Direct intraoperative measurement of isometric contractile properties in living human muscle

Skeletal muscle's isometric contractile properties are one of the classic structure–function relationships in all of biology allowing for extrapolation of single fibre mechanical properties to whole muscle properties based on the muscle's optimal fibre length and physiological cross‐sectional area (PCSA). However, this relationship has only been validated in small animals and then extrapolated to human muscles, which are much larger in terms of length and PCSA. The present study aimed to measure directly the in situ properties and function of the human gracilis muscle to validate this relationship. We leveraged a unique surgical technique in which a human gracilis muscle is transferred from the thigh to the arm, restoring elbow flexion after brachial plexus injury. During this surgery, we directly measured subject specific gracilis muscle force–length relationship in situ and properties ex vivo. Each subject's optimal fibre length was calculated from their muscle's length‐tension properties. Each subject's PCSA was calculated from their muscle volume and optimal fibre length. From these experimental data, we established a human muscle fibre‐specific tension of 171 kPa. We also determined that average gracilis optimal fibre length is 12.9 cm. Using this subject‐specific fibre length, we observed an excellent fit between experimental and theorical active length‐tension curves. However, these fibre lengths were about half of the previously reported optimal fascicle lengths of 23 cm. Thus, the long gracilis muscle appears to be composed of relatively short fibres acting in parallel that may not have been appreciated based on traditional anatomical methods.


