Abstract
We describe a computer-assisted vector wear technique for the determination of polyethylene wear on digital radiographs. Twenty-five hips that had had a total hip arthroplasty were used to evaluate the repeatability and performance of three radiographic techniques to measure wear of the acetabular polyethylene liner: the manual technique with use of calipers described by Livermore et al., the same technique with use of a digitizing tablet, and our new technique of computer-assisted vector wear analysis. We found our new technique to be at least ten times more repeatable than the technique with use of either calipers or a digitizing tablet.Fourteen of the polyethylene liners were retrieved at autopsy, and the actual measurements of wear of those liners were compared with the measurements that had been obtained with the three radiographic techniques of wear analysis. Computer-assisted vector wear analysis outperformed the manual techniques of Livermore et al. When compared with the data obtained from the specimens retrieved at autopsy, the measurement of wear determined with the computer-assisted technique differed by an average of 0.08 millimeter, whereas the measurements obtained with use of calipers and use of a digitizing tablet differed by 0.26 and 0.25 millimeter, respectively.The performance of computer-assisted vector wear analysis in the clinical setting was evaluated with use of controls with known amounts of wear. These were mounted in pelvic phantoms, and radiographs were made with use of a setup that simulated the clinical setting. Analysis of nine controls with 2.0 millimeters of wear yielded an average measurement of wear (and a standard deviation) of 1.99 ± 0.21 millimeters.CLINICAL RELEVANCE: Computer-assisted vector wear analysis demonstrated superior repeatability and accuracy compared with current techniques of manual analysis. Improved repeatability and accuracy in the determination of polyethylene wear should facilitate the investigation of factors related to the prosthesis and to the patient that affect the rates of wear.
Polyethylene wear, with its production of polyethylene debris, has been implicated as a cause of prosthetic loosening and subsequent failure of total hip replacements. Currently, the association between polyethylene wear, osteolysis, and subsequent prosthetic failure is a primary concern in the fields of orthopaedics and biomaterials research5,11,15,17-20. Thus, the accurate determination of polyethylene wear in situ is critical. Analyses of cups retrieved at revision or post mortem usually are limited by the number of devices available.
Livermore et al. and Wroblewski compared manual methods for determining wear from radiographs with direct measurements of wear of retrieved cups and found the accuracy to be 0.075 and 0.2 millimeter, respectively. Other investigators have reported an accuracy of 0.18 millimeter with use of manual techniques2.
Several investigators recently reported on the analysis of polyethylene wear in total hip replacements6,7,9,12,21. Devane et al.6,7 described a computer-assisted technique for three-dimensional analysis of polyethylene wear in porous-coated anatomic acetabular components. Their technique did not incorporate computerized interpretation of digital radiographs; rather, it emphasized the computerized manipulation of manually digitized data points from plain radiographs. They reported an accuracy of ±0.15 millimeter on the basis of analysis of a phantom model with predetermined amounts of wear. Shaver et al. described a technique for two-dimensional analysis of polyethylene wear with use of computerized edge detection on digital radiographs. They reported an average error of 3.6 per cent when compared with measurements of radiographic phantoms with predetermined amounts of wear. The accuracy reported by Devane et al.6,7 and by Shaver et al. was based on contact phantom radiographs, which eliminate the effect of scatter and absorption of the x-ray beam by soft tissues. The performance of their techniques in the clinical setting, based on findings in prostheses retrieved at autopsy, has yet to be determined.
In 1989, Jones et al. reported on the first technique of computerized analysis for the determination of polyethylene wear. The technique was developed for the analysis of Charnley polyethylene acetabular components inserted with cement, and it requires considerable user interaction. They reported a repeatability of 0.01 millimeter for measurements in an experimental model, but they did not report the performance of their technique in the clinical setting.
