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Tibialis Anterior Moment Arm: Effects of Measurement Errors and Assumptions


Medicine & Science in Sports & Exercise: February 2015 - Volume 47 - Issue 2 - p 428–439
doi: 10.1249/MSS.0000000000000399
SPECIAL COMMUNICATIONS: Methodological Advances

ABSTRACT Accurate estimates of tibialis anterior (TA) muscle force are important in many contexts. Two approaches commonly used to estimate moment arms are the tendon excursion (TE) and geometric (GEO) methods. Previous studies report poor agreement between the two approaches.

Purpose: The purposes of this study were to 1) assess the effect of methodological variations in the two methods of moment arm estimation and 2) determine how these variations affect agreement between the methods.

Methods: TA moment arms were determined using TE and GEO. Errors associated with tendon stretch/hysteresis, talus rotation relative to the foot, and the location of the line of action were investigated.

Results: For TE, large errors in moment arm estimates across the range of motion were found when tendon length changes (P = 0.001) were not corrected for. For GEO, the estimated moment arm was reduced at an ankle angle of -15° when discrepancies between talus and foot rotations were accounted for or when an alternative tendon line of action was used either separately (effect size (ES), 0.46 and 0.58, respectively; P > 0.05) or together (ES, 0.89; P > 0.05). TE-derived moment arms were smaller than GEO-derived moment arms (ES, 0.68–4.86, varying by angle) before accounting for sources of error. However, these differences decreased after error correction (ES, 0.09–1.20, P > 0.05). Nonetheless, the shape of the moment arm–joint angle relation was curvilinear for TE but linear for GEO.

Conclusions: Of all methodological modifications, accounting for tendon length changes had the largest effect on TA moment arm estimates. We conclude that the TE method is viable to determine TA moment arms as long as changes in tendon length are accounted for.

1Centre for Sports Medicine and Human Performance, Brunel University, London, UNITED KINGDOM;

2London Sport Institute, Middlesex University, London, UNITED KINGDOM; and

3Centre for Exercise and Sports Science Research, School of Exercise and Health Sciences, Edith Cowan University, AUSTRALIA

Address for correspondence: Thomas Korff, Ph.D., Centre for Sports Medicine and Human Performance, Heinz Wolff Building HW200, Brunel University, Uxbridge UB8 3PH, United Kingdom; E-mail:

Submitted for publication December 2013.

Accepted for publication May 2014.

The muscle–tendon unit (MTU) moment arm is an important factor influencing the external transfer of internal force and thus influences joint torque magnitudes, joint excursion ranges, movement velocity, and movement (especially locomotor) economy. Knowledge of its magnitude is a prerequisite for the estimation of muscle forces from joint moment measurements (4), which is commonly required in musculoskeletal models (8) or in the quantification of MTU characteristics (28,36). Precise measurement of moment arms is essential because small variations introduced by measurement error (1) or by the scaling of generic models based on anthropometry (14,38) can significantly affect muscle force estimates.

The tibialis anterior (TA) muscle is the largest muscle in the anterior compartment of the lower leg, accounting for over 60% of dorsiflexor volume (16) and plays an important role in human movement (10). The TA’s principal function is to dorsiflex the foot, but it also provides assistance during inversion due to its tendon inserting on the medial cuneiform and first metatarsal (7). The TA is important in locomotion where it controls foot drop during heel strike and foot lift during the swing phase to prevent tripping (9). The TA’s activation magnitude and timing can be varied to adapt to varying gait conditions, including those relating to changes in step rate and length (12), footwear (34), and inclination (incline and decline) (23) as well as treadmill use compared with overground gait (24). Because these conditions influence TA activation, they also influence the force it develops and its role during gait. Importantly, the loading of TA has been suggested to be a determining factor in the walk-to-run transition speed (3,19), and the work performed by the TA has been proposed to play a causal role in disabling conditions such as chronic anterior compartment syndrome (5). Previous investigations into the role of TA have predominantly used EMG. To fully understand the role of the TA during movement or disabling conditions, accurate estimates of its force output are vital. Within this context, the accurate knowledge of the TA moment arm is an essential prerequisite.

Two techniques commonly used to obtain the TA moment arm are the tendon excursion (TE) (29,41) and the geometric methods (GEO) (27). The TE method is based on the principle of virtual work, where moment arm is estimated as the derivative of MTU length with respect to joint angle during passive joint rotation. It has been used in cadaveric studies (22,41) and, more recently, in conjunction with in vivo ultrasound imaging techniques (21,29). In contrast, the GEO method estimates the moment arm as the perpendicular distance between the MTU line of action and the corresponding joint center of rotation (COR), with the COR determined using the Reuleaux and Kennedy (35) graphical method. The GEO method is commonly used with magnetic resonance imaging (MRI) or x-ray imaging techniques, which allow clear visualization of the relevant tendon and bony joint structures (27).

