A theoretical analysis of preferred pedaling rate selection in endurance cycling

One objective of this study was to investigate whether neuromuscular quantities were associated with preferred pedaling rate selection during submaximal steady-state cycling from a theoretical perspective using a musculoskeletal model with an optimal control analysis. Specific neuromuscular quantities of interest were the individual muscle activation, force, stress and endurance. To achieve this objective, a forward dynamic model of cycling and optimization framework were used to simulate pedaling at three different rates of 75, 90 and 105 rpm at 265 W. The pedaling simulations were produced by optimizing the individual muscle excitation timing and magnitude to reproduce experimentally collected data. The results from these pedaling simulations indicated that all neuromuscular quantities were minimized at 90 rpm when summed across muscles. In the context of endurance cycling, these results suggest that minimizing neuromuscular fatigue is an important mechanism in pedaling rate selection. A second objective was to determine whether any of these quantities could be used to predict the preferred pedaling rate. By using the quantities with the strongest quadratic trends as the performance criterion to be minimized in an optimal control analysis, these quantities were analyzed to assess whether they could be further minimized at 90 rpm and produce normal pedaling mechanics. The results showed that both the integrated muscle activation and average endurance summed across all muscles could be further minimized at 90 rpm indicating that these quantities cannot be used individually to predict preferred pedaling rates.     

Adaptation of muscle coordination to altered task mechanics during steady-state cycling

The objective of this work was to increase our understanding of how motor patterns are produced during movement tasks by quantifying adaptations in muscle coordination in response to altered task mechanics. We used pedaling as our movement paradigm because it is a constrained cyclical movement that allows for a controlled investigation of test conditions such as movement speed and effort. Altered task mechanics were introduced using an elliptical chainring. The kinematics of the crank were changed from a relatively constant angular velocity using a circular chainring to a widely varying angular velocity using an elliptical chainring. Kinetic, kinematic and muscle activity data were collected from eight competitive cyclists using three different chainrings--one circular and two different orientations of an elliptical chainring. We tested the hypotheses that muscle coordination patterns (EMG timing and magnitude), specifically the regions of active muscle force production, would shift towards regions in the crank cycle in which the crank angular velocity, and hence muscle contraction speeds, were favorable to produce muscle power as defined by the skeletal muscle power-velocity relationship. The results showed that our hypothesis with regards to timing was not supported. Although there were statistically significant shifts in muscle timing, the shifts were minor in absolute terms and appeared to be the result of the muscles accounting for the activation dynamics associated with muscle force development (i.e. the delay in muscle force rise and decay). But, significant changes in the magnitude of muscle EMG during regions of slow crank angular velocity for the tibialis anterior and rectus femoris were observed. Thus, the nervous system used adaptations to the muscle EMG magnitude, rather than the timing, to adapt to the altered task mechanics. The results also suggested that cyclists might work on the descending limb of the power-velocity relationship when pedaling at 90 rpm and sub-maximal power output. This finding might have important implications for preferred pedaling rate selection.     

Determinants of metabolic cost during submaximal cycling.

The metabolic cost of producing submaximal cycling power has been reported to vary with pedaling rate. Pedaling rate, however, governs two physiological phenomena known to influence metabolic cost and efficiency: muscle shortening velocity and the frequency of muscle activation and relaxation. The purpose of this investigation was to determine the relative influence of those two phenomena on metabolic cost during submaximal cycling. Nine trained male cyclists performed submaximal cycling at power outputs intended to elicit 30, 60, and 90% of their individual lactate threshold at four pedaling rates (40, 60, 80, 100 rpm) with three different crank lengths (145, 170, and 195 mm). The combination of four pedaling rates and three crank lengths produced 12 pedal speeds ranging from 0.61 to 2.04 m/s. Metabolic cost was determined by indirect calorimetery, and power output and pedaling rate were recorded. A stepwise multiple linear regression procedure selected mechanical power output, pedal speed, and pedal speed squared as the main determinants of metabolic cost (R(2) = 0.99 +/- 0.01). Neither pedaling rate nor crank length significantly contributed to the regression model. The cost of unloaded cycling and delta efficiency were 150 metabolic watts and 24.7%, respectively, when data from all crank lengths and pedal speeds were included in a regression. Those values increased with increasing pedal speed and ranged from a low of 73 +/- 7 metabolic watts and 22.1 +/- 0.3% (145-mm cranks, 40 rpm) to a high of 297 +/- 23 metabolic watts and 26.6 +/- 0.7% (195-mm cranks, 100 rpm). These results suggest that mechanical power output and pedal speed, a marker for muscle shortening velocity, are the main determinants of metabolic cost during submaximal cycling, whereas pedaling rate (i.e., activation-relaxation rate) does not significantly contribute to metabolic cost.     

