FINITE ELEMENT ANALYSIS : AN EFFECTIVE TOOL FOR PROSTHESES DESIGN

Transcription

1 Trends Biomater. Artif. Organs. Vol. 17(2) pp (2004) http// FINITE ELEMENT ANALYSIS : AN EFFECTIVE TOOL FOR PROSTHESES DESIGN S K Senapati & S.Pal School of Biosc, & Engg, Jadavpur University, Kolkata bioengg@giasclo1.vsnl.net.in Various prostheses and total joint replacements evolved over the past hundred years through a continuous worldwide effort to seek solution to a problem as old man himself. Historically in 1891 an ivory ball and socket joint was designed by Gluck in Germany, which was fixed with nickel-plated screws. Subsequently many more surgeons, scientists worked on hip joint replacement and more then 160 types of prostheses were developed till today. In 1958 Sir John Charnley ( 1970 ) introduced the bone cement for his arthoplasty to fix the metal prostheses, which appeared to solve the problem of anchorage and his design of low friction THR was considered Gold standard even today due to its high success rate 85% after 15 to 21 years of follow up. Till the quest for a trouble free artificial joint which will last for 40 years is on. Now, with the advancement of modern technology it is possible to investigate the internal stress-strain map and other parameters, e.g. principal stress, von Mises' criterion, Tresca's criterion in such a complex in vivo situation having stiff metal, compliant cement and anisotropic bone with regional and local variation of properties. Biomaterial scientists, implant designers, fabricators and surgeons can put their heads together to get an improved design from the point of view of the patient. This is true for the other joint replacements as well, be it knee, elbow or shoulder and smaller joints like finger or temporomandibular joint or a single tooth replacement. We in Jadavpur are trying to do just that. Finite element method (FEM) is a computer-based method that can be used to analyse such complex continua and gives result with in 5-10% of the exact solution depending on the proper finite element model. Following steps are followed: 1) Make a solid model, 2D or 3D and discreatise the model 2) define the element properties 3) assemble the element stiffness matrices 4) apply the loads and boundary conditions 5) solve the system of linear algebraic equations and 6) calculate stresses. FEM can be used for static and dynamic problems as well. Including viscoelastic materials we will illustrate its use through some of our work done recently. This technique is so very powerful that it may save our time and resources used in animal experimentation, while testing the efficacy of newly designed prosthesis or a biomaterial. New biomaterials which are being developed can be tested in silico to know whether the product will be good enough to sustain the load and be stable and stiff enough in the complex multi-dimensional anatomical structural environment with variable material properties. For example one 141

2 S.K. Senapati et. al. may think of the normal hip ( Fig.1) and artificially replaced hip prosthesis, Fig-2. The prosthesis may be hemi-hip, like Austein-Moore or Modular consisting of metal stem,ceramic ball and UHMWPE acetabulur cup, Fig. 4. It consists of one important area, which need to be addressed is the characterization of the biological materials. Until now no systematic work has been undertaken to generate various mechanical properties of various tissues, e.g. hard or soft tissue in our country. Majority of research works are mostly depended on western data which were also very old, when sophisticated measurements technique were not available.now the Fig.1 shows the model of a mid-frontal plane cross-section of a human proximal femur with regional variation of density which is correlated with the modulus of elasticity. However this was done after visual inspection of the trabaecular architecture of the bone. One may assume for the sake of simplification a homogenous structure without variation of properties. Fig. 2 simulates an Austein-Moore hemihip, mounted inside the femur after dissection of the hip ball, which is non-cemented and there are two holes which will allow bony ingrowths and fix it securely in future. Fig. 1 Normal proximal femur with regional variation of properties of carilage (A),cancellous bone areas B,C,D cortical bone, (E) Fig. 2 Artificial hip joint with an Austin Moore hemi-hip prosthesis (Uncemented) Biomechanical behaviour of such construct could be evaluated in silico by using FEM. The entire continuum is to be discretised using finite no. of elements of different geometry and their mechanical properties like modulii of Elasticity, Poisson's ratios and appropriate load and boundary conditions are to be applied and then it will solve the problem. Then the post processing module will generate the various raster mode display of various stress-strain field, like, principal stresses, Fig.6 shear stress, Failure criterion like Von Mises' stress, Fig. 7 & 8.and Tresca criterion.these two frames depicts the effect of considering the regional variation of bone properties. 142

3 Finite Element Analysis Fig. 3. FE model, element Discretization Fig. 4. Artificial hip joint with prosthesis and boundary conditions of a (Cemented fixation) cementless AHJ. Fig. 5. FE model, element discretiszation Fig. 6. Max. Principal stress distribution and boundary conditions of a. (MPa) in a normal femur with regional cemented AHJ variation. It may be seen that the nature designed the system in such a way to keep the stress field more or less constant. This is a very important finding,fig.6. The trabecular struts of femur also run aligned in the principal stress direction, which is quite predominantly visible if one pays attention to a sagittal section of the proximal femur. 143

4 S.K. Senapati et. al. Fig. 7 Von Mises stress distribution Fig. 8 Von Mises stress distribution (MPa) in a normal femur (MPa) in a normal femur with without regional variation regional variation Fig. 9 Axial stress (σy) distribution (MPa) Fig.10 Axial strain (σy) distribution (MPa) in in the bone tissue of natural femur the bone tissue of natural femur The axial stress, Fig.9 in the Y- direction and the strain in same direction, Fig.1 are displayed as continuous field The cortical bone being stiffer generate higher stress. 144

