Scaling relationships between human leg muscle architectural properties and body size

Skeletal muscles demonstrate a wide range of sizes and functions across many species (Alexander, 2003). Because muscle design depends on whether a muscle is used for dexterous manipulation, power production, braking or energy storage, the precise orientation of muscle fibers as well as their relationship to surrounding connective tissue structures necessarily demonstrate a broad range of organizations (Alexander et al., 1981; Lieber and Ward, 2011). It is largely accepted that the number and orientation of muscle fibers within a muscle – its architecture – determines peak muscle force and muscle excursion when a muscle is fully activated. Specifically, muscle fiber length (equivalent to the number of sarcomeres in series) determines the excursion over which a muscle will generate active force (see fig. 4 of Winters et al., 2011; Bodine et al., 1982), whereas physiological cross-sectional area (PCSA) determines peak isometric muscle force (Gans, 1982; Powell et al., 1984).

Scaling describes the way in which one structure changes size/shape relative to another (Schmidt-Nielsen, 1975, 1984). In musculoskeletal biomechanics, scaling is often studied by quantifying the relationship between a structure of interest (e.g. tendon length, muscle property, bony dimension) and another structure (bony segment length, muscle mass, etc.) or even body size, which may be quantified based on its mass, shape or height/length (Alexander et al., 1981; Bennett, 1996; Handsfield et al., 2014; McGowan et al., 2008; Pollock and Shadwick, 1994a). Most previous scaling reports are comparative studies that focus on the relationship between musculoskeletal design and animal locomotion. They typically use a comparative approach that takes advantage of very large size differences amongst various species within the same family (Bennett, 1996; McGowan et al., 2008) or very large size differences in animals with the same mode of locomotion (Alexander et al., 1981; Pollock and Shadwick, 1994a) to reveal underlying design principles. For example, several authors have shown that skeletal muscle force generating capacity and muscle area:tendon area ratios show positive allometry with body mass resulting in a design whereby increased body mass leads to increased elastic strain energy storage and thus increased efficiency during gait (Biewener and Blickhan, 1988; Ker et al., 1986; Pollock and Shadwick, 1994a). This increased strain energy is necessarily accompanied by a decrease in tendon safety factor (Alexander et al., 1981; McGowan et al., 2008), because tendon elastic properties have no scaling relationship with body mass over five orders of magnitude (Pollock and Shadwick, 1994b), even though significant tendon material properties are observed among species. Such scaling interrelationships are often used to argue for an upper limit for the size of an animal given their geometry and mechanism of locomotion (Alexander, 1988; Biewener, 2005; McGowan et al., 2008).

We are interested in the way that skeletal muscle architecture scales with body mass and bony segment lengths in humans, not only to understand the relationship between muscle design and function (Lieber and Ward, 2011) but also to provide quantitative guidance to other investigators using musculoskeletal models to understand function and/or surgical intervention (Lieber and Friden, 2004). Unfortunately, there has never been a large intraspecific study of human muscle architecture and thus, the manner in which human muscle design varies with body size or the scaling laws that should be used in human musculoskeletal models are unknown. The human biomechanical modeling community must necessarily use isometric scaling rules, absent any other data. There are several large datasets that quantify human muscle volume by MRI (Charles et al., 2019; Handsfield et al., 2014; O'Brien et al., 2010), but none of these datasets include measurement-based optimal fiber length, which is required in order to making appropriate scaling calculations (see below). Because these human studies measure only MRI-based muscle volume, they rely on literature values of average muscle fiber length:muscle length ratio, and muscle-specific fiber sarcomere length values. Use of these averages precludes their proper use to quantify scaling rules because they lack natural variability required for proper regression analysis and are highly dependent on the joint position in which the images are acquired.

In their classic interspecific study, in which muscle properties across species were related to body mass, Alexander et al. (1981) showed that muscle properties scaled nearly isometrically with animal size. Specifically, muscle mass scaled slightly positively allometrically with animal mass to the 1.1 power (compared with isometric scaling of 1.0) and muscle fiber length scaled nearly isometrically with animal size to the 0.3 power (compared with isometric scaling of 0.33) (Alexander et al., 1981). This interspecific study of mammalian muscles led to unique insights into mechanisms of locomotion and revealed the dramatic muscular specialization seen specifically in animals that move primarily by hopping.

