Reproducibility and accuracy of angle measurements obtained under static conditions with the Motion Analysis video system.

Key Words: Equipment, Kinentatic analysis, Motion, Video motion analysis.

Advances in technology have made the kinematic analysis of human motion more widely used in clinical and research applications.(1-3) Analysis systems that require hand-digitization of data, such as cinematography, are subject to errors associated with visually identifying joint centers or marker centers on film. in video-based and optoelectric systems, joint centers are digitized automatically, presumably reducing one source of error. Error associated with calculating joint centers or joint angles from active or passive markers is introduced, however, when using these newer, more automated systems. Although the reproducibility and accuracy of measurements obtained with other kinematic analysis systems have been repored,(4,5) the reproducibility and accuracy of angles calculated from reflective markers by the use of the Motion Analysis[TM] system have not to our knowledge been previously investigated. The purpose of this study was to evaluate the reproducibility and accuracy of measurements of angles and distances obtained with the Motion Analysis[TM] system. We used a methodology similar to those Scholz(4) and Haggard and Wing(5) used in evaluating the WATSMART[TM] (Waterloo Spatial Motion Analysis Recording Technique) system.

Method

Instrumentation

The Motion Analysis[TM] Expert Vision[TM] system is a three-dimensional motion tracking and analysis system that can track up to 30 individual retroreflective markers attached to a subject. Up to six video cameras with 8-mm lenses are used to record the images from the retroreflective markers at 60 frames per second. The data may be archived on videotape for later processing or directly processed using a minicomputer. For this study, the data were directly processed. The manufacturer of the Motion Analysis[TM] system indicates that the system has an accuracy of 1: 1,000, or one part in 1,000 across the field of view of each camera. Therefore, with cameras positioned to record data from a 2-m-long section of walkway, one could then expect that the coordinates of a reflective marker could be estimated within 2 mm of the marker's actual location.

Procedure

Static test. Two video cameras were positioned 237 cm apart, 147 cm above the floor and 180 cm from the front edge of a calibration cube that was 163 cm long, 72 cm deep, and 127 cm high (Fig. 1). The cameras were positioned such that the optical axes of the cameras intersected at the center of the calibration cube at an approximate angle of 58 degrees. Sixteen spherical markers, 4 arranged vertically at each comer of the calibration cube, were used to calibrate the system prior to data collection. Spherical passive reflective markers, 2.5 cm in diameter, were attached to the axis near the end of each 24-cm arm of a clear plastic goniometer. Angles between 20 and 180 degrees, in 10-degree increments, were used as reference angles. As the goniometer was calibrated in 1-degree increments, the movable arm of the goniometer could be positioned within 0.5 degree of the reference angle. With the static arm of the goniometer held firmly in place by a small vice, one of the investigators (DVL) moved the other arm of the goniometer to form each of the 17 reference angles in a random order. At each of the reference angles, the reflective markers on the goniometer were recorded for 3 seconds at 60 frames per second to yield 180 data points for each trial. This procedure was repeated 10 times to yield a total of 170 3-second trials (17 reference angles x 10 trials) for each of three locations within the calibration cube (Fig. 1). Location A was 10 cm above the floor, 34 cm from the front boundary of the calibration cube, and 34 cm from the right boundary of the calibration cube. Location B was 96 cm above the floor, 50 cm from the front boundary of the calibration cube, and 34 cm from the left boundary of the calibration cube. In both locations A and B, the arms of the goniometer were parallel with the front boundary of the calibration cube. Location C was identical to location B, but the goniometer was rotated so that the arms were at a 45-degree angle to the front boundary of the calibration cube.

Dynamic test To make a preliminary assessment of the system under dynamic conditions, we used a protocol similar to that used by Haggard and Wing.(5) Two spherical, 2.5-cm-diameter reflective markers were firmly attached 178.5 mm apart on a rigid wooden bar. The vertical plane of the calibration cube x and z axes) was divided into nine rectangles of equal size to form nine cubes that were 54.3 cm long x axis), 42.3 cm high z axis), and 72 cm deep (y axis) (Fig. 2). The wooden bar was then moved randomly in the x, y, and z planes by one of the investigators (DVL) to vary the position of the two reflective markers within each of the nine cubes for 15 seconds while the movement of the reflective markers was recorded by the two cameras. We then attached the bar to the lateral lower leg of a human subject, such that the two reflective markers were aligned along a line bisecting the lateral malleolus and head of the fibula. The reflective markers were recorded by the cameras as the subject walked at a self-paced speed along the x axis within the calibration cube. Last, we attached the bar to the lateral aspect of the thigh of a human subject, such that the two reflective markers were aligned along a line bisecting the greater trochanter and the center of the lateral femoral condyle. The reflective markers were then recorded while the subject rose from a seated to a standing position, within the boundaries of the calibration cube. Three 2-second trials of gait and sit-to-stand were recorded.