We describe a semiautomated computer-assisted technique based on edge detection and vector analysis for the determination of polyethylene wear in metal-backed acetabular components. We evaluated this technique in the clinical setting and compared it with the generally accepted manual techniques of Livermore et al. with use of both manual calipers and a digitizing tablet.
*Although none of the authors has received or will receive benefits for personal or professional use from a commercial party related directly or indirectly to the subject of this article, benefits have been or will be received, but are directed solely to a research fund, foundation, educational institution, or other non-profit organization with which one or more of the authors is associated. Funds were received in total or partial support of the research or clinical study presented in this article. The funding sources were a research grant from the University of Chicago Department of Surgery and Grant AR 39310 from the National Institutes of Health.
†Section of Orthopaedic Surgery and Rehabilitation Medicine, Department of Surgery, The University of Chicago, 5841 South Maryland Avenue, MC 3079, Chicago, Illinois 60637. E-mail address for Dr. Martell:jmartell@surgery.bsd.uchicago.edu.
‡Department of Orthopaedics and Rehabilitation, Yale University School of Medicine, 800 Howard Avenue, New Haven, Connecticut 60510.
Twenty-five total hip replacements in nineteen patients were evaluated in the present study. Each replacement included a twenty-eight-millimeter-diameter cobalt-chromium femoral head and a Harris-Galante metal-backed hemispherical porous-coated acetabular cup (Zimmer, Warsaw, Indiana) that had been inserted without cement. Fourteen of the twenty-five hips were selected because the cups had been retrieved at autopsy. The other eleven were chosen randomly from patients who had been followed for at least six years. We attempted to make anteroposterior radiographs of the pelvis six weeks after the arthroplasty, although the actual duration averaged eight weeks (range, three to fourteen weeks). The most recent radiographs were made at an average of 62.4 months (range, 3.6 to 100.8 months) after the procedure. The radiographs were digitized with a laser scanner (Konica, Tokyo, Japan) with use of a pixel size of 0.171 by 0.171 millimeter and a matrix size of 2048 by 2494. To determine the effect of image resolution on the determination of wear with use of our computerized technique, the radiographs of all fourteen specimens retrieved at autopsy were analyzed with use of 2K (146 dots per inch [2.54 centimeters]) and 4K (292 dots per inch) x-ray scan resolutions. The gray scale used by the scanner was ten bits. When it was digitized, the ten-bit image was converted to an eight-bit image with use of histogram equalization1. This transformation procedure minimized the loss of contrast information in the image during gray-level reduction. The image then was converted into tag image file format (TIFF), a universal image format supported by many software programs. The program that analyzed these images was implemented as a Microsoft Windows program (Redmond, Washington).
Manual Technique of Livermore et al.
Calipers: On the basis of the technique of Livermore et al., we used a transparent overlay with a set of concentric circles to determine manually the center of the femoral head. After the center was located on the most recent radiograph, a compass was used to find the location of the minimum distance between this center and the outer surface of the acetabular cup. The line between this location and the center of the femoral head was defined as the line of maximum wear. We used digital calipers, accurate to 0.01 millimeter, to measure the minimum thickness of the polyethylene along this line. The direction of wear as defined by this line was determined, relative to a line drawn on the ischial tuberosity, with use of a compass with 0.5-degree marks. The line perpendicular to this ischial line was defined as 0 degrees, with wear directed medially defined as positive and wear directed laterally defined as negative. Next, the six-week postoperative radiograph was analyzed by drawing a line on the ischial tuberosities and finding the center of the femoral head. The original thickness of the polyethylene in the direction of maximum wear was measured. The difference between the thickness of the polyethylene on the radiograph made six weeks postoperatively and that on the radiograph made at the time of the latest follow-up was defined as the amount of wear. A correction factor for magnification, based on the known diameter and the measured radiographic diameter of the femoral head, was applied to all measured radiographic distances.
Digitizing tablet: This method of measurement was similar to the other manual technique except that, instead of calipers, we used a Sigma-Scan digitizing tablet (Jandel Scientific, San Rafael, California) with a minimum resolution of 0.025 millimeter to measure distances.
