Specific tension of human muscle in vivo: a systematic review

Abstract

The intrinsic force production capability of human muscle can be expressed as “Specific Tension,” or, the maximum force generated per cross-sectional area of muscle fibers. This value can be used to determine, for example, whether muscle quality changes during exercise, atrophy, disease, or hypertrophy. A value of 22.5 N/cm² for mammalian muscle has generally become accepted based on detailed studies of small mammals. Determining the specific tension of human muscle is much more challenging as almost all determinations are indirect. Calculation of human muscle specific tension requires an understanding of that muscle’s contribution to joint torque, its activation magnitude, tendon compliance, and joint moment arm. Determining any of these parameters is technically challenging in humans and thus, it is no surprise that human specific tension values reported vary from 2 to 73 N/cm². In this systematic review, we screened 1,506 published papers and identified the 30 studies published between 1983 and 2023 that used appropriate methods and which reported 96 human specific tension values. We weighted each parameter based on whether it was directly measured, estimated, or calculated based on the literature, with decreasing weighting used, the more indirect the methods. Based on this exhaustive review of the relevant human literature, we suggest that the most accurate value that should be used for human muscle specific tension is 26.8 N/cm².

INTRODUCTION

Understanding the force-generating capacity of muscle is a vital part of understanding overall muscle function and validating predictive computational musculoskeletal models. The specific tension (ST) of muscle is defined as the force produced per unit of cross-sectional area of muscle, making it the key determinant of intrinsic muscle strength. This metric is directly related to the number of sarcomeres that are acting in parallel and allows comparison of muscle strength among individuals (1), populations (2–4), and in response to interventions, such as training (5–7). In the clinical setting, ST provides valuable information for assessing muscle health and quality. Changes in specific tension may be due to a combination of factors, including muscle fiber atrophy/hypertrophy, changes in muscle fiber type percentage, fatty infiltration, and alterations in the force-generating properties of individual muscle fibers. In addition, loss of motor neurons and subsequent denervation of muscle fibers leads to a decrease in muscle force production, resulting in lower ST.

Although there are a tremendous number of excellent single muscle fiber ST values available, it is not clear that these data translate to the whole human muscle scale. For example, single fiber studies require calcium activation of a skinned fiber that swells during preparation (8) requiring an estimate of fiber CSA that uses some type of osmotic shrinkage or a mathematical “correction factor” to account for this swelling. In addition, an assumption regarding fiber shape (elliptical, circular, other) is required, increasing the difficulty of accurately determining fiber CSA in vitro. Even the ST values are systematically “low” in these preparations compared with whole muscle. Finally, as single cells have no connective tissue and only one fiber type, it is possible that single fiber values may be different compared with those measured from whole muscle simply due to the presence of multiple fiber types and connective tissue in whole muscle. For these reasons, we believe that single-fiber studies fall into a category of their own and should be considered separately. Our interpretation of single-fiber ST values is that they probably represent the best estimate of sarcomere ST but not that of the whole muscle. A direct effect of preparation scale on muscle mechanics has clearly been demonstrated when comparing passive mechanical properties of single cells to small bundles and whole muscle (9) where it was demonstrated that passive stresses do not scale at all with preparation size in any structured manner for three different muscles. Thus, this review focuses on ST values measured or estimated from whole human muscles to scale up to the human performance level.

Accurately determining whole human muscle ST is technically challenging. This largely results from the necessity of performing indirect experimental measurements of the parameters required to calculate ST. First, one directly measures joint moment during “maximal” contraction. Joint moment must be transformed into tendon force, which requires detailed knowledge of the biomechanics of the joint being measured. Moment arm typically varies with joint angle (10) and with muscle activation (11) so that both of these factors may or may not be explicitly included in the moment arm component. Second, as joint moments are produced by multiple muscles, tendon force must be decomposed into the relative forces produced by the various muscles acting on the joint (3, 12, 13). This partitioning might be performed by scaling force to the relative EMGs if all of the muscles are measured, but typically hinges on the assumption of uniform muscle activation across all muscles and defining their relative contribution based on PCSA (3, 12) or the combination of PCSA and moment arm (13). Third, after the calculation of muscle force, to calculate ST, the area across which the force is generated must be determined. Note that this is not the anatomical cross-sectional muscle area in any traditional anatomical plane. The best predictor of the total area producing muscle force is the so-called physiological cross-sectional area [PCSA; (14)]. The PCSA is a calculated parameter involving both muscle volume and optimal muscle fiber length (15). Either one or both of these parameters may be directly measured or indirectly inferred. Calculation of muscle volume via imaging typically involves either magnetic resonance imaging (MRI) or computed tomography (CT). Muscle volume is derived by summing the anatomical cross-sectional areas from multiple muscle slices, typically in the transverse plane. PCSA is then calculated by dividing muscle volume by optimal muscle fiber length (14). Muscle fiber length, in turn, is often estimated using fascicle length measured by ultrasound or MRI at a predefined joint angle (5, 16) or calculated using the fiber length:muscle length ratio derived from the literature (13, 17, 18). By definition, ST represents the maximum stress generated by the muscle. Thus, the fourth determination to be made is the degree to which the muscle is maximally activated. This also introduces further uncertainty in the ST calculation. Typically, electromyography (EMG) is used to capture agonist and antagonist muscle activity from the multiple muscles that contribute to the joint moment. Depending on the experimental setup, assumptions may be made about muscle activation level and/or antagonist co-contraction using these data to then calculate the net joint moment. The degree of activation can also be experimentally “tested” using the twitch interpolation method (19).

