Finite element analysis of the effect of cementing concepts on implant stability and cement fatigue failure

Background and purpose Two contradictory cementing techniques (using an undersized stem versus a canal-filling stem) can both lead to excellent survival rates, a phenomenon known as the “French paradox”. Furthermore, previous studies have indicated that the type of bone supporting the cement mantle may affect implant survival. To further evaluate the mechanical consequences of variations in cementing technique, we studied the effect of implant size and type of bone supporting the cement mantle on the mechanical performance of cemented total hip arthroplasty, using finite element analysis. Methods In a generic 2-dimensional plane-strain finite element model of a transverse section of a cemented total hip arthroplasty with a Charnley-Kerboull stem, we varied implant size and type of bone supporting the cement mantle. The models were subjected to 2 × 106 cycles of an alternating loading pattern of torque and a transverse load. During this loading history, we simulated cement fatigue crack formation and tracked rotational stability of the implant. Results Canal-filling stems produced fewer cement cracks and less rotation than undersized stems. Cement mantles surrounded by trabecular bone produced more cement cracks and implant rotation than cement mantles surrounded by cortical bone. Interpretation Our investigation provides a possible explanation for the good clinical results obtained with canal-filling Charnley-Kerboull implants. Our findings also indicate that inferior mechanical properties are obtained with these implants if the cement is supported by trabecular bone, which may be minimized by an optimal cementing technique.

 A thi cemet matle (Ma et al. 2004) ad cemet matle defects have bee associated with the formatio of cracks i the cemet matle (Jasty et al. 1991), leadig to early failure of total hip arthroplasty (Star et al. 1994). This evidece has resulted i the geerally accepted rule of usig a stem that is udersized compared to the broach used to prepare the itramedullary caal, to produce a cemet matle that is at least 2 mm thick. Usig this techique, excellet survival rates have bee obtaied (Malchau et al. 2002).
I Frace i the early 1970s, a surgical techique was developed that cotradicted this cocept (Laglais et al. 2003, Kerboull et al. 2004. The techique ivolved the removal of as much trabecular boe as feasible ad the implatatio of a caal-fillig stem i a lie-to-lie fashio, so that the size of the implat is equal to the size of the broach used to prepare the itramedullary caal. The goal is to trasfer loads directly from the stem to the cortical boe, ad as such to "protect" the cemet matle (Laglais et al. 2003). The techique results i a very thi cemet matle with multiple defects (Scheer-lick et al. 2006). Surprisigly, this techique also resulted i excellet survival rates (Kerboull et al. 2004, Scheerlick ad Casteley 2006. This pheomeo of two seemigly cotradictory cemetig cocepts leadig to good outcome has bee referred to as the "Frech paradox" (Laglais et al. 2003).
Although both techiques apparetly lead to good cliical results, variatios i implat size, cemet matle thickess, ad boe type surroudig the cemet matle will cause dif-fereces i the respose to fatigue loadig i terms of implat stability ad cemet crack formatio. Previous studies suggested that large implats may provide superior rotatioal stability (Massi et al. 2003), ad that cemet matles supported by trabecular boe produce iferior results . The aim of our study was to further evaluate the mechaical cosequeces of variatios i cemetig tech-ique, usig fiite elemet aalysis (FEA).
We hypothesized that (1) udersized stems surrouded by a thick itact cemet matle would produce fewer cemet fatigue cracks tha caal-fillig stems, (2) large caal-fill-ig stems would rotate less tha udersized stems, ad (3) a cemet matle supported by trabecular boe would produce more cemet cracks ad more implat rotatio tha a cemet matle supported by cortical boe.

Material and methods
We created a geeric 2-dimesioal (2D) plae-strai FEA model of a trasverse slice of a Charley-Kerboull stem replica (CMK; Stratec Medical, Oberdorf, Switzerlad) cemeted i a cadaver femur. This geeric model was subsequetly adapted to simulate arthroplasties resultig from various cemetig techiques. The FEA models were subjected to a history of fatigue loadig, durig which crack formatio ad implat rotatio were simulated.
The model was created from computed tomography (CT) data used previously for geometric aalyses of the cemet matle aroud lie-to-lie ad udersized femoral implats . The model was based o a repre-setative example of a Charley-Kerboull stem implated i a lie-to-lie fashio. For the FEA model, a image of the CT data set was take at the level of the lesser trochater. I the CT image, the cotours of the cortical ad trabecular boe, the cemet matle, ad the stem were idetified as previously described . The model was created based o these cotours usig a automatic mesher (MSC. MARC; MSC Software Corp, Sata Aa, CA). The models had a thickess of 5 mm ad cosisted of approximately 6,000 8-ode brick elemets ad 12,500 odal poits (Figure 1).
