The determination of biomechanical force systems of implanted femurs to obtain adequate strain measurements has been neglected in many published studies. Due to geometric alterations induced by surgery and those inherent to the design of the prosthesis, the loading system changes because the lever arms are modified. This paper discusses the determination of adequate loading of the implanted femur based on the intact femur-loading configuration. Four reconstructions with Lubinus SPII, Charnley Roundback, Müller Straight and Stanmore prostheses were used in the study. Pseudophysiologic and nonphysiologic implanted system forces were generated and assessed with finite element analysis. Using an equilibrium system of forces composed by the Fx (medially direction) component of the hip contact force and the bending moments Mx (median plane) and My (coronal plane) allowed adequate, pseudo-physiological loading of the implanted femur. We suggest that at least the bending moment at the coronal plane must be restored in the implanted femur-loading configuration.

Introduction

Finite element analysis (FEA) is a powerful tool and even though the use of it has been criticized because of the lack of validation, it is the only way forward to explore “possible” solutions, even if quantitative results cannot be obtained due to the missing of biological information (1 2). Besides other merits, finite element models can be used to distinguish and predict the performance of implants.

FE analyses depend on simulation parameters like tissue geometry replication, material properties, boundary conditions (loading and fixation), and finite element selection. Musculoskeletal tissues have irregular geometry and so finite element modeling is increasingly carried out using digitized images generated from computer tomography scanning (1). Bone materials are normally assumed to be isotropic and homogeneous medias, whereas it is known that they are highly anisotropic and inhomogeneous, in particular cancellous bone (see, e.g., (3)). Time-dependent mechanical properties of tissues are also seen as critical to the improvement of biomechanical models (1,4). Loading and fixation conditions are relevant input data that can strongly influence results (5,6). Loads applied to finite element models have been strongly simplified and many papers report all sorts of loading configurations, namely, in total hip and knee replacements (see e.g., (7,8)) and seem to be a strong limitation on the quantitative accuracy of finite element results. Some researchers have focused on the development of improved geometric precision, whereas others have focused on improved representations of material behavior (1).

There are other factors intrinsically related to the FEA itself. The finite element mesh is a key factor for an efficient analysis and much research has been done on meshing and element performance (see, e.g., (9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)). Finite element models must be sufficiently refined to accurately represent the geometry and mechanical behavior of the bone structure (17,19). The results of these models are mesh sensitive and convergence tests must be made to test the model accuracy (16). Convergence tests can be done comparing nodal displacements and/or total strain energy (18,19), or stresses and strains (19).

The biomechanics of the hip is an extremely complex system and the correct knowledge of the functioning of muscles, ligaments, and the hip contact force (HCF) is unknown. Many authors have studied this problem using numerical and experimental models (8,24,25,26,27). Simulation of physiological loading of the hip is of considerable importance to improve prostheses design, bone remodeling simulations and mechanical testing of implants (27).

Other aspect of loading of the implanted femur is related to the change of forces (magnitude and direction) of the hip when a replacement is performed. The HCF and muscle forces are modified due to geometric alterations, as for example, changes of the position of the head or of the great trochanter provoked by surgery. The prosthesis does not exactly restore the original head center and lever arms are different. Although the effect of a femoral head displacement is important from a surgical point of view (28), this variable must be controlled when numerical or experimental studies are performed and since the head location cannot be restored exactly, it is necessary to analyze how it can be misleading in assessing the performance of different designs (28,29 30).

The intact femur undergoes a system of loads and moments that cannot be transposed in simulations of the implanted femur. We remind that the femur is statically undetermined due to the joint, ligaments, and muscle forces. There is no perfect solution when one tries to replicate the three forces and three moments as in the intact femur with identical femora implanted with different stems. Following Cristofolini and Viceconti (5), there are two main options: one that applies the same force magnitude for the hip joint and the abducting force (same forces) and a different moment will be applied due to the changed lever arms; and one that applies the same bending moment to the femur and different force values are required. In this case, the magnitude, direction, and position of the resultant vector force must stay constant with respect to the femoral diaphysis (5).

