MODELLING AND OPTIMIZATION OF PHYSICAL SYSTEMS 8, pp. 113-118, Gliwice 2009 STRAIN–STRESS ANALYSIS OF THE SURFACE REPLACEMENT OF

THE HIP JOINT

PETR VOSYNEK TOMÁŠ NÁVRAT

Brno University of Technology, Institute of Solid Mechanics, Mechatronics and Biomechanics, Technicka 2896/2, 616 69 Brno, petr.vosynek@seznam.cz

Abstract. Today is the surface hip replacement very often surgery because of new studies and improvements. For young and active people it's the best way to delay implantation of a conventional total hip replacement.

The objective of this study was to perform finite-element analyses of computational model of the total surface replacement and physiological hip joint. We obtained strain-stress states from these analyses. All results were compared one another and then were confronted with results of the physiological hip joint. The three-dimensional computational model consists of these components: pelvic and femoral bone, muscles, artificial socket, and surface hip replacement. We were using FEM system ANSYS. The geometrical models of bones were generated by means of computed tomography (CT) images. The FE model of bone reflects two types of the bone tissues (trabecular and cortical bone) and muscles which are important when standing on one leg. The model of the muscle corresponds to isometric contraction. The implants material and bone tissues were modelled as isotropic linear elastic material. The model was loaded by force, corresponding to load by standing on one leg.

1. INTRODUCTION

One of the solutions of the hip joint dysfunction is surface hip replacement. This method is very useful for young active patients because we could suppose good bone quality and after surgery good integration of the implant into human body. The presumption of good bone quality is including good geometric structure of bone too (bone without cysts, dysplasia hip and osteoporosis) [1].

Hip resurfacing is one of the method which is quite new in implant surgery, therefore the surgeons needs more useful information about its behavior in human body. This information means years of collecting data about: durability of implanted hip endoprothesis itself, or in more cases: durability of surrounding bone mass of patient. Better way of testing and investigating implants is computational modeling which comes from biomechanics science which is applying engineering science on medicine problems. So one main advantage of computational modeling is, that we can simulate behavior of engineer structures or (in our case) human implant.

In this work we are investigating possibilities about implanting axis of one part of implant which can be seen in fig. 1 and fig. 2. Main goal of this investigating was comparison

114 P. VOSYNEK, T. NÁVRAT between results of different variation from computational modeling and results from practical medicine about hip resurfacing.

Fig. 1. Bones of hip joint (from left to right:

femur and pelivis bone) [2].

Fig. 2. Resurfacing implant DePuy.

2. MATERIALS AND METHODS

In introduction we are mentioned computational modeling. So what is it and what do we

need for it? Computational modeling is based on finite element method which comes from mathematical theory and in practical use we need few models of problematic system: geometric model, material model; and finally boundary conditions. All of mentioned models we can realize in software ANSYS or ANSYS Workbench, but geometric model it’s usually done by more specialized modelers like: CATIA, ProEngineer, Inventor, etc. with following import to geometric modeler of ANSYS.

2.1. Geometric model All computer modelling were started with computer tomography (CT) scans, which were completed in software RHINOCEROS and reformed into “wired” model. Where CT scans were from hip joint area and we planned to complete them to geometric model of pelvis and proximal part of femur. So this “wired” model were covered by areas and then coupled into volumetric model in software CATIA (fig. 3 and fig. 4). Parts of implant (acetabular and femoral part) were created in CATIA too.

Fig. 3. Geometric model of pelvis bone with

acetabular component.

Fig. 4. Geometric model of pelvis and femur bone with both implant

component.

STRAIN–STRESS ANALYSIS OF THE SURFACE REPLACEMENT OF THE HIP JOINT 115 2.2. Material model

For model of different structures of solved hip joint system were used material data from scientific literature; except material data of bone cement which were taken from experimental measurement. Material model were in all cases linear, isotropic and elastic. Following table 1 shows used material characteristics.

Table 1. Material characteristics.

Material model Young modulus [GPa] Poisson ratio [-] Trabecular bone 0.5 0.3 Cortical bone 14.5 0.3 Acetabular and femoral component of implant 2.1 0.3

Muscles and ligaments 1.105 0.3 Bone cement 3.4 0.3

2.3. Computational model

When we were completed geometric model and material model we were focused on mesh. Mesh is a method where geometric model are “filled” with finite elements which has specific behavior taken from material model.

