Computer-aided diagnosis system based on fuzzy logic for breast cancer categorization
Introduction
Due to the increasing of the amount of digital medical images produced recently, the activities related to acquisition, management and availability of these images have required efforts of researchers and professionals involved in these processes to study and propose computational methods that provide effective support to daily tasks related to image-based diagnosis. Databases containing patient information as well as clinical data have become usual in healthcare environments. Machine learning and data representation techniques allow us to develop tools for computer-aided diagnosis (CAD) [1], [2], [3], which have been shown to improve the quality of the tasks performed by radiologists [4] and thereby the performance of radiological diagnosis [5].
Methods for CAD usually face a significant obstacle: the so-called semantic gap, which is characterized by the divergence between the results of automated methods and the results expected by users, due to the difficulties of these methods to represent real situations [6], [7]. However, regardless of dealing with a specific context, a purely numeric representation of an image attribute is itself a semantic gap, since it is relatively distant from how the human analyst interprets the image. When analyzing the shape of a breast nodule, the diagnosis is generated in natural language, for example slightly irregular contour. In this case, it is very difficult to set a numeric descriptor for the contour that fits the user׳s semantics. So, we decided to use fuzzy concepts in this context. The concepts of fuzzy logic are designed to handle this kind of situation and can be used to simulate human reasoning in decision support systems [8]. Fuzzy sets handle the separation between classes, commonly limited by ranges of numeric values, by membership grades, replacing abrupt transitions. This approach is suitable to situations in which the boundary between the sets is not well delineated, e.g., the assessment performed by a human being. Fuzzy methods can approach objective knowledge (represented by numerical data) and subjective knowledge (represented by linguistic terms).
The Breast Imaging Reporting and Data System (BI-RADS) standard was developed in collaboration with members and committees of the American College of Radiology (ACR) to guide radiologists and physicians in the evaluation of breast nodules and calcifications [9]. This system aims to unify the terminology used in mammography exams, the categories of findings and their appropriate treatment [10]. The use of the BI-RADS lexicon is highly recommended in the decision-making process as it follows a natural language structure: “if the nodule is round, has well-defined margins and low density, it is more likely to be classified as benign”. This kind of structure can be properly modeled through fuzzy sets. Fuzzy logic is also suitable to represent the divergence between radiologists. In clinical practice, the same image can be analyzed in different ways by each expert. Fuzzy inference models can encompass inter- and intra-observer variations.
In related works, some approaches have been proposed using fuzzy logic to assist the diagnosis of breast lesions. In Ref. [11] the authors present a method to distinguish lobulated contours from microlobulated ones. They created membership functions to represent features, such as the number of contour undulations and its size, and in Ref. [12] the authors implemented a fuzzy rule-based method aiming to characterize the shape of nodules in mammograms. In Ref. [13], three distinct regions in mammograms are compared: regions containing tumors; regions containing calcifications and regions containing no injuries. The authors proposed a fuzzy inference system based on the intensity of the pixels of these three regions, inferring the type of lesion (tumor or calcification) or the absence of lesion. In contrast, the methodology used in our project, in addition to treating attributes as fuzzy sets, also provides a fuzzy output, generating a quantitative response which is standardized by the BI-RADS system.
Fuzzy logic is also applied in Ref. [14], which presents an iterative segmentation algorithm to automatically identify regions of interest (ROIs) from nodules considering the breast tissue density and applying a fuzzy classifier for diagnosis. Concerning breast cancer treatment, Garibaldi et al. [15] present a method based on non-stationary fuzzy sets to model the need of recommendation of post-operative treatment considering clinical variables as attributes. This approach yielded better results when compared to standard fuzzy inference systems.
Another applications to support medical diagnosis can be found in Ref. [16] to help the analysis of malformations of the cerebral cortex. The input variables are based on the expert׳s knowledge. In Refs. [17], [18], fuzzy cognitive maps are used to support diagnosis. In computer vision, fuzzy systems can also be used to describe intrinsic attributes of images [19], [20]. Moreover, different studies have applied fuzzy-based techniques to medical applications [21], [22], [23], [24], [25], [26].