In light of the factors described earlier, it can be seen that, due to the numerous experimental complexities used to calculate ST in humans, a variety of assumptions and approaches can be used, all of which will have strengths and weaknesses (as ST is seldom determined based on direct measurement of human muscle force). The numerous anatomical, biomechanical, and neurophysiological assumptions that are inherent in calculating ST may explain why even carefully determined human ST values vary by almost two orders of magnitude in the literature from 2 N/cm² (17) to 73 N/cm² (18). The true source of this variation is not clear. It may be due to the variety of methodologies used, variations in subject characteristics (muscle fiber composition, muscle function, age, and sex), muscle group studied, or other unknown factor(s). In an attempt to unravel these various factors, we performed a systematic literature review to not only establish the “true” numerical value of whole human muscle ST but also to examine the various methodologies used and provide recommendations regarding the “best practices” used to estimate human muscle ST.

METHODS

The Preferred Reporting Items for Systematic reviews and Meta-Analyses (PRISMA) guideline for conducting a systematic review was followed. A Web-based tool (www.covidence.org) was used to screen and extract data. Details of each stage of the systematic review are outlined below under Full Text Screening. No automated tools were used for data extraction and, per PRISMA guidelines, no data were excluded based on an assumed “reasonable range” of ST values.

Search results were first exported from PubMed and Google Scholar and uploaded to Covidence where duplicate studies were automatically removed. The remaining studies went through three stages of screening that were conducted independently by two reviewers (LSP and PPP conducted the first screening stage while LSP and ZW conducted the full-text screening and data extraction). In the first stage, paper titles and abstracts were screened to remove irrelevant studies. Irrelevant studies were classified as those that did not report the specific tension of human muscle. In the second stage, full-length articles were reviewed, at which time the eligibility criteria (see Eligibility Criteria) were applied. Studies that did not conform to these requirements were excluded. In the third stage, data were extracted from each remaining study (see Data Extraction). All extracted data were exported and analyzed using Rstudio (R version 4.3.3) (20).

Literature Search

A search of “specific tension of whole human muscle” was executed on PubMed and Google Scholar on November 7, 2022. PubMed search results were exported in the Research Information Systems (.ris) format and Google Scholar search results were exported as EndNote XML format. Both files were uploaded to Covidence. After this initial search, to identify studies that might have been missed, a Web-based tool called connectedpapers (www.connectedpapers.com) was used to identify similar studies to the Maganaris et al. (11) study entitled “In vivo specific tension of human skeletal muscle.”

Full-Text Screening

Full-length articles were analyzed independently by two reviewers (LSP and ZW). Studies were moved to the data extraction phase once both reviewers were satisfied regarding inclusion criteria. Any differences in reviewers’ opinions were flagged and each paper was discussed until a consensus was reached. Among the 74 articles reviewed in this phase, only four required further discussion.

Eligibility Criteria

Inclusion in this systematic review required that studies 1) calculated muscle physiological cross-sectional area (PCSA) from muscle volume obtained through imaging, 2) measured or calculated fascicle length, and 3) measured or calculated tendon force. Studies that used anatomical cross-sectional area (ACSA) to calculate specific tension were allowed only for elbow flexors as these muscles have a negligible pennation angle and thus ACSA and PCSA are nearly identical. The complete list of inclusion criteria was:

• Specific tension reported for healthy and whole human muscle

• Specific tension reported as stress (force per unit area)

• Muscle fascicle length measured or calculated from measured muscle length

• Muscle PCSA calculated from muscle volume and fascicle length

• Use of ACSA for specific tension calculation allowed only for elbow flexors

• Tendon force calculated or measured

Any study that failed to meet these requirements was excluded. Systematic reviews were also excluded.

Data Extraction

Data were extracted from studies using a custom template in Covidence. This template was independently completed by each reviewer (LSP and ZW) and any differences were automatically flagged by Covidence. When flagged entries were found, both reviewers discussed and resolved the discrepancies. In some cases, flagged values necessitated a re-review of the full-length article to rectify quantitative values or consolidation of both reviewers’ entries for qualitative fields.

For each ST value, a corresponding summary was extracted that outlined the method for measurement or calculation. The following data were extracted:

• Population type: sex, age, height, weight, and count

• Population condition: normal, untrained, or trained

• Muscle(s) or muscle group under examination

• Quantitative values: muscle volume, fascicle length, PCSA, torque, force, and specific tension

• Qualitative values: muscle volume measurement method, fascicle length determination method, PCSA calculation method, torque measurement method, pennation angle method, moment arm determination method, muscle force measurement/calculation method, and specific tension calculation method

• Publication data: authors, year, journal, and country

Quality Assessment

A comprehensive scoring system was developed to judge and compare the quality of the methods used in each study based on our understanding of the accuracy of these various methods. The development of such a scoring system was important for several reasons: first, it captured the inherent assumptions and limitations of the diverse approaches used to calculate ST. Notably, each methodological approach carried its own set of constraints and underlying assumptions, which significantly influenced the accuracy and reliability of the resulting ST values. By systematically assessing and quantifying these factors, our scoring system provided a standardized framework with which to evaluate the robustness and validity of ST measurements. Higher values were assigned to parameters measured directly while those obtained indirectly or from the literature were scored lower. Methods that improved the accuracy of force or PCSA computation were scored higher. These methods might include, for instance, accounting for 100% muscle activation, the effect of antagonist coactivation, or actual measurement of tendon moment arm during the maximum muscle contraction. Figure 1 illustrates the scoring rubric used to quantify the quality of each study.

Figure 1.

