A novel quantitative measure of breast curvature based on catenary

Interfacial Curvature as a Potential Index for Prognosis of Colon Adenocarcinoma

Tumor invasion and metastasis are complex interfacial mechanical processes between the tumor and its surrounding tissue, with the interfacial curvature of tumor playing an important role in cancer progression. In this study, the potential role of interfacial curvature in the prognosis of patients with colon adenocarcinoma is investigated. The front edge interfacial curvature of adenocarcinoma from biopsies of patients in different tumor, lymph node, and metastasis (TNM) stages are calculated and compared, and prognosis assessment is conducted using Kaplan-Meier and Cox proportional hazards regression analyses. Results reveal that patients with larger interfacial curvature of adenocarcinoma are more likely to belong to higher TNM stages. Concomitantly, in the same TNM stage, patients with increased adenocarcinoma interfacial curvature show worse prognosis with higher recurrence and lower survival rates. Besides, interfacial curvature is an independent prognostic factor for cause-specific survival and relapse-free survival among all selected patients. Mechanical models of colon adenocarcinoma invasion and metastasis are established to better understand the close association between interfacial curvature and tumor progression. The results together with hematoxylin and eosin staining indicate that metastasis in stages T3N0M0 and T3N1M0 may be linked to large interfacial curvatures. Therefore, interfacial curvature may serve as a potential index for predicting prognosis in patients with colon adenocarcinoma.

Breast Shape Analysis With Curvature Estimates and Principal Component Analysis for Cosmetic and Reconstructive Breast Surgery

Background

Breast shape is defined utilizing mainly qualitative assessment (full, flat, ptotic) or estimates, such as volume or distances between reference points, that cannot describe it reliably.

Objectives

The authors quantitatively described breast shape with two parameters derived from a statistical methodology denominated by principal component analysis (PCA).

Methods

The authors created a heterogeneous dataset of breast shapes acquired with a commercial infrared 3-dimensional scanner on which PCA was performed. The authors plotted on a Cartesian plane the two highest values of PCA for each breast (principal components 1 and 2). Testing of the methodology on a preoperative and posttreatment surgical case and test-retest was performed by two operators.

Results

The first two principal components derived from PCA characterize the shape of the breast included in the dataset. The test-retest demonstrated that different operators obtain very similar values of PCA. The system is also able to identify major changes in the preoperative and posttreatment stages of a two-stage reconstruction. Even minor changes were correctly detected by the system.

Conclusions

This methodology can reliably describe the shape of a breast. An expert operator and a newly trained operator can reach similar results in a test/re-testing validation. Once developed and after further validation, this methodology could be employed as a good tool for outcome evaluation, auditing, and benchmarking.

Level of Evidence 4

Toward 7T breast MRI clinical study: safety assessment using simulation of heterogeneous breast models in RF exposure

PURPOSE

To facilitate assessment of RF power deposition and temperature rise within the breast, we present a method to seamlessly join heterogeneous breast models with standard whole-body models and demonstrate simulations at 7 T.

METHODS

Finite-difference time-domain electromagnetic and bioheat simulations are performed to analyze the specific absorption rate (SAR) and temperature rise distributions in 36 Breast Imaging Reporting and Data System (BI-RADS) categorized breast models fused to 2 female whole-body models while transmitting from a 7T breast volume coil. The breast models are uncompressed in the prone position and feature heterogeneous tissue contents; fusion with human models uses affine transformation and the level-set method.

RESULTS

The fusion method produces a continuous transient from the chest region to the posterior portion of breast models while preserving the original volume and shape of breast models. Simulation results of both Ella and Hanako models indicate that the maximum local SAR, partial body SAR, and local tissue temperature rise are positively correlated with both breast density and the highest BI-RADS density classification. Additionally, maximum local tissue temperature rise is positively correlated with maximum 10-g SAR values.

CONCLUSION

Fibroglandular tissue content plays an important role in the distribution of SAR and temperature rise within breast tissue. The combined body-breast models preserve the integrity of breast models while concurrently exhibiting the loading of whole-body human models. The procedures presented in this simulation study facilitate safety assessments for breast MRI across the population at both clinical and ultrahigh field strengths.

Inferior Breast-Chest Contour Detection in 3-D Images of the Female Torso

Stereophotogrammetry is finding increased use in clinical breast surgery, both for breast reconstruction after oncological procedures and cosmetic augmentation and reduction. The ability to visualize and quantify morphological features of the breast facilitates pre-operative planning and post-operative outcome assessment. The contour outlining the lower half of the breast is important for the quantitative assessment of breast aesthetics. Based on this inferior breast contour, relevant morphological measures, such as breast symmetry, volume, and ptosis, can be determined. In this paper, we present an approach for automatically detecting the inferior contour of the breast in 3D images. Our approach employs surface curvature analysis and is able to detect the breast contour with high accuracy, achieving an average error of 1.64 mm and a dice coefficient in the range of 0.72–0.87 when compared with the manually annotated contour (ground truth). In addition, the detected contour is used to facilitate the detection of the lowest visible point on the breast, which is an important landmark for breast morphometric analysis.

Closed Shortest Path in the Original Coordinates with an Application to Breast Cancer

Breast cancer is one of the most mediated malignant diseases, because of its high incidence and prevalence, but principally due to its physical and psychological invasiveness. The study of this disease using computer science tools resorts often to the image segmentation operation. Image segmentation, although having been extensively studied, is still an open problem. Shortest path algorithms are extensively used to tackle this problem. There are, however, applications where the starting and ending positions of the shortest path need to be constrained, defining a closed contour enclosing a previously detected seed. Mass and calcification segmentation in mammograms and areola segmentation in digital images are two particular examples of interest within the field of breast cancer research. Usually the closed contour computation is addressed by transforming the image into polar coordinates, where the closed contour is transformed into an open contour between two opposite margins. In this work, after illustrating some of the limitations of this approach, we show how to compute the closed contour in the original coordinate space. After defining a directed acyclic graph appropriate for this task, we address the main difficulty in operating in the original coordinate space. Since small paths collapsing in the seed point are naturally favored, we modulate the cost of the edges to counterbalance this bias. A thorough evaluation is conducted with datasets from the breast cancer field. The algorithm is shown to be fast and reliable and suffers no loss in resolution.

A shape constrained parametric active contour model for breast contour detection

Quantitative measures of breast morphology can help a breast cancer survivor to understand outcomes of reconstructive surgeries. One bottleneck of quantifying breast morphology is that there are only a few reliable automation algorithms for detecting the breast contour. This study proposes a novel approach for detecting the breast contour, which is based on a parametric active contour model. In addition to employing the traditional parametric active contour model, the proposed approach enforces a mathematical shape constraint based on the catenary curve, which has been previously shown to capture the overall shape of the breast contour reliably. The mathematical shape constraint regulates the evolution of the active contour and helps the contour evolve towards the breast, while minimizing the undesired effects of other structures such as, the nipple/areola and scars. The efficacy of the proposed approach was evaluated on anterior posterior photographs of women who underwent or were scheduled for breast reconstruction surgery including autologous tissue reconstruction. The proposed algorithm shows promising results for detecting the breast contour.