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

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.

Effect of gender, muscle type and skinfold thickness on myometric parameters in young people

Background

The aim of the study was to compare the mechanical properties of three human skeletal muscles: biceps brachii (BB), rectus femoris (RF), and tibialis anterior (TA) at rest measured by myoton device in males (n = 16, mean age 21.2 ± 0.6 years) and females (n = 16; 21.2 ± 0.9 years) and to investigate the influence of skin and subcutaneous tissue thickness (skinfold thickness, SFT) and gender on myometric parameters of the three skeletal muscles.

Methods

We measured the following mechanical and viscoelastic muscle properties using MyotonPRO^®: frequency (F [Hz]), decrement (D [log]), stiffness (S [N/m]), relaxation time (R [ms]) and creepability (C [De]). The values of SFT for all selected muscles were assessed by caliper. A mixed-design analysis of variance with gender as between subject comparison was used for assessing the differences between gender and muscles in SFT and each of the myometric parameters separately (F, D, S, R and C). Pearson correlation coefficient or Spearman’s rank correlation coefficient between SFT and myometric parameters was conducted for males, females and males and females together. The level of statistical significance was set at α ≤ 0.05 with Bonferroni correction for multiple comparisons.

Results

The SFT over the RF, TA, and BB muscles in women was statistically significantly larger compared with that of males. In females and males, the SFT over the RF was larger than over the TA and BB, and the SFT over the TA was larger compared with over the BB. The values of F and S recorded for the TA muscle were the highest among the three muscles, while D, C, and R were lowest in TA but highest in the RF muscle in men and women. The values of F and S were smaller in females than in males. Gender comparison of D, C, and R values showed that only D for the RF was significantly lower in females than in males, and C for the RF and TA was significantly larger in females than in males. Some correlation between SFT and myometric parameters were different between males and females. For example, there was a significant, negative correlation between SFT and F for all muscles in females, and a significant, positive correlation between these parameters for BB and TA (not for RF) in males. For pooled data (males and females together), a negative significant correlation between SFT and F was observed for RF and TA (not significant for BB muscle).

Discussion

It is concluded that the TA compared with the BB and RF has significantly greater F and S but the smallest D and C and the shortest R. Gender and muscle differences in the SFT may affect the measurements of muscle properties using MyotonPRO^®. The relationship between SFT and myometric parameters is different in males and females in the RF, TA, and BB muscles. Therefore, the myometric data should be analyzed in males and females separately.

Muscle Synergies Modify Optimization Estimates of Joint Stiffness During Walking

Because of its simplicity, static optimization (SO) is frequently used to resolve the muscle redundancy problem (i.e., more muscles than degrees-of-freedom (DOF) in the human musculoskeletal system). However, SO minimizes antagonistic co-activation and likely joint stiffness as well, which may not be physiologically realistic since the body modulates joint stiffness during movements such as walking. Knowledge of joint stiffness is limited due to the difficulty of measuring it experimentally, leading researchers to estimate it using computational models. This study explores how imposing a synergy structure on the muscle activations estimated by optimization (termed "synergy optimization," or SynO) affects calculated lower body joint stiffnesses during walking. By limiting the achievable muscle activations and coupling all time frames together, a synergy structure provides a potential mechanism for reducing indeterminacy and improving physiological co-activation but at the cost of a larger optimization problem. To compare joint stiffnesses produced by SynO (2-6 synergies) and SO, we used both approaches to estimate lower body muscle activations and forces for sample experimental overground walking data obtained from the first knee grand challenge competition. Both optimizations used a custom Hill-type muscle model that permitted analytic calculation of individual muscle contributions to the stiffness of spanned joints. Both approaches reproduced inverse dynamic joint moments well over the entire gait cycle, though SynO with only two synergies exhibited the largest errors. Maximum and mean joint stiffnesses for hip and knee flexion in particular decreased as the number of synergies increased from 2 to 6, with SO producing the lowest joint stiffness values. Our results suggest that SynO increases joint stiffness by increasing muscle co-activation, and furthermore, that walking with a reduced number of synergies may result in increased joint stiffness and perhaps stability.

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.

Transitory force decrease following a sudden reduction in stimulation frequency in motor units of rat medial gastrocnemius

Effects of a sudden decrease in the stimulation frequency for motor unit force were studied in rat medial gastrocnemius. For 161 functionally isolated single motor units of three types (S, FR, FF), unfused tetanic contractions were evoked by three-phase trains of stimuli (low-high-low frequency). The course of the tetanus at the onset of the third phase of the force recording was analyzed in tetani with variable fusion degree. For 78 units within the third phase of tetanus, a transitory force decrease to a level lower than in the first phase (identical frequency), was observed. This phenomenon was more frequent for fast fatigue resistant (65.9%) than for fast fatigable and slow motor units (27.1% and 35.5%, respectively). Moreover, the force decrease was strongest for fast resistant motor units (up to 36.5%) and when contractions evoked at variable frequencies of stimulation were compared, the highest amplitudes of the studied force decrease were noted for middle-fused tetani (0.50-0.90). A new phenomenon of transitory force decrease in tetanic contractions of motor units with a decrease in stimulation frequency was found. Most probably, the phenomenon is dependent on disturbances in the force transmission by collagen surrounding active muscles fibers.