Although these results are important and illuminating, they do not address the question of how muscle architecture scales with animal mass within a species. In human leg muscles, several studies have been conducted (Charles et al., 2019; Friederich and Brand, 1990; Ward et al., 2009a; Wickiewicz et al., 1983), but, owing to small sample sizes and the relatively small amount of body size variation in these studies, it remains unknown whether any scaling relationship exists, and if so, whether such scaling patterns vary among functional groups or muscles. In addition, of these four studies, only one measured sarcomere length of each muscle fascicle (Ward et al., 2009a). Because the anatomical position used in these human studies preferentially extends the knee and plantarflexes the ankle, lack of sarcomere length data results in a systematic bias in fiber lengths between flexors and extensors (Felder et al., 2005).

To address this issue, we collected a large human architectural dataset consisting of 896 individual human skeletal muscles from 34 cadaveric specimens with an age range of 36–103 years, a height range of 152–188 cm and a body mass range of 58–105 kg. Based on recent United States statistics (Fryar et al., 2021), this height range covers nearly the entire range of the population (91.9% for US females and 93.8% for US males; Fig. S1A,B) and the mass range ∼70% of the US population (Fig. S1C,D). Using detailed architectural analyses of this large sample, including muscle-specific sarcomere length measurements, the purpose of this study was to establish the scaling relationship(s), if any, that exist between human leg muscle architectural properties, body mass and bony dimensions.

Architectural data were obtained from each of 28 muscles obtained from 34 formaldehyde-fixed lower extremities [female/male (F/M): 18/16; age: 70.0±18.1 years; height: 169.1±10.0 cm; mass: 78.5± 13.8 kg] by combining two datasets: the dataset collected from older individuals (F/M: 12/9; age: 82.5±9.4 years; height: 168.4±9.3 cm; mass: 82.7±15.3 kg) that was previously published (Ward et al., 2009a); and a new dataset collected from younger individuals (F/M: 6/7; age: 49.7±5.7 years; height: 167.0±11.3 cm; mass: 73.7±10.6 kg). None of the 34 legs examined were from the same individual. The studied muscles include the psoas (PS), iliacus (IL), gluteus maximus (GMX), gluteus medius (GMD), sartorius (SR), rectus femoris (RF), vastus lateralis (VL), vastus intermedius (VI), vastus medialis (VM), gracilis (GR), adductor longus (ADDL), adductor brevis (ADDB), adductor magnus (ADDM), biceps femoris long head (BFLH), biceps femoris short head (BFSH), semitendinosus (ST), semimembranosus (SM), tibialis anterior (TA), extensor digitorum longus (EDL), extensor hallucis longus (EHL), peroneus longus (PL), peroneus brevis (PB), gastrocnemius medial head (GMH), gastrocnemius lateral head (GLH), soleus (SOL), tibialis posterior (TP), flexor digitorum longus (FDL) and flexor hallucis longus (FHL). The theoretical sample size of 952 (28 muscles×34 extremities; Fig. 1) was not attained owing to either technical problems with a sample, malformed muscles or inability to obtain clear diffraction patterns for sarcomere length measurement. Our sample size thus totaled 896 muscles (∼95% of those sampled). Muscle samples lost were randomly scattered throughout the dataset.

Each muscle was dissected by removing its most proximal origin to its most distal insertion. Muscles were stored in 1× phosphate-buffered saline (PBS) for 24–48 h prior to microdissection. After muscles were excised, representative skeletal measurements (Table 1), including femur length (greater trochanter to tibiofemoral joint line), epicondylar width, tibial length (tibiofemoral joint line to the medial malleolus), tibial plateau width, calcaneal length, calcaneal height and calcaneal width (width of the calcaneal tuberosity), along with body height and body mass were made.

