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.     

Contributions of the individual ankle plantar flexors to support, forward progression and swing initiation during walking.

Walking is a motor task requiring coordination of many muscles. Previous biomechanical studies, based primarily on analyses of the net ankle moment during stance, have concluded different functional roles for the plantar flexors. We hypothesize that some of the disparities in interpretation arise because of the effects of the uniarticular and biarticular muscles that comprise the plantar flexor group have not been separated. Furthermore, we believe that an accurate determination of muscle function requires quantification of the contributions of individual plantar flexor muscles to the energetics of individual body segments. In this study, we examined the individual contributions of the ankle plantar flexors (gastrocnemius (GAS); soleus (SOL)) to the body segment energetics using a musculoskeletal model and optimization framework to generate a forward dynamics simulation of normal walking at 1.5 m/s. At any instant in the gait cycle, the contribution of a muscle to support and forward progression was defined by its contribution to trunk vertical and horizontal acceleration, respectively, and its contribution to swing initiation by the mechanical energy it delivers to the leg in pre-swing (i.e., double-leg stance prior to toe-off). GAS and SOL were both found to provide trunk support during single-leg stance and pre-swing. In early single-leg stance, undergoing eccentric and isometric activity, they accelerate the trunk vertically but decelerate forward trunk progression. In mid single-leg stance, while isometric, GAS delivers energy to the leg while SOL decelerates it, and SOL delivers energy to the trunk while GAS decelerates it. In late single-leg stance through pre-swing, though GAS and SOL both undergo concentric activity and accelerate the trunk forward while decelerating the downward motion of the trunk (i.e., providing forward progression and support), they execute different energetic functions. The energy produced from SOL accelerates the trunk forward, whereas GAS delivers almost all its energy to accelerate the leg to initiate swing. Although GAS and SOL maintain or accelerate forward motion in mid single-leg stance through pre-swing, other muscles acting at the beginning of stance contribute comparably to forward progression. In summary, throughout single-leg stance both SOL and GAS provide vertical support, in mid single-leg stance SOL and GAS have opposite energetic effects on the leg and trunk to ensure support and forward progression of both the leg and trunk, and in pre-swing only GAS contributes to swing initiation.     

Muscle contributions to whole-body sagittal plane angular momentum during walking

Walking is a complex dynamic task that requires the regulation of whole-body angular momentum to maintain dynamic balance while performing walking subtasks such as propelling the body forward and accelerating the leg into swing. In human walking, the primary mechanism to regulate angular momentum is muscle force generation. Muscles accelerate body segments and generate ground reaction forces that alter angular momentum about the body’s center-of-mass to restore and maintain dynamic stability. In addition, gravity contributes to whole-body angular momentum through its contribution to the ground reaction forces. The purpose of this study was to generate a muscle-actuated forward dynamics simulation of normal walking to quantify how individual muscles and gravity contribute to whole-body angular momentum in the sagittal plane. In early stance, the uniarticular hip and knee extensors (GMAX and VAS), biarticular hamstrings (HAM) and ankle dorsiflexors (TA) generated backward angular momentum while the ankle plantar flexors (SOL and GAS) generated forward momentum. In late stance, SOL and GAS were the primary contributors and generated angular momentum in opposite directions. SOL generated primarily forward angular momentum while GAS generated backward angular momentum. The difference between muscles was due to their relative contributions to the horizontal and vertical ground reaction forces. Gravity contributed to the body’s angular momentum in early stance and to a lesser extent in late stance, which was counteracted primarily by the plantar flexors. These results may provide insight into balance and movement disorders and provide a basis for developing locomotor therapies that target specific muscle groups.     

