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Accuracy and precision of radiostereometric analysis in the measurement of THR femoral component translations: human and canine in vitro models
ELSEVIER
Journal of Orthopaedic Research Journal of Orthopaedic Research 19 (2001) 1162-1 167 www.elsevier.com/locate/orthres
Accuracy and precision of radiostereometric analysis in the measurement of THR femoral component translations: human and canine in vitro models Ingemar Onsten
Aivars Berzins ‘, Susan Shott
’,Dale R. Sumner
a,b,*
Dtpurtmmt id’Anntomj., Rush hli~dicizlColleg~,Rush-Pre.rhyteriun-St. Lukr ‘s hlrdicul Center, 600 South Puulinu Street, Chicago. IL 60612-38317, LISA Depurinicni ?f’Ortlioprilic Surgery, Rush Mediic~cilCollugu. Rush- Preshyterian-St. Lukc’s MediLril Center, Chicago, IL, USA Depurtmmt qf’ Orthopiledies, hfulniii Liniiwrsity Hospital, hlulmo, Stveiien Dtyurifiient of 0hsieirk:s m i l Gyircology. Rush Medicul Collegu, Rush- Preyhyterian-St. Luke’s Medic111 Center, Chicago, IL, USA
Abstract
Radiostereometric analysis (RSA) is used to measure translations of joint replacement components with respect to the host bone in vivo. We used two cadaveric models of hip arthroplasty, one human and one canine, to evaluate the accuracy and precision of RSA-based estimates of translations of the femoral component with respect to the femur under ideal conditions. The femoral components were attached rigidly to a micrometer stage that provided standard displacements in increments of 25 and 50 pm in the interval from zero to 500 pni along three orthogonal axes. Radiostereometric examinations were performed for each increment. Accuracy was calculated as the 95% prediction intervals from regression analyses between the measured and actual displacements. Precision was evaluated as the standard deviation of five repeated measurements of a 200 pm displacement along each axis. Both accuracy and precision were best along the longitudinal axis, with a prediction interval of f 4 7 pm in the human model and 1 4 5 pm in the canine model and a standard deviation of 30 pm in the human model and 40 pm in the canine model. The use of only the prosthetic head as a landmark (as opposed to three markers placed on the femoral stem) led to a 3-fold larger prediction interval in the human model and a ’-fold greater prediction interval in the canine model. 0 2001 Orthopaedic Research Society. Published by Elsevier Science Ltd. All rights reserved.
Introduction
Radiostereometric analysis, or roentgen stereophotogrammetric analysis (RSA), is a research tool which has been used mainly for studies related to joint kinematics and implant fixation after joint replacement surgery. The RSA system [ l l ] includes the implantation of radiopaque markers into the skeleton and onto the implant to serve as landmarks, use of stereoradiographs to determine the location of the markers three-dimensionally, and calculation of relative displacements between different bones or between implants and bones. Important properties of any measurement system include accuracy, precision, and bias. According to the American Society for Testing and Materials Standard E 177-90a (Reapproved in 1996), ‘uccztracy is a generic concept of exactness related to the closeness of agree* Corresponding author. Tel.: +I-312-942-8151; fax: +1-312-9327040. E-niuil a i l d r ~ rsumnerccj~rush.edu ~: (D.R. Sumner).
ment between the average of one or more test results and an accepted reference value’ and ‘the precision of a measurement process . . . is a generic concept related to the closeness of agreement between test results obtained under prescribed like conditions’. The accuracy of a given measurement depends upon bias and precision. Bias, which refers ‘to a consistent or systematic difference between a set of test results from the process and an accepted reference value of the property being measured’ can only be determined if imprecision is removed by averaging a large number of test results. While the in vivo within-laboratory precision of the radiostereometric method has been evaluated in several clinical investigations on total hip arthroplasty [5-7,13], the accuracy of the method has only been evaluated for the part of the method that relates to the computations of the three-dimensional coordinates of the landmarks [4,11]. Thus, the accuracy of measuring actual displacements has to our knowledge never been published. Our goal was to evaluate the accuracy and precision of RSA-based measurements of the displacements of
0736-0166101/$ - see front matter Q 7001 Orthopaedic Research Society. Published by Elsevier Science Ltd. All rights reserved. PII: S 0 7 3 6 - 0 2 6 6 ( 0 1 ) 0 0 0 3 9 - 0
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femoral stems in cadaveric models of human and canine hip arthroplasties, thereby forming the basis for future studies on bias. We designed the study to investigate the effects of two practical issues, namely the number and spacing of markers in the femur and the number of femoral component landmarks. The study was performed in vitro and represents the degree of accuracy and precision obtainable under ideal conditions.
