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

Abstract

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.

INTRODUCTION

Stiffness is a well-known marker of muscle performance and integrity, linking muscle structure and activation to the mechanical properties relevant to posture and movement control. Changes in muscle and joint stiffness have been consistently observed with muscle pathology, such as spasticity (22) and Duchenne muscular dystrophy (7), or after stroke and spinal cord injury (24). Muscle stiffness has been further investigated as a marker of muscle adaptation due to exercise (33), injury and recovery (3, 26), or aging (1). For these reasons, there has been a long-standing interest in noninvasive methods for characterizing muscle stiffness. The most prevalent methods assess the mechanical properties of individual joints (19, 37, 48) but cannot uniquely determine the properties of individual muscles except possibly through modeling or optimization (36, 38, 50). In recent years, shear wave ultrasound elastography has been used to assess the mechanical properties of muscles, including stiffness, based on the speed with which induced shear waves propagate in the tissue of interest; faster propagation is used to infer stiffer muscle, as described by its shear modulus (23). Although this technique proved accurate in homogeneous and isotropic tissues, many assumptions are required before shear waves can be used to infer the material properties of different types of tissues, and it is unclear how well these assumptions apply to contracting muscle.

Shear wave velocity (SWV) as measured by ultrasound is known to increase with increases in muscle force generated by either increased activation or the stretching of passive muscle (5, 12, 16, 18). However, it remains unclear whether this occurs as a consequence of the increase in muscle stiffness that accompanies changes in force, a direct influence of the change in muscle tension, or a weighted effect of both. SWV can be used to estimate the Young’s modulus, a measure of intrinsic mechanical properties, for unstressed materials that are homogeneous and isotropic. This relationship has driven the use of elastography for measuring the material properties of liver and breast tissue (8, 15), which are typically unstressed structures with properties that are close to homogeneous and isotropic at the scale relevant to shear wave propagation. In contrast, muscle consists of long, fibrous bundles of contractile tissue, surrounded by a passive extracellular matrix, and one of its fundamental functions is to generate tension. Tension is known to influence shear wave propagation even for fixed material properties (17) and to be the dominant factor contributing to SWV in tendons (29). The use of elastography to infer the mechanical properties of muscle is further complicated by the fact that the mechanical properties of muscle are directly proportional to the tension generated during activation (9, 14, 32). Since many factors can modulate SWV in muscle, these measures have been associated with intrinsic stiffness (11, 16, 42), active forces (4, 18, 46), and passive tension (12, 20). However, we are unaware of any prior work that has teased out the individual contributions of muscle stiffness and tension to SWV. Thus it remains unclear which of these covarying properties can be measured unambiguously by shear wave elastography during the operating conditions relevant to natural force generation. Determining how shear wave propagation depends on the material properties of muscle and the passive and active tensions within that muscle is critical for determining the utility of this technology.

A direct measure of muscle mechanical properties can be obtained by characterizing short-range stiffness (SRS). SRS describes the elastic properties of muscle in response to small, rapid changes in length (41). Measurements of SRS can be made in an in situ muscle preparation that allows for direct measurements of muscle force and length. The SRS of individual muscles scales linearly with actively generated force (10, 32) and is thought to be directly related to the number of attached cross bridges. Changes in temperature alter SRS, while minimally affecting isometric force production in some muscles (14). This phenomenon provides a means to evaluate the relationship between SWV and muscle stiffness, independent from its dependence on force.

The objective of this study was to determine whether SWV is sensitive to changes in muscle SRS. We used changes in muscle temperature to decouple the typical monotonic relationship between muscle force and SRS. We tested the null hypothesis that changes in SWV are not influenced by changes in SRS when muscle force is held constant. Near-simultaneous measurements of SRS and SWV were made within the same soleus muscle of the cat. The main hypothesis was tested during active contractions. To control for temperature changes in tendon, speed of sound, and probe performance, additional measurements were made under passive conditions. Our findings have important implications for interpretation of shear wave measurements made during noninvasive conditions.

METHODS

Animal preparation.

