Impact of lengthening velocity on the generation of eccentric force by slow-twitch muscle fibers in long stretches.

After an initial increase, isovelocity elongation of a muscle fiber can lead to diminishing (referred to as Give in the literature) and subsequently increasing force. How the stretch velocity affects this behavior in slow-twitch fibers remains largely unexplored. Here, we stretched fully activated individual rat soleus muscle fibers from 0.85 to 1.3 optimal fiber length at stretch velocities of 0.01, 0.1, and 1 maximum shortening velocity, vmax, and compared the results with those of rat EDL fast-twitch fibers obtained in similar experimental conditions. In soleus muscle fibers, Give was 7%, 18%, and 44% of maximum isometric force for 0.01, 0.1, and 1 vmax, respectively. As in EDL fibers, the force increased nearly linearly in the second half of the stretch, although the number of crossbridges decreased, and its slope increased with stretch velocity. Our findings are consistent with the concept of a forceful detachment and subsequent crossbridge reattachment in the stretch's first phase and a strong viscoelastic titin contribution to fiber force in the second phase of the stretch. Interestingly, we found interaction effects of stretch velocity and fiber type on force parameters in both stretch phases, hinting at fiber type-specific differences in crossbridge and titin contributions to eccentric force. Whether fiber type-specific combined XB and non-XB models can explain these effects or if they hint at some not fully understood properties of muscle contraction remains to be shown. These results may stimulate new optimization perspectives in sports training and provide a better understanding of structure-function relations of muscle proteins.

Limb dynamics in agility jumps of beginner and advanced dogs.

A considerable body of work has examined the dynamics of different dog gaits, but there are no studies that have focused on limb dynamics in jumping. Jumping is an essential part of dog agility, a dog sport in which handlers direct their dogs through an obstacle course in a limited time. We hypothesized that limb parameters like limb length and stiffness indicate the skill level of dogs. We analyzed global limb parameters in jumping for 10 advanced and 10 beginner dogs. In experiments, we collected 3D kinematics and ground reaction forces during dog jumping at high forward speeds. Our results revealed general strategies of limb control in jumping and highlighted differences between advanced and beginner dogs. In take-off, the spatially leading forelimb was 75% (P<0.001) stiffer than the trailing forelimb. In landing, the trailing forelimb was 14% stiffer (P<0.001) than the leading forelimb. This indicates a strut-like action of the forelimbs to achieve jumping height in take-off and to transfer vertical velocity into horizontal velocity in landing (with switching roles of the forelimbs). During landing, the more (24%) compliant forelimbs of beginner dogs (P=0.005) resulted in 17% (P=0.017) higher limb compression during the stance phase. This was associated with a larger amount of eccentric muscle contraction, which might in turn explain the soft tissue injuries that frequently occur in the shoulder region of beginner dogs. For all limbs, limb length at toe-off was greater for advanced dogs. Hence, limb length and stiffness might be used as objective measures of skill.

Low leg compliance permits grounded running at speeds where the inverted pendulum model gets airborne.

Animals typically switch from grounded (no flight phases) to aerial running at dimensionless speeds u^ < 1. But some birds use grounded running far above u^ = 1, which puzzles biologists because the inverted pendulum becomes airborne at this speed. Here, we combine computer experiments using the spring-mass model with locomotion data from small birds, macaques and humans to understand the relationship between leg function (stiffness, angle of attack), locomotion speed and gait. With our model, we found three-humped ground reaction force profiles for slow grounded running speeds. The minimal single-humped grounded running speed is u^ = 0.4. This speed value roughly coincides with the transition speed from vaulting to bouncing mechanics in bipeds. Maximal grounded running speed in the model is not limited. In experiments, animals changed from grounded to aerial running at dimensionless contact time around 1. Considering these real-world contact times reduces the solution space drastically, but experimental data fit well. The model still predicts maximal grounded running speed  u^ > 1 for low stiffness values used by birds but decreases below u^ = 1 for increasing stiffness. For stiffer legs used in human walking and running, periodic grounded running vanishes. At speeds at which birds and macaques change to aerial running, we found periodic aerial running to intersect grounded running. This could explain why animals can alternate between grounded and aerial running at the same speed and identical leg parameters. Compliant legs enable different gaits and speeds with similar leg parameters, stiff legs require parameter adaptations.

