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VALIDATION OF FE MICROMOTIONS AND STRAINS AROUND A
PRESS-FIT CUP: INTRODUCING A NEW MICROMOTION
MEASURING TECHNIQUE
S G Clarke, A T M Phillips, and A M J Bull
Department of Civil and Environmental Engineering and Department of Bioengineering, Imperial
College London
Abstract
Finite element analysis provides a useful tool with which to analyse the potential performance of
implantations in a variety of surgical, patient and design scenarios. To enable the use of finite
element analysis in the investigation of such implants, models must be experimentally validated.
Validation of a pelvic model with an implanted press-fit cup in terms of micromotion and strain is
presented here. A new method of micromotion has been introduced to better describe the overall
movement of the cup within the pelvis. The method uses a digitizing arm to monitor the relative
movement between markers on the cup and the surrounding acetabulum. Finite element analysis
was used to replicate an experimental set up using a synthetic hemi-pelvis with a press-fitted all-
metal cup was subject to the maximum loading observed during normal walking. The work
presented here has confirmed the ability of finite element models to accurately describe the
mechanical performance of the press-fitted acetabulum and surrounding bone under typical
loading conditions in terms of micromotion and strain distribution, but has demonstrated
limitations in its ability to predict numerical micromotion values. A promising digitizing technique
for measuring acetabular micromotions has also been introduced.
Keywords
FINITE ELEMENT ANALYSIS; ORTHOPAEDIC SURGERY; PELVIS; CEMENTLESS
ACETABULAR CUP; MODELLING; HIP REPLACEMENT
3. Introduction
Cementless, rather than cemented, implants are being implanted with increasing frequency
in total hip replacements (THRs)1. With full bone ingrowth they can provide a more stable
connection to the underlying bone and accommodate larger head sizes than cemented
implants. The long term success of a cementless implant is widely accepted to be heavily
reliant on initial stability2,3; thus initial post-implantation micromotions are considered an
early indicator of long-term THR success4. This has motivated a number of studies on the
primary stability of cementless implants e.g.5,6,7,8. Finite element (FE) analysis offers the
researcher a tool with which they can isolate the effects of a variety of parameters on chosen
outcomes and carry out large-scale multi-factorial studies which are not feasible in in vitro
cadaveric or in vivo work. There have been a range of studies developing and experimentally
validating FE models able to predict the micromotions of implanted cementless femoral
Correspondence: Susannah G. Clarke, Imperial College London, Skempton Building, South Kensington Campus, London SW7 2AZ,
UK, T: +44 (0)20 7594 5963, F: +44 (0)20 7594 5934, susannah.clarke@imperial.ac.uk.
Europe PMC Funders Group
Author Manuscript
Ann Biomed Eng. Author manuscript; available in PMC 2014 April 09.
Published in final edited form as:
Ann Biomed Eng. 2012 July ; 40(7): 1586–1596. doi:10.1007/s10439-012-0523-6.
Europe PMC Funders Author Manuscripts Europe PMC Funders Author Manuscripts
stems e.g.9,10,11. The UK National Joint Registry reports five year revision rates of 6.0% and
2.9% for all-metal and metal-backed cementless cups respectively, compared to 1.8% for
cemented cups1. With significantly low comparative performance, metal on metal hip
replacements have become a controversial bearing type. FE analysis of cup stability can
provide one aspect of investigation into the poor performance of these bearing types,
alongside a range of other research methodologies.
A range of studies assessing acetabular implant micromotions have been carried out
experimentally12,4,13 and using FE modelling14-16. In most reported experimental studies the
acetabular cup micromotion was recorded with uni-directional linear variable differential
transformers (LVDTs) at three sites; this is not enough to provide information on the overall
movement of the cup. Kluess et al.15 attempted to validate their FE predicted micromotions
using optical markers but could not attain acceptable measurement accuracy. Zivkovic et
al.17 validated their FE micromotion predictions using six LVDTs, under a chair-rising
loading, and with a significant proportion of the ilium fully constrained. The work presented
here details an alternative digitization based method of micromotion measurement which
does not require attachment of measuring devices to the given specimen, and from which
micromotion in three orthogonal directions at a large number of sites can be measured.
