Accurate and reliable estimation of muscle moment arms is a prerequisite for the development of musculoskeletal models. Numerous techniques are available to estimate the Achilles tendon moment arm in vivo. The purposes of this study were 1) to compare in vivo Achilles tendon moment arms obtained using the center of rotation (COR) and tendon excursion (TE) methods and 2) to assess the reliability of each method. For the COR method, magnetic resonance (MR) images from nine participants were obtained at ankle angles of −15°, 0°, and +15° and analyzed using Reuleaux' method. For the TE method, the movement of the gastrocnemius medialis-Achilles tendon junction was recorded using ultrasonography as the ankle was passively rotated through its range of motion. The Achilles tendon moment arm was obtained by differentiation of tendon displacement with respect to ankle angular excursion using seven different differentiation techniques. Moment arms obtained using the COR method were significantly greater than those obtained using the TE method (P < 0.01), but results from both methods were well correlated. The coefficient of determination between moment arms derived from the COR and TE methods was highest when tendon displacement was linearly differentiated over a ±10° interval (R2 = 0.94). The between-measurement coefficient of variation was 3.9% for the COR method and 4.5–9.7% for the TE method, depending on the differentiation technique. The high reliabilities and strong relationship between methods demonstrate that both methods are robust against their limitations. The large absolute between-method differences (∼25–30%) in moment arms have significant implications for their use in musculoskeletal models.
- center of rotation
- tendon excursion
- musculoskeletal model
quantification of human muscle forces in vivo is difficult, because direct measurements are highly invasive (3, 4). Therefore, muscle forces are typically estimated indirectly using biomechanical modeling techniques. One method used to estimate muscle forces is calculation of the ratio of the muscular moment about a joint and the moment arm of the muscle or tendon of interest. A number of techniques can be used to obtain muscle moment arms, including cadaver dissection (6, 7, 11, 27), magnetic resonance (MR) imaging (16, 26), and ultrasound imaging (9, 12–14).
Two of these methods in particular have become popular within the scientific community. The first technique uses sagittal plane two-dimensional MR images to estimate the center of rotation (COR) of a joint (25, 26). The perpendicular distance between the center of the joint and the line of action of the muscle or tendon of interest is then measured directly (16, 18, 26). The second technique is the tendon excursion (TE) method. The principle of virtual work (1, 28) is used to compute the moment arm as the ratio of the linear displacement of the tendon to the angular excursion of the corresponding joint (9, 17, 27). Thus it does not require knowledge of the location of the COR.
The COR and TE methods have advantages and disadvantages. One limitation of the COR method is that the multiple steps of manual MR image processing, required to determine the COR, can introduce errors in the COR calculation and, therefore, in the moment arm estimation (16). Another disadvantage of the COR method is the limited accessibility and relatively high costs involved in using MR scanners. A major advantage of MR imaging, however, is the high visibility of the underlying anatomic structures about the joint. In particular, the line of force can be easily identified. The major advantage of the TE method is that it does not require knowledge of the COR or the line of action of muscle or tendon force. In addition, ultrasonography, which is often easier to access and more time- and cost-efficient than MR scanning, can be used for the TE method. The main limitation of the TE method is the assumption that no internal forces, including friction, act in the joint of interest during a passive rotation (principle of virtual work) (1, 28). Thus it is assumed that active and passive forces within the joint are negligible and that all muscles spanning the joint of interest are inactive.
Lee and Piazza (13) used the TE method to determine in vivo values of Achilles tendon moment arms. The moment arms reported by Lee and Piazza are smaller than those reported by Maganaris et al. (16), who used the COR method. While these differences can have multiple explanations (including the use of participants with different anthropometric characteristics), these findings raise the question whether moment arms obtained using these two methods are comparable. However, to our knowledge, a direct comparison between these two methods has not been made. Therefore, differences in the moment arms reported in the literature cannot incontrovertibly be attributed to methodological differences. The first purpose of the present study was to compare moment arm measures of the Achilles tendon using the COR method (MR imaging) and the TE method (ultrasound imaging).
