Finite element analyses of impacted allografts for€¦ · 3 FINITE ELEMENT ANALYSES The non linear finite element analyses reported in this paper were carried out using a program

Finite element analyses of impacted allografts for

total hip arthoplasty

S.P.G. Madabhushi," A.S. Usmani/ D.R. Fairbairn,"

M. Rajalakshmi^

"Department of Civil and Environmental Engineering, University of

Edinburgh, Edinburgh, UK

* Associate, 1 IB Double Hedges Park, Liberton, Edinburgh, UK

ABSTRACT

Over 800,000 total hip replacement (THR) operations are performed each year in the UK. Athird of these operations fail due to aseptic loosening of the prosthesis. The revision surgeriesare carried out using the 'Impaction grafting technique' introduced in Exeter in 1987. Thistechnique largely depends on the mechanical strength of the impacted bone graft into whichthe prosthesis is fixed. As the patient mobilises the bone graft must withstand forces of 2.5 to3.5 times the body weight during normal walking. In this paper we consider the effects of theseforces on the bone graft-prosthesis system. The stresses and deformations in different regionsof the Femur and bone graft under these forces will be analysed. A parameteric study on theeffects of the properties of the Femur, bone graft and the PMMA cement used in the revisionTHR surgeries is presented.

1 INTRODUCTION

Primary hip replacement operations are carried out on over 800,000 patients within the UK. Astainless steel prosthesis is press-fitted into the femur bone in a cementless surgery. Finiteelement analysis was used successfully in estimating the stresses in the femur bone followingthese surgeries by Huiskes (1990). In this paper Huiskes identifies the load transfer mechanismin which the shear stress induced in the femur bone balances the axial force imposed by theprosthesis. Earlier, Crowninshield et al (1980) used an axisymmetric beam model in their finiteelement analysis which simulated the press-fit prosthesis and carried out a parametric study ondifferent kinds of prothesis (Charnley, Aufranc-Turner etc.). Von Mises yield criterion wasused in predicting the octahedral stresses in different regions of the femur bone. More recentlyKang et al (1993) have carried out a three dimensional finite element analyses based onComputerised Tomography (CT) scan images of the femur and the prosthesis. The normal andshear stresses in the femur bone were predicted based on these analyses in which they usesimple elastic constitutive models for the femur bone. All the above analyses led to

a) a better understanding of the load transfer mechanism from the prosthesis into the femurbone,

b) improvements in the design of the prosthesis for more efficient transfer of axial load bygenerating larger shear stresses and

c) established the finite element method as an effective tool in studying the prosthesis-femurbone system.

It is estimated, based on clinical studies, that a third of all the primary total hip replacementsfail due to aseptic loosening of the prosthesis. One of the main reasons for this is ascribed to

Transactions on Biomedicine and Health vol 3, © 1996 WIT Press, www.witpress.com, ISSN 1743-3525

166 Simulation Modelling in Bioengineering

poor bone stock. Kershaw et al (1991) identified that the risk of failure in patients with poorbone stock is six times as much as in the patients with good bone stock.

The techniques of impaction grafting was introduced at Exeter in 1987 to overcome theproblems of poor bone stock. In this technique impacted bone graft (chipped bone) isintroduced into the femur and the prosthesis is inserted into the bone graft. In a recent clinicalstudy Gie et al (1993) have observed that this technique is very successful in all of the revisionsurgeries carried out. The load imposed on the prosthesis is several times more than the bodyweight of the patient. It is estimated that during normal level walking the load on the prosthesisis 2.5 to 3.5 times that of the body weight. Further, for an average person the number ofwalking cycles is as high as 1 x 10* per year. The load transfer mechanism in the impactiongrafted arthoplasties is very different from compared to the press-fitted prosthesis in a primaryTHR operation. The load from the prosthesis is first transferred into the bone graft bygenerating shear stresses generated along the prosthesis-bone graft interface and the endbearing of the prosthesis into the bone graft. The stresses in the bone graft will induce shearstresses along the femur-bone graft interface. It is imperative that there will be sheardeformations within the bone graft before it mobilises its full shear strength. As a result, therewill be subsidence of the prosthesis.