Methods For the human model we used a fresh frozen human cadaveric femur, which was thawed 24 h prior to the experiment. The soft tissues were removed, and the trabecular bone was reamed out from the proximal one-third of the femoral canal. Ten tantalum markers (Industrial Techtonics, Ann Arbor, MI) with a diameter of 0.8 mm were inserted into the greater and lesser trochanter by the use of a spring loaded piston (RSA Biomedical AB, UmeI, Sweden). The cadaveric bone was rigidly attached to a plexiglass base plate in a position simulating 20" of external rotation. For the canine model we used a fresh frozen mongrel canine femur that was thawed and prepared in a manner similar to the human femur. Nine 0.5 mm diameter tantalum markers were inserted into the greater and lesser trochanter with the use of the spring loaded piston. For the human model, a cobaltchromium alloy femoral component (CPT, C size 2, Zimmer, Warsaw, I N ) with a 28 nim diameter cobaltxhromium head was used. For the canine model, we used a cobalt-chromium mono-bloc femoral component (Canine I1 Total Hip, Richards, Memphis, T N ) with a reduced length. Both femoral components had three tantalum markers attached (0.8 and 0.5 mm diameter for the human and canine models, respectively) by plastic studs providing an average offset of 5 mm from the stem. These parameters were chosen to replicate methods used in RSA trials involving patients or, in the case of the canine, methods thought to be relevant to this geometry. The femoral components were rigidly attached to a high precision x , y . z translation stage (model 460, Newport, Irvine, Ca) via a plastic holder and placed within the femur in a position simulating total hip replacement, but with a clearance of at least 1 mm in relation to the bone in each direction. The stage was instrumented with three Vernier micrometers (model SMI 3, Newport, Irvine, CAI. According to the manufacturer the system is accurate to 0.001 mm with an angular deviation less than 0.009". The translation stage was grounded to the same plexiglass base plate as the cadaveric femur (Fig. 1). The plexiglass base plate with the translation stage and the specimen was placed 45 cm above a calibration cage (Cage type 41, RSA Biomedical AB, Umea, Sweden) in a two-shelf cart (Fig. 3). The calibration cage had tantalum markers with known positions embedded in the walls and rasters overlying two radiographic film cassettes, which were held into a built-in cassette holder for standard size film (43 mm I( 36 mm). A uniplanar type of RSA setup was used [I I]. Two radiographic tubes, one stationary and one portable unit, were mounted so that the beams crossed at an angle of approximately 40" (Fig. 2). The stationary and portable radiographic tubes were operated at 83 and 95 kV and 5 and 10 mAs, respectively. Standard diagnostic radiographic film (Iiodak, T-MAT") was used. For both the human and canine models, the base plate with attached femur was visually aligned (without any instrumented aid) to the RSA cage. For the accuracy part of the study, the stem was displaced in one out of three directions at a time from zero to 500 pm in 14 increments. Increments of 25 pm were used in the range between zero and 200 pm, followed by increments of 50 pm between 200 and 500 pm. A simultaneous film pair was exposed following each incremental displacement. Five different series were obtained for each specimen, consisting of distal displacements along the longitudinal axis, medial and lateral displacements along the transverse axis. and anterior and posterior displacements along the sagittal axis. For each of the human and canine models, a total of 75 film pairs were obtained for this part of the study. For the precision part of the study, each specimen was exposed five times at zero and thereafter five times after a
Fig. 1. Placement of femur and X.F.2 translation stage on the plexiglass plate ((a)human and ( b ) canine). The femur and x,y3ztranslation stage were firmly fixed t o the plexiglass plate. In each model. the femoral component was rigidly attached to the translation stage via a truncated cylindric mold. The femoral component was allowed to move freely with respect to the femur, but both the femur and translation stage were fixed with respect to each other through their attachments to the plexiglass plate. single 300 pm displacement along each of the three axes (distally along the longitudinal axis, medially along the transverse axis, and posteriorly along the sagittal axis). Thus, for each model 30 film pairs were obtained for the precision part of the study. For each film pair obtained, the projected images of the markers on the films were marked and digitized on a measurement table (Hasselblad Engineering, Sweden) with a known precision of 0.15'1'0 (coefficient of variation). The three-dimensional coordinates of the implant and bone markers in relation to the cage were computed by the use of the computer programs XRAY90 and Kinema (RSA Biomedical AB, Umel, Sweden). The translations, as measured by RSA. of the femoral components relative to the cadaveric bones were evaluated using the resultant displacement, i.e., the vector length, calculated from the three components of translation. This precluded error due to possible misalignment between the translational stage and the cage. Three separate calculations of the displacement of each femoral component were made based on the number of markers used to identify the femoral component. For one alternative, all three markers attached to the prosthesis were used in combination with the center of the prosthetic head. For a second alternative, only the center of the prosthetic head was used, and for a third alternative only the three tantalum markers attached to the femoral component were used. In the first and third alternatives a segment motion analysis was performed, Le., the computation of the movement was derived from the movement of the center of gravity for the markers representing the segment. In addition, three different combinations of markers in the cadaveric bones were used in order to evaluate the effect of the number of markers and their spatial configuration. The spatial configuration of
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80 cm
calculated using lower and upper bounds of the prediction interval for the mean predicted response. Precision was calculated as the standard deviation of the five repeated measurements of the 200 pm displacement along each axis in both the human and canine models.
Results
E
t’ 7
Fig. 2. Schematic of the entire set-up (side view). The approximate dimensions are shown. Note that the two X-ray tubes were placed so that the beams intersected at approximately 40”, the bone and implant were placed on the top shelf of the cart, and the RSA cage was placed on the bottom shelf of the cart. the markers is characterized by the configuration number in the program Kinema. A low Configuration number reflects a wide spatial distribution of the markers, whereas a high number implies that the markers are spaced close t o a line [14]. In this study we used three different levels of configurations for the human model (50. 100 and 143) and for the canine model (54, 92 and 154), all of which represent common numbers for the RSA method when used to study femoral component displacements in vivo. In the human model the first alternative had eight markers included with a configuration number of 50, the second had five markers with a configuration number of 100 and the third had foLlr markers with a configuration number of 143. In the canine model the first alternative had nine markers with a configuration number of 54, the second had five markers with a configuration number of 92 and the third had five markers with a configuration number of 154. Thus, nine evaluations were made for each axis ( 3 femoral component landmark configurations times 3 bone marker configurations). The radiostereometric computer program has a function, termed the mean error of rigid body fitting (ME) for characterizing relative motion among the markers within each rigid body (i.e., femur and implant) from the first reference examination to all subsequent examinations. In our study the M E values varied from 10 to 88 pm in the human bone and from 15 t o 128 pm for the human femoral component. The corresponding numbers for the canine model were 27-86 ym for the femoral component and 56-120 yni for the bone. Linear regression analysis was used to relate the displacements as measured with RSA to the actual displacements given by the micrometer. For each of the human and canine models, 45 regression equations were examined (five directions: distal longitudinal, medial transverse, lateral transverse, posterior sagittal, and anterior sagittal, times three bone marker configurations, times three stem marker configurations) for a total of 90 regression equations. Accuracy is presented as the 95’16 prediction interval (PI). This interval WAS calculated by determining the lower and upper bounds for the prediction interval for each observation using the variable ‘ICIN’ in the ‘SAVE’ subcommand of the SPSS ‘REGRESSION’ procedure (SPSS, version 8.0 for Windows, Chicago. IL) and then calculating the mean of the intervals for each observation. This is a conservative estimate because the PI calculated in this manner is about twice the width of the PI
With the set of bone and stem markers yielding the most accurate measurements, the prediction interval of the RSA measurements varied from f 4 7 to f 1 2 1 pm in the human model (0.89 < I” < 0.98,P < 0.001, Table 1) and from 414.5 to &74 pm in the canine model (0.96 < r’ < 0.99,P < 0.001, Table 1). In both models, displacements measured along the longitudinal axis were more accurate than displacements measured along the transverse and sagittal axes. Of the 90 calculated regression equations, 33 (22 in the human and 11 in the canine model) had a slope and intercept statistically significantly different from one and zero, respectively. The most accurate measurements in both the human and canine models occurred when three stem markers were used (Table 2). Use of only the calculated center of the femoral head rather than the three stem markers led to a 3-fold degradation in accuracy for the human model and a ’-fold degradation for the canine model. Use of all three femoral stem markers plus the calculated center of the femoral head did not improve the accuracy compared to using only the three stem markers. The highest accuracy was found when the configuration number for the femoral bone was minimized (Table 3). For the human model, the configuration number of 50 led to a 3-fold increase in accuracy compared to the configuration number of 143. For the canine model, the configuration number of 54 led to a 1.5-fold increase in accuracy compared to the configuration number of 154. The precision of 200 pm displacements along the longitudinal axis was 30 pm in the human model and 40 pm in the canine model when the combination of bone and stem markers giving the most accurate results was used (Table 1). Precision was less dependent on using the ideal marker combination than was accuracy (Tables 2 and 3). Nevertheless, the best marker combination for accuracy tended to be the best marker combination for precision. With both the human and canine models the axis with the least precision was sagittal, with the longitudinal and transverse axes having the same precision in the human model and the transverse axis having the best precision in the canine model (Table I ) .