We varied the size of the femoral implat to simulate both caal-fillig ad udersized implats. The udersized implats were based o the origial Charley-Kerboull implat geometry to exclude variability i the implat desig, allowig us to study oly the effect of cemetig cocepts. Cosiderig the cross-sectioal geometry of the Charley-Kerboull stem did ot differ much from that of the origial Charley roudback stem, we chose to use scaled-dow versios of the origial Charley-Kerboull implat for the models of the udersized stems. Cosequetly, the cemet matle thickess was varied iversely with femoral compoet size. 4 cases were created: a model with a icomplete cemet matle (miimum thickess of 0 mm; maximal caal-fillig stem), a thi matle (miimum thickess of 1 mm; caal-fillig stem), a average matle (miimum thickess of 2 mm; udersized stem), ad a thick cemet matle (miimum thickess of 3 mm; severely udersized stem) ( Figure 2). Due to the typical shape of the implat, the thickess of the cemet matle was miimal i the medial ad lateral parts of the recostructio, while the thickess was greater i the aterior ad posterior regios.
The type of boe supportig the cemet matle was varied by chagig the material properties of the elemets surroud-ig the cemet matle. 3 variatios were aalyzed: a cemet matle supported by trabecular boe oly (trabecular boe support, represetig a implatatio techique with poor cemet pressurizatio), a matle supported by trabecular ad cortical boe (mixed boe support, represetig a impla-tatio techique with adequate cemet pressurizatio), ad a matle maximally supported by cortical boe (cortical boe support, represetig a surgical techique i which most of the trabecular boe is broached away or filled with cemet) (Figure 2). To avoid mesh depedecy of the results i the  simulatios, all models were derived from a sigle geeric FEA model. I this model, the mesh architecture was adapted such that all geometric variatios i implat size, cemet matle thickess, ad type of boe support could be modified by merely chagig the material properties assiged to the elemets. The material properties of the cortical boe (Lotz et al. 1991), trabecular boe (Kaeko et al. 2004), boe cemet (Lewis 1997), ad implat were assumed to be isotropic ad liear elastic (Table 1). The implat material was modeled with material properties of stailess steel.
Cotact betwee the implat ad the cemet was modeled usig a ode-to-surface cotact algorithm (MSC.MARC). The implat-cemet iterface was assumed to be deboded from the start of the simulatio, implyig that o tesile loads could be trasferred over the iterface, assumig a worst-case sce-ario. Frictio was modeled usig a Coulomb stick-slip model with a frictio coefficiet of 0.25, simulatig a sati surface fiish for the stem, cosistet with the surface fiish of the Charley-Kerboull stems. The cemet matle was assumed to be fixed to the surroudig cortical ad trabecular boe.
For 2 × 10 6 cycles, the models were alterately loaded with a cyclic torque load ad a trasversal load. The loadig co-figuratios were applied i a ratio of 9:1, meaig that durig 90% of the loadig history a torque load was applied, while durig 10% the trasversal load was applied. The torque load represeted a stair-climbig load, which is critical for implat stability (Bergma et al. 1995). Sice our models were limited to oly a slice of a etire recostructio, the exteral loads had to be scaled dow to the model size. We therefore assumed a torque load of 6.4 Nm actig o the models (Berg-ma et al. 1995). The trasversal load represeted a bedig momet i the frotal plae that ca be as high as 80 Nm (Bergma et al. 1995). As a cosequece, the implat will exert a medial force o the cemet matle i the proximal regio, while more distally lateral forces are trasferred to the cemet. A trasversal load of 400 N actig i the medial directio represeted bedig i the frotal plae i our 2D models. Displacemet i the ateroposterior directio was restricted i the medial ad lateral part of the outer cortex, while displacemet i the mediolateral directio was restricted i the aterior ad posterior part of the outer cortex ( Figure  1B). I this maer, deformatio ad expasio of the cortical boe was allowed, eablig movemet ad deformatio of the stem, cemet, ad boe, while rigid body displacemet of the models was restricted.
Because oly a slice of a etire recostructio was aalyzed, a plae-strai state was assumed i the model. Although 2D elemets are usually used i such a case, we used 3-dime-sioal (3D) brick elemets to make the FEA models compatible with our fatigue crack formatio algorithm. To compesate for this, all odes o the top ad bottom plaes of the model were fixed i the axial directio.