Data Analysis

The Expert Vision[TM] Angle Operator of the software program was used to calculate angles from the three reflective markers attached to the goniometer. For each 3-second trial, the mean system-calculated angle of the 180 data points was obtained. This mean system-calculated angle was obtained for each of 10 trials for each of 17 reference angles in each location. Separate intraclass correlation coefficients (ICC[1,1]) were then calculated for each of the three locations, using between-target variance (reference angles) and within-target variance (trials).(6,7) The within-trial variability, or noise," of the system was described by calculating the standard deviation about the mean of the system-calculated angle for each 3-second trial (180 data points). The mean within-trial variability for 10 trials at each angle and location was then calculated by averaging those standard deviation values across the 10 trials. Last, linear regressions using the mean system-calculated angles and the reference angles were calculated for each of the three locations. For the dynamic trials, descriptive statistics were used to assess how well the system was able to calculate distance between two reflective markers.

Results

Under static conditions, the ICC exceeded .99 for each of the three locations. This demonstrated that the system was consistent in calculating angles from the reflective markers, regardless of the location of the goniometer in the calibration field. The system-calculated angles (averaged for 10 trials) for each reference angle and the three locations are presented in Table 1. Differences between the reference angle and the mean system-calculated angle are shown in Figure 3. The mean system-calculated angles were within 0.5 degree of the reference angle from 20 to 90 degrees. For locations A and B, the differences remained small ([+ or -]0.6[degrees]) from 100 to 160 degrees. For location C, the system overestimated the angle by about 1 degree for angles from 110 to 160 degrees. For all three locations, the system demonstrated the greatest error in calculating the 180-degree angle, underestimating the angle by 1.5 to 2.4 degrees (Tab. 1, Fig. 3).

The mean within-trial variability for each angle and location are presented in Table 2 and Figure 4. The mean within-trial variability was generally less than 0.2 degree for all angles at locations A and B. For location C (rotated 45[degrees]), the within-trial variability was somewhat larger between 60 and 120 degrees (Fig. 4).

Slopes of the linear-regression equations comparing the mean system-calculated angles and reference angles were 0.9962, 0.9999, and 1.0042 degrees for locations A, B, and C, respectively. Calculated intercepts were 0.0685, 0.1433, and -0.2107 degree for locations A, B, and C, respectively, and were not statistically different from zero (P>.05). Pearson product-moment correlations were .99 for the linear-regression equations at each location.

When the wooden bar was moved within the nine calibration cubes, under dynamic conditions, the mean system-calculated distance between the markers ranged from 174.1 to 177.6 mm (Fig. 2). The within-trial variability ranged from 1.39 to 3.04 mm (Fig. 2). During the gait and sit-to-stand trials, the mean system-calculated distance was 177.1 and 176.8 mm, respectively, and the mean within-trial variability was 2.16 and 2.58 mm, respectively.

Discussion

The reproducibility of measurements obtained with the Motion Analysis[TM] system of angles from a stationary goniometer at three locations within the field of view was very high (ICC=.99). Except for the 180-degree reference angle, only in location C (goniometer rotated 45[degrees]) were the mean system-calculated angles different by more than 1 degree from the reference angle. The largest mean system-calculated error was 1.4 degrees 140[degrees] and 150[degrees], location C). Differences between the reference angle and the mean system-calculated angles were slightly less than those reported by Scholz(4) when using the WATSMART[TM] motion analysis system. Both systems demonstrated a larger error when the goniometer was rotated 45 degrees in the calibration cube. In our study, we measured more angles than did Scholz, who measured angles only between 45 and 100 degrees.

The consistently larger error observed at 180 degrees at all locations was likely due to the cosine algorithm the software used to calculate angles from the reflective markers. As angles approach 180 degrees, the cosine approaches 1, and the resolution of the Angle Operator software appears to be limited by the calculation of cosines when the side opposite becomes very small. When using a system such as the Motion Analysis[TM] that automatically calculates angles from reflective markers, we would suggest that, in those instances in which the joint angle of interest may approach 180 degrees, the angle of the individual limb segments be calculated in relation to the horizontal or vertical plane; then, through addition or subtraction, the angle of interest can be obtained. When we used this method to recalculate the angles at 180 degrees, the mean system-calculated angles were found to be 179.24, 180.42, and 180.73 degrees for locations A, B, and C, respectively. In addition, the algorithm used by the Angle Operator software does not calculate angles greater than 180 degrees, so finding the angles of individual segments in relation to horizontal or vertical would allow the calculation of angles greater than 180 degrees. This would be especially important if, for instance, subjects are expected to exhibit knee hyperextension during gait.

