Tibial Insert Micromotion of Various Knee Devices-J of Knee surgery-2010 vol 23-3-Bhimji
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Transcript of Tibial Insert Micromotion of Various Knee Devices-J of Knee surgery-2010 vol 23-3-Bhimji
ORIGINAL ARTICLE
Tibial Insert Micromotion of Various TotalKnee Arthroplasty DevicesSafia Bhimji, M.S.,1 Aiguo Wang, Ph.D.,1 and Thomas Schmalzried, M.D.2
ABSTRACT
The objective of this study was to develop a novel method to quantify rotationalmicromotion of modular tibial components that incorporates physiologic loading con-ditions, a physiologic test environment, and constraint characteristics of the articulatingsurface. The methodology is reviewed and data are presented on four total knee designs.Results showed the design with a rotational stabilizing island to demonstrate the mostcapability in resisting rotational micromotion for a given reacted torque, followed by a fullperipheral capture device, then a partial peripheral capture device, and then a full peripheralcapture device with a posterior lipped edge. Under walking and stair-climbing loads, thefull peripheral capture device imparts more torque to the insert than the other designs dueto the higher constraint of its articulating surface and thus experiences the most micro-motion. The rotational stabilizing island device reveals the least amount of motion, due to acombination of its locking mechanism and a less constrained articular surface.
KEYWORDS: Tibial insert micromotion, total knee arthroplasty, backside wear
Modular tibial components have become com-monplace in total knee arthroplasties (TKAs). Theyallow the surgeon the flexibility during surgery to useany thickness of insert once the baseplate is in place and,if necessary, allow for insert exchange during revision.However, this modularity may allow motion to occurbetween the insert and baseplate, which in turn can leadto backside wear on the insert of some designs.1,2 Theadditional source of wear adds to the total amount ofdebris created within the joint, which may eventuallyinduce osteolysis.3
Many studies have focused on quantifying micro-motion across various knee devices.1,4–7 Parks et al testednine different designs in new condition under anterior/posterior (A/P) and medial/lateral (M/L) loads of up to400 N.3 Testing was performed in an air environment.All designs revealed magnitudes of shear motion largeenough to cause fretting at the insert/baseplate interface.
Wasielewski investigated shear motion of three implantswhen under cyclic axial loading of 2500 N in an airenvironment.7 He found micromotion magnitudes of upto 25 mm in all designs, with the greatest amounts beingin regions of uncontained polyethylene and in thedirection the insert is engaged with the locking mech-anism. Engh et al examined shear micromotion of avariety of designs by testing new components, compo-nents retrieved at revision, and components retrieved atautopsy.4 Testing involved applying a 100-N compres-sive load to the insert in air while cycling A/P and thenM/L loads to 100 N. Results showed micromotion of therevision and autopsy components to be significantlyhigher than that of the new components, illustratingthat locking mechanism instability increases with repet-itive physiologic loading.
There are some limitations to these studies.Whereas they do offer a depiction of locking mechanism
1Stryker Orthopedics, Research and Development, Mahwah, NewJersey; 2Saint Vincent Medical Center, Los Angeles, California.
Address for correspondence and reprint requests: Safia Bhimji,M.S., Stryker Orthopedics–Research and Development, 325 Corpo-rate Drive, Mahwah, NJ 07430 (e-mail: [email protected]).
J Knee Surg 2010;23:153–162. Copyright # 2010 by Thieme
Medical Publishers, Inc., 333 Seventh Avenue, New York, NY 10001,USA. Tel: +1 (212) 584-4662.
Received: June 14, 2010. Accepted after revision: August 23, 2010.Published online: December 6, 2010.DOI: http://dx.doi.org/10.1055/s-0030-1268696.ISSN 1538-8506.
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laxities, they do not give an accurate measure of thefunctional performance of the devices. Loading param-eters were simplified to either shear forces or compres-sive forces and did not reproduce the complex off-axisloading conditions seen in vivo. They only measuredA/P or M/L micromotion, despite retrieval studies byMikulak et al6 and Bradley et al8 that reported evidenceof rotary motion of the insert within the baseplate,especially with posterior stabilized prostheses. Thesestudies also did not examine the effect of constraint ofthe articulating surface of the insert on micromotion.Lastly, although most authors presoaked their inserts, alltesting was performed in an air environment, contrary tothe natural fluid environment of the knee joint.