In this paper, we will investigate the stresses generated in the different regions of the bonegraft by considering it as a granular material. Also the deformation of the bone graft andsettlement of the prosthesis will be investigated. Since the mechanical properties of thisgranular material, namely the bone graft, are not known, these are investigated in the nextsection.

2 MECHANICAL PROPERTIES OF THE BONE GRAFT

A bone graft sample was obtained by putting a freeze dried femoral head through a speciallyconstructed bone mill. The bone graft obtained from the mill are cleaned with formalin,alcohol and water and are dried by centrifuging for 15 minutes. Also, a sample core from thefemoral head is taken from which the apparent density (total weight of the bone sample/totalvolume) of the bone is established. Mueller et al (1966) describe methods for determining theapparent density of bone. Using a similar procedure the apparent density of the bone wasestimated as 285 kg/m . Also, the porosity of the bone is taken as 85 % following Galante et al(1970), which gives the void ratio of the bone as 5.7. The real density of the femoral head canbe obtained from the above values as 1900 kg/m\ These values compare satisfactorily with thestudy of Galente et al (1970) on the physical properties of Trabecular bone.

Stress-Strain Behaviour of

Shear Stress kPa

1600.

1200

800

400

o l

Morcdlised Bone NormalLoad

^ -+-5kgy&g%$&&R̂ ^ P̂. i\̂ *#̂ ^ , * '*-* ̂ y

_x*̂ 20kg^ -y 55 kg

_.iniiiiiiiiiiirir +85̂plpnpiliwyw«v«*y j |

2 4 6 8 10Shear Strain %

Shear S

tress

at Fai

lure kPa

Fig.l Stress-strain behaviour of bone graft

Mohr-Coloumb Envelope forMorcellised Bone

1200 p1000 1800 j.600 |400 -j-200 ,|

100 200Normal Stress kPa

Fig.2 Failure envelope for the bone graft


Simulation Modelling in Bioengineering 167

The bone graft sample was tested in a direct shear apparatus often used to test granularmaterials. The tests on the bone graft were conducted at a constant strain rate of2.5mm/minute. In Fig.l the shear stress-shear strain plots obtained from these tests arepresented. The normal stress was changed in each experiment within a range of 13.625 kPa (5Kg normal load) to 231.625 kPa (85 Kg normal load). From the plots in Fig.l we can see thatthe bone graft material is clearly strain hardening as the shear strain in the test progresses. InFig.2 the shear stress at failure (or 10% strain) is plotted against the normal stress. This plot istraditionally used to identify the Mohr-Coulomb failure surface. From the data points in thisfigure it is clear that a linear Mohr-Coulomb failure surface can be drawn for this material. Thefriction angle of the material is obtained from the slope of the Mohr-Coulomb surface as 27.5°.It must be pointed out that there is a small intercept on the shear stress axis at zero normalstress. This intercept is interpreted as the interlocking of the material. The mechanicalproperties obtained from these tests were used in the finite element analyses.

3 FINITE ELEMENT ANALYSES

The non linear finite element analyses reported in this paper were carried out using a programcalled SWANDYNE, Chan (1988). SWANDYNE is a generalised, fully coupled, effectivestress based code for problems in geomechanics. This code was chosen for following reasons;

a) availability of a wide variety of constitutive models including the Mohr-Coulomb relationwith a non-associative flow rule.

b) it is possible to include the effect of pore fluid (bone marrow, clotted blood etc.) in thebone graft in future analyses.

3.1 Constitutive modelTwo different constitutive models were used in the present analysis. The femur bone wasmodelled as a simple elastic material following Kang et al (1993). However, the bone graftitself was modelled as a Mohr-Coulomb type material with a non associative flow rule. It isknown that the non associative flow rule is essential to capture the behaviour of granularmaterial, Pastor et al (1985). The Mohr-Coulomb type yield surface was used primarily due tothe failure surface in the experiments discussed in the previous section have fitted very closelythis yield criterion. It is possible to use more sophisticated constitutive models in futureanalyses. In Table 1 the material parameters used for the femur bone and bone graft are listed.Note that in Table 1 the friction angle for the interface elements is smaller than that for thebone graft.

