CMM-based method for assessing the volume change of retrieved polyethylene cups in MoP total hip replacements

: Wear occurring at the bearing surface and the consequent generation of wear debris has been identified as the primary cause of aseptic loosening in metal-on-polyethylene (MoP) hip joint replacements. The accurate estimation of volume change in polyethylene cups due to creep and wear is, therefore, an important step for identifying the cause of failure and improving the longevity of MoP prosthesis. The purposes of this study were to present and apply a co-ordinate measuring machine (CMM)-based method for assessing the volume change of retrieved components due to wear and creep by using a combination of CMM data and a bespoke computer programme. The method was firstly validated against the standard gravimetric technique, and then applied to four retrieved polyethylene cups for wear assessment and analysis. The results show that the volume changes calculated using the present method match well with those assessed through the gravimetric technique. The CMM-based method presented in the study is capable of effectively and reliably determining the volume change and characterising the wear patch of retrieved components from MoP hip joint replacements.


Introduction
Hip joint replacements have been widely used in clinical practice for patients who are affected by hip disorders such as osteoarthritis. Whilst clinical studies have shown excellent outcome and high survivorship for the operation [1,2], the service life of the implants has still been limited by the osteolysis and aseptic loosening mainly due to the wear of the components and the consequent wear debris produced at the articulating surface, especially for the implants using polyethylene as an acetabular cup and metal as a femoral head [3,4]. The accurate calculation and estimation of the wear occurring from the prosthesis, particularly from the explanted implants that have undergone physiological condition and loading, is therefore important for understanding the underlying wear mechanism and identifying the cause of the failure for hip joint replacements.
Several techniques have been proposed and applied to assess the wear of hip prostheses. The radiographic analysis was generally carried out in vivo for wear analysis in clinical practice [5,6]. However, the measurement accuracy of the method was limited by the joint alignment at the point where the film was taken and therefore was highly controversial [7]. The in vitro gravimetric method was concluded to be a standard technique for measuring the volumetric wear of joint implants, especially for new joints and materials under laboratory simulated conditions [8,9]. However, such a technique has the limitation of not being able to provide information on the worn surface of the components, such as the penetration depth and area of the worn surface. More importantly, the method is not feasible in the case of retrieved implants where the original or pre-wear data of the components is unknown.
As an alternative, the coordinate measuring machine (CMM)based method has been widely developed for the assessment of wear in explanted components. The method refers to the reconstruction of the original surface and calculation of the wear based on the points taken from the bearing surface of the retrieved components [10]. The accuracy of the method largely relies on the successful identification and reconstruction of the original or pristine surface of the component. Many studies have been conducted for developing reliable wear assessment methods. In 1996, Kothari et al. developed a CMM-based technique to evaluate 22 retrieved McKee-Farrar total hip replacements [11]. In this study, the pristine surface of the component was reconstructed by fitting the points measured on each sample to a sphere using the least-squares regression method. Unfortunately, the iterative process of surface fitting was just performed once in this study and the original surface of the component was not obtained. Carmignato et al. presented a method to evaluate the volumetric wear of nine ceramic femoral heads [12]. In this study, a reference computer-aided design (CAD) model was created using the points measured from the unworn areas of the femoral head. The comparison between measured points and reference CAD model was then performed using a dedicated elaboration algorithm. Bills et al. used the same method to assess the wear of five metal-on-metal hip prostheses and evaluate the impact of measurement uncertainty on the measurement process [13]. In these two studies, the original surface of the component was reconstructed based on the points taken from the unworn region of the component. The unworn region, however, was identified and determined either by visual inspection or manual examination. Therefore, the reliability and repeatability of the method cannot be guaranteed.
In 2011, Lord et al. used a CMM and a bespoke computer programme to assess the volumetric wear of 32 femoral head and 22 acetabular cups for metal-on-metal hip resurfacings [14]. The same technique was then adopted by Uddin to assess the wear of two explanted conventional cross-linked polyethylene and three second-generation highly cross-linked polyethylene cups [15]. In this method, the origin of the spherical component was firstly determined from the unworn area of the bearing surface during the CMM scanning; the radius of the unworn surface of the component was then obtained using a histogram showing the frequency of the measured radii. They assumed that the taller column with most points in the histogram was the unworn radius. In this case, the accuracy of the method depended on the identification of the origin of the component before and during the CMM scanning, which is really challenging and time-consuming. The error of the method would be amplified if the origin of the component was misaligned. In addition, for some retrieved components with severe wear, there is a possibility that the tallest column in the histogram was the radius of the worn area.
The previous study showed that compared to other scanning parameters, misalignment of the origin of the retrieved component had the greatest impact on the calculation of the volumetric wear using the CMM-based method [16]. This study suggested that more efforts should be devoted to the successful identification of the original surface of the component during the wear calculation. Although a number of methods have been proposed to assess the wear of metal or ceramic retrieved implants based on CMM measurement [12,14,16], more efforts should be made to develop a more reliable, efficient and robust methodology for identifying and reconstructing the unworn surface of retrieved component during the calculation and assessment of the wear of retrieved hip replacement, particularly for those that have severe wear areas, such as in metal-on-polyethylene (MoP) hip replacements.
The aim of the present study was therefore to develop a method for reliably identifying the original surface of the retrieved component and calculating the volumetric change of retrieved implants in MoP hip joint replacements by using a combination of CMM and custom-written computer programme. The validation of the method was also performed and the method was applied to four retrieved polyethylene cups for in vivo volume change assessment.

