Journal of Orthopaedic Research

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1 ELSEVIER Journal of Orthopaedic Research 20 (1002) Journal of Orthopaedic Research Experimental assessment of precision and accuracy of radiostereometric analysis for the determination of polyethylene wear in a total hip replacement model * Charles R. Bragdon ', Henrik Malchau ', Xunhua Yuan a, Rebecca Perinchief a, Johan Karrholm ', Niclas Borlin ', Daniel M. Estok a, William H. Harris '' Orthopucdic Biomechunics and Biomutrrials Laboratory,.4dult Rewnstructiw Unit, Department of Orthopurdiic Surgery of General Hospitul und Huriwd hlcdical School, Boston, hl , LISA Department of Orthopedics, lnstitutr of' Surgicul Scilvcrs, Giitrbwg Ckiivrsitj~, Gijtchwg, Swrdrn ' Depurtmmt of' Computing Scirncc. LhI7t.b Ckiwrsitj. Umcw. Suwlrn Mas.sachusetts Abstract The purpose of this study was to develop and test a phantom model based on actual total hip replacement (THR) components to simulate the true penetration of the femoral head resulting from polyethylene wear. This model was used to study both the accuracy and the precision of radiostereometric analysis, RSA, in measuring wear. We also used this model to evaluate optimum tantalurbead configuration for this particular cup design when used in a clinical setting. A physical model of a total hip replacement (a phantom) was constructed which could simulate progressive, three-dimensional (3-D) penetration of the femoral head into the polyethylene component of a THR. Using a coordinate measuring machine (CMM) the positioning of the femoral head using the phantom was measured to be accurate to within 7 pm. The accuracy and precision of an RSA analysis system was determined from five repeat examinations of the phantom using various experimental set-ups of the phantom. The ac-curucy of the radiostereometric analysis, in this optimal experimental set-up studied was 33 pm for the medial direction, 22 pm for the superior direction, 86 pm for the posterior direction and 55 pm for the resultant 3-D vector length. The corresponding precision at the 95% confidence interval of the test results for repositioning the phantom five times, measured 8.4 pm for the medial direction, 5.5 pm for the superior direction, 16.0 pm for the posterior direction, and 13.5 pm for the resultant 3-D vector length. This in vitro model is proposed as a useful tool for developing a standard for the evaluation of radiostereometric and other radiographic methods used to measure in vivo wear Orthopaedic Research Society. Published by Elsevier Science Ltd. All rights reserved. Kiynwd.s: Radiostereometric analysis; Polyethylene wear Introduction Radiostereometric analysis (RSA) was developed by Selvik in the early 1970s as a technique for accurately measuring small relative displacements of body or implant segments in vivo [19]. This method has been used to evaluate fracture healing [17], growth plate viability [lo], joint kinematics [21,23] and spinal fusion stability [9]. In the field of total joint replacement, RSA has been extensively used to evaluate total joint component mi- -Supported by the William H. Harris Foundation. Boston, MA USA. *Corresponding author. Tel.: : fax: +I E-niuil addres.s: wharris.obbl(u,partners.org (W.H. Harris). gration [Ill and also the magnitude and direction of penetration of the femoral head into the acetabular component from wear and creep Few, and to some extent, inconsistent results exist in the literature concerning accuracy and precision of the RSA method [1,5,11,22]. One reason for this is a continuing development of the method corresponding to introduction of new and improved calibration instruments, new mathematical algorithms and development of digital measurements [4]. In addition, there is a need for an international agreement on clear definitions of the two concepts 'precision' and 'accuracy' for the RSA method, as previously discussed in 1974 by Selvik [I91 and Ranstam [18]. In the present paper, we have used the following definitions: /02/$ - see front matter Orthopaedic Research Society. Published by Elsevier Science Ltd. All rights reserved PII: S ( 0 1 )OO

2 C.R. Brugdon rt u1. I Journul of Ortliopurdic Research 20 (2002 J ccuuucy: The closeness of agreement between a test result and an accepted reference value [3]. In clinical practice, the accuracy can only be determined by use of a phantom or against retrieved components. Precision: The closeness of agreement between repeated independent test results obtained under stipulated conditions. In clinical RSA practice, precision has been determined by comparing double examinations of the study group of patients within a short time interval, presuming that implant position is unchanged. An average error and standard deviation is then calculated for the patient group. In hypothesis testing, this is a common method of quantifying the variability of a specific clinical group in order to account for variabilities that are unique to the patient set