Computer-Assisted Vector Wear Analysis
The underlying approach of the computer-assisted vector wear analysis was to find the circles that best fit the prosthetic femoral head and the acetabular component (Appendix). The analysis was performed on radiographs that had been digitized as already described.
A line tangent to the most inferior points on the ischial tuberosities was defined by choosing the two points. Next, with use of image analysis, the program automatically calculated a circle that best fit the femoral head and one that best fit the outer surface of the acetabular component. If the fit was not ideal, the user had the option of employing a manual override to modify the parameters and to perform a repeat analysis of the hip. Finally, these steps were repeated on the radiographs made six weeks postoperatively.
The image-analysis program first extracted the region of interest (the portion of the digital image that is to be the focus of the image analysis) so that it included the femoral bearing and the acetabular component. It then converted the region of interest by a two-step process that better contrasts the edges between the prosthetic head, the acetabular component, and the surrounding bone. The first step of this conversion smoothed the image intensities to reduce the effect of noise and fine texture on the detection of intensity changes with use of a two-dimensional Gaussian function known to provide good performance (Appendix).
The second step accentuated the intensity changes and transformed the image into a representation in which potential prosthetic edges were more distinct (Appendix). For this transformation, the 3 x 3 directional Sobel operator1 was used to detect edges in vertical (up and down) and horizontal (right and left) directions (Fig. 2-B). We designed four additional operators (small matrices used as filters to convolve with an image) that detect edges in diagonal directions (Fig. 1). Processing with one operator resulted in an edge-gradient image of the region of interest, where a large value corresponded to a greater chance of that pixel being a physical edge. Individual edge gradients (edges defined in certain directions) in five directions were calculated and then summed to produce an edge-enhanced image of the region of interest for the acetabular metal shell. Individual edge gradients in seven directions were computed in a similar fashion for the prosthetic femoral head.
The next step in the image analysis was to determine the circles that best fit the acetabular metal shell and the prosthetic femoral head on the basis of the Hough technique for curve detection1. To account for variations in implantation techniques and orientation of the pelvis during radiography, a 225-degree arc was searched to provide complete coverage of the acetabular prosthetic interfaces. The range of predefined valid acetabular circles took into account the known radius of the femoral head as well as variations in magnification and in radii of the cup. After defining the edges of the acetabular component and the femoral head, the program superimposed the best-fit circles onto the displayed image to allow the user to observe the results.
When the superimposed best-fit circles for the prosthetic femoral head and the acetabular shell did not match the image, two manual override techniques were available. The user could choose two points on the inside and the outside of an interface or limit the range of valid centers for either circle by choosing three points on the edge of either the prosthetic femoral head or the acetabular metal shell.
Distances were calculated in terms of pixels and were converted to millimeters on the basis of the known diameter of the prosthetic femoral head. All of the measured angles were adjusted so that the line drawn on the ischial tuberosity represented the horizontal axis.
When the centers of the acetabular component and the femoral head were found, the magnitude and direction of the femoral head vector displacement from the acetabular center were calculated.
Computer-assisted vector wear analysis added the femoral head displacement vectors (the magnitude and the direction of displacement from the acetabular center) on the radiographs made at six weeks and on those made at the latest follow-up examination to compute the resultant wear vector for the follow-up interval. With this method, the center of the femoral head was not assumed to be at the center of the acetabulum on the six-week radiograph.
Analysis of a single hip on either the six-week radiograph (Fig. 2-A) or the most recent radiograph (Fig. 2-C) took approximately fifteen seconds with use of a 120-megahertz workstation with a Pentium processor (Dell, Austin, Texas) running Windows 95 or Windows NT (Microsoft). Repeat analysis of the same hip took approximately five seconds.