A continuum-mechanical skeletal muscle model including actin-titin interaction predicts stable contractions on the descending limb of the force-length relation.

Contractions on the descending limb of the total (active + passive) muscle force-length relationship (i. e. when muscle stiffness is negative) are expected to lead to vast half-sarcomere-length inhomogeneities. This is however not observed in experiments-vast half-sarcomere-length inhomogeneities can be absent in myofibrils contracting in this range, and initial inhomogeneities can even decrease. Here we show that the absence of half-sarcomere-length inhomogeneities can be predicted when considering interactions of the semi-active protein titin with the actin filaments. Including a model of actin-titin interactions within a multi-scale continuum-mechanical model, we demonstrate that stability, accurate forces and nearly homogeneous half-sarcomere lengths can be obtained on the descending limb of the static total force-length relation. This could be a key to durable functioning of the muscle because large local stretches, that might harm, for example, the transverse-tubule system, are avoided.

The active force-length relationship is invisible during extensive eccentric contractions in skinned skeletal muscle fibres.

In contrast to experimentally observed progressive forces in eccentric contractions, cross-bridge and sliding-filament theories of muscle contraction predict that varying myofilament overlap will lead to increases and decreases in active force during eccentric contractions. Non-cross-bridge contributions potentially explain the progressive total forces. However, it is not clear whether underlying abrupt changes in the slope of the nonlinear force-length relationship are visible in long isokinetic stretches, and in which proportion cross-bridges and non-cross-bridges contribute to muscle force. Here, we show that maximally activated single skinned rat muscle fibres behave (almost across the entire working range) like linear springs. The force slope is about three times the maximum isometric force per optimal length. Cross-bridge and non-cross-bridge contributions to the muscle force were investigated using an actomyosin inhibitor. The experiments revealed a nonlinear progressive contribution of non-cross-bridge forces and suggest a nonlinear cross-bridge contribution similar to the active force-length relationship (though with increased optimal length and maximum isometric force). The linear muscle behaviour might significantly reduce the control effort. Moreover, the observed slight increase in slope with initial length is in accordance with current models attributing the non-cross-bridge force to titin.

Increasing trunk flexion transforms human leg function into that of birds despite different leg morphology.

Pronograde trunk orientation in small birds causes prominent intra-limb asymmetries in the leg function. As yet, it is not clear whether these asymmetries induced by the trunk reflect general constraints on the leg function regardless of the specific leg architecture or size of the species. To address this, we instructed 12 human volunteers to walk at a self-selected velocity with four postures: regular erect, or with 30 deg, 50 deg and maximal trunk flexion. In addition, we simulated the axial leg force (along the line connecting hip and centre of pressure) using two simple models: spring and damper in series, and parallel spring and damper. As trunk flexion increases, lower limb joints become more flexed during stance. Similar to birds, the associated posterior shift of the hip relative to the centre of mass leads to a shorter leg at toe-off than at touchdown, and to a flatter angle of attack and a steeper leg angle at toe-off. Furthermore, walking with maximal trunk flexion induces right-skewed vertical and horizontal ground reaction force profiles comparable to those in birds. Interestingly, the spring and damper in series model provides a superior prediction of the axial leg force across trunk-flexed gaits compared with the parallel spring and damper model; in regular erect gait, the damper does not substantially improve the reproduction of the human axial leg force. In conclusion, mimicking the pronograde locomotion of birds by bending the trunk forward in humans causes a leg function similar to that of birds despite the different morphology of the segmented legs.

Myosin filament sliding through the Z-disc relates striated muscle fibre structure to function.