Within-trial variability for locations A and B was slightly less than the within-trial variability reported for the WATSMART[TM] system.(4) Larger within-trial variability was observed for location C between 60 and 120 degrees and was similar to that reported by Scholz(4) when the goniometer was rotated 45 degrees in the field of view. The somewhat larger variability in location C may have been due to distortion of the image of the spherical ball when the goniometer was rotated. If the cameras do not see the target as a sphere, the estimation of the center of the sphere may result in some error, which would increase the within-trial variability. Slopes of the calculated regressions that were near unity (1), with intercepts that were not significantly different from zero, and high product-moment correlation values would suggest that the system was able to accurately estimate angles from the static goniometer throughout the range of angles tested.

During the dynamic portion of the test, the mean system-calculated distance ranged from 174.1 to 177.6 mm for the 178.5-mm distance between reflective markers. The calculated distance was slightly less than the reference distance, regardless of the location within the calibration cube, with the largest difference being 4.4 mm. Within-trial variability ranged from 1.39 to 3.04 mm. The error in estimating distance was slightly greater than that reported by Hazzard and Wing(5) for the WATSMART[TM] system, whereas the within-trial variability was similar to that reported by Haggard and Wing.

Although many sources of error are introduced into kinematic measurements, this study evaluated only the error associated with how the system calculated angles and distances from reflective markers, primarily under static conditions. Given that some system error is present in estimating angles and distance from reflective markers using the Motion Analysis[TM] system and other computerized kinematic analysis systems, clinicians and researchers should be cautioned that small changes in joint angles may be due to system error rather than the effects of clinical or experimental intervention. In addition, other sources of error, which this study did not address, are introduced in clinical studies of human subjects. These sources of error include error associated with marker placement on bony landmarks by one or more investigators, placement of markers on a subject on multiple days, and skin movement over bony landmarks during movement. If these sources of error are not controlled or minimized, the reliability of clinical kinematic measures may be jeopardized.

Although the Motion Analysis[TM] system is computerized and does not require the time-consuming process of hand-digitization of markers, each marker must be "tracked" to ensure that the computer does not become confused in its identification of markers. Rapid movement of an extremity, obstruction of a marker by another body part, or movement that makes two markers come close together or merge" may cause the automated computer processor to become confused. The clinician or researcher must then spend additional time to ensure that all markers of interest are seen correctly by the computer and make corrections interactively with the computer when necessary. This interactive process is a time-consuming, but necessary, part of data analysis that must be done to ensure that the data are not contaminated by computer errors.

The Motion Analysis[TM] system and other kinematic systems allow clinicians to describe human movement in a more quantifiable manner than was possible just a few years ago. Although more data can be generated regarding movement in patients, careful attention to reliability of measurement (eg, system reproducibility and reliability of marker placements) is required before the data are meaningful or helpful in making sound clinical decisions.

Conclustion

This study provides information regarding the reproducibility and accuracy of measurements of angles and distance obtained with the Motion Analysis's system from reflective markers under static conditions. The findings are similar to those reported for other kinematic analysis systems and suggest that the system has acceptable error in calculating angles from reflective markers. The reproducibility and accuracy of measurements obtained with each kinematic analysis system within the environment in which it will be used and under typical conditions of data collection should be established prior to the clinical use of that system.

Acknowledgment 

We thank John P Scholz, PhD, PT, for his suggestions and comments regarding this manuscript.

References

1 Yack HJ. Techniques for clinical assessment of human motion. Phys Ther. 1984;64:17-26.

2 Gronley JK, Perry J. Gait analysis techniques. Phys Ther. 1984;64:27-34.

3 Sutherland DH, Hagy JL. Measurement of gait movements from motion picture film. J Bone joint Surg [Am]. 1972;54:787-798.

4 Scholz JP. Reliability and validity of the WATSMART[TM] three-dimensional optoelectric motion analysis system. Phys Ther. 1989;69: 679-&9.

5 Haggard P, Wing AM. Assessing and reporting the accuracy of position measurements made with optical tracking systems. Journal of Motor Behavior 1990;22:315-321.

6 Winer BJ. Statistical Principles in Experimental Design. 2nd ed. New York, NY: McGraw-Hill Book Co; 1971:283-289.

7 Shrout PE, Fleiss JL. Intraclass correlations: uses in assessing rater reliability. Psychol Bull. 1979;86:420-428.

DW Vander Linden, PhD, PT, is Assistant Professor, Department of Physical Therapy, College of Health Related Professions, University of Florida, Box J-154, Health Science Center, Gainesville, FL 32610 (USA). Address correspondence to Dr Vander Linden.

SJ Carlson, PT, is Senior Physical Therapist, Shands Hospital, University of Florida, Gainesville, FL 32610.

RL Hubbard is Laboratory Coordinator, Human Motion Laboratory, Shands Hospital, University of Florida.

This article was submitted March 11, 1991, and was accepted November 6, 1991.