There seems to be no agreement in the literature on the preferred solution (31). However, Cristofolini and Viceconti (5) refer that to compensate for the unavoidable geometry changes, the implanted femur should be loaded in such a way as to apply the same bending moment, rather than the same forces as in the intact femur. If this is not done, errors can be expected in the strain measurement that possibly overshadow existing differences between implants, or give the impression that the difference exists when, in fact, the variations observed depend merely on the loading setup (5). In several cases in the literature, large strain differences are found below the stem tip in the implanted femur in comparison to the intact femur (32,33 34).

A detailed numerical study was performed to determine how load configurations of the implanted femur can undermine the reliability of strain measurements. Based on the intact femur loading configurations of walking during gait, implanted femora with Lubinus SPII, Charnley Roundback, Müller Straight, and Stanmore loading configurations were analyzed. A set of plausible combinations of forces with bending and torsion moments was simulated and analyzed. The difference of strain in all aspects of the intact and the implanted femur was compared to select the suitable loading configuration(s) for each of the prostheses assessed in this study.

Materials and Methods

The assessment of different types of cemented hip arthroplasties was made through finite element analysis. Three-dimensional (3D) computer aided design (CAD) models representing cemented hip joint reconstructions with Charnley Roundback, Lubinus SPII, Stanmore, and Müller Straight (Fig. 1) prostheses were used. For this purpose, in vitro femoral replacements were performed on synthetic composite femurs (third generation, left, mod. 3306, Pacific Research Labs, Vashon Island, WA) by a surgeon that followed strictly the surgical protocol of each one of the prostheses. The replacements provoked offsets ranging from 28.25mm (Charnley Roundback) to 35.48mm (Stanmore). The large left composite femur (mod. 3306, Pacific Research Labs, Vashon Island, WA) was used as reference geometry for the finite element analysis (35). It is a 3D solid model made available in public domain derived from computer tomography (CT)-scan dataset of the composite femur. The CAD models of the prostheses were obtained by reverse engineering. The geometry of the cement mantle and position of the stem in the femur were determined from CT scans of the reconstructions.

Figure 1
CAD models of Charnley Roundback, Lubinus SPII, Stanmore and Müller Straight cemented prostheses
Figure 1
CAD models of Charnley Roundback, Lubinus SPII, Stanmore and Müller Straight cemented prostheses
Close modal

The numerical simulations were preformed with Hyperworks® 5.1 (Altair Engineering, Inc., Troy, MI) finite element analysis software, using pre- and post-processor HYPERMESH® 5.1 and solver HYPERSTRUCT® 5.1, respectively. Four-node linear tetrahedral elements were selected to generate the numerical models. In Table 1 the number of nodes and elements for the implanted femurs are identified. Convergence tests of the finite element meshes were previously performed and the models refinement was sufficient enough to obtain accurate stress and strain predictions. The experimental models were validated successfully by strain gauge measurements.

Table 1

Nodes elements of the FEA models

ModelLubinus SPIICharnley RoundbackMüller StraightStanmore
Cortical bone38002167051380871660234132818162536291157684
Cancellous bone1645268996168877433419145824131907080483
Cement mantle2647610562123281966122656210937525147105868
Prosthesis1902482821125995393316831732791407260572
ModelLubinus SPIICharnley RoundbackMüller StraightStanmore
Cortical bone38002167051380871660234132818162536291157684
Cancellous bone1645268996168877433419145824131907080483
Cement mantle2647610562123281966122656210937525147105868
Prosthesis1902482821125995393316831732791407260572

The cortical and cancellous bone replicating materials, femoral component and cement mantle were assumed to be isotropic and linearly elastic. The elastic properties of all materials of the reconstructions are presented in Table 2. The loading configuration used in the study represents the one around the hip during the most strenuous phase of the walking cycle (Table 3) (36). The loading comprises the hip contact force (HCF), the glutei, the tensor fasciae latae, and the vastus lateralis (Fig. 2) and was proposed by Bergmann et al. (37,38) and Heller et al. (39) for mechanical testing of hip replacement reconstructions (36).