Striated muscle contraction requires intricate interactions of microstructures. The classic textbook assumption that myosin filaments are compressed at the meshed Z-disc during striated muscle fibre contraction conflicts with experimental evidence. For example, myosin filaments are too stiff to be compressed sufficiently by the muscular force, and, unlike compressed springs, the muscle fibres do not restore their resting length after contractions to short lengths. Further, the dependence of a fibre's maximum contraction velocity on sarcomere length is unexplained to date. In this paper, we present a structurally consistent model of sarcomere contraction that reconciles these findings with the well-accepted sliding filament and crossbridge theories. The few required model parameters are taken from the literature or obtained from reasoning based on structural arguments. In our model, the transition from hexagonal to tetragonal actin filament arrangement near the Z-disc together with a thoughtful titin arrangement enables myosin filament sliding through the Z-disc. This sliding leads to swivelled crossbridges in the adjacent half-sarcomere that dampen contraction. With no fitting of parameters required, the model predicts straightforwardly the fibre's entire force-length behaviour and the dependence of the maximum contraction velocity on sarcomere length. Our model enables a structurally and functionally consistent view of the contractile machinery of the striated fibre with possible implications for muscle diseases and evolution.

Minimizing the cost of locomotion with inclined trunk predicts crouched leg kinematics of small birds at realistic levels of elastic recoil.

Small birds move with pronograde trunk orientation and crouched legs. Although the pronograde trunk has been suggested to be beneficial for grounded running, the cause(s) of the specific leg kinematics are unknown. Here we show that three charadriiform bird species (northern lapwing, oystercatcher, and avocet; great examples of closely related species that differ remarkably in their hind limb design) move their leg segments during stance in a way that minimizes the cost of locomotion. We imposed measured trunk motions and ground reaction forces on a kinematic model of the birds. The model was used to search for leg configurations that minimize leg work that accounts for two factors: elastic recoil in the intertarsal joint, and cheaper negative muscle work relative to positive muscle work. A physiological level of elasticity (∼ 0.6) yielded segment motions that match the experimental data best, with a root mean square of angular deviations of ∼ 2.1 deg. This finding suggests that the exploitation of elastic recoil shapes the crouched leg kinematics of small birds under the constraint of pronograde trunk motion. Considering that an upright trunk and more extended legs likely decrease the cost of locomotion, our results imply that the cost of locomotion is a secondary movement criterion for small birds. Scaling arguments suggest that our approach may be utilized to provide new insights into the motion of extinct species such as dinosaurs.

Positioning the hip with respect to the COM: Consequences for leg operation.

In bipedal runners and hoppers the hip is not located at the center of mass in the sagittal projection. This displacement influences operation and energetics of the leg attached to the hip. To investigate this influence in a first step a simple conservative bouncing template is developed in which a heavy trunk is suspended to a massless spring at a pivot point above the center of mass. This model describes the orientation of the ground reaction forces observed in experiments on running birds. In a second step it is assumed that an effective telescope leg with its hip fixed to the trunk remote from the COM generates the same ground reaction forces as those predicted by the template. For this effective leg the influence of hip placement on leg operation and energetics is investigated. Placing the hip directly below, at, or above the pivot point results in high axial energy storage. Posterior placement increases axial losses and hip work whereas anterior placement would require axial work and absorption at the hip. Shifting the hip far posteriorly as observed in some birds can lead to the production of pure extension torques throughout the stance phase. It is proposed that the relative placement of the hip with respect to the center of mass is an important measure to modify effective leg operation with possible implications for balancing the trunk and the control of legged motion systems.

Trunk orientation causes asymmetries in leg function in small bird terrestrial locomotion.

In contrast to the upright trunk in humans, trunk orientation in most birds is almost horizontal (pronograde). It is conceivable that the orientation of the heavy trunk strongly influences the dynamics of bipedal terrestrial locomotion. Here, we analyse for the first time the effects of a pronograde trunk orientation on leg function and stability during bipedal locomotion. For this, we first inferred the leg function and trunk control strategy applied by a generalized small bird during terrestrial locomotion by analysing synchronously recorded kinematic (three-dimensional X-ray videography) and kinetic (three-dimensional force measurement) quail locomotion data. Then, by simulating quail gaits using a simplistic bioinspired numerical model which made use of parameters obtained in in vivo experiments with real quail, we show that the observed asymmetric leg function (left-skewed ground reaction force and longer leg at touchdown than at lift-off) is necessary for pronograde steady-state locomotion. In addition, steady-state locomotion becomes stable for specific morphological parameters. For quail-like parameters, the most common stable solution is grounded running, a gait preferred by quail and most of the other small birds. We hypothesize that stability of bipedal locomotion is a functional demand that, depending on trunk orientation and centre of mass location, constrains basic hind limb morphology and function, such as leg length, leg stiffness and leg damping.