Fatigue crack formatio ad creep were simulated usig a custom-writte algorithm based o FEA (Stolk et al. 2004). Based o the local cemet stress situatio ad the umber of loadig cycles, a small crack could occur at a certai locatio i the matle. This crack was the accouted for mechaically by locally reducig the stiffess to virtually zero i the direc-tio perpedicular to the crack. At the same locatio, a addi-tioal secod ad third crack could be formed, perpedicular to the first crack. Furthermore, durig the simulatio small cracks could propagate, thereby formig macrocracks that could evetually spa the full thickess of the cemet matle. Similarly, creep deformatio was simulated to occur locally i the cemet matle, also based o the local cemet stress ad the umber of loadig cycles. The formatio of boe cemet cracks was determied usig so-called S-N curves (Murphy ad Predergast 1999, whereas the amout of local creep strai i the cemet matle was calculated usig a creep law (Verdoschot ad Huiskes 1995). This creep-damage algorithm has bee used previously to differetiate betwee the survival of various implat desigs (Jasse et al. 2005, Stolk et al. 2007.
Durig the simulatios, we moitored the umber of cracks formed i the cemet matle. I order to eable comparisos betwee the various models, the umber of cracks was ormalized by dividig by the umber of cracks that would ultimately be possible i the cemet. The total umber of cemet cracks possible i the cemet matle depeded o the size of the implat, ad raged from 17,500 to 38,000 for the models with the largest ad smallest implats, respectively. I additio, the rotatio of the femoral compoet with respect to the cortical boe was calculated ad was cosidered a measure of the level of implat stability. To calculate implat rotatio, iitial elastic deformatios of the models were igored-to display oly the log-term effect of creep ad crack formatio o implat rotatio. To demostrate the effect of type of boe supportig the cemet matle, forma-tio of cemet damage ad implat rotatio as predicted by models with trabecular ad cortical boe support were calculated ad preseted relative to the results of models with mixed boe support, which was cosidered to be the stadard situatio.

Results
I cotrast with our first hypothesis, the caal-fillig stems produced fewer cracks i the cemet matle tha the uder- sized stems (Figure 3). I geeral, the umber of cracks formed i the cemet matle icreased with decreasig size of the implat. Cyclic torque loadig of the models caused cracks to appear i the cemet matle at the posteromedial ad aterolateral corers of the stem (Figure 4). Cracks that crossed the full thickess of the cemet matle appeared first i the aterolateral corer of the cemet matle, which was followed i some cases by a secodary crack i the posteromedial corer. We observed full-thickess cracks i all models with udersized implats, whereas i the models with the maximal caal-fillig implat, full-thickess cracks occurred oly whe the cemet matle was supported by trabecular boe. I two models with a severely udersized stem (cemet matle supported by mixed boe ad cortical boe), full-thick-ess cracks preveted the model from covergig after 1.25 × 10 6 cycles. Deformatios i these models, i combiatio with the alteratig loadig profile, caused istabilities i the cotact algorithm at the implat-cemet iterface. Differeces i crack formatio ad implat rotatio betwee models were therefore ivestigated at 1.25 × 10 6 cycles istead of at 2 × 10 6 cycles. Cosistet with our secod hypothesis, after 1.25 × 10 6 loadig cycles, the caal-fillig stems had rotated less tha the udersized stems ( Figure 5). Creep ad crack formatio i the cemet matle caused progressive rotatio of the stem, particularly durig the first 1 × 10 6 cycles. I some models, sudde icreases i implat rotatio occurred whe chagig from the torque load to the trasversal load. Whe the trasversal load was subsequetly reapplied, the stem settled agai i a Figure 3. In contrast to our first hypothesis, after 1.25 × 10 6 loading cycles, the models with undersized stems produced more cement cracks than models in which a canal-filling stem was simulated. The number of cracks was normalized by dividing by the maximal number of cracks that could possibly be simulated in the cement mantle. ew ad more stable positio, ad implat rotatio decreased agai.
I geeral, models with a cemet matle supported by trabecular boe produced more cracks i the cemet matle ad caused more implat rotatio tha the models i which the cemet matle was supported by a mixture of trabecular ad cortical boe. I additio, icreasig cortical boe reduced implat rotatio ad reduced the umber of cemet cracks (Table 2).

Discussion
Although the FEA model we used was based o accurate ad cliically relevat data for the Charley-Kerboull stem, it obviously had certai limitatios. I our study, we used a 2D model rather tha a 3D oe-to limit the computatioal costs while providig sufficiet detail for aalysis of the effects of chages i the cemet matle geometry. This limited the loads we could apply to i-plae loads, such as a torque load. The effect of axial loads, leadig to implat subsidece ad ta-getial stresses i the cemet matle, was ot simulated i our models. However, it has bee demostrated that torque result-ig from stair-climbig activities is the most detrimetal load for cemet matle failure (Bergma et al. 1995). Moreover, implat subsidece may have bee limited for the implat desig we aalyzed, cosiderig it has a collar.
