Emanuel Azizi

Flexible mechanisms: the diverse roles of biological springs in vertebrate movement

Summary The muscles that power vertebrate locomotion are associated with springy tissues, both within muscle and in connective tissue elements such as tendons. These springs share in common the same simple action: they stretch and store elastic strain energy when force is applied to them and recoil to release energy when force decays. Although this elastic action is simple, it serves a diverse set of functions, including metabolic energy conservation, amplification of muscle power output, attenuation of muscle power input, and rapid mechanical feedback that may aid in stability. In recent years, our understanding of the mechanisms and importance of biological springs in locomotion has advanced significantly, and it has been demonstrated that elastic mechanisms are essential for the effective function of the muscle motors that power movement. Here, we review some recent advances in our understanding of elastic mechanisms, with an emphasis on two proposed organizing principles. First, we review the evidence that the various functions of biological springs allow the locomotor system to operate beyond the bounds of intrinsic muscle properties, including metabolic and mechanical characteristics, as well as motor control processes. Second, we propose that an energy-based framework is useful for interpreting the diverse functions of series-elastic springs. In this framework, the direction and timing of the flow of energy between the body, the elastic element and the contracting muscle determine the function served by the elastic mechanism (e.g. energy conservation vs power amplification). We also review recent work demonstrating that structures such as tendons remodel more actively and behave more dynamically than previously assumed.

Variable gearing in pennate muscles

Muscle fiber architecture, i.e., the physical arrangement of fibers within a muscle, is an important determinant of a muscles mechanical function. In pennate muscles, fibers are oriented at an angle to the muscles line of action and rotate as they shorten, becoming more oblique such that the fraction of force directed along the muscles line of action decreases throughout a contraction. Fiber rotation decreases a muscles output force but increases output velocity by allowing the muscle to function at a higher gear ratio (muscle velocity/fiber velocity). The magnitude of fiber rotation, and therefore gear ratio, depends on how the muscle changes shape in the dimensions orthogonal to the muscles line of action. Here, we show that gear ratio is not fixed for a given muscle but decreases significantly with the force of contraction (P < 0.0001). We find that dynamic muscle-shape changes promote fiber rotation at low forces and resist fiber rotation at high forces. As a result, gearing varies automatically with the load, to favor velocity output during low-load contractions and force output for contractions against high loads. Therefore, muscle-shape changes act as an automatic transmission system allowing a pennate muscle to shift from a high gear during rapid contractions to low gear during forceful contractions. These results suggest that variable gearing in pennate muscles provides a mechanism to modulate muscle performance during mechanically diverse functions.

The series-elastic shock absorber: tendons attenuate muscle power during eccentric actions.

Elastic tendons can act as muscle power amplifiers or energy-conserving springs during locomotion. We used an in situ muscle-tendon preparation to examine the mechanical function of tendons during lengthening contractions, when muscles absorb energy. Force, length, and power were measured in the lateral gastrocnemius muscle of wild turkeys. Sonomicrometry was used to measure muscle fascicle length independently from muscle-tendon unit (MTU) length, as measured by a muscle lever system (servomotor). A series of ramp stretches of varying velocities was applied to the MTU in fully activated muscles. Fascicle length changes were decoupled from length changes imposed on the MTU by the servomotor. Under most conditions, muscle fascicles shortened on average, while the MTU lengthened. Energy input to the MTU during the fastest lengthenings was -54.4 J/kg, while estimated work input to the muscle fascicles during this period was only -11.24 J/kg. This discrepancy indicates that energy was first absorbed by elastic elements, then released to do work on muscle fascicles after the lengthening phase of the contraction. The temporary storage of energy by elastic elements also resulted in a significant attenuation of power input to the muscle fascicles. At the fastest lengthening rates, peak instantaneous power input to the MTU reached -2,143.9 W/kg, while peak power input to the fascicles was only -557.6 W/kg. These results demonstrate that tendons may act as mechanical buffers by limiting peak muscle forces, lengthening rates, and power inputs during energy-absorbing contractions.