Introduction
Skeletal muscle's isometric contractile properties represent one of the classic structure-function relationships in all of biology. One of these relationships, the sarcomere length-tension relationship, was elucidated in isolated frog muscle cells (Edman et al., 1966;Gordon et al., 1966a, b) and later confirmed in mammalian muscle fibre segments (Allen & Moss, 1987). This relationship has been applied in almost every instance where muscle force is predicted from muscle length. Extrapolating single fibre mechanical properties to whole muscle properties is based on the structural argument that increasing the number of fibres acting in parallel increases muscle force proportionally and increasing the number of sarcomeres in series (equivalent to increasing normalized fibre length) increases muscle excursion, the length range over which a muscle can generate active tension. This view of isometric function has been applied to different muscles in terms of skeletal muscle architecture where force is proportional to physiological cross-sectional area (PCSA) and excursion is proportional to fibre length (Gans & Gaunt, 1991;Lieber & Friden, 2000;Wickiewicz et al., 1983).
Despite the logic that whole muscle properties can be predicted from their architecture, experimental validation of this argument is sparse. The best demonstration that force is proportional to PCSA comes from Powell et al. (1984) who showed that, for 26 different guinea pig muscles of varying architectures, peak force was directly proportional to PCSA with a scaling factor (specific tension) of 22.5 N cm -2 (225 kPa). For small mammalian muscles, similar specific tension values of 15−30 N cm -2 are typically reported (Close, 1972). There have been two convincing reports in whole mammalian muscle that excursion is proportional to fibre length. Bodine et al. (1982) measured the isotonic properties of the biarticular cat semitendinosus muscle which, fortuitously, contains two separately innervated muscle compartments separated by a tendinous inscription. By stimulating these compartments first separately and then together, the contractile velocity of the muscle was shown to scale with the length of fibres stimulated. In terms of isometric length-tension properties, Winters et al. (2011) measured the whole muscle length-tension properties of three rabbit muscles of varying architecture and showed that muscle excursion was precisely predicted by the number of sarcomeres in series for each of the three different muscles. Their included meta-analysis of the experimental literature quantified a linear relationship between the width of the whole muscle length-tension curve and the optimal length of the composite muscle fibres (Winters et al., 2011). The width of the muscle length tension curve was highly correlated with fibre length for 10 different muscles across three different species for fibre lengths ranging from 10−40 mm.
Given these experimental results, it has become accepted practice to predict isometric muscles properties when direct measurements cannot or have not been made. In humans, skeletal muscle architectural principles have been generalized to explain healthy and pathological movement (Arnold et al., 2010;Binder-Markey et al., 2019;Halilaj et al., 2018;Melzner et al., 2022;Sartori et al., 2017), guide surgical procedures (Bolsterlee et al., 2013;Delp et al., 1990;Nichols et al., 2016), understand muscle design (Blemker & Delp, 2006;Hosseini Nasab et al., 2022;Kapelner et al., 2020;Tennler et al., 2022) and predict performance (Crotin et al., 2022;Heiderscheit et al., 2022;Sinclair et al., 2022). Despite the scores of predictions made for a number of cases, direct validation is rare, and it is thus critical that we pursue validation of the major assumptions made and used in these human models.
The validity and translatability of animal data to humans must be carefully and critically examined. Human muscles are much larger in terms of length and PCSA than any animal muscle for which direct experimental data are available. Additionally, within the human literature, there is a disconnect between the specific tension of skinned human muscle fibres and whole muscle. For reported skinned human muscle fibres specific tensions vary from 6 N cm -2 to 20 N cm -2 (Bottinelli & Reggiani, 2000;Linari et al., 2004;Trappe et al., 2003), whereas specific tension estimates from whole muscle measurements are much larger and also vary greatly from 10 N cm -2 to more than 100 N cm -2 (Buchanan, 1995;Fukunaga et al., 1996;Kawakami et al., 1994;Maganaris et al., 2001). These variations at both scales are probably a result of inconsistencies when calculating the area from which to normalize the recorded forces among studies. In skinned fibre experiments, there is difficulty accurately correcting for swelling of the fibres, whereas, in the whole muscle experiments, accurately determining PCSA and relative muscle activation may be difficult. Furthermore, there is evidence in longer mammalian muscles that fascicle length and muscle fibre length are not equivalent. Using glycogen depletion of fibres within cat motor units, Ounjian et al. (1991) showed that muscle fibres traverse only a small fraction of the fascicle length. Similarly, using surface electrical stimulation of the very long human sartorius muscle and measuring motor unit potentials along a series of recording electrodes using spike-triggered averaging, Harris et al. (2005) found that their data were consistent with a microanatomical model in which many muscle fibres terminated in the middle of the muscle. Heron & Richmond (1993) and Loeb et al. (1987) used acid digestion of long human muscles demonstrating that the single isolated fibres were often only about one-quarter of the muscle length. Because muscle fibre length is often equated with muscle fascicle length, errors in functional property prediction can occur and be compounded. It is not clear what the functional implications would be of such 'series-fibred' muscles. Because of multiple innervation plates along the muscles (Harris et al. 2005), it is possible that they function as a single long fibre. However, given the complex and extensive extracellular matrix of muscle (Gillies et al., 2014;Purslow, 2020), it is possible that these short fibres act in parallel. It is currently not possible to distinguish between these possibilities because of the lack of direct human data available.
We have been applying our understanding of muscle architectural principles to tendon transfer surgeries by guiding selection of the donor muscle that restores impaired function after spinal cord injury (Friden & Lieber, 2001;Lieber & Friden, 1997;Loren et al., 1996). Recently, we have become interested in predicting the outcome of a unique surgical procedure in which the gracilis muscle is removed from the medial thigh and J Physiol 601.10 transplanted into the bed of the biceps brachii muscle to restore elbow flexion after brachial plexus injury as a free functioning muscle transfer (Maldonado et al., 2017;Maldonado et al., 2022). Based on modelling, the human gracilis muscle would be inadequate to restore elbow flexion function, yet clinical data have shown otherwise. Thus, the present study aimed to make direct measurements of the human gracilis muscle isometric contractile properties and determine whether current animal models accurately predict the function of this long human muscle.

Ethical approval
The protocol for this study was approved by the Institutional Review Board at the Mayo Clinic (IRB #15-0 08865) and conforms to the standards set by the Declaration of Helsinki, except for registration in a database. Prior to surgery and inclusion in this study, each subject provided their written informed consent.

