Mechanical correction of dynamometer moment for the effects of segment motion during isometric knee-extension tests

Abstract

The purpose of this study was to determine the effect of dynamometer and joint axis misalignment on measured isometric knee-extension moments using inverse dynamics based on the actual joint kinematic information derived from the real-time X-ray video and to compare the errors when the moments were calculated using measurements from external anatomical surface markers or obtained from the isokinetic dynamometer. Six healthy males participated in this study. They performed isometric contractions at 90° and 20° of knee flexion, gradually increasing to maximum effort. For the calculation of the actual knee-joint moment and the joint moment relative to the knee-joint center, determined using the external marker, two free body diagrams were used of the Cybex arm and the lower leg segment system. In the first free body diagram, the mean center of the circular profiles of the femoral epicondyles was used as the knee-joint center, whereas in the second diagram, the joint center was assumed to coincide with the external marker. Then, the calculated knee-joint moments were compared with those measured by the dynamometer. The results indicate that 1) the actual knee-joint moment was different from the dynamometer recorded moment (difference ranged between 1.9% and 4.3%) and the moment calculated using the skin marker (difference ranged between 2.5% and 3%), and 2) during isometric knee extension, the internal knee angle changed significantly from rest to the maximum contraction state by about 19°. Therefore, these differences cannot be neglected if the moment–knee-joint angle relationship or the muscle mechanical properties, such as length-tension relationship, need to be determined.

isokinetic dynamometry has been established as the accepted standard for the quantification of muscle strength by measuring joint moments in both static (isometric) and dynamic conditions. Isokinetic dynamometers have also been used to calculate the muscle and joint forces from the joint moments recorded [e.g., refs. (3, 4, 15)] and to determine muscle and tendon mechanical properties (19, 20).

In general, it is assumed that the moment measured by a dynamometer is equivalent to the actual joint moment. However, it has been documented that this is not the case due to 1) gravitational forces (24), 2) inertial forces (9, 22), and 3) misalignment of the joint and dynamometer axes of rotation. In a knee test, for example, the misalignment results from the nonfixed joint axis of rotation and the nonrigid connection between dynamometer arm lower-leg and upper-leg seat systems due to the compliance of the soft tissues and the dynamometer padding (1, 9, 14). Implementation of appropriate methods for the correction of the gravitational and inertial forces has been reported (11, 16, 24), although axes misalignment remains a significant problem.

The movement of the segment relative to the dynamometer is one of the main factors for axes of rotation misalignment and the resulting differences between measured and actual joint moments (9, 14). Several researchers (1, 9, 14) have estimated the error caused by the misalignment of the axis of rotation of the knee joint and the axis of rotation of the dynamometer during contraction. Herzog (9), using a Cybex II dynamometer and a two-dimensional (2D) kinematic analysis system, reported that the maximum differences between the actual knee-joint moment and the recorded moment during isometric and isokinetic at 120° and 240°/s knee-extension trials were only 1.5%, 1.3%, and 2.1%, respectively. Some years later, Kaufman et al. (14) quantified the errors associated with the misalignment of the knee-joint axis and the dynamometer axis of rotation during isokinetic (60° and 180°/s) knee extensions and found that the average differences between the actual and recorded knee-joint moments were 10% and 13% during isokinetic knee extensions at 60° and 180°/s, respectively. More recently, Arampatzis et al. (1) determined the differences between the actual moment and the moment measured by dynamometry at the knee joint during isometric knee extension. A Biodex dynamometer was used for the quantification of joint moments, and a Vicon kinematic analysis system was used for recording 3D kinematic data of the leg. They reported differences between the dynamometer and the actual joint moment (calculated through inverse dynamics) ranging from 0.33% to 17% (average 7.3%). Reimann et al. (21) investigated theoretically the effect of knee-joint axis shift relative to the dynamometer axis (misalignment) on joint moment. They found, in general, the maximum error in moment scales with the percentage displacement of the axes so that, for example, a 10% shift in the axes relative to the length of the segment leads to roughly a 10% maximum error in the moment. The actual error with a 10% shift in the axes ranged from −9% to 6% in the range of motion from 0° (full extension) to 100° of knee flexion.