Optimization algorithm performance in determining optimal controls in human movement analyses

The objective of this study was to evaluate the performance of different multivariate optimization algorithms by solving a "tracking" problem using a forward dynamic model of pedaling. The tracking problem was defined as solving for the muscle controls (muscle stimulation onset, offset, and magnitude) that minimized the error between experimentally collected kinetic and kinematic data and the simulation results of pedaling at 90 rpm and 250 W. Three different algorithms were evaluated: a downhill simplex method, a gradient-based sequential quadratic programming algorithm, and a simulated annealing global optimization routine. The results showed that the simulated annealing algorithm performed for superior to the conventional routines by converging more rapidly and avoiding local minima.     

Performance criteria for generating predictive optimal control simulations of bicycle pedaling

The purpose of this study was to identify one or more performance-based criteria that may be used to generate predictive optimal control simulations of submaximal pedaling. Two-legged pedaling simulations were generated based on minimizing muscle activation, muscle stress, metabolic energy, time derivative of muscle force, and minimizing metabolic energy while pedaling smoothly. The simulations based on minimizing muscle activation and muscle stress most closely matched experimental pedaling data, with the activation criterion better matching experimental muscle activation timing. We conclude that predictive simulations of submaximal pedaling may be generated using a cost function based on minimizing muscle activation.     

Generating dynamic simulations of movement using computed muscle control

Computation of muscle excitation patterns that produce coordinated movements of muscle-actuated dynamic models is an important and challenging problem. Using dynamic optimization to compute excitation patterns comes at a large computational cost, which has limited the use of muscle-actuated simulations. This paper introduces a new algorithm, which we call computed muscle control, that uses static optimization along with feedforward and feedback controls to drive the kinematic trajectory of a musculoskeletal model toward a set of desired kinematics. We illustrate the algorithm by computing a set of muscle excitations that drive a 30-muscle, 3-degree-of-freedom model of pedaling to track measured pedaling kinematics and forces. Only 10 min of computer time were required to compute muscle excitations that reproduced the measured pedaling dynamics, which is over two orders of magnitude faster than conventional dynamic optimization techniques. Simulated kinematics were within 1 degrees of experimental values, simulated pedal forces were within one standard deviation of measured pedal forces for nearly all of the crank cycle, and computed muscle excitations were similar in timing to measured electromyographic patterns. The speed and accuracy of this new algorithm improves the feasibility of using detailed musculoskeletal models to simulate and analyze movement.     

A theoretical analysis of an optimal chainring shape to maximize crank power during isokinetic pedaling

Previous studies have sought to improve cycling performance by altering various aspects of the pedaling motion using novel crank–pedal mechanisms and non-circular chainrings. However, most designs have been based on empirical data and very few have provided significant improvements in cycling performance. The purpose of this study was to use a theoretical framework that included a detailed musculoskeletal model driven by individual muscle actuators, forward dynamic simulations and design optimization to determine if cycling performance (i.e., maximal power output) could be improved by optimizing the chainring shape to maximize average crank power during isokinetic pedaling conditions. The optimization identified a consistent non-circular chainring shape at pedaling rates of 60, 90 and 120 rpm with an average eccentricity of 1.29 that increased crank power by an average of 2.9% compared to a conventional circular chainring. The increase in average crank power was the result of the optimal chainrings slowing down the crank velocity during the downstroke (power phase) to allow muscles to generate power longer and produce more external work. The data also showed that chainrings with higher eccentricity increased negative muscle work following the power phase due to muscle activation–deactivation dynamics. Thus, the chainring shape that maximized average crank power balanced these competing demands by providing enough eccentricity to increase the external work generated by muscles during the power phase while minimizing negative work during the subsequent recovery phase.     

Effect of fatigue on maximal power output at different contraction velocities in humans.

