Practical considerations for volumetric wear analysis of explanted hip arthroplasties

How does a coordinate measuring machine (CMM) work?

A CMM is a precision measurement tool which uses a ruby probe to stroke over the surface of a component, recording data as it does. This data consist of a series of measured points in Cartesian form (e.g., one point would read as: x = 10, y = 0, z = 0). These values are distances (in mm) that the measured point lies away from the ‘origin’ in each direction. The origin in the case of explanted hip measurement is the original centre of the head or cup (i.e., the central point of the sphere immediately after the component has been manufactured). The CMM points are collected in a series of linear scans from the pole to the equator or vice versa. These linear traces are known as contours. As the probe progresses along each contour it measures points at a set interval: called the point ‘pitch’. Figure 1 illustrates these parameters.

Fig. 1

A graphic representation of a metallic hip resurfacing component undergoing CMM examination. The ruby probe makes several linear traces from equator to pole: known as contours. In the image, the CMM has completed one contour trace and is midway through the second. Each dashed line represents a measurement point. The distance in millimetres between each point in the contour is known as the point pitch.

What is a clinically relevant amount of wear?

Of the routinely used bearing surface combinations, ceramics are known to wear at the lowest rate.^20,21 Al-Hajjar et al²² found in a recent simulator study that alumina-on-alumina bearings wore at a mean (standard deviation [sd]) rate of 0.74 mm³/million cycles (sd1.73). The same group studied the difference in wear rates of a popular ceramic on ceramic (CoC) THR under standard and microseparation conditions. They found that the wear rates under microseparation conditions increased to 0.22Â mm³/million cycles from less than 0.1 mm³/million cycles under standard conditions.^22-24 Walter et al²⁵ however reported in vivo rates of 9.7 mm³/year for ceramic components revised for squeaking. Studies of explanted devices have shown that metal-on-metal (MoM) bearings wear at rates from as low as 0.3 mm³/year to as high as 95.5 mm³/year.^7,26 Contemporary metal on polyethylene (MoP) joints have been shown to wear at more than 25Â mm³/year.²⁷

We would argue, therefore, that volumetric wear techniques that can provide results to within an accuracy of 1mm³ provide useful clinical information in the study of MoM and MoP joints and in the differentiation between well-functioning and poorly functioning CoC joints. Errors of 0.5 mm³ and below, we would argue, are only relevant in the lowest wearing ceramic bearings in the idealised environment of the hip simulator. If one considers a total error in the calculation of volumetric loss from a device explanted after, for example, five years in vivo, this total error would equate to an error in wear rate measurement of only 0.1 mm³/year.

Part one: the effect of scanning parameters on volumetric wear calculations

A 36 mm diameter ceramic head was used for the tests reported in the first part of this investigation (Table I). It had been revised after one year due to recurrent instability. A number of different combinations of contours and pitches were used to calculate the volumetric loss from the ceramic component. In between each test the component was removed and then replaced in a different position in order to identify errors resulting from physical alignment of the component on the CMM worktop.

We used a custom designed volumetric wear programme to analyse data produced by a Legex 322Â coordinate measuring machine (Mitutoyo, Andover, United Kingdom) at the North Tees Explant Centre (NTEC). Our methods have been validated using gold standard gravimetric testing and the techniques have been peer reviewed multiple times in orthopaedic journals.^19,26,28-30

Some modifications have been made to our published method in order to identify the unworn area of the scanned component more efficiently. Rather than taking seven individual points to identify unworn surfaces, the CMM operator inputs the number of degrees in two planes, which dictate the surface area over which the ruby performs continuous contour traces. This method allows the unworn surface to be located more rapidly and also has the advantage of recording over 300 points to calculate the spherical form. In general these initial traces consist of 180° traces in one direction and three 70° traces in a perpendicular plane working from 10° above the equator towards the pole. If the initial traces are unsuccessful in locating a spherical form within the manufacturing limits, the coordinate system automatically rotates 10° around the z axis and repeats the sequence. If the CMM fails to identify an unworn surface after rotating around 360°, then the area over which it attempts to locate the original surface is sequentially reduced.