Although the above studies raise important questions for the validity of muscle and joint function assessment using isokinetic equipment without the appropriate and necessary correction methods, their results are based on measurements using external landmarks. This is an important limitation, and it is possible that a large part of the differences and errors reported resulted from digitizing inaccuracies and skin movement, resulting in shifting the external marker away from the joint center or dynamometer axis of rotation, which it was assumed to represent (23). For example, in a relevant study that quantified the relative movement between skin markers over the lateral and medial femoral condyles and the underlying bone using X-ray fluoroscopy, it was found that there is considerable skin marker–bone movement (23). In particular, for the marker that was placed closest to the most prominent point of the lateral femoral condyle, the maximum possible error ranged from 25.11 to 39.52 mm with a mean of 33.86 mm [see Table 2 in ref. (23)]. If such a maximum error is present in locating the center of the knee joint, it is possible that the calculation of the moment arm of the external-resistive dynamometer force relative to the knee-joint center, which ranges, for example, from ∼312–300 mm [e.g., ref. (1)] and is used for the correction of the dynamometer moment, could contain a maximum (worst case scenario) of an ∼10–11% error. This would lead to a similar error in the corrected resultant moment, which is calculated by multiplying the dynamometer-recorded moment with the ratio of the moment arms of the external-resistive force relative to the knee-joint center and the dynamometer center of rotation, respectively. Given that the average differences between recorded and resultant joint moments range from 2% to 13% in the above studies, it is clear that if such errors (maximum ∼10–11%) were present in the corrected resultant moment, then the results and conclusions of these studies could be totally misleading.

To avoid the potential problems described above and to have accurate measurements of the relative position of the knee-joint axis and the axis of the dynamometer and precise quantification of the resulting errors in the measurement of joint moment require direct recordings of the real bone motion during the contraction. This can only be achieved using real-time X-ray video recordings of the bone movements during the dynamometry test. Hence, the main purpose of this study was to determine the effect of dynamometer and joint-axis misalignment on measured isometric knee-extension moments using inverse dynamics based on the actual joint kinematic information derived from the real-time X-ray video and to compare the errors when the moments were calculated using measurements from external anatomical surface markers or obtained from the isokinetic dynamometer.

METHODS

Participants.

Six healthy males (age: 25.3 ± 4.3 years; height: 178.4 ± 5.6 cm; body mass: 72.3 ± 4.7 kg), without any musculoskeletal injuries of the lower limbs, volunteered to participate in this study after signing informed consent and radiation-risk information forms. The maximum radiation exposure time in this study was limited to 15 s for each participant. The experimental procedures were approved by the local ethical committee.

Procedure.

A Cybex Norm (Cybex, Ronkonkoma, New York) isokinetic dynamometer was used for the measurement of knee-extension moment. The dynamometer was fitted with an extended input arm to allow an adequate gap (45 cm) between the chair and the main unit to accommodate the image intensifier of a GE FlexiView 8800 C-arm X-ray system (Fig. 1). The participants were positioned on the chair and were stabilized with the standard belts and hip and thigh straps. Before each knee-extension trial, a metal disc, which was placed on the most prominent point of the femoral epicondyle on the lateral surface of the knee joint, and a metal disc on a panel of Perspex glass, which was rigidly attached to the dynamometer, were aligned with the dynamometer axis of rotation using a laser device. The alignment was performed at 90° of knee flexion under submaximal contraction conditions. A second metal marker was placed on the Perspex glass panel in a way in which the line formed by the two markers was parallel to the Cybex input arm (see Calculation of the knee-joint moments and Fig. 4 for further details). Gravitational corrections were performed to account for the effect of leg and dynamometer arm weight on moment measurements.

Fig. 1.

Photograph of the experimental set-up.

Fig. 4.

Free body diagram of the lower leg. F_D: force of the Cybex arm on the lower leg segment, which is equal and opposite (reaction) to the force applied by the leg onto the Cybex arm; PF: point of application of F_D; PD: center of rotation of the dynamometer; PK: center of rotation of the knee joint; PM: external marker placed on the lateral femoral epicondyle; d_Kc: moment arm of F_D relative to the knee-joint center of rotation; d_D: moment arm of F_D relative to the center of rotation of the Cybex arm; d_Km: moment arm of F_D relative to the external marker placed on the lateral femoral epicondyle; φ: angle between the line segment PFPK and the longitudinal axis of the dynamometer arm; AD: the second marker, which was placed on the Perspex glass panel so that the line segment ADPD was parallel to the Cybex input arm at 90° of flexion; W_D: weight of the dynamometer arm; d_Wd: moment arm of W_D relative to the axis of rotation of the cybex arm; W_SF: weight of the lower leg; d_Wsfc: moment arm of W_SF relative to the knee-joint center of rotation; d_Wsfm: moment arm of W_SF relative to the external marker placed on the lateral femoral epicondyle.