When scientific measurement techniques are evaluated, the reliability of the dependent measure is another important consideration. Coefficients of variation (CVs) of moment arms obtained using the COR method have been reported to be 7.9% (16, 17). The mean between-day difference in moment arms obtained from the TE method has been reported to be ∼5% (13). Together, these results suggest that moment arms obtained using the TE method are potentially more reliable than those obtained using the COR method. Therefore, the second purpose of this study was to compare the reliabilities of the moment arm measures obtained by the COR method with those obtained by the TE method.
When the TE method is used, the moment arm is obtained by mathematical differentiation of the tendon displacement with respect to the corresponding joint angle. Two methods have been used to perform this differentiation. The first method is to fit a straight line between two tendon displacement values over a given angular displacement (6, 9, 14, 16). The second method is to approximate the relationship between linear tendon and angular joint displacements by means of a second- or third-order polynomial and to perform an analytic differentiation (13, 21). Within the context of the present investigation, we sought to understand how different differentiation methods would influence the relationship between the moment arms obtained from the COR method and those obtained from the TE method and how these methods affect the reliability of the findings. Therefore, we used seven differentiation techniques to estimate the moment arm using the TE method.
Finally, there is some evidence that Achilles tendon moment arms obtained from the TE method might differ depending on the movement direction of the passive rotation during which TE and angular displacement are measured (27). It has been speculated that greater active or passive forces during loading (dorsiflexion rotations) than during unloading (plantarflexion rotations) of the tendon could contribute to these differences. Understanding this potential discrepancy is important for two reasons. 1) The presence of active or passive forces violates the principle of virtual work and could affect the accuracy of the moment arm estimate. 2) Differences in the magnitude of forces during loading and unloading could result in differences in the reliability of moment arm measures obtained during different movement directions. Therefore, we also quantified the reliabilities of moment arms derived from the TE method for two rotational directions (dorsi- and plantarflexion rotations) and their relationship with the moment arms obtained from the COR method. To explain potential effects of movement direction on moment arms, we quantified the moments about the ankle joint arising during passive ankle rotation (since the moment is the direct effect of all passive and active forces) and compared it across rotational positions and movement directions.
For comparison of moment arms derived from the COR and TE methods (purpose 1), nine healthy adults (7 men, 2 women) volunteered to participate in the study. Age, stature, and body mass (means ± SD) were as follows: 31 ± 5 yr, 180 ± 10 cm, and 81 ± 15 kg, respectively. Seven of the nine participants (age = 30 ± 5 yr, stature = 183 ± 5 cm, body mass = 85 ± 13 kg) were tested three times for the COR and TE methods to quantify the reliability of each method (purpose 2). All participants were physically active on a recreational basis and reported no recent lower limb musculoskeletal injuries. The study was approved by the Human Research Ethics Committee of Brunel University. The participants provided written informed consent, and they were made aware of their right to withdraw from the study at any time without penalty.
Experimental protocol: MR imaging.
Participants were asked to lie supine on a wooden board (183 × 49 cm2) placed inside a 3-T MR scanner (Magnetom Trio syngo MR 2004A, Siemens, Erlangen, Germany) with the knee straight and the sole of the foot positioned against a custom-made wooden block, which was attached to the board by six pins and two nonelastic Velcro straps. This wooden block determined the angular position of the ankle joint. Ankle position was altered by attachment of different-shaped blocks to the wooden board. MR images (sagittal scans, TR = 600 ms, TE = 12 ms, 3 excitations, 300-mm field of view, 2-mm slice thickness) were obtained at three ankle positions (expressed as the absolute foot angle): 0° (neutral ankle position; the foot being in a vertical position) and +15° and −15° (plantar- and dorsiflexed positions, respectively). Two nonelastic Velcro straps were used to secure the foot to the wooden block in its transverse plane. One additional Velcro strap was secured around the distal part of the thigh.
Participants were instructed to remain relaxed while in the MR scanner. Before the testing, to precondition the muscle-tendon complex, participants were asked to perform three ramped isometric contractions to up to 50% of their perceived maximum at the neutral ankle angle, as well as three maximal voluntary contractions (19). For the testing, sagittal localizer prescans were used at the level of the malleoli to ensure that the orientation of the talus and the Achilles tendon was similar throughout the three ankle angles of interest (16). The duration of each scan was 147 s, and 25 slices were obtained. After each scan, the next wooden ankle block was inserted for the scanning of the foot at a different ankle angle. The order in which the different blocks were presented to the participants was from a plantar- to a dorsiflexed ankle position. Seven of the nine participants were scanned three times at each angle. Once they were scanned at each of the three angles, 1) the participants were removed from the scanner, 2) the wooden blocks were detached from the board, 3) the board was taken out of the scanner, 4) the set-up was reassembled, and 5) the participant was retested. This procedure was repeated twice (resulting in 3 independent scans at each angle) to determine the interexperiment reliability of the scanning method (purpose 2).