Table 2

Mechanical properties of the finite element models

Part of modelMaterial typeElastic modulus (GPa)Poisson’s ratio
Cortical boneGlass-fiber reinforced epoxy14.20.28
Cancellous bonePolyurethane foam0.2800.3
CementPolymethylmethacrylate3.00.3
StemCoCr alloy2100.3
Part of modelMaterial typeElastic modulus (GPa)Poisson’s ratio
Cortical boneGlass-fiber reinforced epoxy14.20.28
Cancellous bonePolyurethane foam0.2800.3
CementPolymethylmethacrylate3.00.3
StemCoCr alloy2100.3
Table 3

Representation of the hip joint and muscle force magnitudes during walking

Vector forces (N)X mediallyY anteriorlyZ proximally
Hip force contact (HCF)4052461719
Abductors (glutei)43532649
Tensor fasciae latae (proximal part)548799
Tensor fasciae latae (distal part)45,3143
Vastus Lateralis7139697
Vector forces (N)X mediallyY anteriorlyZ proximally
Hip force contact (HCF)4052461719
Abductors (glutei)43532649
Tensor fasciae latae (proximal part)548799
Tensor fasciae latae (distal part)45,3143
Vastus Lateralis7139697
Figure 2
CAD model of the intact femur; moments and forces transmitted (Mz-horizontal plane; My-coronal plane, and Mx-median plane) due to loading; x (medially), y (anteriorly), and z (proximally)
Figure 2
CAD model of the intact femur; moments and forces transmitted (Mz-horizontal plane; My-coronal plane, and Mx-median plane) due to loading; x (medially), y (anteriorly), and z (proximally)
Close modal

One possible way to determine the implanted femur loading system is to compare the strain measured below the femoral stem tip before and after implantation. Theoretically, these values must be identical because they belong to an area far from the influence of the implant (5). To determine the changed biomechanical forces of the implanted femur, the moments and forces transmitted through the intact femur must be determined. The moments and forces, at a region of the cortex of the intact femur, far enough from the tip of the prosthesis and from the region of the fixed condyles can be compared with those of the implanted femur. To generate tentative loading configurations for the different hip replacements, intact and implanted femur strains were compared in a region of the diaphysis of the femur out of influence of the stem. To obtain the implanted HC and abductors forces, two situations were analyzed:

  • Equilibrium of forces and moments considering the implanted HC vector force (direction and magnitude) variable;

  • Equilibrium of forces and moments considering the implanted HC and abductors vector forces variable, but the direction of the abductor force was kept unchanged.

The magnitudes and directions of the distal and proximal tensor fasciae latae and the vastus lateralis were kept unchanged.

Considering the equilibrium forces for the intact femur, the following equations can be setup (Figs. 2,3):
Fxint_femur=ABDx+HCFxFyint_femur=ABDy+HCFyFzint_femur=ABDz+HCFzMxint_femur=HCFyaHCFze+ABDydMyint_femur=HCFxaHCFzbABDxd+ABDzcMzint_femur=HCFybABDyc
1
If the abductor force direction is considered unchanged:
ABDy=αABDzABDx=βABDz
2
where k1 and k2 are constants. For the abductors direction force considered, k1=1.490 and k2=0.0741. Figure 3 shows the geometric dimensions (Table 4) used to derive the force systems of the reconstructed femurs. Dimensions c and d (distances from the glutei insertion point) were kept constant. The system of Eqs. 1 allows 35 possible combinations, where 27 have solutions and 8 have indeterminate solutions. All solutions were analyzed, but only the first nine load cases (Table 5) are discussed in this paper that includes physiological and non-physiological load configuration systems.
Table 4

Geometric dimensions of intact and implanted femurs

abcde
Intact femur23044252050
Charnley Roundback227.1628.25252050.50
Lubinus SPII223.5533.37252051.51
Stanmore230.4835.48252050.61
Muller Straight221.8332.79252054.71
abcde
Intact femur23044252050
Charnley Roundback227.1628.25252050.50
Lubinus SPII223.5533.37252051.51
Stanmore230.4835.48252050.61
Muller Straight221.8332.79252054.71
Table 5