To examine for any differences in bending between the standard input arm provided by the manufacturer and the extended input arm, preliminary studies were performed before the actual experiments. Three participants were asked to perform isometric knee extensions at a specific level of torque (100 Nm) against the dynamometer when the standard and the extended input arm were used. Simultaneously, the knee-joint angle was recorded using an electrogoniometer to determine any differences in joint angle due to the different level of bending of the two input arms. The data from the electrogoniometer indicated that the change in knee-joint angle induced by the contraction was on average only 1° higher when the extended input arm was used compared with the standard input arm.

Prior to testing, the C-arm of the X-ray system was positioned next to the right knee of the participant to enable the recording of lateral knee-joint images in the sagittal plane. The Perspex glass panel with the metal markers was positioned in front of the image intensifier to allow identification of a reference position for the dynamometer axis on the X-ray images recorded.

The six participants performed isometric contractions at 20° and 90° of knee flexion in front of the X-ray image intensifier, starting from rest and increasing gradually to maximum voluntary contraction (MVC) effort (or 100% MVC) over a period of ∼3 s. Moment data from the analog data output card of the isokinetic dynamometer were recorded with an acquisition system (Acknowledge, Biopac Systems, Santa Barbara, CA) at a sampling frequency of 200 Hz. The internal tibiofemoral joint kinematics were recorded using a pulsed-mode X-ray fluoroscopy digital video captured at 25 frames/s. An external voltage (10 V) trigger was used to initiate and synchronize the X-ray and analog data acquisition.

Analysis of knee kinematics.

The X-ray images were used to determine the center of rotation and the actual knee-joint flexion angle. The knee-joint center of rotation was defined as the center of the circular profiles of the posterior condyles [e.g., ref. (5)]. To determine this center, several arbitrary points were digitized over the femoral posterior condyles in such way to follow the main curvature of each condyle. An optimization technique was then applied to the data set from each of the two femoral posterior condyles, and the best-fit circles for the medial and lateral posterior condyles were determined using a MATLAB-based script [for further details, see ref. (10)]. The midpoint of the line between the centers of these two condylar curves was defined as the knee-joint center (10) (Fig. 2).

Fig. 2.

Schematic representation of the lateral view of the distal femur showing the knee-joint center. Well-fitted circles to medial and lateral condyles are shown also.

The actual knee angle was defined as the angle between the tibial and femoral long axes (Fig. 3). The tibial axis was defined as the posterior border of the tibia, and the femoral axis was defined as the posterior border of the lower diaphysis of the femur (18).

Fig. 3.

Schematic showing the calculation of the actual knee-joint flexion angle.

The coordinates of the center of the metallic disc, which was placed externally on the most prominent point of the femoral epicondyle on the lateral surface of the knee joint, were measured using the X-ray images during the isometric knee extensions. These data were used for the calculation of joint moment (see below for further details, and Fig. 4).

Prior to the determination of the aforementioned kinematic parameters, the geometric pin-cushion and sigmoidal optical distortions of the X-ray images, due to the curvature of the image intensifier and the deflection of the electrons inside the image intensifier caused by the external magnetic field, respectively, were corrected using a thin-plate splines method (8).

Calculation of the knee-joint moments.

For the calculation of the actual knee-joint moment and the joint moment relative to the knee-joint center determined using the external marker, two free body diagrams were used of the Cybex arm and the lower leg segment system [for further details, see refs. (9) and (1), respectively (Fig. 4)]. In the first free body diagram, the mean center of the circular profiles of the femoral epicondyles was used as the knee-joint center (see methods and Fig. 2), whereas in the second diagram, the joint center was assumed to coincide with the external metallic marker, which was placed on the most prominent point of the lateral femoral epicondyle. The equations for the calculation of the actual knee-joint moment are