Data were obtained from six female cats (Felis catus; 3.2 ± 0.3 kg). In four animals we tested changes in force, SRS, and SWV in active muscle, and in four animals we tested also for changes in force, SRS, and SWV in passive muscle. All animals were anesthetized with isoflurane during the surgical procedures and data collection. The soleus muscle of the left hindlimb was partially isolated by removing the skin and the connective tissues of the crural fascia and carefully dissecting the gastrocnemius muscle-tendon unit. The nerve and blood supply to soleus were preserved, whereas anterior and peroneal crural muscles were denervated by cutting the peroneus nerve, the tibial nerve distal to the branch to soleus, and the high muscular branch of the sciatic nerve. The distal tendon of soleus was dissected free from the rest of the Achilles tendon and attached to a servomechanism (Thrust tube linear motor; Dunkermotoren GmbH, Bonndorf, Germany) that allows application of fast changes to soleus muscle-tendon unit length. The soleus remained attached to a bone chip from the calcaneus, facilitating a secure connection to the servomechanism. Muscle-tendon unit force was measured with a load cell (model 31; Honeywell, Golden Valley) mounted on the motor shaft. The knee and ankle joints were fixed to metal clamps. The whole right hindlimb was submerged in a temperature-controlled saline bath to permit ultrasound imaging without the transducer contacting the muscle (Fig. 1A). All animals were obtained from a designated breeding establishment for scientific research. Animals were housed at Northwestern University’s Center for Comparative Medicine, an AAALAC accredited animal research program. All procedures were approved by the Institutional Animal Care and Use Committee at Northwestern University.

Fig. 1.

Overview of experimental setup and data collection. A: schematics of the muscle preparation and setup. The cat left hindlimb was submerged in a saline bath and fixed with metal clamps (orange circles) at the pelvis, knee, and ankle joints. A cuff electrode was placed on the sciatic nerve, and the tendon insertion of soleus muscle (red) was attached to a puller equipped with a force transducer for manipulating muscle-tendon unit (MTU) length increments (ΔL) while simultaneously measuring soleus tendon force (F) over time. The ultrasound probe was submerged in the bath and placed <1 cm away from soleus dorsal muscle belly surface. LG: lateral gastrocnemius; SO: soleus; STIM: stimulation. B: exemplar of the DICOM image obtained from the ultrasound machine. Top: a heat map of the velocity of propagation of the shear wave in the tissue as provided by the Aixplorer, superimposed on a conventional B-mode image of the cat soleus. Bottom: the B-mode image only, with the soleus muscle belly manually segmented (red) and the region used for calculating the shear wave velocity (dashed white rectangle). C, top: passive and total force time series, showing tetanic plateau over a 5-s stimulation and the force response to the mechanical perturbation at t = 4 s (dashed rectangle). Middle: simultaneous recording of the puller position, showing the MTU length imposed on the muscle relative to slack and the 2 m/s fast ramp occurring 3 s after onset of the 40-Hz stimulation (bottom). The time windows for extraction of shear wave velocity (SWV) and short-range stiffness (SRS) are labeled above the plots. D: force response of the muscle tissue plotted over absolute length changes obtained during the perturbation ramp (thin line). The linear part of the slope (circles) was used to calculate SRS. ΔL, length increment. E: graphical representation of the depth-averaged displacement field over time d(x,t), where x is lateral distance, with superimposed linear fitting and confidence bounds (red) used to calculate values of SWV.

Nerve stimulation.

A bipolar cuff electrode connected to a programmable stimulus isolation unit (Grass stimulator S8800) was folded around the sciatic nerve. Supramaximal muscle stimulation was applied at 40 Hz to avoid fatigue. A 100-Hz stimulation train lasting 6 s has been shown to produce high-frequency fatigue in cat soleus (43), whereas 40-Hz stimulation produced a fused tetanus with similar maximal force levels without signs of fatigue. One twitch was evoked before each contraction to enable the muscle to adapt to its current length, minimizing history effects. A 2-min recovery time was allowed between subsequent stimulations.

Shear wave ultrasound.

