Effects of mechanical testing device variables on polymer composite femoral stem strains

Biomafericds

PI1

ELSEVIER

SO142-9612(96)00070-l

17 [1996)

2211-2217

Elsevier Science Limited Printed in Great Britain, All rights reserved 014%9612/96/$15.00 0

1996

Effects of mechanical testing device variables on polymer composite femoral stem strains Anneliese D. Heiner, Stanley A. Brown* and Dwight T. Davy+ Departments of Biomedical fngineering University. Cleveland. Off 44106, USA

and tMechanical and Aerospace Engineermg, Case Western Reserve

Polymer composite femoral stems do not have a well-established in vitro mechanical testing method. The objective of this study was to examine mechanical testing devices for pressfit composite stems, using finite element analysis. The goals were to examine the effects of testing device design variables (geometry, material, interface friction, embedding height and applied load angle) and to reproduce the maximum strains of the stem implanted in a femur. The stem strains were affected by design changes to the testing device. The maximum normal and interlaminar shear strains of the composite stem in the femur were not as well reproduced by the testing device as were the maximum in-plane tensile strains. Decreasing the embedding height increased the stem strains and shifted the stem failure location from the neck to the embedding height. Testing a femoral stem using a testing device with a low embedding height may be inappropriate when trying to induce neck failure, since failure may occur at the embedding height instead of in the neck. A single-material teshng device of birchwood, an orthotropic material with a longitudinal stiffness in the range of bone, best simulated a femur in this study. 0 1996 Elsevier Science Limited. Keywords: Femoral stem, finite element analysis, mechanical

testing method, polymer

composite

Received 5 September 1995; accepted 9 April 1996

bone’l. Because of this, a mechanical testing method for femoral stems designed to prevent proximal such as composite stems, should be resorption, different from a mechanical testing method for femoral stems which result in proximal resorption. Testing configurations, in which the femoral stem is supported up to its neck, model the case when no proximal resorption of the femur occurs (Figure lb). This testing configuration is found in the literature7*‘0-17 and in an international standard”. However, because composite stems are so new, there is no large collection of in viva failed stems with which to compare stems that have been failed using this testing configuration. Additionally, details such as geometry and dimensions of the configuration have not been standardized. In the field of total hip replacement, finite element analysis has been used to corn are different femoral stem geometries*g*20, materials’ f ‘21-23, interfaces with the bonez4sz5 and load angles’“, and has shown that these variables affect the stress state on the stem and the surrounding bone. There are only a few finite element models of mechanical testing devices for femoral stems13’ I67“; however, it has been recognized that variables of the testing device may affect the stem stresses’. The objective of this study was to investigate the design of a mechanical testing method for a pressfit

Metallic femoral sterns, which exhibit high rigidity, or stems which are cemented into the femur can cause stress shielding and proximal resorption of the femur. This proximal resorption is modelled during mechanical testing by fixating only the distal part of the stem (Figure la)., and loading the top of the stem. This is the most commonly used mechanical testing configuration for femoral stems; it is found in nationalle3 and international43 5 standards, and in the literature”-lo. For metallic stems, this testing configuration produces failures that are similar to in viva failuresg. Polymer composite femoral stems, with their decreased stiffness, should reduce or prevent proximal resorption, as should stems which are bonded to the proximal part of the femur. Even if some proximal resorption did occur with a composite stem, the lower stiffness of the composite may allow the stem to displace far enough under load so that it would contact and be supported by the remaining proximal Correspondence to Dr A. D. Heiner, presently at University of Miami School of Medicine, Department of Orthopaedics and Rehahi&ation (R-21, P.U. Box 016960, Miami, FL 33101, USA. *S.A. Brown presently

at FDAICDRH,

and Materials Science., 12200 Wilkins 20852,

Division of Mechanics Ave. Rockville, MD

USA.

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Biomaterials 1996, Vol. 17 No, 23

Effects

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of testing

device

Table 1

variables

Variations

on femoral

studied

rr Fixture outer radius (mm) Es Embedding compound modulus (GPa) Er Fixture modulus (GPa) p interface friction a Load angle (in-planeloutof-plane) h Embedding height’ (mm)

in testing

stems:

A.D. Heiner

et al.

devicea

45, 50, 55, 60 3, 5, 10, 20 3, 15.2b, 20, 70, 100, 200 0, 0.2, 0.4, 0.6, 1.2, 1.6, 2 16/12, 10/O, 1019, 0110 132, 129, 120, 113, 103,93,

63

aThe underlined variations were those used in the baseline model: except where indicated otherwise, when one parameter was varied, all other parameters remained the same as for the baseline model. bOrthotropic material. ‘Measured from stem midline.