Optimal muscular coordination strategies for jumping

This paper presents a detailed analysis of an optimal control solution to a maximum height squat jump, based upon how muscles accelerate and contribute power to the body segments during the ground contact phase of jumping. Quantitative comparisons of model and experimental results expose a proximal-to-distal sequence of muscle activation (i.e. from hip to knee to ankle). We found that the contribution of muscles dominates both the angular acceleration and the instantaneous power of the segments. However, the contributions of gravity and segmental motion are insignificant, except the latter become important during the final 10% of the jump. Vasti and gluteus maximus muscles are the major energy producers of the lower extremity. These muscles are the prime movers of the lower extremity because they dominate the angular acceleration of the hip toward extension and the instantaneous power of the trunk. In contrast, the ankle plantarflexors (soleus, gastrocnemius, and the other plantarflexors) dominate the total energy of the thigh, though these muscles also contribute appreciably to trunk power during the final 20% of the jump. Therefore, the contribution of these muscles to overall jumping performance cannot be neglected. We found that the biarticular gastrocnemius increases jump height (i.e. the net vertical displacement of the center of mass of the body from standing) by as much as 25%. However, this increase is not due to any unique biarticular action (e.g. proximal-to-distal power transfer from the knee to the ankle), since jumping performance is similar when gastrocnemius is replaced with a uniarticular ankle plantarflexor.     

Comparison of global and joint-to-joint methods for estimating the hip joint load and the muscle forces during walking

A three-dimensional musculoskeletal model of the lower limb was developed to study the influence of biarticular muscles on the muscle force distribution and joint loads during walking. A complete walking cycle was recorded for 9 healthy subjects using the standard optoelectronic motion tracking system. Ground contact forces were also measured using a 6-axes force plate. Inverse dynamics was used to compute net joint reactions (forces and torques) in the lower limb. A static optimization method was then used to estimate muscle forces. Two different approaches were used: in the first one named global method, the biarticular muscles exerted a torque on the two joints they spanned at the same time, and in the second one called joint-by-joint method, these biarticular muscles were divided into two mono-articular muscles with geometrical (insertion, origin, via points) and physiological properties remained unchanged. The hip joint load during the gait cycle was then calculated taking into account the effect of muscle contractions. The two approaches resulted in different muscle force repartition: the biarticular muscles were favoured over any set of single-joint muscles with the same physiological function when using the global method. While the two approaches yielded only little difference in the resultant hip load, the examination of muscle power showed that biarticular muscles could produce positive work at one joint and negative work at the other, transferring energy between body segments and thus decreasing the metabolic cost of movement.     

The effects of Achilles tendon compliance on triceps surae mechanics and energetics in walking

Achilles tendon (AT) compliance can affect the generation and transmission of triceps surae muscle forces, and thus has important biomechanical consequences for walking performance. However, the uniarticular soleus (SOL) and the biarticular (GAS) function differently during walking, with in vivo evidence suggesting that their associated fascicles and tendinous structures exhibit unique kinematics during walking. Given the strong association between muscle fiber length, velocity and force production, we conjectured that SOL and GAS mechanics and energetic behavior would respond differently to altered AT compliance. To test this, we characterized GAS and SOL muscle and tendon mechanics and energetics due to systematic changes in tendon compliance using musculoskeletal simulations of walking. Increased tendon compliance enlarged GAS and SOL tendon excursions, shortened fiber operation lengths and affected muscle excitation patterns. For both muscles, an optimal tendon compliance (tendon strains of approximately 5% with maximum isometric force) existed that minimized metabolic energy consumption. However, GAS muscle-tendon mechanics and energetics were significantly more sensitive to changes in tendon compliance than were those for SOL. In addition, GAS was not able to return stored tendon energy during push-off as effectively as SOL, particularly for larger values of tendon compliance. These fundamental differences between GAS and SOL sensitivity to altered tendon compliance seem to arise from the biarticular nature of GAS. These insights are potentially important for understanding the functional consequences of altered Achilles tendon compliance due to aging, injury, or disease.     