Micromotion is measured under a normal walking load case, without fully constraining the
ilium.
FE validation of pelvic strains, rather than micromotions, is more commonly reported in the
literature e.g.18,15,19; though validation of strains on a pelvis implanted with a press-fitted
cup could not be sourced. The mechanical situation and associated strains for a press-fitted
cup are substantially different to those for a cemented or in-line fit cup. It is paramount to
validate any FE model concerning press-fit cups before it is used to analyse implant
behaviour.
The aim of this study is to test whether FE models can accurately predict cup-bone
micromotions and the strain around an acetabulum implanted with a press-fit cup, and
whether a new technique for micromotion measurement can accurately measure cup
micromotions. These points will be explored through FE modelling and experimental
measurements taken from a synthetic hemipelvis subject to joint loading representative of
the maximum load occurring during normal walking20. A synthetic hemipelvis was used
rather than a cadaveric specimen to isolate the errors associated with press-fit implantation
from those associated with estimation of cadaveric bone stiffnesses. Previous work has
demonstrated errors of up to 30% between FE predicted and experimentally measured
principal strains on cadaveric specimens19. A large amount of this error is likely to stem
from the necessary approximations of material stiffness and directionality of the cadaveric
bone. The homogeneity of the materials comprising the synthetic pelvis allow for a more
certain description.
4. Materials and methods
4.1 Experimental set-up
A synthetic biomechanical hemi-pelvis (Large Left Fourth Generation Composite Pelvis,
Item 3405, Sawbones, Pacific Research Laboratories Inc, Sweden) was CT-scanned at
0.75mm intervals with a resolution of 512x512 pixels (Sensation 16, Siemens Plc, Munich,
Germany). The resulting CT-scan was semi-automatically segmented (MIMICS, v12.11,
Materialise NV, Leuven, Belgium) and a tetrahedral mesh produced. The synthetic hemi-
pelvis comprises a short-fibre-filled epoxy cortical shell and a polyurethane foam trabecular
inner.
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For spatial fixation in all degrees of freedom, a steel block was attached to the ilium, at the
sacroiliac joint, through four steel pins which penetrated through the medial cortical shell
and into the trabecular foam, but not through to the lateral side of the ilium (Fig. 1D). Bone
cement (Kemdent, Associated Dental Products Ltd, Swindon, UK) was used to fill in the
gaps between the flat steel block and the contoured cortical surface. Two alignment screws
were inserted to aid positioning of the block.
A 62mm ADEPT® porous HA-coated cobalt-chrome hemispherical monoblock acetabular
cup with a 4mm rim thickness (Finsbury Orthopaedics Ltd, Leatherhead, UK) was chosen
for implantation after visual templating from the pelvic mesh. A series of reamers, up to
61mm, were used to ream the acetabulum of the hemi-pelvis; the trial cup confirmed
adequate stability. A digitizing arm (FARO Gage, FARO GmbH, Munich, Germany) with a
needle-point probe was used to spatially measure the location and size of the reamed
acetabulum within the hemi-pelvis. The cup was orientated at 45° anatomical inclination and
15° anatomical anteversion21. A sphere was fitted to the digitized acetabular points using a
least-squares sphere-fitting algorithm (MATLAB, vR2010a, The Mathworks Inc, MA,
USA), the rms error between best-fit sphere and points was 0.14mm. The CT-mesh was
updated to include the size and location of the reamed cavity by referencing the physical
bone to the CT-mesh (MATLAB) and performing a Boolean operation on the mesh to
subtract the fitted sphere (RHINO, v4.0, Robert McNeel & Associates, WA, USA). The cup
was impacted into the acetabulum. The digitizing arm was used to locate the position of the
cup within the reamed cavity (MATLAB), and superposition onto the reamed mesh ensured
full seating had been achieved (RHINO).
Four 45°/90° three-element rosette strain gauges (GFRA-3-50, TML, Tokyo Sokki
Kenkyujo Ltd, Tokyo, Japan) were attached to the cortical surface. The gauges were
positioned around the acetabulum (Fig. 1), in areas of predicted high strain. An extra control
gauge (gauge 5 in Fig. 1) was positioned in an area of predicted low strain. Strain data and
load data were collected every second throughout the loading regime.
