Axial stress determines the velocity of shear wave propagation in passive but not active muscles in vivo.

Ultrasound shear wave elastography can be used to characterize mechanical properties of unstressed tissue by measuring shear wave velocity (SWV), which increases with increasing tissue stiffness. Measurements of SWV have often been assumed to be directly related to the stiffness of muscle. Some have also used measures of SWV to estimate stress, since muscle stiffness and stress covary during active contractions, but few have considered the direct influence of muscle stress on SWV. Rather, it is often assumed that stress alters the material properties of muscle, and in turn, shear wave propagation. The objective of this study was to determine how well the theoretical dependency of SWV on stress can account for measured changes of SWV in passive and active muscles. Data were collected from six isoflurane-anesthetized cats; three soleus muscles and three medial gastrocnemius muscles. Muscle stress and stiffness were measured directly along with SWV. Measurements were made across a range of passively and actively generated stresses, obtained by varying muscle length and activation, which was controlled by stimulating the sciatic nerve. Our results show that SWV depends primarily on the stress in a passively stretched muscle. In contrast, the SWV in active muscle is higher than would be predicted by considering only stress, presumably due to activation-dependent changes in muscle stiffness. Our results demonstrate that while SWV is sensitive to changes in muscle stress and activation, there is not a unique relationship between SWV and either of these quantities when considered in isolation.NEW & NOTEWORTHY Ultrasound shear wave elastography may be an inexpensive way to measure muscle stress in passive muscle. Here, using a cat model we directly measured shear wave velocity (SWV), muscle stress, and muscle stiffness. Our results show that SWV depends primarily on the stress in a passively stretched muscle. In contrast, the SWV in active muscle is higher than would be predicted by considering only stress, presumably due to activation-dependent changes in muscle stiffness.

Shear wave velocity is sensitive to changes in muscle stiffness that occur independently from changes in force.

Clinical assessments for many musculoskeletal disorders involve evaluation of muscle stiffness, although it is not yet possible to obtain quantitative estimates from individual muscles. Ultrasound elastography can be used to estimate the material properties of unstressed, homogeneous, and isotropic materials by tracking the speed of shear wave propagation; these waves propagate faster in stiffer materials. Although elastography has been applied to skeletal muscle, there is little evidence that shear wave velocity (SWV) can directly estimate muscle stiffness since this tissue violates many of the assumptions required for there to be a direct relationship between SWV and stiffness. The objective of this study was to evaluate the relationship between SWV and direct measurements of muscle force and stiffness in contracting muscle. Data were collected from six isoflurane-anesthetized cats. We measured the short-range stiffness in the soleus via direct mechanical testing in situ and SWV via ultrasound imaging. Measurements were taken during supramaximal activation at optimum muscle length, with muscle temperature varying between 26°C and 38°C. An increase in temperature causes a decrease in muscle stiffness at a given force, thus decoupling the tension-stiffness relationship normally present in muscle. We found that increasing muscle temperature decreased active stiffness from 4.0 ± 0.3 MPa to 3.3 ± 0.3 MPa and SWV from 16.9 ± 1.5 m/s to 15.9 ± 1.6 m/s while force remained unchanged (mean ± SD). These results demonstrate that SWV is sensitive to changes in muscle stiffness during active contractions. Future work is needed to determine how this relationship is influenced by changes in muscle structure and tension.NEW & NOTEWORTHY Shear wave ultrasound elastography is a noninvasive tool for characterizing the material properties of muscle. This study is the first to compare direct measurements of stiffness with ultrasound measurements of shear wave velocity (SWV) in a contracting muscle. We found that SWV is sensitive to changes in muscle stiffness, even when controlling for muscle tension, another factor that influences SWV. These results are an important step toward developing noninvasive tools for characterizing muscle structure and function.

Vastus lateralis and vastus medialis produce distinct mediolateral forces on the patella but similar forces on the tibia in the rat.