Conditt et al overcame some of these limitations;translational and rotational micromotion of implantsretrieved at revision were measured in a saline solutionunder walking conditions.1 Results were compared withthose of laxity testing using the methods of Engh et al.4
The findings showed that the laxity testing yieldedsignificantly more micromotion than the physiologictesting, demonstrating the need for more clinically rele-vant methodologies.
The objective of the current study was to developa novel method to quantify rotational micromotion ofmodular tibial components that incorporates physiologicloading conditions, a physiologic test environment, andconstraint characteristics of the articulating surface.Specifically, the purpose of this article is to review themethodology developed and present data generated fromit on four total knee designs.
MATERIALS AND METHODS
Test Samples
Three samples of each knee design were evaluated in thisstudy. All samples represented the thinnest, medium-sized components offered by the manufacturer.
Locking mechanism designs varied among thecomponents (Fig. 1). Design A featured a full peripheralcapture locking mechanism with a posterior lipped edgeand a rotational stabilizing island (Triathlon PS; StrykerOrthopaedics, Mahwah, NJ). Design B featured a fullperipheral capture locking mechanism (PFC SigmaStabilized; DePuy, Warsaw, IN). Design C featured afull peripheral capture locking mechanism with a poste-rior lipped edge (NexGen LPS; Zimmer, Warsaw, IN).Design D featured a partial peripheral capture lockingmechanism with a posterior lipped edge and an anteriorconstraint (Genesis II PS; Smith & Nephew, Mem-phis, TN). A summary of the designs is provided inTable 1.
Test Apparatus
All testing was performed on a multiaxis servo-hydraulictest frame (MTS Bionix 858; MTS Corporation, EdenPrairie, MN) consisting of two actuators: a coupled axial/torsional actuator oriented vertically to apply compressiveloads and internal/external torques to the components,and an axial actuator oriented parallel to the floor to applyshear loads (referred to as the side actuator).
Test Setup
All inserts were soaked in water at 378C for a minimumof 1 week prior to testing. Three spherical probes werethen rigidly mounted to each insert (two probes anteriorand one probe posterior) and each insert assembled to itsrespective baseplate.
The femoral components and insert/baseplate as-semblies were rigidly mounted to stainless steel holdingfixtures. Six linear variable differential transducers(LVDTs) (Type DS40AW and DS200AW; RDPGroup, Pottstown, PA) were mounted to the baseplatefixture. Three were placed on the anterior side, withtwo in the superior/inferior (S/I) direction and one in
Figure 1 Implant locking mechanism designs.
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the M/L direction. The remaining three were placed onthe posterior side, with one in the A/P direction, one inthe M/L direction, and one in the S/I direction. TheLVDTs were positioned such that the plunger contactedthe spherical probes on the inserts.
The insert/baseplate/LVDT assembly wasmounted at a 0-degree slope to a bath and the baththen mounted to a bearing table connected to the sideactuator of the test frame. The assembly was mounted intwo different orientations (Fig. 2); one such that the sideactuator applied a load in the A/P direction of thecomponent assembly while allowing M/L motion to beunrestricted, and the other such that the side actuatorapplied a load in the M/L direction while allowing A/Pmotion to be unrestricted.
The femoral component was mounted to theaxial/torsional actuator via fixturing that allowed theflexion angle to be adjusted to the desired setting andvarus/valgus rotation to be unrestricted.
To mimic the in vivo lubrication conditions of theknee, serum (Alpha Calf Fraction Serum; HycloneLaboratories, Logan UT), diluted with water (1 partserum:6 parts water) was added to the bath such that thefluid level completely covered the level of tibiofemoralarticulation. The temperature was heated to 378C usinga heater (time to heat was �30 minutes), and circulationwas maintained using a pump.
To initially align the femoral component to theinsert at each flexion angle, a 200-N compressive force
was applied while the femoral component was rotatedthrough� 10 degrees. The insert was allowed to float inthe A/P and M/L directions to find its natural restingposition.