of a continuous variable. For descriptive statistics, it is judged that "about 95% of a set of observations will be within two standard deviations of the mean". This value is commonly referred to as the measure of precision. It is actually an expression of imprecision and is computed using the standard deviation of test results [3]. However, as explained by Altman et al., when referring to a population estimation in contrast to hypothesis testing, precision is an estimate of the true value of a population and they advocate calculation of precision as a confidence interval using the standard error [2]. In comparative clinical studies where hypothesis testing is utilized and the true value is not known, the standard deviation is valuable in judging how much difference between two groups is necessary to claim significance. However, for this phantom study, where a true value is known and an accuracy value can be calculated, precision should be calculated as a confidence interval based on the standard error. RSA requires each segment of interest to be defined by a minimum of three and preferably up to nine tantalum markers. For the examination, a calibration cage and the object of interest (such as the hip) is radiographed using two X-ray tubes to create near simultaneous exposure. These two tubes are positioned at approximately a 40" angle to each other. The calibration cage contains radioopaque tantalum markers that define a three-dimensional (3-D) coordinate system. Each group of patient markers can be treated as a rigid body segment and relative displacements between the two segments are measured over time on successive radiographic examinations. In addition, the center of the femoral head can be determined by edge detection, and the 3-D motion of this point can be calculated relative to a rigid body segment. Several software packages have been developed to facilitate the analysis [4,16,24]. The purpose of this study was to develop and test a phantom model based on actual THR components to simulate the true penetration of the femoral head. This model was used to study both the accuracy and the precision of RSA in measuring femoral head penetration into polyethylene in a simulated THR. We also used this model to evaluate optimum configuration of the tantalum bead for this particular cup design. Materials and methods The physical model (Fig. I) consisted of a replica of the hemi-pelvis with an inserted acetabular component and a mating femoral component. The hemi-pelvis (Sawbones, Pacific Research Labs, Vashon, WA) containing the acetabular component was the non-movable portion of the phantom. The acetabular component was a 55 mm titanium acetabular Inter-OpTM, nine hole revision shell (Sulzer Orthopaedics, Austin, TX) positioned in 45" of abduction and 30" of anteversion. The hemi-pelvis was firmly fixed to a Plexiglas plate attached to a Plexiglas frame with a plastic, radiolucent bolt. This attachment allowed for adjustment of both the height and flexion of the pelvis. After initially defining the zero (or no wear or creep) position by seating the femoral head into the polyethylene, the polyethylene liner was removed from the shell so that the femoral head was free to be moved three-dimensionally within the shell. The second part of the phantom was a metallic platform capable of motion in three dimensions onto which was attached a femoral stem (Snlzer Orthopaedics, Austin, TX) with a 32 mm femoral head. The platform consisted of an A-Y microscope stage fitted with two springloaded micrometers (Mitutoyo, Japan) having a resolution of 1 pm, The third dimension, the vertical motion, was controlled using the focus control of a Zeiss microscope and was measured using a dial indicator gauge (Starrett Co., Athol MA) having a resolution of 1.54 Pm. The precision and accuracy of the micrometers to position the femoral head in 3-D was quantified using a MicroVal PFx coordinate measuring machine (CMM) (Brown and Sharpe. N. Kingston. RI) fitted with a 3 mm ruby tipped stylus. The 3-D position of the center of a 19.1 mm calibration sphere was determined 10 times for each increment of motion starting with zero and subsequently for each increment of 10, 20, 50, and 100 pm of motion in each of the three planes.. The marking of the acetabular shell with the tantalum beads was accomplished by using the cam lock feature of the holes in the acetabular shell. The tantalum beads were inserted into the end of specially designed titanium alloy cylinders or 'towers', which had the male cam lock feature at the base. The prototype tower used in this study incorporates a polyethylene insert to hold the tantalum bead. An all titanium version of the tower has been designed for future use (Fig. 2). With the shell properly positioned in the sawbone hemi-pelvis and held there by the threaded rod, these towers were passed through the screw holes of the metal shell and locked in place. For this study, the five towers used were all 10 mm in length. The RSA