Data collection
Four retrieved polyethylene acetabular cups were considered. After retrieval, all the samples were rinsed in deionised water and soaked in 10% formalin. They were then cleaned carefully using detergent water and a 1% Trigene solution to remove any debris. After cleaning, the samples were scanned using a coordinate measuring machine (CMM, Legex 322, Mitutoyo, UK) ( Fig. 1) in the form of traces starting at the pole and ending at the rim.
A single straight stylus configuration with a stylus diameter of 2 mm was used to scan the retrieved cups. The definition of accuracy in ISO 10360-4:2000 was accepted in the present study to evaluate the measurement accuracy [17]. For the present set-up, the accuracy stated by Mitutoyo is (0.8 + 2L/1000) μm, where L is the measurement length in mm. The largest value of L for a 22.225 mm diameter cup was 17.45 mm, which corresponded to a measurement accuracy of 0.804 μm in the present study.
At the beginning of scanning, the retrieved cup was placed on the slate bed of the machine with its rim plane parallel to the machine's XY plane. It was critical to creating an individual coordinate system on the component before the measurement. For this purpose, a reference plane was first identified from the measurement of the rim plane of the cup and aligned as the XY plane of the coordinate system. The origin of the coordinate system was determined by roughly taking 25 points over the unworn part of the component's surface. The alignment of the X-axis was achieved by measuring a line through the introducer holes in the cup. Once the coordinate system was developed, the acetabular cup was scanned by taking 4, 608 points in the form of 72 traces rotated by 5°from each other about the Z-axis passing through the origin of the defined coordinate system. Each trace consisted of 64 points with a pitch of 0.5 mm starting at the pole and finishing at the rim of the cup. All the points were recorded as X, Y and Z coordinate values relative to the defined coordinate system.

Surface geometry reconstruction and volume change calculation
Coordinate data (originate data) collected from the CMM was imported into a custom-written MATLAB programme for surface reconstruction and volume change calculation. The coordinate data was characterised by a matrix (original matrix), which included the Cartesian coordinate value of each measured point. In order to determine the original surface of the cup, a spherical surface was fitted to the Cartesian coordinate data of the measured points in the original matrix using the least-squares regression algorithm [18]. The deviation of each point in the original matrix (i.e. the error between the radius of the spherical surface and the distance from the point to the centre of the spherical surface) was calculated. If the maximum deviation of the points was larger than the manufacturing tolerance of 10 μm [15,19], a threshold value (t) equal to 90% of the maximum deviation was set. Any point for which the calculated deviation was greater than the threshold value was discarded. The remaining points were retained to form a new matrix and a new spherical surface was fitted to the remaining data in the new matrix. The process was repeated until the maximum deviation of all the points in the new matrix was <10 µm. The spherical surface fitted at this stage was then assumed as the original surface of the cup. In order to speed up the fitting process, for the severely worn cup, the points at the apparent worn area of the bearing surface were discarded before the first surface fitting. In order to do this, the coordinate data collected from CMM was split into 72 traces and each trace was characterized by a 3 × 64 submatrix. The coordinate data in all of the traces were imported into a two-dimensional coordinate system. The data in the traces that were apparently away from other traces were discarded and the remaining data were selected for the first surface fitting, as shown in Fig. 2.
Once the original surface of the cup was determined, the deviation of each point in the original matrix to the original surface was calculated. The maximum deviation was assumed as the maximum penetration depth and the penetration direction was calculated based on the maximum deviation. The penetration angle was defined using the angle between the rim plane of the cup and vector from the centre of the cup to the maximum deviation point, as shown in Fig. 3, which was calculated using the following equation: where a is the vector parallel to the rim plane of the cup and b is the vector pointed from the centre of the cup to the maximum deviation point.