Improper activation of the quadriceps muscles vastus medialis (VM) and vastus lateralis (VL) has been implicated in the development of patellofemoral pain (PFP). This explanation of PFP assumes that VM and VL produce opposing mediolateral forces on the patella. Although studies have provided evidence for opposing actions of VM and VL on the patella, other studies have suggested that their actions might be similar. In this study, we took advantage of the experimental accessibility of the rat to directly measure the forces on the patella produced by VM and VL. We found that VM and VL produce opposing mediolateral forces on the patella when the patella was lifted away from the femur. These distinct mediolateral forces were not transmitted to the tibia, however: forces measured at the distal tibia were very similar for VM and VL. Further, when the patella was placed within the trochlear groove, the forces on the patella produced by VM and VL were very similar to one another. These results suggest that mediolateral forces produced by VM and VL are balanced by reaction forces from the trochlear groove and so are not transmitted to the tibia. These results provide a rich characterization of the mechanical actions of VM and VL and have implications about the potential role of these muscles in PFP and their neural control during behavior.

An action potential-driven model of soleus muscle activation dynamics for locomotor-like movements.

OBJECTIVE: The goal of this study was to develop a physiologically plausible, computationally robust model for muscle activation dynamics (A(t)) under physiologically relevant excitation and movement. APPROACH: The interaction of excitation and movement on A(t) was investigated comparing the force production between a cat soleus muscle and its Hill-type model. For capturing A(t) under excitation and movement variation, a modular modeling framework was proposed comprising of three compartments: (1) spikes-to-[Ca(2+)]; (2) [Ca(2+)]-to-A; and (3) A-to-force transformation. The individual signal transformations were modeled based on physiological factors so that the parameter values could be separately determined for individual modules directly based on experimental data. MAIN RESULTS: The strong dependency of A(t) on excitation frequency and muscle length was found during both isometric and dynamically-moving contractions. The identified dependencies of A(t) under the static and dynamic conditions could be incorporated in the modular modeling framework by modulating the model parameters as a function of movement input. The new modeling approach was also applicable to cat soleus muscles producing waveforms independent of those used to set the model parameters. SIGNIFICANCE: This study provides a modeling framework for spike-driven muscle responses during movement, that is suitable not only for insights into molecular mechanisms underlying muscle behaviors but also for large scale simulations.

Passive elastic properties of the rat ankle.

Passive properties of muscles and tendons, including their elasticity, have been suggested to influence motor control. We examine here the potential role of passive elastic muscle properties at the rat ankle joint, focusing on their potential to specify an equilibrium position of the ankle. We measured the position-dependent passive torques at the rat ankle before and after sequential cuts of flexor (a.k.a. dorsiflexor) and extensor (a.k.a. plantarflexor) ankle muscles. We found that there was a passive equilibrium position of the ankle that shifted systematically with the cuts, demonstrating that the passive torques produced by ankle flexor and extensor muscles work in opposition in order to maintain a stable equilibrium. The mean equilibrium position of the intact rat ankle ranged from 9.3° to 15.7° in extension relative to the orthogonal position, depending on the torque metric. The mean shift in equilibrium position due to severing extensors ranged from 4.4° to 7.7°, and the mean shift due to severing flexors was smaller, ranging from 0.9° to 2.5°. The restoring torques generated by passive elasticity are large enough (approximately 1.5-5 mNm for displacements of 18° from equilibrium) to affect ankle movement during the swing phase of locomotion, and the asymmetry of larger extension vs. flexion torques is consistent with weight support, demonstrating the importance of accounting for passive muscle properties when considering the neural control of movement.

Transducer and base compliance alter the in situ 6 dof force measured from muscle during an isometric contraction in a multi-joint limb.