The test set-up is shown in Fig. 2B. The steel block was clamped to the bed of the test
machine (Instron 5866 Universal Test Instrument, Instron Co, MA, USA), orientated to
allow direct loading into the acetabular cup to produce a resultant force of 2kN in the same
direction as the maximum force occurring during normal walking20. Loading was applied
through a 54mm modular femoral head which was vertically loaded through a compression
piece. The compression piece interfaced with the modular head through a tapered block
which was polished and PTFE coated on its upper side to allow free sliding in a horizontal
plane; thus only vertical forces were transferred into the cup (Fig. 2A). Ten cycles of 2.5kN
loading were applied to ensure settlement of the apparatus, before loading to 2kN.
Measurements were taken for FE comparison at 250N and 2kN, after the load was
maintained for twenty minutes to account for the viscoelastic creep of the synthetic pelvis22.
The strain reported was therefore the difference in strain between the two loading points of
250N and 2kN. The test protocol was repeated three times, with complete dismantlement of
the apparatus between each test.
4.2 Measurement of micromotion
Micromotion was measured using the digitizing arm (Fig. 2C) to spatially locate points on
the pelvis and cup before and after loading; this enabled the calculation of relative implant-
bone movement under loading at each of the points. Total cup rotation was also calculated
by fitting a plane through each marker point and calculating the rotation of the plane normal
of the cup relative to the bone. To allow repeatable spatial location of these points, the
female part of a plastic snap fastener was applied to the chosen surface with Cyanoacrylate.
A 3mm ceramic ball probe was used to locate the internal ring of the snap fastener. Twelve
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snap fastener markers were adhered around the implanted cup rim. Twelve further markers
were attached to the cortical surface, located as close to the rim markers as possible. The
marker locations are shown in Fig. 3. Micromotion was reported as the relative movement
between these twelve marker pairs. This method was chosen after investigation and
verification of a number of different location methods. The mean error in repeatability of
measurement in situ was 6μm, although errors as high as 30μm were observed (99%
confidence) at marker 1. This is higher than the manufacturer quoted accuracy of 5μm for
the robot because of the cramped situation on the test bed which necessitated the close
proximity of the digitising arm base and the test piece (ideal measurement is taken
perpendicular to the surface of the test sample and requires more space). All markers were
digitized three times for each measurement, and the mean of these three measurements taken
as the reading. Four markers were also attached to the steel fixture block, at the ends of the
four pins inserted into the ilium, to monitor possible movement of the sacroiliac fixture.
4.3 Finite element modelling
An FE model was created and solved in ABAQUS (v6.8, Dassault Systemes Inc, Velizy-
Villacoublay, France) to simulate the experimental set up. The reamed CT-mesh was
orientated to match the position of the physical model, using spatial positioning data from
the digitizing arm. The mesh was re-meshed with approximately 120,000 four-node linear
tetrahedral elements. A three-node triangular shell mesh was extracted from the tetrahedral
mesh surface to represent the cortical bone. The cup geometry was provided by Finsbury
Orthopaedics and the 3D model was created in ABAQUS and meshed with approximately
45,000 ten-node tetrahedral elements. All mesh densities were verified with convergence
studies. The porous HA-coated surface was not included in the model; the cup was modelled
with a smooth surface and the roughened coating accounted for with a frictional coefficient.