Summation of slow motor unit forces at constant and variable interpulse intervals in rat soleus muscle

Effects of the summation of forces generated by functionally isolated slow-twitch motor units (MU) of the rat soleus muscle were examined in this study. Initially, the twitch, fused tetanic and unfused tetanic contractions evoked by trains of stimuli at variable interpulse intervals were recorded for each MU. Then, two, three or four MUs were co-activated, and the recorded forces were compared to the algebraic sum of the forces of individual MUs. The mean cumulative force of twitches and the mean cumulative force of fused tetani were not statistically different from the respective algebraic sums of forces, which revealed a high degree of linearity in the summation. However, relaxation of the recorded tetanic contractions (either fused or unfused) was faster than that predicted by the linear summation of individual contractions. Moreover, for twitch and tetanic contractions, a tendency to shorten relaxation with an increasing number of co-active MUs was noted. The results indicate that forces of rat soleus slow MUs sum up more linearly than in the respective cat muscle as well as more linearly than for fast MUs in the medial gastrocnemius muscle.

Modeling and simulating the neuromuscular mechanisms regulating ankle and knee joint stiffness during human locomotion

This work presents an electrophysiologically and dynamically consistent musculoskeletal model to predict stiffness in the human ankle and knee joints as derived from the joints constituent biological tissues (i.e., the spanning musculotendon units). The modeling method we propose uses electromyography (EMG) recordings from 13 muscle groups to drive forward dynamic simulations of the human leg in five healthy subjects during overground walking and running. The EMG-driven musculoskeletal model estimates musculotendon and resulting joint stiffness that is consistent with experimental EMG data as well as with the experimental joint moments. This provides a framework that allows for the first time observing 1) the elastic interplay between the knee and ankle joints, 2) the individual muscle contribution to joint stiffness, and 3) the underlying co-contraction strategies. It provides a theoretical description of how stiffness modulates as a function of muscle activation, fiber contraction, and interacting tendon dynamics. Furthermore, it describes how this differs from currently available stiffness definitions, including quasi-stiffness and short-range stiffness. This work offers a theoretical and computational basis for describing and investigating the neuromuscular mechanisms underlying human locomotion.

Knee stiffness estimation in physiological gait

During physiological gait, humans continuously modulate their knee stiffness, depending on the demands of the activity and the terrain. A similar functionality could be provided by modern actuators in transfemoral prosthesis. However, quantitative data on how knee stiffness is modulated during physiological gait is still missing. This is likely due to the experimental difficulties associated with identifying knee stiffness by applying perturbations during gait. It is our goal to quantify such stiffness modulation during gait without the need to apply perturbations. Therefore, we have recently presented an approach to quantify knee stiffness from kinematic, kinetic and electromyographic (EMG) measurements, and have validated it in isometric conditions. The goal of this paper is to extend this approach to non-isometric conditions by combining inverse dynamics and EMG measurements, and to quantify physiological stiffness modulation in the example of level-ground walking. We show that stiffness varies substantially throughout a gait cycle, with a stiffness of around 100 Nm/rad during swing phase, and a peak of 450 Nm/rad in stance phase. These quantitative results may be beneficial for design and control of transfemoral prostheses and orthoses that aim to restore physiological function.

The dynamic effect of muscle activation on knee stiffness

Adapting limb mechanics in a task and environment dependent manner is one component of human motor control. Joint mechanics have been extensively studied under static postural conditions, but less so under time-varying movement conditions. The limited studies that have investigated joint mechanics during movement, have found a drop in joint stiffness during movement, however the source of this decrease in stiffness remains unknown. Here in this paper we investigate whether time-varying muscle activation, which occurs during volitional movement, can lead to the drop in stiffness seen during movement. We found that under time-varying isometric conditions stiffness dropped when subjects transitioned from extension to flexion and vice-versa, a phenomenon that could not be explained by simply superimposing extension and flexion contractions. These findings suggest that dynamics of muscle activation may be responsible for the complex pattern of stiffness changes seen during simple movements. Furthermore, these results imply that EMG-based estimates of stiffness, which work well for steady-state postural conditions, will need to be augmented to account for the highly non-linear relationship between muscle activation and stiffness before they can also be used to estimate stiffness during dynamic contractions.

Model-based estimation of knee stiffness

During natural locomotion, the stiffness of the human knee is modulated continuously and subconsciously according to the demands of activity and terrain. Given modern actuator technology, powered transfemoral prostheses could theoretically provide a similar degree of sophistication and function. However, experimentally quantifying knee stiffness modulation during natural gait is challenging. Alternatively, joint stiffness could be estimated in a less disruptive manner using electromyography (EMG) combined with kinetic and kinematic measurements to estimate muscle force, together with models that relate muscle force to stiffness. Here we present the first step in that process, where we develop such an approach and evaluate it in isometric conditions, where experimental measurements are more feasible. Our EMG-guided modeling approach allows us to consider conditions with antagonistic muscle activation, a phenomenon commonly observed in physiological gait. Our validation shows that model-based estimates of knee joint stiffness coincide well with experimental data obtained using conventional perturbation techniques. We conclude that knee stiffness can be accurately estimated in isometric conditions without applying perturbations, which presents an important step toward our ultimate goal of quantifying knee stiffness during gait.