Scoring system used to assess the quality of reported specific tension (ST) values. ST is typically calculated as force divided by physiological cross-sectional area (PCSA) or anatomical cross-sectional area (ACSA) for elbow flexors. Scores are represented by bold text in each box. Each study’s methodologies are assessed using each column, and the total score for each study was determined by summing individual scores across columns for force and PCSA or ACSA. The maximum score that can be achieved is 31.

Weighted Median ST Value

To obtain an overall representative value of human muscle ST, we used a weighted value of study quality in combination with each ST value reported (Table 2). Study quality was used as a weighting factor to emphasize the higher-quality studies. The weighted median was chosen as the appropriate descriptive statistic as the raw ST values formed a distribution that was slightly skewed (skew = 0.74) and kurtotic (kurtosis = 0.51). In other words, the distribution was skewed to the right and broader compared with the normal distribution. These are precisely the conditions under which the weighted median provides the most representative value (21). This parameter allows nonuniform statistical weights related to varying weights for the varying measurements in the sample.

Table 2.

Evaluation of specific tension methodology across included studies and their assigned score (based on Fig. 1)

Summary of Methods	Authors	Year	Muscle (s)	ST Value, N/cm2	Score
• Torque not used in calculation • Tendon force measured via stimulation of the motor nerve • Moment arm not used in calculation • Muscle volume estimated by 3-D photogrammetric reconstruction • Fascicle length calculated from measured muscle length, active force-length curve parameter FWHM, and literature FWHM-optimal fiber length relationship • Pennation angle taken from literature • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Binder-Markey et al. (23)	2023	Gracilis	17.1	27
• MVC torque measured using ITT to correct for muscle activation and EMG to correct for antagonist activation • Tendon force = TQ/MA • Moment arm measured (MRI) during rest and not corresponding to max. torque joint angle • Muscle volume estimated by summation of MRI axial images • Fascicle length measured (US) during max. torque trial • Pennation angle measured during max. torque trial • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Erskine et al. (7)	2011	Quadriceps femoris	26.5	24
	O'Brien et al. (3)	2010	Quadriceps femoris	55.0	24
• MVC torque measured using ITT to correct for muscle activation and EMG to correct for antagonist activation • Tendon force = TQ/MA • Moment arm measured (MRI) during rest and corrected using literature values to reflect MVC conditions and max. torque joint angle • Muscle volume estimated by summation of MRI axial images • Fascicle length measured (US) during max. torque trial • Pennation angle measured during max. torque trial • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Erskine et al. (34) Erskine et al. (24)	2010 2009	Quadriceps femoris Quadriceps femoris	29.5 30.3	24
• Max. torque measured (percutaneous electrical stimulation) and EMG correction for antagonist activation • Tendon force = TQ/MA • Moment arm measured (MRI) during rest and corresponding to max. torque joint angle • Muscle volume estimated by summation of MRI axial images • Fascicle length measured (US) during max. torque trial • Pennation angle measured during max. torque trial • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Maganaris et al. (11)	2001	Soleus Tibialis anterior	15.0 15.5	23
• MVC torque measured using ITT to correct for muscle activation and EMG to correct for antagonist activation • Component tendon force calculated using relative PCSA • Moment arm measured (US) during torque trials at max. torque joint angle • Muscle volume estimated by summation of MRI axial images • Fascicle length measured (US) during max. torque trial • Pennation angle measured during max. torque trial • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Kubo et al. (35)	2006	Vastus lateralis	23.1	22
• MVC torque measured with EMG to correct for antagonist activation • Tendon force = TQ/MA • Moment arm measured (MRI) during rest and corrected using literature values to correspond to max. torque joint angle • Muscle volume estimated by summation of MRI axial images • Fascicle length measured (US) during rest • Pennation angle measured during max. torque trial • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Maden-Wilkinson et al. (36)	2020	Quadriceps femoris	33.3	21
• MVC torque measured using ITT to correct for muscle activation • Tendon force = TQ/MA • Moment arm measured (MRI) during rest and corrected using literature values to reflect MVC conditions and max. torque joint angle • Muscle volume estimated by summation of MRI axial images • Fascicle length measured (US) during max. torque trial • Pennation angle taken from literature • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	McPhee et al. (16)	2018	Quadriceps femoris	29.0	21
• MVC torque measured using ITT to correct for muscle activation and EMG to correct for antagonist activation • Component tendon force calculated using relative PCSA • Moment arm measured (MRI) during rest and not corresponding to max. torque joint angle • Muscle volume estimated by summation of MRI axial images • Fascicle length measured (US) during max. torque trial • Pennation angle measured during max. torque trial • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Morse et al. (5) Morse et al. (30)	2007 2005	Gastrocnemius lateralis Gastrocnemius lateralis	8.9 13.1	21
• MVC torque measured using ITT to correct for muscle activation and EMG to correct for antagonist activation • Component tendon force calculated using relative PCSA • Moment arm measured (MRI) during rest and corrected using literature values to reflect MVC conditions and max. torque joint angle • Muscle volume estimated by summation of MRI axial images • Fascicle length measured (US) during rest • Pennation angle measured during max. torque trial • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Valamatos et al. (37)	2018	Vastus lateralis	31.8	20
• MVC torque measured using ITT to correct for muscle activation and EMG to correct for antagonist activation • Component tendon force calculated using relative contribution taken from literature • Moment arm measured (MRI) during rest and corrected using literature values to correspond to max. torque joint angle • Muscle volume estimated by summation of MRI axial images • Fascicle length measured (US) during rest • Pennation angle measured during max. torque trial • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Reeves et al. (4)	2004	Vastus lateralis	27.0	19
• MVC torque measured with EMG to correct for antagonist activation • Component tendon force calculated using relative PCSA • Moment arm measured (MRI) during rest and corrected using literature values to correspond to max. torque joint angle • Muscle volume estimated by summation of MRI axial images • Fascicle length measured (US) during max. torque trial • Pennation angle measured during max. torque trial • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Morse et al. (2)	2008	Gastrocnemius lateralis	13.1	19
• Max. torque measured (surface neuromuscular electrical stimulation) • Tendon force = TQ/MA • Moment arm corresponding to a value taken from literature at the max. torque joint angle. This value was corrected for cadaver shrinkage and changes during MVC. • Muscle volume estimated by summation of MRI axial images for activated ACSA • Fascicle length calculated from measured muscle length and literature ratio • Pennation angle taken from literature • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Gorgey et al. (25)	2006	Quadriceps femoris	25.0	19
• MVC torque measured using ITT to correct for muscle activation and EMG to correct for antagonist activation • Tendon force = TQ/MA • Moment arm measured (MRI) during rest and corrected using literature values to reflect MVC conditions and max. torque joint angle • Muscle volume estimated (MRI) from max. ACSA and literature regression relationship • Fascicle length measured (US) during max. torque trial in a representative muscle (vastus lateralis) • Pennation angle measured (US) during max. torque trial in a representative muscle (vastus lateralis) • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Erskine et al. (40)	2014	Quadriceps femoris	25.6	18