Procedural overview
All data in the present study were collected during brachial plexus reconstructive surgery which had, as a part of it, a gracilis free functional muscle transfer to reconstruct elbow flexion (Giuffre et al., 2012;Maldonado et al., 2017). The surgery is indicated for patients with pan brachial plexus injuries that result in paralysis of the upper extremity. The details of the surgical procedure and experimental data collection protocol have been reported previously (Giuffre et al., 2012;Persad et al., 2022).
Prior to surgery, 34 patients consented and were enrolled. However, as a result of the intraoperative complexities of the surgery and data collection, 12 complete data sets were collected. For the remaining 22 incomplete datasets, in 13 cases, no forces were recorded as a result of technical difficulties (buckle transducer electronic problems, anatomic variations of the gracilis making data collection risky, intraoperative decision to curtail data collection by surgeon) and eight cases had missing force recordings in either one or two of the joint configurations or inconsistent force data resulting in the inability to calculate adequate quadratic fits (see below). During the surgical procedure and prior to removing the gracilis muscle, in situ measurements of muscle-tendon unit (MTU) length, passive sarcomere length, passive MTU tension, and active muscle twitch and tetanic tension were made as the lower limb was placed in four joint configurations (JC1 to JC4) (Persad et al., 2021). The joint configurations were designed to gradually lengthen the gracilis through its anatomical range by progressively increasing knee extension and hip abduction angles. After in situ data collection, the muscle was removed and resting MTU length, resting muscle length, resting external tendon length and the mass of the muscle plus its associated skin paddle were obtained (Giuffre et al., 2012;Maldonado et al., 2017).

Intraoperative measurements
At each JC, MTU length was measured by threading a 2-0 braided nylon suture along the MTU via prior incisions at the origin and insertion of the proximal and distal gracilis tendons. One suture end was held at the muscle's origin and other extended to the distal insertion site where surgical clips were placed at each JC. Muscle biopsies were taken at three of the four JCs to measure passive sarcomere length from muscle tissue (Persad et al., 2021(Persad et al., , 2022Ward, Takahashi et al., 2009). The muscle biopsies were held in specialized clamps and placed in 10% formalin for 48 h, followed by a triple rinse using phosphate-buffered saline and subsequent storage in phosphate-buffered saline at 4°C until biopsy segments were dissected for sarcomere length measurements (Lieber et al., 1984).
In situ passive and active tension were directly measured using a buckle force transducer (BFT) placed on the distal gracilis tendon   (Fig. 1, inset). Passive tension was measured at each JC prior to muscle stimulation. To produce active tension, the anterior branch of the obturator nerve was stimulated using a bipolar hooked nerve stimulator probe ( Fig. 1, inset). At each JC, the current necessary to produce the maximum compound muscle action potential (CMAP) was determined through a series of single twitches ( Fig. 2A). This was done to ensure that, at each JC, we used the appropriate current that would elicit a maximum CMAP. This amount of current varied substantially among JCs (Persad et al., 2022), presumably as a result of movement between the stimulating electrode and the obturator nerve. To eliminate any movement artifact that occurred during tetanic stimulation at maximum CMAP current, stimulation current was reduced to 50% of the joint-specific maximum CMAP current and the nerve was stimulated at 20 Hz (see rationale below). Two consecutive 2 s 20 Hz trains at 50% current of the maximum CMAP stimulation intensity were used to determine active muscle force. Force data were filtered using a fourth-order low-pass Butterworth filter with a cut-off frequency of 30 Hz.

Maximum muscle force calculation
Because it was impossible to stimulate the muscle maximally during tetanic contractions without significant movement artifact, we calculated each patient's maximum force capacity at each JC based on the force measured at 20 Hz at 50% current of the maximum CMAP stimulation intensity. Force recorded by the BFT was then scaled up based on the twitch force change recorded for each subject at each JC at 50% and 100% CMAP stimulation intensity (Tw 50 and Tw 100 respectively) ( Fig. 2A). Calculating this scaling factor across JCs within each subject thus incorporated any muscle length-dependent activation variability. An additional 6% force increment was measured when the muscle was stimulated at the maximum frequency of 50 Hz (P 50 ) compared to the submaximal value of 20 Hz (P 20 ) (Fig. 2B). Thus, maximum isometric force (P o ) was calculated for each subject at each JC as: Across all subjects, the Tw 100 Tw 50 ratio at JC1 averaged 1.36 and, at JCs 2-4, the JC averages ranged from 1.24 to 1.29 indicating slight length-dependent activation dynamics that were accounted for and corrected. P 50 P 20 was 1.06. Thus,

Figure 1. Schematic of a subject's leg undergoing gracilis-to-biceps free-flap transfer
Obturator nerve is isolated and stimulated with the probe to produce isometric contraction (left inset), whereas gracilis force is measured from the distal insertion tendon using a buckle force transducer (right inset).

