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1.  A Novel Quantitative Measure of Breast Curvature Based on Catenary 
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.
doi:10.1109/TBME.2012.2184541
PMCID: PMC3334380  PMID: 22271826
Breast cancer; breast curvature; breast reconstruction; catenary; digital photographs
2.  3D Symmetry Measure Invariant to Subject Pose During Image Acquisition 
In this study we evaluate the influence of subject pose during image acquisition on quantitative analysis of breast morphology. Three (3D) and two-dimensional (2D) images of the torso of 12 female subjects in two different poses; (1) hands-on-hip (HH) and (2) hands-down (HD) were obtained. In order to quantify the effect of pose, we introduce a new measure; the 3D pBRA (Percentage Breast Retraction Assessment) index, and validate its use against the 2D pBRA index. Our data suggests that the 3D pBRA index is linearly correlated with the 2D counterpart for both of the poses, and is independent of the localization of fiducial points within a tolerance limit of 7 mm. The quantitative assessment of 3D asymmetry was found to be invariant of subject pose. This study further corroborates the advantages of 3D stereophotogrammetry over 2D photography. Problems with pose that are inherent in 2D photographs are avoided and fiducial point identification is made easier by being able to panoramically rotate the 3D surface enabling views from any desired angle.
doi:10.4137/BCBCR.S7140
PMCID: PMC3140267  PMID: 21792310
three-dimensional; stereophotogrammetry; subject pose; validation; breast; symmetry; surgical planning; pBRA
3.  Validation of Stereophotogrammetry of the Human Torso 
The objective of this study was to determine if measurements of breast morphology computed from three-dimensional (3D) stereophotogrammetry are equivalent to traditional anthropometric measurements obtained directly on a subject using a tape measure. 3D torso images of 23 women ranged in age from 36 to 63 who underwent or were scheduled for breast reconstruction surgery were obtained using a 3dMD torso system (3Q Technologies Inc., Atlanta, GA). Two different types (contoured and line-of-sight distances) of a total of nine distances were computed from 3D images of each participant. Each participant was photographed twice, first without fiducial points marked (referred to as unmarked image) and second with fiducial points marked prior to imaging (referred to as marked image). Stereophotogrammetry was compared to traditional direct anthropometry, in which measurements were taken with a tape measure on participants. Three statistical analyses were used to evaluate the agreement between stereophotogrammetry and direct anthropometry. Seven out of nine distances showed excellent agreement between stereophotogrammetry and direct anthropometry (both marked and unmarked images). In addition, stereophotogrammetry from the unmarked image was equivalent to that of the marked image (both line-of-sight and contoured distances). A lower level of agreement was observed for some measures because of difficulty in localizing more vaguely defined fiducial points, such as lowest visible point of breast mound, and inability of the imaging system in capturing areas obscured by the breast, such as the inframammary fold. Stereophotogrammetry from 3D images obtained from the 3dMD torso system is effective for quantifying breast morphology. Tools for surgical planning and evaluation based on stereophotogrammetry have the potential to improve breast surgery outcomes.
doi:10.4137/BCBCR.S6352
PMCID: PMC3076012  PMID: 21494398
three-dimensional; anthropometry; validation; breast; photogrammetry; stereophotogrammetry; surgical planning
4.  Analysis of Breast Contour using Rotated Catenary 
Surgical reconstruction of natural-appearing breasts is a challenging task. Currently, surgical planning is limited to the surgeon’s subjective assessment of breast morphology. Therefore, it is useful to develop objective measurements of breast contour. In this paper, a novel quantitative measure of the breast contour based on catenary theory is introduced. A catenary curve is fitted on the breast contour (lateral and inferior) and the key parameter determining the shape of the curve is extracted. The new catenary analysis was applied to pre- and post-operative clinical photographs of women who underwent tissue expander/implant (TE/Implant) reconstruction. A logistic regression model was developed to predict the probability that the observed contour is that of a TE/Implant reconstruction from the catenary parameter, patient age, and patient body mass index. It was demonstrated that the parameters contain useful information for distinguishing TE/Implant reconstructed breasts from pre-operative breasts.
PMCID: PMC3041438  PMID: 21347015

Results 1-4 (4)