Muscle architectural properties were measured from three regions of each muscle as defined and mapped by Ward et al. (2009a, see their fig. 1), according to the methods originally developed by Sacks and Roy (1982). Briefly, muscle specimens were removed from PBS, blotted dry and weighed. Muscle mass (M_m) was not corrected for formaldehyde fixation, but external tendons, connective tissue and fat were removed before weighing. Muscle length (L_m) was defined as the distance from the origin of the most proximal fibers to the insertion of the most distal fibers. Raw fiber length (L_f) was measured from the previously mapped three regions in each muscle using a digital caliper (accuracy, 0.01 mm). Muscle fascicles were carefully dissected from the proximal tendon to the distal tendon of each mapped muscle region. Surface pennation angle (θ) was measured in each of these regions with a standard goniometer. Fascicles were then placed in mild sulfuric acid solution (15% v/v) for 30 min to partially digest surrounding connective tissue, enabling fascicle dissection, and then rinsed in PBS. Three small muscle fiber bundles (consisting of approximately 50 single muscle fibers) were then isolated from each muscle region and mounted on slides. Bundle sarcomere length (L_s) was measured by laser diffraction as previously described by Lieber et al. (1984). To permit optimal fiber length comparison among muscles and compensate for variations in joint angle (Felder et al., 2005; Lieber, 1997), normalized fiber length (L_f) was calculated as L_f=L_f′ (L_s,opt/L_s), where L_s,opt is optimal sarcomere length for human muscle (2.7 µm) based on quantitative electron microscopy previously reported (Lieber et al., 1994). PCSA was calculated as PCSA=mcosθ(ρL_f), where m is muscle mass and ρ is muscle density (i.e. 1.056 g cm⁻³) (Ward and Lieber, 2005).

Architectural scaling with body mass was quantified using the allometric scaling power function y=ax^b, where y is the muscle architectural property, a is a scaling factor, x is body mass and b is the exponent of a power or the allometric scaling coefficient. In practice, the equation was log-log transformed to enable linear regression analysis to be used to solve the equation log(y)=log(a)+blog(x), where log(y) is the log-transformed muscle architectural property, log(a) is the intercept, b is the slope (i.e. the exponent of the allometric scaling power function) and log(x) is the log-transformed body mass. We confirmed that both the linear and nonlinear fitting methods yielded similar results, and thus linear regression results with log-log transformed data are presented for convenience.

It is suggested that linear regression is appropriate to test for an association between variables whereas reduced major axis (RMA) regression is appropriate to test whether the slope equals a specific value (Warton et al., 2006). We thus performed linear regression using the ‘fitlm’ function in MATLAB software (R2022b, The MathWorks, Inc., Natick, MA, USA) to determine the association (if any) between body mass and the specific muscle architectural property, and the RMA regression using ‘gmregress’ function (available at https://www.mathworks.com/matlabcentral/fileexchange/27918-gmregress) to calculate all slopes (i.e. exponent b) of the relationships. Significance of each association was tested using the P-value of the corresponding linear regression model. All P-values were adjusted using the Benjamini–Hochberg method (Benjamini and Hochberg, 1995) that accounts for potential correlations among the architectural parameters among the muscles from the same specimen or among the body size-related parameters. Coefficients of determination (r²) of each linear regression model were used to determine the proportion of variation in the dependent variable predicted by the model. Slopes calculated from the RMA regression were multiplied by the corresponding correlation coefficients (r), and the corrected slopes and 95% confidence interval (CI) were then used to compare to isometric scaling in which body mass versus muscle mass scales to b=1.0, body mass versus muscle PCSA scales to b=0.66, and body mass versus fiber length scales to b=0.33 (Alexander et al., 1981). All tests were performed using MATLAB software. The significance level was set to P<0.05. All values are reported as means±s.d. unless otherwise noted.

Architectural features of the 28 lower extremity muscles from ‘younger’ individuals in this study (Table S1; 33 years younger than in Ward et al., 2009a,b) were similar to those reported previously for ‘older’ individuals (see table 2 of Ward et al., 2009a,b). Across the entire dataset that includes older, younger, male and female specimens (Fig. 2), the four muscles with the largest M_m (Fig. 2A) were GMX (575.8±194.2 g), VL (385.7±139.1 g), ADDM (341.9±135.4 g) and SOL (278.4±86.6 g). The muscle with the largest PCSA (Fig. 2B) was SOL (53.9±17.2 cm²), which was ∼50% larger than VL (36.5±15.9 cm²), GMD (34.4±14.2 cm²) and GMX (33.7±10.2 cm²). The muscles with the longest fibers (L_f; Fig. 2C) were SR (40.9±4.0 cm), GR (23.3±3.6 cm), ST (19.5± 4.0 cm) and GMX (16.3±2.8 cm). The average coefficient of variation across all muscles and all specimens was largest for M_m (41.4±7.4%), followed by PCSA (40.3±6.5%) and L_f (19.9±5.7%). Bony dimensions largely correlated significantly with one another, as evidenced by the correlation matrix of these parameters demonstrating significance in 25 of the 45 pairs of 10 variables (Fig. 3).