Both methods are subject to important assumptions, however, which may introduce error into the moment arm estimates. For the TE method, the work performed by the MTU (force × [DELTA]length) is assumed to be equal to the work performed by the joint (moment × [DELTA]angle). The moment arm, which is traditionally presented as the ratio between joint moment and MTU force, can then be calculated as the ratio of MTU length change to joint angle change (i.e., moment arm = moment/force = [DELTA]length/[DELTA]angle). Previous studies have tracked the muscle–tendon junction (MTJ) or the aponeurosis–muscle fascicle intersection using ultrasound imaging during joint rotation (21,27). In doing so, only the change in length of the MTU proximal to the point being tracked is included in the calculation of MTU moment arm. However, the change in length of the TA tendon (distal to the MTJ) can contribute up to 45% to MTU length change during passive joint rotation (18). Consequently, the moment arm estimated using MTJ displacement could be nearly half that when estimated using MTU length change. In addition to the method used to account for MTU length change, the movement direction (i.e., plantar- vs dorsiflexion) could also affect moment arm estimates. The reason for this is that force levels within the muscle and tendon can vary differently between MTU shortening and lengthening because of different mechanical properties (e.g., hysteresis) of the muscle and tendon (33,42). Therefore, a difference between muscle lengthening and shortening would be recorded for a given joint angle change when tracking the MTJ. This variation would result in different moment arm estimates. Thus, both the choice of the method of tracking MTU length changes (i.e., muscle or muscle and tendon) and the choice of joint rotation direction are likely to influence TA moment arm estimates.

For the GEO method, the COR is located using the Reuleaux and Kennedy (35) method, in which the movement of a segment (typically the talus for the ankle joint COR) is tracked between two angular positions equidistant from either side of the angle of interest. In practice, these two joint positions are typically defined by the angle enclosed by the sole of the foot and the lower leg (subsequently referred to as “foot angle”) (27,37). Thus, the assumption that foot angle change is reflective of talus angle change is made. However, this has been shown not to be the case because talus rotation is nonlinearly related to foot rotation (11,26,39). This could lead to errors in COR estimation and, therefore, the TA moment arm. A second methodological issue within the GEO method relates to the location of the line of action of the TA. In previous studies, the line of action was assumed to be a line connecting the most proximal and distal points of the extensor retinaculum (27,37). However, because the TA tendon inserts onto the foot and thus exerts its force anteriorly to the retinaculum, the line of action would be more accurately obtained at the tendon’s insertion onto the foot (i.e., a line bisecting the tendon at the insertion into the first metatarsal). These two lines of action (retinaculum and insertion) are not likely to be similar because the path of the tendon passes anteriorly to the ankle’s joint center and curves over the foot, thus changing its path (i.e., line of action) before insertion on the medial cuneiform and first metatarsal bones (7).

The individual and combined effects of these potential sources of error (i.e., rotation direction and tendon length change for the TE method and talus rotation and line of action location for the GEO method) on both the estimated moment arm and the agreement between the two methods (i.e., TE and GEO methods) have not been investigated. Given this, the first aim of the present study was to examine the potential effect of different methodological approaches to both TE- and GEO-based moment arm estimates. Regarding the TE methods, we assessed how the direction of passive ankle rotation (plantar- vs dorsiflexion) would affect TA moment arm estimates and whether these estimates would be dependent upon how MTU shortening is modeled (i.e., muscle alone vs whole MTU length change). Regarding the GEO method, we determined whether the procedure used to determine the COR (foot angle change vs talus angle change) and the method of modeling the tendon line of action (retinaculum vs tendon insertion) would affect TA moment arm estimates. The second aim of this study was to examine the effect of the different methodological approaches on agreement between moment arms obtained from TE and GEO methods.

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Eight adults (seven men and one woman) who were free from musculoskeletal injury gave their written informed consent and volunteered for the study (age, 28 ± 4 yr; height, 1.81 ± 0.06 m; mass, 1 ± 9.3 kg; mean ± SD). Ethics approval was granted by the Brunel University Ethics Committee, and all procedures were conducted in accordance with the Declaration of Helsinki.

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Testing overview.

The participants reported to the laboratory on two separate days (TE and GEO testing were performed separately) at least 1 wk apart and at the same time of day. All participants abstained from exercise for 48 h before testing. Before the testing days, each participant went through a familiarization session in which the methods involved in both the TE and GEO testing protocols were extensively practiced.

On both testing days, each participant performed three submaximal isometric contractions (at 50%, 75%, and 90% of perceived maximum voluntary effort) and five maximal contractions of both the plantar- and dorsiflexors (foot in the neutral position and the knee straight, 0°). This was done to precondition the respective tendons (32) to minimize changes in tendon stiffness and muscle thixotropy (2) during the testing. Before TE measurements, participants were also refamiliarized with the passive ankle rotation maneuver (see section below) by slowly rotating the ankle through its full range of motion (ROM).

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TE method.