• MVC torque measured using ITT to correct for muscle activation and EMG to correct for antagonist activation • Tendon force = TQ/MA • Moment arm measured (MRI) during rest and not corresponding to max. torque joint angle • Muscle volume estimated (MRI) from max. ACSA and literature regression relationship • Fascicle length measured (US) during max. torque trial in a representative muscle (vastus lateralis) • Pennation angle measured (US) during max. torque trial in a representative muscle (vastus lateralis) • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Erskine et al. (7)	2011	Quadriceps femoris	25.9	18
• MVC torque measured using ITT to correct for muscle activation and EMG to correct for antagonist activation • Tendon force = TQ/MA • Moment arm measured (MRI) during rest and corrected using literature values to reflect MVC conditions and max. torque joint angle • Muscle volume estimated (MRI) from max. ACSA and literature regression relationship • Fascicle length measured (US) during max. torque trial in a representative muscle (vastus lateralis) • Pennation angle measured (US) during max. torque trial in a representative muscle (vastus lateralis) • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Erskine et al. (6) Erskine et al. (24)	2010 2009	Quadriceps femoris Quadriceps femoris	29.1 25.6	18
• MVC torque measured • Tendon force = TQ/MA • Moment arm measured (MRI) during rest and corresponding to max. torque joint angle • Muscle volume estimated by summation of MRI axial images • Fascicle length calculated from measured muscle length and literature ratio • Pennation angle taken from literature • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Kawakami et al. (18)	1994	Elbow extensors	65.4	18
• MVC torque measured using ITT to correct for muscle activation and EMG to correct for antagonist activation • Component tendon force calculated using relative contribution taken from literature • Moment arm measured (X-ray) at max. torque joint angle during rest • Muscle volume estimated (US) from max. ACSA and literature regression relationship • Fascicle length measured (US) during max. torque trial • Pennation angle measured during max. torque trial • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Sims et al. (26)	2018	Vastus lateralis	23.6	17
• MVC torque measured • Tendon force = TQ/MA • Moment arm measured (MRI) during rest and not corresponding to max. torque joint angle • Muscle volume estimated by summation of MRI axial images • Fascicle length calculated from measured muscle length and literature ratio • Pennation angle taken from literature • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Fukunaga et al. (12)	1996	Triceps surae Plantar flexors Dorsiflexors	10.8 8.0 24.5	17
• MVC torque measured • Tendon force = TQ/MA • Moment arm measured (MRI) during rest and corresponding to max. torque joint angle • Muscle volume estimated by summation of MRI axial images • Fascicle length calculated from measured muscle length and literature ratio • Pennation angle not used in calculation • PCSA = Muscle vol/Fiber length	Kawakami et al. (18)	1994	Elbow flexors	72.7	17
• MVC torque measured using ITT to correct for muscle activation and EMG to correct for antagonist activation • Tendon force approximated from external limb force • Moment arm not used in calculation • Muscle volume estimated by summation of MRI axial images • Fascicle length calculated from measured muscle length and literature ratio • Pennation angle taken from literature • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Klein et al. (31)	2001	Elbow extensors	5.5	16
• MVC torque measured • Component tendon force calculated using relative PCSA × MA • Moment arm measured (MRI) during rest and corrected using literature values to correspond to max. torque joint angle • Muscle volume estimated by summation of MRI axial images • Fascicle length calculated from measured muscle length and literature ratio • Pennation angle taken from literature • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Marchetta et al. (13)	2012	Biceps Brachii Brachialis Brachioradialis	53.4 56.5 53.5	15
• MVC torque measured with gravity correction • Tendon force = TQ/MA • Moment arm measured (MRI) during rest and not corresponding to max. torque joint angle • Muscle volume estimated by summation of MRI axial images • Fascicle length taken from literature • Pennation angle taken from literature • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Maganaris et al. (11)	2001	Soleus Tibialis anterior	10.4 65.8	15
• MVC torque measured using ITT to correct for muscle activation and EMG to correct for antagonist activation • Tendon force approximated from external limb force • Moment arm not used in calculation • Muscle volume estimated by summation of MRI axial images • Fascicle length calculated from measured muscle length and literature ratio • Pennation angle not used in calculation • PCSA = Muscle vol/Fiber length	Klein et al. (30)	2001	Elbow flexors	16.5	15
• Torque not used in calculation • Tendon force approximated from external limb force • Moment arm not used in calculation • Muscle volume estimated by summation of MRI axial images • Fascicle length measured (US) during max. torque trial • Pennation angle measured during max. torque trial • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Narici et al. (27)	1996	Gastrocnemius medialis	13.3	15
• MVC torque measured • Component tendon force calculated using relative PCSA × MA • Moment arm measured (MRI) during rest and corresponding to max. torque joint angle • Muscle volume estimated by summation of MRI axial images • Fascicle length calculated from measured muscle length and literature ratio • Pennation angle not used in calculation • PCSA = Muscle vol/Fiber length	Kawakami et al. (17)	1994	Biceps Brachii Brachialis Brachioradialis	72.3 72.3 71.9	15
• Torque not used in calculation • Tendon force approximated from external limb force • Moment arm corresponding to a value taken from literature at the max. torque joint angle • Muscle volume estimated by summation of MRI axial images • Fascicle length measured (MRI) during rest • Pennation angle measured during max. torque trial • PCSA = (Muscle vol/muscle thickness) × sin(pennation angle)	Narici et al. (27)	1992	Vastus lateralis Vastus intermedius Vastus medialis Rectus femoris	23.7 24.1 27.9 24.3	14
• Torque not used in calculation • Tendon force approximated from external limb force • Moment arm not used in calculation • Muscle volume estimated by summation of MRI axial images • Fascicle length calculated from measured muscle length and literature ratio • Pennation angle taken from literature • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Bamman et al. (17)	2000	Triceps surae	1.97	12
• MVC torque measured • Component tendon force calculated using relative contribution taken from literature • Moment arm corresponding to a value taken from literature at the max. torque joint angle • Muscle volume not used in calculation • Fascicle length not used in calculation • Pennation angle not used in calculation • ACSA = Max. ACSA measured (CT) during rest and corrected using literature data to correspond to ACSA during max. Torque	Klitgaard et al. (32)	1990	Elbow flexors	65.4	12
	Nygaard et al. (23)	1983	Biceps brachii	35.6	12
• MVC torque measured with gravity correction • Component tendon force calculated using relative contribution taken from literature • Moment arm corresponding to a value taken from literature at the max. torque joint angle • Muscle volume estimated by summation of MRI axial images • Fascicle length taken from literature • Pennation angle measured during max. torque trial • PCSA = (Muscle vol/Fiber length) × cos(pennation angle)	Aagaard et al. (33)	2001	Quadriceps femoris	42.6	10
• MVC torque measured • Component tendon force calculated using relative PCSA × MA • Moment arm corresponding to a value taken from literature at the max. torque joint angle • Muscle volume not used in calculation • Fascicle length not used in calculation • Pennation angle not used in calculation • ACSA = Max. ACSA measured (CT) during rest	Dowling et al. (38)	1994	Elbow flexors	69.0	10
• MVC torque measured • Tendon force approximated from external limb force • Limb length used as moment arm • Muscle volume not used in calculation • Fascicle length not used in calculation • Pennation angle not used in calculation • ACSA = Max. ACSA measured (MRI)	Akagi et al. (31)	2009	Elbow flexors	14.7	9