Moments and forces considered in the tentative load cases studied

FxFyFzMxMyMz
Case_0Intact hip force system
Case_11XXX
Case_21XXX
Case_31XXX
Case_41XXX
Case_5XXXX
Case_6XXXX
Case_7XXXX
Case_8XXXX
Case_9XXXX
Case_10XXX
Case_11XXX
Case_12XXX
Case_13XXX
Case_14XXX
Case_15XXX
Case_16XXX
Case_17XXX
Case_18XXX
Case_19XXXX
Case_20XXXX
Case_21XXXX
Case_22XXXX
Case_23XXXX
Case_24XXXX
Case_25XXXX
Case_26XXXX
Case_27XXXX
FxFyFzMxMyMz
Case_0Intact hip force system
Case_11XXX
Case_21XXX
Case_31XXX
Case_41XXX
Case_5XXXX
Case_6XXXX
Case_7XXXX
Case_8XXXX
Case_9XXXX
Case_10XXX
Case_11XXX
Case_12XXX
Case_13XXX
Case_14XXX
Case_15XXX
Case_16XXX
Case_17XXX
Case_18XXX
Case_19XXXX
Case_20XXXX
Case_21XXXX
Case_22XXXX
Case_23XXXX
Case_24XXXX
Case_25XXXX
Case_26XXXX
Case_27XXXX

Abductors force magnitude and direction unchanged.

Figure 3
Geometric and dimensional variables of the implanted femur
Figure 3
Geometric and dimensional variables of the implanted femur
Close modal

For load Case_1, load Case_2, load Case_3, and load Case_4 the HCF was allowed to change in magnitude and direction and the other muscle forces were kept unchangeable. For the other cases studied, the HCF and the abductors force was allowed to change in magnitude, maintaining the direction of the abductors force unchangeable. Table 6 contains the HCF and abductor forces derived using Eqs. 1,2 for the four hip reconstructions analyzed and for the load cases selected for discussion. These load cases were simulated and strains compared with those obtained for the intact femur. Table 7 contains all the other (18) possible load configurations.

Table 6

HC and abductors force components used in the simulations of reconstructed femurs (first nine load cases of Table 5)

Lubinus SPIICharnley RoundbackMüller StraightStanmore
Force (N)Med.Ant.Prox.Med.Ant.Prox.Med.Ant.Prox.Med.Ant.Prox.
HFC4052461719405246171940524617194052461719
Case_0ABD43532649435326494353264943532649
HFC2913831719137349171911732817191423551719
Case_1ABD43532649435326494353264943532649
HFC4053832637405349534740532851084053555420
Case_2ABD43532649435326494353264943532649
HFC2912531719335265171934125017193332921719
Case_3ABD43532649435326494353264943532649
HFC4052552637405268218840525121374053022206
Case_4ABD43532649435326494353264943532649
HFC8582802394634263206063426320616352632062
Case_5ABD888661324664499906644999166549992
HFC1492320315012892842808918282239119012633500
Case_6ABD13941032080116687173888666132116301212430
HFC1461324207128514401697228819495362614887
Case_7ABD1491111222328212094207100274149453924008042
HFC2465375430929225130415583163136633192622
Case_8ABD21721613239157122341385103206630122449
HFC1365320315011362842808856282239116002633500
Case_9ABD13941032080116687173888666132116301212430
Lubinus SPIICharnley RoundbackMüller StraightStanmore
Force (N)Med.Ant.Prox.Med.Ant.Prox.Med.Ant.Prox.Med.Ant.Prox.
HFC4052461719405246171940524617194052461719
Case_0ABD43532649435326494353264943532649
HFC2913831719137349171911732817191423551719
Case_1ABD43532649435326494353264943532649
HFC4053832637405349534740532851084053555420
Case_2ABD43532649435326494353264943532649
HFC2912531719335265171934125017193332921719
Case_3ABD43532649435326494353264943532649
HFC4052552637405268218840525121374053022206
Case_4ABD43532649435326494353264943532649
HFC8582802394634263206063426320616352632062
Case_5ABD888661324664499906644999166549992
HFC1492320315012892842808918282239119012633500
Case_6ABD13941032080116687173888666132116301212430
HFC1461324207128514401697228819495362614887
Case_7ABD1491111222328212094207100274149453924008042
HFC2465375430929225130415583163136633192622
Case_8ABD21721613239157122341385103206630122449
HFC1365320315011362842808856282239116002633500
Case_9ABD13941032080116687173888666132116301212430
Table 7