3.2 Finite element meshThe total hip arthoplasty using impaction graftinginvolves fixing the prosthesis in the bone graft. In thisfigure the femur bone, bone graft and prosthesis areclearly seen. However, in the finite element analysisinterface elements were introduced at the Femur-bonegraft interface as well as the bone graft-prosthesisinterface. In Fig.3 the finite element mesh used for allthe analyses discussed in this paper is presented. In thisfigure all the five regions considered in the analyses areidentified. The finite element mesh consisted of a totalof 172 isoparametric, quadrilateral and triangularelements. The quadrilateral elements were used for thefemur and the prosthesis while triangular elements wereused for bone graft as shear deformations are expectedin this region. Also the left hand corner node at the baseof the FE mesh is fixed in both x and y directions to

Prosthesis

Femur-Bone graft

- Interface

Prosthesis-Bone graftInterface

Femur-

Fig.3 Finite element mesh usedin the present analyses



prevent lateral translation of the femur.

Table 1 Material ParametersZone

FemurBone graftProsthesis

Femur-Bone graftInter.

Bone Graft-ProsthInter.

Const.Model

ElasticMohr-Clmb*

ElasticMohr-Clmb*

Mohr-Clmb*

YoungsMod.(kPa)14.0E61100200E6110

2.0E6

Poissonratio

0.30.30.20.3

0.23

FrictionAngle

0

27.5

20

15

DilatanAngle

5

5

10

cyo

' Mohr-Coulomb criterion with Non Associated Flow Rule

4 FORCES ON THEFEMUR

The results from the fouranalyses are presented inTable 2. From this table itcan be seen that as theforce transferred to theprosthesis is increased thesettlement of the prosthesisincreases. Also the lateralmovements of the femurincrease with load and alsoalong the height of thefemur bone. Further, theunsymmetric structure ofthe bone and the inclinedapplication of the loadingresulted in a differencebetween the movements onthe left and right of thefemur. The stresses justbelow the prosthesis

Fig.4 Deformed mesh afterload of 2000 N was appliedto the prosthesis

Fig.5 Directions of major andminor prinicipal stresses after2000 N was applied

increase with load but their magnitude is lower than that would be expected in a press-fittedprosthesis, Huiskies (1990). On the other hand the settlements predicted are higher than inpress-fitted prosthesis. This is reasonable as the bone graft is much more compressible and willrequire the shear deformations to mobilise the strength to support the external load applied bythe prosthesis. The force transferred to the femur bone is several times that of the body weightof the patient. In the previous work of Crowninshield et al (1980) the force on the femur wastaken as 200 N. Huiskies (1990) has considered a much larger force of 3000 N. In this paperfour analyses were carried out in which the force applied to the femur is changed from 1000 Nto 4000 N. These analyses are designated as FC-1 to FC-4. Material parameters for theseanalyses are taken from Table 1. It must be noted that this force is a static force under whichshear deformations occur as the equilibrium is reached.

The deformed mesh for the analysis carried out with a prosthesis load of 2000 N is presentedin Fig. 4. In this figure the undeformed mesh is overlain to show the extent of settlement of theprosthesis. From this figure it is seen that the prosthesis has suffered significant settlement.This settlement also induced shear deformations in the bone graft which induces shear stresses



in the femur bone via the interface elements. The directions of major and minor principalstresses in this analysis are shown in Fig.5. From this figure it can be seen that the maximumstress rotation occurs in the right hand corner of the femur bone. Some stress rotation occurs inthe left hand side of the femur. This figure suggests that the load transfer mechanism is viashear and the load is finally carried into the femur (with a bias on the right hand side owing toinclined loading and unsymmetrical geometry). This fact is reinforced by the fact that thestresses just below the prosthesis are relatively small as the load is carried via shear in theinterface elements between prosthesis and the bone graft.

Table 2 Results of FE analyses with a variation of prosthesis loadsAnal-ysis

FC-1F02FC3FC-4

Force(N)

1000200030004000

Prosth.Settle-ment(mm)

1.0242.02613034.041

Femoral lateralMwemt. atHt-1*W

Left Right-0.23 1.23-0.46 2.47-069 3.70-0.93 4.93

Femoral lateralMovemt. at Ht-2*W

Left Right-9.64 46.75-19.42 93.93-29.07 140.85-38.79 187.84

Femoral lateralMwemt. at Ht-3*W

Left Right-18.2 97.93-36.65 196.9-54.83 295.3-73.16 393.8

Stresses underProsthesis (kPa)