The modular femoral head was modelled as a sphere with approximately 61,000 ten-node
tetrahedral elements. The properties of cobalt chrome (E=210GPa, v=0.323) were assigned
to the cup and head. Three point bending tests were conducted on test samples of epoxy and
polyurethane, obtained from Sawbones, to ascertain material Young’s moduli, as well as on
a test piece cut from an identical biomechanical hemi-pelvis from the same batch as that
used for the experiment. The measured Young’s moduli were 10GPa and 155MPa for epoxy
resin and polyurethane; these were respectively assigned to the outer cortical shell mesh and
the trabecular tetrahedral mesh. The measured polyurethane Young’s modulus agreed with
the values published by Sawbones, but the epoxy Young’s modulus was less than that
published24. The temperature-dependency of epoxy Young’s modulus has been reported
previously for Sawbone’s femurs25; the epoxy is also short-fibre-filled, adding to potential
variability. Both materials were assigned a Poisson’s ratio of 0.326. An algorithm was
developed to assign a varying cortical bone thickness on the shell mesh, as is commonly
implemented in such models, e.g.18,19. The algorithmic inputs were two meshes (produced
from MIMICS) of the outer bone surface and the inner trabecular volume. The algorithm
calculated thickness as the perpendicular distance between each outer mesh element and the
inner trabecular volume. In areas of high curvature (e.g. acetabular rim) special
consideration was required to derive the thickness; the approach used has been reported in
work by Anderson et al.18. Free sliding was permitted at the cup-head interface, and penalty
sliding was implemented at the cup-pelvis interface, with a friction coefficient of 0.5,
representing that measured experimentally between porous coated metal and trabecular
bone27. As the reported friction coefficient was not derived from experiments involving
synthetic bones, a sensitivity analysis was carried out which showed that varying the
coefficient of friction by ±0.1 altered output micromotions and strains by 5% and 2%
respectively.
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The FE simulation was implemented through three steps: cup implantation; loading to 250N
and loading to 2kN. Cup implantation was simulated by introducing the cup into the
acetabulum from a 50mm distance perpendicular to the cup rim. The cup was displacement
driven into its pre-loading position28,17, forcing the surrounding acetabulum to
circumferentially expand to accommodate the cup, thus introducing the pre-strain required
for the press-fit; a perfect fit was not enforced between the implant and acetabulum. Slight
movements at the sacroiliac joint necessitated a displacement driven, rather than load driven,
simulation; the model was therefore not fixed in space at any specific coordinate. The two
loading stages were simulated with displacement criteria at the femoral head and at the four
steel pins in the sacroiliac fixture (Fig. 1D). The required input displacements were
measured in situ with the loading machine (in the case of the femoral head) and the
digitizing arm (in the case of the sacroiliac pins); the mean values from the three
experimental runs were used. The resulting load measured at the femoral head in the FE
simulation was within 1% of that applied in the experiment. It is most common to control an
FE model with load criteria, rather than displacement; two further FE simulations were
therefore undertaken to test whether the displacement driven model responds in the same
manner as the load-driven model. The comparative models were identical to the test set-up,
but to enable comparison, both had rigid fixation at the sacroiliac joint.
5. Results
Cup-bone micromotions and maximum and minimum principal strains occurring between
loads of 250N and 2kN at the implanted acetabulum were predicted by the FE model and
compared to those measured in situ. A magnitudinal comparison between experimentally
measured and FE predicted micromotions is provided in Table 1, with the match-up of all
directional components shown in Fig. 4. The match-up of cup rotation is shown in Table 2.
The mean and peak percentage errors in predictive micromotion were 27% and 110%
respectively. The highest percentage error occurred at marker 1 (Fig 3), all remaining errors
were below 36%. The gradient of the regression line in Fig. 4 is steeper than 1, at 1.21 and
the y intercept is −6.4μm, with an R2 value of 0.90 This indicates that the FE model under-
predicts micromotion, as can be observed from Fig. 4. Similarly the FE model under-
predicts whole cup rotation, by 14%; this error is reduced to 4% when the 95% confidence
value is reported. The intraclass correlation coefficient between methods was high at 0.92.
The limits of agreement on the Bland-Altman plot (Fig. 5) are 81 and −86μm, indicating the
level of magnitudinal error in the FE model micromotion predictions. The directions of cup-
bone micromotion measured in the experiment and predicted in the FE model are shown in
Fig. 6.
The FE predicted distribution of maximum principal microstrain and associated principal
strain directions at the gauge sites are shown in Fig. 7. The control strain gauge (gauge five
in Fig. 1) reported cup strains in the range 29-44 microstrain in an area of known low strain.