The other HC and abductors force components of reconstructed femurs

Lubinus SPIICharnley RoundbackMüller StraightStanmore
Force (N)Med.Ant.Prox.Med.Ant.Prox.Med.Ant.Prox.Med.Ant.Prox.
HFC4052461719405246171940524617194052461719
Case_10ABD43532649435326494353264943532649
HFC40524613974052461051405246194405246427
Case_11ABD43532649435326494353264943532649
HFC4052461489724052464836040524612431240524615356
Case_12ABD43532649435326494353264943532649
HFC4052531719405241171940525017194052191719
Case_13ABD43532649435326494353264943532649
HFC4053831719405324171940530517194053301719
Case_14ABD43532649435326494353264943532649
HFC812461719672461719812461719422461719
Case_15ABD43532649435326494353264943532649
HFC4053836091340532410551405305225144053303534
Case_16ABD43532649435326494353264943532649
HFC7424613977124610517724619470246427
Case_17ABD43532649435326494353264943532649
HFC2113836091315032410551136305225141543303534
Case_18ABD43532649435326494353264943532649
HFC21423754309127225130413553163136331191622
Case_19ABD21721613239157122341385103206630122449
HFC1386319318310092912620872281241610492942679
Case_20ABD1416105211210397715509026713461079801609
HFC488957813336411552123285934656173163830500481
Case_21ABD49193657336414530761825964442889538602865757
HFC13863191827100929150087228116411049294256
Case_22ABD1416105211210397715509026713461079801609
HFC1386319119285100929140863872281115266104929412561
Case_23ABD1416105211210397715509026713461079801609
HFC5044578863849935078561628766110491639343910650
Case_24ABD50743767568502337274916317468942164234769580
HFC11313223183716276262057428324167252422679
Case_25ABD1416105211210397715509026713461079801609
HFC253557623789560246811281263618515202172724176248559
Case_26ABD250518637355994444893935882665352721153510754
HFC112831918277302915005722811641111294256
Case_27ABD1416105211210397715509026713461079801609
Lubinus SPIICharnley RoundbackMüller StraightStanmore
Force (N)Med.Ant.Prox.Med.Ant.Prox.Med.Ant.Prox.Med.Ant.Prox.
HFC4052461719405246171940524617194052461719
Case_10ABD43532649435326494353264943532649
HFC40524613974052461051405246194405246427
Case_11ABD43532649435326494353264943532649
HFC4052461489724052464836040524612431240524615356
Case_12ABD43532649435326494353264943532649
HFC4052531719405241171940525017194052191719
Case_13ABD43532649435326494353264943532649
HFC4053831719405324171940530517194053301719
Case_14ABD43532649435326494353264943532649
HFC812461719672461719812461719422461719
Case_15ABD43532649435326494353264943532649
HFC4053836091340532410551405305225144053303534
Case_16ABD43532649435326494353264943532649
HFC7424613977124610517724619470246427
Case_17ABD43532649435326494353264943532649
HFC2113836091315032410551136305225141543303534
Case_18ABD43532649435326494353264943532649
HFC21423754309127225130413553163136331191622
Case_19ABD21721613239157122341385103206630122449
HFC1386319318310092912620872281241610492942679
Case_20ABD1416105211210397715509026713461079801609
HFC488957813336411552123285934656173163830500481
Case_21ABD49193657336414530761825964442889538602865757
HFC13863191827100929150087228116411049294256
Case_22ABD1416105211210397715509026713461079801609
HFC1386319119285100929140863872281115266104929412561
Case_23ABD1416105211210397715509026713461079801609
HFC5044578863849935078561628766110491639343910650
Case_24ABD50743767568502337274916317468942164234769580
HFC11313223183716276262057428324167252422679
Case_25ABD1416105211210397715509026713461079801609
HFC253557623789560246811281263618515202172724176248559
Case_26ABD250518637355994444893935882665352721153510754
HFC112831918277302915005722811641111294256
Case_27ABD1416105211210397715509026713461079801609
An equivalent strain value that takes into account the strain values at the medial, lateral, anterior, and posterior aspects of the femur was obtained using the following equation:
Δε=(ϵMintϵMimp)2+(ϵLintϵLimp)2+(ϵAintϵAimp)2+(ϵPintϵPimp)24
3
being eM, eL, eA, and eP the strain at the medial, lateral, anterior, and posterior aspects of the intact (int) and implanted (imp) femur. This root-mean-squared strain value approximates in excess the difference between the intact and implanted strains.