determination of the penetration of the femoral head into the acetabular shell was performed using two methods. In one, the 3-D center of the femoral head was determined by using an edge detection algorithm of the UMRSA DIGITAL MEASURE VI o software (RSA BioMedical, Umea, Sweden) using 29 points along the edge of the femoral head of each pair of stereoradiographs. This edge detection method was used to detect the femoral head center. The subsequent calculation of the relative motions of this point is called the 'point motion' method. In the second method, the position of the center of the femoral stem was defined as a 'rigid body segment' by four points. The four femoral points were the three tantalum markers, one each fixed to the medial aspect of the collar, the proximal lateral and the mid-medial aspect of the stem, and the fourth point being the center of the femoral head as defined by its edge detection. This method is called the 'segment motion' method. Each radiographic analysis was performed from a pair of radiographs (radio-pair) taken 'simultaneously' (within 0.3 s) at approximately a 40" angle to each other. The RSA calibration cage (cage 11, RSA BioMedical, Umei, Sweden) containing the tantalum markers needed to create the 3-D coordinates and the built-in film cassette holders were placed behind the phantom (Fig. 3). We defined one data set as consisting of 17 pairs of stereoradiographs (radio-pairs) taken at various settings simulating different amounts of wear. An example of

3 690 C, R. Brugdon ef ul. I Journal qf' Orthopuedic Research 20 (2002 i Fig. I. Phantom with attached femoral component. The stem can be moved in three dimensions. The two micrometers (A + B) control and measure displacement in the medial and posterior direction. The knob (C) controls the superior displacement which was measured using the dial indicator (D). the stereoradiographs is shown in Fig. 4. The 17 film pairs consisted of live repeat radio-pairs at zero displacement, followed sequentially by one radio-pair taken after each motion. Motion was first in the medial direction, to the extent of 50 pm, then 100 pm, then 150 pm and finally 200 pm into the acetabular component, followed by sequential posterior displacement of 50, 100, 150 and 200 bun, and thereafter followed hy sequential motion in the superior direction using the same distances of.50, 100, 150 and 200 pm. As noted above, each set of 17 such radiopairs represents one data set of the phantom. Five data sets were obtained at the RSA laboratory at Sahlgrenska Hospital in Goteborg, Sweden. The X-ray films were digitized using a Mirage flatbed scanner (LrMAN Data Systems Inc., Taiwan) at a resolution of 300 DPI. Using the first 'zero' examination as a reference, the displacement of the femora1 head relative to the acetabular component was calculated for the 16 comparisons of each data set for the three planes of motion as well as the resultant 3-D wear vector using both the point motion and segment motion algorithms of the umrsa 3.0 analysis software, (RSA BioMedical, Umea, Sweden). With the point motion method, the motion of the center of the femoral head is calculated relative to the cup markers. With the segment motion method three stem markers and the center of the femoral head defined the position of the stem. Relative niotion of the stem was calculated relative to the position of the cup. The error value of each parameter for the 16 comparisons in each examination was determined by subtracting the measured value from the true value. The total average error and standard deviation was determined from all eighty error values. From this standard deviation, the standard error of the total average error was calculated. The average error and standard deviation for each parameter within each examination was calculated and was used to calculate the standard deviation of the average error of the five examinations. In addition, the average error and standard deviation were calculated for each displacement in each plane and the average resultant vector for each displacement from the five examinations. These values were compared using a one sided analysis of variance in order to determine if the error varies significantly with increased displacement. The accuracy, a, of both the point motion and segment motion methods was determined using an analysis of variance, by taking into account the variance within each examination and the variance between ail examinations using the formula where x = for 95",0 confidence level with four degrees of freedom, 0, is standard deviation of the total average error, ~2 is the standard deviation of the average error of the five examinations (n = 5). rn is number of error observations per examination, n is number of examinations, nzn = 80. The precision, p. for each method was calculated as described by Altman et al., using the formulap = f(~y)(se), where SE is the.stundud error. of the total average error, y = for 95% confidence level with 79 degrees of freedom.