The participants were positioned in an isokinetic dynamometer (Biodex System 3; Biodex Medical Systems, Inc., Shirley, NY) so that the lateral malleolus was aligned with the COR of the dynamometer and the relative knee and hip angles in the sagittal plane were at 0° and 85°, respectively (0° being full extension). Hook-and-loop straps were securely fastened over the metatarsals to prevent movement of the foot relative to the footplate, and straps were placed tightly across the thigh, torso, and waist to limit movement of the upper body, leg, and ankle joint. A foot angle of 0° was taken as neutral (taken when the sole of the foot was perpendicular to the tibia), with plantarflexion being a positive angle and dorsiflexion being negative. Each participant’s full ROM was determined and used as the ROM during testing. The ankle was then rotated passively at 20° per second through its ROM for three consecutive rotations (start and finish in dorsiflexion); the three consecutive rotations accounted for one test. A 10-MHz, 50-mm linear-array, B-mode ultrasound probe (Megas GPX; Esaote, Genova, Italy) was housed in a custom-made foam case and strapped to the anterior lower leg in line with the TA tendon–aponeurosis complex to track the MTJ during the passive ankle rotations (Fig. 1). An electroconductive gel was placed on the surface of the probe before fixation to aid acoustic contact, with a thin echo-absorbent strip being placed on the skin under the probe to allow for any potential probe movement to be accounted for; corrections were achieved during the digitization procedure by tracking the MTJ displacement relative to the shadow produced by the echo-absorbent strip. The ultrasound images were continuously recorded to a VHS tape at 25 Hz and synchronized with the dynamometer-derived joint angle data using a 5-V electrical trigger (model DS7A stimulator; Digitimer, Hertfordshire, United Kingdom). The joint angle data underwent analog-to-digital conversion at 1000 Hz and were captured using Spike 2 software (version 5; CED, Cambridge, United Kingdom).



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Processing methods (TE).

Displacement of the MTJ ([DELTA]MTJ) was derived by manual digitization across all frames (50 Hz, Peak Motus; Peak Performance Technologies Inc., Colorado) and the data were low-pass–filtered with a sixth-order, zero-lag, Butterworth filter with a 1-Hz cutoff frequency. This filter was chosen on the basis of the knowledge of the movement frequency being approximately 0.17 Hz, with analysis of the power density spectrum supporting this. Joint angle data were filtered using a 14-Hz low-pass, fourth-order, zero-lag Butterworth filter after a residual analysis. For each test, [DELTA]MTJ was numerically differentiated with respect to joint angle ([theta]) through the ROM, over which constant angular velocity was achieved. The moment arm was calculated using plantar- and dorsiflexion rotations separately with differentiation being performed over a 2° angle range. Both ankle rotation directions were analyzed to examine the potentially different effects of muscle and tendon stretch and hysteresis (41). The moment arm values from all three rotations of the same direction (i.e., plantar- or dorsiflexion) were combined, and a second-order polynomial was fitted to the moment arm–joint angle data to allow calculation of the moment arm at each angle. Moment arms derived using the TE method were named using the direction of rotation, i.e., TEPF or TEDF, for moment arms derived using plantar- or dorsiflexion rotations, respectively. Intraexperimenter reliability (digitization of ultrasound video and subsequent processing of same data three times) of the digitizing procedure was high (coefficient of variation (CV), 7.4%, 1.0%, 2.1%, and 2.0% for 30°, 15°, 0°, and -15°, respectively).

Previously, Fath et al. (15) fitted both second- and third-order polynomials to the [DELTA]MTJ–[theta] data and then differentiated these to estimate the Achilles tendon moment arm. During preliminary analysis, this method was found to not be suitable for the full ROM. The direction of the third-order polynomial, and thus the resultant second-order polynomial, was highly dependent upon the data at the end-ROM; Fath et al. (15) focused their analysis of the moment arm on the neutral (0°) joint position. The second-order polynomial was not fitted to the [DELTA]MTJ–[theta] data because differentiating this would result in a linear moment arm–angle relation; previous research has shown the moment arm–angle relation to be nonlinear for the TA (21,27,41). Furthermore, differentiation ranges up to 30° have been used for estimation of the moment arm using the TE method (21,27). During preliminary analysis, although differences in estimated moment arms were less than 3 mm (maximum difference between differentiation ranges for n = 8) when differentiation ranges of 2°, 4°, 10°, 20°, and 30° were used, the intra- (three tests where participants remained seated in the dynamometer and the ultrasound probe remained in place) and intertest (three tests where the participant was removed from the dynamometer and the ultrasound probe was removed before each repeat test) reliabilities were improved when the smaller ranges were used. Thus, a 2° differentiation range was used for the TE method for the main analysis.

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Tendon elongation.

In previous studies in which the TE method was used in vivo, the change in position of the TA MTJ was differentiated with respect to foot angle (21,27), allowing the authors to only account for length change proximal to this point. Therefore, an error in the estimated moment arm would occur, if a tendon length change was present during the passive rotation. The change in tendon length was therefore calculated in the present study by subtracting the change in muscle length (measured from the ultrasound images) from the change in MTU length (measured from MRI scans, described in a later section and shown in Fig. 1). Because the proximal insertion point of the MTU did not move during testing, any change in MTU length would be caused by rotation of the ankle. Using the MRI scans and a DICOM viewer (OsiriX version 3.7.1), the tendon was tracked through three-dimensional space from the most distal insertion point on the medial cuneiform and first metatarsal bones to 5 cm proximal to the distal head of the tibia (located in the MRI slice in which the TA tendon passed anterior to the tibia head) (Fig. 1) at each joint position. The change in length of the tendon across successive joint rotations was accepted as the change in MTU length due to ankle rotation. Muscle length change can be considered equal to the change in MTJ position recorded from the ultrasound because the distal end of the muscle moves during ankle rotation while the proximal end of the muscle is directly fixed to the stationary tibia. The change in tendon length was calculated by subtracting the change in muscle length from the change in MTU length for each 15° rotation (Fig. 1). The moment arm was then estimated using the TE method using the change in MTU length instead of the change in MTJ position to correct for potential changes in tendon length (TE corrected (TECORR)).