Although musculoskeletal models are commonly used, validating the muscle actions predicted by such models is often difficult. In situ isometric measurements are a possible solution. The base of the skeleton is immobilized and the endpoint of the limb is rigidly attached to a 6-axis force transducer. Individual muscles are stimulated and the resulting forces and moments recorded. Such analyses generally assume idealized conditions. In this study we have developed an analysis taking into account the compliances due to imperfect fixation of the skeleton, imperfect attachment of the force transducer, and extra degrees of freedom (dof) in the joints that sometimes become necessary in fixed end contractions. We use simulations of the rat hindlimb to illustrate the consequences of such compliances. We show that when the limb is overconstrained, i.e., when there are fewer dof within the limb than are restrained by the skeletal fixation, the compliances of the skeletal fixation and of the transducer attachment can significantly affect measured forces and moments. When the limb dofs and restrained dofs are matched, however, the measured forces and moments are independent of these compliances. We also show that this framework can be used to model limb dofs, so that rather than simply omitting dofs in which a limb does not move (e.g., abduction at the knee), the limited motion of the limb in these dofs can be more realistically modeled as a very low compliance. Finally, we discuss the practical implications of these results to experimental measurements of muscle actions.

Estimation of musculoskeletal models from in situ measurements of muscle action in the rat hindlimb.

Musculoskeletal models are often created by making detailed anatomical measurements of muscle properties. These measurements can then be used to determine the parameters of canonical models of muscle action. We describe here a complementary approach for developing and validating muscle models, using in situ measurements of muscle actions. We characterized the actions of two rat hindlimb muscles: the gracilis posticus (GRp) and the posterior head of biceps femoris (BFp; excluding the anterior head with vertebral origin). The GRp is a relatively simple muscle, with a circumscribed origin and insertion. The BFp is more complex, with an insertion distributed along the tibia. We measured the six-dimensional isometric forces and moments at the ankle evoked from stimulating each muscle at a range of limb configurations. The variation of forces and moments across the workspace provides a succinct characterization of muscle action. We then used this data to create a simple muscle model with a single point insertion and origin. The model parameters were optimized to best explain the observed force-moment data. This model explained the relatively simple muscle, GRp, very well (R(2)>0.85). Surprisingly, this simple model was also able to explain the action of the BFp, despite its greater complexity (R(2)>0.84). We then compared the actions observed here with those predicted using recently published anatomical measurements. Although the forces and moments predicted for the GRp were very similar to those observed here, the predictions for the BFp differed. These results show the potential utility of the approach described here for the development and refinement of musculoskeletal models based on in situ measurements of muscle actions.

Force transmission between synergistic skeletal muscles through connective tissue linkages.

The classic view of skeletal muscle is that force is generated within its muscle fibers and then directly transmitted in-series, usually via tendon, onto the skeleton. In contrast, recent results suggest that muscles are mechanically connected to surrounding structures and cannot be considered as independent actuators. This article will review experiments on mechanical interactions between muscles mediated by such epimuscular myofascial force transmission in physiological and pathological muscle conditions. In a reduced preparation, involving supraphysiological muscle conditions, it is shown that connective tissues surrounding muscles are capable of transmitting substantial force. In more physiologically relevant conditions of intact muscles, however, it appears that the role of this myofascial pathway is small. In addition, it is hypothesized that connective tissues can serve as a safety net for traumatic events in muscle or tendon. Future studies are needed to investigate the importance of intermuscular force transmission during movement in health and disease.

In situ estimation of tendon material properties: differences between muscles of the feline hindlimb.

Recent experiments to characterize the short-range stiffness (SRS)-force relationship in several cat hindlimb muscles suggested that the there are differences in the tendon elastic moduli across muscles [Cui, L., Perreault, E.J., Maas, H., Sandercock, T.G., 2008. Modeling short-range stiffness of feline lower hindlimb muscles. J. Biomech. 41 (9), 1945-1952.]. Those conclusions were inferred from whole muscle experiments and a computational model of SRS. The present study sought to directly measure tendon elasticity, the material property most relevant to SRS, during physiological loading to confirm the previous modeling results. Measurements were made from the medial gastrocnemius (MG), tibialis anterior (TA) and extensor digitorum longus (EDL) muscles during loading. For the latter, the model indicated a substantially different elastic modulus than for MG and TA. For each muscle, the stress-strain relationship of the external tendon was measured in situ during the loading phase of isometric contractions conducted at optimum length. Young's moduli were assessed at equal strain levels (1%, 2% and 3%), as well as at peak strain. The stress-strain relationship was significantly different between EDL and MG/TA, but not between MG and TA. EDL had a more apparent toe region (i.e., lower Young's modulus at 1% strain), followed by a more rapid increase in the slope of the stress-strain curve (i.e., higher Young's modulus at 2% and 3% strain). Young's modulus at peak strain also was significantly higher in EDL compared to MG/TA, whereas no significant difference was found between MG and TA. These results indicate that during natural loading, tendon Young's moduli can vary considerably across muscles. This creates challenges to estimating muscle behavior in biomechanical models for which direct measures of tendon properties are not available.

