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Research Papers

# Robust Design for Acetabular Cup Stability Accounting for Patient and Surgical Variability

[+] Author and Article Information
Kevin L. Ong1

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

Thomas J. Santner

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

Donald L. Bartel

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

1

Corresponding author.

J Biomech Eng 130(3), 031001 (Apr 21, 2008) (11 pages) doi:10.1115/1.2907764 History: Received January 25, 2007; Revised January 16, 2008; Published April 21, 2008

## Abstract

The stability of cementless acetabular cups depends on a close fit between the components and reamed acetabular cavities to promote bone ingrowth. Cup performance and stability are affected by both design and environmental (patient-dependent and surgical) factors. This study used a statistically based metamodel to determine the relative influences of design and environmental factors on acetabular cup stability by incorporating a comprehensive set of patient-dependent and surgical variables. Cup designs with $2mm$ or $3mm$ intended equatorial bone-implant interferences appeared to perform the best, improving implant stability with smaller mean and variability in cup relative motions and greater mean and smaller variability in ingrowth areas. Cup eccentricity was found to have no effect on implant performance. Design variables did not contribute as much to the variation in performance measures compared to the environmental variables, except for potential ingrowth areas.

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## Figures

Figure 1

Panel (a): Nominal statistical density-modulus relation (E¯i) derived from (37) and (4). W identified a ρ‐E relation within the upper (E¯i+) and lower (E¯i−) bounds for assigning material properties in the FE model. Panel (b): Nominal reaming deviations at the equator (δe,a) and pole (δp,a) of the acetabulum to represent variations in reamed acetabular geometry. Panel (c): Schematic of radial reaming deviations in the transverse (left) and cross-sectional (right) planes. The deviations periodically varied about the nominal least-squares-fit surface (dashed lines) whose frequencies were controlled by ω1 and ω2. For a given transverse slice in the plane parallel to the equator (α fixed), the peak deviation was constant within that slice. For each cross-sectional slice through the pole and in the plane perpendicular to the equator (θ fixed), the peak deviations exponentially decreased as they progressed to the pole.

Figure 2

For each cup design, the estimated mean: (1) change in gap volume (upper-left panel), final gap volume (upper-right panel), cup relative motion (lower-left panel), and potential ingrowth area (lower-right panel)

Figure 3

For each cup design, 95th percentile of the change in gap volume (upper-left panel), final gap volume (upper-right panel), and cup relative motion (lower-left panel); and 5th percentile of the potential ingrowth area (lower-right panel)

Figure 4

The predicted mean (left panel) and 5th percentile (right panel) ingrowth areas, for high stiffness (W=1) under-, average-, and overweight patients with Fg=2.2 (yellow∕light), 3.7 (orange∕gray), and 5.5 (blue∕dark) BW, respectively. These responses were similar for the three weight groups.

Figure 5

For the average-weight group (Fg=3.7BW), the percent difference of the low (W=0) and high (W=1) stiffness subgroups of the predicted means (left panels) and 95th percentile (right panels; 5th percentile for ingrowth area) for the change in gap volume (top row), final gap volume (second row), cup relative motion (third row), and potential ingrowth area (bottom row)

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