Soft biological tissues are typical examples of soft solids. Their shear elastic modulus ( μ ) is a mechanical parameter that characterizes the stiffness of the media and provides relevant information about the physiological processes related to their intrinsic mechanical state [1]. Particularly, in the skeletal muscle, as their functions are closely related to the change in its mechanical properties, the reliable measurement of its shear elastic modulus is of great interest within biomechanics and related fields. In this regard, in the last few years, elastography has become a helpful tool for measuring muscle stiffness in vivo and non-invasively.

Elastography has been initially employed as a complementary tool for the medical diagnosis of different diseases associated with the change of soft tissue elasticity, such as liver fibrosis and breast tumors [2–5]. The shear wave elastography (SWE) methods, such as transient elastography (TE) and supersonic shear imaging (SSI), have been the gold standard methodology for such a purpose [6, 7]. The SSI is based on the TE technology but replaces the external vibrator with acoustic radiation pressure to excite shear wave propagation. Recently, SWE methods have also begun to be adopted as the reference methodology to assess skeletal muscle elasticity in vivo. This has provided a novel way to measure the change in the mechanical properties of such tissue, thus driving a new approach in the studies on muscle biomechanics. In this sense, previous works have addressed complex biomechanical problems by using SWE, such as the relation of muscle shear elasticity with joint angle, contraction intensity, and electromyography (EMG) activity level [8–16]. Other works have used SWE methods to characterize, both in normal and fatiguing conditions, the load sharing, force production, and the dynamics of muscle contraction of the synergistic muscles by measuring the change in its shear elastic modulus [9, 13, 17–19]. Likewise, SWE has also been applied to assess differences in passive muscle shear elasticity after a force training program of trained vs non-trained subjects, the passive behavior of individual muscles in different stretching positions, and regional differences in muscle elasticity after eccentric exercise [20–23]. On the other hand, the application of SWE in skeletal muscle is also being considered for its clinical use in sports medicine [24]. The main advantages of the SWE methods are that they combine high-frequency ultrasonic waves (within the order of MHz) with low-frequency waves (100–1,000 Hz). As ultrasound imaging utilizes pulsed waves of several MHz of central frequency, their wavelength in tissues (assuming the sound speed is 1,500 m/s) is sub-millimeter-sized. The spatial resolution of the imaging system is limited by diffraction to the order of the wavelength. Therefore, using high frequencies (MHz) allows for high spatial resolution. On the other hand, the elasticity contrast in the image is not necessarily related to the acoustic impedance but to Young’s modulus of the material. Low-frequency waves are sensitive to changes in Young’s modulus since they propagate mainly as shear waves. In this way, SWE methods exhibit high spatial resolution (<1 mm) and good contrast in the characterization of shear elastic modulus [25]. However, the proper application of SWE methods for biomechanical research needs some infrastructure, such as those found in a clinic or laboratory. Furthermore, its relatively high cost is a limiting factor for clinics and laboratories having low resources.

As an alternative to the SWE, other elastography methods based exclusively on low-frequency (∼100 Hz) surface waves propagation have recently emerged [26–31]. By eliminating ultrasound frequencies, the spatial information is lost, so it is not possible to construct an elastic map of the medium. However, the information regarding the elasticity is preserved, so a numerical value about the mean elasticity of the tissue in a region of interest (ROI) can be obtained. In general terms, these methods record the velocity of the surface waves by measuring the surface wave propagation using either laser vibrometry or contact sensors. Some authors assume a Rayleigh wave model for the surface waves [32]. In this case, the measured velocity has a simple relation to the shear elastic modulus of the medium. However, since typical values of shear wave velocity in muscles at rest range between 2–4 m/s, If the excitation frequency is 100 Hz, the shear wavelength is between 2 and 4 cm. This value is of the same order of the muscle depth. Therefore, the muscle cannot be assumed as a semi-infinite but a bounded one, so guided wave propagation takes place. In order to retrieve the correct value for the shear wave velocity, a guided wave propagation model is needed. Besides, the wavefield is usually measured in the near-field of the source. Those combined effects introduce biases in the estimation of the shear elastic modulus [33]. In this regard, Benech et al. [34] developed a non-ultrasonic surface wave elastography (NU-SWE) method by designing new algorithms that correct the incidence of such effects on the elasticity estimates. This method has the advantages of being small, portable, low-cost, and easy to manipulate. Their first application in skeletal muscle was made by Grinspan et al. [25], who assessed the relationship between the change in muscle elasticity, joint torque, and the EMG activity level. This work showed analogous results to those obtained with SWE, thus showing the potential utility of the NU-SWE for biomechanical research.