None of the architectural properties measured scaled isometrically with body mass and all scaling exponents were either highly positively or negatively allometric. All 28 muscles studied demonstrated a significant relationship between muscle mass and body mass (Fig. 4A). On average, these data were well explained by the scaling relationships, with an average coefficient of determination (r²) of 0.34±0.09 (Fig. 4B). The average slope of this linearized relationship was 1.30 with 95% CI of [1.20, 1.40] (solid line, Fig. 4C), which was higher than isometric scaling of 1.0 (dotted line, Fig. 4C). The relatively high scaling exponent reveals that muscle mass shows positive allometry relative to body mass; however, several muscles showed negative allometry (i.e. PS, IL, GMX, GMD and GMH) for reasons that are not known and were not pursued.

Twenty-two of the 28 muscles demonstrated a significant relationship between PCSA and body mass (Fig. 5A). Similar to muscle mass, these data were well explained by scaling relationships, with an average r² of 0.29±0.13 (Fig. 5B). The average slope of the linearized relationship was 1.17 with 95% CI of [1.04, 1.29] (solid line, Fig. 5C), which was higher than isometric scaling of 0.66 (dotted line, Fig. 5C). Given that this exponent is nearly twice that predicted by isometric scaling, this represents a tremendous departure from isometric scaling.

None of the 28 muscles demonstrated any significant relationship between L_f and body mass (Fig. 6A), and thus there was no scaling relationship for L_f among these muscles, as supported by the very low average r² of 0.04±0.05 (Fig. 6B). The average slope of this relationship was 0.13 with 95% CI of [0.04, 0.21] (solid line, Fig. 6C), which was lower than isometric scaling of 0.33 (dotted line, Fig. 6C). All of these quantitative data clearly demonstrate that L_f does not scale with body mass, whereas muscle mass and PCSA scale strongly positively allometrically with body mass.

The L_f–body mass scaling relationships vary widely among species, but nearly isometric scaling between L_f and bone length is often observed (Alexander et al., 1981; Pollock and Shadwick, 1994a). We thus quantified the scaling relationship between normalized muscle fiber length (i.e. raw measured fiber length that is normalized to the sarcomere length of each specimen) and the appropriate bone length for that muscle in both the femur (Fig. 7) and tibia (Fig. 8). None of the 13 muscles of the femur demonstrated a significant association between fiber length and bony length (Fig. 7A), as supported by the very low average r² of 0.06±0.06 (Fig. 7B). The average scaling exponent was different from isometric scaling of 1.0 (Fig. 7C). Similarly, none of the 11 muscles of the tibia demonstrated a significant correlation between fiber length and bony length (Fig. 8A). However, in this case, the average scaling exponent was nearly identical to isometric scaling of 1.0 (Fig. 8C), but again with no significant relationship (Fig. 8B).

Unlike the more complete comparative musculoskeletal studies performed by others, we did not explicitly measure tendon dimensions or moment arms. However, fortuitously, we did measure calcaneal length in 24 of our 34 specimens (Table 1), and thus we attempted to correlate fiber length of the eight muscles inserting onto the calcaneus with calcaneal length (Fig. S2). None of the fiber lengths were significantly correlated with calcaneal length (Fig. S2A and B), and the average scaling exponent was again different from isometric scaling of 1.0 (dotted line, Fig. S2C).

With regard to gender, muscle mass and PCSA (both body mass-related architectural parameters) were significantly different for 26 of 28 muscles (average difference of ∼40%; Fig. S3A) but, surprisingly, this did not extend to fiber length, which was significantly different between genders for only 13 muscles, with the magnitude of this difference being relatively small (average difference of ∼10%; Fig. S3B).

The purpose of this study was to quantify the scaling relationships between muscle architectural parameters and body size (i.e. body mass and bony dimensions) across a wide range of human female and male body masses and heights. To our knowledge, this dataset of 896 muscles from 34 lower extremities with a size range that includes ∼90% of the US population based on height and ∼70% based on mass is both the largest human muscle architectural dataset and the largest single-species muscle architectural dataset ever assembled. Our main finding is that muscle fiber length, one of the most important determinants (directly and indirectly) of muscle function, does not scale with body size whereas muscle mass and PCSA strongly scale positively allometrically with body mass.