An Aixplorer V9.1.1 ultrasound system (Supersonic Imagine, Aix-en-Provence, France) coupled with a linear transducer array (4–15 MHz, 256 elements, SuperLinear 15-4; Vermon, Tours, France) was used for all ultrasound elastography. The parameters of the system were set to 1) mode: MSK—foot and ankle, 2) opt: std, 3) persist: no, to maximize the sampling rate and avoid bias due to locked proprietary data after processing. The research-grade software on our system provides shear wave movie data sampled at 8 kHz in sequences of 42 frames for each acoustic radiation pulse, recorded simultaneously with a single B-mode ultrasound image. The size of the region of interest was selected to include the belly of the muscle (up to 4 × 1 cm), and the speed of the compressional sound wave in the tissues was assumed to be 1,540 m/s. A custom-built frame held the transducer in a constant position relative to muscle, with the transducer oriented parallel to the fascicle plane.

Data collection.

Trials were performed with the saline bath temperature at either 26°C or 38°C, controlled by a thermocouple and a heating element. All measurements at a single temperature were made together, followed by the second temperature. The order of temperature presentation was randomized across animals, and the muscle was allowed to adapt to each new temperature for 15 min before new data were collected. Soleus muscle-tendon unit length was kept at optimum length (L₀), obtained by preliminary characterization of the force-length curve. A long tetanic plateau (6 s) was required for the ultrasound machine operator to record elastographic data of the muscle during contraction (Fig. 1B). One B-mode image and one shear wave movie were captured simultaneously for each passive and active condition. We measured SRS with a fast length perturbation before the end of tetanic stimulation (Fig. 1C). The perturbation had a displacement of 2 mm and a speed of 2 m/s. For this cat soleus, this corresponds to a displacement of ~2.7% of soleus fascicle length (l_F) and a nominal speed of 54 × l_F/s. The value of average l_F was reported in previous work performed by our laboratory on animals with similar body mass, for soleus l_F = 37 ± 3 mm (11), and verified by manual digitization of soleus fascicles from ultrasound B-mode images with muscle held at optimum length. Acquisition of ultrasound images and collection of the muscle data were synchronized with a trigger pulse from the ultrasound machine. A MATLAB xPC controller (MathWorks, Natick, MA) was used to control the muscle puller and sequence nerve stimulation and record all data.

Short-range stiffness of active muscle.

SRS was measured during active muscle contractions (n = 4). Muscle tension at rest was subtracted from the active tension during tetanic plateau to estimate the active contributions to SRS (Fig. 1C, left). In addition to removing passive muscle contributions from the total muscle force, this procedure allowed us to remove the mechanical artifacts associated with the inertia of the measurement apparatus and the viscous forces associated with moving this apparatus through the saline bath. SRS was defined as the change in muscle-tendon unit force divided by the imposed change in muscle-tendon unit length obtained with a fast perturbation in response to which muscle has been shown to respond elastically (41). To compare across muscles with different size and to provide a measure for comparison to literature (12), we normalized SRS by the physiological cross-sectional area (PCSA) of muscle to obtain an estimate of Young’s modulus (E):

$$E=\text{SRS}\times \frac{l_{\text{F}}}{\text{PCSA}}\left(\text{Pa}\right)$$ (1)

where PCSA was estimated based on muscle optimum force and the specific tension for muscle [22.5 N/cm² (39)]. It should be noted that the Young’s modulus reported here includes effects due to the contractile properties of the muscle and the passive elements connected in series. Hence, the magnitude of the observed changes in stiffness is smaller than would be expected if only the active contributions to SRS could have been quantified (9). Moreover, the areas scanned with ultrasound elastography included only muscle tissue. Although this would imply a discrepancy between SRS estimates due to changes in the tendon elasticity with different tensional states, all the measurements of active SRS reported here were collected with constant muscle-tendon unit length and supramaximal stimulation, so that changes to the in-series tendon elasticity between conditions can be assumed to be negligible (40). Finally, it should also be noted that SRS represents the mechanical response of the entire muscle to an axial stretch. In contrast, SWV provides a more local measurement. In comparing these measurement modalities, we made the assumptions that 1) measurements of SRS are distributed homogeneously throughout the muscle and that 2) local measurements of SWV are representative of the material properties throughout the muscle. We believe that these are reasonable assumptions for the soleus, which has a simple architecture, but that they may not hold for muscles with a more complex structure.