Figure 2. Mechanical force records of human gracilis muscles
A, intraoperative spatial summation demonstrated by increasing current to elicit maximum compound muscle action potential (CMAP), and then decreasing the current by 50%, decreases force to 77% of that achieved by the CMAP. Patient-specific data are shown to right. B, intraoperative temporal summation measured by varying stimulation frequency. Stimulating muscle at the selected 20 Hz reduces force to ∼94% of that seen during 50 Hz stimulation. Using this approach, we show that, on average, a 20 Hz tetanic stimulation is ∼72% (77% × 94%) of the muscle's maximum force.
J Physiol 601.10 on average, P 20 was 72% of P o . Importantly, because detailed physiological measurements such as these can be difficult to obtain, it was important to demonstrate that the twitch tension records demonstrated the familiar asymmetric rise and fall times ( Fig. 2A) and that the individual stimuli could be resolved on the tetanic tension records (Fig. 2B). The presence of these clear features in the contractile records indicate that the measurements were made without excessive compliance in the system and that the muscle was not adherent to surrounding tissue.

Direct ex vivo measurements
After removal of the gracilis, resting MTU length, muscle length and external tendon length were measured. We measured resting MTU length as the end-to-end distance when the MTU was placed on a sterile surgical towel (Fig. 3A). We defined resting muscle length as the distance from the most proximal to the most distal muscle fibres, and external tendon as the distance from the most distal muscle fibres to the distal end of the tendon (Fig. 3A).

Figure 3. Human gracilis muscle anatomical and physiological properties
A, image of the dissected gracilis muscle on a surgical towel after removal from the leg. This was the position in which resting values were measured. Schematic of length definitions are shown beneath the photograph. B, representative muscle force vs. length data with quadratic fit to determine the full width at half maximum (FWHM). C, relative FWHM vs. optimal fibre length relationship established from three species (rat, rabbit, and cat) across 10 different muscles corrected for interspecies differences in optimal sarcomere length (data replotted from Winters et al. 2011).

Muscle volume calculation
Because the skin paddle was required to monitor the perfusion of the gracilis and thus could not be removed, measured MTU mass overestimated the amount of muscle tissue in the graft (by 23% ± 2%, n = 21). Thus, we used a three-dimensional photogrammetry approach to estimate muscle volume for PCSA calculation in which the entire specimen was first scanned and then the skin flap was removed electronically using editing software (Persad et al., 2021(Persad et al., , 2022. Average volume errors using this software using cadaveric tissue and a water displacement standard was 7% (n = 6 gracilis muscles).

Sarcomere length measurement
Three fibre bundles were microdissected from each chemically fixed biopsy and sarcomere length measured by laser diffraction (Lieber et al., 1984). This was performed at three equally spaced locations along the bundle yielding nine sarcomere lengths per biopsy per JC.
To quantify the accuracy of this method, we measured grating spacing of a 3.33 µm diffraction grating before and after each sample. This method yielded a mean ± SD error of 0.13% ± 0.48%.

Patient-specific optimal fibre length calculation
Because we could not measure optimal fibre length directly in our subjects during isometric testing, we used a functional surrogate for optimal fibre length, the full-width at half maximum (FWHM) calculated from their force vs. length relationship. The FWHM is the width of the active force vs. muscle length curve at half the maximum force (Fig. 3B). A linear relationship between FWHM and optimal fibre length has been established across several mammalian species and muscles (Winters et al., 2011) (Fig. 3C). To calculate FWHM, we fit each patient's calculated fully active force vs. muscle length data to a quadratic curve and then calculated width at half the calculated maximum force from the equation. Optimal fibre length was then calculated from the previously established linear relationship between FWHM and optimal fibre length (Fig. 3C).