Our model was based o a sigle cross sectio at the level of the lesser trochater, ot takig ito accout differeces i the cross-sectioal shape of other parts of the implats. However, our fidigs are similar to those of a FEA ivestigatio of Massi et al. (2003) who used 3D FEA models of etire cemeted recostructios to aalyze the effects of implat-cemet bod ad implat size. I that study, the proximal caal fill of implats was varied (100% to 90% to 80% to 70% of the optimal fill). The results of that study showed that a optimal fill (large implat) icreased the rotatioal stability. I additio, they demostrated that loads are maily trasferred i the proximal regio of the recostructio, which provides further justificatio for our choice of performig aalyses at the level of the lesser trochater. Ufortuately, to our kowledge o data are available o experimetal mechaical testig or implat retrieval aalysis agaist which we ca verify our fidigs.
Regardless of the fact that oly oe level of the cemeted recostructio was aalyzed, our results may to some extet have bee depedet o the specific geometry that we used. We modeled a specific cross sectio of the CT dataset rather tha creatig a average shape, because we expected that a specific geometry would eable our models to differetiate better betwee the various cases. We selected a "represetative" cross sectio from a previous study . This cross sectio comprised typical features of lieto-lie recostructios, such as a thi cemet matle i the atero-medial regio .
A additioal limitatio to our study was the fact that we oly aalyzed the Charley-Kerboull implat, eve though it is used most widely whe performig lie-to-lie recostruc-tios (Scheerlick ad Casteley 2006). Cosequetly, our results ad subsequet coclusios oly apply to this implat. This choice limited the scope of our work, sice we did ot aalyze variatios i desig such as implat shape ad surface roughess. Such variatios may have cosequeces for the implat-cemet bod, implat subsidece, ad cemet matle abrasio. I our study, however, we assumed that the stem was ot boded to the cemet matle from the start of the simulatio, as several studies have show that implat-cemet debodig occurs relatively early i the lifespa of a cemeted recostructio (Jasty et al. 1991). I additio, varia-tios i the surface roughess of a implat may affect cemet matle abrasio. For istace, polished, collarless implats may be more susceptible to subsidece ad micromotios tha collared implats with a high degree of surface rough-ess, although they may produce less abrasive wear debris (Verdoschot ad Huiskes 1998). These pheomea were ot icluded i the curret calculatios.
I the models with a udersized stem ad maximal cortical cemet matle support, we assumed that all trabecular boe was filled with boe cemet. As a result of the lack of fatigue data o iterdigitated cemet, this iterdigitated regio was represeted i the FEA model by material properties of boe cemet, although its stregth may be lower tha that of pure boe cemet (Race et al. 2003). Thus, our FEA model possibly over-predicted the mechaical properties of the cemet surroudig the udersized stems i the case of maximal cortical boe support.
Based o the excellet survival rates (Malchau et al. 2002), oe would expect that a thick, itact cemet matle would be more advatageous tha a cemet matle with defects. I cotrast, our data idicate that a caal-fillig stem performs better tha a udersized implat. This may be explaied by the fact that whe usig a larger implat, the loads applied to the implat are trasferred over a larger stem-cemet iterface, reducig cemet stresses ad fatigue crack formatio. I additio, direct load trasfer from implat to femoral boe may reduce the cemet stresses further. This suggests that decreasig the stem size to achieve a thicker cemet matle may ot always pay, at least ot from a mechaical poit of view. As such, our results give a possible explaatio for the good results obtaied by surgeos adherig to the lie-to-lie implatatio techique.
Biological factors such as postoperative boe remodelig ad particle-iduced osteolysis were ot take ito accout i our simulatios. For example, periprosthetic boe resorptio may be more proouced i recostructios with caal-fillig implats, thereby affectig the mechaical behavior. Furthermore, the larger umber of cemet matle defects aroud caal-fillig stems ) may be detrimetal i vivo, because they allow easier access of cemet ad polyeth-ylee debris particles to the boe-cemet iterface, iducig osteolysis (Maloey et al. 1990). Hece, from this perspective, udersized stems would be beeficial. O the other had, udersized stems caused full-thickess cemet matle cracks to occur earlier, thereby also creatig early pathways for particles to reach the surroudig boe. Noetheless, biological processes that play a role i vivo may provide a additioal explaatio for why udersized stems are so successful, while i this study they were iferior to caal-fillig stems.
Our data idicate that trabecular boe support results i a mechaically iferior cemet matle. These data are cosis-tet with those of , who reported that trabecular boe support elevates the stresses i the cemet matle. This emphasizes the importace of the use of pressure lavage ad adequate cemet pressurizatio i order to achieve maximal cemet peetratio ito cacellous boe, if possible up to the stiff ier cortex.
I coclusio, our data suggest that (1) udersized stems surrouded by a thick, itact cemet matle produce more cemet fatigue cracks tha caal-fillig stems surrouded by a thi cemet matle, (2) large caal-fillig stems rotate less tha udersized stems, ad (3) a cemet matle supported by trabecular boe produces more cemet cracks ad implat rotatio tha a cemet matle supported by cortical boe.