0% Gy T%y-4.3 -1.6 18.4-6.63 -2.5 28.1-9.88 -3.6 42.1-13.2 -4.7 56.1

*Ht-l, Ht-2 and Ht-3 refer to the base, middle and top levels of the femur bone

5 Variation of the properties of the Femur

The properties of the femur will effect the behaviour of the prosthesis-bone graft-femursystem. The modulus and the Poisson's ratio of the femur were varied in this study. Themodulus of the Femur was discussed by Huiskes (1990). Clearly the modulus depends on thebone quality and the type of bone (Cancellous or Cortical). In this section the results from thefinite element analysis with different bone modulus of the femur are presented. The bonemodulus is varied from 5.0 GPa to 20.0 GPa. The results from each of these analysis ispresented in tables 3 and 4. In table 3 the lateral movement of the femur at three differentheights are presented. From the values in this table we can see that as the bone modulusincreases the lateral movements are reduced at every height. Also the lateral movement on theleft hand side of the femur are smaller than those on the right hand side. This is to be expectedas the loading is inclined. In table 4 the variation of stresses in the femur as well as in the bonegraft are presented as the modulus of the bone is changed. We can see from this table that thestresses in the femur at any one height increase with increase in the bone modulus. Also thestress component Cy is larger compared to the other two components. Similar analyses werecarried out by varying the poison's ratio of the femur and results suggested that both the lateralmovements and the stresses are not effected with the change in the poison's ratio in the rangestudied (v = 0.2 - 0.35).

Table 3 Variation of lateral movements in the Femur with change in Bone ModulusAnaly Modulus Lateral movement at Lateral movement at Lateral movement atsis Id. of the Height-1 Height-2 Height-3

Bone (m) (m) (m)

BM-1BM-2BM-3BM-4

(GPa)5.010.014.020.0

Left-0.1739E-5-0.9518E-6-0.6993E-6-0.5012E-6

Right0.9595E-50.5085E-50.3701E-50.2630E-5

Left-0.6881E-4-0.3916E-4-0.2908E-4-0.2103E-4

0.0.0.0.

Right3508E-3I917E-31409E-3.1008E-3

Left-0.1294E-3-0.7382E-4-0.5484E-4-0.3970E-4

Right0.7292E-30.4011E-30.2953E-30.2117E-3



Table 4 Variation of Stresses in the Femur with change in Bone ModulusStressLoc.*

a,MPa

BL 0.29BR -1.52ML 0.13MR -0.75TL 0.001

BM-1

a,,MPa0.73-3.520.29-1.790.009

*xyMPa

°xMPa

0.08 0.33-0.47 -1.620.06 0.15-0.39 -0.84

0.001

BM-2

°yMPa0.82-3.77033-2.020.01

*\vMPa

c\MPa

0.1 0.34-0.53 -1.660.07 016-0.45 -0.88

0.001

BM-3

<j\MPa0.85-3.850.35-2.100.01

TXVMPa

(\MPa

0.103 0.35-0.54 -1.690.07 0.16-0.47 -0.90

0.001

BM-4

a,.MPa0.87-3.92036-2.160.01

TXVMPa0.107-0.560.07-0.49

TR

JBP

FBP

0.003

0.005

0.039

0.001

0.003

0.104

0.0040.002

0.043

0.002

0.004

0.009

0.038

0.001

0.003

0.102

0.0040.002

0.042

0.002

0.005-0.01

0.038

0.002

0.004

0.101

0.0040.003

0.042

0.002

0.005-0.01

0.038

0.002

0.004

0.101

0.0040.003

0.042

0.002' BL- base left, BR- base right, ML- middle left, MR- middle right, TL- top left, TR- top right, JBP- Justbelow Prosthesis, FBP- Far below prosthesis

6 Properties of the bone graft

The mechanical properties of the bone graft are presented earlier in Sec.2. However, theproperties of the bone graft will change depending upon the type of bone mill used and thequality and condition (frozen or thawed) of the femoral head being ground. In the absence ofthis data we need to carry out a parametric study by changing the significant properties. In thissection the results from the finite element analysis by changing the modulus, friction angle andthe dilataricy of the bone graft are presented.