Gravimetric validation
In order to validate the CMM-based method, the method was compared with the standard gravimetric method by assessing the wear volume of a polyethylene component sample (Marathon, DePuy International, UK). Prior to the test, the sample was soaked in deionised water for ∼16 weeks to allow moisture uptake to stabilise. Before measurement, the sample was cleaned thoroughly using detergent water and a 1% Trigene solution and was ultrasonicated for 10 min. It was then placed in an atmosphere-controlled room for 12 h and weighed on a high precision balance (Mettler AT201, Leicester, UK, sensitivity 0.01 mg). Each sample was weighed five times and the average was taken as a datum.
A wear testing was then performed on the sample in the Leeds ProSim hip joint simulator under standard gait cycle conditions (Fig. 5). The simulator applied two independently controlled motions, extension/flexion (−15°/ + 30°) and internal/external rotation (±10°). A twin-peak time-dependent loading was applied with a peak load of 3 kN at heel strike and toe-off and a swing phase load of 50 N. The wear-test was carried out in 25% new-born calf serum with 0.03% sodium azide to inhibit bacterial growth. The lubrication was changed every 0.33 million cycles. After two million cycle simulation, the sample was taken out and cleaned to remove any particles and debris. It was then weighed five times and the average was taken. The volumetric loss of the sample was calculated by dividing the weight loss by the density of 0.934 mg/mm 3 for the polyethylene material [20]. The sample was also scanned using CMM (Legex 322, Mitutoyo, UK) as per the methodology in Section 2.1. The process was repeated after three and five million cycles' simulation. The volume change of the sample calculated from the CMM scan using the present method was compared to that measured from the gravimetric method for two, three, and five million cycles. Table 1 shows the comparison of measurements between the gravimetric technique and CMM-based method in the validation study. The results matched well between the measurements using the two methods across the three stages of wear test, with differences of 1.38, 2.01, and 4.12 mm 3 , respectively for the two, three, and five million cycle simulation.

Retrieved components analysis
The calculated component radius, maximum penetration depth, penetration angle, and volume change for each of the retrieved cups are presented in Table 2. Fig. 6 shows the mapped wear scar for each retrieved cup showing the distribution and pattern of the wear. The colour scale bar in the figure shows the penetration depth in mm. The colours with a positive value of penetration depth indicated worn area while the colour with a value of 0 and a negative value represents the unworn region. The dark red shows the maximum penetration depth.
The mean maximum penetration depth and volume change of the retrieval cups except cup 2 were 1.82 mm (range 1.70-1.93 mm) and 540.36 mm 3 (range 530.89-546.47 mm 3 ), respectively. The corresponding mean penetration angle was 36.4°(range 32.5-40.4°). The maximum penetration depth of the cup 2 was 0.23 mm, which was observed at the rim of the cup. The volume change was estimated to be 93.5 mm 3 .