Short-range stiffness of passive muscle.

Data collected in animals ex vivo show that the mechanical properties of collagen and perimysia are affected by temperature, up to a denaturation point that occurs beyond 50°C in perimysia of beef semitendinosus (6) and collagen of rat tail tendon (30). Temperature-related effects have also been suggested to impact tendon performance in vivo during repetitive loading (51). Our muscle preparation underwent homogeneous temperature changes from 26°C to 38°C. Therefore, we tested the possibility that muscle and tendon tissues may undergo physical changes due to temperature that are relevant for SRS. SRS was estimated during passive conditions by imposing changes in muscle-tendon unit length from 30 mm to 38 mm (relative to slack length), the latter yielding tension corresponding to half of the muscle’s maximum force. Higher force levels, corresponding to those measured during the active muscle trials, could not be achieved without damaging muscle tissue. At each length, we applied a fast perturbation with the same characteristic and timing as in the active trials and measured passive muscle force. Passive muscle tension was normalized to optimum force to account for the individual animal’s force capacity.

Changes in shear wave velocity due to probe-fascicle angle.

As SWV measurements may be sensitive to transducer orientation relative to the fascicle plane [transverse vs. parallel (13)] and fascicle orientation [pennation angle (31)], alignment of the transducer was tested by measuring SWV while applying randomized changes in transducer orientation relative to the soleus muscle belly, for a total of 70 trials across four muscles. The angle of the probe face was varied from −1° to +14° with respect to the fascicle direction, which is comparable to pennation angle changes occurring during data collection and to those that are due to the relative displacement between ultrasound probe and fascicles throughout tetanus. Probe-fascicle angle was calculated by digitizing the angle between the transducer axis and the fascicle direction from B-mode images.

Shear wave data processing.

SWV was calculated from the collected shear wave movies. Each movie frame d(x,z,t) shows the tissue displacement over a lateral distance x, a focal depth z, and time t. The displacement data from each frame were averaged across a depth of 8.5 mm in the z-dimension to improve signal-to-noise ratio (Fig. 1, B–E). SWV was estimated from the averaged data with a time-to-peak method (34) over a lateral distance x up to 12 mm from the remotely induced pressure source. A single operator performed all ultrasound scans to minimize interobserver variability (35). For unstressed, homogeneous, isotropic, and nondispersive materials, shear modulus is proportional to the square of the shear wave group velocity (11). Since our objective was to determine whether SWV could be used to detect changes in the mechanical properties of muscle, we report most of our results in terms of the squared SWV.

Statistics.

Linear mixed-effects models were used for all hypothesis tests. Our primary hypothesis that SWV is sensitive to changes in SRS that vary independent of muscle force was tested by modeling the temperature-dependent change in SWV, SRS, and force with separate models. For each model, temperature was considered as a fixed effect (26°C or 38°C) and subject as a random effect. Although we designed our experiment to control for muscle force, small force variations were helpful to estimate the relative effects of temperature-dependent stiffness and force on the squared SWV about the operating point of our experiments. This was accomplished with a linear mixed-effects model that considered force as a continuous variable and temperature as a fixed variable; each animal was considered as a random effect. Similar linear mixed-effects models were used to test our control conditions. The form of these models is described along with their results below. We ran our statistics on a total of 287 trials across four animals: 131 trials in active conditions and 156 trials in passive conditions. The size of these samples for active muscle conditions is appreciable from the individual data in Fig. 2 and corresponds to an average of 16 trials per animal per temperature condition. Direct measurements of muscle force and stiffness are remarkably consistent for the controlled experimental conditions that can be achieved in an animal model. In contrast, measurements of SWV proved to be more variable. With four animals in our primary experiment and an average of 16 repeated measurements for each condition, we were able to detect a 5% minimum difference in squared SWV across the two temperatures studied with a power of 0.83. All statistical analyses were performed in MATLAB.

Fig. 2.