This project aims to investigate the effectiveness of fuzzy representation of the evaluation parameters of breast lesions. For this purpose, we have developed a fuzzy system to provide an automated quantitative analysis of breast nodules and calcifications, based on image visual assessment parameters supplied by the users. This system is based on a new method proposed in Ref. [27] for designing of membership functions in fuzzy sets. This algorithm uses training sets to determine the data distribution for each class and establishes the design of the membership functions to be used by the fuzzy inference model. The system provides a second opinion to aid the radiologist (or other clinicians) to define the diagnosis and the patient׳s mammography classification. For this computerized analysis, we have used the main attributes related to mammographic findings in the reports of the nodules and calcifications. We have also used the BI-RADS evaluation categories and their corresponding prognosis. We have designed and implemented a CAD tool for generating BI-RADS diagnosis. We have evaluated our proposed methodology by the effectiveness in generating results more closer to the ones expected by users. Furthermore, the use of parameters and rules defined in terms of natural language should contribute to an effective adoption of CAD systems by the radiologists.
This paper is organized as follows: Section 2 presents the technical background related to fuzzy logic and the BI-RADS standard; Section 3 describes the proposed methodology for the representation of the BI-RADS attributes as fuzzy sets as well as their evaluation categories; Section 4 presents the experiments and the consequent results; Section 5 presents discussions and Section 6 presents conclusions.
Section snippets
Fuzzy inference model
Fuzzy set theory distinguishes from the classical set theory since it concerns vague aspects related to information. This theory is less restrictive and can be more suitable to handle information given by humans. It extends the classical binary logic (0 or 1) to the continuous domain (0 to 1), through a gradual transition between pertinence and non-pertinence of an element within a set [8], [28]. There are several fuzzy inference models. The most known is the Mamdani model, where the semantic
Material and methods
The proposed methodology is described in the following sections.
Design of membership functions
In the evaluation of nodules, we obtained 126 values of malignancy degrees for the shape coefficient and for the density coefficient. For the margin coefficient we obtained 180 values of malignancy degrees due to the fact that the radiologist could select more than one characteristic to this attribute during his/her analysis. After applying the Fuzzy-Omega algorithm, two or three membership functions were generated for each attribute. However, subsequent tests indicated that the use of only two
Discussion
The implemented system and the results presented in the previous section lead us to carry out some comments on certain issues.
Conclusion
This paper presents a method for the fuzzy characterization of the main linguistic terminology descriptors used in the evaluation of breast nodules and calcifications, as well as the BI-RADS categories associated with them, for mammographic images. The proposed system was developed in collaboration with domain specialists. Computational methods supported the steps of the system modeling and implementation. The result is a CAD system that suggests to the user a BI-RADS category following the
Summary
CAD systems based on medical imaging aim to assist and improve accuracy of diagnosis through the use of a computer, indicating suspicious areas in the image as well as abnormalities. This assistance can be very important since the radiologist׳s diagnosis is based on subjective analysis and personal variations, such as visual fatigue or distraction, image quality and overlay structures, among others. Throughout its evolution, research projects addressing methods for CAD encountered a significant
Conflicts of interest statement
None declared.
Acknowledgments
The authors thank the radiologists of School Hospital of Medicine of University of São Paulo at Ribeirão Preto, Brazil, for the analysis of the selected images.
This research was supported by the São Paulo Research Foundation (FAPESP) (Grant no. 07/59862-0).
Gisele H.B. Miranda received the B.Sc. degree in Biomedical Informatics from the University of São Paulo, Brazil, in 2009 and the M.Sc. in Bioinformatics also from the University of São Paulo, Brazil, in 2011. Presently she holds a fellowship in a medical systems company. Her research interests include image processing and analysis, complex networks and computer-aided diagnosis.
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Gisele H.B. Miranda received the B.Sc. degree in Biomedical Informatics from the University of São Paulo, Brazil, in 2009 and the M.Sc. in Bioinformatics also from the University of São Paulo, Brazil, in 2011. Presently she holds a fellowship in a medical systems company. Her research interests include image processing and analysis, complex networks and computer-aided diagnosis.
Joaquim C. Felipe received the B.Sc. degree in Mechanical Engineering from the University of São Paulo, Brazil, in 1986, the M.Sc. degree in Computer Science from the Federal University of São Carlos, Brazil, in 2000 and the Ph.D. degree in Computer Science from the University of Sao Paulo, Brazil, in 2005. He is currently a full Professor in the Computing and Mathematics Department of University of São Paulo at Ribeirão Preto, Brazil. His research interests include medical imaging, image processing and analysis, computer-aided diagnosis and bioinformatics.
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