The intact femur load system was used for the implanted configurations and is referred as load Case_0. The other load cases were simulated to illustrate the relevance of the vector components of the HCF on the bending (all load configurations) and torsional moments (Case_1, Case_2, Case_6, and Case_9). Some of the load cases were simulated to show that although the force system is in equilibrium, they can provoke non-physiological load configurations (e.g., Case_7 for the Charnley Roundback and Stanmore prostheses and Case_8 for all designs). The strains were compared in the x, y, and z directions. The most suitable loading configuration of the implanted femur will be the one that minimizes the difference in strains (intact femur strain minus implanted femur strain).

Results and Discussion

Considering the HC and abductors forces derived from Eqs. 1,2 and although the system forces is in equilibrium, loading configurations for which the sense of the force is opposite to the physiological one can be obtained (for Case_7 and Stanmore prosthesis we can observe that the sense of the HCF is toward proximal, whereas physiologically it is toward distal) and the intensity is significantly different than what is observed in vivo (e.g., Case_2,Case_6, and Case_9 provoke very high intensity forces and Case_7 and Case_8 provoke very low intensity forces). Other load cases show considerable high or low force magnitudes that are unlikely to occur in vivo. Interesting to note that independently on the prosthesis design, the z component of the HCF is considerable higher for all implanted configurations. The z component of the HCF of the implanted reconstruction for load Case_4, relatively to the intact femur, is higher in an excess of 918, 469, 418, and 487N for the Lubinus SPII, Charnley Roundback, Müller Straight, and Stanmore prostheses, respectively.

For the load cases presented in Table 6, the strain values in the x, y, and z directions were picked at a distance of 20mm down from the tip of the longest stem (Lubinus SPII). This region of the femur is out of the influence of the stem, which was confirmed numerically with finite element models and with uniaxial strain gauges glued to composite replica femurs. The absolute difference (Dez=ezintactezimplanted) between strains generated by the intact and implanted femurs are presented in Table 8. Table 9 presents the mean-squared strain difference for the tentative solutions analyzed.

Table 8

Absolute difference between strains generated by the intact and implanted femurs (all tentative load configurations)