Moment arm calculation using the COR method.
MR images were processed using the iPACS viewer (version 4.230, San Bruno, CA). For every participant, the COR of the ankle joint, the line of action of the force (represented by the orientation of the Achilles tendon), and the Achilles moment arm were determined for the neutral foot position (ankle angle of 0°). A detailed description of this technique has been published previously (16). Briefly, with use of Reuleaux' method (25), the COR at an ankle angle of 0° was assessed using the MR scans obtained at ankle angles of −15° and +15° (Fig. 1). The tibia was assumed to be fixed, and the talus was assumed to be the rotating segment. The outline of the tibia and talus was drawn onto an overhead transparency with the foot in the dorsiflexed position (ankle angle of −15°). Two well-defined anatomic points on the talus (A and B) were chosen. On the basis of the short distance between the points A and B, two straight lines were drawn subtending at a right angle 10 cm proximal to the talus (15, 16). The shape of the tibia was then superimposed onto the image taken at the plantarflexed position (ankle angle of +15°), and the shape of the talus was drawn onto the same transparency. The same two anatomic points of the talus (A′ and B′) in this second position were marked on the initial transparency. Again, points A′ and B′ were extended and drawn 10 cm proximal to the talus using two straight lines subtending at a right angle. The COR was geometrically constructed as the intersection of the perpendicular bisector of lines AA′ and BB′ as illustrated in Fig. 1. The line of force was defined as the line connecting the point of insertion of the Achilles tendon into the calcaneus and the point 6 cm more proximal on the midline of the Achilles tendon. For the definition of this line, the MR image obtained at the neutral foot position (ankle angle of 0°) was used. The moment arm was then measured as the perpendicular distance from the line of force to the COR.
All morphometric measurements were analyzed three times by the same investigator for each MR image, and mean values across the three moment arm measures were taken for further analysis. The CV across all participants for analysis of an image three times (mean ± SD) was 3.3 ± 1.5%. To quantify the reliability of moment arms derived from the COR methods between interexperiment set-ups (purpose 2), the CVs were calculated using the moment arm values obtained from repeated testing as described above (see Moment arm calculation using the COR method).
Experimental protocol: ultrasonography.
Ultrasound imaging was conducted on a separate day, but at the same time of day, as the MR imaging. Participants were seated on an isokinetic dynamometer (System 3, Biodex Medical Systems) with the right ankle securely fixed with Velcro straps to a footplate to prevent heel movement. The knee was fully extended, and the relative hip angle was set to 85°. The center of the lateral malleolus was aligned with the shaft of rotation of the dynamometer. The thigh was securely fixed to the dynamometer seat with nonelastic straps to prevent medial or lateral changes in the orientation of the ankle alignment. To precondition the muscle-tendon complex, participants performed five ramped isometric plantarflexions to up to 50% of their perceived maximum, as well as three maximum voluntary contractions (19). The maximal range of motion of the ankle joint was then determined for each participant by manual rotation of the dynamometer until the participant felt discomfort; for all participants, the limits of the range of motion were greater than −15° and 30° (dorsi- and plantarflexed positions, respectively).
Before the testing, the ankle was passively rotated through its range of motion at a constant velocity of 10°/s to familiarize the participant with the rotation. For the actual test, the ankle was rotated passively through its range of motion five consecutive times: three times from a dorsi- to a plantarflexed position and twice from a plantar- to a dorsiflexed position (Fig. 2). The mechanical concept underlying the TE method is the principle of virtual work (1, 28). To minimize internal forces, we asked our participants to relax their muscles throughout the range of motion.