Repeated measurements of Young’s modulus and shear wave velocity for all animals. A: estimate of Young’s modulus over isometric active force obtained by measuring short-range stiffness (SRS) at 2 different temperatures in 4 animals. Young’s modulus is expressed as % of the maximum value measured in the muscle. B: estimates of shear wave velocity squared (SWV²) plotted over SRS values for the 2 temperature conditions. SWV² was obtained by calculating the velocity of propagation of shear waves in muscle tissue and is expressed as % of the maximum velocity obtained in each of the 4 muscles. Data on left and right of each row correspond to the same animal.

RESULTS

Effects of temperature on short-range stiffness and shear wave velocity.

In the active state, the SRS estimates of Young’s modulus decreased with increasing temperature (e.g., Fig. 2A). Young’s modulus decreased from 4.0 ± 0.3 MPa to 3.3 ± 0.2 MPa (18%, P < 0.001, n = 4; Fig. 3A) as temperature was increased from 26°C to 38°C. This occurred even though there was not a corresponding significant temperature-dependent change in muscle force (1.4% change, P = 0.298, n = 4; Fig. 3B).

Fig. 3.

Covariation of ultrasound shear wave velocity squared (SWV²) and short-range stiffness (SRS) Young’s modulus with nearly constant optimum force for soleus muscle of the cat: comparison of the absolute average values (means ± SD, n = 4) of Young’s modulus estimates (A), active isometric force (B), and % variation of SWV² (C), for the 2 temperature conditions. SWV² is expressed as % of maximum SWV² for each animal across all conditions. SRS estimates decreased by 18% between 26°C and 38°C, with similar force levels between conditions (~23 N), whereas SWV² decreased by 12%. *P value < 0.001.

SWV changed with temperature in each subject (e.g., Fig. 2B), decreasing on average from 16.9 ± 1.5 m/s to 15.9 ± 1.6 m/s as temperature increased from 26°C to 38°C. Over the population, the increase in temperature produced a 12% decrease in squared SWV (P < 0.001, n = 4; Fig. 3C), consistent with the decrease in SRS reported above. This result demonstrates that SWV is sensitive to changes in muscle SRS even when muscle force is held constant.

Effects of force on shear wave velocity.

Although there were negligible effects of temperature on force over the whole population, small trial-to-trial variations (up to 2 N) occurred within each animal. These variations were helpful to estimate the relative effects of stiffness- and force-dependent changes on the squared SWV about the operating point of our experiments. The effects of force and temperature were found to be highly significant (P < 0.001 for both effects, n = 4). The mean force in our active experiments was ~23 N. About this operating point, a 1-N increase or decrease in muscle force led to an average change in SWV of 0.5 m/s, whereas our experimentally controlled decrease in temperature of 12°C caused SWV to increase by 1.0 m/s.

Controlling for other possible effects of temperature.

The temperature-dependent change in SRS observed during active contractions might result from temperature-dependent changes in the passive properties of the soleus muscle-tendon unit. This was evaluated by measuring the SRS of passive muscles from three animals, each at the same two temperatures used for the active contraction experiments. Measurements were made at four levels of passive tension, controlled by stretching these muscles up to 38 mm beyond slack length. Temperature had a small but statistically significant effect on passive SRS. We observed a linear relationship between the passive force resulting from changing the length of the muscle-tendon unit and the square of the measured passive SRS (e.g., Fig. 4A). This was characterized in four animals by a linear mixed-effects model; with the squared value of SRS as the dependent measure, force normalized on the optimum as a continuous factor, temperature as a fixed factor, and subject as a random factor. The effect of passive force on SRS changed significantly with temperature (P < 0.001). Interestingly, increases in temperature increased the passive SRS, which is opposite to the effects of temperature on active SRS. In addition, the effects on passive SRS were small, increasing SRS by an average prediction of only 0.25 (N/mm)² at passive forces corresponding to 0.5 maximum isometric force (e.g., Fig. 4A) or 0.02 MPa when using the same scale as in Fig. 3A. These results indicate that the changes in active SRS due to temperature cannot be explained by altered mechanical properties of passive connective tissues.

Fig. 4.