Discussion In these two models of femoral component displacement relative to cadaveric bone, we have shown that under ideal circumstances translations up to 500 p m can
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Table 1 Comparison of accuracy and precision between the different axes" Axis (direction) of displacement
Accuracy
Precision
R2b
95?'11prediction
Human model
Longitudinal (distal) Transverse (medial) Transverse (lateral) Sagittal (posterior) Sagittal (anterior)
0.98 0.96 0.89 0.96 0.96
3146.5 f76.5 *I21 &71.5 *75
30 30 nd 104 nd
Canine model
Longitudinal (distal) Transverse (medial) Transverse (lateral) Sagittal (posterior) Sagittal (anterior)
0.99 0.98 0.98 0.96 0.96
&45 148.5 f48 174 f74
40 24 nd 54 nd
a For both models, the calculated translations were based on all markers in the femur and three markers in the stem, Le., the set of markers which yielded the most accurate measurements as detailed in Tables 2 and 3. For each equation, P < 0.001. nd: not determined.
Table 2 The influence of the number of markers on the femoral component for displacements measured along the longitudinal axis" Markers used
Accuracy ~2 b
Precision Standard deviation of a 200 pm displacement (urn)
9 5 " b prediction interval (pm)
~~
Human model
Canine model
~
Three stem markers only Femoral head only Three stem markers + femoral head
0.98 0.86 0.98
Three stem markers only Femoral head only Three stem markers + femoral head
0.99 0.94 0.99
H6.5 zt139.5
30 28 36
&56 *45
40 46 50
f95 f45
"In both models, the calculations were based on the minimum configuration number for the femoral bone markers (configuration number of 54 for the human model and 50 for the canine model). bFor each equation, P < 0.001.
Table 3 The influence of the number of markers in the femur for displacements measured along the longitudinal axis"
Human model
Number of markers in the femur (configuration n urn ber )
Accuracy
4 (143) 5 (100) 8 (50)
0.86 0.97 0.98
5 (154) 5 (93) 9 (54)
0.97 0.98 0.99
R2b
01111)
Precision Standard deviation of a 200 pm displacement (um)
1139 168 346.5
38 30
95041 prediction interval
170 158.5 f45 a In both models, the calculations were based on using the three tantalum markers on the femoral component. For each equation, P < 0.00 I . Canine model
be measured by RSA with an accuracy of approximately +45 pm and translations of 200 pm can be measured with a precision of 3 0 4 0 pm. The longitudinal axis had the highest accuracy and precision in both the human and animal models. This was expected because the
18
52 46 40
movements along this axis take place in a plane orthogonal to the radiographic beams. The precision was poorest along the sagittal axis in both the models. In our study, we did not eliminate the random component of the measurement error in the calculation of
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the prediction interval. Hence, we assessed accuracy and not bias. Specifically, we reported the accuracy of single measurements of each translation with respect to the reference value by using regression models to calculate the prediction intervals. We did measure the precision of the measurement for one level, namely a 200 pm displacement. At this level, the standard deviaition was typically about 15-20'%, of the mean (i.e., about 30-40 pm). Elimination of the random measurement error is usually accomplished by averaging a large number of test results, often 30 or more, at each level of measurement. Thus, further work would need to be done to calculate the bias of RSA, using the American Society for Testing and Materials definition of bias. The most important factors influencing the precision of RSA as applied to the study of joint implant stability in hips and knees are the number of markers, stability of the markers expressed as the mean error of rigid body fitting [9], and the spatial configuration of the markers expressed as the condition number [13]. The distance between the segments being studied and the size of the translation step are other factors known to affect the error of the method [15]. Recently, modified cages with an increased number of markers used for the determination of the foci as well as new digital measurement techniques of the radiographs have been shown to reduce the error of the method [2]. The films in our study were measured on a manually operated measurement table. Recently developed measurement systems, where the films are scanned and marker positions located with a computer, or even the use of digital films, can be expected to improve the precision compared to what was found in our study. Since our films were obtained under in vitro conditions, we did to some extent avoid the problem of poor image quality, a commonly encountered limiting factor under in vivo conditions. In that respect, the results of our study should be interpreted as what can be expected under ideal conditions in an in vivo study. Our primary interest in this study was to assess the accuracy and precision of translations of the femoral component. The RSA system does, however, also have the option of rotation analysis. The finding, that the addition of the prosthetic head as a landmark to the three tantalum markers placed on the femoral component actually degraded the accuracy and precision in comparison to the use of only the three tantalum markers on the stem, is striking. An even greater degradation occurred when only the the prosthetic head was used as a landmark. These findings imply that the reliability of the computed center of the prosthetic head as a landmark is much less than that of markers placed on the femoral stem. The reason for this finding is unclear, but it is possible that future improvements in the computational algorithms for the femoral head center could strengthen the use of the femoral head as a reliable landmark.