Influence of bicycle seat tube angle and hand position on lower extremity kinematics and neuromuscular control: implications for triathlon running performance

We investigated how varying seat tube angle (STA) and hand position affect muscle kinematics and activation patterns during cycling in order to better understand how triathlon-specific bike geometries might mitigate the biomechanical challenges associated with the bike-to-run transition. Whole body motion and lower extremity muscle activities were recorded from 14 triathletes during a series of cycling and treadmill running trials. A total of nine cycling trials were conducted in three hand positions (aero, drops, hoods) and at three STAs (73°, 76°, 79°). Participants also ran on a treadmill at 80, 90, and 100% of their 10-km triathlon race pace. Compared with cycling, running necessitated significantly longer peak musculotendon lengths from the uniarticular hip flexors, knee extensors, ankle plantar flexors and the biarticular hamstrings, rectus femoris, and gastrocnemius muscles. Running also involved significantly longer periods of active muscle lengthening from the quadriceps and ankle plantar flexors. During cycling, increasing the STA alone had no affect on muscle kinematics but did induce significantly greater rectus femoris activity during the upstroke of the crank cycle. Increasing hip extension by varying the hand position induced an increase in hamstring muscle activity, and moved the operating lengths of the uniarticular hip flexor and extensor muscles slightly closer to those seen during running. These combined changes in muscle kinematics and coordination could potentially contribute to the improved running performances that have been previously observed immediately after cycling on a triathlon-specific bicycle.     

Muscle contributions to specific biomechanical functions do not change in forward versus backward pedaling

Previous work had identified six biomechanical functions that need to be executed by each limb in order to produce a variety of pedaling tasks. The functions can be organized into three antagonistic pairs: an Ext/Flex pair that accelerates the foot into extension or flexion with respect to the pelvis, an Ant/Post pair that accelerates the foot anteriorly or posteriorly with respect to the pelvis, and a Plant/Dorsi pair that accelerates the foot into plantarflexion or dorsiflexion. Previous analyses of experimental data have inferred that muscles perform the same function during different pedaling tasks (e.g. forward versus backward pedaling) because the EMG timing was similar, but they did not present rigorous biomechanical analyses to assess whether a muscle performed the same biomechanical function, and if so, to what degree. Therefore, the objective of this study was to determine how individual muscles contribute to these biomechanical functions during two different motor tasks, forward and backward pedaling, through a theoretical analysis of experimental data. To achieve this objective, forward and backward pedaling simulations were generated and a mechanical energy analysis was used to examine how muscles generate, absorb or transfer energy to perform the pedaling tasks. The results showed that the muscles contributed to the same primary Biomechanical functions in both pedaling directions and that synergistic performance of certain functions effectively accelerated the crank. The gluteus maximus worked synergistically with the soleus, the hip flexors worked synergistically with the tibialis anterior, and the vasti and hamstrings functioned independently to accelerate the crank. The rectus femoris used complex biomechanical mechanisms including negative muscle work to accelerate the crank. The negative muscle work was used to transfer energy generated elsewhere (primarily from other muscles) to the pedal reaction force in order to accelerate the crank. Consistent with experimental data, a phase shift was required from those muscles contributing to the Ant/Post functions as a result of the different limb kinematics between forward and backward pedaling, although they performed the same biomechanical function. The pedaling simulations proved necessary to interpret the experimental data and identify motor control mechanisms used to accomplish specific motor tasks, as the mechanisms were often complex and not always intuitively obvious.     

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.     

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.     

Muscle mechanical work requirements during normal walking: the energetic cost of raising the body's center-of-mass is significant

Inverted pendulum models of walking predict that little muscle work is required for the exchange of body potential and kinetic energy in single-limb support. External power during walking (product of the measured ground reaction force and body center-of-mass (COM) velocity) is often analyzed to deduce net work output or mechanical energetic cost by muscles. Based on external power analyses and inverted pendulum theory, it has been suggested that a primary mechanical energetic cost may be associated with the mechanical work required to redirect the COM motion at the step-to-step transition. However, these models do not capture the multi-muscle, multi-segmental properties of walking, co-excitation of muscles to coordinate segmental energetic flow, and simultaneous production of positive and negative muscle work. In this study, a muscle-actuated forward dynamic simulation of walking was used to assess whether: (1). potential and kinetic energy of the body are exchanged with little muscle work; (2). external mechanical power can estimate the mechanical energetic cost for muscles; and (3.) the net work output and the mechanical energetic cost for muscles occurs mostly in double support. We found that the net work output by muscles cannot be estimated from external power and was the highest when the COM moved upward in early single-limb support even though kinetic and potential energy were exchanged, and muscle mechanical (and most likely metabolic) energetic cost is dominated not only by the need to redirect the COM in double support but also by the need to raise the COM in single support.     