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Geometric method.

For the GEO method, MRI scans of the ankle joint were taken as described by Fath et al. (15). The participant rested supine within the MRI scanner (Magnetom Trio syngo MR 2004A; Siemens, Erlangen, Germany). Localizing scans were performed to determine the orientation of the lower leg before sagittal plane images (TR, 600 ms; TE, 12 ms; three excitations, 300-mm field of view, 2-mm slice thickness, 25 slices) of the foot, ankle, and lower leg were taken. The foot was securely strapped to specifically shaped wooden blocks that ensured the ankle joint was held at the required foot angle, with scans being taken at 15° increments from 45° (plantarflexion) to -30° (dorsiflexion) to allow for the moment arm to be calculated at 30°, 15°, 0°, and -15°. All procedures and analyses for the GEO were located in two dimensions in the sagittal plane.

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Processing methods (GEO).

Moment arm calculation involved two stages: 1) determining the location of the COR using the GEO presented by Reuleaux and Kennedy (35) and 2) measuring the perpendicular distance between the COR and the line of action of the tendon (15,29). All processing was performed using a DICOM viewer (OsiriX version 3.7.1) and a custom MATLAB program (version R2011b; MathWorks).

Changes in position of the talus from 45° to 15°, 30° to 0°, 15° to 15°, and 0° to 30° were used to calculate the COR for 30°, 15°, 0°, and -15° joint angles, respectively. The tibia was assumed to be the stationary segment, with the rotation of the talus representing the rotation of the foot. One point was placed anteriorly (T1) and one point posteriorly (T2) to the talus in the neutral image. The talus outline and points were then traced and superimposed onto all subsequent images. The coordinates (assigned by the OsiriX software) of these points (T1 and T2 for all angles) were then exported into MATLAB where the COR was calculated. The perpendicular bisector of the two T1 points from the foot position 15° of either side of the ankle angle of interest was calculated geometrically. This was repeated for the two T2 points, with the point at which these two perpendicular bisectors met being taken as the COR. Here, we used the foot angle to create the angular distances, and subsequently to model the talus rotation, in line with previous studies (27,37). Because foot rotation and talus rotation may not be synonymous (11,26,39), a second approach was also used (see later section).

The TA tendon travels along a curved path anterior to the ankle. As such, the true line of action of the TA tendon force can be difficult to determine. To maintain consistency with previous studies (30,37), the action line of the TA was modeled as a straight line connecting the proximal and distal points on the tendon slice at the retinaculum. The perpendicular distance (calculated geometrically using the coordinates of the COR and the two points locating the tendon line of action) from the TA action line that passed through the COR was recorded as the moment arm. Processing of data at each angle was performed three times, with the mean being taken as the moment arm (GEO retinaculum (GEORET)). The mean ± SD CV across participants for each angle were 6.2% ± 3.2%, 3.6% ± 1.6%, 4.9% ± 4.1%, and 3.3% ± 2.1% for 30°, 15°, 0°, and -15°, respectively.

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Talus versus foot rotation.

An important assumption underlying the use of the GEO method is that the magnitude of foot rotation is synonymous with talus rotation, which may not be accurate (11,26,39). The rotation of the talus was therefore examined in relation to the change in foot angle by measuring the angle between the line connecting T1 and T2 (Fig. 1) for successive 15° foot rotations relative to the tibia. This was repeated three times for each rotation, with the mean being used for analysis (mean ± SD CV across participants for each rotation was 8.2% ± 5.0%, 6.5% ± 3.7%, 5.2% ± 2.1%, 6.4% ± 2.5%, and 8.8% ± 4.8% for the 45°–30°, 30°–15°, 15°–0°, 0°–15°, and -15° to 30° rotations, respectively). To assess the effect that a discrepancy between the talus rotation and foot rotation has on the estimated moment arm, the GEORET method calculations were repeated using the change in talus angle instead of change in foot angle (retinaculum line of action with talus correction (GEORET,TAL)) to determine COR. Because MRI scans were only taken at 15° foot angle increments, a second-order polynomial was fitted to the coordinates of T1 and T2 against talus angle (R2 (mean ± SD) = 0.99 ± 0.02 and 0.98 ± 0.04 for T1 and T2, respectively). These curves were then used to determine the location of the talus markers at any talus angle. The COR at 30°, 15°, 0°, and -15° ankle angles were then calculated (Reuleaux method (35); see previous discussion) using the rotation of T1 and T2 from the talus position at 15° of either side of the talus angle at the ankle angle of interest. Using this new COR, the moment arm was then calculated, as previously discussed, using the straight line connecting the proximal and distal points on the tendon slice at the retinaculum. This was performed three times for each moment arm estimation, with mean ± SD CV across participants for each angle of 3.7% ± 2.2%, 2.5% ± 1.2%, 2.4% ± 1.4%, and 2.0% ± 1.3% for 30°, 15°, 0°, and -15°, respectively.

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Tendon line of action.