Posture-induced modulation of lower-limb joint powers in perturbed running.

Despite evidence on trunk flexion's impact on locomotion mechanics, its role in modulating lower-limb energetics during perturbed running remains underexplored. Therefore, we investigated posture-induced power redistribution in the lower-limb joints (hip, knee, and ankle), along with the relative contribution from each joint to total lower-limb average positive and negative mechanical powers (i.e., over time) during perturbed running. Twelve runners (50% female) ran at self-selected (~15°) and three more sagittal trunk inclinations (backward, ~0°; low forward, ~20°; high forward, ~25°) on a custom-built runway, incorporating both a level surface and a 10 cm visible drop-step positioned midway, while simultaneously recording three-dimensional kinematics and kinetics. We used inverse dynamics analysis to determine moments and powers in lower-limb joints. Increasing the trunk forward inclination yielded the following changes in lower-limb mechanics: a) an elevation in total positive power with a distoproximal shift and a reduction in total negative power; b) systematic increases in hip positive power, coupled with decreased and increased contribution to total negative (during level-step) and positive (during drop-step) powers, respectively; c) reductions in both negative and positive knee powers, along with a decrease in its contribution to total positive power. Regardless of the trunk posture, accommodating drop-steps while running demands elevated total limb negative and positive powers with the ankle as a primary source of energy absorption and generation. Leaning the trunk more forward induces a distoproximal shift in positive power, whereas leaning backward exerts an opposing influence on negative power within the lower-limb joints.

Grounded running in quails: simulations indicate benefits of observed fixed aperture angle between legs before touch-down.

Many birds use grounded running (running without aerial phases) in a wide range of speeds. Contrary to walking and running, numerical investigations of this gait based on the BSLIP (bipedal spring loaded inverted pendulum) template are rare. To obtain template related parameters of quails (e.g. leg stiffness) we used x-ray cinematography combined with ground reaction force measurements of quail grounded running. Interestingly, with speed the quails did not adjust the swing leg's angle of attack with respect to the ground but adapted the angle between legs (which we termed aperture angle), and fixed it about 30ms before touchdown. In simulations with the BSLIP we compared this swing leg alignment policy with the fixed angle of attack with respect to the ground typically used in the literature. We found symmetric periodic grounded running in a simply connected subset comprising one third of the investigated parameter space. The fixed aperture angle strategy revealed improved local stability and surprising tolerance with respect to large perturbations. Starting with the periodic solutions, after step-down step-up or step-up step-down perturbations of 10% leg rest length, in the vast majority of cases the bipedal SLIP could accomplish at least 50 steps to fall. The fixed angle of attack strategy was not feasible. We propose that, in small animals in particular, grounded running may be a common gait that allows highly compliant systems to exploit energy storage without the necessity of quick changes in the locomotor program when facing perturbations.

How velocity impacts eccentric force generation of fully activated skinned skeletal muscle fibers in long stretches.

Ecccentric muscle contractions are fundamental to everyday life. They occur markedly in jumping, running, and accidents. Following an initial force rise, stretching of a fully activated muscle can result in a phase of decreasing force ("Give") followed by force redevelopment. However, how the stretch velocity affects "Give" and force redevelopment remains largely unknown. We investigated the force produced by fully activated single-skinned fibers of rat extensor digitorum longus muscles during long stretches. Fibers were pulled from length 0.85 to 1.3 optimal fiber length at a rate of 1%, 10%, and 100% of the estimated maximum shortening velocity. "Give" was absent in slow stretches. Medium and fast stretches yielded a clear "Give." After the initial force peak, forces decreased by 11.2% and 27.8% relative to the initial peak force before rising again. During the last half of the stretch (from 1.07 to 1.3 optimal fiber length, which is within the range of the expected descending limb of the force-length relationship), the linear force slope tripled from slow to medium stretch and increased further by 60% from medium to fast stretch. These results are compatible with forcible cross-bridge detachment and redevelopment of a cross-bridge distribution, and a viscoelastic titin contribution to fiber force. Accounting for these results can improve muscle models and predictions of multibody simulations.NEW & NOTEWORTHY Eccentric muscle contractions are part of our daily lives. We found that force increased monotonically during slow stretches of fully activated muscle fibers, whereas higher stretch velocities resulted in an increasing drop in force after an initial increase and a final steeper rise in force. Cross-bridges cannot explain the observed force traces. This requires a viscoelastic non-cross-bridge contribution. Considering these results can improve muscle models and predictions of multibody simulations.

