In vivo human gracilis whole-muscle passive stress–sarcomere strain relationship

Skeletal muscle is remarkable in its ability to produce the active and passive forces needed for joint mobility and stability. Passive muscle mechanical properties play a large role in understanding muscle function as they significantly contribute to joint range of motion (Brown et al., 2012; Lieber and Friden, 1998, 2019; Ward et al., 2009c) and, in humans, if significantly altered, can lead to instability or increased resistance to movement, impairing function. Passive mechanical properties change with age (Noonan et al., 2020b; Pavan et al., 2020), upper motor neuron lesion (Smith et al., 2011), tendon injury (Silldorff et al., 2014) and exercise training (Noonan et al., 2020a). These properties vary amongst species as well, with the most common interspecies report being that mammalian muscle is typically stiffer compared with anuran muscle (Azizi and Roberts, 2010; Brown et al., 1996; Meyer and Lieber, 2018). Given that different animals may have fundamentally different locomotion mechanisms (quadruped versus biped; acceleration versus energy storage), the degree to which passive mechanical properties differ amongst species as well as the functional basis for any differences is still unknown.

It is becoming increasingly common to model human musculoskeletal systems to understand normal movement (Arnold et al., 2010) and pathological adaptation (Virgilio et al., 2021), and to predict effects of surgical intervention (Bolsterlee et al., 2013; Delp et al., 1990; Nichols et al., 2016). These models rely heavily on literature values to populate model parameters but, unfortunately, reports of human whole-muscle passive mechanical properties are very rare. As a result, current human studies must infer whole-muscle passive mechanics from data obtained on single human fibers and/or bundles of fibers. Studies show that skeletal muscle passive mechanical properties differ between single fibers and bundles of fibers in mouse (Meyer and Lieber, 2011), rabbit (Ward et al., 2020) and human (Smith et al., 2011; Ward et al., 2009c) muscle. In contrast, Magid and Law (1985) demonstrated that single fibers and whole muscle in frogs have the same passive modulus, which led to the concept that the passive load-bearing structures in frog muscle are intracellular where the protein titin was discovered to be the primary source of passive tension (Magid and Law, 1985). Other studies have since reported that, while this may be true for frogs, it may not be generalizable to other species where the extracellular matrix (ECM), composed of more complex connective tissues of endomysium, perimysium and epimysium, contributes significantly to passive tension in bundles (Brown et al., 1996; Meyer and Lieber, 2018) and whole muscle (Ward et al., 2020).

Therefore, variation in published muscle passive mechanical properties may not simply be attributed to differences among species or muscle type but may also depend on the specimen size that was tested. Recently, we specifically cautioned against inferring whole-muscle properties from muscle biopsy properties based on the highly non-linear scaling of passive mechanics among single fibers, fiber bundles, fascicles and whole-rabbit muscle (Ward et al., 2020). Typically, bundles exhibit a non-linear stress–strain relationship with a larger passive modulus, whereas in single fibers, this relationship is much more linear (e.g. compare fig. 2A and B in Friden and Lieber, 2003). It is hypothesized that this non-linear scaling of passive mechanics from fiber to whole muscle is also true for human muscle.

Because of the highly invasive nature of studying human muscle, there are few studies that report passive mechanics for humans. Even though studies have quantified differences between human fibers and bundles (Noonan et al., 2020b; Pavan et al., 2020; Silldorff et al., 2014; Smith et al., 2011), passive mechanical properties for whole human muscle are rarely measured. A handful of studies directly measured human muscle passive tension during surgery (Freehafer et al., 1979; Lieber et al., 2005; Schuind et al., 1992) but it is difficult to use these previous measurements as muscle dimensions and strains were not measured. This makes it impossible to derive material properties from these force measurements alone. Similarly, sarcomere length, which serves as an excellent predictor of relative active force in whole muscle (Winters et al., 2011), is almost never measured in human studies but can be used as a ‘physiological strain’ which may also be helpful in deriving material properties and comparing strains across scales.

To address the gaps in our knowledge regarding the passive mechanical properties of human muscle, we exploited a unique surgery performed at the Mayo Clinic by which the gracilis muscle, a leg abductor, is harvested as a myocutaneous free-functioning muscle, transplanted into the biceps brachii bed to restore elbow flexion in patients with traumatic brachial plexus injuries (Adams et al., 2009; Barrie et al., 2004; Giuffre et al., 2012; Maldonado et al., 2017). The free-tissue transfer surgery allowed us complete access to the muscle, enabling measurement of contractile properties, passive mechanical properties, sarcomere length and muscle shape. Our objective was to define the in vivo passive force–length properties of the whole human gracilis muscle and compare this value with that for other mammalian muscles.