$${\text{M}}_{jc}={\text{M}}_D\cdot \frac{d_{Kc}}{d_D}+{\text{W}}_D\cdot {\text{d}}_{W_D}\cdot \frac{d_{Kc}}{d_D}+{\text{W}}_{SF}\cdot d_{WSFc}+{\text{I}}_D\cdot {\dot{\omega }}_D\cdot \frac{d_{Kc}}{d_D}+{\text{I}}_{SF}\cdot {\dot{\omega }}_{SF}$$ (1)

$${\text{M}}_{jm}={\text{M}}_D\cdot \frac{d_{Km}}{d_D}+{\text{W}}_D\cdot {\text{d}}_{W_D}\cdot \frac{d_{Km}}{d_D}+{\text{W}}_{SF}\cdot {\text{d}}_{WSFm}+{\text{I}}_D\cdot {\dot{\omega }}_D\cdot \frac{d_{Km}}{d_D}+{\text{I}}_{SF}\cdot {\dot{\omega }}_{SF}$$ (2)

where

• M_jc = actual knee-joint moment (calculated based on the bony landmarks from X-ray images)

• M_jm = knee-joint moment calculated based on the external marker

• M_D = knee-joint moment recorded by the dynamometer

• d_Kc = moment arm of the force of the Cybex arm on the lower leg segment, which is equal and opposite (reaction) to the force applied by the leg onto the Cybex arm (F_D) relative to the knee-joint center of rotation

• d_Km = moment arm of F_D relative to the external marker placed on the lateral femoral epicondyle

• d_D = moment arm of F_D relative to the axis of rotation of the cybex arm

• W_D = weight of the dynamometer arm

• d_Wd = moment arm of W_D relative to the axis of rotation of the dynamometer arm

• W_SF = weight of the lower leg

• d_Wsfc = moment arm of W_SF relative to the knee-joint center of rotation

• d_Wsfm = moment arm of W_SF relative to the external marker placed on the lateral femoral epicondyle

• I_D = moment of inertia of the dynamometer arm about its axis of rotation

• ω_D = angular acceleration of the dynamometer arm

• I_SF = moment of inertia of the lower leg about a transverse axis through the knee joint

• ω_SF = angular acceleration of the lower leg.

Considering that the gravity-effect torque of the dynamometer arm and the human shank-foot segment were corrected prior the moment measurements, equations (1) and (2) become

$${\text{M}}_{jc}={\text{M}}_D\cdot \frac{d_{Kc}}{{\text{d}}_D}+{\text{I}}_D\cdot {\dot{\omega }}_D\cdot \frac{d_{Kc}}{d_D}+{\text{I}}_{SF}\cdot {\dot{\omega }}_{SF}$$ (3)

$${\text{M}}_{jm}={\text{M}}_D\cdot \frac{d_{Km}}{d_D}+{\text{I}}_D\cdot {\dot{\omega }}_D\cdot \frac{d_{Km}}{d_D}+{\text{I}}_{SF}\cdot {\dot{\omega }}_{SF}$$ (4)

The second term on the right-hand side of equations (3) and (4) represents the effect of the inertial forces on the resultant knee-joint moment and is equal to zero for this study, since we examined only isometric knee extensions (ω=0). Hence

$${\text{M}}_{jc}={\text{M}}_D\cdot \frac{d_{Kc}}{d_D}$$ (5)

$${\text{M}}_{jm}={\text{M}}_D\cdot \frac{d_{Km}}{d_D}$$ (6)

The length of d_Kc was determined by multiplying the distance between the application point of F_D (PF) and the flexion axis of the knee joint (PK) with the cosine of the angle between line segment PFPK and the longitudinal axis of the dynamometer arm (PDPF).

The length of d_Km was determined by multiplying the distance between the PF and the position of the external marker (PM) with the cosine of the angle between line segment PFPM and the PDPF. The distance between points PF and PK, PF and PM, and the angles between the line segments PFPK-PDPF and PFPM-PDPF cannot be measured directly on the X-ray images, but they were calculated using trigonometric functions (Fig. 5). The length of d_D was measured using a precision metal ruler marked with 0.5 mm increments.

Fig. 5.

