Statistical Modeling of Breast Shape from 3-Dimensional Surface Imaging

Introduction: : Three-dimensional (3D) surface imaging is increasingly applied in reconstructive breast surgery to support surgical planning, customization, and outcome assessment. However, its clinical utility remains limited by the absence of advanced tools for accurate breast shape simulation [1–3]. Existing commercial simulation tools are primarily designed for cosmetic procedures and lack applicability in reconstructive contexts. Approaches using biomechanical modeling face significant limitations due to high computational demands and the need for biological tissue samples to determine biomechanical characteristics of the breast. Statistical models based on 3D surface imaging offer a promising alternative, but current studies are limited and often include the entire torso rather than isolating the breast morphology [4–6]

Here, we present the development and validation of a novel shape simulation tool designed to enhance the clinical application of 3D imaging in breast reconstruction. The key contributions of this work are: (i) the development of a curated dataset of 3D breast surface images, (ii) the application of statistical shape modeling and simulation using spherical harmonics (SPHARM) [7] and active shape modeling (ASM) [8], and (iii) a clinical utility study demonstrating the relevance and potential impact of the simulation tool in reconstructive practice.

Materials and

Methods: : A dataset of 334 3D breast images was used to construct a statistical shape model. The dataset included natural breasts, reconstructed breasts (implant-based and autologous), and intermediate reconstruction stages, such as tissue expanders. An independent test set of 364 images was used for model evaluation. All images were acquired at The University of Texas MD Anderson Cancer Center under IRB-approved protocols with informed consent.

Each 3D breast surface was parameterized using SPHARM [7], a set of orthogonal basis functions defined on a unit sphere. SPHARM modeling provides a compact representation of closed 3D surfaces via linear combinations of these basis functions. SPHARM descriptors [9] extracted from the 334 training images were used to construct a statistical shape model using Active Shape Modeling [8]. ASM captures the average shape and the directions of variations across the dataset. These directions of variations are called principal components (PC) or eigenvectors. Modifying the weights along these PCs or eigenvectors enables simulation of new breast shapes based on an initial configuration, facilitating modeling of postoperative shape outcomes.

A utility study was conducted to assess the clinical relevance of the simulation tool. Ten board-certified plastic surgeons were recruited and provided with a demonstration of the shape simulation interface. Feedback was collected via a structured Likert-scale questionnaire. Nine of the ten participants completed the survey.

Results, Conclusions, and Discussions:: Model performance was assessed using two metrics: (i) root mean squared distance (RMSD) between the original and ASM-reconstructed SPHARM descriptors, and (ii) Hausdorff distance (HD) between the original and reconstructed 3D surface vertices. As seen in Figure 1a, the first 5, 10, 15, 20, and 23 PCs accounted for 41%, 93%, 96%, 97%, and 98% of the shape variance, respectively. Beyond 23 PCs, gains in accuracy were minimal (Figure 1b). Using 23 PCs, the average RMSD and HD on the test dataset were 2.2 and 6.3, respectively.

Specific PCs were associated with changes in breast height, width, and projection, enabling targeted shape simulation (Figure 2). The utility study revealed strong support for clinical application: all respondents (100%) "strongly agreed" on the tool’s value as a visual aid in patient consultations, and 77% "strongly agreed" on its utility in surgical planning and case discussions (Figure 3).

To conclude, we developed a statistical shape model for 3D breast morphology using SPHARM and ASM, demonstrating its accuracy and clinical relevance. Unlike traditional parametric or biomechanical models, our approach captures subtle morphological variations critical to individualized aesthetic outcomes. The utility study confirmed the tool’s potential to enhance patient communication and surgical planning. Future work will focus on integrating statistical shape modeling with biomechanical constraints to produce simulations that are both statistically plausible and physically realistic.

Acknowledgements and/or References (Optional):: Acknowledgements
This work was supported in part by funding from the NIH NCI (R01CA203984, R01 CA286648 and R41CA272122).

References

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