Finite element analyses of impacted allografts for 3 FINITE ELEMENT ANALYSES The non linear finite element

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  • 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. A third of these operations fail due to aseptic loosening of the prosthesis. The revision surgeries are carried out using the 'Impaction grafting technique' introduced in Exeter in 1987. This technique largely depends on the mechanical strength of the impacted bone graft into which the prosthesis is fixed. As the patient mobilises the bone graft must withstand forces of 2.5 to 3.5 times the body weight during normal walking. In this paper we consider the effects of these forces on the bone graft-prosthesis system. The stresses and deformations in different regions of the Femur and bone graft under these forces will be analysed. A parameteric study on the effects of the properties of the Femur, bone graft and the PMMA cement used in the revision THR surgeries is presented.

    1 INTRODUCTION

    Primary hip replacement operations are carried out on over 800,000 patients within the UK. A stainless steel prosthesis is press-fitted into the femur bone in a cementless surgery. Finite element analysis was used successfully in estimating the stresses in the femur bone following these surgeries by Huiskes (1990). In this paper Huiskes identifies the load transfer mechanism in which the shear stress induced in the femur bone balances the axial force imposed by the prosthesis. Earlier, Crowninshield et al (1980) used an axisymmetric beam model in their finite element analysis which simulated the press-fit prosthesis and carried out a parametric study on different kinds of prothesis (Charnley, Aufranc-Turner etc.). Von Mises yield criterion was used in predicting the octahedral stresses in different regions of the femur bone. More recently Kang et al (1993) have carried out a three dimensional finite element analyses based on Computerised Tomography (CT) scan images of the femur and the prosthesis. The normal and shear stresses in the femur bone were predicted based on these analyses in which they use simple 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 femur bone,

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

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

    It is estimated, based on clinical studies, that a third of all the primary total hip replacements fail 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 poor bone 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 the problems of poor bone stock. In this technique impacted bone graft (chipped bone) is introduced into the femur and the prosthesis is inserted into the bone graft. In a recent clinical study Gie et al (1993) have observed that this technique is very successful in all of the revision surgeries carried out. The load imposed on the prosthesis is several times more than the body weight of the patient. It is estimated that during normal level walking the load on the prosthesis is 2.5 to 3.5 times that of the body weight. Further, for an average person the number of walking cycles is as high as 1 x 10* per year. The load transfer mechanism in the impaction grafted arthoplasties is very different from compared to the press-fitted prosthesis in a primary THR operation. The load from the prosthesis is first transferred into the bone graft by generating shear stresses generated along the prosthesis-bone graft interface and the end bearing of the prosthesis into the bone graft. The stresses in the bone graft will induce shear stresses along the femur-bone graft interface. It is imperative that there will be shear deformations within the bone graft before it mobilises its full shear strength. As a result, there will be subsidence of the prosthesis.

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

    2 MECHANICAL PROPERTIES OF THE BONE GRAFT

    A bone graft sample was obtained by putting a freeze dried femoral head through a specially constructed 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 the femoral head is taken from which the apparent density (total weight of the bone sample/total volume) of the bone is established. Mueller et al (1966) describe methods for determining the apparent density of bone. Using a similar procedure the apparent density of the bone was estimated 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 can be obtained from the above values as 1900 kg/m\ These values compare satisfactorily with the study of Galente et al (1970) on the physical properties of Trabecular bone.

    Stress-Strain Behaviour of

    Sh ea r St re ss k Pa

    1600.

    1200

    800

    400

    o l

    Morcdlised Bone Normal Load

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

    _x*̂ 20kg ^ -y 55 kg

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

    2 4 6 8 10 Shear Strain %

    Sh ea r S

    tre ss

    at Fai

    lur e kPa

    Fig.l Stress-strain behaviour of bone graft

    Mohr-Coloumb Envelope for Morcellised Bone

    1200 p 1000 1 800 j. 600 | 400 -j- 200 ,|

    100 200 Normal Stress kPa

    Fig.2 Failure envelope for the bone graft

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

  • Simulation Modelling in Bioengineering 167

    The bone graft sample was tested in a direct shear apparatus often used to test granular materials. The tests on the bone graft were conducted at a constant strain rate of 2.5mm/minute. In Fig.l the shear stress-shear strain plots obtained from these tests are presented. The normal stress was changed in each experiment within a range of 13.625 kPa (5 Kg normal load) to 231.625 kPa (85 Kg normal load). From the plots in Fig.l we can see that the bone graft material is clearly strain hardening as the shear strain in the test progresses. In Fig.2 the shear stress at failure (or 10% strain) is plotted against the normal stress. This plot is traditionally used to identify the Mohr-Coulomb failure surface. From the data points in this figure it is clear that a linear Mohr-Coulomb failure surface can be drawn for this material. The friction 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 normal stress. This intercept is interpreted as the interlocking of the material. The mechanical properties 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 program called SWANDYNE, Chan (1988). SWANDYNE is a generalised, fully coupled, effective stress 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 relation with a non-associative flow rule.

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

    3.1 Constitutive model Two different constitutive models were used in the present analysis. The femur bone was modelled as a simple elastic material following Kang et al (1993). However, the bone graft itself was

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