Strain (με)Lubinus SPIIChamleyMüller StraightStanmore
MedPostAntLatMedPostAntLatMedPostAntLatMedPostAntLat
εx1616252116923739751024423491296170
Case_0εy15364512689442877824422541092382
εz52421016838930113810724231514998180405194247
εx6511511524444851234554271111142667387115176481
Case_1εy4511510527469681084554834798490443120151451
εz19237835992152826338115511498185342164113743931641573
εx2418012229633406207423600314196503538524332445
Case_2εy117611534681378200438683300158503626518309423
εz5158515139021801317181237172105103753116551905168610601455
εx4556301224437236411020544227910
Case_3εy30523281851295124114143338195
εz12718411596416210628913466491491397319
ϵx31220436296147120321118
Case_4εy151119149152071386158297
εz1447582039777142438517453810
εx327545141738333274815295411611
Case_5εy167047810462542482125264141
εz842451675844146932359159878214424423
εx2081502826052232148143721552945
Case_6εy27752248694429747203617503557
εz40267185107822315996341578411025187118163
εx72174653648992741
Case_7εy60163713524973439
εz218564245139129325130124
εx01016648382729273561955
Case_8εy209568483635203328532660
εz29333241183120106779326182104177
εx1128533160151633718145495105274644360
Case_9εy1367944158165733618575.549171013265614359
εz40827115455652923212262618716168334986405421204
Strain (με)Lubinus SPIIChamleyMüller StraightStanmore
MedPostAntLatMedPostAntLatMedPostAntLatMedPostAntLat
εx1616252116923739751024423491296170
Case_0εy15364512689442877824422541092382
εz52421016838930113810724231514998180405194247
εx6511511524444851234554271111142667387115176481
Case_1εy4511510527469681084554834798490443120151451
εz19237835992152826338115511498185342164113743931641573
εx2418012229633406207423600314196503538524332445
Case_2εy117611534681378200438683300158503626518309423
εz5158515139021801317181237172105103753116551905168610601455
εx4556301224437236411020544227910
Case_3εy30523281851295124114143338195
εz12718411596416210628913466491491397319
ϵx31220436296147120321118
Case_4εy151119149152071386158297
εz1447582039777142438517453810
εx327545141738333274815295411611
Case_5εy167047810462542482125264141
εz842451675844146932359159878214424423
εx2081502826052232148143721552945
Case_6εy27752248694429747203617503557
εz40267185107822315996341578411025187118163
εx72174653648992741
Case_7εy60163713524973439
εz218564245139129325130124
εx01016648382729273561955
Case_8εy209568483635203328532660
εz29333241183120106779326182104177
εx1128533160151633718145495105274644360
Case_9εy1367944158165733618575.549171013265614359
εz40827115455652923212262618716168334986405421204
Table 9

Root-mean-squared strain difference (all tentative load configurations)

Load CaseLubinus SPIICharnley Round.Müller StraightStanmore
Case_0279171189159
Case_1226886981993
Case_2499163012541174
Case_3998212371
Case_431363328
Case_5123716082
Case_613511511085
Case_726510011411156
Case_8177811221111
Case_9300342637170
Load CaseLubinus SPIICharnley Round.Müller StraightStanmore
Case_0279171189159
Case_1226886981993
Case_2499163012541174
Case_3998212371
Case_431363328
Case_5123716082
Case_613511511085
Case_726510011411156
Case_8177811221111
Case_9300342637170

Ideally, the most adequate implanted femur-loading configuration should provoke the same strain magnitudes as the ones provoked by the intact femur. However, this is not possible, unless extra forces are added to the loading system. Therefore, the suitable loading configuration is the one that minimizes the differences in strains in all aspects of the femur. Due to the higher magnitudes of strains in the axial direction of the femur (z direction) at the lateral and medial aspects of the femur, the εz component of the strain seems to be an adequate parameter to select the suitable loading configuration for each of the hip replacements assessed.

Figure 4a shows the strain (εz) distribution at the medial aspect of the femur considering all the reconstructions loaded with the loading configuration of the intact femur (Case_0), which does not take into account the correction of the load system. Figure 4b illustrates identical results but with the loading configuration corrected (Case_4). The comparison of these two figures show that it can be misleading in assessing the performance of different designs if the implanted loading system is not derived adequately. Figure 4b also shows the strain shielding effect, which does not depend on the stem geometry since very similar strain magnitudes were observed for all designs.

Figure 4
Strain distribution at the medial aspect of the implanted femur: (a) intact femur load system; (b) implanted femur load (Case_4) system
Figure 4
Strain distribution at the medial aspect of the implanted femur: (a) intact femur load system; (b) implanted femur load (Case_4) system
Close modal