SWE devices for clinical use have a sampling rate between 1 and 2 Hz. Due to this, experimental protocols must consider slow and controlled long-time tasks (for example, 20–30 s) to obtain enough data and perform a proper analysis. Thus, for example, it is currently not possible to assess the change in muscle elasticity for different contraction rates, as is possible for other related variables such as EMG activity. On the other hand, surface wave methods do not need to retrieve the low-frequency field from speckle tracking algorithms, on which SWE methods are based for calculating the displacements [35, 36]. In addition, they do not measure bulk wave propagation but only the field at the surface of the muscle. Thus, it is possible to increase the sampling rate by sending several short pulses and storing the field for post-processing.

In this context, the present work shows an updated version of the NU-SWE elastography, which overcomes the previous limitations of elastographic methods for the biomechanical study of skeletal muscle. Specifically, this version of the NU-SWE comprises a free-hand device that can measure the shear elasticity without applying pressure on the medium (as with the US probe), in more than one muscle simultaneously and at a higher sample rate. Thus, we applied these new features of the method to characterize the change of the shear elasticity of the biceps brachii (BB) and brachioradialis (BR) muscles during the execution of isometric flexions of the elbow joint at different contraction velocities. We also measured the EMG activity of both muscles during such tasks. This allowed us to account for the temporal dependence regarding the relationship between the elastic and electric behavior of these muscles during their synergistic action, which are emergent properties derived from the new measurement capabilities of the updated NU-SWE method.

As is shown in Table 1, the ICC values obtained for BB and BR muscles denote good reproducibility between the peak V s ∥ measured in both trials for each condition. In this sense, the averaged values of the peak V s ∥ and EMG RMS activities from both trials are representative of each task. Therefore, in what follows, the analysis is performed based on such mean values for both muscles in each condition ( V ¯ s ∥ B B max , V ¯ s ∥ B R max   ;   E M G   R M S ¯ B B max , E M G   R M S ¯ B R max ).

Figure 4 shows individual curves of V s ∥ obtained simultaneously in BB and BR for two volunteers in each condition. In addition to having been obtained simultaneously for each muscle, the V s ∥ values were measured with a sufficiently temporal resolution, thus allowing an adequate characterization of the contractions during the execution of each task. As is observed for both subjects, when the task duration is shorter, the peak V s ∥ of BR reaches higher values than BB. As time increases, the peak V s ∥ of BR decreases while those of BB increase. In this way, for tasks of longer duration, the relative magnitude of the peak V s ∥ values tend to invert with respect to tasks performed in shorter times.

Comparing the V ¯ s ∥ max values at the intra-muscular level, the results for the BB and BR muscles of the entire data set behaved in the same way. Thus, the t-test revealed the existence of significant differences between the V ¯ s ∥ B R max and V ¯ s ∥ B B max values obtained between the ramps of 5 vs 15 and 20 s (p = 0.04 and 0.03, respectively, for BR; p = 0.02 and 0.01, respectively, for BB), not being significant between 5 vs 10 s, 10 vs 15 s, 10 vs 20 s, 15 vs 20 s (p = 0.12, 0.29, 0.25, 0.44, respectively, for BR; p = 0.05, 0.32, 0.09, 0.16, for BB). On the other hand, inter-muscular comparisons showed the existence of significant differences between the V ¯ s ∥ B R max and V ¯ s ∥ B B max values for the 5, 10, and 15 s tasks (p = 0.00, 0.00 and 0.04, respectively), being not significantly different for the 20 s task (p = 0.29). All these results are summarized in Table 2 and Figure 5.

The normalized E M G   R M S ¯ B R max and E M G   R M S ¯ B B max activities showed the same behavior as the V ¯ s ∥ B R max and V ¯ s ∥ B B max . As seen in Figure 6, for each condition, such normalized values decreased and increased with task duration, for BR and BB, respectively. Nevertheless, the results of the t-test did not show significant differences at the intra-muscular level concerning the normalized E M G   R M S ¯ B R max (p = 0.37, 0.20, 0.20, for 5 vs 10, 15, 20 s, respectively; p = 0.32, 0.31, for 10 vs 15 and 10 vs 20 s, respectively; p = 0.48, for 15 vs 20 s). The normalized E M G   R M S ¯ B B max only showed a significant difference between the values at 5 vs 20 s (p = 0.03), while this was not observed for the other inter-muscle comparisons (p = 0.21 and 0.07 for 5 vs 10 s and 5 vs 15 s, respectively; p = 0.22 and 0.13, for 10 vs 15 and 10 vs 20 s, respectively; p = 0.37, for 15 vs 20 s). At the inter-muscular level, significant differences were found between the normalized E M G   R M S ¯ B R max and E M G   R M S ¯ B B max for 5 s (p = 0.03), while no significant differences were found for 10, 15 and 20 s (p = 0.19, 0.36, 0.24, respectively).