Comparisons of experimentally measured principal microstrains and those predicted are
listed in Table 3 and graphically compared in Fig. 8. The mean percentage error in
microstrain was 151%. Percentage error increased significantly at microstrains
experimentally measured below 50 microstrain. The mean and peak percentage error in
principal microstrain prediction above 50 microstrain was 27% and 67% respectively. The
gradient and y intercept of the regression line are 0.94 and 28 microstrain with an R2 value
of 0.85. Unlike with the cup-bone micromotion, the FE model does not consistently under or
overpredict microstrain. The intraclass correlation for estimating the microstrain between the
two methods is 0.91. The Bland-Altman plot shown in Fig. 9 has limits of agreement of 199
and −88 microstrain.
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The mean differences in principal microstrain and micromotion measurements between the
load driven and displacement driven comparative models were 2.3 microstrain and 1.04 μm
respectively; these represent 0.65% and 2.0% of the mean overall measurements.
6. Discussion
The primary aim of the work presented here was to verify the accuracy with which FE
models can predict the cup-bone micromotion and the strain around an acetabulum
implanted with a cementless cup. This was investigated by comparing micromotion and
strain data measured experimentally with that predicted using FE analysis. The presented
study is limited by a number of factors. The focus of this study is the acetabulum, not the
pelvis, and as such the experimental and computational models include a single hemi-pelvis
fixed at the sacroiliac joint, rather than a complete pelvis. Future modelling based on this
validation experiment will be limited to the acetabular region, as the full bone was not
physiologically represented in this experiment. The computational model was subject to
further limitations by the simplification of the cup backside surface coating as a smooth
surface with substantial friction, and the idealisation of the reamed cavity as spherical.
Together with the assumption of free sliding at the bearing interface, these limitations may
have impacted on the accuracy of model prediction. A further necessary limitation of this
work is the assumption of material properties as linear elastic and isotropic; both of these
simplifications may influence the match-up of results, though the repeatability of the
experimental measurements demonstrate a lack of material yielding during the loading
phase. Had cadaveric bone been used in this study, the consequences of this assumption are
likely to be more dominant, though it should be noted that good strain and micromotion FE
predictions have been achieved in published cadaveric-based studies which also assume
linear elastic isotropic properties18,19.
A secondary aim of this work was to test the suitability of a new micromotion measuring
technique. The error bars plotted on Fig. 4 and Fig. 8 communicate the variability of
measurements over the three experiment runs. This variability is attributable to both the
measurement technique and the different environmental conditions. The low variation in
measured data, along with a mean error in micromotion measurement repeatability of 6μm
verifies the accuracy of both measurement techniques. The use of a digitizing arm allowed
accurate measurement of micromotion in three directions at twelve points, totalling 36
measurements. This technique is a viable alternative to LVDTs. Assuming rigid body
motion, six LVDTs are required to describe cup-bone micromotion; arrangement of such a
number is restrictive to the experimental set up.
Strong linear regression correlations (R2=0.90) and a high intraclass correlation coefficient
(0.92) were found between experimentally measured and predicted cup-bone micromotions.
The plots in Fig. 4 show the correlation between all directional micromotion components
confirming that the FE micromotion predictions captured the anterior shift of the cup within
the pelvis as well as the scooping and turning mechanisms which were observed in the
experiment (Fig. 6). The mean percentage micromotion error was 20% (95% confidence
interval) and the error in prediction of whole cup rotation angle was 4% (95% confidence
interval). The higher accuracy of cup rotation prediction suggests that the main source of
error may be the axis of cup rotation. Fig. 8 shows that the FE model tends to under-predict
micromotion. The cup-bone interface description has a dominant effect on the micromotions
at this face. The uncertainties associated with the consistency of cup diameter considering
the porous beaded surface, and the potential nonsphericity of the reamed cavity may have
contributed to the under-estimation. When using FE to predict potential failure mechanisms
of implanted cups it is paramount that the mechanism of movement is captured as well as
the general magnitude to ensure full confidence can be placed in results. The only other
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reported validation of FE predicted micromotion on a cementless acetabular cup compared
their data in terms of the angle of cup rotation17 and managed to predict the rotation of the
cup within 5% of the measured value under a chair rising load. FE predicted cup rotation for
the current study was also within 5% (95% confidence interval) of the experimental value,
though observed rotations were significantly lower than those measured in the previous
study17. Reggiani et al.10 compared a single tangential micromotion measure of an
implanted femoral head under a torque load, achieving an error of 12% between predicted
and experimentally measured micromotion. A quarter of the predicted micromotions in this
study were within this accuracy, but the remaining predictions exceeded it. There was,
however, no directional component to measure in the femoral stem study, where torque
loading was applied and measured directly perpendicular to the implanted stem. The
acetabular cup in the present study was free to slide under the spherical head loading device
and therefore was not constrained to move in any known direction. The results observed in
this study demonstrate good correlations and accurate directional micromotion predictions
and cup rotation, but less accurate magnitude estimation. This supports the use of FE to
assess relative differences between acetabular cup modelling scenarios, but the authors
would advise caution in using FE to predict explicit numerical micromotion values, such as
the 150μm failure criteria posed by Pilliar et al.3 in the case of a press-fit implant.