ACSA, anatomical cross-sectional area; CT, computed tomography; EMG, electromyography; ITT, interpolated twitch technique; MA, moment arm; MRI, magnetic resonance imaging; MVC, maximum voluntary contraction; PCSA, physiological cross-sectional area; TQ, torque; US, ultrasound.

Risk of Bias

Studies included in this review focused on nonpathological muscle, with the primary outcome being the calculation of ST. Although the observational nature of these studies suggests a lower inherent risk of bias compared with interventional studies that are part of randomized controlled trials, we implemented several methods to mitigate against bias. First, a team of three researchers screened the papers and independently performed data extraction steps. Thus, each study was independently reviewed by three researchers. Second, we devised the scoring rubric to assess objectively the quality of each study. The final reported ST value was calculated using the weighted median to account for the skewed value distribution. Finally, we considered potential confounding factors, such as age, sex, and training status, that could systematically influence the final calculated ST. We were not able to clearly identify any systematic bias in the data.

RESULTS

Literature Search

A total of 1,506 papers were screened of which 1,436 were deemed irrelevant as no ST value was reported. Twenty-five studies remained that satisfied the inclusion criteria. The reasons for excluding the remaining 45 studies are shown in Fig. 2. Four additional studies were identified by searching for studies that were similar to the Maganaris et al.’s (11) representative study. In the end, a total of 30 studies met the inclusion criteria and are included in this review.

Figure 2.

PRISMA flowchart for current literature search.

A total of 96 ST values were extracted from the 29 research papers published between 1983 and 2023 (Fig. 3A). The most frequent journal and country represented were the Journal of Applied Physiology and the United Kingdom, respectively (Fig. 3, B and C).

Figure 3.

Summary of specific tension (ST) values extracted from the included studies (n = 29). A: distribution of reported ST values by year. B: distribution of reported ST value by journal. C: distribution of reported ST value by country.

The quadriceps femoris (QF) was the most studied followed by the vastus lateralis (VL) and then the elbow flexors (Fig. 4A). The cumulative number of subjects for each muscle varied widely (Fig. 4B). A total of 413 QF muscles were studied followed by 184 elbow flexors then 73 gastrocnemius lateralis. When grouped by muscle function, knee extensors, elbow flexors, and plantar flexors comprised 94% of all ST values reported (Fig. 4C). Most ST values were reported from young subjects (aged 18–34) (Fig. 4D).

Figure 4.

