AMERICAN SOCIETY OF BIOMECHANICS Presented at the Twenty-First Annual Meeting of the American Society of Biomechanics Clemson University, South Carolina September 24-27, 1997

INTRODUCTION

Osseocompatibility tests usually involve the implantation of cylindrical "plugs" transcortically into the long bones of test animals. After a specified period of implantation, the implants are retrieved and the bone/implant interface is assessed either histologically or mechanically. However, using this test method, different studies have obtained contradictory results when evaluating essentially the same material. One factor that influences the results of the test is bone remodeling around the implant, which in turn is influenced by the strain state in bone surrounding the implant [1]. Therefore, the objective of this study was to develop a finite element (FE) model to predict the stress and strain states in bone around a transcortical implant.

REVIEW AND THEORY

Adaptive bone remodeling occurs when bone is strained differently from its natural state. Thus, any variable that affects the strain state will affect remodeling around the implant and may also affect the results of a transcortical test. A previous study using a simplified mathematical analysis suggested that the strains around transcortical implants may vary with position around the implant, location of the implant along long axis of the bone, implant stiffness and bone/implant interface conditions [2]. A later experiment showed that the results evaluated using the push out tests vary with location of the implant [3]. However a FE model of the intact caprine femur predicted that strains in bone do not vary with location in the region in which implants are normally placed [4]. Relatively few studies have measured strains in vivo near a transcortical implant [5,6]. However, due to large animal to animal variations these studies have not been able to show statistically significant differences with implant location and modulus.

These previous studies have given us a good insight into the problem. However the previous models used several idealizations and the in vivo measurements were limited to a few locations and orientations. Therefore, to overcome some of these limitations we decided to use the FE method to predict the stress (or strain) state in bone surrounding implants of different moduli and different bone/implant interface conditions.

PROCEDURES

Since the lateral side of a goat femur is consistently under uniaxial tension [4] and the region of implantation is relatively flat, bone was considered as orthotropic square plate under uniaxial tensile loading and implant was inserted into the center of the plate. Due to symmetry, only one quarter of the model was built (Figure1). Two different implant materials (UHMWPE and Ti6Al4V, Table 1) and three interface cases were investigated: Case 1 was based on the most ideal case in which the transcortical implant was assumed to be perfectly bonded to the surrounding bone; Case 2 accounted for the partial debonding that inevitably occurs between the implant and the bone if complete adhesion has not been achieved; Case 3 determined the effect that a press fit implant has on the magnitude of the stresses at the bone/implant interface. In this case, the radius of implant was assumed to be 4% larger than the radius of the hole.

RESULTS AND DISCUSSION

Figures 2, 3 and 4 depict the radial stresses at the bone/ implant interface at different positions around implant in the three cases. q denotes the angle to the long axis of the bone and b denotes the debonding angle. As expected, radial stresses are highest when q=0 and decrease as q increase. Further the larger the modulus of the implant, the higher the radial stress at interface. In the perfect bond case, the interface is consistently under radial tension at any orientation around implant though this tension decreases with q. In the partial debonding case, stresses are singular at q=b (i.e., at the debonding crack tip), but then decrease sharply with q. The oversized implant induces high compressive interfacial stresses, which increase dramatically with modulus of the implant.

Our model has predicted the initial stresses in bone near transcortical implants for different interfacial conditions. The results illustrate that the dynamic nature of the interface between implant and bone will cause a large variation in stresses over time. Further, the modulus of the implant and the amount of press fit also play a role in stress perturbations. This suggests that these factors may play an important role in the influencing the results of a trancortical implant test.

	E1 ( GPa )	E2 ( GPa )	n12	G12 ( GPa )
Bone	20.0	10.0	0.200	5.50
UHMWPE	1.40	----	0.300	0.54
Ti6Ai4V	100.7	----	0.361	37.0

Table 1. Material Properties. (The "1" direction is along the long axis of the bone)

Figure 1. Schematic Diagram of the FE Model. (The FE mesh has been omitted for clarity)

Figure 2. Radial Stresses at the Interface of a Perfectly Bonded Implant

Figure 3. Radial Stresses at the Interface of a Partially Debonded Implant

Figure 4. Radial Stresses at the Interface of a Press Fit Implant

REFERENCES

1. J. Wolff. Law of bone remodeling, Berlin (1892)

2. V.M.Gharpuray et al, J.Biomed. Mater. Res.

3. J.E.Dalton and S.D.Cook, J. Biomed. Mater. Res., 29, 133-6 (1995)

4. S.Zyblewski, Thesis, Clemson Univ. (1995)

5. M. J. Hiatt, Thesis, Clemson Univ. (1996)

6. Yi-Xian Qin et al, J. Orthop. Res., 14: 862-70 (1996)

ACKNOWLEDGMENTS

NIH GRANT 1-R15-AR-42726