We found significant positive allometry between muscle mass and body mass (Fig. 4A,C), with an average scaling exponent of 1.3 across all muscles. This finding is consistent with previous demonstrations of a muscle mass–body mass correlation across animals with numerous forms of locomotion and across body masses that span five orders of magnitude (see fig. 1 of Alexander et al., 1981) as well as the large study of the superfamily Macropodoidea (see fig. 3 of McGowan et al., 2008), but is much more positive than demonstrated in either study. The traditional interpretation of these data is that increased muscle mass is required to move increased body mass. Indeed, our data are completely consistent with those of Alexander et al. (1981) for adductor, hamstrings, quadriceps and ankle extensors (Fig. S4A) as well as deep hindlimb flexors (Fig. S4B). The data are also consistent with those of McGowan et al. (2008) for the Macropodoidea superfamily hip extensors, knee extensors and ankle extensors. With regard to previous human studies, the large human dataset of 840 muscles from 24 individuals reported by Handsfield et al. (2014) also showed that muscle mass scaled positively allometrically with body mass. This group has also shown that the relative distribution of muscle mass among different types of elite athletes varies according to sport, a result that may have implications for the diagnosis and treatment of ligament injuries (Kuenze et al., 2016). Unfortunately, because the data from this group are based on magnetic resonance images (i.e. cannot resolve sarcomere lengths or fiber lengths), the architectural scaling properties of their muscles are unknown.

The unique aspect of the present study was quantifying muscle architectural parameter scaling relative to body mass. Muscle physiologists have known for decades that muscle mass is a relatively poor predictor of muscle function owing to the fact that a fixed volume (or mass) of muscle fibers can be arranged in a variety of ways to create muscles of differing function in the same way that identical bricks can be arranged to form structures of different properties (Lieber and Fridén, 2000). At the two extremes are muscles with very short fibers packed in such a way so as to create a large PCSA (SOL is an example of this design), compared with those with very long fibers packed in such a way so as to create large excursion (GR is an example of this design). The tremendous variation in muscle architecture has been the topic of study in many species, such as dogs (Braund et al., 1982; Dries et al., 2018; Mathewson et al., 2014; Shahar and Milgram, 2001), cats (Sacks and Roy, 1982; Spector et al., 1980), mice (Charles et al., 2016; Mathewson et al., 2014; Roy et al., 1984b), rats (Eng et al., 2008; Mathewson et al., 2014; Roy et al., 1984b), nonhuman primates (Kikuchi, 2010; Mathewson et al., 2014; Richmond et al., 2001; Roy et al., 1984a; Serlin and Schieber, 1993), birds (Bribiesca-Contreras et al., 2019) and humans (Charles et al., 2019; Friederich and Brand, 1990; Lieber et al., 1990, 1992; Mathewson et al., 2014; Ward et al., 2009 a; Wickiewicz et al., 1983). Because many nonhuman species have stereotypical forms of locomotion, it is often possible to identify specific muscle architectural ‘designs’ that make teleological sense for specific muscle groups. In this way, it has been possible to take advantage of the many orders of magnitude size variation in such studies to extract the scaling relationships for various muscles (Alexander et al., 1981; McGowan et al., 2008; Pollock and Shadwick, 1994a). Humans present a unique challenge in that their size range is relatively small compared with interspecific size ranges and because their muscles are relatively large. This makes collection of large human muscle architectural datasets challenging. The use of magnetic resonance imaging (MRI) and segmentation has permitted the generation of relatively large volume datasets in young, healthy humans (Charles et al., 2019; Handsfield et al., 2014; O'Brien et al., 2010) as well as patients (Handsfield et al., 2016; Kuenze et al., 2016; Oberhofer et al., 2010). These MRI studies have concluded that muscle masses measured from cadaveric specimens are 30–50% smaller in terms of muscle mass. The extent to which this mass decrease affects the scaling relationships quantified here is not known.