Muscle fiber angle, segment bulging and architectural gear ratio in segmented musculature

SUMMARY The anatomical complexity of myomeres and myosepta has made it difficult to develop a comprehensive understanding of the relationship between muscle fiber architecture, connective tissue mechanics, and locomotor function of segmented axial musculature in fishes. The lateral hypaxial musculature (LHM) of salamanders is less anatomically complex and therefore a good system for exploring the basic mechanics of segmented musculature. Here, we derive a mathematical model of the LHM and test our model using sonomicrometry and electromyography during steady swimming in an aquatic salamander, Siren lacertina. The model predicts longitudinal segment strain well, with predicted and measured values differing by less than 5% strain over most of the range. Deviations between predicted and measured results are unbiased and probably result from the salamanders performing slight turns with associated body torsion in our unconstrained trackway swimming experiments. Model simulations of muscle fiber contraction and segment shortening indicate that longitudinal segment strain, for a given amount of muscle fiber strain, increases with increasing initial fiber angle. This increase in architectural gear ratio (AGR = longitudinal strain/fiber strain) is mediated by muscle fiber rotation; the higher the initial fiber angle, the more the fibers rotate during contraction and the higher the AGR. Muscle fiber rotation is additionally impacted by bulging in the dorsoventral (DV) and/or mediolateral (ML) dimensions during longitudinal segment shortening. In segments with obliquely oriented muscle fibers, DV bulging increases muscle fiber rotation, thereby increasing the AGR. Extending the model to include force and work indicates that force decreases with increasing initial muscle fiber angle and increasing DV bulging and that both longitudinal shortening and DV bulging must be included for accurate calculation of segment work.

The hydrodynamics of locomotion at intermediate Reynolds numbers: undulatory swimming in ascidian larvae (Botrylloides sp.).

SUMMARY Understanding how the shape and motion of an aquatic animal affects the performance of swimming requires knowledge of the fluid forces that generate thrust and drag. These forces are poorly understood for the large diversity of animals that swim at Reynolds numbers (Re) between 100 and 102. We experimentally tested quasi-steady and unsteady blade-element models of the hydrodynamics of undulatory swimming in the larvae of the ascidian Botrylloides sp. by comparing the forces predicted by these models with measured forces generated by tethered larvae and by comparing the swimming speeds predicted with measurements of the speed of freely swimming larvae. Although both models predicted mean forces that were statistically indistinguishable from measurements, the quasi-steady model predicted the timing of force production and mean swimming speed more accurately than the unsteady model. This suggests that unsteady force (i.e. the acceleration reaction) does not play a role in the dynamics of steady undulatory swimming at Re≈102. We explored the relative contribution of viscous and inertial force to the generation of thrust and drag at 100<Re<102 by running a series of mathematical simulations with the quasi-steady model. These simulations predicted that thrust and drag are dominated by viscous force (i.e. skin friction) at Re≈100 and that inertial force (i.e. form force) generates a greater proportion of thrust and drag at higher Re than at lower Re. However, thrust was predicted to be generated primarily by inertial force, while drag was predicted to be generated more by viscous than inertial force at Re≈102. Unlike swimming at high (>102) and low (<100) Re, the fluid forces that generate thrust cannot be assumed to be the same as those that generate drag at intermediate Re.

Muscle power attenuation by tendon during energy dissipation.

An important function of skeletal muscle is deceleration via active muscle fascicle lengthening, which dissipates movement energy. The mechanical interplay between muscle contraction and tendon elasticity is critical when muscles produce energy. However, the role of tendon elasticity during muscular energy dissipation remains unknown. We tested the hypothesis that tendon elasticity functions as a mechanical buffer, preventing high (and probably damaging) velocities and powers during active muscle fascicle lengthening. We directly measured lateral gastrocnemius muscle force and length in wild turkeys during controlled landings requiring rapid energy dissipation. Muscle-tendon unit (MTU) strain was measured via video kinematics, independent of muscle fascicle strain (measured via sonomicrometry). We found that rapid MTU lengthening immediately following impact involved little or no muscle fascicle lengthening. Therefore, joint flexion had to be accommodated by tendon stretch. After the early contact period, muscle fascicles lengthened and absorbed energy. This late lengthening occurred after most of the joint flexion, and was thus mainly driven by tendon recoil. Temporary tendon energy storage led to a significant reduction in muscle fascicle lengthening velocity and the rate of energy absorption. We conclude that tendons function as power attenuators that probably protect muscles against damage from rapid and forceful lengthening during energy dissipation.

Morphology and mechanics of myosepta in a swimming salamander (Siren lacertina)

In contrast to the complex, three-dimensional shape of myomeres in teleost fishes, the lateral hypaxial muscles of salamanders are nearly planar and their myosepta run in a roughly straight line from mid-lateral to mid-ventral. We used this relatively simple system as the basis for a mathematical model of segmented musculature. Model results highlight the importance of the mechanics of myosepta in determining the shortening characteristics of a muscle segment. We used sonomicrometry to measure the longitudinal deformation of myomeres and the dorsoventral deformation of myosepta in a swimming salamander (Siren lacertina). Sonomicrometry results show that the myosepta allow some dorsoventral lengthening, indicating an amplification of myomere shortening that is greater than that produced by muscle fiber angle alone (10% muscle fiber shortening produces 28.7% myomere shortening). Polarized light and DIC microscopy of isolated hypaxial myosepta revealed that the collagen fiber orientation in hypaxial myomeres is primarily mediolateral. The mediolateral collagen fiber orientation, combined with our finding that the hypaxial myosepta lengthen dorsoventrally during swimming, suggests that one possible function of hypaxial myosepta in S. lacertina is to increase the strain amplification of the muscle fibers by reducing the mediolateral bulging of the myomeres and redirecting the bulging toward the dorsoventral direction.