6.1 Variation of the modulus of the bone graftThe graft modulus in these analyses is varied from 0.5 MPa to 4.5 MPa. The results from eachof these analysis is presented in tables 5 and 6. In table 5 the lateral movement of the femur atthree different heights are presented. From the values in this table we can see that as the bonegraft modulus increases the lateral movements are reduced at every height. As before thelateral movement on the left hand side of the femur are smaller than those on the right handside. In table 6 the variation of stresses in the femur as well as in the bone graft are presentedas the modulus of the bone graft is changed. We can see from this table that the stresses in thefemur at any one height decrease with increase in the bone graft modulus. This suggests thatwith the increase in modulus, the bone graft is able to sustain more of the load from theprosthesis thereby resulting in a smaller stress in the femur. Also the stress in the Qy is thelargest compared to the other two components.

Table 5 Variation of lateral movements in femur with change in bone graft modulusAnal-ysis'id.

GM-1GM-2GM-3GM-4

Modulusofthe

Bone graft(MPa)0.51.53.04.5

Lateral moveHeight(m)

Left-0.7312E-6-0.6148E-6-0.6232E-6-0.5769E-6

iment at-1

Right0.3807E-50.3575E-50.3436E-50.3274E-5

Lateral moviHeight(m)

Left-0.3094E-4-0.2378E-4-0.2465E-4-0.2201E-4

sment at_7

Right0.1468E-3O.I352E-3'0.1258E-30.1167E-3

Lateral moviHeight(m)

Left-0.5844E-4-0.4450E-4-0.4642E-4-0.4126E-4

:ment at-3

Right0.3087E-30.2833E-30.2616E-30.2413E-3



Table 6 Variation of Stresses in the Femur with change in bone graft modulusStressLoc.*

BLBRMLMRTL

MPa036-1.710.17-0.92

GM-1

G\.MPa0.90-3.970.37-2.21

TXVMPa0.110.570.070.500.003

o%MPa0.29-1.600.12-0.840.001

GM-2

GyMPa012-3.700.27-2.000.008

T\vMPa0.08-0.520.05-0.45

x̂MPa029-1.520.13-0.750.001

GM-3

GVMPa0.74-3.53029-1.800.009

*xvMPa0.085-0.480.06-0.39

x̂MPa026-1.440.11-0.680.001

GM-4

a,MPa0.67-3.33025-1.630.008

TXVMPa0.07-0.440.05-0.35

TR

JBP

FBP

0.006

0.0060.01

-0.04

0.002

0.002

0.004-0.10

0.003

0.042

0.002

0.004

0.007-0.04

0.001

0.003-0.11

0.0030.002

0.04

0.001

0.003

0.005-0.04

0.001

0.003

0.103

0.0030.002

0.04

0.001

0.002

0.002-0.04

.0001

0.001-0.1

0.0030.001

0.04

0.001* BL- base left, BR- base right, ML- middle left, MR- middle right, TL- top left, TR- top right, JBP- Justbelow Prosthesis, FBP- Far below prosthesis

6.2 Variation of the friction angle of the bone graftThe friction angle of the bone graft in these analyses is varied from 20 ° to 50 °. The resultsfrom each of these analysis is presented in tables 7 and 8. In table 7 the lateral movement ofthe femur at three different heights are presented. From the values in this table we can see thatas the friction angle increases the lateral movements are reduced at every height. As before thelateral movement on the left hand side of the femur are smaller than those on the right handside. In table 8 the variation of stresses in the femur as well as in the bone graft are presentedas the friction angle of the bone graft is changed. We can see from this table that the stresses inthe femur at any one height decrease with increase in the friction angle of the bone graft. Thissuggests that with the increase in friction angle, the bone graft is able to sustain more of theload from the prosthesis thereby resulting in a smaller stress in the femur. Also the stress in theGy is the largest compared to the other two components.

Table 7 Variation of lateral movements in femur with change in friction angle of bone graftAnal-ysisId.