A: changes in short-range stiffness (SRS) squared with increasing passive muscle tension in 1 exemplar animal. Muscle-tendon unit length was increased up to 38 mm relative to slack length, eliciting a change in passive tension over a range of ~60% of the muscle’s force capacity. This protocol was repeated with the muscle immersed in a saline bath at 26°C and 38°C. Passive tension (F) was normalized to maximum isometric force (F_o). Over the whole population, changing muscle temperature significantly affected the relationship between SRS and force (P < 0.001); the fitted linear mixed-effects model is represented for 26°C and 38°C. B: changes in shear wave group velocity squared with increasing passive muscle tension in the same muscle. Experimental data collected at 26°C and 38°C are shown together with the fitted model for testing the effects of temperature on the shear wave velocity (SWV) measurement system. SWV calculated from the passive trials was not significantly different between the 2 temperatures (P = 0.11), nor was the relationship between SWV² and force affected (P = 0.39).

Temperature can alter the speed of sound in muscle (27) and affect the output of ultrasound transducer elements (49). Therefore, in four animals we evaluated the influence of temperature on the squared SWV obtained from the passive experiments. Force was considered as a continuous factor, temperature as a fixed factor, and subject as a random factor. The temperature did not significantly affect the average SWV (P = 0.11; Fig. 4B) or the relationship between force and SWV (P = 0.39, n = 4; Fig. 4B). These results suggest that effects of temperature variations on the functioning of the ultrasound transducer and on the speed of sound in the tissue were limited.

Finally, SWV was not sensitive to the changes in probe misalignment tested in this study. In all four animals, we evaluated rotations of up to 15° of the probe within the fascicle plane to mimic the range of angles between ultrasound transducer and muscle fascicles during tetanic contraction, mainly due to contraction-dependent changes in pennation angle. We tested for effects of ultrasound probe orientation on SWV with a linear mixed-effect model in which SWV was the dependent variable, probe angle was a continuous factor, and subject was a random factor. Changes in probe angle did not contribute to systematic changes in SWV (P = 0.84, n = 4). Post hoc power analysis (power = 0.8, α = 0.05) determined a minimum detectable difference of 0.02 m/s per degree of probe angle.

DISCUSSION

The objective of this study was to determine whether SWV is sensitive to changes in the stiffness of contracting muscles when controlling for the confounding influence of muscle tension on both stiffness and SWV. This was accomplished by exploiting the temperature dependence of active muscle stiffness, allowing us to evaluate how SWV varied with changes in muscle stiffness at a constant force level. We found that SWV was sensitive to changes in muscle stiffness even when force was held constant. However, our results demonstrate that the scaling factor used to relate SWV to the stiffness of unstressed, isotropic, homogeneous materials does not apply to muscle. These results are the first to compare SWV with direct measurements of muscle mechanics in contracting muscle. Our findings indicate that SWV may be useful as part of a noninvasive tool for tracking muscle mechanics in vivo.

Shear wave velocity can detect changes in muscle stiffness.

Ultrasound elastography has been in use for more than 20 years, and its promise and limitations for measuring Young’s modulus in homogeneous, isotropic tissues such as liver and breast are well documented (2, 15, 47). However, there are many reasons to suspect that SWV may not be directly related to Young’s modulus in active muscle. Beyond the anisotropic and heterogeneous structure of muscle, it is important to consider that muscle behaves, to a first approximation, as a nonlinear spring; muscle stiffness changes with force resulting from changes in muscle length and activation (14, 32, 40). This covariation of muscle force and stiffness has led to confusion in the literature with respect to which properties of muscle can be measured with shear wave elastography.