Test Procedure
Resultant joint loads of 2600 N and 3800 N were appliedto the insert using the vector sum of the axial and sideactuators. These loads were chosen to represent max-imum peak loads throughout the motion cycle of walk-ing and stair-climbing activities.9 The loads were reactedthrough the femur-insert interface. The orientation ofthe loads were varied both in the A/P and M/L direc-tions (Fig. 3). In the A/P direction, loading varied from17 degrees anterior to 1.5 degrees posterior, with theanterior orientations simulating the resultant knee loadvectors of various activities including gait, stair climbing,and rising from a seated position. The posterior orien-tation was included to simulate resultant load vectorsthat could occur in hyperextension due to anteriorimpingement of the femoral component on the tibialpost. The M/L orientations ranged from 5 degreeslateral to 5 degrees medial, representing resultant loadvectors that could occur due to off-axis loading as well asvarus/valgus malalignments at the knee.10 A summary ofthe load vectors tested can be found in Table 2.
Each insert was tested in all A/P and M/L loadingconditions at five flexion angles: 0, 15, 60, 90 degrees, anda hyperextension angle. The first four were chosen toencompass the range of flexion angles normally achievedthroughout various activities of daily living.11 A hyper-extension angle was also included because total kneesmay be implanted with femoral flexion and/or tibialposterior slope, resulting in relative hyperextension of
Table 1 Implant/Locking Mechanism Design Summary
Design
Implant and
Manufacturer Locking Mechanism
A Triathlon PS, Stryker Orthopaedics Full peripheral capture locking mechanism with a posterior lipped
edge and a rotational stabilizing island
B PFC Sigma Stabilized, DePuy Full peripheral capture locking mechanism
C NexGen LPS, Zimmer Full peripheral capture locking mechanism with a posterior lipped edge
D Genesis II PS, Smith & Nephew Partial peripheral capture locking mechanism with a posterior lipped
edge and an anterior constraint
Figure 2 A/P loading setup. Figure 3 Load orientations.
TIBIAL INSERT MICROMOTION OF VARIOUS TKA DEVICES/BHIMJI ET AL 155
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the components during some phases of the walkingcycle.12 The hyperextension angle tested was designdependent and represented the angle at which the fem-oral component first contacted the anterior side of thetibial insert post when in its natural A/P-M/L restingposition, so-called hyperextension impingement.
Once the resultant load had been applied, thefemoral component was rotated between� 5 degrees ofinternal/external rotation at 5 deg/s for 5 cycles, and thenincrementally increased to� 10,� 15, and� 20 degreesfor 5 cycles each. A torque limit of 35 N�m was used toprevent damage to the inserts. Axial load and displace-ment, shear load and displacement, torsional torque andangle, and the six LVDT signals were recorded at 12.5Hz throughout the loading process.
Analysis of Results
ARTICULAR SURFACE CONSTRAINT
Articular surface constraint was measured at each flexionangle as the amount of torque required to rotate thefemoral component on the insert from –20 toþ 20degrees. Comparisons between designs were made byplotting rotational torque data as a function of femoralrotation in the 0-degree load orientation condition.
INSERT/BASEPLATE MICROMOTION
In this study, micromotion was defined as the amount ofrotation the insert undergoes within the plane of the
baseplate as a result of torques applied at the articulatingsurface. Details on calculation of this motion for theLVDT data can be found in Appendix A.
MICROMOTION VERSUS REACTIVE TORQUE
For each test condition, insert rotation was calculatedfrom the LVDT data and graphed as a function ofreactive torque. Figure 4 displays a sample plot for onetest condition (i.e., data for one flexion angle/loadmagnitude/load orientation combination). From thisplot, the peak-to-peak magnitudes of insert rotationand reactive torque were determined for each level offemoral rotation (� 5,� 10,� 15,� 20 degrees). Scat-terplots, with best-fit linear regression lines, of thesepeak-to-peak magnitudes across all load orientations andfemoral rotations were then generated for each flexionangle under the 3800-N load condition. A two-factorANCOVA with a¼ 0.05 was used to test for significantdifferences between designs across the range of torquesobtained at each flexion angle.