4 C. R. Bragdon et u1. I Journul of Ortlioput~fic Reseurth 20 (-7002) I Fig. 2. The prototype tower used to position the tantalum bead behind the shell. The 1.0 mm tantalum bead is press fit into the polyethylene insert. Also shown is the all titanium tower designed for clinical use. In this case, the tantalum bead is secured by crimping the end of the tower. The 'condition number' [20] is a measure of the sufficiency of scatter of the tantalum markers defining the rigid body segment and is calculated by the umearsa software. The lower the value of this number, the better the scatter of the markers. Given the fact that in the clinical situation, two of the five screw holes may be used for screw fixation of the acetabular shell, the condition number was calculated for all combinations of three individual towers, and the motion analysis was repeated using both the optimal and worst case combination of three markers. A desired condition number is in the range of Results The CMM analysis of the phantom displacement system showed that the accuracy of the stage in positioning the femoral head was within 7 pm for all displacements tested. This value is within the accuracy of the CMM and did not change over time. The condition numbers for all three-bead combinations of acetabular towers were calculated. The condition number ranged in value from 55 when using all five acetabular markers were used to a high of 306 when towers numbers 2, 3, 4 are used. Six combinations of three beads resulted in a condition number in the eighties. Of these, combination 1,2, 5 was chosen for the motion analysis in this study. The result of the ANOVA analysis showed that there was no significant difference between the average error calculated for any parameter (i.e. medial, superior, or posterior) and the resultant vector when the true dis- placement was zero and the average error when the true displacement was 200 pm. This result validates the use of all the error values for the accuracy and precision calculations. The results of the accuracy and precision analysis for each 3-D plane and for the resultant vector length using all five acetabular markers at the 95% confidence level are shown in Table 1 along with the average and standard deviation of the displacements between the examinations and the total average and standard deviation of all 79 error values. The corresponding results using the best and worst case combinations of the three marker combination as judged by the condition number is also shown in Table 1. Minimal changes in accuracy and precision occur when the analysis is repeated using three acetabular markers to define the rigid body segment, as the condition number increases to 85. However, when using the worst case combination of three markers, the higher condition number led to a deleterious effect on both accuracy and precision in the medial, posterior, and resultant vector determinations. In this case, the accuracy and precision of the superior motion measurement was little affected using three acetabular markers to define the rigid body segment when the condition number increased to 305. This, however, is unique to this particular configuration of markers that, though falling in a straight line, are arranged perpendicular to the plane of motion.

5 C.R. Brugdon cli ul. 1 Journul of Orthopat& Resrcrrch 20 ( Fig. 3. The radiographic setup at Sahlgrensha Hospital in Sweden. The phantom 1s positioned between the calibration cage, which holds the two film cassettes, and the two X-ray tubes. An 8 cm thick slab of Plexiglas is positioned in front of each cassette to simulate soft tissue attenuation. Discussion This THR phantom has been shown to be a useful tool in assessing radiographic methods for determining femoral head penetration into the acetabular shell. The accuracy of the radiostereometric analysis in this optimal experimental setup was 33 pm for the medial direction, 22 pm for the superior direction, 86 pm for the posterior direction and 55 pm for the resultant 3-D vector length. The corresponding precision at the 95% level of the test results measured 8, 6, 16, and 14 pm, respectively. For the first time, a highly accurate in vitro model has been created to determine the ultimate accuracy and precision of the UmRSA system in determining migration of the femoral head into the acetabular component due to polyethylene wear and creep. A novel method for defining the position of a metal backed acetabular component in an RSA analysis has been evaluated. Two methods for identifying the position of the femoral head were studied, the point motion method and the segment motion method. 'The shortcomings of the phantom used in this presentation are as follows. We did not replicate all of the variable penetration patterns of the head that occur over time in vivo such as non-cylindrical wear. All motions imparted on the phantom followed the three coordinate axes and the stepwise movement of the phantom. Each comparison of a film pair which only includes motions in the frontal plane may contribute to a reduction of the 3-D error and potentially reduce the error of the 3-D vector calculation since the error is considerably smaller along the x and y axes compared to the z-axis. The phantom cannot at this time mimic the complex 3-D motion, for example combined rotation of the femoral component or varus/valgus tilt of the stem. In the clinical situation, there is always a difference in patient placement between examinations, which may add to the total error analysis. In this study, the quality of the radiographic technique allowed visualization of the entire