During the passive rotations, the displacement of the muscle-tendon junction (MTJ) was recorded using B-mode ultrasound with a 10-MHz, 40-mm linear probe (GPX, Esaote Megas, Genoa, Italy). The probe was fixed in a custom-built foam cast, which was aligned smoothly with the skin. A water-based transmission gel was placed between the skin surface and the ultrasound probe to aid acoustic coupling and to avoid skin deformation. Care was taken to align the probe with the movement direction of the MTJ in the sagittal plane. The ultrasound probe was attached to the shank with zinc oxide tape to prevent probe movement.
The same subset of participants that was tested for the reliability of the COR method was tested for the reliability of the TE method. For these participants, the probe was removed and reattached. Before reattachment of the ultrasound probe, any marks left by the gel and the probe were removed to avoid bias in the replacement of the probe. This change in set-up was repeated twice for the purpose of quantifying the reliability of the TE method between three experimental set-ups.
All data were collected using Cortex 1.1.4 software (MotionAnalysis, Santa Rosa, CA) on a personal computer. Raw position and moment data from the isokinetic dynamometer were subjected to analog-to-digital conversion at 1,000 Hz using a 12-bit analog-to-digital card (model PCI-6071E, National Instruments, Austin, TX). Analog ultrasound video data, sampled at 25 Hz, were digitally converted with a digital video recorder (model ADVC55, Grass Valley, Conflans St. Honorine, France) connected via the S-VHS port and saved onto a personal computer as an uncompressed AVI (720 × 576) file. Ultrasound, position, and moment data were synchronized using an electrical trigger (model DS7A stimulator, Digitimer, Hertfordshire, UK).
The MTJ of the gastrocnemius medialis was manually digitized using specialized imaging software (ImageJ, 1.42q, National Institutes of Health) for all three probe placements and five full rotations (3 plantar- and 2 dorsiflexion rotations). Raw TE, raw angular position, and raw moment data were processed in Matlab (version 7.4, MathWorks, Natick, MA). The raw angular position and moment data were filtered using a low-pass digital fourth-order, zero-lag Butterworth filter with cutoff frequencies of 3.75 Hz for angular position and 12.47 Hz for moment. The filtered position data were downsampled to 25 Hz to match the ultrasound data. Pixel coordinates of the raw TE data were converted to millimeters with a conversion factor of 9.2 pixels per millimeter and filtered with a digital low-pass, fourth-order zero-lag Butterworth filter with a cutoff frequency of 2.62 Hz. The cutoff frequencies for the low-pass filters were determined by means of residual analyses (29).
Moment arm calculation using the TE method and determination of moments about the ankle joint.
The moment arm at an ankle angle of 0° was calculated as the first derivative of tendon displacement with respect to ankle angle (Fig. 3). It was obtained using seven different differentiation methods. The slope of the lines connecting the tendon displacement data over five different angular intervals (±1°, ±2°, ±5°, ±10°, and ±15°) was calculated. Because of the relatively low resolution of the tendon displacement data, they were spline-fitted, so that the exact values at the ankle angles of interest could be found. In addition, second- and third-order polynomials were fitted to the tendon displacement data. These polynomials were analytically differentiated at an ankle angle of 0°. These seven different differentiation techniques were performed for each of the three passive plantarflexion and the two passive dorsiflexion rotations. Moment arms were taken as the average across the plantar- and dorsiflexion rotations, respectively, resulting in 14 different conditions (7 differentiation methods × 2 movement directions). To quantify the effect of passive and active forces acting at the joint during the passive rotations, which would violate the virtual work principle, we used data recorded by the isokinetic dynamometer during the passive rotations to measure moments about the ankle joint. These moments were extracted at the ankle angles of +25°, +15°, and +5° (plantarflexed position) and −5° and −15° (dorsiflexed position) for both movement directions and averaged across rotations and participants.
To determine the absolute difference between the moment arms obtained from the two methods, two-tailed paired t-tests (with Bonferroni's correction) were performed. To determine the relationship between the moment arms obtained using the COR and TE methods, 14 Pearson's product-moment correlations and CVs were calculated. These represented the relationship between the moment arms obtained using the COR method and those obtained using each of the 14 variations of the TE method. To quantify the reliability of the moment arm measures between experimental set-ups, we calculated the CV for each participant for each method of determining the moment arm. These CVs were then averaged across participants within each condition. To compare the moments between movement directions, we performed a repeated-measures multivariate ANOVA (MANOVA). Dependent measures were the moments measured about the ankle joint at the aforementioned ankle angles (+25°, +15°, +5°, −5°, and −15°). Post hoc t-tests (with Bonferroni's correction) were then performed at each angle. SPSS statistical software (version 15.0, LEAD Technologies) was used for all analyses. Statistical significance was accepted at P < 0.05.