Summary of muscle(s) studied. A: number of reported specific tension (ST) value by muscle. B: cumulative number of subjects studied per muscle. C: muscle functional groups for reported ST values. D: age distribution for reported ST value.

The median specific tension (ST) values for various muscle groups were as follows: elbow flexors, 53.4 N/cm²; elbow extensors, 9.5 N/cm²; knee extensors, 29 N/cm²; hip adductors, 17.1 N/cm²; plantarflexors, 10.4 N/cm²; and dorsiflexors, 24.5 N/cm² (Fig. 5A). Significant differences in ST were observed across various muscles when grouped by anatomical location or training status. For example, there was a significant difference between upper arm and lower leg muscles, with ST values of 52.0 N/cm² and 11.2 N/cm², respectively (Fig. 5B) and between upper leg and lower leg muscles, with ST values of 29.0 N/cm² and 11.2 N/cm², respectively (Fig. 5B). Training interventions also significantly influenced ST, evidenced by pre- and posttraining ST values of 25.9 N/cm² and 33.8 N/cm², respectively (Fig. 5D). In addition, differences were observed between elder and younger subjects, with respective ST values of 15.7 N/cm² and 29.5 N/cm². An inverse relationship was noted between the percentage of type 1 muscle fibers (Table 1) and specific tension, suggesting a decrease in ST with an increase in type 1 fiber composition. Conversely, an increase in type 2A fiber composition corresponded to higher ST values (Fig. 5C).

Figure 5.

Distribution of specific tension values (N/cm²) for each muscle group. Data are grouped by muscle function (A), anatomical location (B), fiber type composition (C), and training status (D). B and D display P values indicating significant differences between groups. In studies assessing the impact of training on specific tension, the control group is considered part of the normal group while the trained and untrained groups represent the experimental group before and after training. Data points represent 96 specific tension values from 30 studies.

Table 1.

Muscle groups and fiber composition

		Fiber Composition, %
Abbreviation	Muscle Name	Type 1	Type 2A	Type 2X	Muscle Function	Anatomical Location
BIC	Biceps Brachii	55.6	25.5	19.0	Elbow flexion	Upper arm
BRA	Brachialis	65.9	20.1	13.9	Elbow flexion	Upper arm
BRD	Brachioradialis	45.5	32.0	22.5	Elbow flexion	Upper arm
EF	Elbow Flexors	54.6	25.9	19.5	Elbow flexion	Upper arm
TRI	Triceps Brachii	45.3	34.0	20.8	Elbow extension	Upper arm
EE	Elbow Extensors	49.7	32.9	17.5	Elbow extension	Upper arm
QF	Quadriceps Femoris	53.5	30.9	15.7	Knee extension	Upper Leg
RF	Rectus Femoris	49.7	26.9	23.4	Knee extension	Upper Leg
VI	Vastus Intermedius	63.0	25.3	11.7	Knee extension	Upper Leg
VM	Vastus Medialis	52.8	33.7	13.5	Knee extension	Upper Leg
VL	Vastus Lateralis	48.3	37.5	14.2	Knee extension	Upper Leg
GRA	Gracilis	65.5	19.0	15.6	Hip adduction	Lower leg
PF	Plantar Flexors	63.4	18.0	18.5	Ankle plantarflexion	Lower leg
Sol	Soleus	68.1	20.1	11.8	Ankle plantarflexion	Lower leg
GL	Gastrocnemius Lateralis	65.4	15.0	19.6	Ankle plantarflexion	Lower leg
GM	Gastrocnemius Medialis	57.9	16.9	25.1	Ankle plantarflexion	Lower leg
TS	Triceps Surae	63.8	17.3	18.8	Ankle plantarflexion	Lower leg
DF	Dorsiflexor	72.4	21.0	6.5	Ankle dorsiflexion	Lower leg
TA	Tibialis Anterior	79.4	15.4	5.1	Ankle dorsiflexion	Lower leg

Muscle fibers are classified as: Type1-myosin heavy chain isoform (MHC) slow type 1, Type2A-MHC intermediate type 2A, and Type2X- MHC fast 2X. Muscle fiber type percentages from Tirrell et al. (22).

Frequently, multiple ST values were reported in a single study, reflecting variations in the muscles studied, comparisons between control and experimental groups, or before and after a training intervention program. These values exhibit a broad range, from 1.8 to 72.7 N/cm² (Fig. 6B). Notably, only studies published before 2004 reported values exceeding 60 N/cm² (Fig. 6A); however, when aggregating all data, the median ST value converged on 26.8 N/cm² (Fig. 6B).

Figure 6.

Specific tension (ST) values reported by each study. A: reported ST values for each included study in chronological order. B: median ST value for all included studies shown in A. Multiple ST values are reported for studies that report values for both control and experimental groups before and after training. Note the value of 26.2 is the unweighted ST value, in contrast to Fig. 8, which is the weighted value.

Assessment of Methods

Each of the included studies can be categorized into one of three main groups: physiological investigation of ST in healthy muscle (3, 11–13, 17, 18, 23–29), examination of the effect of aging on ST (5, 16, 30–33), or exploration of the effect of training on ST (4–7, 34–39). Sims et al. (26) investigated the change in ST in the VL in adults with achondroplasia; however, only data from their normal controls were included in our analysis.