5 Finite Element Analysis SY DIST Fig. 11 σy (MPa) path plot along the path below greater trochanter from lateral to medial side of an uncemented AHJ SY DIST Fig. 12 σy (MPa) path plot along the path below greater trochanter from lateral side to medial side of a cemented AHJ. Another important feature of FEM is that it can display the stress profile about any particular line in a construct as indicated in Fig.3 and Fig.4 and in Fig.11 and Fig.12, as shown respectively. Notice the change of level of stress in the uncemented and cemented prosthesis. The level of stress in the Austein-Moore is much higher as per the analysis, which is just push fit. Figures 13 & 14 showed the axial stress in Y- direction and the principal stress, which is the maximum stress due the all the stresses combined together. If a 145

6 S.K. Senapati et. al. ductile material is used we have to consider whether any where the ultimate stress was exceeded or not. In fact in actual design it has to be much less as a factor of safety is to be considered. Stress Shielding : This is an important phenomenon as the metals are a decade order stiffer (modulus of elasticity ) compared to bone and bone is 5-6 times stiffer than bone cement, the major stress is shared by the stiffer materials leaving the bone shielded from the stress flow, which may go below the physiological level of stress leading to disuse osteoporosis and failure of the construct. To mitigate a lesser stiff material was proposed. In fact we developed a ceramic-polymer (UHMWPE) composite material (UH-CE). The mechanical property of which closely match to that of bone. We also tried plane UHMWPE as well for making of prosthesis. Fig. 15 shows the max. principle stress in normal hip joint(nhj), Co-Cr-Mo alloy, stainless steel(316l), Ti6Al4v alloy, ultra high molecular weight polyethylene--alumina (UH-CER) and UHMWPE implant cemented as modular hip. Fig. 13 Axial stress (σy) distribution Fig. 14 Max. Principal stress (σ1) distribution (MPa) in the bone tissue of an (MPa) in the bone-tissue of an uncemented uncemented AHJ using CoCrMo. AHJ using CoCrMo implant. alloy implant Fig. 15 Comparison of max. Principal stresses Fig. 16 Comparison of von Mises equivalent in the bone tissue of NHJ and AHJ stresses in the bone tissue of NHJ and using different implant materials AHJ using different implant materials (Cemented) (Cemented) 146

7 Finite Element Analysis Fig. 17 σeqv (von Mises) stress distribution (MPa) in the original prosthesis Fig. 18 σeqv (von Mises) stress distribution in the revised Now let us discuss about a modified prosthesis used for a bone cancer patient whose proximal femur was surgically removed as shown in Fig.17, which obviously had some design error due to sharp change in cross-section at the collar. The Upper part of the femur and muscle were removed. We modified it using profuse radius at the junction and the stress map was much better in Fig.18. Now the analyses we considered was 2-dimensional, which is based on the assumption of plane stress problem, meaning the figures are extruded out of the plane of the paper and of unit thickness. However 3- dimensional construct could be built and result obtained as depicted in Figs.19 &20. One of our scholars recently working on human pelvis using 3-D Construct having 88.9 thousand finite element and 16.4 nodes as shown in Fig. 21 and Fig. 22 showed the boundary conditions he used Fig 19. Max Principal stress (σ1 ) Fig. 20 Von Mises stress distribution (MPa) distribution in the cortical in the cortical bone tissue of an intact femur bone of a normal femur 147

8 S.K. Senapati et. al. Fig. 21Anterior view of the 3-D Pelvis model Fig. 22 Load and boundary conditions of Pelvis Now we can study the behavior, stress-strain map under different load, may be static or dynamic and study the efficacy of any fracture fixation device by using the same modeling technique. Reference : 1. Huiskes, R., Stress shielding and bone resorption in THA; Clinical versus computer simulation studies, Acta Orthopaedica, Belgica. 2. Huiskes, R., Validation of the adaptive bone remodeling simulation models. In: Lowet, G. et al. (Eds), Bone Research in Biomechanics, IOS Press, Amesterdam, Harkess, J. W., Arthroplasty of Hip, Campbell's Operatives Orthopaedics, Edited by A. H. Crenshaw, 8th Edition, Chapter Harris, W. H., The 1st 32 years of total hip arthroplasty, Clinical Orthopaedic Related Research 274, Hedia, H S., Barton,D. C., Fisher, J., Elmidany, T. T., 1996, A method for shape optimization of a hip prosthesis to maximize fatigue strength of cement. Medical Engineering Physics 18, Huiskes, R., Bocklagen, R., Mathematical shape optimization of hip prosthesis design, Journal Biomechanics,22, Charnley, J., Acrylic Cement in Orthopaedic Surgery, E and S Living stone; Edinberg and London.Pal, S., Debnath, U. K., Development of human joint prosthesis and its cementless fixation with bone, National and international status,, published by School of Biosc. & Engg. Jadavpur University. 7. Roy, S., Pal, S., Development of polymer ceramic composite used as metal substitute implantable biomaterials, Bulletin of Material Science, 25(7),