Uneven running: How does trunk-leaning affect the lower-limb joint mechanics and energetics?

This study aimed to investigate the role of trunk posture in running locomotion. Twelve recreational runners ran in the laboratory across even and uneven ground surface (expected 10 cm drop-step) with three trunk-lean angles from the vertical (self-selected, ∼15°; anterior, ∼25°; posterior, ∼0°) while 3D kinematic and kinetic data were collected using a 3D motion-capture-system and two embedded force-plates. Two-way repeated measures ANOVAs (α = 0.05) compared lower-limb joint mechanics (angles, moments, energy absorption and generation) and ground-reaction-force parameters (braking and propulsive impulse) between Step (level and drop) and Posture conditions. The Step-by-Posture interaction revealed decreased hip energy generation, and greater peak knee extension moment in the drop-step during running with posterior versus anterior trunk-lean. Furthermore, energy absorption across hip and ankle nearly doubled in the drop-step across all running conditions. The Step main effect revealed that the knee and ankle energy absorption, ankle energy generation, ground-reaction-force, and braking impulse significantly increased in the drop-step. The Posture main effect revealed that, compared with a self-selected trunk-lean, the knee's energy absorption/generation, ankle's energy generation and the braking impulse were either retained or attenuated when leaning the trunk anteriorly. The opposite effects occurred with a posterior trunk-lean. In conclusion, while the pronounced mechanical ankle stress in drop-steps is marginally affected by posture, changing the trunk-lean reorganizes the load distribution across the knee and hip joints. Leaning the trunk anteriorly in running shifts loading from the knee to the hip not only in level running but also when coping with ground-level changes.HighlightsChanging the trunk-lean when running reorganizes the load distribution across the knee and hip joints.Leaning the trunk anteriorly from a habitual trunk posture during running attenuates the mechanical stress on the knee, while the opposite effect occurs with a posterior trunk-lean, irrespective to the ground surface uniformity.The effect of posture on pronounced mechanical ankle stress in small perturbation height during running is marginal.Leaning the trunk anteriorly shifts loading from the knee to the hip not only in level running but also when coping with small perturbation height.

Ultrastructural and kinetic evidence support that thick filaments slide through the Z-disc.

How myofilaments operate at short mammalian skeletal muscle lengths is unknown. A common assumption is that thick (myosin-containing) filaments get compressed at the Z-disc. We provide ultrastructural evidence of sarcomeres contracting down to 0.44 µm-approximately a quarter of thick filament resting length-in long-lasting contractions while apparently keeping a regular, parallel thick filament arrangement. Sarcomeres produced force at such extremely short lengths. Furthermore, sarcomeres adopted a bimodal length distribution with both modes below lengths where sarcomeres are expected to generate force in classic force-length measurements. Mammalian fibres did not restore resting length but remained short after deactivation, as previously reported for amphibian fibres, and showed increased forces during passive re-elongation. These findings are incompatible with viscoelastic thick filament compression but agree with predictions of a model incorporating thick filament sliding through the Z-disc. This more coherent picture of mechanical mammalian skeletal fibre functioning opens new perspectives on muscle physiology.

Single limb dynamics of jumping turns in dogs.