Force summation between muscles: are muscles independent actuators?

Muscle force can be transmitted via connective tissues to neighboring muscles. The goal of this research is to determine the extent to which this effects force summation between synergists during physiological conditions. This manuscript reviews two studies examining the interaction between synergists in cat hindlimb. Deeply anesthetized cats were mounted in a rigid frame with the foot secured to a six-degree-of-freedom load cell coupled to a robotic arm. Muscles were stimulated by implanted nerve cuff electrodes. In the first study, force summation was measured during isometric contractions. Interactions were studied between the lateral gastrocnemius (LG)/soleus (SOL) and the medial gastrocnemius (MG) as well as between rectus femoris and vastus lateralis. Invariably, nonlinear force summation was less than 10% of maximum force for all three translational directions and all three rotational directions. The second study investigated if force transmission from SOL fibers was affected by length changes of its two-joint synergists. Ankle plantar flexor moment, upon activation of only SOL, was measured for various knee angles (70 degrees -140 degrees ), which involved substantial length changes of LG, MG, and plantaris muscles. Ankle angle was kept constant (80 degrees -90 degrees ). SOL ankle moment was not significantly (P = 0.11) affected by changes in knee angle, neither were the half-relaxation time and the maximal rate of relaxation. The connective tissue links between SOL and LG were further studied during a tenotomy of the SOL and demonstrated that the connective links can transmit approximately 50% of the force from the SOL to the LG in nonphysiological conditions. In conclusion, despite strong connective tissue linkages, in cat hindlimb synergistic muscles appear to be independent actuators if acting in physiological conditions.

Modeling short-range stiffness of feline lower hindlimb muscles.

The short-range stiffness (SRS) of skeletal muscles is a critical property for understanding muscle contributions to limb stability, since it represents a muscle's capacity to resist external perturbations before reflexes or voluntary actions can intervene. A number of studies have demonstrated that a simple model, consisting of a force-dependent active stiffness connected in series with a constant passive stiffness, is sufficient to characterize the SRS of individual muscles over the entire range of obtainable forces. The purpose of this study was to determine if such a model could be used to characterize the SRS-force relationship in a number of architecturally distinct muscles. Specifically, we hypothesized that the active and passive stiffness components for a specific muscle can be estimated from anatomical measurements, assuming uniform active and passive stiffness properties across all muscles. This hypothesis was evaluated in six feline lower hindlimb muscle types with different motor unit compositions and architectures. The SRS-force relationships for each muscle type were predicted based on anatomical measurements and compared to experimental data. The model predictions were accurate to within 30%, when uniform scaling properties were assumed across all muscles. Errors were the greatest for the extensor digitorum longus (EDL). When this muscle was removed from the analysis, prediction errors dropped to less than 8%. Subsequent analyses suggested that these errors might have resulted from differences in the tendon elastic modulus, as compared to the other muscles tested.

Are skeletal muscles independent actuators? Force transmission from soleus muscle in the cat.