Specific tension calculation
Specific tension, S i , was calculated for each muscle from P o and muscle PCSA (Powell et al., 1984), where P o was determined as described above, and PCSA was calculated using standard equations (Lieber & Friden, 2000), where muscle volume was obtained optically for each muscle as described above and fibre length was estimated for each muscle based on the FWHM of their muscle length-tension curve determined intraoperatively.

Predicting the whole muscle length-tension relationship
Subject-specific architectural properties (optimal fibre length and PCSA) were used to scale the sarcomere length-tension relationship (Gordon et al. 1966b) to whole muscle and was compared to the measured data. We calculated each patient's fibre length-to-muscle length ratio and used this ratio to scale the normalized fibre length-tension relationship to estimate the whole muscle length tension relationship (Winters et al., 2011). Force was normalized to each subject's P o and length was normalized to the muscle length at which P o occurred. All data are presented as the mean ± SD of n = 12 procedures unless otherwise noted

Results
The basic nature of the passive and active length-tension relationships obtained were as expected. Passive force increased non-linearly with length, whereas active force showed the familiar ascending limb, plateau and descending limb features of the mammalian length-tension curve (Fig. 4A). The majority of cases (7 of 12) produced their maximum force when stimulated in JC2, the remainder at JC3. Using subject-specific values for PCSA, the subjects' gracilis produced a mean ± SD stress of 150 ± 86 kPa at JC2 and 150 ± 65 kPa at JC3 (Fig. 4B). Passive sarcomere lengths were all on the descending limb of the length-tension curve, even at the shortest in vivo muscle length (JC1; 3.17 ± 0.3 µm). With the gracilis at its longest length (JC4), passive sarcomere length was 3.55 ± 0.17 µm (Fig. 4A), implying that sarcomeres shortened significantly upon activation.
Using the quadratic fit of each subjects' muscle length-tension relationship (see Methods), optimal fibre length was calculated from FWHM as 12.9 ± 3.3 cm across all subjects (Figs 5B and 6A). Average fit of the quadratic relationship used for FWHM calculations was r 2 = 0.87 ± 0.15 (Fig. 5A). Combining each patient-specific value for muscle volume and muscle optimal fibre length, we calculated PCSA across subjects as 13.1 ± 7.1 cm 2 , which yielded a specific tension value of the human gracilis muscle of 171 ± 84 kPa (Fig. 6B).
From calculated subject-specific data, an average fibre length-to-muscle length ratio of 0.35 (0.07) was measured and the predicted muscle length-tension relationship fit very well to the summarized experimental data (Fig. 4C, open triangles superimposed upon the solid grey line). Error between predicted and measured force across the subjects and JCs averaged 13.7%, with the maximum error J Physiol 601.10 of 24.5% at JC1, and errors between 7% and 13% at the remaining JCs.

Discussion
The present study aimed to measure the isometric contractile properties of the in situ human gracilis muscle. Direct measurements of human muscle contractile properties are exceedingly rare, and, to our knowledge, this is the first time that such direct data are available. Acquisition of these physiological data allows a better understanding of muscle fibre structure-function relationships in this long human muscle.
Currently, the vast majority of general human muscle contractile properties are inferred based on indirect measurements of joint torque, which is transformed into muscle force using a number of calculations that are based on multiple assumptions. Consequently, it is not surprising that human muscle specific tension estimates vary widely from ∼100 kPa to over 1000 kPa as a result of the use of these indirect methods (Buchanan, 1995;Fukunaga et al., 1996;Kawakami et al., 1994;Maganaris et al., 2001). Such indirect methods require a number of steps and assumptions. First, joint torque is converted to tendon force based on the relationship between joint angle and moment arm. Ideally, this moment arm is measured Gracilis passive force-MTU length measured at each JC (grey circles). Passive sarcomere length measured at each JC shown above each symbol. B, calculated maximally active and passive muscle stress-muscle length relationships determined as described in the Methods using patient-specific values for muscle volume and optimal fibre length. C, normalized muscle force-length relationship compared to predicted muscle length-tension relationship using subject-specific fibre lengths (solid grey line) and literature values (dashed grey line) (mean ± SD for n = 12 experimental subjects).