Simulation analysis of muscle activity changes with altered body orientations during pedaling

Testing hypotheses related to the effect of gravitational orientation on neural control mechanisms is difficult for most locomotor tasks, like walking, because body orientation with respect to gravity affects both sensorimotor control and task mechanics. To examine the mechanical effect of body orientation independently from changes in workload and posture, Brown et al. (J. Biomech. 29 p. 1349, 1996) studied pedaling at altered body orientations. They found that subjects pedaling at different orientations changed needlessly their muscle excitations, putatively to preserve body-upright pedaling kinematics. We tested the feasibility of this hypothesis using simulations based on a three biomechanical-function pair organization for control of lower limb muscles (limb extension/flexion pair, extension/flexion transition pair, and foot plantarflexion/dorsiflexion pair), where each pair consists of alternating agonistic/antagonistic muscles. Adjustment of only three parameters, one to scale the muscle excitations of each pair, was sufficient to preserve pedaling kinematics to altered body orientation. Because these adjustments produced changes in muscle excitation and net joint moments similar to those observed in pedaling subjects, the hypothesis is supported. Moreover, the effectiveness of a decoupled gain adjustment procedure where each parameter was adjusted by error in only one aspect of the pedaling trajectory during each iteration (i.e., cadence adjusted the Ext/Flex parameter; peak-to-peak variation in crank velocity over the cycle adjusted the transition parameter; average ankle angle over the cycle adjusted the foot parameter) further supports the distinct function of each muscle pair.     

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.     

Differences in muscle function during walking and running at the same speed

Individual muscle contributions to body segment mechanical energetics and the functional tasks of body support and forward propulsion in walking and running at the same speed were quantified using forward dynamical simulations to elucidate differences in muscle function between the two different gait modes. Simulations that emulated experimentally measured kinesiological data of young adults walking and running at the preferred walk-to-run transition speed revealed that muscles use similar biomechanical mechanisms to provide support and forward propulsion during the two tasks. The primary exception was a decreased contribution of the soleus to forward propulsion in running, which was previously found to be significant in walking. In addition, the soleus distributed its mechanical power differently to individual body segments between the two gait modes from mid- to late stance. In walking, the soleus transferred mechanical energy from the leg to the trunk to provide support, but in running it delivered energy to both the leg and trunk. In running, earlier soleus excitation resulted in it working in synergy with the hip and knee extensors near mid-stance to provide the vertical acceleration for the subsequent flight phase in running. In addition, greater power output was produced by the soleus and hip and knee extensors in running. All other muscle groups distributed mechanical power among the body segments and provided support and forward propulsion in a qualitatively similar manner in both walking and running.     

The force resulting from the action of mono- and biarticular muscles in a limb.

Human and animal limbs can be modelled as a chain of segments connected at joints. For a static limb, the force exerted at the endpoint due to the force of a single muscle has been calculated. It turns out that there are marked differences in the action of mono- vs. biarticular muscles. Monoarticular muscles produce an endpoint force that is directed in the lengthwise direction of the limb, i.e. in the direction of one of the segments. The force from biarticular muscles can have a marked transverse component. The 'principal direction' of this endpoint force is also the movement direction of the endpoint which is the most favourable for the muscle to do work. The reasoning presented can explain e.g. the differences in the activity of mono- and biarticular muscles in cycling.     

