between 40 and 100 ms after touch-down, the vertical forces are mainly limited by rotation of the support lower leg. At the instant that Fz reaches its first peak, net moments about ankle, knee and hip joints of the support leg are virtually zero. The net moment about the knee joint changed from -100 Nm (flexion) at touch-down to +200 Nm (extension) 50 ms after touch-down. These changes are too rapid to be explained by variations in the muscle activation levels and were ascribed to spring-like behavior of pre-activated knee flexor and knee extensor muscles. These results imply that the runners investigated had no opportunity to control the rotations of body segments during the first part of the contact phase, other than by selecting a certain geometry of the body and muscular (co-)activation levels prior to touch-down.     

Bottom-up estimation of joint moments during manual lifting using orientation sensors instead of position sensors

L5/S1, hip and knee moments during manual lifting tasks are, in a laboratory environment, frequently established by bottom-up inverse dynamics, using force plates to measure ground reaction forces (GRFs) and an optoelectronic system to measure segment positions and orientations. For field measurements, alternative measurement systems are being developed. One alternative is the use of small body-mounted inertial/magnetic sensors (IMSs) and instrumented force shoes to measure segment orientation and GRFs, respectively. However, because IMSs measure segment orientations only, the positions of segments relative to each other and relative to the GRFs have to be determined by linking them, assuming fixed segment lengths and zero joint translation. This will affect the estimated joint positions and joint moments. This study investigated the effect of using segment orientations only (orientation-based method) instead of using orientations and positions (reference method) on three-dimensional joint moments. To compare analysis methods (and not measurement methods), GRFs were measured with a force plate and segment positions and/or orientations were measured using optoelectronic marker clusters for both analysis methods. Eleven male subjects lifted a box from floor level using three lifting techniques: a stoop, a semi-squat and a squat technique. The difference between the two analysis methods remained small for the knee moments: <4%. For the hip and L5/S1 moments, the differences were more substantial: up to 8% for the stoop and semi-squat techniques and up to 14% for the squat technique. In conclusion, joint moments during lifting can be estimated with good accuracy at the knee joint and with reasonable accuracy at the hip and L5/S1 joints using segment orientation and GRF data only.     

Coordination of the leg muscles in backlift and leglift.

Net joint moments are often used to quantify the loading of structures (e.g. the intervertebral disc at L5S1) during lifting. This quantification method is also used to evaluate the loading of the knee, for instance, to determine the effect of backlifting as opposed to leglifting. However, the true loading of the joint as derived from net joint moments can be obscured by a possible co-contraction of antagonists. To unravel the mechanisms that determine the net joint moments in the knee, the leglift was compared to the backlift. Although a completely different net knee moment curve was found when comparing the two lifting techniques, it appeared to be closely related to the ground reaction force vector and its orientation with respect to the joint centre of rotation (R > 0.995). This close relation was established by co-contraction of both flexors and extensors of the knee. Furthermore, a close relation appeared to exist between the joint moment difference between hip and knee and the activity difference between rectus femoris muscle and hamstring (R = 0.72 and 0.83 in leglift and backlift, respectively). The knee-ankle joint moment difference and the activity of the gastrocnemius showed a close relation as well (R = -0.89 and 0.96 in leglift and backlift, respectively). These relations can be interpreted as a mechanism to distribute net moments across joints. It is concluded that during lifting tasks the intermuscular coordination is aimed at coupling of joint moments, such that the ground reaction force points in a direction that provides balance during the movement. The use of net joint moments as direct indicators for joint loading (e.g. knee) seems, therefore, questionable.