LI

a

b

C

Figure 1 Finite element model of the composite stem in: a, testing device with the lowest embedding height (distal potting). This embedding he$$t is close to that specified, in b, baseline testing device the relevant IS0 standards (proximal potting, only half the testing device shown); c, human femur (only half the femur shown).

polymer composite femoral stem, using finite element analysis. The goals were to examine the effects of testing device variations on the stem strains, and to determine a mechanical testing device which came closest to reproducing the maximum stem strains on a finite element model of a composite stem implanted in a human femur.

MATERIALS

AND METHODS

Three-dimensional finite element models of a composite stem implanted in either a human femur or a testing device were constructed with quadratic elements. The models were analysed using the finite element package ABAQUS 5.2-1, on a SunfSPARC workstation. Large displacement analysis was used. The material for the femoral stem was a quasiisotropic carbon fibrelpolysulphone lay-up, with the plies in the frontal plane. This corresponded to an experimental stem constructed for this study (Hercules, Inc.). The finite element geometry of the composite stem was determined from a blueprint of the stem (Biomet, Inc.); the stem was symmetrical and straight (Figure 1). The models included interface elements between the stem and the femur or testing device. The applied load was distributed around the top edge of the stem. This load distribution modelled a ‘tip fit’ of the head, seen when the head bore angle is greater than the stem cone angle. The material properties and shape of the human femur were determined from a computerized The femur geometry was tomography (CT) scar?. simplified to consist of cylindrical and elliptical crosssections (Figure lc). The modulus of the cortical bone was 20GPa. The modulus of the cancellous bone varied between 18.33 GPa distally and 5GPa proximally. The coefficient of friction between the stem and the femur was 0.4’~. The baseline testing device was a cylindrical fixture Biomaterials

1996,

Vol. 17 No. 23

with an outer radius of 45 mm and an inner radius of 35 mm (Figure lb). The modulus of the fixture was 70GPa, to represent aluminium. The embedding compound between the fixture and the stem was bone cement, with a modulus of 3GPa. The coefficient of friction between the stem and the bone cement was 0.4. The applied load was 4671 N, which is six times a body weight of 778N (175lb). Parameters varied within the testing device model were fixture outer radius (rf), embedding compound modulus (Es), fixture modulus (Er), stem/embedding compound interface friction (p), applied load angle (a) and embedding height (h) (Table 1). The baseline outer fixture radius of 45 mm had an inner radius of 35mm; this resulted in a minimum embedding compound thickness of 10mm. This is the compound thickness minimum embedding recommended in ASTM F1440-92’. The fixture thickness was kept constant at 10 mm. Solid fixtures with elastic moduli of 3, 15.2, 20, 70, 100 and 200GPa represented testing devices made out of only delrin (or acrylic), birchwood, isoelastic material, aluminium, titanium and cobalt-chrome, respectively. There was no embedding compound. The birchwood was orthotropic instead of isotropic; its longitudinal modulus was 15.2 GPa, its radial modulus was 1.19GPa and its transverse modulus was 0.762 GPaz7. The transverse and radial directions were oriented in the anterior-posterior and medial-lateral directions, respectively; reversing these orientations had little effect on the results. The friction of the stem/ embedding compound or stem/bone interface is unknownz4~ ‘s. The baseline value of /J= 0.4 was a composite stem/bone interface friction used previously in finite element analysis of implanted composite stemsz6. The load angles were designated by their in-plane/ out-of-plane values. The baseline load angle, 16/12, represented a load angle seen during horizontal walking: 16.3” in-plane and 11.8” out-of-planez6. The other load angles were found in femoral stem testing standards and articles: 10/01s3s4, 1O/92'5and O/lO1’. The embedding height of 132mm represented full proximal support or proximal potting; the stem was supported up to its neck (Figure lb). The embedding height of 83 mm resulted in 81.8mm of the femoral stem being unsupported, as measured from the top centre of the stem (Figure 1 a). This embedding height was close to the unsupported femoral stem length of 80 mm, measured from the centre of the head, which is