The weak link: do muscle properties determine locomotor performance in frogs?

Muscles power movement, yet the conceptual link between muscle performance and locomotor performance is poorly developed. Frog jumping provides an ideal system to probe the relationship between muscle capacity and locomotor performance, because a jump is a single discrete event and mechanical power output is a critical determinant of jump distance. We tested the hypothesis that interspecific variation in jump performance could be explained by variability in available muscle power. We used force plate ergometry to measure power produced during jumping in Cuban tree frogs (Osteopilus septentrionalis), leopard frogs (Rana pipiens) and cane toads (Bufo marinus). We also measured peak isotonic power output in isolated plantaris muscles for each species. As expected, jump performance varied widely. Osteopilus septentrionalis developed peak power outputs of 1047.0 ± 119.7 W kg−1 hindlimb muscle mass, about five times that of B. marinus (198.5 ± 54.5 W kg−1). Values for R. pipiens were intermediate (543.9 ± 96.2 W kg−1). These differences in jump power were not matched by differences in available muscle power, which were 312.7 ± 28.9, 321.8 ± 48.5 and 262.8 ± 23.2 W kg−1 muscle mass for O. septentrionalis, R. pipiens and B. marinus, respectively. The lack of correlation between available muscle power and jump power suggests that non-muscular mechanisms (e.g. elastic energy storage) can obscure the link between muscle mechanical performance and locomotor performance.

Mechanical properties of the gastrocnemius aponeurosis in wild turkeys

In many muscles, the tendinous structures include both an extramuscular free tendon as well as a sheet-like aponeurosis. In both free tendons and aponeuroses the collagen fascicles are oriented primarily longitudinally, along the muscles line of action. It is generally assumed that this axis represents the direction of loading for these structures. This assumption is well founded for free tendons, but aponeuroses undergo a more complex loading regime. Unlike free tendons, aponeuroses surround a substantial portion of the muscle belly and are therefore loaded both parallel (longitudinal) and perpendicular (transverse) to a muscles line of action when contracting muscles bulge to maintain a constant volume. Given this biaxial loading pattern, it is critical to understand the mechanical properties of aponeuroses in both the longitudinal and transverse directions. In this study, we use uniaxial testing of isolated tissue samples from the aponeurosis of the lateral gastrocnemius of wild turkeys to determine mechanical properties of samples loaded longitudinally (along the muscles line of action) and transversely (orthogonal to the line of action). We find that the aponeurosis has a significantly higher Youngs modulus in the longitudinal than in the transverse direction. Our results also show that aponeuroses can behave as efficient springs in both the longitudinal and transverse directions, losing little energy to hysteresis. We also test the failure properties of aponeuroses to quantify the likely safety factor with which these structures operate during muscular force production. These results provide an essential foundation for understanding the mechanical function of aponeuroses as biaxially loaded biological springs.

Geared up to stretch: pennate muscle behavior during active lengthening.

Many locomotor activities require muscles to actively lengthen, dissipate energy and decelerate the body. These eccentric contractions can disrupt cytoskeletal structures within myofibrils and reduce force output. We examined how architectural features of pennate muscles can provide a protective mechanism against eccentric muscle damage by limiting fascicle lengthening. It has been previously shown that the angled fibers of pennate muscles change orientation when shortening. This change in fiber orientation can amplify fascicle shortening, resulting in a velocity advantage at the level of the muscle–tendon unit (MTU) that is characterized by a gear ratio (MTU velocity/fascicle velocity). A muscles architectural gear ratio (AGR) has been shown to vary as a function of force during shortening, while AGR during lengthening remains largely unknown. We independently measured fascicle length and MTU length in vitro in the bullfrog plantaris. We characterized the muscles force–velocity curve and AGR during both shortening and lengthening across a broad range of forces (10–190% peak isometric force). AGR was measured during the isotonic portion of each contraction, to eliminate possible contributions of series elasticity to MTU length changes. We found that gear ratio varies with force during both shortening and lengthening contractions. The highest AGR was observed during lengthening contractions, indicating that lengthening of the MTU can occur with relatively little stretch of the fascicle. As fascicle strain is considered an important determinant of muscle damage, a high gear ratio may afford pennate muscles protection against the damaging effects of active lengthening.