Evaluation of the Techniques
In order to evaluate the repeatability of wear measurements, we analyzed each hip with both manual techniques—that is, with use of calipers and with use of the digitizer—as well as with computer-assisted vector wear analysis.
To determine the reproducibility of the results between successive measurements by the same observer (intraobserver repeatability), one observer measured each hip twice with computer-assisted vector wear analysis and twice with each of the two manual techniques. To determine interobserver repeatability, another observer measured each hip once with computer-assisted vector wear analysis and once with each of the manual techniques.
The limits of agreement and repeatability for the measurements were calculated according to the method of Bland and Altman. The limits of agreement define the 95 per cent confidence interval of the differences between two techniques. The repeatability coefficient is twice the standard deviation of the differences between two sets of measurements.
The fourteen polyethylene liners retrieved at autopsy were analyzed for wear with use of an ultrasonic probe (model M112H; Panametrics, Waltham, Massachusetts) capable of measurements within 0.012 millimeter. The maximum wear was calculated by subtracting the thickness of the thinnest region of the retrieved liner from the thickness of an identical, unused liner.
The performance of computer-assisted vector wear analysis was evaluated with a radiographic technique that simulated the clinical setting. Controls of 0.5, 1.0, and 2.0 millimeters of wear were created with use of a computer-aided design system interfaced with a milling machine. A twenty-eight-millimeter-diameter wear path was milled at a direction of 45 degrees into the face of the polyethylene liners. An identical, unused matching twenty-eight-millimeter-diameter liner was used to simulate the liner when the six-week postoperative radiograph was made. Liners with 0.0, 0.5, 1.0, or 2.0 millimeters of simulated wear were seated into three different designs of titanium acetabular shells that accepted the same liner. These consisted of a hemispherical shell, a hemispherical shell with a peripheral 1.8-millimeter oversized rim, and a hemispherical dome with a conical peripheral rim geometry (dual geometry) (all manufactured by Osteonics, Allendale, New Jersey). The shells were implanted into radiopaque models of the pelvis (Pacific Research Laboratories, Vashon, Washington) in 0, 15, or 30 degrees of anteversion. Radiographs were made of all of the liners mounted within each of the acetabular shells with use of a clinical simulation setup. Thus, a total of nine radiographs were made for each simulated-wear control. The radiographic geometry and the exposures used for the clinical simulation were identical to those of the standard technique for anteroposterior radiographs of the pelvis with a tube-to-film distance of 100 centimeters. Six inches (15.2 centimeters) of tissue-equivalent Lucite was used to simulate soft-tissue absorption and scatter effects (Appendix). The direction of the polyethylene wear was placed near the plane of the radiograph in all cases. The resulting radiographs of the pelvic phantoms were digitized and analyzed for vector wear as already described.
The mean wear in the twenty-five hips, as measured with the three techniques, was found to be 0.236, 0.185, and 0.207 millimeter per year (Table I). When determining the amount of wear, the computer-assisted method was at least ten times more repeatable than either of the manual techniques. With the exception of the measurements made manually with calipers, measurements made by the same observer were generally more repeatable than measurements made by different observers. Analysis of the specimens retrieved at autopsy showed the computer-assisted technique to be three times more accurate than the manual methods (Table I).
With regard to the determination of wear direction, the computer-assisted technique produced results that were at least four times more repeatable than those produced by manual measurement (Table II). Results obtained by the same observer were more repeatable than results obtained by different observers.
The measurements of the amount of wear obtained with the manual techniques were highly correlated with those obtained with the computer-assisted technique (r = 0.952); however, the manual and the computer-assisted techniques showed poor limits of agreement (-0.51 to 0.61 millimeter).