Effects of testing device variables

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on femoral stems: A.D. Heiner et al.

specified in IS0 standards involving distal potting of femoral stems4’5. The other intermediate embedding heights represented different degrees of loosening or proximal resorption7,10. The finite element model results were compared on the basis of calculated strains, including the maximum tensile stem strains in the x, y and z directions (e,, en, and eZZ), averaged at the nodes. The x direction was anterior-posterior, the y direction was medial-lateral and the z direction was superior-inferior. The value was calculated as a measure of (ezXY+ ezXJ1” interlaminar shear strain (eil). These strains would lead to different failure modes within the composite. The composite plies were in the y-z plane, so the stem strains en, and eZZwould lead to tensile failure within the composite planes. Stem strains e,, and eil would lead to interlaminar failure, by normal tensile strain and shear strain, respectively. Maximum values of these strains were normalized to the maximum stem strains from the baseline testing device, and to the maximum stem strains from the femur.

l.l1.OQu) 1.06. .E E 1.07E 0 1.06ti .o 0 1.05 p g

1.04.

:

1.03-

i ‘Z l.OZg

l.Oll0.994

44

46

46

50 52 54 Fixture outer radius (mm)

56

56

1

2 Effects of fixture outer radius on maximum stem strains: W, eXX; +, eyy; 0, eZZ; A, err. Fixture inner radius was 1Omm less than the fixture outer radius. Strains were normalized to the baseline testing device values. Figure

RESULTS The maximum strains of the composite stem in the baseline testing device ranged from 1.83 x lop3 to 8.02 x 1O-3 (Table 2). Maximum stem eXXwas located just above the embedding height, maximum stem eW was located on the superior flat surface of the composite stem, maximum stem eZZwas located at the embedding height, a:nd maximum stem eil was located just below the embedding height. As the outer fixture radius increased to 60mm, only maximum stem eil changed noticeably, increasing to 106% of the baseline value (Figure 2). The node locations for the maximum stem strains were the same as those for the baseline testing device. As the embeddkng compound modulus (EE) increased, only maximum stem eZZ and eil showed much change; at the highest EE (ZOGPa), maximum stem eil increased to 124% of the baseline value and maximum stem e,, increased to 108% of the baseline value (Figure 3). The node locations for the maximum stem strains were the same as those for the baseline testing device. As the stem/embedding compound interface friction (p) increased, only maximum stem e,, and ql showed much change; at p := 2.0, they increased to 106 and 106% of the baseline values, respectively (Figure 4). Except for eit, the maximum stem strains started to level off at p > 0.8. The node location for maximum stem eil changed from that of the baseline testing device when p > 1.2. Maximum tensile baseline testing device

Table 2

strains

of composite

Strain (10m3) eXX

eyy

eZZ @la %terlaminar

1.827 5.273 1.962 8.019 shear strain = (a*, + ezxz)“*

stem

0.95

2

4

6 6 10 12 14 16 Embedding compound modulus (GPa)

16

20

Effects of embedding compound modulus on maximum stem strains: W, eXX; f, eyy; Cl, e,; A, err. Strains were normalized to the baseline testrng device values. Figure 3

in 0.97+ 0

I 0.2

0.4

0.6 0.6 1 1.2 1.4 1.6 Stem/embedding compound friction

1.6

I 2

Figure 4 Effects of stem/embedding compound interface friction on maximum stem strains: W, eXx; +, eyy; Cl, eZZ; A, eir. Strains were normalized to the baseline testing device values. The node location for maximum stem eir was different from that of the baseline tester when p > 1.2.

Biomaterials

1996, Vol. 17 No. 23

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0

80

Effects of testing device variables

90

110 120 100 Embedding height at stem midline (mm)

130

140

Figure 5 Effects of load angle on maximum stem erz. Load angles: n , 16/12; +, 10/O; 0, 10/9; A, 0110. Strains were normalized to the values for load angle 16/12 at the highest embedding height. At embedding heights < 120mm, the location of the maximum stem strain switched from the stem neck to the embedding height.