INSERT/BASEPLATE MICROMOTION: EFFECT OF WALKING
AND STAIR-CLIMBING CONDITIONS ACROSS DESIGNS
Because insert/baseplate micromotion causes backsidewear, an investigation of this motion under repetitiveclinical activities that could lead to wear is useful. Twoactivities were chosen for analysis: walking, which rep-resents a high-cycle/low-load activity, and stair climb-ing, which represents a low-cycle/high-load activity. Acombination of loading conditions that most closely
Table 2 Load Vector Magnitudes and Orientations for A/P Loading
Load Magnitude A/P Load Orientations M/L Load Orientations
2600 N 1.5 degrees posterior, 0, 1.5 degrees
anterior, 10 degrees anterior, 17 degrees
anterior
5 degrees medial, 1.5 degrees medial, 0, 1.5 degrees
lateral, 5 degrees lateral
3800 N 1.5 degrees posterior, 0, 1.5 degrees
anterior, 10 degrees anterior, 17 degrees
anterior
5 degrees medial, 1.5 degrees medial, 0, 1.5 degrees
lateral, 5 degrees lateral
Figure 4 Sample insert rotation versus torque curve. Abbreviations: Pk-pk, peak to peak.
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represent these two activities were chosen from thematrix of conditions tested.
For walking, loading conditions were chosen thatmost closely matched the loading profiles specified in theInternational Organization for Standardization (ISO)specification for wear testing of total knee prosthe-ses.13,14 Table 3 provides a summary of the loadssuggested in this specification for each of the flexionangles tested. Table 4 provides a summary of the loadingcombinations chosen from the test matrix to most closelyrepresent the parameters of Table 3. A hyperextensionangle was added to Table 4, as many knees are implantedwith a posterior slope, placing the knee into hyper-extension during some phases of the walking cycle.12
For stair climbing, loading conditions werechosen that most closely matched those found in theliterature. Table 5 provides a summary of the loadsspecified in literature for each of the flexion anglestested.15 Table 6 provides a summary of the loadingcombinations chosen from the test matrix to most closelyrepresent the parameters of Table 5. Again, the reacted
torques and resulting insert rotations of these loadingconditions were compared across designs.
RESULTS
Articular Surface Constraint
Rotational constraint of each design has been previouslypublished by the authors.16 To summarize, be-tween� 10 degrees of rotation, results show designs A(Triathlon) and C (NexGen) to have similar rotationalconstraint characteristics at 0, 15, and 90 degrees offlexion and to be the least constrained of the five designs.In hyperextension and 60 degrees, NexGen shows lowerconstraint in internal rotation. Across all designs, thedesign B (PFC) demonstrates the most constraint.
Beyond� 10 degrees of rotation, PFC continuesto show high levels of constraint, while Triathlon’s beginsto rapidly increase. In internal rotation, NexGen is theleast constrained, and PFC and design D (Genesis II) arethe most constrained. In external rotation, NexGen and
Table 3 Loading Parameters from ISO Standard for Wear Testing of Total Knee Arthroplasties, Walking
Flexion
Angle (deg)
Compressive
Force (N)
A/P Force
(N)
Load Orientation
(deg)
Internal/External
Rotation (deg)
0 167.6 0 0 1.6 external
15 2600 109.6 anterior 2 anterior 1.1 internal
60 167.6 47.0 anterior 16 anterior 3.9 internal
Table 4 Loading Combinations Chosen from Test Matrix to Represent ISO Walking Profile
Flexion Angle (deg) Resultant Load (N) Load Orientation (deg)
Internal/External
Rotation (deg)
Hyperextension 2600 1.5 posterior � 5
0 2600 0 � 5
15 2600 1.5 anterior � 5
60 2600 17 anterior � 5
Table 5 Loading Parameters from Literature for Stair Climbing
Flexion
Angle (deg)
Compressive
Force (N) Assuming
BW¼ 91 kg
A/P Force (N)
Assuming
BW¼ 91 kg
Load Orientation
(deg)
Internal/External
Rotation (deg)
15 3640 346 anterior 5.4 anterior 2.5 external
60 3185 346 posterior 6.2 posterior 2.5 external
90 0 182 anterior 90 anterior 3 external
Abbreviations: BW, body weight.
Table 6 Loading Combinations Chosen from Test Matrix to Represent Stair Climbing
Flexion
Angle (deg)
Resultant
Load (N)
Load Orientation
(deg)
Internal/External
Rotation (deg)
15 3800 10 anterior � 5
60 3800 1.5 posterior � 5
90 3800 17 anterior � 5
TIBIAL INSERT MICROMOTION OF VARIOUS TKA DEVICES/BHIMJI ET AL 157
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Genesis II are the least constrained, and PFC is the mostconstrained. These trends vary somewhat across flexionangles. Note that NexGen did not reach� 20 degrees ofrotation at 90 degrees due to deformation of the posteriorlip of the insert condyles at the extreme range of rotation.