Short range stiffness elastic limit depends on joint velocity

Muscles behave as elastic springs during the initial strain phase, indicated as short range stiffness (SRS). Beyond a certain amount of strain the muscle demonstrates a more viscous behavior. The strain at which the muscle transits from elastic- to viscous-like behavior is called the elastic limit and is believed to be the result of breakage of cross-bridges between the contractile filaments. The aim of this study was to test whether the elastic limit, measured in vivo at the wrist joint, depended on the speed of lengthening. Brief extension rotations were imposed to the wrist joint (n=8) at four different speeds and at three different levels of voluntary torque using a servo controlled electrical motor. Using a recently published identification scheme, we quantified the elastic limit from measured joint angle and torque. The results showed that the elastic limit significantly increased with speed in a linear way, indicating to a constant time of approximately 30 ms before cross-bridges break. The implications for movement control of the joint are discussed.

Muscle short-range stiffness can be used to estimate the endpoint stiffness of the human arm

The mechanical properties of the human arm are regulated to maintain stability across many tasks. The static mechanics of the arm can be characterized by estimates of endpoint stiffness, considered especially relevant for the maintenance of posture. At a fixed posture, endpoint stiffness can be regulated by changes in muscle activation, but which activation-dependent muscle properties contribute to this global measure of limb mechanics remains unclear. We evaluated the role of muscle properties in the regulation of endpoint stiffness by incorporating scalable models of muscle stiffness into a three-dimensional musculoskeletal model of the human arm. Two classes of muscle models were tested: one characterizing short-range stiffness and two estimating stiffness from the slope of the force-length curve. All models were compared with previously collected experimental data describing how endpoint stiffness varies with changes in voluntary force. Importantly, muscle properties were not fit to the experimental data but scaled only by the geometry of individual muscles in the model. We found that force-dependent variations in endpoint stiffness were accurately described by the short-range stiffness of active arm muscles. Over the wide range of evaluated arm postures and voluntary forces, the musculoskeletal model incorporating short-range stiffness accounted for 98 ± 2, 91 ± 4, and 82 ± 12% of the variance in stiffness orientation, shape, and area, respectively, across all simulated subjects. In contrast, estimates based on muscle force-length curves were less accurate in all measures, especially stiffness area. These results suggest that muscle short-range stiffness is a major contributor to endpoint stiffness of the human arm. Furthermore, the developed model provides an important tool for assessing how the nervous system may regulate endpoint stiffness via changes in muscle activation.

In vivo estimation of the short-range stiffness of cross-bridges from joint rotation

Short-range stiffness (SRS) is a mechanical property of muscles that is characterized by a disproportionally high stiffness within a short length range during both lengthening and shortening movements. SRS is attributed to the cross-bridges and is beneficial for stabilizing a joint during, e.g., postural conditions. Thus far, SRS has been estimated mainly on isolated mammalian muscles. In this study we presented a method to estimate SRS in vivo in the human wrist joint. SRS was estimated at joint level in the angular domain (Nm/rad) for both flexion and extension rotations of the human wrist in nine healthy subjects. Wrist rotations of 0.15rad at 3rad/s were imposed at eight levels of voluntary contraction ranging from 0 to 2.1Nm by means of a single axis manipulator. Flexion and extension SRS of the wrist joint was estimated consistently and accurately using a dynamic nonlinear model that was fitted onto the recorded wrist torque. SRS increased monotonically with torque in a way consistent with previous studies on isolated muscles. It is concluded that in vivo measurement of joint SRS represents the population of coupled cross-bridges in wrist flexor and extensor muscles. In its current form, the presented technique can be used for clinical applications in many neurological and muscular diseases where altered joint torque and (dissociated) joint stiffness are important clinical parameters.

Summation of motor unit forces in rat medial gastrocnemius muscle

The summation of contractile forces of motor units (MUs) was analyzed by comparing the recorded force during parallel stimulation of two and four individual MUs or four groups of MUs to the algebraic sum of their individual forces. Contractions of functionally-isolated single MUs of the medial gastrocnemius muscle were evoked by electrical stimulation of thin filaments of the split L5 or L4 ventral roots of spinal nerves. Additionally, contractions of large groups of MUs were evoked by stimuli delivered to four parts of the divided L5 ventral root. Single twitches, 40Hz unfused tetani, and 150Hz fused maximum tetani were recorded. In these experimental situations the summation was more effective for unfused tetani than for twitches or maximum tetani. The results obtained for pairs of MUs were highly variable (more- or less-than-linear summation), but coactivation of more units led to progressively weaker effects of summation, which were usually less-than-linear in comparison to the algebraic sums of the individual forces. The variability of the results highlights the importance of the structure of the muscle and the architecture of its MUs. Moreover, the simultaneous activity of fast and slow MUs was considerably more effective than that of two fast units.

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.

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.