It is unclear if skeletal muscles act mechanically as independent actuators. The purpose of the present study was to investigate force transmission from soleus (SO) muscle for physiological lengths as well as relative positions in the intact cat hindlimb. We hypothesized that force transmission from SO fibers will be affected by length changes of its two-joint synergists. Ankle plantar flexor moment on excitation of the SO was measured for various knee angles (70-140 degrees ). This involved substantial length changes of gastrocnemius and plantaris muscles. Ankle angle was kept constant (80 degrees -90 degrees ). However, SO ankle moment was not significantly affected by changes in knee angle; neither were half-relaxation time and the maximal rate of relaxation (P > 0.05). Following tenotomy, SO ankle moment decreased substantially (55 +/- 16%) but did not reach zero, indicating force transmission via connective tissues to the Achilles tendon (i.e., epimuscular myofascial force transmission). During contraction SO muscle shortened to a much greater extent than in the intact case (16.0 +/- 0.6 vs. 1.0 +/- 0.1 mm), which resulted in a major position shift relative to its synergists. If the SO was moved back to its position corresponding to the intact condition, SO ankle moment approached zero, and most muscle force was exerted at the distal SO tendon. Our results also suggested that in vivo the lumped intact tissues linking SO to its synergists are slack or are operating on the toe region of the stress-strain curve. Thus, within the experimental conditions of the present study, the intact cat soleus muscle appears to act mechanically as an independent actuator.

Motor unit composition has little effect on the short-range stiffness of feline medial gastrocnemius muscle.

Studies on skinned fibers and single motor units have indicated that slow-twitch fibers are stiffer than fast-twitch fibers. This suggests that skeletal muscles with different motor unit compositions may have different short-range stiffness (SRS) properties. Furthermore, the natural recruitment of slow before fast motor units may result in an SRS-force profile that is different from electrical stimulation. However, muscle architecture and the mechanical properties of surrounding tissues also contribute to the net SRS of a muscle, and it remains unclear how these structural features each contribute to the SRS of a muscle. In this study, the SRS-force characteristics of cat medial gastrocnemius muscle were measured during natural activation using the crossed-extension reflex, which activates slow before fast motor units, and during electrical activation, in which all motor units are activated synchronously. Short, rapid, isovelocity stretches were applied using a linear puller to measure SRS across the range of muscle forces. Data were collected from eight animals. Although there was a trend toward greater stiffness during natural activation, this trend was small and not statistically significant across the population of animals tested. A simple model, in which the slow-twitch fibers were assumed to be 30% stiffer than the fast-twitch fibers, was used to simulate the experimental results. Experimental and simulated results show that motor unit composition or firing rate has little effect on the SRS property of the cat MG muscle, suggesting that architectural features may be the primary determinant of SRS.

Extra force from asynchronous stimulation of cat soleus muscle results from minimizing the stretch of the common elastic elements.

Rack and Westbury showed that low-frequency asynchronous stimulation of a muscle produces greater force compared with synchronous stimulation. This study tested the hypothesis that the difference results from the dynamic stretch of the common elastic elements. In eight anesthetized cats, the soleus was attached to a servomechanism to control muscle length and record force. The ventral roots were divided into four bundles so each innervated approximately 1/4 of the soleus. The elasticity shared by each part of the muscle was estimated and the servomechanism programmed to compensate for its stretch. At each test frequency (5, 7.5, and 10 Hz), the muscle was stimulated by asynchronous stimulation, synchronous stimulation, summation of force with each part stimulated individually, and summation with each part stimulated individually and the servomechanism mimicking tendon stretch during asynchronous stimulation. Muscle length was isometric except for the last protocol. The observed differences were small. The greatest difference occurred during stimulation at 5 Hz with muscle length on the ascending limb of the length-tension curve. Here, the average forces, normalized by asynchronous force, were asynchronous, 100%; synchronous, 73%; summation, 110%; and summation with stretch compensation, 98%. The results support the hypothesis and suggest that the common elasticity can be used to predict force gains from asynchronous stimulation.

Summation of motor unit force in passive and active muscle.

Nonlinear summation of force has been observed between motor units. The complex structure of muscle suggests many reasons why this could happen. When large portions of the muscle are active, however, the nonlinearities are small, and generally explained by stretch of the common elasticity. This suggests that the type of nonlinearity observed between motor units may not be physiologically significant.

