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TECHNICAL BRIEFS

# A New Methodology to Determine the Anatomical Center and Radius of Curved Joint Surfaces

[+] Author and Article Information
Dominik C. Meyer

Department of Orthopaedics, University of Zürich, Balgrist, Forchstr. 340, 8008 Zürich, Switzerlanddominik.meyer@balgrist.ch

Norman Espinosa, Peter P. Koch

Department of Orthopaedics, University of Zürich, Balgrist, Forchstr. 340, 8008 Zürich, Switzerland

Urs Lang

Department of Mathematics, ETH Zentrum, 8092 Zürich, Switzerland

J. Med. Devices 1(2), 173-175 (Aug 27, 2006) (3 pages) doi:10.1115/1.2735973 History: Received January 13, 2006; Revised August 27, 2006

## Abstract

This study describes a mechanical tool which allows us to determine the radius and center of curved joint surfaces both intraoperatively and in vitro. The tool is composed of longitudinal parallel hinges, connected with cross bars on one end. In the middle of each cross bar, one needle is attached at an angle of $90deg$ to both the hinges and the cross bars. When the parallel hinges are held against a curved surface, they will adapt to the curvature and the needles on the cross bars will cross each other. The crossing point of two needles represents the mean center of the curvature within the plane spanned by the needles. The radius is the distance between the center of curvature and the joint surface. The proposed tool and method allow us to determine the mean center of convex or concave curvatures, which often represent the isometric point of a corresponding curved joint surface. Knowing the radius and center of curvature may facilitate various surgical procedures such as collateral or cruciate ligament reconstruction. Appropriate adaptations of the tool appear to be a useful basis for biomechanical and anatomical joint analyses in the laboratory.

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## Figures

Figure 5

Intraoperative use: The tool is applied to the anterior aspect of an exposed left distal femur. The lateral condyle is visible, and the hinges are in simultaneous contact with the medial (hidden under surgeon’s glove) and lateral condyles. The proximal arc between points “B” and “E” appears to be nearly circular, while more distally, the radius increases and the center of the curve between “A” and C” is more proximal.

Figure 1

View of the tool on a flat surface: The mutually parallel hinges “h” are connected with cross bars “cb.” To the middle of each cross bar, an orthogonal needle “n” is attached.

Figure 2

View of the tool on a circular surface: The cross bars “cb” represent secants to the circular surface, the needles “n” cross each other in the center of curvature “Z” (arrow). For this, the hinges must be parallel to the cylinder axis.

Figure 3

Geometrical principle: the two connecting lines between the points “A”, “B” and “C” represent secants to the circle. In the middle of each secant, an orthogonal line is drawn, corresponding to the needles in Fig. 2. The intersection of the two lines (needles) represents the center of curvature “Z.” The radius of the circle represents the distance between “Z” and any of the points A, B, C.

Figure 4

On a curvature with variable radius as the depicted ellipse, “Z1” represents the mean center of curvature between the points “A” and “C,” “Z2,” the mean center of the arc between “B” and “D,” etc. A connection between the points “Z1” and “Z4” approximates the line on which the centers of curvature of the ellipse are aligned.

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