Figure 5. Optimal fiber length predicted from length-tension curve
A, average quadratic fit (thick solid black line) and individual fits (thin grey lines) to active muscle force-muscle length data obtained in four joint configurations; average fit across subjects was r 2 = 0.87. Each subject's FWHM was used to calculate optimal fibre length (cm). B, relative FWHM vs. optimal fibre length of small animal data (black circles) along with extrapolated relationship (dashed line) used to calculate optimal fibre length for the individual subjects (open red circles). Solid red circle represents the mean ± SD FWHM and calculated optimal fibre length for n = 12 subjects. on a subject specific basis (Erskine et al., 2009), but average literature values are usually used (O'Brien et al., 2010). Second, torque is decomposed into the force that each muscle exerts on that joint. The best strategy to perform such a decomposition is debatable. One strategy is to distribute joint torque across all muscles according to their PCSA (Fukunaga et al., 1996;O'Brien et al., 2010). This approach assumes that all muscles are activated to the same relative level and operate on the identical portion of their length-tension relationship. In the case where the EMG can be measured simultaneously, joint torque may be partitioned based on the relative activation of each muscle. This assumes that the EMG provides a quantitative estimate of relative muscle activation, which, in the case of isometric force generation, is a very good assumption (Enoka, 1988;Perry & Bekey, 1981). Another strategy often used to the distribute the force contributed by each muscle is based on modelling all the muscles to best reproduce the experimental torque record (Hicks et al., 2015;Rajagopal et al., 2016). This is typically performed by simply summing muscle force at the measured joint angles and adjusting the modelled muscle operating range to match the experimental torque data. Unfortunately, all such models are indeterminate and there is no unique solution to the mathematical problem. Accordingly, additional assumptions and constraints must be imposed upon the model to permit a solution. The net result of this process is that indirect methods all require a series of assumptions related to anatomical, biomechanical and neurophysiological unknowns to predict muscle force from joint torque. Within the present study, we have eliminated these assumptions by directly measuring the gracilis muscle force from its tendon using a BFT and muscle PCSA via direct mass measurements.
The raw gracilis muscle length-tension relationship had the expected shape obtained from whole muscle, essentially comprising an inverted parabola (Fig. 4A). It is interesting that the gracilis muscle appears to be able Figure 6. Subject mean ± SD (red lines) and individual data (red circles) A, optimal fibre length. B, peak stress (specific tension) for n = 12 subjects. [Colour figure can be viewed at wileyonlinelibrary.com] to operate across the range of the entire length-curve given sufficient knee extension and hip abduction (JC4). The classic interpretation of the length-tension curve's descending limb is that it is mechanically unstable because shorter stronger sarcomeres stretch longer weaker sarcomeres, creating a positive feedback loop (Hill, 1953). This mechanical instability formed the basis for the sophisticated experiments in which a spot-follower feedback device was required to even measure maximum tetanic tension at sarcomere lengths above optimum (Gordon et al., 1966a, b) and led to a fascinating theory of sarcomere 'popping' during eccentric contractions (Morgan et al., 1982(Morgan et al., , 2002. The long sarcomere lengths measured here and prominent descending limb (Fig. 4A) support the concept that the gracilis functions eccentrically as a knee flexor during terminal swing prior to heel strike (Arnold et al., 2010).
Importantly, we gathered subject-specific muscle volume and optimal fibre length, which allowed us to transform contractile force into stress (Fig. 4B), thus permitting quantitative comparison to experimental data obtained from other mammalian muscles. The most significant result was examining the peak stress developed by the muscle which, in the parlance of the muscle literature, is referred to as specific tension. As described in the Introduction, the best demonstration that specific tension is a constant across muscles of widely varying architecture was provided by Powell et al. (1984) in 26 guinea pig muscles for which both contractile force and architectural properties were measured (as in the present study). Unfortunately, because of the plethora of assumptions required to transform joint torque into muscle force and subsequent assumptions to transform whole muscle force into specific tension as mentioned