In the femur, the number of bone markers used in the RSA calculations and their configuration number influenced the accuracy (i.e., width of the prediction intervals) by a factor of about 3 from the best to the worst combination. Taken together with the findings regarding the femoral head as a sole landmark, these findings suggest that whenever the center of the femoral head is used as a sole landmark for the femoral component, a wide spatial distribution of the landmarks in the femoral bone is imperative; otherwise the accumulated error in accuracy will be quite large. As described in the methods section, the RSA computer program indicates the instability of the markers by means of the ME value. For in vivo studies the ME value represents the sum of the marker instability in the skeleton (or the implant) between different examinations and the error of the film digitization procedure. In this in vitro study, where the markers were glued to the specimens and were assumed to be stable, the bone was dead and neither bone nor implant was subject to any significant loads, this value represents merely the digitization error. Our ME values were all less than 130 pm, whereas in vivo studies typically have ME values of 300 pm or less [8,9]. We did not attempt to determine the effect of the ME value on accuracy or precision, but the ME values obtained in the present study represent minima that one could reasonably hope to obtain. Assuming that the level of digitization error was approximately the same in the present study and Ryd's study [9], one can surmise that about 50% of the ME value obtained in vivo is caused by lack of strict adherence to rigid body assumptions. Even with ME values up to 300 pm, there is only a slight effect on precision [9]. Thus, this lack of complete adherence to rigid body assumptions in vivo does not necessarily degrade precision. It should, however, be pointed out that recent computer simulation studies have shown that the influence on the accuracy of the ME-values and the configuration number varies considerably with the application of the method and with the direction of movement being analyzed. Previous workers have suggested that implant displacements less than 200-300 pm are not detectable by RSA [7,12] based on in vivo studies of precision and theoretical estimates of accuracy. The present study indicates that under ideal in vitro conditions, the minimum detectable displacement by RSA is of the order of 100 pm (given a prediction interval of approximately 90 pm and a precision of 150/0). In vivo it would probably be impossible to achieve this level of accuracy and precision because of the addition of other sources of error (such as suboptimal radiographic images). In addition, it is possible that the degree of accuracy and precision in the present experiment may not be perfectly representative of in vivo measurements because the order of displacements in the experiment was not randomized.
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Nevertheless, the present in vitro study helps to characterize the degree of accuracy and precision one could hope to obtain with RSA under ideal circumstances. The stability of joint replacement components is of interest in understanding tissue regeneration and ingrowth at the interface and in predicting long-term implant loosening [l]. The length scale of interest for the former is of the order of tens of micrometers ( m) while the length scale for the latter is of the order of hundreds of micrometers or even millimeters ( 10-4-10-3 m). It should be noted that RSA is not the preferred method of measuring in vitro implant displacement because other techniques with much higher accuracy and better precision are already available [I]. Presumably, initial excessive motion leads to long-term migration, but these early small displacment events will never be measurable by RSA even under ideal circumstances unless significant improvements in the technology are made. However, the observation that migration as detected by RSA in the second year after joint replacement is predictive of long-term loosening [3,1O] where the accumulated migration approaches hundreds of micrometers or even millimeters, remains an important finding. In approximately one-third of the regression equations the slope and the intercept for the regression lines were different from one and zero, respectively. Thus, for most of the measurements the RSA calculations would not need to be corrected and could be interpreted directly. However, before comparing values between laboratories, each laboratory would need to perform a calibration procedure. Depending on the results it might be necessary to calculate the ‘true’ displacements based on laboratory-specific regression equations and then to compare these calculated displacements. For longitudinal studies within one laboratory, this would be unnecessary.
Acknowledgements This project was partially supported by NIH Grants AR16485 and AR42862.
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References [l] Berzins A, Sumner D R . In vitro measurements of implant stability. In: An YH, Draughn RA, editors. Mechanical testing of bone and the bone-implant interface. Boca Raton: C R C Press; 2000. p. 515-26. [2] Borlin N, Karrholm J. Radiostereometry based on digitised radiographs. Trans ORS 1997;22:626-626. [3] KCrrholm J, Borssen B, Lowenhielm G, Snorrason F. Does earlys micromotion of femoral stem protheses matter?. .I Bone Joint Surg (Br) 1994;76:912-7. [4] Kirrholm J, Herberts P, Hultmark P, Malchau H, Nivbrant B, Thanner J. Radiostereometry of hip prostheses. Clin Orthop 1997;344:94-I 10. [S] Karrholm J, Malchau H, Snorrason F, Herberts P. Micromotion of cemented, hydroxyapatite and porous coated femoral stems. Randomized study using roentgen stereophotogrammetric analysis. J Bone Joint Surg (Am) 1994;76A:1691 705. [6] Mjoberg B, Selvik G, Hansson LI. Mechanical loosening of total hip prostheses. A radiographic and roentgen stereophotogrammetric study. J Bone Joint Surg Br 1986;77W. [7] Onsten I, Akesson K, Besjakov J, Obrant KJ. Migration of the Charnley stem in rheumatoid arthritis and osteoarthritis. A roentgen stereophotogrammetric study. J Bone Joint Surg (Br) 1995;77B: 18-22. [8] Onsten I, Carlson AS, Ohlin A. Nilsson JA. Migration of acetabular components, inserted with and without cement, in one-stage bilateral hip arthroplasty. J Bone Joint Surg ( A m ) 1994;76-A:185--94. Ryd L. Micromotion in knee arthroplasty. Acta Orthop Scand 1986;57(suppl). Ryd L, Albrektsson BEJ, Carlsson L, Dansgard F, Herberts P. Lindstraand A, et al. Roentgen stereophotogrammetric analysis as a predictor of mechanical loosening knee prostheses. J Bone Joint Surg (Br) 1995:77:377-83. Selvik G. Roentgen sterophotogrammetry. A method for the study of thekinematics of the skeletal system. Reprint from the orignal 1974 thesis. Acta Orthop Scand 1989;60 (Suppl 232). Snosrrason F, Karrholm J , Malchau H, Herberts P. Early loosening of revision hip arthroplasty. A roentgen stereophotogrammetric analysis. J Arthroplasty 1990;5:317-29. Soderkvist I, Wedin PA. Determining the movements of the skeleton using well-configured markers. J Biomech 199326: 1473 7. Soderqvist I. Computing parameters in nonlinear least squares models. P h D Thesis, University of Umea, Sweden. 1993. Yuan X, Ryd L, Blankevoort L. Error propagation for relative motion determined from marker positions. J Biomech 1997:30:989-92.