A geometrical model for the calculation of the distance between the points PK and PF and φ. The length of PFPK d(PK,PF) was calculated using the law of cosines for the triangle PD PK PF

$${\left[d\left(PK,PF\right)\right]}^2={\left[d\left(PD,PK\right)\right]}^2+{\left[d\left(PD,PF\right)\right]}^2-2\cdot \left[d\left(PD,PK\right)\right]\cdot \left[d\left(PD,PF\right)\right]\cdot \cos a$$

The length of PDPK was measured from the X-ray image, and the length of PDPF was measured directly using a precision ruler. Angle α was calculated as α = δ − ε. Angle δ is the Cybex input arm angle acquired from the dynamometer interface, and angle ε was obtained from the X-ray video images. Then, angle γ was calculated using the law of sines

$$\frac{\left[d\left(PD,PK\right)\right]}{\sin \gamma }=\frac{\left[d\left(PK,PF\right)\right]}{\sin a}\Rightarrow \sin \gamma =\frac{\left[d\left(PD,PK\right)\right]\cdot \left(\sin \alpha \right)}{\left[d\left(PK,PF\right)\right]}$$

Finally, φ = γ, since d_Kc is parallel to PDPF. A similar process was followed for the calculation of the distance between the points PM and PF and the angle between the line segment PFPM and the longitudinal axis of the dynamometer arm.

Statistics.

Two-way ANOVAwas used to test differences between the dynamometer-measured knee-joint moment and the joint moments obtained relative to the knee-joint center, determined using X-ray imaging and the external landmark at different contraction intensities [0% (rest), 25%, 50%, 75%, and 100% MVC moment levels] during isometric knee extensions. Tukey post hoc analysis was used to determine significant differences between mean values. A Student's t-test was also used to test for differences between the actual knee angle and the dynamometer arm angle. One-way ANOVA was used to test for differences in the actual knee-joint angle among rest, 25%, 50%, 75%, and 100% of the MVC moment. Tukey post hoc analysis was used to determine significant differences between mean values. Pearson correlation coefficients were used to examine the relationships between the individual errors and the recorded maximum moment. The level of significance was set at α = 0.05.

RESULTS

Our two-way ANOVA analysis showed that during isometric knee extension at 90° of knee flexion, the moment recorded by the isokinetic dynamometer was significantly different from the actual joint moment [average difference 4.3% (7.7 Nm; P < 0.05); Fig. 6] and the marker-based calculated moment [average difference 2.5% (4.5 Nm; P < 0.05); Fig. 6] but only during the MVC state in both cases. Statistical differences at 100% MVC were also found between the actual joint moment and the moment calculated based on the external marker [average difference ∼2% (3.3 Nm; P < 0.05); Fig. 6]. During the isometric knee extension at 20° of knee flexion, no significant statistical differences were observed between the recorded and the actual joint moment [average difference ∼1.9% (2.6 Nm; P > 0.05; Fig. 6)]. However, at this angular position, the moment calculated using the external marker was significantly higher than the recorded moment [average difference ∼4.9% (6.74 Nm; P < 0.001; Fig. 6)] and the actual joint moment [average difference ∼3% (3.5 Nm; P < 0.05; Fig. 6)].

Fig. 6.

Actual (M_jc), recorded (M_D), and calculated (M_jm) knee-joint moment using the external marker (A) during isometric knee extension at 90° of knee flexion and (B) during isometric knee extension at 20° of knee flexion. MVC, maximum voluntary contraction.

The above differences indicate that in most cases, d_Kc was different from the d_D and d_Km. The average difference between d_D and d_Kc during the isometric knee extensions was ∼1.1 cm. The average difference between d_D and d_Km was ∼1.4 cm and between d_Kc and d_Km ∼1 cm (Fig. 7).

Fig. 7.

d_Kc (12), d_D, and d_Km (A) during isometric knee extension at 90° of knee flexion and (B) during isometric knee extension at 20° of knee flexion.

The rotation of the knee joint during the “isometric” knee extension at 20° and 90° of knee flexion is shown in Table 1. The knee angle showed statistically significant differences between the different moment levels. The actual knee flexion angle during the maximum contraction state was always at a more extended position than the knee-joint angle during rest. Moreover, statistically significant differences were found between the recorded angle and the actual knee-joint angle. The actual knee flexion angle during the MVC was always less than the angle recorded by the dynamometer. Furthermore, the correlation analysis showed that there isn't any significant relation between the individual errors and the maximum moment at different modes of contraction. The Pearson correlation coefficients obtained were r = 0.524 (P > 0.05) and r = 0.123 (P > 0.05) for the isometric knee extensions at 90° and 20° of knee flexion, respectively.

Table 1.