As mentioned above, a significant weakness in most previous scaling studies in both humans and animals is the lack of sarcomere length measurements that are associated with the muscle fascicle lengths measured that enable calculation of optimal fiber length. For MRI, this method is simply too low resolution to permit sarcomere length measurements, so the sarcomere lengths measured from cadaveric studies are simply used for ‘normalization’ assuming an identical joint position in the living humans as in the cadaveric specimens. This has not been documented. Additionally, such an approach lacks the normal specimen-to-specimen variability that is a requirement for proper use of regression methods. In addition to providing variability for regression, the effect that sarcomere length normalization has on muscle architecture is to systematically increase optimal flexor muscle fiber length and systematically decrease optimal extensor muscle fiber length because cadaveric samples are typically fixed in extended knee and ankle positions. We have calculated these values, and it can be seen that the effects are large (Fig. S5); thus, not measuring sarcomere length introduces systematic bias into previous datasets. For most animal studies, muscles typically were not fixed appropriately (Felder et al., 2005) and thus sarcomere length was impossible to measure.

Although muscle mass scaled well with body mass, fiber length did not. Fiber length of individual muscles also did not correlate well with the appropriate bone length (Figs 7 and 8) and fiber length of the eight muscles inserting onto the calcaneus did not correlate with calcaneal length (Fig. S2), the maximum moment arm of these muscles. A priori, we believed that it was reasonable to expect that muscle fiber length would scale with bone length or muscle insertion moment arm. We used the following logic: it is known that joint moment arms, which determine the excursion of a muscle–tendon unit (MTU), scale with bone length (Murray et al., 2002) and that moment arms geometrically scale with bone length (Biewener, 1983), also shown in this study (Fig. 3). We have measured the relationship between human muscle sarcomere length and joint angle intraoperatively in human wrist flexors (Lieber and Friden, 1997; Lieber et al., 1996), extensors (Lieber et al., 1994), quadriceps (Son et al., 2018) and lumbar multifidus (Ward et al., 2009b) muscles and have found that sarcomere length operating range is relatively consistent across individuals. Given that muscle fibers represent sarcomeres arranged in series, a similar sarcomere length operating range across individuals of varying size implies that serial sarcomere number (i.e. fiber length) would also scale with bony length or moment arm. However, this was clearly not the case in our dataset. Considering that the current sample size is larger than a recommended size for this regression study (Jenkins and Quintana-Ascencio, 2020), and that our regression analyses for muscle mass and PCSA achieved an average power of ∼90% and ∼70%, respectively, based on a post hoc power analysis using G*Power software (Faul et al., 2009), we believe that we had sufficient dataset to resolve a scaling relationship between fiber length and bony length should one exist. However, there was simply no hint of a significant fiber length scaling relationship, with extremely low correlations in fits calculated (Figs 7 and 8; Fig. S2). Taken together, it appears that although fiber length varies tremendously across muscles (as supported by the fact that fiber length across muscles of different individuals had a very wide coefficient of variation of ∼70%), this length is ‘built in’ to each adult human muscle.

This study has two main limitations. First, these data were obtained from cadaveric specimens, which are often donated by individuals with chronic diseases that can clearly affect muscle mass. The magnitude of this effect on muscle mass was estimated as 50% by Handsfield et al. (2014) based on their MRI data. The effect (if any) of mass decrease on muscle fiber length is not known, although the atrophy presumed in cadaveric specimens would have the effect of decreasing the pennation angle (Kawakami et al., 1993). Second, there was a large degree of unexplained variability in our dataset. Indeed, our coefficients of determination, even for significant results in the regression analyses (Figs 4B and 5B), were less than 0.5, indicating that over 50% of the variance in muscle mass and PCSA was attributable to factors other than body mass. Variability in exponents across muscles was also observed (e.g. SR and ST in Fig. 4; and SR, VI and SM in Fig. 5), but no pattern was obvious to us. Thus, remaining sources of variability are yet to be determined.

In conclusion, we have assembled a large human lower extremity muscle architectural dataset, representative of the general population, and have shown that although muscle mass scales well with body mass, muscle fiber length does not. This result is in contrast with prior interspecific studies of muscle fiber length scaling with body mass (Alexander et al., 1981) and closer to the result from the Macropodoidea super family in which fiber length scaled with negative allometry to body mass (McGowan et al., 2008). This lack of scaling relationship in our dataset has implications for biomechanical modeling studies in which subject-specific architectural models are created based on a previously assumed linear relationship between fiber length and body segment length or body height. We suggest that human muscle models should not scale fiber length with body size or bony segment length.

We thank Prof. Andy Biewener for extensive and insightful comments on this work.