Most studies that have used shear waves to characterize muscle have assumed that the changes in shear wave speed result from changes in the shear modulus of muscle. For instance, covariation of shear wave speed with joint angle (25) or joint torque or EMG (21) has been interpreted as an indicator of muscle elastic properties at rest or during contraction, respectively. However, the original formulation of the shear wave propagation problem (45) considered a medium without the effect of any tensional stress, which is instead expected in muscle tissue. This assumption has been used to justify using shear wave speed as a biomarker for muscle stiffness (12, 20) or muscle force (4, 46) because of its covariation with muscle stiffness. Few studies have considered the fact that tension alone can alter shear wave speed independent of any alterations that result from changes in the material properties of muscle. Martin et al. (2018) (29) demonstrated that shear wave propagation in tendon is dominated by the tension within the tendon and largely insensitive to changes in shear modulus for all but the smallest of loads. Our results show that muscle is different. At matched forces, SWV was still strongly sensitive to changes in muscle SRS. By examining the trial-to-trial variations in muscle force and their influence on SWV at each of the experimental temperatures, we were able to demonstrate that SWV is sensitive to changes in muscle force as well as stiffness. We used the results of this analysis to estimate how much of the force-dependent change in SWV about the operating point of our experiments could be attributed to force-dependent changes in muscle stiffness and how much could be attributed solely to changes in force. This was done assuming that muscle stiffness scaled linearly with force in proportion to previously reported results (9). Given this assumption, the net change in SWV could be attributed in nearly equal proportions to changes in muscle force (55%) and force-dependent changes in stiffness (45%). This estimate emphasizes the importance of force and stiffness in determining how shear waves propagate in muscle.

Limitations.

It is important to note that the estimates of SWV were quite noisy, exhibiting high trial-to-trial variability during active contractions (Fig. 2B). This might be attributed to the small size of the muscle we imaged and to trial-to-trial variation in the relative orientation of the muscle fascicles with respect to the ultrasound probe. We limited our active data collection to peak muscle activation at a single length so that averaging could be used to mitigate the effects of noise. However, this variability could limit the feasibility of more complex experimental designs. In addition, most ultrasound systems use proprietary algorithms that could influence measurement noise. We attempted to control for as many algorithmic variables as possible by computing SWV from the high-speed ultrasound images, but it would still be better if the complete processing chain from radio-frequency (RF) data to images was available.

The choice to report SRS measurements in terms of a scalar Young’s modulus remains a simplified representation of muscle mechanical properties. Nonetheless, it provides a useful proxy for overall tissue elasticity that can be readily compared with the literature on shear wave elastography and tissue material properties. Also, the value of E was calculated according to definition as the ratio between tensile stress and extension during a fast perturbation for which muscle has been shown to be largely elastic.

We provided an estimate of the relative contributions of muscle stiffness and muscle tension to SWV. It is important to recognize that this estimate is only valid for the cat soleus muscle about the operating conditions of this experiment. The relationship between temperature and force is complex and difficult to predict. Temperature can have a large effect on the dynamics of muscle contraction, especially in fast muscles. Higher temperatures applied for longer periods can even produce necrotic damage (44), altering the material properties of muscle from the reversible conditions we studied. Hence, further exploration is needed to determine the generalizability of this result to other muscles or a broader operating range.

Conclusions.

We demonstrated that SWV varies with changes in muscle stiffness, as has been previously assumed but not tested directly in active muscle. In addition, we further demonstrated that SWV is also directly influenced by muscle tension. This finding may help explain previous observations that SWV is correlated with the Young’s modulus of passively stretched muscle but that the slope of this relationship is greater than would be expected from nonstressed tissues. The increased slope may arise from the direct contribution of muscle tension to SWV in addition to the length-dependent material properties considered previously. Our experimental paradigm allowed us to decouple muscle stiffness and tension in a manner that is not typical during physiological conditions. Hence, within a single muscle, it would be expected that SWV will be strongly correlated with muscle force and stiffness, as has been reported by others. How to use measurements of SWV to uniquely infer muscle stiffness and force remains an important problem in the field of muscle elastography.

GRANTS

This study was supported by National Institute of Health Grant 5R01-AR-071162-02 to E. J. Perreault.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

S.S.M.L., E.J.P., and T.G.S. conceived and designed research; M.B., S.S.M.L., and T.G.S. performed experiments; M.B. analyzed data; M.B., S.S.M.L., E.J.P., and T.G.S. interpreted results of experiments; M.B. prepared figures; M.B. drafted manuscript; M.B., S.S.M.L., E.J.P., and T.G.S. edited and revised manuscript; M.B., S.S.M.L., E.J.P., and T.G.S. approved final version of manuscript.