The purpose of this work was to show the performance of the updated version of the NU-SWE method and the novel measuring capabilities that arise from its new features. In this regard, the work showed that this method is able to measure muscle elasticity in experimental conditions that have been impracticable with the current ultrasonic and low-frequency elastographic methods. In this way, interesting mechanical properties of skeletal muscle emerged from using this version of the NU-SWE. Therefore, the results of the present study could be a first step in order to continue delving into the knowledge of muscle biomechanics based on the application of elastography.

The results of the isometric flexion ramps performed up to 40% MVC in 20 s are the most adequate to compare the results of the previous studies regarding the present work. In this task of our protocol, the contraction rate was 2% of MVC/s, being comparable to most of the biomechanical studies performed in skeletal muscle with others elastographic methods. In these conditions, different works have reported μ L values for the BB and BR muscles ranging from ∼10–150 and 5–60 kPa, respectively, between 0%–40% MVC, both using SWE as well as the previous version of NU-SWE [12, 14, 15, 18, 19]. These values agree, both qualitatively and quantitatively, with the range of shear velocities shown in Figures 4, 5.

The tasks performed in 5, 10 and 15 s correspond to rates of contraction of 8, 4% and 2.67% MVC/s, respectively. These rates are higher than those usually induced by the protocols that can be applied with SWE, which must be slow and controlled contractions due to their limited sample frequency (∼1–2 Hz). Particularly, the measurements of the present work were carried out at 15 Hz. No previous work has described muscle elasticity measurements at such a sampling frequency, either with surface wave elastography or shear wave elastography (SWE). In our previous work with NU-SWE, the highest sampling rate reached in the measurements was 1.4 Hz [25]. On the other hand, the sampling rates reported in the literature regarding the application of the SWE methods in skeletal muscle ranges between 1–2 Hz. The SWE method generates a “push" over most of the tissue using extended sonification times of approximately 200 μs each. The dimension of a typical region of interest (ROI) for imaging elasticity in muscles is 2–3 cm wide and 2–3 cm deep. Imaging this area requires several pushes, not less than 8 (4 in lateral dimension and at least 2 in-depth). Therefore, only the pulsation time lasts approximately 1 m. The duration of the ultrafast sequence to track the propagation of the shear wave depends on the depth of observation of the ROI, but the typical PRF is between 3 and 5 kHz, adding times on the order of 300 μs to each frame. If this information were to be stored in memory for offline processing, the theoretical sampling rate is on the order of 10² Hz. However, this theoretical limit cannot be reached in practice, as it would imply sending pushes every ∼0.01 s, which could seriously damage the transducer. Besides, in commercially available devices, the time required for memory transfer and online processing for real-time display eventually reduces the frame rate to values of 1–2 Hz. To our knowledge, there are no commercial SWE devices with elasticity frame rates higher than this, so the updated version of the NU-SWE represents a novel alternative in this regard.

The above allows performing protocols involving faster contractions, thus emerging novel muscular elastic behaviors as those described by our results. In this sense, our measurements showed, both at the individual and average level, a temporal dependence regarding the elastic behavior of the BB and BR muscles during the isometric flexion of the elbow joint. Such temporal dependence was manifested both at the inter-muscular and intra-muscular level, through the differences in the peak V ¯ s ∥ B R max and the V ¯ s ∥ B B max values. While the maximum shear elasticity reached by the BR decreases with the task duration, the opposite behavior was observed in the BB (Figures 4, 5). Thus, at the intra-muscle level, significant differences were found between the values of the tasks executed in 5 s compared to 15 and 20 s. On the other hand, the inter-muscle comparison showed that the peak V ¯ s ∥ values of BB and BR were significantly different between all conditions, except for the 20 s-task, which agrees with the results of the previously referred works. As far as we know, these behaviors have not been previously described with elastography. Since the muscle elasticity reflects the force exerted by the muscle, the above may have important connotations concerning the motor control of the synergistic elbow flexor muscles and the temporal dependence of the load sharing between them [18, 19].