This study was approved by the Institutional Review Board of the Mayo Clinic (IRB # 15-008865). Subjects were identified during their routine clinical visit for brachial plexus injury and were scheduled to undergo a free-functioning muscle transfer surgery of the gracilis to restore elbow flexion (Giuffre et al., 2012; Maldonado et al., 2017). All subjects provided written informed consent prior to participation in the study. Twelve subjects were recruited from January 2019 to February 2021, with one subject declining after they expressed concern about biopsies being taken. Data were successfully obtained from 11 subjects (1 female and 10 males, age: 33±12 years, mass: 89±23 kg, height: 177±8 cm).

Gracilis muscle–tendon unit (MTU) length was measured in vivo in each of four joint configurations (Fig. 1), prior to removal from the leg. These positions were chosen to range the muscle from nearly slack length (JC1) to its longest anatomical length in full hip abduction and knee extension (JC4). The method used to identify and isolate the gracilis MTU was previously described by Giuffre et al. (2012). Briefly, gracilis harvest commenced with identification of the distal tendon at the level of the pes anserine of the medial proximal tibia. A handheld doppler device was used to define the anterior and posterior muscle borders as well as the proximal vascular perforators. After the gracilis was freed from surrounding tissue with its vascular pedicle, origin and insertion intact, the obturator motor branch to the gracilis was identified and verified using a handheld nerve stimulator.

MTU length was then measured using a suture threaded parallel to the muscle along its length, which ran from the gracilis origin on the inferior pubic ramus to its insertion. The leg was then manipulated into each of the four distinct joint configurations and the suture was held steady proximally at the origin of the muscle, and the length of the MTU, denoted by the tendon insertion, was marked on the suture using surgical clips. The four lengths marked on the suture were subsequently measured to yield the MTU length for that specimen.

In vivo passive muscle force was measured using a buckle force transducer (BFT; Fig. 2) (An et al., 1990) placed on the distal gracilis tendon. The leg was positioned into each configuration while the BFT recorded MTU passive tension with a sampling frequency of 1 kHz. The force transducer was calibrated according to An et al. (1990) accounting for subject-specific tendon thickness. Briefly, the BFT was calibrated between 0 and 36 N by first mounting it on a length of rope and then incrementally suspending four 0.9 kg (2 lb) weights. This resulted in a linear force–voltage relationship that yielded the conversion factor (voltage to force) and had a regression coefficient of determination exceeding 0.99. The calibration steps were repeated for ropes of varying thickness to provide the correct conversion factor as a function of tendon thickness (Fig. S3). Force data were filtered using a fourth-order low-pass Butterworth filter and a cutoff of 50 Hz.

To measure sarcomere length corresponding to muscle length in each joint configuration, fixed-length muscle tissue biopsies were collected at JC1, JC2 and JC4 using a muscle biopsy clamp, which was validated against intraoperative laser diffraction-measured sarcomere lengths in rabbit muscle (Ward et al., 2009b). To obtain samples in each joint configuration, the gracilis was accessed and great care was taken to avoid stretching muscle during this process by ensuring that, prior to clamping, samples were brought to their normal in vivo position with no extra tension. Immediately after clamping, the sample was submerged in 10% buffered formalin for 2 days. After fixation, clamps were removed, and the samples placed in 200 ml of 0.1 mol l⁻¹ phosphate-buffered saline (PBS) solution and stored at 4°C. To measure sarcomere length in each sample, three straight fiber bundles, fixed without bending or twisting (Fig. 3), were microdissected from each sample and sarcomere length was measured in three equally spaced locations along each fiber bundle via laser diffraction (Lieber et al., 1984). The average of the 9 measurements (3 bundles×3 measurements per bundle) defined the sarcomere length for each joint configuration. Sarcomere length was not measured for JC3, it was approximated by first fitting a line to sarcomere length versus muscle length data for the three measured joint configurations. Then, the sarcomere length value at JC3 was interpolated based on muscle length at JC3.