Journal of Orthopaedic Research Journal of Orthopaedic Research 19 (2001) 1162-1 167 www.elsevier.com/locate/orthres
Accuracy and precision of radiostereometric analysis in the measurement of THR femoral component translations: human and canine in vitro models Ingemar Onsten
Aivars Berzins ‘, Susan Shott
’,Dale R. Sumner
a,b,*
Dtpurtmmt id’Anntomj., Rush hli~dicizlColleg~,Rush-Pre.rhyteriun-St. Lukr ‘s hlrdicul Center, 600 South Puulinu Street, Chicago. IL 60612-38317, LISA Depurinicni ?f’Ortlioprilic Surgery, Rush Mediic~cilCollugu. Rush- Preshyterian-St. Lukc’s MediLril Center, Chicago, IL, USA Depurtmmt qf’ Orthopiledies, hfulniii Liniiwrsity Hospital, hlulmo, Stveiien Dtyurifiient of 0hsieirk:s m i l Gyircology. Rush Medicul Collegu, Rush- Preyhyterian-St. Luke’s Medic111 Center, Chicago, IL, USA
Abstract
Radiostereometric analysis (RSA) is used to measure translations of joint replacement components with respect to the host bone in vivo. We used two cadaveric models of hip arthroplasty, one human and one canine, to evaluate the accuracy and precision of RSA-based estimates of translations of the femoral component with respect to the femur under ideal conditions. The femoral components were attached rigidly to a micrometer stage that provided standard displacements in increments of 25 and 50 pm in the interval from zero to 500 pni along three orthogonal axes. Radiostereometric examinations were performed for each increment. Accuracy was calculated as the 95% prediction intervals from regression analyses between the measured and actual displacements. Precision was evaluated as the standard deviation of five repeated measurements of a 200 pm displacement along each axis. Both accuracy and precision were best along the longitudinal axis, with a prediction interval of f 4 7 pm in the human model and 1 4 5 pm in the canine model and a standard deviation of 30 pm in the human model and 40 pm in the canine model. The use of only the prosthetic head as a landmark (as opposed to three markers placed on the femoral stem) led to a 3-fold larger prediction interval in the human model and a ’-fold greater prediction interval in the canine model. 0 2001 Orthopaedic Research Society. Published by Elsevier Science Ltd. All rights reserved.
Introduction
Radiostereometric analysis, or roentgen stereophotogrammetric analysis (RSA), is a research tool which has been used mainly for studies related to joint kinematics and implant fixation after joint replacement surgery. The RSA system [ l l ] includes the implantation of radiopaque markers into the skeleton and onto the implant to serve as landmarks, use of stereoradiographs to determine the location of the markers three-dimensionally, and calculation of relative displacements between different bones or between implants and bones. Important properties of any measurement system include accuracy, precision, and bias. According to the American Society for Testing and Materials Standard E 177-90a (Reapproved in 1996), ‘uccztracy is a generic concept of exactness related to the closeness of agree* Corresponding author. Tel.: +I-312-942-8151; fax: +1-312-9327040. E-niuil a i l d r ~ rsumnerccj~rush.edu ~: (D.R. Sumner).
ment between the average of one or more test results and an accepted reference value’ and ‘the precision of a measurement process . . . is a generic concept related to the closeness of agreement between test results obtained under prescribed like conditions’. The accuracy of a given measurement depends upon bias and precision. Bias, which refers ‘to a consistent or systematic difference between a set of test results from the process and an accepted reference value of the property being measured’ can only be determined if imprecision is removed by averaging a large number of test results. While the in vivo within-laboratory precision of the radiostereometric method has been evaluated in several clinical investigations on total hip arthroplasty [5-7,13], the accuracy of the method has only been evaluated for the part of the method that relates to the computations of the three-dimensional coordinates of the landmarks [4,11]. Thus, the accuracy of measuring actual displacements has to our knowledge never been published. Our goal was to evaluate the accuracy and precision of RSA-based measurements of the displacements of
0736-0166101/$ - see front matter Q 7001 Orthopaedic Research Society. Published by Elsevier Science Ltd. All rights reserved. PII: S 0 7 3 6 - 0 2 6 6 ( 0 1 ) 0 0 0 3 9 - 0
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femoral stems in cadaveric models of human and canine hip arthroplasties, thereby forming the basis for future studies on bias. We designed the study to investigate the effects of two practical issues, namely the number and spacing of markers in the femur and the number of femoral component landmarks. The study was performed in vitro and represents the degree of accuracy and precision obtainable under ideal conditions.