As presented previously, the line of action of the TA tendon force was estimated from the point at which the tendon passes under the extensor retinaculum. In fact, the TA tendon curves anteriorly past the ankle and, therefore, the point at which the tendon passes under the extensor retinaculum may not be valid for representing the line of action of the TA tendon force applied to the foot. We therefore investigated the effect on the estimated moment arm of using a line of action taken near the insertion of the tendon on the foot. For this purpose, the centroid of the tendon slice was manually located within the three MRI slices proximal to the slice in which the insertion first became observed (see Fig. 1 for an example of tendon slices). This resulted in the mean ± SD tendon segment lengths (distances between the centroid of the tendon within the first and third MRI slice used) being 18.4 ± 5.9, 17.0 ± 5.6, 17.7 ± 4.7, and 16.8 ±3.9 mm for the 30°, 15°, 0°, and -15° foot angles, respectively. A linear fit was applied to the two-dimensional coordinates (sagittal plane) of the centroids from the three MRI slices, which acted as the new line of action. The moment arm was geometrically calculated as the perpendicular distance between the new line of action and the COR using either the COR estimated using the original method (GEO insertion (GEOINS)) or the talus correction method (TAL insertion (GEOINS,TAL)). This was performed three times for each moment arm estimation, with mean ± SD CV across participants for each angle of 7.1% ± 2.8%, 5.0% ± 2.5%, 6.0% ± 4.1%, and 3.0% ± 1.8% for GEOINS and 4.9% ± 3.3%, 3.0% ± 1.8%, 3.8% ± 2.4%, and 2.7% ± 1.8% for GEOINS,TAL for 30°, 15°, 0°, and -15°, respectively.

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Statistical analysis.

The effect of rotation direction on moment arm estimate using the TE method (i.e., TEPF vs TEDF) was analyzed using a two-way ANOVA with repeated measures (2 × 4; direction × angle). Least significant difference post hoc pairwise comparisons were used at each angle after a significant interaction.

The difference in change in length of the muscle and tendon was assessed using a 2 × 5 (tissue × angle) repeated-measures ANOVA. Planned repeated comparisons were performed after a significant interaction effect to locate the angle ranges in which length change differed between the muscle and tendon. To determine the joint range over which the muscle and tendon were lengthening, a one-way repeated-measures ANOVA was performed for each tissue, with repeated planned comparisons being used to establish over which range the length change was occurring.

Differences between foot rotation (set to 15° using wooden blocks) and talus rotation were assessed using a one-sample t-test for each rotation. Consistency of talus rotation across the ROM, which is required for the Reuleaux method (35), was assessed using a one-way repeated-measures ANOVA. Planned repeated comparisons comparing talus rotations over consecutive 15° ankle rotations were performed.

To assess the effect of different methodological approaches to the TE method on moment arm estimations, a two-way ANOVA (3 × 4; method × angle) was used. The uncorrected moment arms were derived from the dorsiflexion and the plantarflexion directions separately, which were compared with the TECORR method. For the GEO method, the effect of different methodological approaches was assessed using a two-way ANOVA (4 × 4; method × angle). The individual and combined effects of accounting for talus rotation and the alternative location of the line of action were assessed for the GEO method. Significant interactions within the two-way ANOVA were followed up with Bonferroni corrected one-way ANOVA at each of the four angles. Significant main effects of method within either the two-way (if interaction was not significant) or one-way ANOVA were followed up with simple planned comparisons between moment arm estimates before and after accounting for the individual assumptions, i.e., TEPF versus TECORR and TEDF versus TECORR for the TE approach, and GEORET versus GEORET,TAL, GEORET versus GEOINS and GEORET versus GEOINS,TAL for the GEO approach.

A two-way ANOVA with repeated measures (5 × 4; method × angle) was used to investigate the effect of the assumptions on the agreement between TE and GEO moment arm estimates. Follow-up analyses were similar to that previously discussed, with Bonferroni-corrected one-way ANOVA at each angle. Simple planned comparisons (TEPF vs GEORET, TEDF vs GEORET, TECORR vs GEOINS,TAL) were performed after a significant main effect of method within either the two-way (if interaction was not significant) or one-way ANOVA. The consistency between the TE and GEO methods before and after accounting for the individual assumptions was assessed using a two-way random intraclass correlation with absolute agreement (43).

Effect sizes (ES) were calculated using Cohen d. The pooled SD was used as the standardizer, being calculated as the square root of the mean variances (13). The Greenhouse–Geisser correction was used in some instances where the assumption of sphericity was violated within the ANOVA (assessed using the Mauchly test of sphericity). Statistical significance was accepted at P < 0.05. Data are presented as mean ± SD.

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TE Method

Effect of direction of ankle rotation.

A significant interaction of rotation direction (TEPF vs TEDF) and angle was evident (interaction effect, P = 0.047), with moment arm estimates being similar at 30° (P = 0.27), 15° (P = 0.49), and 0° (P = 0.41) between TEPF and TEDF, but moment arms obtained using TEPF were larger than those obtained using TEDF at -15° (ES, 0.84; P = 0.045). Both TEPF and TEDF were used for subsequent comparison with TECORR and GEOINS,TAL because of this difference in estimated moment arms.

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Tendon length change.