Thirty distinct methodological approaches were identified across included studies to calculate human muscle ST (Table 2). None of the studies achieved the maximum quality score of 31. The highest score of 27 was attained by Binder-Markey et al. (23) followed by Erskine et al. (7, 24, 34) and O'Brien et al. (3) with scores of 24. Notably, all top-scoring studies (score >20) examined lower extremity muscles, with reported ST values ranging from 9 to 60 N/cm². Particularly low values were reported by Morse et al. (5, 30) who exclusively investigated the elderly population. Linear regression analysis of ST against score revealed a slight decreasing trend as the score increased, as illustrated in Fig. 7. When using the study quality score (0–31) to weight ST values, the weighted median was 26.8 N/m² (IQR = 20–43) (Fig. 8). The difference between unweighted and weighted specific tension values is shown in Fig. 8. The mean unweighted specific tension was 30.9 ± 19.1 N/cm² (means ± SD) (28, 36).

Figure 7.

Scatter plot demonstrating the relationship between specific tension (ST) (N/cm²) and study quality score. The linear regression line is overlaid in red revealing a weak negative association between ST value and quality score.

Figure 8.

Comparison of unweighted (black) and weighted (gray) specific tension values. Vertical dashed line shows the median value. In this presentation, a shorter line connecting dots indicates a study that would have a stronger weight in calculating the weighted mean value. Note that the weighted value of 26.8 is in contrast to the unweighted value in Fig. 6B.

DISCUSSION

Specific tension is a critical metric in muscle physiology, calculated from measurement of muscle force and physiological cross-sectional area (PCSA). However, accurately estimating these parameters in vivo in human subjects is challenging. This systematic review revealed a spectrum of specific tension values in the literature, even within the same muscle (Fig. 6) or among muscle groups (Fig. 5). For instance, the VL, a commonly studied muscle has reported values that vary threefold from 17 to 57 N/cm² among young, normal subjects. Therefore, removing other extrinsic factors such as subject age, training status, or muscle function, the variation in ST may be attributed to methodological diversity. Through the definition of study quality performed in this review (Table 2), we suggest that the best value for specific tension of whole human muscle is 26.8 N/cm².

Accuracy of the reported ST value hinges on the meticulousness of experimental methodologies that mitigate potential sources of error. For this reason, each study was scored by careful consideration of methodologies used in how muscle force (e.g., direct measurement, dynamometry, electrical stimulation) and PCSA were obtained. Each approach has its own limitations and underlying assumptions that impact the accuracy of the resulting value. Although many studies adhered to a standardized equation for PCSA calculation—formulated as the ratio of muscle volume to fiber length, adjusted by the cosine of the pennation angle—differences emerged in determining or measuring other parameters such as muscle force, moment arm, muscle volume, fiber length, and pennation angle. Moreover, inconsistencies arose among studies striving to delineate force and PCSA values specific to individual muscles or muscle groups being examined. Some studies, for example, attempted to account for submaximal activation, antagonist co-activation, and used varying methodologies for partitioning net joint force into individual muscle force. None of the studies included in this systematic review have considered variation in fascicle length along or across the muscle, nor have they accounted for the fact that both pennation angle and fascicle length vary with joint angle. This is a “weakness” in all of the studies considered.

Joint angle and contraction intensity alter muscle architecture and the resulting PCSA estimation. Such errors compromise the accuracy of the calculated specific tension. O’Brien et al. (3) investigated this and found that a 10° error in the joint angle where MVC occurs resulted in an ST error of 2.9 N/cm² when compared with ST calculated with muscle architecture measured at the actual joint angle where MVC was produced. Similarly, using muscle architecture from contraction at 90% of MVC resulted in an error of 1.4 N/cm² when compared with specific tension calculated with muscle architecture measured at 100% contraction. Therefore, the potential error from not measuring muscle architecture at the optimal joint angle is small (∼4%). For this reason, studies that minimize assumptions in force and moment arm measurements were scored higher and justified the difference in maximum score for calculating muscle force versus PCSA (20 vs. 11) (Fig. 1).

Upon initiation of this review, we suspected that human muscle ST values might be converging upon a specific value with time as methodology improved. This was not the case as can be seen in Fig. 6A. In fact, the significant variation among functional muscle groups (Fig. 5A) and anatomical location (Fig. 5B) might actually represent true differences. The reason for such a discrepancy is not clear. Similarly, although there is a weak positive correlation between type 2A fiber type percentage and ST, and a weak negative correlation between type 1 fiber type percentage and ST, correction for muscle fiber type percentage did not decrease differences observed (Table 1; Fig. 5C).

Although it may seem reasonable to compare ST when stratified by training status, the diverse methods used introduce confounding complexities that hinder standardized comparisons. This complexity makes it challenging to fairly assess the impact of training, sex, or muscle group. However, we have presented all the data to allow readers to make relevant calculations for their specific factor of interest. The difficulty in generalizing across age, training status, and anatomical location highlights the variability of the methods used and underscores the necessity for standardized procedures.

Importantly, the highest-rated study in this review (23) was the only one that directly measured muscle force in situ. The ST value for this muscle was calculated using a minimum set of assumptions (see limitations below) as 17.1 N/cm². This value was lower than that reported for most other mammalian muscles, but after correcting for gracilis muscle fiber type percentage (22), it is close to the ST that would be expected of a mammalian muscle. The fact that rodent muscles are composed of a high proportion of fast muscle fibers probably accounts for the fact that ST values from these muscles are typically much higher.

Our scoring rubric may not capture some of the nuances of specific experimental setups that include factors such as testing configuration and prevention of compensation. Such considerations would have to be performed on a joint-by-joint basis. For example, concerning knee extensors, the contribution of the four quadriceps as well as antagonist hamstring activation can be quantified. However, for more complicated biomechanical systems such as elbow flexors, it is extremely difficult to separate primary elbow flexors (biceps brachii, brachialis, and brachioradialis) from finger and wrist flexors that may, indeed contribute to elbow flexion moment. This idea forms the basis for our highest quality score in studies that performed the most direct muscle force measurement possible.