As is depicted in Figure 6, the measurements of the EMG RMS showed the same behavior pattern as the elastography concerning the average peak activity as a function of the task duration, exhibiting a correlation factor of 0.96 and 0.95 for the BB and BR, respectively. While the normalized E M G   R M S ¯ B R max tends to decrease as the total time of the flexion ramps increases, the normalized E M G   R M S ¯ B B max exhibits the opposite trend. This is consistent with previous works that have shown the close relationship between the muscle shear elastic modulus and their EMG activity [12, 14–16, 25]. Such studies have suggested the validity of the linear model to describe this relationship, during the isometric flexion of the elbow flexors according to similar contraction intensities to those of the present work. Only the inter-muscular comparison between E M G   R M S ¯ B R max and E M G   R M S ¯ B B max for the 5 s-task exhibited significant differences. In addition to their corresponding results of V ¯ s ∥ max for such tasks (Figure 5), this clearly reflects the biomechanical role of the BR muscle in stabilizing the elbow joint at fast contraction velocities, through the coaptation of radius head to the capitulum of the humerus, offering an adequate support for the subsequent action of the BB. This process tends to be balanced out at smoother contractions as task execution time increases. At the intra-muscular level, only the mean activities of the BB muscle between the 5 and 20 s-tasks were significantly different. This denotes the functional variability of the BB concerning its isometric contraction at different velocities, agreeing with the corresponding results of V ¯ s ∥ max . In the context of our study, the absence of significant differences in the inter and intra-muscular comparisons between the values of the normalized E M G   R M S ¯ B R max and E M G   R M S ¯ B B max , compared to the respective comparisons of V ¯ s ∥ max , does not necessarily indicate the absence of differences in peak EMG RMS activity in such situations. The above could have been conditioned by the limited size of the sample since specific variations in the measurements can significantly affect their standard deviation. Besides, the EMG signals of the BB and BR muscles in each condition may also have been affected by the crosstalk of other adjacent muscles [49, 50]. This phenomenon does not affect the elastographic measurements since their nature is mechanical and not electrical, which is a possible cause of the discrepancy in the results. In this sense, it has been proposed that elastography can help to reconsider our current understanding of muscle co-contraction [50, 51]. Particularly, the updated version of the NU-SWE provides the opportunity to add the simultaneity and the temporal dimension to this approach, unlike other elastographic methods.

All of the above indicates that mean elasticity measurements using surface waves add advantageous features in biomechanical research. The device used in this work is portable, low cost and easy to handle. It allows measuring on several muscles simultaneously and at a high sample rate. If a proper strategy for locating and positioning the wave source and sensors is followed, no significant errors in the results occur due to the placement of the device. This is supported by the repeatability analysis performed in our previous work with NU-SWE where, although the manipulation of the wave source during measurements could have introduced variation between measurements, it was not reflected in the results [25]. In this sense, the new configuration of the NU-SWE employed in this work overcame such a limitation, adding even more certainty regarding the reproducibility of the measurements. Concerning the relative alignment of the array of sensors and the fibers' orientation, it is important to highlight that, as the BB and BR are parallel and fusiform muscles, knowing their anatomical location on the arm is sufficient to identify the fiber orientation accurately. However, in pennate muscles, identifying the fibers' orientation before measurements by B-mode ultrasound and aligning the sensors accordingly, may be helpful to avoid biases related to wave propagation in more complex media.

Although in the present study, the selected sample rate was 15 Hz as it was considered adequate to characterize the contractions of the different tasks, this can be even higher by adjusting the ∆ t between signals according to the requirements. Thus, the updated version of the NU-SWE allows obtaining μ L curves with higher temporal resolution, being able to be used both for isometric estimates, as in the present work, and eventually also for measurements in dynamic conditions (e.g., walking, jumps). In this way, the advantageous features of the present version of the NU-SWE are similar to the low-frequency method proposed by Martin et al. [31] and Keuler et al. [52] to measure elasticity in tendons. However, this method cannot measure skeletal muscle elasticity as it is based on the Timoshenko beam model, which does not apply to this tissue [53, 54]. On the other hand, it is important to point out that the NU-SWE has been preliminary validated regarding the SWE methods in phantoms and beef samples [28, 34, 55]. Further validation in skeletal muscle in vivo is being carried out in our laboratory with promising results. Therefore, we think NU-SWE provides a novel and valuable alternative to measure muscle elasticity reliably and in conditions hitherto impracticable with ultrasound elastography. In this sense, the results of the present study could be a first step in order to widen the current applications of elastography in muscle biomechanics.

This work shows that surface wave elastography has some features that can potentially widen the spectrum of applications of elastography in skeletal muscle. Themethod used in this work (NU-SWE) can measure the elasticity of several muscles simultaneously and at a higher sample rate than previous surface wave methods and the classic SWE. In the present study we used these characteristics of the method to perform a proof of concept of an experimental protocol previously impracticable with elastography. We measured the elasticity changes of the BB and BR muscles simultaneously during the isometric flexion of the elbow joint at different contraction velocities. As a result, we found that the peak elasticity value for each muscle has a different behavior depending on the time required for the task. For short times, the peak value for BR is significantly higher than for BB. As the time of the task increases, these values approach each other. Such behavior was also observed at the level of the EMG activity of both muscles, indicating that the elastographic results correlate with other methods for characterizing muscle activity. Considering the above, the methodological advances presented in this work widen the applications of elastography in skeletal muscle in vivo to delve into the knowledge of muscle biomechanics.