After muscle harvest and weighing, the freed MTU was placed on a sterile surgical towel and photographed while both proximal and distal ends were free (Fig. S1). MTU, muscle and tendon length measured directly from the harvested MTU defined the actual slack length as, under these conditions, there was zero passive tension. External tendon length was measured from the point where the muscle fibers terminated on the proximal portion of the distal tendon to the tendinous insertion site. Muscle slack length was defined as MTU slack length minus external tendon length. Whole-muscle strain was calculated relative to actual muscle slack length.

The harvested MTU was held vertically and rotated about its long axis and video was captured. All muscle images were captured with a ruler adjacent to its length for calibration. MTU dimensions from these images were measured in Blender version 2.9 (Community, 2018) to enable high-resolution muscle volume and physiological cross-sectional area measurements. After these images were captured, the gracilis muscle was transferred to the upper extremity for the surgical restoration of elbow flexion.

A meta-analysis was performed on selected passive stress–strain relationships published for whole muscle, bundles and single fibers across various species. These studies reported passive mechanical properties of human, rabbit, cat, mouse and frog muscles, all of which were derived from direct mechanical measurements (Table 1). The passive stress–sarcomere length relationship was converted to a passive stress–sarcomere strain relationship by calculating strain relative to the optimal sarcomere length for that species (see table 1 of Burkholder and Lieber, 2001). Passive stress was then linearized by natural log-transformation and plotted versus sarcomere strain (Fig. S2). The slope of the linearized stress–strain data was used to compare among species and specimen size without having to arbitrarily choose a strain at which to make this comparison.

To understand the passive force–length relationship of the gracilis, passive force–muscle length data were plotted to demonstrate the passive elastic behavior of the gracilis muscle. For a physiological perspective, passive force was then normalized to the estimated maximum tetanic tension of the muscle calculated as the product of PCSA and a specific tension of 22.5 N cm⁻² (Close, 1972; Powell et al., 1984) and muscle length was normalized to slack length to create normalized passive force versus muscle strain plots. Finally, to determine the muscle's passive stress–strain relationship, passive force was divided by muscle PCSA to yield stress, and sarcomere strain was calculated relative to an optimal length of 2.7 µm using the sarcomere length values measured in each joint configuration, and then plotted. A natural exponential curve (Magid and Law, 1985) was fitted to these three relationships of experimental data. All experimental data were grouped to provide a better fit (Morrow et al., 2010). Data are reported as means±s.e.m. unless otherwise noted. All data were processed using MATLAB (R2018a, MathWorks). Goodness of fit of the various exponential relationships was performed by non-linear least squares regression and the coefficient of determination (r²) quantified this fit.

Slack (i.e. zero tension) MTU length of the harvested gracilis (Table 2) was always less than MTU length measured in the first and shortest joint configuration, implying that the muscle was always under some, albeit very little, residual tension in vivo. Elongation of the MTU from a resting length of 39.9±1.2 cm to JC1–JC4 amounted to 3.3±1.0, 7.7±1.2, 10.5±1.3 and 13.4±1.2 cm, respectively, corresponding to 15%, 34%, 46% and 59% muscle fiber strain, respectively (Ward et al., 2009a).

Gracilis muscle volume calculated based on only its mass was, on average, 25% greater than the volume estimated from the segmented 3D model and reflected the added volume of the external tendon and neurovascular skin paddle. Average volume of the gracilis muscle alone was calculated as 160.9±18.8 cm³ and average muscle mass was thus 169.9±19.8 g. Muscle volume and an average optimal fiber length of 23.1±0.7 cm yielded in an average muscle PCSA of 6.8±0.7 cm², which is approximately 3 times that measured previously from cadaveric specimens (Ward et al., 2009b).

When the MTU was at its longest measured length and greatest strain, passive force measured intraoperatively ranged from 4% to 27% of its calculated maximum active isometric tetanic tension value (Fig. 5A,B). Absolute passive tension increased from 0.90±0.21 N in JC1 to 16.50±2.64 N in JC4, corresponding to a passive stress of 1.60±0.42 kPa in JC1 to 27.83±5.46 kPa in JC4. As expected, sarcomere length also increased with passive muscle lengthening from an average sarcomere of 3.24±0.08 µm in JC1 to 3.63±0.07 µm in JC4, which are on the descending limb of the human sarcomere length–tension curve (Lieber et al., 1994). The passive modulus ranged from 44.8 MPa in JC1 to 125.7 MPa in JC4.