The effect of the number of scan contours

Our published method (the LJL method¹⁹) uses 72 contour traces progressing from the equator to the pole at intervals of 5°. Points are taken every 0.3 mm along the trace (the ‘pitch’) using a measurement speed of 5 mm per second. With an implant of this diameter, this leaves the points a maximum distance of 1.57 mm apart. The ISOÂ 14242Â standard recommends that the point distance be no greater than 1 mm.¹⁸ We therefore carried out four tests to examine the effect of point spacing. The first scan used 16 contours (maximum point spacing of 7.07 mm), the next 32 contours (maximum point spacing of 3.53 mm), the third 72 contours (maximum point spacing of 1.57 mm) and the final scan used 144Â contours, which gave a maximum point spacing of 0.78 mm. A point pitch of 0.5 mm was used throughout and the resulting volumetric loss was calculated.

The effect of point pitch

A total of 13 tests were carried out to investigate the effect of the point pitch. Firstly, using 16Â contour scan programmes, points were taken at a distance of 0.5 mm, 0.3 mm and 0.1 mm apart (a 1 mm pitch with this limited number of contours produced too few points to allow the software to calculate a volume). Next, using 32 contour programmes, scans were carried out with point pitches of 1 mm, 0.5 mm, 0.3 mm and 0.1Â mm. Finally, 72 and 144 contour programmes with pitches of 1 mm, 0.5 mm and 0.3 mm were performed (for these longer scans the large amounts of data produced with 0.1 mm cannot be handled satisfactorily by the memory of the hardware).

The effect of misalignment of the origin (centre of the sphere) in the x or y direction

In our experience, it is the failure to identify the remaining unworn surface to a reasonable degree of accuracy that is the primary cause of inaccurate and/or irreproducible measurements. In order to investigate this effect, we used theoretical worst outcome scenarios to compound this source of error. As Bills et al¹³ and Carmignato et al¹⁴ suggested that measurement errors are magnified when smaller numbers of points are recorded, the data generated by the 16 contour 0.5 mm pitch scan and 16 contour 0.3 mm scans (the scan sets with the smallest number of points) were fed back into the CMM. The origin (the calculated centre of the sphere) was then shifted sequentially by one micron, two microns and three microns in the positive and negative x, y and z directions. The volumetric wear was recalculated at every stage. A further test was carried out to examine the effect of a multidirectional shift. This took the form of a three micron shift in the x direction, followed by a three micron shift in the y direction and then a three micron shift in the z direction. This was then also performed for the scan with the largest number of points: the 144 contour 0.3 mm pitch scan.

Part two: blinded gravimetric study

Six Finsbury 42Â mm diameter femoral head components were sent from the precision engineering company Redlux. The diameters of the components had been measured using Mitutoyo (Andover, United Kingdom) laser micrometers (LSM-506 and LSM-600) at Finsbury (DePuy, Leeds, United Kingdom) – and were weighed. The components had then undergone material removal and been weighed to determine by gravimetric means the volume of material which had been removed.

These tests had been carried out as part of an internal validation process for explant analysis for the Redlux company itself. No information was given to the NTEC about the dimensions, amount of material lost or the form of the components and the area of material removal was not identifiable. An operator at the NTEC, with no previous experience of explant testing, performed all of the tests which involved single scans using 0.3 mm point pitch consisting of 16, 72 and 270 contour programme scans. The 270 scan size was chosen so that point spacing at the equator of the component was less than 0.5 mm. The wear depth and dimensional results obtained from the laser micrometers were also compared with the CMM generated results.

Part One: the effect of varying contours, pitches and total number of points

Varying contour numbers, point pitch and total number of points had no consistent effect on the measurement of volumetric wear (Table II) (Figures 2 and 3). Progressing from theoretically the most inaccurate result of 0.70 mm³ (a 16 contour trace at 0.5 mm pitch with only 1072 points) to theoretically the most accurate result of 0.64 mm³ (a 144 contour trace with point pitch of 0.3 mm and a total number of points of 15 984), there was a total volumetric difference of 0.06 mm³.

Fig. 2

Graph showing the effect of increasing the maximum distance between the measured points and the calculated volumetric loss.

Fig. 3

Graph showing the effect of the number of measured points and the number of scan contours on the calculated volumetric loss. The Y axis is extended to 3 mm³ in order to allow comparison with the effects of the centre point shifts in Figure 4.

