INTRODUCTION

Kinematics of the normal, injured, or prosthetically replaced knee joint are a complex combination of rolling, gliding and rotational motions which are significantly influenced by activity, integrity of the ligaments and capsular structures, muscle activity, and articular geometry. Accurate kinematic information is critical to understanding the function and pathogenesis of the knee, particularly during weight bearing dynamic activities. The present study was undertaken to characterize the accuracy of a non-invasive fluoroscopic technique for measuring dynamic three-dimensional (3D) knee motions in individuals whose knees have not been prosthetically replaced. This technique utilizes orthogonal planar radiographic views of the knee to create a 3D contour model of consistently identifiable bony features for both the tibia/fibula and femur. The measurement technique is implemented by projecting the contour model onto digitized fluoroscopic images of the moving knee, and determining the translations and rotations which give the best correspondence between the projected contour model and the radiographic projection of the bone. Controlled in vitro assessment of the technique resulted in an average rotational accuracy of 1.1 degrees and a sagittal plane translational accuracy of 1.3 mm.

REVIEW AND THEORY

The functional motions of the normal human knee joint, although complex, are relatively constrained when the menisci, cruciate ligaments, and collateral ligaments are intact. Loss of any of these soft tissue constraints can increase the envelope of motion, and lead to knee instability, accelerated degenerative changes, and impaired functional capabilities. There continues to be great interest in accurate quantitative assessment of knee function in order to better understand normal knee mechanics, injury mechanisms, surgical and rehabilitative treatments, and the function of knee replacements.

Many techniques have been reported for the measurement of dynamic knee motion in vivo. However, most of these techniques suffer from one or more fundamental limitations: body surface mounted markers or fixtures which can move relative to the bones, insufficient frame rates, inability to measure dynamic weight bearing activities, and surgical or invasive attachment of markers to the bones.

Banks, et al., (1996) recently reported a technique for the accurate 3D measurement of knee replacement motions using single-plane fluoroscopy. This technique provides a direct measurement of prosthesis motion at frame rates up to 200Hz using current video technology. The technique is based upon precise knowledge of the prosthesis surface geometry and the optical geometry of the fluoroscope, which are used to implement a shape matching technique for pose determination. However, this technique is not well suited for the measurement of anatomic (non-implanted) knee motions because precise individualized 3D bone models are not readily available, and would be cost prohibitive for all but the smallest of studies or clinical implementations.

This paper reports on the implementation and initial characterization of a simple technique for 3D kinematic measurement of the anatomic knee using single-plane fluoroscopy. We hypothesized for both the tibia/fibula and femur, that anatomic contours representing lines of maximum convexity or concavity could be identified and used to generate a 3D 'contour model', which could well represent the salient features of knee radiographs over a functional range of translations and rotations. The measurement procedure consists of two parts: model generation from orthogonal planar views of the knee, and matching projected model contours with fluoroscopic images of the moving knee.

PROCEDURES

Data Acquisition

An intact frozen knee specimen was rigidly mounted to the actuator of a biaxial (linear/rotary) servohydraulic testing machine (Instron model 8521, verified to ASTM E4, E74). The specimen was mounted so that the knee was in approximate alignment with the linear axis of the actuator. An orthogonal metal triad was fixed to the anterior aspect of the knee for alignment and absolute scale reference. A fluoroscope with 23cm diameter image intensifier was positioned to obtain a lateral view of the knee with the femoral condyles superimposed, and the knee center in the middle of the image. The knee was rotated 90 degrees about the long axis to obtain an anterior/posterior view of the joint centered in the image. The knee was again positioned in the lateral view, and images were recorded as the knee was rotated about the long axis from -16.0 degrees to +16.0 degrees in 2.0 degree increments. This procedure was repeated for +2.54cm displacements of the linear axis of the actuator (superior/ inferior displacements). The knee was repositioned with the patella facing upward, and it was rotated about the anterior to posterior axis from -7.0 degrees to +7.0 degrees in 1.0 degree increments (abduction/adduction of the knee). This procedure was also repeated for +2.54cm displacements of the linear actuator. The perspective projection parameters (principal distance and principal point) of the fluoroscope were determined using previously reported procedures (Banks, et al., 1996). All images were recorded on Hi-8mm videotape.