above, estimates of human muscle specific tension vary widely from ∼100 kPa to over 1000 kPa (Buchanan, 1995;Fukunaga et al., 1996;Kawakami et al., 1994;Maganaris et al., 2001). Using a minimum set of assumptions (see Methods and limitations below), we calculated gracilis specific tension as 171 ± 84 kPa (Fig. 6B). This value is lower than that reported for most small mammalian muscles (Close, 1972), but it should be noted that previous values are typically measured from mice, rats, cats and rabbits, which have a much greater fast fibre type percentage compared to humans (Tirrell et al., 2012). Indeed, it is interesting to note that, in study by Powell et al. (1984) mentioned above, the only muscle deviating significantly from the specific tension of 225 kPa was the guinea pig soleus muscle, which contains mainly slow fibre type, yielding a specific tension of 152 kPa, which is much closer to the value reported here. We thus suggest that the value of ∼170 kPa be considered as the best current estimate of human muscle specific tension. It should be noted that this calculation was based on the short, inferred fibre length of ∼13 cm. Our previous J Physiol 601.10 report ) of a fascicle length of ∼23 cm (determined from anatomical measurements) in the gracilis would yield a smaller PCSA by about a factor of two and a much higher 'apparent' specific tension. This finding emphasizes that our field requires direct functional muscle measurements without overly relying on anatomical values and assumed relationships.
A recent report of the myosin heavy chain (MHC) composition of 92 different human muscles from six fresh human cadavers reported that the human gracilis muscle contains 65% type 1, 19% type 2A and 16% type 2X MHC, which is remarkably close to the whole human body average of 65% type 1, 22% type 2A and 13% type 2X MHC, suggesting that the gracilis is actually a very representative 'average' human muscle and our measured value of 171 kPa is probably representative as well (Tirrell et al., 2012). Furthermore, if human fast fibres generate ∼225 kPa and slow fibres generate ∼155 kPa of active stress in accordance with Powell et al. (1984), a mixed muscle such as the gracilis would be expected to generate ∼180 kPa of active stress (0.65 × 155 + 0.35 × 225) providing further support that human fast and slow muscle fibres produce the same stresses as other commonly measured mammalian muscles.
Our direct measurements also allow us to predict the shape of the human gracilis muscle length-tension relationship using a minimum of assumptions. We relied on the highly linear relationship between FWHM and optimal fibre length ( Fig. 4B of Winters et al., 2011) to calculate optimal fibre length on a subject-specific basis, which in turn required at least four experimental data points per subject. It is important to note that our subject-specific prediction of fibre length required a large extrapolation of this relationship, defined for muscles with fibres between 1 and 4 cm in length, to a FWHM that predicted a ∼13 cm fibre length (red symbol in Fig. 5B). Using these subject specific values to predict the length-tension relationship (scaling to an optimal human sarcomere length of 2.7 µm (Lieber et al., 1994;Walker & Schrodt, 1974), a good fit between experiment and prediction was obtained (r 2 = 0.79 of average of n = 12 to the solid grey line in Fig. 4C).
The approach described above yielded an average gracilis fibre length of 12.9 ± 3.3 cm (Fig. 6A) which is much shorter than the gracilis fascicle length of 23 cm previously reported in the anatomical literature (Ward, Eng et al., 2009;Wickiewicz et al., 1983). The reason for this discrepancy is not clear. We consider the most probable explanation is that the very long fascicles that we and others have dissected from cadaveric specimens are composed of shorter muscle fibres that are simply staggered along the fascicle and act in parallel with each other within the muscle's extracellular matrix (ECM). Support for this idea first comes from prior anatomical dissections of human sartorius and gracilis muscles (Heron & Richmond, 1993;Loeb et al., 1987). The physiological explanation provided in these previous studies for shorter fibres in longer fascicles proposed that the relatively slow conduction velocity of human muscle fibres (40 m s -1 ) precluded very long lengths because significant sarcomere non-uniformities would develop as one portion of a single fibre contracted actively against a compliant, inactivated portion. The anatomical study concluded by stating that, '… these data provide compelling evidence that many fibres in sartorius and gracilis run only about one fourth to one fifth of the length of the whole muscle' (Heron & Richmond, 1993) on page 40, column 2. Additionally, these staggered short fibres acting