Computer-assisted vector wear analysis determined eighty-seven (87 per cent) of the 100 prosthetic interfaces automatically (Table III). On four radiographs, the manual override was needed to find the edge of the prosthetic femoral head because of poor exposure of the film. On two other radiographs, a screw-hole was superimposed on the edge of an otherwise poorly visualized femoral head. The resulting strong edge in the location of the screw-hole skewed the best-fit circle for the femoral head away from the true edge. On seven radiographs, a manual override was needed to find the edge of the acetabular metal shell because it was in close proximity to the medial pelvic margin and the film exposures were poor. It was difficult for computer-assisted vector wear analysis to identify the bone-prosthesis interface under these circumstances. The radiographs of two hips demonstrated such dense condensation of bone against the metal shell that the true bone-prosthesis interface was visible only at the periphery of the shell. All of the radiographs that needed a manual override were successfully analyzed.
In order to identify sources of error for the manual technique of Livermore et al., the repeatability of the measurement instruments was assessed. Measurement of the same distance twice resulted in an intrameasurement repeatability coefficient of 0.208 and 0.141 millimeter for the calipers and the digitizer, respectively. This represents the variation introduced by the mechanics of manual measurement with each instrument.
Computer-assisted vector wear analysis of the nine control liners (in the pelvic phantoms) with 2.0 millimeters of wear in a direction of 45 degrees demonstrated an average wear (and standard deviation) of 1.99 ± 0.21 millimeter in an average direction of 52.1 ± 4.8 degrees. The corresponding values were 0.63 ± 0.15 millimeter and 51 ± 17.9 degrees for the controls with 0.5 millimeter of wear and 1.20 ± 0.17 millimeters and 52.3 ± 7.5 degrees for those with 1.0 millimeter of wear (Table IV).
Doubling of the radiographic scanning density had no apparent effect (p = 0.172, two-tailed paired t test) on the results of the computer-assisted vector wear analysis. The 4K scans (292 dots per inch [2.54 centimeters]) showed an average of 0.086 millimeter less wear than did the 2K scans (146 dots per inch).
Mean Wear per Year
The mean wear (between 0.185 and 0.236 millimeter per year), as determined with the different techniques, was within the range that has been reported in the literature4,8,14,15,22.
Manual Techniques with Use of Calipers or a Digitizer
The inferior repeatability of the two manual techniques of Livermore et al. largely was due to the difficulty in determining the center of the femoral head and the direction of wear as well as, in part, to the difficulty in obtaining reproducible results with the primary measuring instruments. Although the primary measuring instruments are a significant source of error (repeatability coefficient, 0.208 and 0.141 millimeter for the calipers and the digitizer, respectively), most of the repeatability error (repeatability coefficient, 0.723 and 0.609 millimeter for the calipers and the digitizer, respectively) could not be attributed to the instruments. Finding the center of the femoral head is crucial to both manual techniques as it indirectly determines the direction of wear and the measurement of the thickness of the polyethylene. Determining the direction of wear often was difficult because the exact location of the minimum thickness of the polyethylene was difficult to identify. The problems with determining the center of the femoral head and the direction of wear are demonstrated by the large intraobserver repeatability coefficient of 41.3 degrees for determining the direction of wear with use of the manual technique of Livermore et al. with calipers.
We found that, with the numbers available, use of the digitizer instead of the calipers did not significantly increase the repeatability of the manual technique (repeatability coefficient for different observers, 0.690 and 0.680 millimeter for the calipers and the digitizer, respectively). Although the digitizer somewhat improved the intrameasurement repeatability (repeatability coefficient, 0.141 and 0.208 millimeter for the digitizer and the calipers, respectively), it did not affect how the center of the femoral head was located or how the direction of wear was determined.
The geometry of the manual technique is based on the assumption that the centers of the prosthetic femoral head and the acetabular metal shell coincide on the six-week postoperative radiograph. This assumption leads to errors in calculations of wear when the centers do not coincide (Fig. 3). The manual technique defines the direction of maximum wear by the minimum thickness of the polyethylene on the later follow-up radiograph. However, if, for example (Fig. 3), the center of the femoral head, at six weeks, was lateral to the acetabular center, the value obtained with use of the manual technique differs from the amount of wear determined with vector wear analysis.