Image Processing, Model Generation, and Matching

Images were digitized and geometric distortions were corrected using bilinear interpolation. The femoral contour model was created by manually tracing the contours of the posterior and inferior aspects of the medial and lateral condyles, and a contour running from the anterior cortex, through the intercondylar notch, and up along the posterior cortex. The frontal plane view was used to determine the medial/lateral displacements of the sagittal contours. All contours were represented in 3D space through the appropriate inverse perspective scaling. The tibial contour model was similarly generated by tracing the contours of the superior fibular head, the posterior aspect of the medial tibial plateau, and the contour following the anterior tibial tubercle, the intercondylar eminence and the posterior cortical margin.

Matching and pose estimation were performed by projecting the contour model onto the fluoroscopic image of the knee in an unknown pose, and manually varying the model's 3D position and orientation until the best visual match between contours was achieved. The translations and rotations required to superimpose the contour model over the image were taken as the unknown 3D pose of the bones.

Analysis

The coordinate transformations between the reference frame of the knee and the actuator, and the actuator and the fluoroscope, were determined by minimizing the mean errors between the known actuator motions and the estimated knee motions (Banks, et al., 1996, this procedure assumes that the measurement is unbiased). Given these transformations, it is possible to model the actuator motions in the measurement reference frame, and to compare these motions with the image matching based estimates. The calculated errors are zero mean, by definition, and therefore the standard deviation of these errors represents the error expected for a single measurement. The errors for the abduction/adduction tests were averaged with the long axis rotation and translation tests for the appropriate anatomical rotations and translations.

An alternative method to assess the errors is to compute the standard deviation of the 'motions' between the femur and tibia/fibula. Since the knee joint was frozen, the net motions were zero, and the standard deviation represents the error for measuring relative motions.

RESULTS

Table 1 gives the standard errors for the femur and tibia/fibula in the global reference frame. Matching results are consistently better for the femur than the tibia/fibula. Errors in relative motion estimates, which are approximately equal to the sum of the individual estimation errors, indicate that the measurement errors are uncorrelated.

Standard Errors	Femur	Tibia/Fibula	Relative Motion
Anterior/Posterior Translations (mm)	0.5	1.6	3.1
Superior/Inferior Translations (mm)	1.2	1.6	0.6
Medial/Lateral Translations (mm)	0.6	4.7	7.2
Ab/Adduction Rotations (deg)	0.8	1.8	1.6
Internal/External Rotations (deg)	0.7	1.3	1.9
Flexion/Extension (deg)	0.9	0.9	1.6

Table 1: Standard errors for the femur and tibia/fibula in the global reference frame, and their relative motions.

DISCUSSION

The initial experience with this measurement concept has been quite encouraging. The primitive, manual implementation of the matching technique provides knee kinematic estimates which have accuracy comparable to, or better than, many previously reported techniques. This technique provides a direct measurement of bone motion, thus the accuracy achieved for the calibration studies should also be realized for in vivo measurements.

The least accurate measurement using this technique is for translations perpendicular to the image plane, corresponding to medial/lateral displacements. This inaccuracy does not pose a serious limitation for the measurement of knee kinematics due to the very small magnitude of medial/lateral translations which occur in normal, pathological, and joint replaced knees.

The accuracy in tracking the femur was consistently better than that for tracking the tibia/fibula. This is due to differences in bony geometry, which affect both the ability of the 'contour model' to accurately represent the surface geometry of the bone(s), and the degree to which rotations and translations influence the shape of the bone's projection. We anticipate that with more complete models of the bony anatomy, and an optimization based automatic matching algorithm, we will be able to demonstrate significantly greater measurement accuracies than reported in this communication. We believe that this measurement concept has the potential to provide an accurate, clinically useful diagnostic tool using equipment which is already available in most hospitals.

REFERENCES

Banks, S.A., and Hodge, W.A., 1996, "Accurate measurement of three-dimensional knee replacement kinematics using single-plane fluoroscopy," in press IEEE Trans. Biomed. Eng., Vol. 43, No. 6.