For the hip replacements simulated with loading configuration of the intact femur simulated, the Lubinus SPII provoked the highest strain differences in all aspects of the femur; the Charnley Roundback and Müller Straight provoked very similar differences and the Stanmore provoked differences of strains higher at the proximal portion of the femur. The results presented in Fig. 4 clearly show that it is not correct to use the same loading configuration for the intact and implanted femurs. Apparently, and observing Fig. 4a we are forced to conclude that the Lubinus SPII prosthesis provokes higher strain shielding, when in fact this does not really occur. Figure 4b shows that strain shielding is very similar for all prostheses if the loading configuration is corrected. Since the head location of the prosthesis cannot be restored, the lever arms change and also the force system and if this difference is not considered, errors can be expected in the strain measurements as evidenced in Fig. 4a. It is necessary to determine how the consequences of this unavoidable source of error can be minimized (5). Many authors have realized numerical and experimental studies using the same force system for the intact and implanted femurs (40,41,42,43,44,45,46,47 48).

Load Case_4, that considers the force Fx and moments Mx and My (with the abductor force direction kept unchanged), was of all loading configurations simulated the one that provoked the lowest strain deviations either using the absolute strain difference (Table 7) or the root-mean-squared strain (Table 8) parameter. Other loading configurations, like load Case_1 and load Case_2, provoked significant differences in strains and seem to be nonsuitable implantable load configurations. It is interesting to note that the load cases that provoke the lowest strain differences all include the bending moment My, reinforcing that this bending moment at the coronal plane must be restored in simulations of implanted hip reconstructions. This moment plays a key role because it is obtained using the highest vector force magnitudes and lever arms.

Cristofolini and Viceconti (5) suggest that to compensate for the unavoidable geometry changes, the implanted femur should be loaded in such a way as to apply the same bending moment as in the intact femur. In fact, the strain deviations for load cases that included the two bending moments (Case_3, Case_4, Case_6, Case_7, and Case_8) were significantly lower. Load Case_5 that includes all forces (Fx, Fy, and Fz) and the My moment allowed relatively lower strain deviations, partially due to the influence of this bending moment (My). Overall, the load cases considering the torsional moment (Mz) (Case_1, Case_2, and Case_9) provoked very high strain deviations and it is therefore questionable the relevance of replicating this moment in the implanted femur system force, although it plays an important key role in the fixation of prostheses. It must be said that the load transfer mechanism between the intact and implanted femur is inherently different and the bending moments are reflected more pronouncedly in the strain pattern, while the torsional moment is more deleterious at the bone-prosthesis interface.

Figure 5 shows the highest strain error committed if the load system of the intact femur is used in implanted femur simulations. Depending on the type of geometry, some designs provoke higher errors than others. The highest errors were observed at the medial aspect of the femur and for the Lubinus SPII stem. Errors were smaller at the anterior and posterior aspects of the femur. We can also observe that the Lubinus SP II stem provoked the highest error differences which seem too be related to its anatomical geometry. All other stems provoked similar strain differences.

Figure 5
Maximum strain error measurement (intact femur strain minus implanted femur strain for load Case_4)
Figure 5
Maximum strain error measurement (intact femur strain minus implanted femur strain for load Case_4)
Close modal

The study showed that it is important to derive correctly the implanted femur-loading configuration, especially if different designs are being compared. For a certain design, including bending in the coronal plane can be sufficient; for others probably not. It is necessary to understand which the most critical load component is and try to restore the constant conditions for that one, having in mind that for others the deviations are less relevant. The adequate determination of the load configuration for implanted femurs has not been realized in many studies published (40,41,42,43,44,45,46,47 48).

Concluding Remarks

The study performed aimed to derive adequate loading configurations for implanted femurs with different hip femoral components. If so is not done, errors can be expected in the strain distributions that possibly hide differences between different femoral designs. For the designs analyzed, adequate implanted system forces were generated using for the equilibrium system the Fx (medially direction) of the HCF and the bending moments (Mx and My) provoked by the HCF and abductors forces. We suggest that at least the bending moment at the coronal plane must be restored in the implanted femur-loading configuration.

Acknowledgment

The authors gratefully acknowledge Fundação para a Ciência e a Tecnologia do Ministério da Ciência e do Ensino Superior for funding António Ramos with Grant No. SFRH/BD/63217/2002. Part of the work was supported by Project No. POCTI/EME/38367/2001 and No. POCTI/EME/44644/2002.

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