Actual and dynamometer-recorded knee angles at different percentage levels of the maximum actual joint moment during isometric knee extensions

	Isometric Knee Extension at 90° of Knee Flexion		Isometric Knee Extension at 20° of Knee Flexion
Moment	Actual knee flexion angle	Dynamometer arm angle	Actual knee angle	Dynamometer arm angle
(%)	(deg)	(deg)	(deg)	(deg)
0	93.4 ± 2.5	90	25.8 ± 3.2	20
25	89.2 ± 3.6	90	16.7 ± 4.1	20
50	83.2 ± 3.6	90	13.3 ± 3.6	20
75	79.2 ± 4.4	90	10.1 ± 3.6	20
100	73.6 ± 7.5	90	8.2 ± 3.5	20

DISCUSSION

Accurate measurements of actual knee-joint moment require a precise alignment between the knee joint and dynamometer axes of rotation. To achieve this, a careful stabilization of the participant prior to each knee-extension trial is necessary. However, due to the knee-joint kinematics, the compliance of the dynamometer components (seat and attachment pad), and the deformation of the soft tissues, a precise alignment between the two axes is not possible, and some error in the estimation of the actual knee-joint moment is, therefore, inevitable. The present study showed that for the knee joint, the mean difference between the recorded and the actual isometric moment ranged between 1.9% and 4.3% (the minimum and maximum error found was 0.3% and 7.9%, respectively). Moreover, the actual knee-joint moment was significantly different from the moment calculated using the skin marker at both angular positions. In one case (during the isometric knee extension at 20° of knee flexion), the knee-joint moment calculated relative to the external marker contained a larger error compared with the dynamometer moment, which was likely due to the considerable skin marker movement relative to the bone (23). If such typical errors were present in previous investigations [e.g., refs. (9) and (1), respectively], the results and conclusions of these studies could be overestimating the moment errors.

Furthermore, the knee-joint moment error was totally inconsistent between the two isometric tests. According to our findings, the isometric knee-joint moment measured by the dynamometer was higher by 4.3% and lower by 1.9% than the actual knee-joint moment, at 90° and 20° of knee flexion, respectively. This is a strong indication of the complex nature of the joint moment error because of the changing tissue/dynamometer component deformation depending on the test conditions. Another strong indication of the unpredictable nature of the joint moment error is the nonsignificant correlation between the participants' individual moment error and their respective maximum recorded moments.

The average difference between the actual and the measured knee-joint moment during the isometric knee extensions in the present study is slightly lower than the average difference (7.3%) reported by Arampatzis et al. (1) and higher than the difference (∼1.5%) reported by Herzog (9). Moreover, these differences are considerably lower compared with the ones (10–13%) reported by Kaufman et al. (14). Differences in the d_Km/d_D ratio are due to the positioning and stabilizing methods used and movement of the segment during the test. Therefore, the different procedures used in the previous studies would affect the calculated joint moment error. For example, all previous investigators who estimated the error caused by the misalignment of the dynamometer and knee-joint axes of rotation aligned the two axes under passive conditions, probably resulting in a misalignment during the contraction. This effect can lead to errors in the estimation of the moment arm of the force of the dynamometer arm on the lower leg segment with respect to the knee-joint center of rotation and consequently, also in the estimation of the knee-joint moment. In this study, we aligned the segment and dynamometer axes of rotation under submaximal contraction conditions, and this should be the standard alignment process. Although perfect alignment is not possible, if the alignment is performed at a joint angle and at a contraction level close to the expected testing conditions, then the misalignment error is minimized. The axes alignment in this study was performed at submaximal conditions at 90° of knee flexion, and it is clear from Figs. 6 and 7 that the misalignment error is minimal at 90° and 25% MVC (close to the axes alignment conditions) and is increased at higher contraction intensities due to further movement of the segment and especially at the 20° of knee flexion test, which was even further away from the alignment angle of 90°. This is a clear indication that to minimize the misalignment error at the MVC level, the axes alignment during the test preparation must be done under near-maximal contraction conditions and close to the expected joint angle during the MVC test conditions. The lower average errors calculated here compared with previous studies may be partly due to this better alignment procedure under some submaximal contraction, at least so that the segment and dynamometer axes are closer at the start of the MVC test. Furthermore, in our study, the input parameters of the biomechanical model for the calculation of the actual knee-joint moment are based on a video X-ray imaging method. This method can be used to measure more accurately the kinematics of the underlying bones by avoiding the errors from the use of skin-mounted markers and external devices, enabling a more reliable estimation of the actual knee-joint moment. Herzog (9) examined a single participant, and the small differences reported indicate that the nonrigidity of the dynamometer arm–lower leg system did not produce large errors between the actual and the measured knee-joint moment. Although such small errors by individual subjects have also been found in the present and previous studies (1), the range of the reported differences shows a substantial variability between the participants, and therefore, accurate conclusions from a single subject cannot be drawn.