GF-1GF-2GF-3GF-4

Fric. Angleof the

Bone graft0

20.033.040.050.0

Lateral mov<Height(m)

Left-0.8952E-6-0.5941E-6-0.5970E-6-0.4723E-6

:ment at-1

Right0.4073E-50.3507E-50.3359E-50.3279E-5

Lateral movement atHeight -2(m)

Left Right-0.3607E-4 0.1535E-3-02558E-4 0.1345E-3-02326E-4 0.1294E-3-02191E-4 0.1266E-3

Lateral mov<Height(m)

Left-0.6772E-4-0.4851E-4-0.4442E-4-0.4210E-4

sment at-3

Right0.3219E-302819E-30.2710E-302650E-3

6.3 Variation of the dilatancy of the bone graftThe dilatancy angle of the bone graft in these analyses is varied from 0° to 20°. The resultsfrom each of these analysis is presented in tables 9 and 10. In table 9 the lateral movement ofthe femur at three different heights are presented. From the values in this table we can see thatwith the increase in the dilatancy the lateral movements increase. As before the lateralmovement on the left hand side of the femur are smaller than those on the right hand side. Intable 10 the variation of stresses in the femur as well as in the bone graft are presented as thedilatancy of the bone graft is changed. We can see from this table that the stresses in thefemur at any one height increase with increase in the dilatancy angle of the bone graft. Thissuggests that with the increase in dilatancy angle, the bone graft is getting thereby resulting ina larger stress in the femur. Also the stress in the Oy is the largest compared to the other two



components.

Table 8 Variation of Stresses in the Femur with change in friction angle of bone graftStressLoc.*

BLBRMLMRTL

TR

JBP

FBP

*BL-bbelow F

Table ̂Anal-ysisId.

GD-1GD-2GD-3GD-4

c\MPa0.43-1.820.19-0.950.002

0.0060.012

0.052ase left, Irosthesis

) VariatDilataAngletheBgra0O.C5.C10.20.

GF-1

SMPa1.08-4.200.42-2.260.013

0.002

0.007-0.11

3R- base, FBP- F<

ion of lancy:ofoneft

03

T̂ .MPa0.130.580.08-0.52

0.0050.003

0.044

0.002right. MIir below

teral moLater

Left-0.67521-0.6993!-0.72361-0.7685]

GXMPa0.29-1.580.14-0.840.001

0.004

0.008

0.029^- middleDrosthesi

vementsal moverHeight -(m)

5-6E-6B-6S-6

GF-2

OyMPa0.73-3.670.31-2.010.009

0.001

0.002

0.098left, MRs

in feminent at1

Right3.3593E-3.3701E-3.3796E-13955E-

T%yMPa0.09-0.520.06-0.45

0.0040.002

0.041

0.002- middle

ir with cI

5 -0.5 -0.5 -0.5 -0.

(3%MPa0.26-1.510.13-0.810.001

0.004

0.007

0.026right, TL

hange in,ateral rr

Hei(

Left2860E-42908E-42966E-43102E-4

GF-3

°yMPa0.64-3.53029-1.940.009

0.001

0.001

0.092- top left

dilatanlovemengat -2m)

Ri0.13:0.1 4C0.14:0.153

\̂vMPa0.084-0.510.06-0.43

0.0030.002

0.04

0.002TR- top

:y of thetat

ght4E-39E-36E-36E-3

(3%MPa0.24-1.480.13-0.790.001

0.004

0.007-0.03

right, JB

bone grLater

Left-0.5433-0.5484-0.5556-0.5749

GF-4

CyMPa0.59-3.45029-1.900.008

0.0010.0

-0.09

P- Just

aftal moveHeight -(m)

E-4 CE-4 CE-4 CE-4 0

TXVMPa0.078-0.500.06-0.42

0.0030.002

0.039

0.002

ment at3

Right.2833E-3.2953E-3.3057E-3.3234E-3

Table 10 Variation of Stresses in the Femur with change in dilatancy of the bone graftStressLoc.*

QXMPa

BL 0.33BR -1.61ML 0.06MR -0.83TL 0.001

GD-1

<JyMPa0.82-3.73035-2.00.011

TXVMPa

x̂MPa

0.10 0.34-0.53 -1.660.072 0.16-0.45 -0.88

0.001

GD-2

dyMPa0.85-3.850.35-2.100.01

TxyMPa

cr%MPa

0.10 0.35-0.54 -1.700.069 0.16-0.47 -0.91

0.001

GD-3

OyMPa0.88-3.950.35-2.180.01

?xyMPa

o%MPa

0.11 0.37-0.56 -1.780.067 0.16-0.49 -0.97

0.001

GD-4

*yMPa0.93-4.13035-2.320.009

T̂MPa0.11-0.590.064-0.53

TR

JBP

FBP

0.004 0.001

0.0040.002

0.044

0.0040.003

0.009-0.04

0.006

0.005 0.002

0.010 0.004

0.005 0.002

0.010 0.004

0.0040.003

0.0400.006 0.003

0.011 0.006

* BL-below

base left. BR- base riProsthesis. FBP- Far

ght. ML- middle left. MR- middle right. TL- top left. TR- top right. JBP- Justbelow prosthesis