Out of all 13 tests, there was a maximum difference between the largest and the smallest measured volume of 0.19 mm³. Multiple regression of log normalised data using the number of contours and point pitch distance as explanatory variables, identified that these variables had no significant effect on the calculated volumetric material loss (r squared = 0.114, p = 0.547).

Shifting the determined centre of the sphere had a greater impact on the calculated volumetric loss than the scanning parameters discussed above. Figure 4 shows the impact of the failure to identify the unworn surface accurately and Figure 5 shows the distribution of the measurement points when such an error takes place.

Fig. 4

Graph showing the effect of misalignment of the centre of the sphere. The two charts show the effect of various extents of shifts (measured in microns) of the centre of the sphere on the calculated volumetric loss. In the tests on the left, a point pitch of 0.1 mm was used. On the right, a point pitch of 0.5Â mm was used.

Fig. 5

This frequency histogram shows the point distribution of measured data. Each point is a distance from the centre of the sphere. If this centre point is improperly calculated, spurious measurements can occur, as is shown here. If the measured data is expressed using a histogram, the effect of misalignment can be identified. This histogram was generated from a multiaxial 3 micron XYZ shift. The point distribution is highly irregular - see Figure 6 for comparison.

Part two: blinded study

The LJL method was found to overestimate the wear volume consistently. The errors were normally distributed. For the 16 contour scans the mean (sd) error was 0.470 mm³ (sd 0.264), for the 72Â contour scans it was 0.525 mm³ (sd 0.185) and for the 270 contour scan it was 0.480 mm³ (sd 0.210).

The CMM determined radius of the components was a mean of -0.3 microns (sd 0.69) from the laser measurements (i.e., within the stated resolution of the CMM accuracy). This accurate identification of the original dimensions of the components, coupled with the appearance of the histograms, made it highly likely that the root cause of the overestimation of wear was due to the measurement of form deviation as wear.

The imageinFigure 6 shows a histogram, representative of the scans in this study. In the published LJL method the modal radius value is taken as the ‘start point’ for the wear measurements. It is clear however that in low wear cases such as those in this analysis, the ‘form’, which is in essence the ‘waviness’ of the manufactured surface, can account for a large proportion of the measured ‘wear’. The LJL method can easily be modified to account for this form error, if the operator has prior knowledge of the spherical form typically produced by the manufacturer of the examined component. Or, it can easily be identified post analysis from the normal distribution of the histogram. In the example shown in Figure 6, over 70% of the measured points are within two microns of the modal value. As the point distribution is essentially normally distributed, the modal value is within one micron of the mean value. The operator can therefore apply a form filter by inputting a radial value which, rather than the modal value, is “modal value - (0.5* standard deviation)” (Fig. 7). Applying this form filter to the results increased the accuracy as shown in Figure 8. Regression analysis using the 16, 72 and 270Â contour scans to explain the variation in gravimetric results returned R squared values of 88.8, 99.5, and 98.0 (p < 0.001 in each case).

Fig. 6

This histogram was generated from one of the successful head scans in the blinded study. The points in this histogram are normally distributed as the area and extent of wear was small and localised. Wear depths were less than five microns in this case. Using the LJL method, which assumes wear for all measurements smaller than the modal radius (i.e., all points to the left of the dashed line in this case), a volumetric loss of 0.61 mm³ was calculated.

Fig. 7

In cases with extremely low wear and a known form, the accuracy of the measurements can be enhanced by using a form filter. In this histogram, instead of commencing the wear measurements from the modal radius, wear is only assumed if the measured points are a distance of 1 micron less than the modal radius (dashed line).

Fig. 8

Graph showing the accuracy of the CMM calculated values with and without form filter, compared with the gold standard gravimetric tests.

Scanning time required to obtain results with clinical relevance

Using 16 contour scans, two complete bearing surfaces (two heads and two cups) can be completed in a mean time of forty five minutes. CMMs can also run automated programmes overnight unsupervised. During a normal working week this would mean (allowing for preparation and transfer of the components to and from the CMM workspace) that 40 head and cup combinations could be scanned at a comfortable working pace. This would mean that in a year, an efficiently running facility could process over 2500 head and cup combinations. This amounts to roughly one quarter of the revision burden of England and Wales.¹⁵