Discussion
A novel CMM-based method that can calculate the geometry and volume changes of retrieved components for MoP hip joint replacements was presented and applied to four retrieved polyethylene cups in the present study. The innovation and advantage of the method were that the unworn surface of the retrieved component can be identified and determined automatically using a loop algorithm as an automated process, which was more efficient and reliable compared to the methods in the previous studies [14,15]. The validation of the present method was conducted by comparing with the gravimetric method and results showed that the volume changes calculated using the present method were in good agreement with those of gravimetric measurement, with differences within 4.1 mm 3 for a different level of wear. The maximum percentage of differences between the present calculation and the standard gravimetric measurement was determined to be 9.9%. This was found to be comparable with the accuracy level in previous studies, which reported an error of 10.4% for metallic implants [14] and 8.4% for polyethylene components [15].
The rates of volume change for cup 1 and cup 4 were calculated to be 54.6 and 45.3 mm 3 /year, respectively, with penetration rates of 0.17 and 0.16 mm/year, respectively. These rates were found to be comparable to the in vivo wear rates of MoP hip prostheses reported previously, which were demonstrated to be 35-62 mm 3 / year for volumetric wear rates and 0.10-0.18 mm/year for linear wear rates [21,22]. Considering these wear rates, the time to retrieval for cup 3 was estimated to be between 8 and 15 years. It is interesting to note that cup 3 had a greater penetration depth but smaller volume change compared to cup 1. This was probably due to the fact that although cup 1 had a smaller penetration depth, the penetration was distributed across a larger surface area in cup 1 compared to cup 3, as shown in Fig. 6, where a larger worn surface was observed for cup 1. A maximum penetration depth of 0.23 mm was calculated for cup 2 at the very rim of the cup, this rarely happens. However, two cases were reported by Wroblewski in which extreme wear was found at the very rim of the socket for the 22 mm Charnley sockets [23]. This occurred probably due to   the edge loading taking place at the rim of the cup usually caused by steep cup inclination and/or micro-separation during daily activities [24][25][26][27]. The mean penetration angle for all of the cups except cup 2 was calculated to be 36.4°, which was found to be comparable to the mean penetration angle of retrieved Charnley sockets (38.5°) reported by Hall et al. [28]. As the information on cup orientation angles during implantation was not available for these components, the penetration angle of the sockets relative to the median plane of the human body was unknown. However, considering a cup inclination angle of 45°, the penetration angle of 36.4°relative to the rim of the cup calculated in the present study corresponded to a penetration direction of 8.6°laterally with respect to the human body median plane. This may be due to the complex motion taking place at the articulation during different daily activities. Murray and O'Connor presented a novel explanation on the direction of penetration in the acetabular cup and pointed out that the penetration of the polyethylene cup is a combination of creep which is mainly superomedial in the direction of the force vector and wear which is superior and slightly lateral [29]. It is also interesting to note that the polyethylene cup with higher penetration and volume change had more lateral penetration direction. This showed a potential relationship between the penetration depths and penetration directions, as proposed by Hall et al. [28] and Murray and O'Connor [29]. However, more data should be analysed before any conclusion is drawn.
Although the CMM-based method is the most effective way to assess the volume change of retrieved prosthesis, such a technique has potential limitations. The primary limitation was that creep/plastic deformation was not differentiated from the calculated volume change. It must, therefore, be acknowledged that the calculated volume change in the present study included the creep and true wear of the polyethylene cup [30]. In addition, the accuracy of the method is dependent on the scanning point distances. Normally a more accurate wear measurement will be obtained with smaller scanning point distance, which requires more scanning time. However, a recent study to evaluate the wear of hip implant using the CMM method indicated that the number of scanning points has an insignificant effect on the wear quality and measurement uncertainty while enough scanning points are guaranteed, e.g. the mesh spacing between the scanning points must be <1 mm [31]. The sensitivity of the scanning points distance on the volumetric measurement should be evaluated in the future to balance the accuracy and the scanning efficiency. Moreover, the CMM measurement was not taken across the whole chamfer of the cup. Therefore, the volume change at the chamfer of the cup was not considered in the calculated results reported in the present study. These limitations may be the main reason caused the different results between the CMM-based methods and gravimetric methods. It has been reported that the CMM techniques and radiographic measurements appear to overestimate the wear volume, while computational simulation may underestimate the prostheses wear [31,32]. It is, therefore, recommended that the CMM-based methods should be used alongside the gravimetric analysis and computing process, especially under some adverse conditions, under which wear may mainly occur at the rim of the component [25,33].
Another major limitation for the present study was that no uncertainty evaluation was conducted to assess the reliability of the method and analyse the error sources. According to the ISO 15530-3: 2011, the overall uncertainty of the CMM-based measurement can be derived by taking the systematic error (c) and three main uncertainty components into account, including the uncertainty of the calibration of CMM u 2 cal , the uncertainty of the wear measurement procedure (u 2 p ), and the uncertainty of the material and manufacturing tolerance of the sample u 2 m , in the form of U = k × u 2 cal + u 2 p + u 2 m + |c| [34]. While the uncertainty of the CMM can be obtained from the supplier, it is difficult to get the uncertainty of the wear measurement procedure and the material and manufacturing tolerance of the polyethylene cups used in the present study, therefore, the uncertainty analysis was not conducted. However, the CMM-based method in the present study has been validated by comparing the CMM-based measurement with the gravity measurement, and overall agreements between the two measurements were observed. The uncertainty analysis of the present method will be performed in the future by scanning a calibrated metallic femoral head several times and applying the present method to the scanned data. The present study was also limited to a small sample size with just four retrieved components being considered. Therefore, any results and conclusion with respect to the retrieval analysis should be treated with caution. Nevertheless, the robust methodology presented in the study could be an effective tool to perform retrieval analysis for explanted hip replacements. Hence, future studies will focus on applying the novel method to a large group of subjects to better understand the performance of hip prostheses. In addition, it would be advisable that the approach presented in the present study can be used in other prosthetic components with different geometries, such as knee and ankle replacements [10].

Conclusions
A novel CMM-based methodology for calculating and assessing the volume change of retrieved polyethylene cups for MoP total hip replacements using a combination of CMM data and the bespoke computer programme was developed and presented in this study. The methodology was first validated against the standard gravimetric method, and then applied to four retrieved polyethylene cups for volume change calculation. The following conclusions can be drawn from this work: † The volume changes calculated using the CMM-based method matched well with the measurements using the gravimetric technique, with differences within 4.1 mm 3 , showing the accuracy and reliability of the CMM-based method in the present study. † The maximum penetration depths and volume change of retrieved polyethylene cups considered in the present study were calculated to range from 0.23 to 1.93 mm and from 93.5 to 546.47 mm 3 , respectively, by using the present method. Edgewear in component for retrieved cup 2 was predicted. † The application of the CMM-based method to the retrieved polyethylene cups showed that the CMM-based method was capable of effectively and reliably calculating the volume change and characterising the wear patch of retrieved components by showing the shape, location, orientation and depth of penetration for retrieved total hip replacements in which no pre-wear data, CAD model, and original design drawing were available.