in parallel is based on the idea that fibres embedded in the ECM transfer their force into the complex ECM network, which then transits these forces throughout the muscle to tendon (Huijing, 1999;Trotter, 2002). However, we do not have a satisfactory mechanistic model to explain how this occurs because we are just starting to understand the complexity of the muscle's ECM. We speculate that the fibre force is laterally transmitted to the endomysium (Garcia-Pelagio & Bloch, 2021;Street, 1983). We then propose that the lateral transmission via the endomysium within the fascicle is transmitted via the perimysium to the tendon, potentially via distinct perimysial cables (Gillies & Lieber, 2011;Purslow, 2020;Sharafi & Blemker, 2011). This allows force to bypass the other staggered fibres, allowing shorter fibres to act independently in parallel rather than in series. Direct structural evidence for this mechanism operating in a whole muscle is very difficult to generate and is currently lacking. However, our physiological studies support these assertions because we observe the gracilis muscle behaving as a muscle with shorter fibres than previously measured fascicles.
It is possible that the large extrapolation shown in Fig. 5B is not appropriate. The large gap between fibre lengths in smaller mammals and humans with no intervening data points makes such an extrapolation problematic. However, it should be noted that when we created the predicted gracilis length-tension relationship using literature values based on anatomically measured fascicle lengths, the fit between our experiments and that prediction was extremely poor (r 2 = 0.0 average of n = 12 to the dashed grey line in Fig. 4C). The fact that the length-tension curve based on these literature values is not close to the experimental values calls into question the direct use of anatomical parameters to predict muscle functional properties in such long muscles.
To produce the physiological data reported in the present study, our laboratory employed essentially the same methods as those used in Winters et al. (2011). Similarly, to produce the human anatomical data (Ward, Eng et al., 2009), we employed the same methods as those used in our previous studies of small rabbit muscles (Lieber & Blevins, 1989). There is clearly a disconnect. We consider that there may be a 'maximum' fibre length for long human muscles, somewhere between 4 and 13 cm, as stated previously (Heron & Richmond, 1993;Loeb et al., 1987), so that the very long fascicle lengths reported for such muscles as the gracilis, gluteus maximus, adductor magnus, sartorius and semitendinosus (Ward, Eng et al., 2009) may not be functionally relevant because of limitations in our ability to dissect muscle fibres from whole muscles. Future studies are required to address this question in a systematic manner.
Although we are excited to report these high-resolution data, the present study has many limitations. Our values for volume, which directly affect our PCSA values and thus our specific tension calculations, were based on 'optical removal' of the skin paddle, which was surgically required for postoperative muscle monitoring after transplantation to the arm. We simply did this by smoothing the surface of the image, which was subjective. Additionally, the actual value for P o that yielded S i was calculated using eqn (1) because tetanic contractions were experimentally initiated at only 50% current of the maximum CMAP stimulation intensity and a submaximal stimulation frequency of 20 Hz. Indeed, we calculate that our measured values are ∼70% of the 'true' maximum tetanic tension (see Methods). This approach assumes that twitch tension force scales equivalently to tetanic tension force with increasing recruitment. Additionally, our approach assumes that the force-frequency curve of all gracilis muscles is the same, which has not been experimentally verified. However, we estimate that these assumptions would affect the P o calculations by less than 10%. Given the practical and ethical limitations of intraoperative muscle contractile measurements, it is not clear how to overcome these stimulation limitations.
Taken together, these experiments provide novel and unique measurements using minimal calculations and assumptions establishing human muscle fibre-specific tension of ∼170 kPa and an excellent fit between experiment and theory (r 2 = 0.79 of average of n = 12 to the solid grey line in Fig. 4C) when subject-specific fibre length is calculated for each subject from the width of the active length-tension curve as opposed to using historical anatomical fascicle literature values. The gracilis muscle appears to be composed of relatively short fibres acting in parallel, a finding that may not have been appreciated based on traditional anatomical studies.