Micromotion Versus Reactive Torque
Figure 5 displays an insert rotation versus torque re-gression plot for hyperextension. Plots for the remainingflexion angles are also shown; however, for purposes of
clarity, only the regression lines are shown. R2 values foreach of these regressions can be found in Table 7.
Results demonstrated that increasing torques re-acted at the articulating surface of the insert are trans-lated to the baseplate interface, resulting in increasedrotations of the insert. When comparing across designs,NexGen demonstrated the largest amount of insertrotation for a given torque at the lower flexion angles,followed by Genesis II, and then by PFC. At 60 and 90degrees, Genesis II showed the most motion. Triathlondemonstrated the least amount of insert rotation of the
Figure 5 Insert rotation versus torque scatterplot: hyperextension, 0, 15, 60, and 90 degrees of flexion.
Table 7 Linear Regression R2 Values
Design
R2
Hyperextension 0- 15- 60- 90-
Design A 0.96 0.95 0.84 0.74 0.54
Design B 0.86 0.78 0.78 0.73 0.51
Design C 0.51 0.72 0.69 0.57 0.70
Design D 0.73 0.85 0.84 0.67 0.23
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five designs across all flexion angles for the same torque.In general, these differences tend to become morepronounced as a function of torque, with the designsbeing similar at levels less than �30 N�m, and differingat higher levels. Results of the ANCOVA showedstatistically significant differences between most of thedesigns at each angle (Table 8).
Insert/Baseplate Micromotion: Effect of
Walking and Stair-Climbing Conditions across
Designs
Figure 6 displays the reacted torques and resultinginsert rotations of the test conditions that most closelysimulate walking. The graphs display the average andstandard deviation over the three trials of each kneedesign. Results showed the range of applied torques tobe lowest for Triathlon, similar for NexGen andGenesis II, and highest for PFC. Resulting insertrotations were lowest for Triathlon and highest forPFC. NexGen demonstrates particularly high motionwhen in hyperextension. Similar results were seen forthe test conditions simulating a stair-climb activity, asshown in Fig.7.
DISCUSSIONThe objective of this study was to investigate insert/baseplate micromotion under physiologic conditionsacross four total knee designs, focusing on the effectof articular surface constraint and locking mechanismdesign.
Results showed that induced insert/baseplate mi-cromotion has a direct linear relationship with themagnitude of torque reacted at the articulating surfaceof the insert. The constraint characteristics of a kneedesign thus play an important role in induced micro-motion. The more constrained a knee is, the more torqueis transferred to the insert/baseplate interface, and hencethe more stress induced in the locking mechanism. Thisfinding is supported by Bradley et al8 in a study that
Table 8 Two-Factor ANCOVA p Values at Each Flexion Angle
Design A Design B Design C
Hyperextension
Design B 0.980
Design C <0.005 < 0.005
Design D 0.265 0.554 < 0.005
0 degrees
Design B 0.266
Design C <0.005 < 0.005
Design D 0.024 < 0.005 < 0.005
15 degrees
Design B 0.551
Design C <0.005 < 0.005
Design D <0.005 < 0.005 < 0.005
60 degrees
Design B <0.005
Design C <0.005 0.681
Design D <0.005 < 0.005 0.037
90 degrees
Design B <0.005
Design C <0.005 1.000
Design D <0.005 < 0.005 < 0.005
Figure 6 Reacted torque and micromotion during walking
conditions.
TIBIAL INSERT MICROMOTION OF VARIOUS TKA DEVICES/BHIMJI ET AL 159
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compared wear patterns of 14 retrieved posterior stabi-lized (PS) components to 13 retrieved cruciate retaining(CR) components, both of the PFC design. Seventy-onepercent of the PS trays displayed existence of rotarymotion, whereas only 31% of the CR componentsdisplayed the same. Evidence of rotary motion has alsobeen reported by Mikulak et al6 in an examination of 16retrieved PS PFC devices. Across the four designsevaluated in the current study, Triathlon and NexGen,in general, demonstrated similar constraint character-istics between� 10 degrees of rotation and were the leastconstrained of the designs, and PFC was the mostconstrained.