Methods For the human model we used a fresh frozen human cadaveric femur, which was thawed 24 h prior to the experiment. The soft tissues were removed, and the trabecular bone was reamed out from the proximal one-third of the femoral canal. Ten tantalum markers (Industrial Techtonics, Ann Arbor, MI) with a diameter of 0.8 mm were inserted into the greater and lesser trochanter by the use of a spring loaded piston (RSA Biomedical AB, UmeI, Sweden). The cadaveric bone was rigidly attached to a plexiglass base plate in a position simulating 20" of external rotation. For the canine model we used a fresh frozen mongrel canine femur that was thawed and prepared in a manner similar to the human femur. Nine 0.5 mm diameter tantalum markers were inserted into the greater and lesser trochanter with the use of the spring loaded piston. For the human model, a cobaltchromium alloy femoral component (CPT, C size 2, Zimmer, Warsaw, I N ) with a 28 nim diameter cobaltxhromium head was used. For the canine model, we used a cobalt-chromium mono-bloc femoral component (Canine I1 Total Hip, Richards, Memphis, T N ) with a reduced length. Both femoral components had three tantalum markers attached (0.8 and 0.5 mm diameter for the human and canine models, respectively) by plastic studs providing an average offset of 5 mm from the stem. These parameters were chosen to replicate methods used in RSA trials involving patients or, in the case of the canine, methods thought to be relevant to this geometry. The femoral components were rigidly attached to a high precision x , y . z translation stage (model 460, Newport, Irvine, Ca) via a plastic holder and placed within the femur in a position simulating total hip replacement, but with a clearance of at least 1 mm in relation to the bone in each direction. The stage was instrumented with three Vernier micrometers (model SMI 3, Newport, Irvine, CAI. According to the manufacturer the system is accurate to 0.001 mm with an angular deviation less than 0.009". The translation stage was grounded to the same plexiglass base plate as the cadaveric femur (Fig. 1). The plexiglass base plate with the translation stage and the specimen was placed 45 cm above a calibration cage (Cage type 41, RSA Biomedical AB, Umea, Sweden) in a two-shelf cart (Fig. 3). The calibration cage had tantalum markers with known positions embedded in the walls and rasters overlying two radiographic film cassettes, which were held into a built-in cassette holder for standard size film (43 mm I( 36 mm). A uniplanar type of RSA setup was used [I I]. Two radiographic tubes, one stationary and one portable unit, were mounted so that the beams crossed at an angle of approximately 40" (Fig. 2). The stationary and portable radiographic tubes were operated at 83 and 95 kV and 5 and 10 mAs, respectively. Standard diagnostic radiographic film (Iiodak, T-MAT") was used. For both the human and canine models, the base plate with attached femur was visually aligned (without any instrumented aid) to the RSA cage. For the accuracy part of the study, the stem was displaced in one out of three directions at a time from zero to 500 pm in 14 increments. Increments of 25 pm were used in the range between zero and 200 pm, followed by increments of 50 pm between 200 and 500 pm. A simultaneous film pair was exposed following each incremental displacement. Five different series were obtained for each specimen, consisting of distal displacements along the longitudinal axis, medial and lateral displacements along the transverse axis. and anterior and posterior displacements along the sagittal axis. For each of the human and canine models, a total of 75 film pairs were obtained for this part of the study. For the precision part of the study, each specimen was exposed five times at zero and thereafter five times after a
Fig. 1. Placement of femur and X.F.2 translation stage on the plexiglass plate ((a)human and ( b ) canine). The femur and x,y3ztranslation stage were firmly fixed t o the plexiglass plate. In each model. the femoral component was rigidly attached to the translation stage via a truncated cylindric mold. The femoral component was allowed to move freely with respect to the femur, but both the femur and translation stage were fixed with respect to each other through their attachments to the plexiglass plate. single 300 pm displacement along each of the three axes (distally along the longitudinal axis, medially along the transverse axis, and posteriorly along the sagittal axis). Thus, for each model 30 film pairs were obtained for the precision part of the study. For each film pair obtained, the projected images of the markers on the films were marked and digitized on a measurement table (Hasselblad Engineering, Sweden) with a known precision of 0.15'1'0 (coefficient of variation). The three-dimensional coordinates of the implant and bone markers in relation to the cage were computed by the use of the computer programs XRAY90 and Kinema (RSA Biomedical AB, Umel, Sweden). The translations, as measured by RSA. of the femoral components relative to the cadaveric bones were evaluated using the resultant displacement, i.e., the vector length, calculated from the three components of translation. This precluded error due to possible misalignment between the translational stage and the cage. Three separate calculations of the displacement of each femoral component were made based on the number of markers used to identify the femoral component. For one alternative, all three markers attached to the prosthesis were used in combination with the center of the prosthetic head. For a second alternative, only the center of the prosthetic head was used, and for a third alternative only the three tantalum markers attached to the femoral component were used. In the first and third alternatives a segment motion analysis was performed, Le., the computation of the movement was derived from the movement of the center of gravity for the markers representing the segment. In addition, three different combinations of markers in the cadaveric bones were used in order to evaluate the effect of the number of markers and their spatial configuration. The spatial configuration of
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80 cm
calculated using lower and upper bounds of the prediction interval for the mean predicted response. Precision was calculated as the standard deviation of the five repeated measurements of the 200 pm displacement along each axis in both the human and canine models.
Results
E
t’ 7
Fig. 2. Schematic of the entire set-up (side view). The approximate dimensions are shown. Note that the two X-ray tubes were placed so that the beams intersected at approximately 40”, the bone and implant were placed on the top shelf of the cart, and the RSA cage was placed on the bottom shelf of the cart. the markers is characterized by the configuration number in the program Kinema. A low Configuration number reflects a wide spatial distribution of the markers, whereas a high number implies that the markers are spaced close t o a line [14]. In this study we used three different levels of configurations for the human model (50. 100 and 143) and for the canine model (54, 92 and 154), all of which represent common numbers for the RSA method when used to study femoral component displacements in vivo. In the human model the first alternative had eight markers included with a configuration number of 50, the second had five markers with a configuration number of 100 and the third had foLlr markers with a configuration number of 143. In the canine model the first alternative had nine markers with a configuration number of 54, the second had five markers with a configuration number of 92 and the third had five markers with a configuration number of 154. Thus, nine evaluations were made for each axis ( 3 femoral component landmark configurations times 3 bone marker configurations). The radiostereometric computer program has a function, termed the mean error of rigid body fitting (ME) for characterizing relative motion among the markers within each rigid body (i.e., femur and implant) from the first reference examination to all subsequent examinations. In our study the M E values varied from 10 to 88 pm in the human bone and from 15 t o 128 pm for the human femoral component. The corresponding numbers for the canine model were 27-86 ym for the femoral component and 56-120 yni for the bone. Linear regression analysis was used to relate the displacements as measured with RSA to the actual displacements given by the micrometer. For each of the human and canine models, 45 regression equations were examined (five directions: distal longitudinal, medial transverse, lateral transverse, posterior sagittal, and anterior sagittal, times three bone marker configurations, times three stem marker configurations) for a total of 90 regression equations. Accuracy is presented as the 95’16 prediction interval (PI). This interval WAS calculated by determining the lower and upper bounds for the prediction interval for each observation using the variable ‘ICIN’ in the ‘SAVE’ subcommand of the SPSS ‘REGRESSION’ procedure (SPSS, version 8.0 for Windows, Chicago. IL) and then calculating the mean of the intervals for each observation. This is a conservative estimate because the PI calculated in this manner is about twice the width of the PI
With the set of bone and stem markers yielding the most accurate measurements, the prediction interval of the RSA measurements varied from f 4 7 to f 1 2 1 pm in the human model (0.89 < I” < 0.98,P < 0.001, Table 1) and from 414.5 to &74 pm in the canine model (0.96 < r’ < 0.99,P < 0.001, Table 1). In both models, displacements measured along the longitudinal axis were more accurate than displacements measured along the transverse and sagittal axes. Of the 90 calculated regression equations, 33 (22 in the human and 11 in the canine model) had a slope and intercept statistically significantly different from one and zero, respectively. The most accurate measurements in both the human and canine models occurred when three stem markers were used (Table 2). Use of only the calculated center of the femoral head rather than the three stem markers led to a 3-fold degradation in accuracy for the human model and a ’-fold degradation for the canine model. Use of all three femoral stem markers plus the calculated center of the femoral head did not improve the accuracy compared to using only the three stem markers. The highest accuracy was found when the configuration number for the femoral bone was minimized (Table 3). For the human model, the configuration number of 50 led to a 3-fold increase in accuracy compared to the configuration number of 143. For the canine model, the configuration number of 54 led to a 1.5-fold increase in accuracy compared to the configuration number of 154. The precision of 200 pm displacements along the longitudinal axis was 30 pm in the human model and 40 pm in the canine model when the combination of bone and stem markers giving the most accurate results was used (Table 1). Precision was less dependent on using the ideal marker combination than was accuracy (Tables 2 and 3). Nevertheless, the best marker combination for accuracy tended to be the best marker combination for precision. With both the human and canine models the axis with the least precision was sagittal, with the longitudinal and transverse axes having the same precision in the human model and the transverse axis having the best precision in the canine model (Table I ) .