The effect of fatigue as a result of a standard submaximal dynamic exercise on maximal short-term power output generated at different contraction velocities was studied in humans. Six subjects performed 25-s maximal efforts on an isokinetic cycle ergometer at five different pedaling rates (60, 75, 90, 105, and 120 rpm). Measurements of maximal power output were made under control conditions [after 6 min of cycling at 30% maximal O2 uptake (VO2max)] and after fatiguing exercise that consisted of 6 min of cycling at 90% VO2max with a pedaling rate of 90 rpm. Compared with control values, maximal peak power measured after fatiguing exercise was significantly reduced by 23 +/- 19, 28 +/- 11, and 25 +/- 11% at pedaling rates of 90, 105, and 120 rpm, respectively. Reductions in maximum peak power of 11 +/- 8 and 14 +/- 8% at 60 and 75 rpm, respectively, were not significant. The rate of decline in peak power during the 25-s control measurement was least at 60 rpm (5.1 +/- 2.3 W/s) and greatest at 120 rpm (26.3 +/- 13.9 W/s). After fatiguing exercise, the rate of decline in peak power at pedaling rates of 105 and 120 rpm decreased significantly from 21.5 +/- 9.0 and 26.3 +/- 13.9 W/s to 10.0 +/- 7.3 and 13.3 +/- 6.9 W/s, respectively. These experiments indicate that fatigue induced by submaximal dynamic exercise results in a velocity-dependent effect on muscle power. It is suggested that the reduced maximal power at the higher velocities was due to a selective effect of fatigue on the faster fatigue-sensitive fibers of the active muscle mass.     

The effects of changing bone and muscle size on limb inertial properties and limb dynamics: a computer simulation

The magnitude and distribution of bone and muscle mass within limbs affect limb inertial properties, maximum movement speed and the energy required to maintain submaximal movements. Musculoskeletal modeling and movement simulations were used to determine how changes in bone and muscle cross-sectional area (and thus mass) affect human thigh and shank inertial properties, the maximum speed of unloaded single-leg cycling and the energy required to sustain submaximal single-leg cycling. Depending on initial conditions, shank moments of inertia increased 61-72 kg cm2 per kg added bone and 72-100 kg cm2 per kg added muscle. Thigh moments of inertia increased 46-63 kg cm2 per kg bone and 180-225 kg cm2 per kg muscle. Maximum unloaded cycling velocity increased with increased muscle mass (approximately 2.2-2.9 rpm/kg muscle), but decreased with increased cortical bone mass (approximately 2.0-2.8 rpm/kg bone). The internal work associated with unloaded submaximal cycling increased with increased muscle mass (approximately 0.42-0.48 J/kg muscle) and bone mass (approximately 0.18-0.22 J/kg bone).     

Reproducibility of eight lower limb muscles activity level in the course of an incremental pedaling exercise.

Despite the wide use of surface electromyography (EMG) recorded during dynamic exercises, the reproducibility of EMG variables has not been fully established in a course of a dynamic leg exercise. The aim of this study was to investigate the reproducibility of eight lower limb muscles activity level during a pedaling exercise performed until exhaustion. Eight male were tested on two days held three days apart. Surface EMG was recorded from vastus lateralis, rectus femoris (RF), vastus medialis, semimembranosus, biceps femoris, gastrocnemius lateral, gastrocnemius medianus and tibialis anterior during incremental exercise test. The root mean square, an index of global EMG activity, was averaged every five crank revolutions (corresponding to about 3 s at 85 rpm) throughout the tests. Despite inter-subjects variations, we showed a high reproducibility of the activity level of lower limb muscles during a progressive pedaling exercise performed until exhaustion. However, RF muscle seemed to be the less reproducible of the eight muscles investigated during incremental pedaling exercise. These results suggest that each subject adopt a personal muscle activation strategy in a course of an incremental cycling exercise but fatigue phenomenon can induce some variations in the most fatigable muscles (RF).     