Moment arms obtained from the TE method were significantly smaller for all differentiation methods and both rotational directions than those obtained from the COR method (P < 0.01; Table 1, Fig. 4). The percent differences (means ± SD) across all participants and differentiation methods were 29.3 ± 5.7% for plantarflexion rotations and 26.2 ± 6.0% for dorsiflexion rotations. Despite the absolute differences between methods, the moment arms obtained using the COR method correlated well with those obtained using the TE method. The strength of this relationship was dependent on the mathematical differentiation technique and the movement direction of the ankle used for the TE method. For the passive plantarflexion rotations, the relationship between moment arms obtained from the TE and the COR methods was stronger than that for the passive dorsiflexion rotations (0.64 ≤ R2 ≤ 0.94 and 0.40 ≤ R2 ≤ 0.60 for plantar- and dorsiflexion rotations, respectively; Table 1). With the exception of two conditions (±5° and 2nd-order polynomial during the dorsiflexion rotation), all correlations were statistically significant (P < 0.05; Table 1). In general, the use of polynomial differentiation and linear differentiation over larger intervals (±15° and ±10°) resulted in stronger correlations between both methods. The strongest relationship between the two methods was found when tendon displacement was differentiated over an angular interval of ±10° (R2 = 0.94) during plantarflexion rotations (Fig. 5).
The CV for the moment arms obtained using the COR method was 3.9%. For the moment arms obtained using the TE method, the CV was 4.5–9.7%. These CVs were dependent on the differentiation technique and the direction of the passive foot rotation. Passive plantarflexion rotations tended to produce moment arms more reliably than passive dorsiflexion rotations (Table 1). When the TE method was used, the smallest CV was found when a second-order polynomial was fitted to the ratio of tendon to angular displacement data and differentiated at 0° (CV = 4.5%). Furthermore, linear differentiation over the smaller angular intervals produced less reliable moment arms than polynomial differentiation or linear differentiation over larger intervals. The CV for the differentiation method with the strongest relationship between the two methods (linear differentiation over ±10° ankle angle during plantarflexion rotations) was 5.1% (Table 1).
The repeated-measures MANOVA revealed a significant main effect of rotational direction on moments about the ankle joint [Wilks' Δ = 0.036, F(5,4) = 21.36, P < 0.005]. Post hoc tests revealed that moments about the ankle joint derived during the plantarflexion rotations were significantly smaller than those during dorsiflexion rotations at all foot angles (Fig. 6).
In an additional analysis, we quantified the differences between moment arms derived from the COR and TE methods over a range of angles. For this analysis, six of the nine participants were tested for a moment arm comparison on three additional ankle angles for both methods (+30° and +15° plantar, −15° dorsi). For the COR method, the moment arm was derived as described for the neutral ankle angle using MR images obtained at ±15° of the angle of interest and applying Reuleaux' geometric approach to find the COR of the ankle joint and, subsequently, determine the moment arm. For the TE method, we fitted a second-order polynomial to the ratio of tendon to angular displacement data obtained during passive plantarflexion rotations, as this was found to provide the most reliable measure at the neutral angle, as well as to be strongly correlated with the COR method. The moment arms were obtained by differentiation of the second-order polynomial at the four ankle angles of interest. To test whether moment arms derived from the COR method were different from those derived from the TE method across a range of ankle angles, we performed a repeated-measures MANOVA with post hoc paired t-tests (with Bonferroni's correction). Furthermore, we calculated correlations between the COR and TE methods at each of these angles (+30°, +15°, and −15°). Finally, we quantified the CV between experimental set-ups for TE at each of these angles. The repeated-measures MANOVA revealed a significant main effect for method [Wilks' Δ = 0.015, F(4,2) = 33.37, P = 0.03]. Post hoc tests revealed that moment arms derived from the TE method were significantly smaller than those derived from the COR method at all angles. The percent differences for all participants (mean ± SD) were 35.7 ± 10.4%, 34.8 ± 7.7%, 32.4 ± 6.6%, and 25.1 ± 9.5% at +30°, +15°, 0°, and −15° angles, respectively. Correlations between the moment arms derived from both methods at the three additional angles (+30°, +15°, and −15°) were slightly lower than at 0° and not statistically significant (0.52 ≤ R2 ≤ 0.62; Table 2). The CVs were slightly greater at these additional angles (5.3 ≤ CV ≤ 7.7) than at 0° (Table 2).