Relatively strong correlations (R2=0.85) and a high intraclass correlation coefficient (0.91)
were observed between predicted microstrains and those measured experimentally. The
strain directions were well predicted at all gauges. Very high percentage errors were found
between all measured strains below 50 microstrain and those predicted. Such high errors
have not been observed in other reported pelvic validation studies18,15,19. The strain
reported from the experiment is the difference in strain between two loading points: 250N
and 2kN, not absolute strain. Before loading commences the cup is impacted into the
acetabulum, which is therefore pre-strained. Cadaveric specimens have shown press-fitted
cups causing an acetabular pre-strain of up to 700 microstrain29. The FE analysis predicted
impaction pre-strains in the region of 2000 microstrain. The absolute strains being measured
are thus a lot higher than the reported values in Table 3. Percentage error is therefore an
unsuitable metric to use in this circumstance. Predicted strain magnitude is highly dependent
on the specific interference level and cup seating, which are in turn dictated by the
diametrical difference between the reamed acetabular cavity and the porous-beaded cup
surface. The support provided to the cup by the reamed acetabulum is likely to vary around
the cup, leading to a varying distribution of pre-strain. This is demonstrated by the high
variation in surrounding acetabular strains shown in Fig. 8. The predicted value in strain
measurement is thus highly dependent on location and a slight difference in pelvic
orientation and cup movement may lead to a large difference in strain prediction. The
strength of the correlation is comparable to published validated pelvis models without press-
fit acetabular cups18,15,19, and principal component direction is well predicted. This again
demonstrates the ability of FE analysis to accurately predict the strain distribution and
direction around a press-fitted acetabular cup, but less well the magnitudinal values of strain.
The discrepancy between predicted and measured micromotions and microstrains may have
arisen from a number of sources. The close agreement between the FE resolved joint loading
force and that experimentally applied (within 1%) suggests that the model was well defined;
together with the low error in cup rotation prediction this suggests that the source of error
may have been the precise direction of cup translation and axis of rotation within the bone.
The definition of the implant-bone interface was thus very important. The implant-bone
friction coefficient was estimated, and both micromotions and microstrains have been shown
to be sensitive to the choice of coefficient. Fixation at the sacroiliac joint provided a more
physiological joint description than is provided by the common fixation of a large section of
the ilium e.g.18,17; this is more difficult to accurately describe with FE modelling, despite
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use of the digitizing arm. The majority of discrepancies are likely to be attributable to the
measured level of press-fit; this has been shown to have a significant effect on cup-bone
micromotions17, but is difficult to accurately quantify. Effort was made to accurately
describe the press-fit between the cup and acetabulum in this study; errors may have arisen
from the assumption of the reamed surface as spherical30, the assumption that the beaded
cup surface was consistent and the final placement of the cup. The cup was assumed to be
fully seated based on superposition of the cup onto the unreamed CT-mesh. Errors in the
description of the reamed surface or the level of cup seating would impact significantly on
cup stability and pelvic pre-strain. This study was also limited by the use of a synthetic,
rather than cadaveric, specimen. Based on previous work18,15,19, the authors do not have any
reason to believe that the techniques and conclusions here would not be applicable to
subject-specific FE models.
Acknowledgments
The authors would like to thank the Engineering and Physical Sciences Research Council (EPSRC) and Finsbury
Orthopaedics Ltd for supporting this work.
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Clarke et al. Page 9
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Figure 1.
