Quantitative, objective measurements of breast curvature computed from clinical photographs could be used to investigate factors that impact reconstruction and facilitate surgical planning. This paper introduces a novel quantitative measure of breast curvature based on catenary. A catenary curve is used to approximate the overall curvature of the breast contour, and the curvature measure is extracted from the catenary curve. The catenary curve was verified by comparing its length, the area enclosed by the curve, and the curvature measure from the catenary curve to those from manual tracings of the breast contour. The evaluation of the proposed analysis employed untreated and postoperative clinical photographs of women who were undergoing tissue expander/implant (TE/Implant) reconstruction. Logistic regression models were developed to distinguish between the curvature of breasts undergoing TE/Implant reconstruction and that of untreated breasts based on the curvature measure and patient variables (age and body mass index). The relationships between the curvature measures of untreated breasts and patient variables were also investigated. The catenary curve approximates breast curvature reliably. The curvature measure contains useful information for quantifying the curvature differences between breasts undergoing TE/Implant reconstruction and untreated breasts, and identifying the effect of patient variables on the breast shape.
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