0.0040.003

0.037

0.105 0.002 0.038 0.101 0.002 0.037 0.098 0.002 0.035 0.093 0.002



7 Properties of the cement between the prosthesis and bone graft interface

PMMA cement is injected in the THA surgery which sets at the bone graft-prosthesis interface.The properties of the cement were discussed by Gie et al (1993). The modulus of the PMMAcement is known to be in the range of 1 to 4 GPa. This aspect is studied in this section. Theresults from each of these analysis is presented in tables 11 and 12. In table 11 the lateralmovement of the femur at three different heights are presented. From the values in this tablewe can see that with the increase in the modulus of the cement the lateral movements remainunchanged. As before the lateral movement on the left hand side of the femur are smaller thanthose on the right hand side. In table 12 the variation of stresses in the femur as well as in thebone graft are presented as the modulus of the cement is changed. We can see from this tablethat the stresses in the femur at any one height remain unchanged as the modulus of the cementis changed.

Table 11 Variation of lateral movements in femur with change in modulus of PMMA cementAnal- Modulus Lateral movement at Lateral movement at Lateral movement atysis of the Height-1 Height-2 Height-3Id. Bone graft (m) (m) (m)

CM-1CM-2CM-3CM-4

(GPa)1.02.03.04.0

Left-0.699 1E-6-0.6993E-6-0.6994E-6-0.6995E-6

Right0.3701E-50.3701E-50.3701E-50.3701E-5

Left-0.2906E-4-0.2908E-4-0.2908E-4-0.2909E-4

Right0.1408E-30.1409E-30.1409E-30.1409E-3

Left-0.548 1E-4-0.5485E-4-0.5485E-4-0.5486E-4

Right0.2952E-30.2953E-30.2953E-30.2953E-3

Table 12 Variation of Stresses in the Femur with change in modulus of PMMA cement failureStressLoc.*

BLBR

ML

(\MPa034-1.66

0.16

CM-1

CTyMPa0.85-3.85

0.35

TXVMPa0.100.54

0.069

o\MPa034-1.66

0.16

CM-2

dyMPa0.85-3.85

035

T%yMPa0.10-0.54

x̂MPa0.341-1.66

0.157

CM-3

a,.MPa0.85-3.85

0.348

I xvMPa0.103

0.5420.069

c%MPa0.341-1.66

0.157

CM-4

C7yMPa0.85-3.85

0.348

T\vMPa0.103

0.5420.069ML

MRTL

TR

JBP

FBP

0.16

-0.880.001

0.005-0.01

0.038

035

-2.100.01

0.002

0.004

0.101

0.069

-0.47

0.004

0.0030.042

0.002

0.16

-088

0.001

0.005-0.01

0.038

035

-2.10-0.01

0.002

0.004

0.101

0.069-0.47

0.004

0.003

0.042

0.002

0.157

-0.88

0.001-0.05

-0.01

0.038

0.348

-2.100.01

0.002

0.004

0.101

0.069

-0.47

0.0040.003

0.042

0.002

0.157

-0.880.001

0.005-0.01

0.038

0348

-2.100.01

0.002

0.004

0.101

0.069

-0.47

0.0040.003

0.042

0.002* BL- base left, BR- base right. ML- middle left, MR- middle right. TL- top left. TR- top right. JBP- Justbelow Prosthesis, FBP- Far below prosthesis