Positions of delta rosette strain gauges on synthetic pelvis.
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Figure 2.
A. Close up of loading configuration – a tapered block is fitted into the modular head, the
topside of which is free to slide against the compression piece. B. The whole experimental
test set up, with digitizing arm clamped to the base. C. The digitizing arm. D. The sacroiliac
fixture – four pins (highlighted) are embedded in the synthetic pelvis at the sacroiliac joint
and held rigidly into a steel block.
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Figure 3.
Positions of snap fastener markers around the rim of the implanted cup.
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Figure 4.
Comparison of all experimentally measured (y axis) and FE predicted (x axis) directional
micromotion components. Best fit line and R2 value labelled on plot. Datapoints are marked
with a point, and vertical error bars are added to communicate the range of measured
experimental values.
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Figure 5.
Bland-Altman plot comparing FE micromotion prediction with experimentally measured
micromotion, with limits of agreement represented by dashed lines.
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Figure 6.
Direction of micromotion measured experimentally (above) and FE predicted (below) at
twelve marker points around the cup rim (arrows are not to scale). The crosses represent the
location of the four sacroiliac pins, and the large arrow the direction of loading.
Clarke et al. Page 15
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Figure 7.
FE predicted distribution of maximum principal microstrain (top). Direction of maximum
(red) and minimum (blue) principal microstrain measured experimentally (middle) and FE
predicted (bottom).
Clarke et al. Page 16
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Figure 8.
Comparison of all experimentally measured (y axis) and FE predicted (x axis) directional
components of maximum and minimum principal microstrains. Best fit line and R2 value
labelled on plot. Datapoints are marked with a point, and vertical error bars are added to
communicate the range of measured experimental values.
Clarke et al. Page 17
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Figure 9.
Bland-Altman plot comparing FE microstrain prediction with experimentally measured
microstrain, with limits of agreement represented by dashed lines.
Clarke et al. Page 18
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Clarke et al. Page 19
Table 1
Comparison of experimentally measured and FE predicted micromotion magnitudes at 12 marker points
around the cup rim
Marker number Experimentally measured micromotion
magnitude (µ m) FE predicted micromotion
magnitude (µ m) Error (µ m) Error (%)
1 69.1 (range 66.3–71.3) 141 77 110
2 129 (range 128–130) 147 19 15
3 221 (range 205–242) 205 19 7.6
4 295 (range 291–299) 222 72 25
5 197 (range 195–203) 179 19 9.6
6 231 (range 228–234) 178 53 23
7 231 (range 227–238) 151 80 35
8 256 (range 247–264) 198 59 23
9 219 (range 216–224) 149 70 32
10 225 (range 220–230) 204 21 9.4
11 272 (range 262–279) 220 51 19
12 318 (range 316–320) 249 70 22
Mean error (95% confidence interval) 51 (48) 27 (20)
Marker point locations are shown in Fig. 3
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Clarke et al. Page 20
Table 2
Comparison of experimentally measured and FE predicted cup rotation, radians
Experimentally measured cup rotation (radians) FE predicted cup rotation (radians) Error (radians) Error (%)
0.0051 0.0044 0.0007 14
Error (95% confidence interval)*0.0001 4
*The 95% confidence interval value was derived by using 95% of the marker points to calculate the cup normal
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Clarke et al. Page 21
Table 3
Comparison of experimentally measured and FE predicted principal microstrain at four gauge sites
Gauge number Experimentally measured
principal microstrain Maximum/minimum FE predicted
principal
microstrain Error (microstrain) Error (%)
1 386 (range 369–393) Maximum 389 3.2 0.82
2 590 (range 571–639) Maximum 388 200 34
3 29.8 (range 17.3–42.1) Maximum 112 82 280
4 215 (range 209–220) Maximum 359 140 67
1 −317 (range −295 to −332) Minimum −223 94 30
2 −413 (range −410 to −418) Minimum −421 8 1.9
3 6.76 (range 3.98–11.9) Minimum 15.3 8.5 130
4 37.4 (range 32.6–44.3) Minimum 290 250 680
Mean error (measured strains below 50 microstrain removed) 99 (90) 151 (27)
Gauge locations are shown in Fig. 1
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