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TECHNICAL PAPERS: Bone/Orthopedics

# Cortical Bone Viscoelasticity and Fixation Strength of Press-Fit Femoral Stems: A Finite Element Model

[+] Author and Article Information
T. R. Shultz

National Energy Technology Laboratory, 3610 Collins Ferry Road, P.O. Box 880, MS D06, Morgantown, WV 26507-0880

J. D. Blaha

Department of Orthopedics,  University of Michigan, Ann Arbor, MI 48109

T. A. Gruen

Zonal Concepts, 31153 Shaker Circle, Wesley Chapel, FL 33543

T. L. Norman1

Department of Engineering, 251 N. Main St.,  Cedarville University, Cedarville, OH 45314tnorman@cedarville.edu

1

To whom correspondence should be addressed.

J Biomech Eng 128(1), 7-12 (May 07, 2005) (6 pages) doi:10.1115/1.2133765 History: Received July 20, 2004; Revised May 07, 2005

## Abstract

Many cementless implant designs rely upon a diaphyseal press-fit in conjunction with a porous coated implant surface to achieve primary or short term fixation, thereby constraining interface micromotion to such a level that bone ingrowth and consequent secondary or long-term fixation, i.e., osseointegration, can occur. Bone viscoelasticity, however, has been found to affect stem primary stability by reducing push-out load. In this investigation, an axisymmetric finite element model of a cylindrical stem and diaphyseal cortical bone section was created in order to parametrically evaluate the effect of bone viscoelasticity on stem push-out while controlling coefficient of friction ($μ=0.15$, 0.40, and 1.00) and stem-bone diametral interference ($δ=0.01$, 0.05, 0.10, and $0.50mm$). Based on results from a previous study, it was hypothesized that stem-bone interference (i.e., press-fit) would elicit a bone viscoelastic response which would reduce the initial fixation of the stem as measured by push-out load. Results indicate that for all examined combinations of $μ$ and $δ$, bone viscoelastic behavior reduced the push-out load by a range of 2.6–82.6% due to stress relaxation of the bone. It was found that the push-out load increased with $μ$ for each value of $δ$, but minimal increases in the push-out load (2.9–4.9%) were observed as $δ$ was increased beyond $0.10mm$. Within the range of variables reported for this study, it was concluded that bone viscoelastic behavior, namely stress relaxation, has an asymptotic affect on stem contact pressure, which reduces stem push-out load. It was also found that higher levels of coefficient of friction are beneficial to primary fixation, and that an interference “threshold” exists beyond which no additional gains in push-out load are achieved.

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## Figures

Figure 1

Axisymmetric model of the cortical bone (424 elements) and the press-fit cylindrical stem (420 elements), swept 180deg about the axis for illustration purposes. The axial load is applied uniformly to the top surface of the stem in the −2 direction. Boundary conditions at the bottom surface of the cortical bone tube restrict motion to zero in the 2 direction.

Figure 2

Push-out load as a function of diametral interference (δ), using the linear elastic and viscoelastic cortical bone models plotted for three coefficients of friction (μ). Push-out load decreased with coefficient of friction and from the viscoelastic behavior of bone.

Figure 3

Variation of contact pressure at a centrally located node (node 235) on the cortical bone—implant interface as a function of time for the three values of diametral interference δ. The maximum contact pressure value at time equal to zero corresponds the initial linear elastic value. Only the first hour of the analysis is shown for detail purposes.

Figure 4

Viscoelastic load ratio plotted against stem-bone interference for the three stem-bone coefficients of friction. The lower friction stems slip sooner after bone relaxation occurs consistent with the finding that the viscoelastic effect was lower for the high friction stems.

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