8 CONCLUSIONS

The technique of impaction grafting was developed at Exeter for revision total hip arthoplastyoperations. This technique, while being extremely successful, depends to a large extent on themechanical strength of the bone graft. Based on initial direct shear box experiments the stress-strain curve of the bone graft was determined. The data suggested that a Mohr-Coulomb typecriterion is suitable, at least as a first approximation, to carry out the finite element analysis ofthe prosthesis-bone graft-femur system. Using the data from the direct shear box experiments,finite element analyses were carried out to study the stresses in the bone graft and load transfer



mechanisms in the femur-impacted bone graft-prosthesis systems. The load transferred to theprosthesis was varied in the range of 1000 N to 4000 N. In this paper we carried out the finiteelement analyses using a non-associative form of Mohr-Coulomb yield criterion for the bonegraft. Interface elements were used between the prosthesis and the bone graft as well as thefemur and the bone graft. The results of the FE analyses indicate that the load is transferredfrom the prosthesis into the bone graft and then into the femur bone.

Based on the analyses in which force on the prosthesis is varied it appears that the magnitudeof stresses induced in the femur in the impaction grafting technique is smaller than thoseinduced by the press-fitted prosthesis. However, the magnitude of settlement of the prosthesisis larger compared to the press-fitted prosthesis. This is due to the nature of load transfermechanism which carries the load from the prosthesis via the bone graft into the femur. Whenthe shear deformations in the bone graft occur the bone graft is able to mobilise its strengththus transferring the load into the femur bone.

A parametric study on the properties of the femur has been carried out. The results from theanalyses in which the modulus of the femur was varied indicate that the stronger femur bonewill result in lower lateral movements at every height of the femur. Also the lateral movementon the left hand side of the femur are smaller than those on the right hand side and the stressesincrease with increase in the bone modulus. The stress component Oy is larger compared to theother two components. A similar parametric study was carried out by changing the modulus ofthe bone graft, the friction angle and the dilatancy of the bone graft and the modulus of thePMMA cement used in the THA surgeries.

ACKNOWLEDGEMENTS

We wish to express our gratitude for the helpful discussions of Prof. W.J. Gillespie, Mr. ColinHowie and Mr. Nigel Brewster of Princess Margaret Rose Orthopaedic Hospital, Edinburgh.

REFERENCESI.Chan, A.H.C., (1988), A unified finite element solution to static and dynamic problems ofGeomechanics, Ph.D thesis, University college of Swansea, Swansea.

2.Crowninshield, R.D., Brand, R.A., Johnston, R.C. and Milroy, J.C., (1980), An Analysis ofFemoral Component Stem Design in Total Hip Arthoplasty, Jnl. of Bone and Joint Surgery,Vol.62-A,No.l,pp 68-78.

3.Galante,J., Rostoker, W. and Ray, R.D., (1970), Physical properties of Trabecular Bone, JnlCa/c.7%M.#&y., Vol.5, pp 236-246.

4.Gie, G.A., Under, L., Ling, R.S.M., Simon, J.P., Slooff, T.J.J.H. and Timperley, A.J.,(1993), Impacted cancellous allografts and cement for revision total hip arthoplasty, Jnl. ofBone and Joint Surgery, Vol.75-B, No.l, pp 14-21.

5.Huiskes, R., (1990), The various stress patterns of press-fit, ingrown and cemented femoralstems, Clinical Orthopaedics and Related Research, No.261, pp 27-38.

6.Kang, Y.K, Park, H.C., Youm,Y., Lee, I.K., Ahn, M.H. and Ihn, J.C., (1993), Threedimensional shape reconstruction and finite element analysis of femur before and after thecementless type of total hip replacement, Jnl Biomed. Eng., Vol.15, pp497-504.

7.Kershaw, C.J., Atkins, R.M., Dodd, C.A.F. and Bulstrode, C.J.K.,(1991), Revision total hiparthoplasty for aseptic failure: a review of 276 cases, J Bone Joint Surg., Vol.73-B, pp 564-568.

8.Mueller,K.H., Trias, A. and Ray, R.D., (1966), Bone density and composition, Jnl. of Boneand Joint Surgery, Vol.48-A.,No.l, pp 140-148.

9.Pastor, M., Lueng, K.H. and Zienkiewicz, O.C., (1985), Simple model for transient soilloading in earthquake analysis, Part II: Non associative model for sands, Int. Jnl for Num.and Anal, methods in Geomechanics, Vol.9.


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Finite element analyses of impacted allografts for€¦ · 3 FINITE ELEMENT ANALYSES The non linear finite element analyses reported in this paper were carried out using a program