Discussion In these two models of femoral component displacement relative to cadaveric bone, we have shown that under ideal circumstances translations up to 500 p m can
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Table 1 Comparison of accuracy and precision between the different axes" Axis (direction) of displacement
Accuracy
Precision
R2b
95?'11prediction
Human model
Longitudinal (distal) Transverse (medial) Transverse (lateral) Sagittal (posterior) Sagittal (anterior)
0.98 0.96 0.89 0.96 0.96
3146.5 f76.5 *I21 &71.5 *75
30 30 nd 104 nd
Canine model
Longitudinal (distal) Transverse (medial) Transverse (lateral) Sagittal (posterior) Sagittal (anterior)
0.99 0.98 0.98 0.96 0.96
&45 148.5 f48 174 f74
40 24 nd 54 nd
a For both models, the calculated translations were based on all markers in the femur and three markers in the stem, Le., the set of markers which yielded the most accurate measurements as detailed in Tables 2 and 3. For each equation, P < 0.001. nd: not determined.
Table 2 The influence of the number of markers on the femoral component for displacements measured along the longitudinal axis" Markers used
Accuracy ~2 b
Precision Standard deviation of a 200 pm displacement (urn)
9 5 " b prediction interval (pm)
~~
Human model
Canine model
~
Three stem markers only Femoral head only Three stem markers + femoral head
0.98 0.86 0.98
Three stem markers only Femoral head only Three stem markers + femoral head
0.99 0.94 0.99
H6.5 zt139.5
30 28 36
&56 *45
40 46 50
f95 f45
"In both models, the calculations were based on the minimum configuration number for the femoral bone markers (configuration number of 54 for the human model and 50 for the canine model). bFor each equation, P < 0.001.
Table 3 The influence of the number of markers in the femur for displacements measured along the longitudinal axis"
Human model
Number of markers in the femur (configuration n urn ber )
Accuracy
4 (143) 5 (100) 8 (50)
0.86 0.97 0.98
5 (154) 5 (93) 9 (54)
0.97 0.98 0.99
R2b
01111)
Precision Standard deviation of a 200 pm displacement (um)
1139 168 346.5
38 30
95041 prediction interval
170 158.5 f45 a In both models, the calculations were based on using the three tantalum markers on the femoral component. For each equation, P < 0.00 I . Canine model
be measured by RSA with an accuracy of approximately +45 pm and translations of 200 pm can be measured with a precision of 3 0 4 0 pm. The longitudinal axis had the highest accuracy and precision in both the human and animal models. This was expected because the
18
52 46 40
movements along this axis take place in a plane orthogonal to the radiographic beams. The precision was poorest along the sagittal axis in both the models. In our study, we did not eliminate the random component of the measurement error in the calculation of
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the prediction interval. Hence, we assessed accuracy and not bias. Specifically, we reported the accuracy of single measurements of each translation with respect to the reference value by using regression models to calculate the prediction intervals. We did measure the precision of the measurement for one level, namely a 200 pm displacement. At this level, the standard deviaition was typically about 15-20'%, of the mean (i.e., about 30-40 pm). Elimination of the random measurement error is usually accomplished by averaging a large number of test results, often 30 or more, at each level of measurement. Thus, further work would need to be done to calculate the bias of RSA, using the American Society for Testing and Materials definition of bias. The most important factors influencing the precision of RSA as applied to the study of joint implant stability in hips and knees are the number of markers, stability of the markers expressed as the mean error of rigid body fitting [9], and the spatial configuration of the markers expressed as the condition number [13]. The distance between the segments being studied and the size of the translation step are other factors known to affect the error of the method [15]. Recently, modified cages with an increased number of markers used for the determination of the foci as well as new digital measurement techniques of the radiographs have been shown to reduce the error of the method [2]. The films in our study were measured on a manually operated measurement table. Recently developed measurement systems, where the films are scanned and marker positions located with a computer, or even the use of digital films, can be expected to improve the precision compared to what was found in our study. Since our films were obtained under in vitro conditions, we did to some extent avoid the problem of poor image quality, a commonly encountered limiting factor under in vivo conditions. In that respect, the results of our study should be interpreted as what can be expected under ideal conditions in an in vivo study. Our primary interest in this study was to assess the accuracy and precision of translations of the femoral component. The RSA system does, however, also have the option of rotation analysis. The finding, that the addition of the prosthetic head as a landmark to the three tantalum markers placed on the femoral component actually degraded the accuracy and precision in comparison to the use of only the three tantalum markers on the stem, is striking. An even greater degradation occurred when only the the prosthetic head was used as a landmark. These findings imply that the reliability of the computed center of the prosthetic head as a landmark is much less than that of markers placed on the femoral stem. The reason for this finding is unclear, but it is possible that future improvements in the computational algorithms for the femoral head center could strengthen the use of the femoral head as a reliable landmark.