To directly compare the performance of eachdesign’s locking mechanism, the amount of inducedmicromotion was evaluated as a function of the magni-tude of torque reacted at the insert, regardless of themotions being applied at the articulating surface. Resultsdemonstrated NexGen and Genesis II had the largestamount of insert rotation for a given torque, dependingon flexion angle, followed by PFC. Triathlon demon-strated the least amount of insert rotation across the fivedesigns for the same torque. This finding is consistentwith the design of Triathlon’s locking mechanism,which has a rotational stabilizing island not found inthe other devices. The magnitudes of the observedmotions tended to decrease with increasing flexionangles. A possible explanation could be that becausecam/post engagement occurs at these angles, the insertsmay become pushed up against the anterior lip of thebaseplates, minimizing the amount of potential micro-motion.
To compare the functional performance of eachdesign, the effect of loading conditions during twophysiologically relevant activities was also investigated:walking and stair climbing. Results showed Triathlonto have the least amount of micromotion, due to acombination of its rotational stabilizing locking mech-anism and a less constrained articular surface. NexGenand Genesis II demonstrated similar amounts of re-acted torque during both activities, with NexGendisplaying more motion during walking and GenesisII more motion during stair climbing. PFC, due to itshighly constrained articular surface, revealed the high-est amounts of reacted torque for each activity acrossall the designs and also some of the highest motions. Itshould be noted that, because the load magnitudesinvestigated in this study represented peak loads foreach activity, an exact match to the referenced loadingconditions at each flexion angle was not possible. Inparticular, the load magnitudes used at 0 and 60degrees for walking and 90 degrees for stair climbingare higher than the load magnitudes referenced in theliterature at those flexion angles. The relative compar-isons between the designs, however, are expected toremain the same.
Comparison of the current results with those ofprevious studies is difficult as the majority did notevaluate micromotion under physiologically relevantloading conditions, nor did they examine rotation ofthe insert. One exception is a study performed byConditt et al1 that measured insert rotation underwalking conditions. Although the loading scenariosvaried somewhat from the current study, their resultsof 153� 109 millidegrees of motion are comparable withthe results reported here. Conditt et al also comparedtheir physiologic loading results with testing that meas-ured locking mechanism laxity in an unloaded condition,a method used by many other investigators. Their find-ings indicated micromotion to be 8 times larger in theunloaded condition than in the physiologically loadedone, stressing the need for more clinically relevantstudies such as the current one.
This study investigated micromotion between theinsert and baseplate of four modular total knee designs.This motion has been shown to potentially lead tobackside wear on the insert, which may eventually induceosteolysis.1–3 Correlations between the magnitudes ofmotion measured in this study and backside wear need tobe established. Also, results represent micromotion ofbrand-new devices and do not account for any break-down of the locking mechanisms that may occur over thein situ duration.
CONCLUSIONThe locking mechanism of Triathlon demonstrated themost capability in resisting rotational micromotion for a
Figure 7 Reacted torque and micromotion during stair-
climbing conditions.
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given reacted torque, followed by PFC, and then Nex-Gen and Genesis II. Under walking and stair-climbingloads, PFC imparted more torque to the insert than thatof the other designs due to the higher constraint of itsarticulating surface and thus experiences the most micro-motion. Triathlon revealed the least amount of motiondue to a combination of its locking mechanism, whichfeatures a rotational stabilizing island not found in theother designs, and a less constrained articular surface.Correlations between the magnitudes of motion meas-ured in this study and backside wear need to be estab-lished.
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APPENDIX AIn this study, micromotion was defined as the amount ofrotation the insert undergoes within the plane of thebaseplate as a result of torques applied at the articulatingsurface. To calculate this motion, a coordinate systemwas established on the insert with the x-axis correspond-ing with the A/P axis, the y-axis with the M/L axis, andthe z-axis with the S/I axis (Fig. A-1). Insert rotationwas calculated about the z-axis using the equationsbelow and LVDT displacement data of the three spheresshown (AL, AM, and P):
where are initial positions ofspheres AL, P, and AM along the y- and z-axes beforetesting is started; are posi-tions of those spheres along the y- and z-axes at everytime interval collected; and are distancesbetween the spheres as illustrated in Fig. A-1.
TIBIAL INSERT MICROMOTION OF VARIOUS TKA DEVICES/BHIMJI ET AL 161
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where wz is defined as rotation of the insert within theplane of the baseplate.
Figure A-1 Sphere locations and coordinate system defi-
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162 THE JOURNAL OF KNEE SURGERY/VOLUME 23, NUMBER 3 2010
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