The TA muscle and tendon both lengthened as the ankle was plantarflexed. However, most of this length change occurred in the muscle (Fig. 2). Specifically, muscle length increases were greater than the tendon for the -15° to 0° (ES, 4.6, P < 0.001), 0°–15° (ES, 4.7; P < 0.001), and 15°–30° (ES, 1.3; P = 0.1) rotations. Toward the end of the rotation (30°–45°), more of the increase in MTU length was taken up by the tendon (ES, 1.2; P = 0.09). As such, measurement of MTJ displacement was not considered to be a valid representation of the displacement of the tendon insertion.



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Geometric Method

Talus rotation.

Talus rotation was not consistent across the 15° ankle rotation increments (P = 0.042) and was always less than 15° (P < 0.05). Although differences between successive rotations were not significantly different (planned repeated comparisons), moderate-to-large ES were calculated between the -30° to 15° and -15° to 0° (ES, 0.65; P = 0.28), 0°–15° and 15°–30° (ES, 0.83; P = 0.16), and the 15°–30° and 30°–45° (ES, 0.99; P = 0.096) rotations (Fig. 3). Therefore, the change in angle between the sole of the foot and the tibia shaft (i.e., foot angle) cannot be used to represent the change in the talocrural joint angle (i.e., talus rotation).



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Agreement between TE and GEO Methods and the Effect of Different Methodological Approaches

Accounting for each of the three methodological variations (tendon length change, TECORR; talus rotation, GEORET,TAL; location of the line of action, GEOINS) had different effects on the estimated moment arm (Fig. 4). For the TE method, estimates of moment arm after accounting for tendon length changes (TECORR) were larger than moment arm estimates using either TEPF or TEDF (P = 0.001 for both). The effect of accounting for tendon lengthening was similar for TEPF and TEDF at 30°, 15°, and 0° but not at -15° where there was a larger effect for TEDF compared with that for TEPF (ES, 1.02 and 0.20, respectively) (Fig. 4), although this interaction effect did not reach significance (P = 0.051).



Accounting for either talus rotation (GEORET,TAL), an alternative line of action (GEOINS) or both (GEOINS,TAL) within the GEO approach did not significantly alter the moment arm estimates (main effect, P = 0.48; interaction effect, P = 0.15). However, estimates made at -15° did produce moderate-to-large ES when sources of error were accounted for. Specifically, moment arm estimates were smaller after accounting for talus rotation an alternative line of action, or both at -15° (ES, 0.46, 0.58, and 0.89, respectively) (Fig. 4).

Agreement between TE and GEO was assessed before (i.e., TEPF vs GEORET and TEDF vs GEORET) and after (i.e., TECORR vs GEOINS,TAL), accounting for assumptions. Before accounting for assumptions, agreement was poor at 30°, 15°, and -15° when either TEPF or TEDF was compared with GEORET (Fig. 5). At 0°, although differences between the uncorrected TE and GEO methods were not significant, moderate-to-large ES were calculated (0.68, P = 0.20; 0.92, P = 0.11; for TEPF vs GEORET and TEDF vs GEORET, respectively). After correction for the three assumptions, agreement was good between TECORR and GEOINS,TAL for -15° (P = 0.80), 0° (P = 0.46), and 15° (P = 0.61), although a large effect was seen at 30° (ES, 1.20; P = 0.052). There was an improvement in agreement between TE- and GEO-derived moment arms at all angles after all assumptions had been accounted for (Fig. 5). However, despite the reduction in the magnitude of difference between the TE and GEO methods after assumption correction, the consistency (two-way random ICC with absolute agreement) between the TE and GEO methodologies was still poor for each angle (Table 1).





Although no significant differences were seen between TECORR and GEOINS,TAL, visual inspection of the two curves (Fig. 5) shows differences in the relation between moment arm and ankle angle. To assess the nature of this, each participant’s individual moment arm–joint angle data set was fitted with both a linear and second-order polynomial. The root mean square of the percentage difference (%RMSdiff) between the linear and second-order polynomials was then calculated for TECORR and GEOINS,TAL, with a paired t-test being used to compare between the two methods. The use of a second-order polynomial improved the curve fit more for TECORR than for GEOINS,TAL (ES, 1.00; P = 0.094). This indicates that the relation between moment arm and ankle angle is more curvilinear when the moment arm is estimated using TECORR compared with GEOINS,TAL.

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The first purpose of the present study was to determine the potential effect of different methodological approaches to the TE and GEO methods on TA moment arm estimations. With regard to the TE method, we assessed the effect of movement direction and the effect of accounting for tendon length changes during the passive ankle rotation. TA moment arm estimations were larger at the most dorsiflexed position when the plantarflexion rotation was used compared with that when the dorsiflexion rotation was used. In this condition, muscle length changes were assumed to be indicative of MTU length changes. However, MTU length changes (which are determined by changes in joint angle) were the same across both movement directions. Together, these results imply that differences in muscle length change between the rotation directions occurred simultaneously with differences in tendon lengthening. While the muscle consists predominantly of the aponeurosis and fascicles, the TA aponeurosis does not change length during a passive rotation (42). As such, the greater muscle length change during the plantarflexion rotation is likely due to a greater reduction in fascicle stiffness compared with tendon stiffness after the stretch caused by the plantarflexion rotation. Support for this suggestion comes from Morse et al. (33) who showed that stiffness of the fascicles is reduced after a prolonged stretch whereas tendon stiffness is not significantly affected. Therefore, the larger TA moment arm estimated using the plantarflexion rotation compared with the dorsiflexion rotation is likely due to a greater hysteresis within the muscle fascicles compared with that in the tendon.