The load angle O/10 resulted in the highest maximum stem strains for most of the embedding heights and strains; results for maximum stem e,, are shown in Figure 5. The load angle 10/O resulted in the lowest maximum stem strains for most of the embedding heights and strains. As the embedding height decreased, the maximum stem strains increased, and the location of the maximum stem strain switched from the stem neck to the embedding height (Figure 6). The embedding height at which this location switch occurred varied with stem strain and load angle; maximum stem err, however, stayed in the stem neck for all embedding heights and load angles studied. The maximum strains in the neck portion of the composite stem were also examined, to determine how those strains changed with embedding height (Figure 7). The node locations were taken as those for the maximum strains at the highest embedding height. Maximum eil showed the most change; it increased by nearly 2.5 times between the highest and lowest embedding height. Maximum en, showed the least change; it increased 14% between the highest and lowest embedding height. Maximum eXX decreased at the lowest embedding height, after staying fairly constant for the other embedding heights. As the fixture modulus (I$) increased, the maximum stem strains levelled off (Figure 8). These strains were normalized to the strain of the stem in the femur. Maximum stem e,,,, and eZZ approached the femur values, and were close to the femur values for most of the fixture moduli studied. Maximum stem e, decreased horn 74 to 38% of the femur value, with the exception of the orthotropic birchwood fixture, which increased maximum stem e, to 82% of the femur value. Maximum stem eil levelled off at 72% of the femur value; the birchwood fixture slightly increased maximum stem eil. The node locations for maximum stem en, and eZZ were the same for the stem in the femur and for the Biomaterials

1996. Vol. 17 No. 23

80

90

on femoral stems: A.D. Heiner et al.

100 110 120 Embedding height at stem midline (mm)

130

1 10

Figure 6 Effects of embedding height on the maximum stem strains for load angle 16112: W, eXX; f, eyY; 0, e,,; A, eiI. Strains were normalized to the values at the highest embedding height. The embedding height at which the location of the maximum stem strain switched from the stem neck to the embedding height was 113mm for eXX, 113 mm for eZz and 103 mm for err. Maximum stem eyY stayed in the stem neck for all embedding heights and load angles studied. The other load angles showed similar results.

90

1W 110 120 130 Embedding height at stem midline (mm)

140

Figure 7 Effects of embedding height on the maximum stem strains in the neck for load angle 16112: W, eXX; +, eYY; 0, eZZ; A, ei,. Strains were normalized to the values at the highest embedding height. The other load angles showed similar results.

stem in all testing device variations with full proximal support and load angle 16/12. However, the node locations for maximum stem e,, and eil for the stem in the femur were different from those for the stem in all the testing device variations. All of the testing devices fell short with regards to considering the femur, when the simulating maximum stem strains. The birchwood fixture, however, was chosen as the best testing device within the context of the finite element model, as far as reproducing the maximum stem strains of the stem in the femur was concerned. The birchwood testing device especially improved the simulation of maximum stem e,, and eil, relative to the other testing device variations studied.

Effects of testing device variables

e

zi

on femoral

stems: A.D. Heiner et al.

I

0.8.

f

z 0 w I=

0.7-

“E 6 0.6: .z

0.5-

I I 0.4-

0.31I

*,

0

20

40

60

80 Fiiure

100 modulus

I20

140

160

iao

200

(GPa)

8 Effects of fixture modulus on the maximum stem strains: W, eXX; +, eyy; 0, ezz; A, e,,. The material at 15.2 GPa was birchwood, an orthotropic material; 15.2 GPa was the longitudinal modulus. The transverse modulus was 0.762GPa, and the radial modulus was 1.19GPa. Strains were normalized to the femur values. Figure

