Rationale and Objectives
To evaluate fractal-based computerized image analyses of mammographic parenchymal patterns in the task of differentiating between women at high risk and women at low risk for developing breast cancer.
Materials and Methods
The fractal-based texture analyses are based on a box-counting method and a Minkowski dimension, and were performed within the parenchymal regions of normal mammograms. Four approaches were evaluated: 1) a conventional box-counting method, 2) a modified box-counting technique using linear discriminant analysis (LDA), 3) a global Minkowski dimension, and 4) a modified Minkowski technique using LDA. These fractal based texture features were extracted from regions of interest to assess the mammographic parenchymal patterns of the images. Receiver operating characteristic analysis was used to evaluate the performance of these features in the task of differentiating between the two groups of women.
Results
Receiver operating characteristic analysis yielded an A z value of 0.74 based on the conventional box-counting technique and an A z value of 0.84 based on the global Minkowski dimension in the task of distinguishing between the two groups. By using LDA to assess the characteristics of mammograms, A z values of 0.90 and 0.93 were obtained in differentiating the two groups, for the modified box-counting and Minkowski techniques, respectively. Statistically significant improvement was achieved ( P < .05) with the new techniques compared to the conventional fractal analysis methods. A simulation study, which used the slope and intercept extracted from the least square fit of the experimental data with the LDA approaches, yielded A z values similar to those obtained with the conventional approaches in the task of differentiating between the two groups.
Conclusions
The proposed LDA approach improved significantly the separation between the two groups based on experimental data. Because this approach was used as a linear classifier rather than as a regression function, it combined the fractal analysis with the knowledge of the high- and low-risk patterns, and thus better characterized the multifractal nature of the parenchymal patterns. We believe that the proposed analyses based on the LDA technique to characterize mammographic parenchymal patterns may potentially yield radiographic markers for assessing breast cancer risk.
Breast cancer is the most frequently diagnosed non–skin cancer and the second leading cause of death among women living in North America. An estimated 212,920 new invasive cases, 61,980 new noninvasive cases, and 40,970 deaths are anticipated from breast cancer for the year 2006 in the United States ( ). Several studies show that mammography is the most valuable imaging technique for early detection of breast cancer ( ). The decrease in breast cancer mortality has been largely attributed to the regular use of screening mammography ( ). In addition, women who inherit susceptibility genes, BRCA1 or BRCA2, face a 35%–87% lifetime risk of developing breast cancer ( ). These deleteriously mutated genes account for approximately 5%–10% of all breast cancer cases ( ). Correct and precise estimates of cancer risks associated with these gene mutation carriers are expected to be relevant to screening, early cancer detection, chemoprevention, and risk reduction surgery.
Mammographic parenchymal patterns have been extensively studied for several decades. Visual assessment of such patterns has been performed using Wolfe patterns, which classify the mammographic parenchyma into N1, P1, P2, and DY categories according to the relationship between the prominent duct pattern and breast cancer risk ( ). Breast Imaging Reporting and Data System notation has also been recommended by the American College of Radiology to relate breast density with risk ( ). Because of large variability in the visual assessment in risk estimation, semiquantitative, and quantitative methods have been introduced to characterize mammographic density and their association with breast cancer risks ( ). Computerized texture features that are used to quantify the density and texture of the breast have been also investigated and related to the breast cancer risk ( ). Such studies have shown that there is an increased risk of developing breast cancer associated with increased mammographic density ( ).
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Materials and methods
Database
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Fractal-Based Computer-Extracted Features
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DM(f)=limr→0log[Vg(r)/r3]log[1/r], D
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Vg(r)=∑256i=1∑256j=1{(f⊕rg)−(f⊗rg)}, V
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Performance Evaluation and Statistical Analysis
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Results
Correlation Between the Fractal-Based Features
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Performance of the Fractal-Based Features
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Table 1
Performance of Fractal-Based Computer-Extracted Features in Differentiating Between BRCA1/BRCA2 Gene-Mutation Carriers and Low-Risk Cases in Terms of A z
LDA: linear discriminant analysis.
\* P value is calculated with Z -score test and used to indicate the significance of the difference in terms of A z between fractal feature extracted using the conventional method and fractal feature extracted using the LDA method.
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Discussion
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Table 2
Performance of Fractal-Based Computer-Extracted Features in Differentiating Between BRCA1/BRCA2 Gene-Mutation Carriers and Low-Risk Cases in Terms of A z with Both Experimental and Simulation Data
LDA: linear discriminant analysis.
\* P value is calculated with Z -score test and used to indicate the significance of the difference in terms of A z between fractal feature extracted using the conventional method and fractal feature extracted using the LDA method.
Bold face type indicates results were generated using simulation data.
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Conclusion
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Acknowledgments
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