Several approaches were used to quantify gracilis passive muscle properties. Simply plotting absolute passive force versus actual muscle length had the greatest variability (Fig. 5A) and the exponential relationship explained only 18% of the experimental variability. When passive force was normalized to maximum tetanic tension and muscle length to strain (relative to actual measured slack length), the amount of the variability explained by the exponential nearly doubled to 30% (Fig. 5B). Finally, when muscle strain was expressed in terms of sarcomere length rather than muscle slack length, the percentage of the variance explained by the model nearly doubled again from 30% to 57% (Fig. 5C).

To our knowledge, Fig. 5C represents the first human muscle stress–sarcomere strain relationship published based on directly measured experimental data. This relationship for the gracilis was compared with other species' published data that we digitized and linearized as described in Materials and Methods (Fig. 6). Nominal modulus values were compared across scales within species based on the slope of this relationship. Across the five species examined, rabbit slopes exhibited the most dramatic increase from 2.0 to 2.7 to 22.9 for single fibers, fiber bundles and whole muscles. Frog single fiber, fiber bundle and whole muscle properties were all similar, with slopes of 4.2, 5.0 and 4.9, respectively. For humans, single fiber, fiber bundle and whole-muscle slopes were 4.2, 7.3 and 8.2. Importantly, the human muscle fiber bundle and whole-muscle properties did not show the dramatic disparities that were observed in our previous studies of rabbit muscle (Fig. 6). Fig. 7 shows the stress–strain curves for each species that were digitized from the literature. When comparing whole-muscle passive stress, human muscle was more compliant than rabbit muscle but less compliant than frog muscle (Fig. 7C).

The purpose of this study was to characterize the passive mechanical properties of the human gracilis muscle based on direct measurement of all its appropriate structural and mechanical properties in the operating room and in the laboratory. Our goal was to define the comparative scaling relationships of human muscle as compared with that of other species and increase our understanding of human muscle structure. Our results demonstrate that the gracilis muscle is a relatively compliant muscle compared with rabbit muscle and similar in passive modulus to muscle of mice and rats. At nearly its longest anatomical MTU length, at an average muscle fiber strain of 59%, the gracilis average force was only 16.5 N or an average passive stress of 27.8 kPa. In contrast, at their longest length, the three rabbit muscles tested all exceeded 2 GPa in stress which is ∼8 times the maximum tetanic tension that can be generated by those muscles (Ward et al., 2020). Furthermore, while the gracilis passive modulus increased with scale compared with our previously published data (Smith et al. (2011), the magnitude of this non-linear increase was far less than in our previous report on rabbit muscle (Ward et al., 2020). Thus, the major conclusion of this study is that the gracilis muscle represents a muscle with only modest increases in modulus as we proceed from the single fiber to the bundle to the whole muscle, similar to that observed in rat and mouse muscle (Fig. 6). Currently, rabbit passive mechanical properties should probably be viewed as the anomaly amongst species reported. We acknowledge the limitation of this cross-species comparison as these data from the literature may not be representative of all muscles of a particular species and were generated using varying methodologies that each has its own degree of uncertainty.

It must be emphasized that gracilis modulus values were based on deterministic calculations from directly measured muscle properties. We did not estimate properties based on other assumed relationships or use the optimization approaches that often must be used for human muscles. While other estimates of human muscle stress–strain relationships exist, they often rely on estimates of load sharing amongst many muscles crossing the same joint and structural dimensions inferred from various imaging modalities. No such estimates were implemented in this study.