Sloped muscle excitation waveforms improve the accuracy of forward dynamic simulations

Mathematical models of the muscle excitation are useful in forward dynamic simulations of human movement tasks. One objective was to demonstrate that sloped as opposed to rectangular excitation waveforms improve the accuracy of forward dynamic simulations. A second objective was to demonstrate the differences in simulated muscle forces using sloped versus rectangular waveforms. To fulfill these objectives, surface EMG signals from the triceps brachii and elbow joint angle were recorded and the intersegmental moment of the elbow joint was computed from 14 subjects who performed two cyclic elbow extension experiments at 200 and 300 deg/s. Additionally, the surface EMG signals from the leg musculature, joint angles, and pedal forces were recorded and joint intersegmental moments were computed during a more complex pedaling task (90 rpm at 250 W). Using forward dynamic simulations, four optimizations were performed in which the experimental intersegmental moment was tracked for the elbow extension tasks and four optimizations were performed in which the experimental pedal angle, pedal forces, and joint intersegmental moments were tracked for the pedaling task. In these optimizations the three parameters (onset and offset time, and peak excitation) defining the sloped (triangular, quadratic, and Hanning) and rectangular excitation waveforms were varied to minimize the difference between the simulated and experimentally tracked quantities. For the elbow extension task, the intersegmental elbow moment root mean squared error, onset timing error, and offset timing error were less from simulations using a sloped excitation waveform compared to a rectangular excitation waveform (p<0.001). The average and peak muscle forces were from 7% to 16% larger and 20-28% larger, respectively, when using a rectangular excitation waveform. The tracking error for pedaling also decreased when using a sloped excitation waveform, with the quadratic waveform generating the smallest tracking errors for both tasks. These results support the use of sloped over rectangular excitation waveforms to establish greater confidence in the results of forward dynamic simulations.     

Intra-session repeatability of lower limb muscles activation pattern during pedaling

Assessment of intra-session repeatability of muscle activation pattern is of considerable relevance for research settings, especially when used to determine changes over time. However, the repeatability of lower limb muscles activation pattern during pedaling is not fully established. Thus, we tested the intra-session repeatability of the activation pattern of 10 lower limb muscles during a sub-maximal cycling exercise.Eleven triathletes participated to this study. The experimental session consisted in a reference sub-maximal cycling exercise (i.e. 150 W) performed before and after a 53-min simulated training session (mean power output = 200 ± 12 W). Repeatability of EMG patterns was assessed in terms of muscle activity level (i.e. RMS of the mean pedaling cycle and burst) and muscle activation timing (i.e. onset and offset of the EMG burst) for the 10 following lower limb muscles: gluteus maximus (GMax), semimembranosus (SM), Biceps femoris (BF), vastus medialis (VM), rectus femoris (RF), vastus lateralis (VL), gastrocnemius medianus (GM) and lateralis (GL), soleus (SOL) and tibialis anterior (TA).No significant differences concerning the muscle activation level were found between test and retest for all the muscles investigated. Only VM, SOL and TA showed significant differences in muscle activation timing parameters. Whereas ICC and SEM values confirmed this weak repeatability, cross-correlation coefficients suggest a good repeatability of the activation timing parameters for all the studied muscles.Overall, the main finding of this work is the good repeatability of the EMG pattern during pedaling both in term of muscle activity level and muscle activation timing.     

Optimal pedalling velocity characteristics during maximal and submaximal cycling in humans

The aim of this study was to compare optimal pedalling velocities during maximal (OVM) and submaximal (OVSM) cycling in human, subjects with different training backgrounds. A group of 22 subjects [6 explosive (EX), 6 endurance (EN) and 10 non-specialised subjects] sprint cycled on a friction-loaded ergometer four maximal sprints lasting 6 s each followed by five 3-min periods of steady-state cycling at 150 W with pedalling frequencies varying from 40 to 120 rpm. The OVM and OVSM were defined as the velocities corresponding to the maximal power production and the lowest oxygen consumption, respectively. A significant linear relationship (r2 = 0.52, P < 0.001) was found between individual OVM [mean 123.1 (SD 11.2) rpm] and OVSM [mean 57.0 (SD 4.9) rpm, P < 0.001] values, suggesting that the same functional properties of leg extensor muscles influence both OVM and OVSM. Since EX was greater than EN in both OVM and OVSM (134.3 compared to 110.9 rpm and 60.8 compared to 54.0 rpm, P < 0.01 and P < 0.05, respectively) it could be hypothesised that the distribution of muscle fibre type plays an important role in optimising both maximal and submaximal cycling performance.     