Summation of forces from multiple motor units in the cat soleus muscle.

Nearly all muscle models and most motor control concepts assume that forces from individual muscle fibers and motor units sum in an additive manner once effects of in-series tendon compliance are taken into account. Due to the numerous mechanical linkages between individual fibers, though, it is unclear whether this assumption is warranted. This work examined motor unit force summation over a wide range of muscle forces in the cat soleus. Nonadditive summation implies a nonlinear summation of motor unit forces. Summation nonlinearities were quantified during interactions of 10 individual motor units and 4 motor unit bundles containing approximately 10 units each. These protocols allowed motor unit force summation to be examined from approximately 0 to 25% of tetanic muscle force. Nonlinear summation was assessed by comparing the actual forces to the algebraic sum of individual units and bundles stimulated in isolation. Superadditive summation meant that the actual force exceeded the algebraic sum, whereas subadditive summation meant that the actual force was smaller than the algebraic sum. Experiments tested the hypothesis that superadditive summation occurs at low force levels when few motor units are recruited, whereas subadditive summation prevails above 10% of tetanic force. Results were consistent with this hypothesis. As in previous studies, nonlinear summation in the soleus was modest, but a clear transition from predominately superadditive to predominantly subadditive summation occurred in the range of 6-8% of tetanic force. The largest nonlinearities were transient and appeared at the onset of recruitment and derecruitment of groups of motor units. The results are discussed in terms of the mechanical properties of the connective tissue forming the tendon and linking muscle fibers.

Hill muscle model errors during movement are greatest within the physiologically relevant range of motor unit firing rates.

This study evaluated the accuracy of Hill-type muscle models during movement. Hill-type models are ubiquitous in biomechanical simulations. They are attractive because of their computational simplicity and close relation to commonly measured experimental variables, but there have been surprisingly few experimental validations of these models during functionally relevant conditions. Our hypothesis was that model errors during movement are largest at the low motor unit firing rates most relevant to normal movement conditions. This hypothesis was evaluated in the cat soleus muscle activated either by electrical stimulation at physiological rates or via the crossed-extension reflex (CXR) thereby obtaining normal patterns of motor unit recruitment and rate modulation. These activation paradigms were applied during continuous movements approximately matched to locomotor length changes. The resulting muscle force was modeled using a common Hill model incorporating independent activation, tetanic length-tension and tetanic force-velocity properties. Errors for this model were greatest for stimulation rates between approximately 10-20Hz. Errors were especially large for muscles activated via the CXR, where most motor units appear to fire within this range. For large muscle excursions, such as those seen during normal locomotion, the errors for naturally activated muscle typically exceeded 50%, supporting our hypothesis and indicating that the Hill model is not appropriate for these conditions. Subsequent analysis suggested that model errors were due to the common Hill model's inability to account for the coupling between muscle activation and force-velocity properties that is most prevalent at the low motor unit firing rates relevant to normal activation.

Nonlinear summation of force in cat tibialis anterior: a muscle with intrafascicularly terminating fibers.

The complex connective tissue structure of muscle and tendon suggests that forces from two parts of a muscle may not summate linearly, particularly in muscles with intrafasciculary terminating fibers, such as cat tibialis anterior (TA). In four anesthetized cats, the TA was attached to a servomechanism to control muscle length and record force. The ventral roots were divided into two bundles, each innervating about half the TA, so the two parts could be stimulated alone or together. Nonlinear summation of force (F(nl)) was measured during isometric contractions. F(nl) was small and negative, indicating less than linear summation of the parts, which is consistent with the predicted F(nl) of muscle fibers connected in series. F(nl) was more significant when smaller parts of the muscle were tested (21.8 vs. 8% for whole muscle). These data were fit to a model where both parts of the muscle were assumed to stretch a common elasticity. Compensatory movements of the servomechanism showed the common elasticity is very stiff, and the model cannot account for F(nl) in cat TA.