The first purpose of this study was to compare moment arm measures of the Achilles tendon using the COR method (MR imaging) and the TE method (ultrasound imaging). Previous research suggests that the use of different methodologies to determine muscle-tendon moment arm of the Achilles tendon may lead to differences in moment arm estimates. However, this speculation has not been confirmed conclusively. Our results demonstrate that the moment arm magnitude depends on the method employed. Absolute moment arm values obtained from the COR method were >25% greater than those obtained from the TE method. Possible explanations for these differences in moment arms lie in the assumptions of each method. When the COR method is used, it is assumed that the ankle is a hinge joint and that the talus, as the rotating segment, moves in the sagittal plane. The fact that ankle plantar- and dorsiflexion rotations are typically accompanied by inversion or eversion at the subtalar joint (2, 8) is therefore neglected. Any inversion or eversion could change the shape and orientation of the talus and, therefore, cause errors in the determination of the two anatomic reference points needed to calculate the COR. Furthermore, the repeated need for the manual drawing of lines to geometrically construct the COR may result in an erroneous estimation of its position (22, 23). The summation of these errors could lead to an overestimation of the moment arm, which is a potential explanation for greater moment arms derived from the COR method than from the TE method. When the TE method is used, it is assumed that no forces are present during the passive rotation (principle of virtual work) (1, 28). However, during dorsiflexion rotations, we found increases in the moments measured about the ankle joint, suggesting an influence of active and passive forces on the length of the muscle-tendon unit and, therefore, on the position of the MTJ. Such forces could result in an underestimation of tendon displacement for a given joint angular displacement. A possible consequence is an underestimation of the moment arm, which is a potential explanation for the smaller moment arms derived from the TE method than from the COR method.
Our observed dependence of moment arms on the method employed has vast implications regarding the development and interpretation of musculoskeletal models. First, knowledge of the method used to determine Achilles tendon moment arm is crucial to accurate interpretation of results derived from musculoskeletal models. Second, these results need to be taken into consideration when developing such models. When developing a musculoskeletal model, it is important to test the sensitivity of its outputs to variations in the estimation of its parameters. The range for such sensitivity analysis is typically ≤10% of the relevant estimated parameter (24, 30). Our results suggest that sensitivity analyses should cover a wide range (i.e., up to 30%) when a model's sensitivity to variations in Achilles tendon moment arm is evaluated.
Our findings raise the question as to which method is the most appropriate to use. When Reuleaux' geometric approach (25) is used, the determination of the COR coordinates is susceptible to errors due to the numerous manual processing steps (22, 23). A recent study used a modified version of the COR method with fewer processing steps and, therefore, less potential for errors (20). The authors assumed the COR to be the midpoint of the line connecting the medial and lateral malleoli and measured the distance between this point and the line of action of the force. The resulting moment arms were similar to those obtained from the TE method in the present investigation. Moment arms obtained from cadavers (27) are also more similar to our moment arms derived from the TE method than those derived from the COR method. Therefore, the moment arms obtained from the TE method are potentially closer to the true moment arm of the Achilles tendon than those obtained from the COR method.
Despite the differences in absolute moment arm values, an important finding of the present study was a strong relationship between the moment arms obtained from the TE method and those obtained from the COR method when measured at the neutral ankle angle. The strength of this relationship was dependent on the differentiation method and the direction of the passive foot movement. Stronger relationships between the COR method and the TE method were found when the foot was passively plantarflexed. A possible explanation for the dependence of the strength of the relationship on movement direction is the difference in moments about the ankle joint between plantar- and dorsiflexion rotations (10). The greater moments observed during dorsi- than plantarflexion rotations could potentially result in a reduction in tendon elongation for a given ankle rotation and, therefore, a less accurate moment arm estimate and weaker relationship with the moment arms derived from the COR method. Furthermore, the moment arms derived from the TE method were more strongly correlated to those obtained from the COR method when linear differentiation was performed over larger angular intervals. When polynomials were used to differentiate the TE data, the correlations were similar to those obtained from the linear differentiation over the large intervals. The result that both methods correlated well across participants is important, as it suggests that moment arm differences and changes across participants (e.g., during growth) are independent of the method being used.