The second methodological issue within the TE methodology that we examined was how moment arm estimations would change when changes in tendon length were accounted for. In the current study, as in previous studies (e.g., 21,27), the MTJ displacement was tracked to estimate MTU length change when using TE. However, this allows only the change in length of tissues proximal to this point (i.e., the muscle belly) to be measured and neglects any potential tendon lengthening (18). Indeed, we found a significant tendon elongation during the passive joint rotations, which is consistent with results from the study of Herbert et al. (18). Accordingly, TA moment arms were approximately 40% larger when tendon length was accounted for compared with that in the uncorrected method.

When the TE method has been used in cadaveric studies, the tendon was commonly loaded with a constant tension during the joint rotation (6,20,40). Because the load was constant, the tendon would not likely have elongated during the joint rotation. However, using the present in vivo methodology, the rotating segment pulls on the tendon, causing a stretch of increasing magnitude (Fig. 2). Ito et al. (21) used the TE method both without muscle activation and while the participants contracted at 30% and 60% MVC. Interestingly, the moment arms reported by Ito et al. (21) in the passive condition were smaller than the uncorrected moment arms (i.e., TEPF and TEDF) in the present study, whereas the moment arms reported during the active rotations within the study of Ito et al. (21) are very similar (particularly at 30°, 15°, and 0°) to our moment arms that took tendon elongation into consideration (i.e., TECORR). This indicates that moment arms in the experiment of Ito et al. (21) were only similar to our TECORR estimates when the tendon was elongated by loading and therefore less likely to elongate during joint rotation. Although some of this change could be attributed to a straightening of the tendon during loading (21), which would have increased the tendon’s distance from the joint COR, tendon loading might be a useful strategy to minimize the effects of tendon lengthening during joint rotation. It would therefore be interesting to examine the validity and reliability of moment arm estimations obtained during constant muscular contractions in the future.

Of all the methodological variations investigated within the current study, the incorporation of tendon length change into the TE method had the greatest effect on moment arm estimations. Therefore, tendon length change should be taken into account when using the TE method to estimate TA moment arms. Acknowledging that this can be experimentally difficult, we developed a regression equation to predict differences in corrected versus uncorrected moment arm as a function of ankle angle. The mean differences in estimated moment arms between the corrected and uncorrected TE approaches were modeled using a second-order polynomial (see Fig. 4 legend for equations). Although our R2 values indicate a very good fit, caution should be taken when using the equation because interindividual differences in muscle–tendon dimensions and mechanical properties exist.

With regard to the GEO method, we assessed whether change in foot angle was indicative of the change in talus angle andwhether the method of modeling the tendon line of action would affect moment arm estimates. We found that talus rotation was not indicative of foot rotation. Previously, a nonlinear relation between talus and foot rotation has been reported in cadaveric (11,39) and in vivo (26) studies. We have found that for a given foot angular displacement, talus angular displacement was noticeably smaller. Importantly, talus rotation per degree of foot rotation was not consistent across the ROM (Fig. 3). When this discrepancy was accounted for, we found moderate changes in TA estimates at the most dorsiflexed ankle angle. Because the magnitude of rotation of the talus relative to the foot is due to the material properties of ligaments and other tissues (11), the reduced rotation at the end of the ROM is likely due to a greater stiffness within these tissues upon stretch. As such, when using the GEO method to derive TA moment arms, it is advisable to use a constant talus angular displacement around the foot position of interest (as opposed to a constant foot angular displacement).

We also found that for the GEO method, the location of the line of action (i.e., retinaculum vs insertion) affected the moment arm estimates at the most dorsiflexed angle. When the GEO method has been used previously, the TA tendon line of action has been taken as the line bisecting the tendon as it passes under the extensor retinaculum (30,37). However, due to the nonlinear path of the TA tendon between its insertion and its intersection with the extensor retinaculum, this line of action may not be representative of that measured at the insertion, i.e., the point where the force is applied to the foot segment. Indeed, the way the tendon line of action was modeled resulted in moderate-to-large effects in TA moment arm estimates. This was most evident at the more dorsiflexed angle (-15°) where a greater TA tendon curvature is evident because of the more acute angle between the foot and tibia. Although the line of action located at the tendon insertion into the foot seems more appropriate, future studies need to address the validity of this location for representing the TA tendon line of action.

The second aim of this study was to examine the effect of the different methodological approaches on agreement between moment arms obtained from TE and GEO methods. When the uncorrected methodologies were used, the TE-derived moment arms were approximately 27% smaller than GEO-derived moment arms, which is consistent with results from previous studies, which indicated significant differences between moment arms derived from TE and GEO methodologies (15,27,31,44,46).