Maneuverability is of paramount importance for many animals, e.g., in predator-prey interactions. Despite this fact, quadrupedal limb behavior in complicated maneuvers like simultaneous jumping and turning are not well studied. Twenty adult sport Border Collies were recorded while jumping over an obstacle and simultaneously turning. Kinetic and kinematic data were captured in synchrony using eight force plates and sixteen infrared cameras. These dogs were familiar with the task through regular participation in the dog sport agility. The experiments revealed that during landing, higher lateral forces acting in the forelimbs compared to hindlimbs. During landing, the outer limbs produced about twice the inner limbs' force in both vertical and lateral directions, showing their dominant contribution to turning. Advanced dogs showed significantly higher lateral impulse and stronger inner-outer limb asymmetry regarding lateral impulses than beginner dogs, leading to significantly stronger turning for advanced dogs. Somewhat unexpected, skill effects rarely explained global limb dynamics, indicating that landing a turn jump is a constrained motion. Constrained motions leave little space for individual techniques suggesting that the results can be generalized to quadrupedal turn jumps in other animals.

A simple geometrical model accounting for 3D muscle architectural changes across muscle lengths.

Muscle architecture parameters change when the muscle changes in length. This has multiple effects on the function of the muscle, e.g. on force production and on contraction velocity. Here we present a versatile geometrical model that predicts changes in muscle architecture as a consequence of length changes of the muscle on the basis of the known architecture at a given muscle length. The model accounts for small changes in aponeuroses' dimensions relative to changes in fascicle length and keeps muscle volume constant. We evaluate the model on the rabbit soleus muscle by comparing model predictions of fascicle lengths and pennation angles with experimental data. For this, we determined the internal architecture of the soleus muscle at different muscle belly lengths (67.8 mm at 35° ankle angle and 59.3 mm at 80° ankle angle). The long and the short soleus muscle exhibited mean fascicle lengths and pennation angles of 20.8 ± 1.3 mm, 4 ± 2° and 13.5 ± 1 mm, 10 ± 4°, respectively. The model predicted reasonable mean fascicle lengths and pennation angles for the long and short soleus that differed only by 1 mm and 1° from the measured data, respectively. Differences between predicted and measured distributions seem to stem from interindividual variability in muscle architecture. Even if the proposed approach has been used for the soleus muscle, which is relatively simple in architecture, it is not restricted to homogeneous unipennate architectures.

Titin-induced force enhancement and force depression: a 'sticky-spring' mechanism in muscle contractions?

The sliding filament and crossbridge theories do not suffice to explain a number of muscle experiments. For example, from the entire muscle to myofibrils, predictions of these theories were shown to underestimate the force output during and after active tissue stretch. The converse applies to active tissue shortening. In addition to the crossbridge cycle, we propose that another molecular mechanism is effective in sarcomere force generation. We suggest that, when due to activation, myosin binding sites are available on actin, the giant protein titin's PEVK region attaches itself to the actin filament at those sites. As a result, the molecular spring length is dramatically reduced. This leads to increased passive force when the sarcomere is stretched and to decreased or even negative passive force when the sarcomere shortens. Moreover, during shortening, the proposed mechanism interferes with active-force production by inhibiting crossbridges. Incorporation of a simple 'sticky-spring' mechanism model into a Hill-type model of sarcomere dynamics offers explanations for several force-enhancement and force-depression effects. For example, the increase of the sarcomere force compared to the force predicted solely by the sliding filament and crossbridge theories depends on the stretch amplitude and on the working range. The same applies to the decrease of sarcomere force during and after shortening. Using only literature data for its parameterization, the model predicts forces similar to experimental results.

Analyzing Moment Arm Profiles in a Full-Muscle Rat Hindlimb Model.

Understanding the kinematics of a hindlimb model is a fundamental aspect of modeling coordinated locomotion. This work describes the development process of a rat hindlimb model that contains a complete muscular system and incorporates physiological walking data to examine realistic muscle movements during a step cycle. Moment arm profiles for selected muscles are analyzed and presented as the first steps to calculating torque generation at hindlimb joints. A technique for calculating muscle moment arms from muscle attachment points in a three-dimensional (3D) space has been established. This model accounts for the configuration of adjacent joints, a critical aspect of biarticular moment arm analysis that must be considered when calculating joint torque. Moment arm profiles from isolated muscle motions are compared to two existing models. The dependence of biarticular muscle's moment arms on the configuration of the adjacent joint is a critical aspect of moment arm analysis that must be considered when calculating joint torque. The variability in moment arm profiles suggests changes in muscle function during a step.