Muscle and prosthesis contributions to amputee walking mechanics: A modeling study

Unilateral, below-knee amputees have altered gait mechanics, which can significantly affect their mobility. Below-knee amputees lose the functional use of the ankle muscles, which are critical during walking to provide body support, forward propulsion, leg-swing initiation and mediolateral balance. Thus, either muscles must compensate or the prosthesis must provide the functional tasks normally provided by the ankle muscles. Three-dimensional (3D) forward dynamics simulations of amputee and non-amputee walking were generated to identify muscle and prosthesis contributions to amputee walking mechanics, including the subtasks of body support, forward propulsion, leg-swing initiation and mediolateral balance. Results showed that the prosthesis provided body support in the absence of the ankle muscles. The prosthesis contributed to braking from early to mid-stance and propulsion in late stance. The prosthesis also functioned like the uniarticular soleus muscle by transferring energy from the residual leg to the trunk to provide trunk propulsion. The residual-leg vasti and rectus femoris reduced their contributions to braking in early stance, which mitigated braking from the prosthesis during this period. The prosthesis did not replace the function of the gastrocnemius, which normally generates energy to the leg to initiate swing. As a result, lower overall energy was delivered to the residual leg. The prosthesis also acted to accelerate the body laterally in the absence of the ankle muscles. These results provide further insight into muscle and prosthesis function in below-knee amputee walking and can help guide rehabilitation methods and device designs to improve amputee mobility.     

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).     

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.     

Elastic energy savings and active energy cost in a simple model of running

The energetic economy of running benefits from tendon and other tissues that store and return elastic energy, thus saving muscles from costly mechanical work. The classic “Spring-mass” computational model successfully explains the forces, displacements and mechanical power of running, as the outcome of dynamical interactions between the body center of mass and a purely elastic spring for the leg. However, the Spring-mass model does not include active muscles and cannot explain the metabolic energy cost of running, whether on level ground or on a slope. Here we add explicit actuation and dissipation to the Spring-mass model, and show how they explain substantial active (and thus costly) work during human running, and much of the associated energetic cost. Dissipation is modeled as modest energy losses (5% of total mechanical energy for running at 3 m s^-1) from hysteresis and foot-ground collisions, that must be restored by active work each step. Even with substantial elastic energy return (59% of positive work, comparable to empirical observations), the active work could account for most of the metabolic cost of human running (about 68%, assuming human-like muscle efficiency). We also introduce a previously unappreciated energetic cost for rapid production of force, that helps explain the relatively smooth ground reaction forces of running, and why muscles might also actively perform negative work. With both work and rapid force costs, the model reproduces the energetics of human running at a range of speeds on level ground and on slopes. Although elastic return is key to energy savings, there are still losses that require restorative muscle work, which can cost substantial energy during running.     

Why is the force-velocity relationship in leg press tasks quasi-linear rather than hyperbolic?

Force-velocity relationships reported in the literature for functional tasks involving a combination of joint rotations tend to be quasi-linear. The purpose of this study was to explain why they are not hyperbolic, like Hill's relationship. For this purpose, a leg press task was simulated with a musculoskeletal model of the human leg, which had stimulation of knee extensor muscles as only independent input. In the task the ankles moved linearly, away from the hips, against an imposed external force that was reduced over contractions from 95 to 5% of the maximum isometric value. Contractions started at 70% of leg length, and force and velocity values were extracted when 80% of leg length was reached. It was shown that the relationship between leg extension velocity and external force was quasi-linear, while the relationship between leg extension velocity and muscle force was hyperbolic. The discrepancy was explained by the fact that segmental dynamics canceled more and more of the muscle force as the external force was further reduced and velocity became higher. External power output peaked when the imposed external force was ～50% of maximum, while muscle power output peaked when the imposed force was only ～15% of maximum; in the latter case ～70% of muscle power was buffered by the leg segments. According to the results of this study, there is no need to appeal to neural mechanisms to explain why, in leg press tasks, the force-velocity relationship is quasi-linear rather than hyperbolic.