These method-related discrepancies raise the question of validity. Currently, there is no agreement about which methodology (TE or GEO) is the most valid. One approach to determine validity is to examine the agreement between different methodologies (i.e., convergent validity), with a better agreement suggesting higher degree of validity. Therefore, we examined how the previously mentioned variations in the TE and GEO methodologies would affect the agreement between the two approaches. We found that differences in moment arms between the uncorrected methods largely disappeared when tendon length changes were accounted for within TE, and retinaculum rotation was used with the line of action being modeled at the TA insertion for GEO (Fig. 5). Using the approach of convergent validity, one could argue that the moment arms derived from the corrected methods (TECORR and GEOINS,TAL) yielded more accurate moment arm estimates.

In comparison with previous attempts to measure TA moment arm, variations in values were found between the corrected methods within the current study and both cadaver and in vivo approaches from other studies. Cadaver studies (22,41) using TE have shown a relation between joint angle and moment arm that was opposite to that shown in the current and other in vivo studies (21,27,37) regardless of methodologies used. In addition, moment arm ranges reported in cadaveric studies were similar (41) or slightly smaller (22) than the corrected methods in the current study. However, the moment arm values derived using the corrected approaches within the current study (4.3–3.2 cm; DF–PF) are within the large range of those reported in vivo when either TE or GEO approaches have been used under passive (2.8–4.8 cm; DF–PF) (18,22,31) or active (3.1–6.0 cm; DF–PF) (21,27) conditions. These comparisons suggest that differences exist both between methodologies (i.e., TE vs GEO, passive vs active) and between the sample used (cadaver vs in vivo).

Although accounting for tendon elongation within the TE method had the greatest effect on moment arm estimations, it is important to acknowledge that a lack of accounting for tendon elongation during joint rotation does not fully explain the difference in moment arm magnitudes between the TE and GEO methods reported in the current and previous studies. For example, cadaver studies using both methods have shown variations (6), no difference (40), and larger (20) TE-derived moment arms when compared with GEO-derived moment arms, whereas in vivo TE-derived moment arms have been found to be smaller (15), larger (44,46), or similar (27,31) to those derived using GEO. If tendon elongation in the TE method was the only cause for the reported differences, then TE-derived moment arms would always be smaller than those estimated using the GEO method. The different moment arm estimations that have been observed between the uncorrected TE and GEO methods (i.e., 15,27,31,44,46) are therefore likely due to a combination of the methodological variations addressed within the current study.

These findings demonstrate that accounting for various assumptions significantly affect TA moment arm estimates and the agreement between TE and GEO methods, which has direct implications for future research. In particular, when using the TE method, we recommend accounting for tendon elongation using either direct tendon elongation measurement or using the equation presented in Figure 4. For the GEO methodology, the line of action should be modeled at the tendon insertion, with an equidistant talus angular displacement being used around the ankle angle of interest.

Although moment arm estimates were similar between the TECORR and GEOINS,TAL methods, the shape of the relation between moment arm and ankle angle was different (curvilinear (TECORR) vs linear (GEOINS,TAL)). Rotation of the ankle joint complex occurs simultaneously around the subtalar and talocrural axes (25), neither of which results in rotation strictly in the sagittal plane. As such, the use of a single point to represent COR (used within GEO method) may not be appropriate (45). The TE method does not require estimation of COR and therefore is not susceptible to such errors. A further explanation for the difference in moment arm–joint angle relation between the two methods is that the TECORR method estimates the moment arm in three dimensions, whereas the GEOINS,TAL estimates the moment arm only in two dimensions (sagittal plane). Previously, Hashizume et al. (17) found the GEO-derived Achilles moment arm to change linearly with angle when measured two dimensionally but to have a curvilinear relation with angle when measured in three dimensions (Fig. 4 in reference 17). Unfortunately, Hashizume et al. (17) did not compare the GEO and TE methods because they deemed the TE method to be invalid because of the estimated moment arms being smaller (on the basis of their interpretation of Fath et al. [15]). Interestingly, the estimated three-dimensional geometric moment arms were also smaller than the two-dimensional geometric moment arms in their study (17). Therefore, the TE method (corrected for tendon lengthening, i.e., TECORR) could be more valid than the GEO method for determining the three-dimensional moment arm in vivo, especially when the tendon traverses multiple joints.

The TA muscle plays an important role in a range of human movements (10). However, previous investigations have focused predominantly on the measurement of muscle activation. To fully understand the TA’s role during movement the estimation of its force in vivo is vital. Because in vivo forces during movement are typically derived from joint moments, accurate knowledge of TA moment arms is essential. Thus, results from our study will allow researchers to estimate TA forces more accurately, which in turn may increase our ability to optimize performance (10, 12) or to reduce injury (5,9).

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In summary, we found that TA moment arm estimates were smaller when calculated using the TE method (ultrasound) compared with the GEO method (MRI), although several sources of error affected each method’s estimate of the TA moment arm. Differences between TE- and GEO-derived moment arm estimates were removed after accounting for tendon lengthening in the TE method as well as the talus rotation and line of action errors in the GEO method; these violations should thus be accounted for in future studies. According to the present results, however, the ideal methodology is to measure whole MTU length change in the TE method. If the complex methodologies required for this are not available, the ultrasound-based TE method may be used with a correction factor being applied to account for tendon lengthening.

This study was financially supported by the Headley Court Trust.

The authors report no conflict of interest. The results of the present study do not constitute endorsement by the American College of Sports Medicine.

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