The second purpose of the present study was to determine the reliability of repeated moment arm measurements for COR and TE methods. The mean CV describing the reliability of moment arms obtained from the COR method between experimental set-ups (3.9%) is similar to previously published values (13, 17) and demonstrates good reliability of the COR method. The CVs describing reliability between experimental set-ups for moment arms obtained from the TE method ranged from 4.5% to 9.7% for plantarflexion rotations and from 7.0% to 9.0% for dorsiflexion rotations, depending on the differentiation method used. The magnitude of this variability is also comparable to that reported in previous studies (5, 9, 13). Our findings extend previous results by demonstrating that the TE method is most reliable when polynomial fitting is used to differentiate tendon displacement with respect to joint rotation. Furthermore, moment arms were more reliable when tendon displacement was differentiated over larger angular intervals (±15° and ±10°) than over smaller angular intervals (±1° and ±2°) during plantarflexion rotations. The likely reason for this finding is that minor deviations in TE resulting from errors in digitizing the position of the MTJ are magnified when tendon length is differentiated over smaller angular intervals.
Another important finding was that the variability of the moment arms between experimental set-ups was considerably greater during dorsi- than plantarflexion rotations, independent of the differentiation method (Table 1). The higher CVs observed during dorsiflexion rotations can potentially be explained by the significantly higher moments about the ankle joint for this movement direction. These are indicative of active or passive forces, which violate the assumption of virtual work and could, thereby, reduce the reliability of the moment arm estimates.
Our results have implications for researchers who wish to use the TE method to derive Achilles tendon moment arm; on the basis of the smaller CVs and the stronger correlations with MR imaging-derived moment arms, we recommend use of passive plantarflexion rotations and polynomial or large-interval differentiation. An additional advantage of using a polynomial fitting to differentiate TE with respect to ankle angle is that the moment arm can be determined over the recorded range of angles (although the validity and reliability of such a procedure were not addressed in this study).
In an additional analysis, we demonstrated that our results are consistent across a wide range of ankle angles (+30°, +15°, and −15°). For all these angles, moment arms derived from the TE method were significantly smaller than those derived from the COR method. The reliability of these moment arms and their correlations with moment arms derived from the COR method at these angles were similar to those observed at the neutral ankle position. Together, these results demonstrate that our findings are robust across a range of angles, which has potential implications for researchers who wish to use musculoskeletal models for ecologically valid tasks during which the ankle angle changes (e.g., gait or cycling).
In summary, we have found significant differences in absolute Achilles moment arms derived from the COR (MR imaging) and the TE (ultrasound imaging) methods. This result has important implications for musculoskeletal modeling, as the method used to determine Achilles tendon moment arm can substantially influence the output of such models. From our results, it is clear that when Achilles tendon moment arms are used (e.g., for musculoskeletal modeling), serious consideration needs to be given to the limitations associated with the method used to derive them. This could be done by choosing appropriate limits for performing sensitivity analyses on moment arm to account for the significant (up to 30%) between-method differences. Furthermore, the present results allow us to retrospectively compare published tendon force data more accurately, as we have shown considerable absolute differences but strong relationships between the two methods. These findings are useful for researchers who are interested in examining moment arm differences between populations (e.g., training-, sex-, or growth-related), as population differences are likely to be consistent, independent of the method used. Finally, we have demonstrated a good reliability of both methods, which suggests that they are robust against their limitations. Collectively, the present results will help researchers make more informed decisions about which method to use when determining Achilles tendon moment arm in vivo.
This study was supported by Engineering and Physical Sciences Research Council (United Kingdom) Grant EP/E013007/1.
No conflicts of interest, financial or otherwise, are declared by the authors.
- Copyright © 2010 the American Physiological Society