This systematic review had several limitations. Higher-scoring studies focused only on leg muscles, which restricted our ability to compare muscle groups by anatomical location, fiber composition, sex, and age, thereby precluding a comprehensive analysis of differences among these groups throughout the body. Furthermore, our scoring system may not have captured all experimental nuances that influenced specific tension. For instance, accounting for force transmission losses between quadriceps and patellar tendons was not consistently addressed in all studies. O’Brien et al. (3) attempted to address this issue by converting calculated quadriceps tendon force from patellar tendon force using a literature ratio, as the patella does not act as a frictionless pulley for force transmission. They found that, at a mean knee angle of 65°, force loss equaled one-third of net quadriceps force. Therefore, studies that do not account for this transmission loss may underestimate ST. Moreover, variations in methods used to quantify muscle moment arm can significantly impact specific tension estimation. Although the scoring scheme rewarded studies that measured the moment arm at the correct joint angle during MVC, it did not consider the specific method for measuring the moment arm (e.g., anatomical landmarks vs. instant center of rotation). Finally, the use of MVC as a measure of maximal force production can be affected by factors such as fatigue and motivation that cannot accurately be assessed by this review. Even given these limitations, based on what we believe is an exhaustive review of the relevant human literature, we suggest that the most accurate value, calculated from the weighted median across all studies, is 26.8 N/cm² (IQR = 20–43) for human whole muscle-specific tension (Table 2).

Best Practice Recommendations to Measure ST

To accurately estimate ST, several factors that influence the determination of muscle force production and architecture must be considered. Such factors include methods of decomposing torque measurement, muscle activation level, moment arm length, muscle volume, fascicle length, and pennation angle. Each of these factors plays a significant role in tendon force calculation and PCSA. Our systematic review identified best practices for measuring these variables to ensure the highest accuracy in ST estimation. Based on this analysis, we make the following methodological recommendations for future studies:

Torque MVC measurement.

Standardized warm-up trials and familiarizing subjects with testing protocols are recommended before MVC measurement. The MVC torque is directly measured on a dynamometer at the optimal joint angle. Irrelevant limbs should be immobilized to minimize movement and multiple trials with rest intervals should be tested with maximal oral encouragement. The interpolated twitch technique (ITT) (41) was used to adjust for agonist activation level. Antagonists’ coactivation torque is adjusted via EMG monitoring, which is assumed to be linearly related to joint torque (4). Antagonists’ maximal torque and EMG should be measured separately (3, 24).

Whole muscle volume.

An MRI-based protocol is commonly used before strength testing to avoid exercise-induced fluid shift. Subjects are placed in a comfortable position when a series of continuous MRI scans along the whole muscle is performed vertically to the long axis with a slice thickness of less than 10 mm. The ACSAs of each scanned image are measured and summed up, which is then multiplied by slice thickness to yield the muscle volume (3, 11, 24).

Tendon moment arm.

The MRI scan is conducted over the joint center and target muscle under the same position and joint angle where the MVC trials are performed. Subjects are instructed to perform MVC during the scan. The vertical distance between joint center and tendon force line yields tendon moment arm. Literature data of the moment arm can be used after adjustment to the body size of specific subjects (11, 24).

Total tendon/muscle force.

When MVC torque as previously described is available, tendon force can be calculated as torque/moment arm (7, 11). For the QF, O’Brien et al. (3) took into consideration that the patellar is not a frictionless pulley and accounted for force transmission from the QF to the tibia. Persad et al. (42) described a method for measuring gracilis tendon force directly using a buckle force transducer intraoperatively. This highly invasive approach offers the distinct advantage of avoiding any need for correction due to forces produced by other muscles and/or passive structures, as well as eliminating the need for moment arm measurement. However, its invasiveness makes replication difficult.

Muscle architecture measurements.

Optimal fiber length can be calculated through muscle excursion measurement, i.e., FWHM (half width at half maximum) divided by 0.68 (43). However, this measurement requires multiple measurements at different joint positions. An alternative approach is using a long ultrasound probe to record and image the muscle during MVC at the same joint angle as torque is measured. Fascicle length is then measured between proximal and distal insertion points (3). Muscle pennation angle (θ) is measured as well.

PCSA calculation.

PCSA is calculated using the standard formula PCSA = (Muscle Volume/Fiber length) × cos (θ) (3, 11, 24).

Specific tension calculation.

Specific tension is calculated as ST = Tendon force/PCSA (in units of N/cm²). Note that even when ST is provided in units of N/cm², it is critical to understand the source of both the force and the area measurement.

DATA AVAILABILITY

Data will be made available upon reasonable request.

GRANTS

This work was supported by NIH Grant P2CHD101899 (to R.L.L.) and US Department of Veterans Affairs Grants I01 RX002462 and IK6 RX003351 (to R.L.L.).

DISCLOSURES

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

AUTHOR CONTRIBUTIONS

L.S.P., K.R.K., and R.L.L. conceived and designed research; L.S.P., Z.W., and P.A.P. performed experiments; L.S.P., Z.W., P.A.P., B.I.B.-M, K.R.K., and R.L.L. analyzed data; L.S.P., Z.W., B.I.B.-M., K.R.K., and R.L.L. interpreted results of experiments; L.S.P., Z.W., K.R.K., and R.L.L. prepared figures; L.S.P., K.R.K., and R.L.L. drafted manuscript; L.S.P., Z.W., P.A.P., B.I.B.-M., K.R.K., and R.L.L. edited and revised manuscript; L.S.P., Z.W., B.I.B.-M., K.R.K., and R.L.L. approved final version of manuscript.