In terms of the actual scaling of modulus with size, we previously reported the passive mechanical properties of the typically developing gracilis muscle (Smith et al., 2011). We used this previous study in our analysis of gracilis passive properties across scale for two reasons. First, the sarcomere stress–length curves reported by Smith et al. (2011) had a very low inter-individual coefficient of variation of approximately 10% (see fig. 2A,C of Smith et al., 2011) and, second, because of time constraints in the operating room, we decided against repeating this measurement and instead focused on measuring the very important whole-muscle passive force. Comparing single fiber and fiber bundle stress–strain data from that study with whole-muscle gracilis data presented in the present study, the slope of the stress–strain relationships for single fiber, fiber bundle and whole muscle was 4.0, 7.6 and 8.2, respectively. As mentioned above, this is a relatively modest increase compared with the 2.0 to 2.7 to 22.9 values, respectively observed in rabbit muscle (Ward et al., 2020). These findings are thus consistent with literature reports that suggest that the ECM plays a larger role in passive mechanical properties at larger scales but the actual amount of the increase across scales varies by species. Definitive statements about the structural basis for the differences across scales and species cannot at present be made based on the relatively sparse data currently available. Different muscles may be measured in different animal models, so it is not clear whether passive mechanical properties relate to the specific muscle studied, animal size, style of locomotion or some combination of these. Such a comparative statement was made by Biewener and colleagues, who compared the mechanical properties of the Achilles tendon of the kangaroo rat with those of kangaroos (Alexander and Vernon, 2009; Biewener and Blickhan, 1988; McGowan et al., 2008). Finding a much greater stiffness in the kangaroo rat, they concluded that the smaller animal connective tissue represented a ‘design’ for acceleration and escape from prey rather than a ‘design’ for locomotion efficiency as observed in the energy storage/release pattern in kangaroos. Currently, no such statement can be made for the passive mechanical properties of human muscle.

Another important result from this study emerges from comparison of muscle length measurement expressed as absolute length (Fig. 5A), strain relative to measured slack length (Fig. 5B) or strain relative to optimal sarcomere length (Fig. 5C). The important decision to be made in defining such relationships is the reference length that is used to calculate strain. While it is clear that either slack length or sarcomere length is an appropriate reference for strain definitions, sarcomere strain appears to offer greater explanatory value for the experimental data (increase in r² from 0.30 when using slack length to 0.57 when using sarcomere strain; Fig. 5B,C). The important implication of this observation is that it appears that the muscle development or remodeling process revolves around the resting length of the sarcomere, which is only roughly correlated with muscle fascicle length. In other words, fascicle length and sarcomere length may be dissociated even though this is often an explicit assumption that is part of all models.

The dissociation between fascicle length and sarcomere length was observed most dramatically recently in our study of children with cerebral palsy contractures (Mathewson et al., 2015). In that study, fascicle length was measured by ultrasound just prior to surgery and then sarcomere length was measured intraoperatively using the same methods as described here for the gracilis. The dramatic result revealed a similar fascicle length between children with cerebral palsy and their typically developing counterparts which, at first glance, implies the muscles had similar structures. However, the in vivo sarcomere length (4.07 µm) of those with cerebral palsy was 88% greater than that of their typically developing counterparts (2.71 µm), which had significant implications for their force-generating properties and planning their surgical release. That study and the present results strongly suggest that sarcomere length is a functionally important and physiologically relevant strain indicator in skeletal muscle. Several methods are currently available to measure sarcomere length including intraoperative laser diffraction (Lieber et al., 1984), biopsy clamps (Ward et al., 2009b), microendoscopy (Llewellyn et al., 2008) and resonant reflection spectroscopy (Young et al., 2017). Each of these methods has strengths and weaknesses that must be evaluated in light of the experimental question addressed and logistical limitations of their use.

This study has a number of limitations. First, muscle length, sarcomere length and passive force were all measured separately and involved repeated positioning of the leg for each measurement at each JC. This source of error was limited by having a single surgeon perform these measures in each position for all subjects. Second, muscle fiber length was not directly measured but was calculated from our previously published muscle architectural data (Ward et al., 2009a). While cadaveric muscle is clearly smaller in size compared with healthy living human muscle, there is no evidence that the fiber length:muscle length ratios differ between cadaveric and living human tissue. Finally, we assumed a maximum specific tension of 22.5 N cm⁻² based on previously published mammalian muscle (Close, 1972; Powell et al., 1984). If this number does not hold for human muscle, it would change the relative passive force of the muscle but would not affect the scaling conclusions reached. The methods described herein represent our best approach to measuring muscle properties given intraoperative constraints.

In conclusion, these data represent the first direct quantification of whole human muscle passive mechanical properties. The data demonstrate that gracilis passive modulus increases non-linearly from fiber to whole muscle; however, this increase was smaller than observed for other mammalian species. Also, the gracilis muscle is similar in properties to rodent muscle, where moderate passive tension is generated up to a strain of 50%. These data may ultimately improve our ability to generate accurate models of human locomotion as direct access to human muscle for experimentation is very limited.

The authors would like to acknowledge the subjects who participated in this study for their commitment to the project.