DISCUSSION There has been considerable variation in the The testing of composite stems. mechanical international standard IS0 7206/6l*, for testing the head and neck of femoral stems, specifies that the stem testing device is proximally potted. A specific :not given. Christel et aLz2 configuration is mechanically tested a carbon-carbon stem using a test method based on an IS0 draft involving distal potting. Ainsworth and Tarrzg designed a composite stem based on the stresses produced using distal potting. A mechanical testing device developed by Humphrey for a and Gilbertson13, a.nd designed specifically composite stem, was a variation on proximal potting; the proximal and distal femoral stem were supported and the midstem was free. The criteria used in this study to determine the were the effects of changing testing parameters maximum stem strains e,,, en,, ezz and Q (interlaminar shear strain). Based on these criteria, varying the future radius had little effect, except for maximum stem eil. Varying the embedding compound modulus only affected maximum stem ezz and eil. Varying the stem/embedding cornpound interface friction slightly affected maximum stem e,, ezz and eii. At the highest embedding height, many of the maximum stem strains levelled off at larger parameter values. The load angle O/10 caused the highest maximum stem strains, and the load angle 10/O caused the lowest maximum stem strai:ns. This demonstrated the severity of out-of-plane or torsional loads on the femoral stem, and was consistent with previous studies on the testing of metallic stem8* and uncemented stems30z31. The different load angles resulted in maximum stem strains having different magnitudes and node locations, indicating that the different load angles on the stem would result in different failure load magnitudes and locations. The embedding height can have a profound effect on

2215

the stem stresses7, and is a variation used in the testing of metallic stems to obtain realistic stem failuresg. In this study, decreasing the embedding height increased the stem strains, both in the neck and in the stem overall, As the embedding height decreased, the maximum stem strains increased, and the location of the maximum stem strain switched from the neck to the embedding height. These results have been seen with metallic stems7’10. At the lowest embedding height, equivalent to that specified in the IS0 standards for the testing of femoral stems using distal potting, all of the maximum composite stem strains, except for en,, occurred at the embedding height; this was seen for all four load angles studied. If a femoral stem were tested at a lower embedding height, to raise the strains in the neck and cause neck failure, this objective might not be fulfilled. Although neck failures are seen in femoral stems, mechanically testing a stem at too low an embedding height would mask neck failure, since failure would occur at the embedding height instead of in the neck. Alternatively, a lower embedding height may not cause stem failure at the embedding height; the highest stem strains may still be in the neck. The maximum stem strains eXXand eii in the testing devices were always worse in terms of matching the stem strains in the femur than were ew and ezz. Maximum stem e,, and eil would lead to composite interlaminar failure, by normal and shear strain, respectively. Interlaminar failure is one of the failure modes for thick composites, and has been observed in simplified composite femoral stems’l. The testing devices studied here could suppress these interlaminar failures in a composite stem, relative to the stem in a femur. The worse match of maximum stem e,, and eil also indicated that interlaminar failures would be suppressed, relative to the in-plane tensile failures indicated by maximum stem en, and ezz. Additionally, the locations for maximum stem e= and eil were predicted to be different between the stem in the femur and the stem in the testing devices. The best choice of testing device in this parametric study was a birchwood fixture which supported the stem up to its neck. Birchwood is an orthotropic, nearly transversely isotropic, material; it is considerably less stiff in the transverse and radial (x and y) directions than it is in the longitudinal (z) direction. A similar hardwood, beech, has been used as a femoral stem testing device14. In addition to the longitudinal modulus of birchwood being in the range of bone, the orthotropy of birchwood may be why this fixture better simulated a femur.

CONCLUSIONS The strains on a polymer composite femoral stem were affected by design changes to its testing device. Results from femoral stems tested in different testing devices may or may not be comparable. Birchwood was the best testing device for the composite stem out of the testing devices studied. As a testing device with full proximal support, the birchwood best simulated a femur. Testing devices which incorporated an Biomaterials 1996, Vol.

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Effects of testing device variables

embedding compound were not as good as the birchwood single-material fixture. Future studies could further contribute to the design of a composite stem testing device. The reproducibility of birchwood from fixture to fixture may be questionable; a reproducible, transversely isotropic composite material could be investigated. Static and fatigue strength of the testing device would also have to evaluated. The cylindrical geometry of the testing device, while widely used, may not be the best choice; other testing device geometries and configurations should be evaluated. A finite element program with thick composite analysis capability would indicate initial failure in the composite stem. A testing device which works for one stem design might not work for another, such as a straight stem versus a curved stem, or a pressfit stem versus a porous ingrowth stem. Experimental stress analysis of the stem/testing device system would allow verification of the finite element results. If clinical data demonstrate some loss of proximal support with composite stems, the testing device may be modified to reflect this.

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14

15

ACKNOWLEDGEMENTS The authors wish to thank Hercules, Inc. (Magna, UT, USA), and Biomet, Inc. (Warsaw, IN, USA), for providing a composite stem. This study was supported by a National Science Foundation fellowship.

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