After creating usefully mesh – it takes a lot of time of course – we could focus on applying boundary conditions. We were supposing standing on one leg which corresponding to load our model by force which is equal to human weight. The most problematic area of computational model was contact between femoral and acetabular component of implant. This problem was taken very much time because we were solving nonlinear computational model and for illustration one solution of one variation takes around twelve hours. So preparing computational model was not so easy like it looks like. 2.4. Variants

Because we were wanted to investigate a nine ways of implant axis of femoral component a nine computation models must be made. And two variants were done additionally. Firstly physiological variant of hip joint because we had to compare results from resurfaced hip joint variants. And secondly computational model to investigate a range of motions of resurfaced hip joint. Some variants are summarized in following picture.

116 P. VOSYNEK, T. NÁVRAT

Fig. 5. Variants of implant axis (VX_Y, X –

simulates kolodiafyzarni angle, Y – antetorsion angle.

Fig. 6. Computational model for ranges of motion.

3. RESULTS

From our investigation of hip resurfacing by computational modeling we can summarize

following points of results: 3.1. Range of motions

Motions were done in three points because hip joint has a spherical constrain between femoral and acetabular component. So we can investigate rotations about three local axes but this investigation is so strict – we were allowing in each case only one rotation! This doesn’t happen in physiological hip joint because we can’t strictly rotate the femur only in one axis. Following table 2 is summarizing results of practical medical research and computational model.

Table 2. Range of motions of the resurfaced hip joint.Motion Medical research Computational model

Flection 0° - 140° 0° - 75°

Flexction with little adduction - 0° - 138°

Extension 0° - 15° 0° - 60°

Adduction 0° - 45° 0° - 50°

Abduction 0° - 30° 0° - 70°

STRAIN–STRESS ANALYSIS OF THE SURFACE REPLACEMENT OF THE HIP JOINT 117 3.2. Strain – stress distribution in femur

We wanted to compare physiological and resurfaced hip joint by computational modeling. So the best way to demonstrate the result is to show them in pictures which are showing stress distribution where normal axis of stress is the same with implant axis. With this presumption we are looking on bending stress.

Fig. 7. Physiological variant of hip joint stress

distribution.

Fig. 8. Variant of resurfaced hip joint (V135_10) of hip joint stress

distribution. And when we are put some numerous from pictures into graph trough path shown next to graph, we can quantitative stress distribution by following graph.

Fig. 9. Stress distribution trough path shown on the right top site of the figure.

118 P. VOSYNEK, T. NÁVRAT 4. CONCLUSION

From this work we can summarize following points of conclusion: ‐  Nine variants of computational model of human hip joint with applied endoprothesis

were created. Where we were simulate different implant axis of femoral implant. ‐  Ranges of motions investigation were done on model of resurfaced hip joint

(impingement symptom). ‐  Experimental measurement of Young modulus of bone cement was done. ‐  Strain-stress analysis and comparison analysis were done with following conclusion:

o Stress distribution of resurfaced hip joint is close to stress distribution of physiological hip joint except places with concentration of stresses because of drilling bone mass. Where this conclusion were mentioned in medical literature too.

o Given results were compared with practical medical research and we could say that computational model can predict behavior of implant in human body of course with some presumption.

REFERENCES

1. Vosynek, P.: Strain-stress analysis of the surface replacement of the hip joint. Brno

University of Technology, Institute of Solid Mechanics, Mechatronics and Biomechanics, 2008.

2. Čihák, R.: Anatomie 1, druhé vydání, 2001.

DEFORMAČNĚ NAPĚŤOVÁ ANALÝZA POVRCHOVÉ NÁHRADY KYČELNÍHO KLOUBU

Summary. Cílem této práce bylo určit deformačně-napěťové stavy v kyčelním

kloubu s aplikovanou totální povrchovou náhradou pro různá ustavení femorální komponenty vůči stehenní kosti a srovnat je s deformačně-napěťovými stavy zjištěnými u fyziologického kloubu. Řešená soustava se skládá z křížové, pánevní, stehenní kosti, svalů, umělé jamky a femorální komponenty. Výpočty byly provedeny v konečnoprvkovém systému ANSYS. Geometrický model kostí byl vytvořen pomocí řezů získaných z počítačové tomografie. Zatížení odpovídá stoji na jedné dolní končetině. V práci je prezentována srovnávací analýza a výsledky deformačně-napěťových analýz, z nichž vyplývá celá řada velmi zajímavých poznatků.