Computer-Assisted Vector Wear Analysis
Computer-assisted vector wear analysis resulted in a tenfold increase in the interobserver repeatability (repeatability coefficient, 0.060 millimeter) compared with the techniques of Livermore et al. for manual measurement with use of calipers or a digitizer (repeatability coefficients, 0.690 and 0.680 millimeter, respectively).
Vector wear analysis had inferior interobserver repeatability compared with intraobserver repeatability because, in several instances, manual override had been required to analyze the radiograph successfully. When these radiographs were eliminated from the repeatability analysis, the intraobserver and interobserver repeatability coefficients were virtually identical (0.004 millimeter each for the amount of wear and 1.87 and 2.02 degrees, respectively, for the direction of wear). Similar intraobserver and interobserver repeatability should be expected from a technique in which the computer identifies the femoral and acetabular centers and calculates wear on the basis of a digital radiographic image with use of identical image-analysis techniques.
With the computer-assisted technique, the center of the prosthetic head was not assumed to coincide with that of the acetabular metal shell on the postoperative radiograph. In some prosthetic devices, the femoral and acetabular centers are not designed to coincide. In other devices, the centers of the components may not coincide because of small variations in the manufacturing of the outer acetabular metal shell. In addition, the centers of the components may not coincide because of incomplete seating of the polyethylene liner at the time of the operation.
Displacement of the femoral head with respect to the acetabular center was followed over time with use of the computer-assisted vector wear technique. This technique should allow the accurate determination of wear for a wider variety of prosthetic designs than can be analyzed with the manual techniques of Livermore et al.
On the basis of the excellent agreement between the computer-assisted measurements of wear and those made on specimens retrieved at autopsy, and on the basis of our validation with use of the control phantoms, we believe that the computer-assisted vector wear analysis performs well in the clinical arena.
Convolution
Convolution is the process of transforming a digitized image by applying a filter. An example showing convolution of a 5 x 6 image with a 1 x 3 operator is given.
The 5 x 6 image (left) shows a vertical interface between two surfaces with a different intensity (columns three and four). Assuming that values greater than 3 on the transformed image (right) represent an edge, the 1 x 3 operator (center) is able to find a vertical edge between the two surfaces. Note that, when an image is convolved with an operator (a small filter), the borders of the image are not defined; thus, question marks are indicated.
Two-Dimensional Smoothing Gaussian Function
The Gaussian function, where s is the standard deviation, was used in the present study as it is known to give good performance. The region of interest was convolved with a 5 x 5 matrix derived from this equation so that the sum of the matrix was 1.0. Smoothing is necessary as the sampling and transduction of light introduces spurious changes of light intensity that do not correspond to substantial physical changes in the image10.
Vector Wear
Vector wear analysis refers to the technique defined by the current paper to determine linear wear. Vector wear is based on the vector defined between the center of the femoral head on the six-week postoperative radiograph and the center of the femoral head on the most recent radiograph. The center of the acetabular cup on one radiograph is superimposed on the other to provide a reference point when determining the amount of vector wear.
Setup of the Phantom Pelvis for Radiography
Three inches (76.2 millimeters) of tissue-equivalent Lucite was positioned above and below the pelvic model to simulate soft-tissue density. The tube-to-film distance was 100 centimeters, and the exposure was seventy kilovolt peak and sixteen milliampere-seconds. A Lanex medium screen and TMG film (Eastman Kodak, Rochester, New York) were used. A 12:1 grid was used on the x-ray cassette.
NOTE: The authors thank Dr. Jorge O. Galante for providing the patients used in the present study, Dr. Aivars Berzins for the analysis of the specimens retrieved at autopsy, and the Kurt Rossmann Laboratories for use of their radiographic digitizing facilities. The authors also thank Theodore Karrison, Ph.D., for his assistance in performing the repeatability analysis.
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