In the femur, the number of bone markers used in the RSA calculations and their configuration number influenced the accuracy (i.e., width of the prediction intervals) by a factor of about 3 from the best to the worst combination. Taken together with the findings regarding the femoral head as a sole landmark, these findings suggest that whenever the center of the femoral head is used as a sole landmark for the femoral component, a wide spatial distribution of the landmarks in the femoral bone is imperative; otherwise the accumulated error in accuracy will be quite large. As described in the methods section, the RSA computer program indicates the instability of the markers by means of the ME value. For in vivo studies the ME value represents the sum of the marker instability in the skeleton (or the implant) between different examinations and the error of the film digitization procedure. In this in vitro study, where the markers were glued to the specimens and were assumed to be stable, the bone was dead and neither bone nor implant was subject to any significant loads, this value represents merely the digitization error. Our ME values were all less than 130 pm, whereas in vivo studies typically have ME values of 300 pm or less [8,9]. We did not attempt to determine the effect of the ME value on accuracy or precision, but the ME values obtained in the present study represent minima that one could reasonably hope to obtain. Assuming that the level of digitization error was approximately the same in the present study and Ryd's study [9], one can surmise that about 50% of the ME value obtained in vivo is caused by lack of strict adherence to rigid body assumptions. Even with ME values up to 300 pm, there is only a slight effect on precision [9]. Thus, this lack of complete adherence to rigid body assumptions in vivo does not necessarily degrade precision. It should, however, be pointed out that recent computer simulation studies have shown that the influence on the accuracy of the ME-values and the configuration number varies considerably with the application of the method and with the direction of movement being analyzed. Previous workers have suggested that implant displacements less than 200-300 pm are not detectable by RSA [7,12] based on in vivo studies of precision and theoretical estimates of accuracy. The present study indicates that under ideal in vitro conditions, the minimum detectable displacement by RSA is of the order of 100 pm (given a prediction interval of approximately 90 pm and a precision of 150/0). In vivo it would probably be impossible to achieve this level of accuracy and precision because of the addition of other sources of error (such as suboptimal radiographic images). In addition, it is possible that the degree of accuracy and precision in the present experiment may not be perfectly representative of in vivo measurements because the order of displacements in the experiment was not randomized.
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Nevertheless, the present in vitro study helps to characterize the degree of accuracy and precision one could hope to obtain with RSA under ideal circumstances. The stability of joint replacement components is of interest in understanding tissue regeneration and ingrowth at the interface and in predicting long-term implant loosening [l]. The length scale of interest for the former is of the order of tens of micrometers ( m) while the length scale for the latter is of the order of hundreds of micrometers or even millimeters ( 10-4-10-3 m). It should be noted that RSA is not the preferred method of measuring in vitro implant displacement because other techniques with much higher accuracy and better precision are already available [I]. Presumably, initial excessive motion leads to long-term migration, but these early small displacment events will never be measurable by RSA even under ideal circumstances unless significant improvements in the technology are made. However, the observation that migration as detected by RSA in the second year after joint replacement is predictive of long-term loosening [3,1O] where the accumulated migration approaches hundreds of micrometers or even millimeters, remains an important finding. In approximately one-third of the regression equations the slope and the intercept for the regression lines were different from one and zero, respectively. Thus, for most of the measurements the RSA calculations would not need to be corrected and could be interpreted directly. However, before comparing values between laboratories, each laboratory would need to perform a calibration procedure. Depending on the results it might be necessary to calculate the ‘true’ displacements based on laboratory-specific regression equations and then to compare these calculated displacements. For longitudinal studies within one laboratory, this would be unnecessary.
Acknowledgements This project was partially supported by NIH Grants AR16485 and AR42862.
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References [l] Berzins A, Sumner D R . In vitro measurements of implant stability. In: An YH, Draughn RA, editors. Mechanical testing of bone and the bone-implant interface. Boca Raton: C R C Press; 2000. p. 515-26. [2] Borlin N, Karrholm J. Radiostereometry based on digitised radiographs. Trans ORS 1997;22:626-626. [3] KCrrholm J, Borssen B, Lowenhielm G, Snorrason F. Does earlys micromotion of femoral stem protheses matter?. .I Bone Joint Surg (Br) 1994;76:912-7. [4] Kirrholm J, Herberts P, Hultmark P, Malchau H, Nivbrant B, Thanner J. Radiostereometry of hip prostheses. Clin Orthop 1997;344:94-I 10. [S] Karrholm J, Malchau H, Snorrason F, Herberts P. Micromotion of cemented, hydroxyapatite and porous coated femoral stems. Randomized study using roentgen stereophotogrammetric analysis. J Bone Joint Surg (Am) 1994;76A:1691 705. [6] Mjoberg B, Selvik G, Hansson LI. Mechanical loosening of total hip prostheses. A radiographic and roentgen stereophotogrammetric study. J Bone Joint Surg Br 1986;77W. [7] Onsten I, Akesson K, Besjakov J, Obrant KJ. Migration of the Charnley stem in rheumatoid arthritis and osteoarthritis. A roentgen stereophotogrammetric study. J Bone Joint Surg (Br) 1995;77B: 18-22. [8] Onsten I, Carlson AS, Ohlin A. Nilsson JA. Migration of acetabular components, inserted with and without cement, in one-stage bilateral hip arthroplasty. J Bone Joint Surg ( A m ) 1994;76-A:185--94. Ryd L. Micromotion in knee arthroplasty. Acta Orthop Scand 1986;57(suppl). Ryd L, Albrektsson BEJ, Carlsson L, Dansgard F, Herberts P. Lindstraand A, et al. Roentgen stereophotogrammetric analysis as a predictor of mechanical loosening knee prostheses. J Bone Joint Surg (Br) 1995:77:377-83. Selvik G. Roentgen sterophotogrammetry. A method for the study of thekinematics of the skeletal system. Reprint from the orignal 1974 thesis. Acta Orthop Scand 1989;60 (Suppl 232). Snosrrason F, Karrholm J , Malchau H, Herberts P. Early loosening of revision hip arthroplasty. A roentgen stereophotogrammetric analysis. J Arthroplasty 1990;5:317-29. Soderkvist I, Wedin PA. Determining the movements of the skeleton using well-configured markers. J Biomech 199326: 1473 7. Soderqvist I. Computing parameters in nonlinear least squares models. P h D Thesis, University of Umea, Sweden. 1993. Yuan X, Ryd L, Blankevoort L. Error propagation for relative motion determined from marker positions. J Biomech 1997:30:989-92.