Biomechanical assessments of the effect of visual feedback on cycling for patients with stroke

Stroke patients exhibit abnormal pattern in leg cycling exercise. The aim of this study was to investigate the effects of visual feedback on the control of cycling motion in stroke patients from kinesiological, kinematic and kinetic aspects. The cycling performance derived from cycling electromyography (EMG), cycling cadence, and torque of forty stroke subjects was evaluated under conditions with and without visual feedback of cycling cadence. Kinesiological indices, shape symmetry index (SSI) and area symmetry index (ASI) were extracted from EMG linear envelopes to evaluate the symmetry of muscle firing patterns during cycling. Roughness index (RI) was calculated from cycling cadence to represent cycling smoothness from kinematic aspects. Averaged cycling power (Pav), the product of cadence and torque, was used to represent force output. The rectus femoris EMG showed significantly greater ASI with visual feedback, however, the difference in SSI between the two conditions was not significant. For the biceps femoris, there was a significant decrease in SSI with visual feedback, while the ASI was not affected significantly by the task conditions. The cycling smoothness was better and the average power generated was larger when visual feedback was provided. This study found that the addition of visual feedback improved both neuromuscular control and overall performance. Such improvement is likely to be the result of better control of the rectus femoris muscle activation and coordination of both legs.     

The association between negative muscle work and pedaling rate.

The objective of this research was to use a pedal force decomposition approach to quantify the amount of negative muscular crank torque generated by a group of competitive cyclists across a range of pedaling rates. We hypothesized that negative muscular crank torque increases at high pedaling rates as a result of the activation dynamics associated with muscle force development and the need for movement control, and that there is a correlation between negative muscular crank torque and pedaling rate. To test this hypothesis, data were collected during 60, 75, 90, 105 and 120 revolutions per minute (rpm) pedaling at a power output of 260 W. The statistical analysis supported our hypothesis. A significant pedaling rate effect was detected in the average negative muscular crank torque with all pedaling rates significantly different from each other (p < 0.05). There was no negative muscular crank torque generated at 60 rpm and negligible amounts at 75 and 90 rpm. But substantial negative muscular crank torque was generated at the two highest pedaling rates (105 and 120 rpm) that increased with increasing pedaling rates. This result suggested that there is a correlation between negative muscle work and the pedaling rates preferred by cyclists (near 90 rpm), and that the cyclists' ability to effectively accelerate the crank with the working muscles diminishes at high pedaling rates.     

The influence of pedaling rate on bilateral asymmetry in cycling.

The objectives of this study were to (1) determine whether bilateral asymmetry in cycling changed systematically with pedaling rate, (2) determine whether the dominant leg as identified by kicking contributed more to average power over a crank cycle than the other leg, and (3) determine whether the dominant leg asymmetry changed systematically with pedaling rate. To achieve these objectives, data were collected from 11 subjects who pedaled at five different pedaling rates ranging from 60 to 120 rpm at a constant workrate of 260 W. Bilateral pedal dynamometers measured two orthogonal force components in the plane of the bicycle. From these measurements, asymmetry was quantified by three dependent variables, the percent differences in average positive power (%AP), average negative power (%AN), and average crank power (%AC). Differences were taken for two cases--with respect to the leg generating the greater total average for each power quantity at 60 rpm disregarding the measure of dominance, and with respect to the dominant leg as determined by kicking. Simple linear regression analyses were performed on these quantities both for the subject sample and for individual subjects. For the subject sample, only the percent difference in average negative power exhibited a significant linear relationship with pedaling rate; as pedaling rate increased, the asymmetry decreased. Although the kicking dominant leg contributed significantly greater average crank power than the non-dominant leg for the subject sample, the non-dominant leg contributed significantly greater average positive power and average negative power than the dominant leg. However, no significant linear relationships for any of these three quantities with pedaling rate were evident for the subject sample because of high variability in asymmetry among the subjects. For example, significant linear relationships existed between pedaling rates and percent difference in total average power per leg for only four of the 11 subjects and the nature of these relationships was different (e.g. positive versus negative slopes). It was concluded that pedaling asymmetry is highly variable among subjects and that individual subjects may exhibit different systematic changes in asymmetry with pedaling rate depending on the quantity of interest.     