In the present investigation, it was found that the true knee-joint flexion angle during the isometric contractions changed significantly (Table 1) from the resting state angle and was significantly smaller than the angle recorded by the isokinetic dynamometer (i.e., knee joint in a more extended position). The angular changes in the present study (∼18–20°) are slightly higher than the values reported by Kaufman et al. (14) (10–13°) and Arampatzis et al. (1) (10–15°). These small differences between the studies could be due to differences in the exerted maximal knee-joint moments during the contractions and the differences in the dynamometer compliance. Another likely reason for this variation among the three studies could be due to methodological differences. Kaufman et al. (14) measured the knee angle using a segment-mounted triaxial electrogoniometer and Arampatzis et al. (1), using external surface markers. In our study, the knee angle was measured using X-ray images of the joint and tibia-femur motion in vivo. In contrast to the X-ray video method, the description of human joint kinematics using external markers or goniometry is affected by some errors caused by the deformation of soft tissues or the slippage of the electrogoniometry.

The substantial changes of the knee-joint flexion angle during isometric knee-extension tests cannot be neglected if the muscle and tendon mechanical properties, such as length-tension relation, need to be determined. For example, in the case of the ankle joint, a change in the ankle angle during isometric contraction has been reported, and this induced a displacement of the tendon ∼3 mm and a decrease of the fascicle length ∼15 mm (13, 17).

It is important to point out the major assumptions in our work. The knee joint was modeled as a planar mechanism, and the center of rotation of the knee joint was defined as the point that coincides with the average center of the circular profiles of the posterior condyles. This approach is based on some novel biomechanical representations of the human knee function (5–7). Therefore, the center of rotation of the knee joint is represented as a fixed center rather than as a changing, instantaneous center of rotation. Hence, the translation of the tibia with respect to the femur and the “screw-home mechanism” that occurs during knee extension/flexion are not included in our knee model kinematics. For the construction of the above biomechanical model, the reaction force at the leg was assumed to be perpendicular to the input arm of the isokinetic dynamometer. Although this may influence the calculation of the actual knee-joint moments, it is a reasonable approximation, because Kaufman et al. (14) reported that during isokinetic knee extension (60° and 180°/s) at the early portion of the extension, the resistive force component perpendicular to the input arm of the dynamometer was 95–98% of the total force and decreased to 80–85% near full extension (corresponding roughly to joint angles of 90° and 20° of knee flexion, respectively, in the tests of this study). Hence, the values of the shear forces were 2–5% and 15–20% at the early part of extension and near full extension, respectively. So, based on simple trigonometric analysis, the deviation of the resistive force vector from the perpendicular to the dynamometer arm was 1.1–2.9° at more flexed angles and 8.6–11.5° near full extension (2). Thus the estimated moments due to the shear forces were 1.9–4.7% and 14.4–19% of the actual knee-joint moment during the early and the late portion of the knee extension, respectively, in that study. Our results present a similar pattern, and although our overall misalignment errors are smaller, it is clear that the segment and dynamometer misalignment is higher at more extended knee-joint angles (20° knee flexion), leading to application of the force on the input arm at a higher angle, resulting in larger shear forces that are not recorded by the dynamometer.

The significant joint moment errors reported by the present study show that the accurate measurement of joint moment with dynamometry is only possible after correction for axes misalignment using in vivo skeletal imaging methods. However, in everyday applications, where use of such systems is not available or possibly due to ethical or other issues, misalignment of axes, measured with external skin markers using simple video or optoelectronic systems, is a reasonable alternative. If no correction is applied, then it must be accepted that a degree of error, which is estimated to range anywhere from 0.3% to 17% [values from the present study and ref. (1)], will be present in the joint moment measurements, and any conclusions about muscle function or effects of interventions must be made in the context of these likely errors.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).