6 C. R. Brqdon et ul. I Journul of' Ortl~opurtlic. Rrsrurc (NO? i Fig. 4. An example of the stereoradiographs of the phantom. The border of thc femoral head can be clearly discerned within the shell in each view. The five acetabular markers and the three femoral markers are used to define the components its rigid body segments. The additional cage markers, used to reconstruct the 3-D coordinate system can also be seen border of the femoral head. Though this quality is sometimes obtainable in the clinical setting, variable film quality obtained in clinical studies can have a strong effect on the results. For these reasons, the study represents a best-case scenario not fully representative of the 'in vivo' situation. The segment motion analysis in the present paper shows better precision than the point motion method. However, a specific point transfer algorithm has to be used which, to an uncertain degree, might influence the error. In general, it is preferable to have the moving segment encircled as much as possible by the markers of the reference segment, as is the case with the point motion method. The different precision and accuracy values obtained with the two methods highlight the importance of the relationship between improved bead scatter and higher precision in the RSA analysis. In the clinical setting, variability in the positioning and scatter of the tantalum markers between patients in a study group may affect the results. Finally, this current study only evaluates accuracy and precision using a 33 mm femoral head size. Several 3-D and 3-D techniques have been used to determine the magnitude of wear and creep of the articular surface of the metal on polyethylene THR in vivo 171. However, few authors report precision and accuracy of wear measurement techniques. When reported, various methods are used to calculate these values. Kiss et al. [ 121 reported accuracy determined by measuring the positions of accurately constructed, randomly arranged balls with nine repeated measurements from different orientations. The clinical relevance of their model is under discussion and their reported accuracy is difficult to relate to accuracy evaluated by a different experimental setup. They authors report the error (two standard deviations) for the overall 3-D vector to be 0.32 and mm for a rigid body defined by three balls. Alfaro-Adrian et al. [l] reported the clinical accuracy (i.e., precision) of their system, defined as two standard deviations of the difference between seven double examinations, to be 0.35 mm for the.y axis and 0.78 mm along the J' and z axes [l]. Using the double examination method, the precision of RSA in measuring penetration of the femoral head into the acetabulum in patients, calculated using the standard deviation, has been reported to be between 50 and 150 pm under different circumstances [5]. The few studies performed for determination of the accuracy of the RSA technique have reported accuracy in the range of mm [ 13,191. For comparison of different measurement techniques, the precision of the specific study is of utmost importance. The method advocated by Altman et al. for calculating precision from mean values has been used in this study. Though this method has not previously been applied to precision calculations in this field, it appears to be the most appropriate approach and might be considered as a standard method. In this study, the precision was calculated as a global value using all 80 error values. It can be argued that all error values are

7 694 C. R. Bragdon et al. I Journal of Orthopaedic Reserrrch 20 (2002) Table 1 Accuracy and precision at a confidence level of 95% and the total average error (standard deviation), resulting from the three condition numbers for the two analysis methods (wm) X medial I' superior Z posterior Resultant Usingjre tonws in the cup segment for the two methods (condition number 55) Segment motion method Accuracy Precision Total average (SD) (37.31) (24.39) (71.56) Point motion method Accuracy Precision Total average (SD) 7.65 (44.12) 0.16 (38.09) (111.61) Using the optimally selected three towers in the cup segment for the two methods (condition number 851 Segment motion method Accuracy 41.@ Precision Total average (SD) (41.18) (30.79) (74.36) Point motion method Accuracy Precision Total average (SD) 7.86 (50.62) 1.75 (37.24) (114.06) ({.sing the worst cuse condition oj'thrre towers in the cup segment Jor flit two methods (condition nunihrr 305) Segment motion method Accuracy Precision Total average (SD) (186.69) (85.73) (93.35) Point motion method Accuracy Precision Total average (SD) (127.94) 9.96 (38.29) (114.93) (60.43) (80.55) (63.08) (83.66) (124.58) (111.52) not independent since they are drawn from five repeat examinations. For the comparative purpose of this paper, the precision calculation coupled with the accuracy values give the best depiction of the relative effect of the different bead configurations. In addition, standardization of the terminology and calculations will facilitate such comparisons. We feel it should be mandatory to include this information especially when new measurement techniques are proposed for clinical evaluation [I,6,8,13,14]. In analogy with the continuous quality controls that biomedical laboratories are facing [3], an international standard for RSA accuracy should be defined. For that purpose it would seem necessary to use one standard phantom in the documentation of different measurement systems. Having a standard phantom would also allow precision determination, optimization of bead configuration on the implants and the bone prior to clinical studies, and such a universal phantom could serve as a benchmark for software improvements. In conclusion, RSA investigations on implant stability and head penetration rate offer a unique possibility for early prediction of mid-term clinical outcome. To enable future comparisons between RSA results presented from different centers and with different software, an international agreement on the definition and calculation of accuracy and precision is proposed. Accuracy and precision data should be included in all reports in order to facilitate interpretation of the results. Ideally, for accuracy determination, a standard phantom should be used. References [l] Alfaro-Adrian J, Gill HS, Murray DW. Cement migration after THR. A comparison of charnley elite and exeter femoral stems using RSA. J Bone Joint Surg-Brit Vol 1999;81:1304. [2] Altman DG. Statistics with confidence: confidence intervals and statistical guidelines. London: BMJ books; [3] ASTM. Annual Book of ASTM Standards. Standard practice for use of the terms precision and bias in ASTM tets methods. Designation: E a (reapproved 1996), [4] Borlin N. Model-based measurements in digital radiographs. PhD Thesis, Sweden: Department of Computing Science, Umed University, [5] Borlin N, Thien T, Karrholm J. The precision of radiostereometric measurements. Manual vs. digital measurements. J Biomech, submitted for publication.

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