Neuromuscular adjustments that constrain submaximal EMG amplitude at task failure of sustained isometric contractions

The amplitude of the surface EMG does not reach the level achieved during a maximal voluntary contraction force at the end of a sustained, submaximal contraction, despite near-maximal levels of voluntary effort. The depression of EMG amplitude may be explained by several neural and muscular adjustments during fatiguing contractions, including decreased net neural drive to the muscle, changes in the shape of the motor unit action potentials, and EMG amplitude cancellation. The changes in these parameters for the entire motor unit pool, however, cannot be measured experimentally. The present study used a computational model to simulate the adjustments during sustained isometric contractions and thereby determine the relative importance of these factors in explaining the submaximal levels of EMG amplitude at task failure. The simulation results indicated that the amount of amplitude cancellation in the simulated EMG (～ 40%) exhibited a negligible change during the fatiguing contractions. Instead, the main determinant of the submaximal EMG amplitude at task failure was a decrease in muscle activation (number of muscle fiber action potentials), due to a reduction in the net synaptic input to motor neurons, with a lesser contribution from changes in the shape of the motor unit action potentials. Despite the association between the submaximal EMG amplitude and reduced muscle activation, the deficit in EMG amplitude at task failure was not consistently associated with the decrease in neural drive (number of motor unit action potentials) to the muscle. This indicates that the EMG amplitude cannot be used as an index of neural drive.     

Functional roles of the leg muscles when pedaling in the recumbent versus the upright position

An understanding of the coordination of the leg muscles in recumbent pedaling would be useful to the design of rehabilitative pedaling exercises. The objectives of this work were to (i) determine whether patterns of muscle activity while pedaling in the recumbent and upright positions are similar when the different orientation in the gravity field is considered, (ii) compare the functional roles of the leg muscles while pedaling in the recumbent position to the upright position to the upright position and (iii) determine whether leg muscle onset and offset timing for recumbent and upright pedaling respond similarly to changes in pedaling rate. To fulfill these objectives, surface electromyograms were recorded from 10 muscles of 15 subjects who pedaled in both the recumbent and upright positions at 75, 90, and 105 rpm and at a constant workrate of 250 W. Patterns of muscle activation were compared over the crank cycle. Functional roles of muscles in recumbent and upright pedaling were compared using the percent of integrated activation in crank cycle regions determined previously for upright pedaling. Muscle onset and offset timing were also compared. When the crank cycle was adjusted for orientation in the gravity field, the activation patterns for the two positions were similar. Functional roles of the muscles in the two positions were similar as well. In recumbent pedaling, the uniarticular hip and knee extensors functioned primarily to produce power during the extension region of the crank cycle, whereas the biarticular muscles crossing the hip and knee functioned to propel the leg through the transition regions of the crank cycle. The adaptations of the muscles to changes in pedaling rate were also similar for the two body positions with the uniarticular power producing muscles of the hip and knee advancing their activity to earlier in the crank cycle as the pedaling rate increased. This information on the functional roles of the leg muscles provides a basis by which to form functional groups, such as power-producing muscles and transition muscles, to aid in the development of rehabilitative pedaling exercises and recumbent pedaling simulations to further our understanding of task-dependent muscle coordination.     

Muscle recruitment patterns regulate physiological responses during exercise of the same intensity

On different days, 10 men performed 30-min sessions of cycling at 50-55% of their peak oxygen uptake (VO(2)); one at 40 rpm and another at 80 rpm. Rectal temperature, heart rate (HR), mean arterial pressure (MAP), plasma lactate, glucose, insulin, and cortisol were measured before exercise, during the 15th and 30th min of exercise, and at 5 and 10 min postexercise. Rating of perceived exertion (RPE) was assessed 15 and 30 min into exercise. Electromyography established cadence-specific different intensities of quadriceps activation during cycling. At minute 30 of exercise and 5 min postexercise, HR was significantly (P < 0.05) greater at 40 rpm than at 80 rpm. MAP remained elevated longer after the 40-rpm than after the 80-rpm bout. Similarly, exercise-induced increases in plasma lactate persisted longer after the 40-rpm bout. Cortisol levels were elevated only at 40 rpm. RPE was higher during the slower cadence. These data indicated that the more pronounced muscle activation pattern associated with pedaling at 40 rpm resulted in greater physiological and psychophysiological stress than that observed at 80 rpm even though VO(2) was the same.