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TECHNICAL PAPERS: Bone/Orthopedic

# Acetabular Cup Geometry and Bone-Implant Interference have More Influence on Initial Periprosthetic Joint Space than Joint Loading and Surgical Cup Insertion

[+] Author and Article Information
Kevin L. Ong1

Exponent, 3401 Market St., Suite 300, Philadelphia, PA 19104kong@exponent.com

Jeffrey Lehman, William I. Notz, Thomas J. Santner

Department of Statistics,  Ohio State University, Columbus, OH 43210

Donald L. Bartel

Sibley School of Mechanical & Aerospace Engineering,  Cornell University, Ithaca, NY 14853

1

Corresponding author.

J Biomech Eng 128(2), 169-175 (Nov 05, 2005) (7 pages) doi:10.1115/1.2165701 History: Received July 14, 2003; Revised November 05, 2005

## Abstract

Environmental variations in patient-dependent and surgical factors were modeled using robust optimization with a finite element acetabular cup-pelvis model. A previously developed statistical optimization scheme was used to: (1) determine the cup geometry and the optimal cup-bone interference that maximized bone-implant contact areas and minimized changes in the gap volume between the implant and bone surface during gait loading and unloading; and (2) determine the relative contributions of design, patient-dependent, and surgical factors to variations in bone-implant contact areas and a change in gap volume. The statistical analyses indicated that the design variables, namely the equatorial diameter and eccentricity, explained most of the variations in the performance measures. Further, the hemispherical designs performed better than the nonhemispherical designs. The $58mm$ hemispherical cup, with $2mm$ diametral interferences, minimized the change in gap volume and attained 82% and 81% of the maximum predicted total and rim contact areas, respectively. The equatorial diameter and eccentricity, not the patient-dependent and surgical factors, explained most of the variations in the performance measures. Perfect surface apposition was not attained with any of the cup designs.

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## Figures

Figure 1

3-D FE model of the cadaver pelvis (left) including superelements at the ischiopubic ramus and iliac crest (shaded in gray). Spatial distribution of bone moduli (right) in the acetabulum (view from the polar direction). 64% of the bone elements in the acetabulum had moduli of less than 1GPa and 79% less than 2GPa (SUP: superior; INF: inferior; ANT: anterior; POS: posterior).

Figure 2

Schematic of design (left) and environmental (center and right) variable descriptors. Left: cup equatorial diameter (2×re) and eccentricity (2×re−2×rp); center: cup penetration, p, as the acetabular dome is displaced during cup insertion; right: load magnitude, F, and polar direction, θ, during peak gait load application.

Figure 3

Predicted mean change in gap volume (left), mean rim contact area (middle), and mean total contact area (right) averaged over the distribution of environmental variables. The minimum change in gap volume occurred with a cup design of 58mm equatorial diameter and zero eccentricity, i.e., a 58mm hemispherical cup with 2mm equatorial and polar interferences. The maximum rim contact area was predicted for the 56mm hemispherical cup. Rim contact area was relatively insensitive to eccentricity, except for an equatorial diameter of 56mm. The maximum mean contact area was predicted for the 56mm hemispherical cup. The total contact areas decreased when the equatorial diameter or eccentricity increased.

Figure 4

Spatial distribution of gaps at the end of the loading history for Model 11 (Stage 1). Views from the polar (left) and superior (right) directions are shown. Most of the gaps were located primarily around the dome region as well as sporadically around the acetabular periphery. Some of these peripheral gaps were found at the inferior edge of acetabular rim in the Zone III region (SUP: superior; INF: inferior; ANT: anterior; POS: posterior).

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