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Staging of breast cancer based on the area of the primary tumour

Breast cancer is one of the most common and alarming diseases for women. With early detection and diagnosis, the chances of successful treatment and survival would improve. The diagnosis includes classification or staging of the breast cancer, which plays an important role in the prognosis of the disease hence determining the best treatment for the disease. Breast cancer staging is a way of describing the size of a cancer and how far it has grown. One of the staging numbering systems is the Tumour-Node-Metastasis (TNM) system, which categories cancer into several stages. Most types of cancer have four stages, numbered from I to IV. Normally, staging is determined by doctors by examining the pathology information which describes the spreading area of the cancer. In this study, a series of computer algorithms is applied to produce the area information of the cancerous region. The methodology consists of four phases which are image gathering; image pre-processing using Median filter and PCA; image segmentation using FCM; and staging using the area of the primary tumour as a representation of size in the TNM system. From thirty-five randomly selected mammography images of Malaysian women with malignant tumour, 14.3% is in stage I, 5.7% is in stage II and 80% in stage III. Experimental results also shows that 96.4% accuracy is obtained for stage III but higher errors occur at the boundaries of the staging scale.


Introduction
Cancer incidence and mortality are growing worldwide with breast cancer rapidly becomes the leading cause of mortality among women in 2018. This disease contributed to 15% from the total of 4.2 million female cancer deaths [1]. Awareness and early detection of breast cancer may reduce the risk of death [2], [3]. A common modality for breast cancer screening is digital mammography, which is an efficient method to detect breast cancer, even at the early stage [4]. With an increase in the awareness of screening for breast cancer, huge number of mammography images are produced and manual visual examination by expert radiologists becomes a burden. Furthermore, due to human factor, detection of suspicious cancerous may be misinterpreted as a cancer and vice versa, hence leading to false results. Studies have shown that an error between 10% to 30% may occur during the detection process [5] which lead to much effort ( [4], [6]) on the automatic process of detection and classification of breast cancer. With the advance in computer technology, computer aided diagnosis (CAD) systems have been developed to assist or act as the second-eye to radiologists, and the application of CAD has proven to improve the performance of radiologists in cancer detection [7].
Many research ( [8], [9]) have agreed that accurate diagnosis and treatments are crucial for the survival of cancer patients. The determination of the stage of the cancer remains the most important factor in evaluating the prognosis and choosing the most appropriate treatment for patients with cancer.  [9] the staging procedure is based on combining several findings; whether the cancer has metastasized, whether it exhibits invasive characteristics, the diameter of the primary tumour, and the number of malignant lymph nodes. Meanwhile the procedural examination for staging involves physical examination, pathological examination of the tumour, biopsy examination as well as imaging and laboratory blood tests [10]. An accurate estimation of the tumour size is the most basic significant factor in deciding the treatment planning for the cancer disease. Once a cancer is diagnosed, the tumour stage must be accurately determined before therapy can be chosen and the prognosis can be known. Therefore, optimum imaging technique is essential to get good result for initial staging of cancer [10], [11].
Several cancer staging systems have been developed such as Dukes' system and Tumour-Node-Metastasis (TNM) system, but the Tumour-Node-Metastasis (TNM) system is the most widely applied. The TNM system classifies the stage of cancer based on three major morphological attributes of the malignant tumours, which are the size of the primary tumour (T), the presence and extent of the regional lymph node involvement (N), and the presence of distant metastases (M). Nevertheless, the size of the primary tumour (T) is the most dominant component of the TNM staging system [12], [13], [14]. Both [13] and [14] used area of the primary tumour in mammography images as the representation of size in the TNM staging system. [13] proposed the pixel area scale for stage I, II, and III using Region Growing method and Sample Fuzzy K-means clustering algorithm. Stage IV was not considered because the tumour cancer would vary in size and had spread to other parts of the body, hence further examination was needed. Meanwhile [14] used a different pixel area scale for staging of breast cancer. They applied Fuzzy clustering and Artificial Neural Networks (ANN) and the largest error, 25% occur in stage II using input image from the Mammography Image Analysis Society (MIAS) database. In this study, we applied an improved Fuzzy C-means (FCM) clustering algorithm with image pre-processing using Principal Component Analysis (PCA) and median filter to produce the area information as the representation of the size of the primary tumour in mammography image. In addition, we acquire thirtyfive mammography images from the National Cancer Society of Malaysia to investigate staging information of Malaysian women.

Mathematical Representation of PCA and FCM
The PCA algorithm is described as follows [15], let be an m-component vector variable and the sample matrix of x is denoted by where the discrete samples of , The ith row of the sample matrix X is called the sample vector of i x and is written as The mean value of Xi is given as Hence, the centralised matrix of X is Finally, the co-variance matrix, Ω of the centralised data, X is calculated as Fuzzy C-means clustering (FCM) is an algorithm that optimizes the objective function (7) [16]: Where X = {x1, x2, x3, . . ., xn} ⊆ Rp is the sample set. , for i = 1, . . . , n

Implementation
The implementation of this study consists of four main parts, namely input image, image pre-processing, image segmentation, and staging based on the area of the primary tumour as the representation of size in the TNM system. The process is summarised by the flow chart in figure 1. The input are thirty-five randomly selected mammography images with malignant tumour acquired from the National Cancer Society of Malaysia. Images are cropped at the region of interest (ROI) at the size of 200 by 200 pixels, in order to trim down the volume of the dark background since it was not important in the segmentation process [17], inevitably reducing the computational time. The ROI images are preprocessed using Median filter followed by PCA. An important property of PCA is that it can distinguish between the input data and noise in the PCA domain [15], hence might be a suitable noise removal method. The next phase is the segmentation process using Fuzzy C-means (FCM) clustering algorithm as we have proposed in [18]. In the segmentation process, images are clustered into two clusters, namely the foreground (the primary tumour) and the background (the surrounding tissues). Finally, area of the primary tumour is calculated and staging is determined based on the scale proposed by [14] as shown in table 1. Table 1. Staging based on pixel area of primary tumour.

Stage
Lower limit (pixel) Upper limit (pixel) I 0001 2800 II 2800 3100 III >3100 The procedures of this study are summarised in figure 2.

Result and Discussion
From the random selection of thirty-five sample of mammography images of Malaysian women with malignant tumour showed that five patients or 14.3% are in stage I, two patients or 5.7% are in stage II and 28 patients or 80% are in stage III. The pie chart in figure 3 summaries the results. These results are consistent with the findings by [19] who stated that the incidence of breast cancer in Asia is rising and is associated with increased mortality. Thus, high percentage of stage III patients contributes to increase in death rate. On the other hand, although the incidence is also increasing in the western countries, the mortality rate is decreasing [19]. Experimental results shown in table 2 indicate that higher percentage accuracy, 96.4% is obtained for classification of stage III breast cancer, and this may be due to bigger pixel area in the third category. Also, since the number of mammography images in stage I and II is small, the staging errors in both categories are bigger. Error occurs for images with primary tumour area near the boundaries of the staging scale, which are 2800 and 3100. A more suitable staging classification using fuzzy method may be able to overcome the problem of staging for tumour areas near the boundaries.

Conclusion
In conclusion, staging information from a randomly selected mammography images of Malaysian women shows similar trend of higher incidence and mortality rates of breast cancer among Asian women. Also, the proposed series of algorithms using median filter, PCA and FCM was able to correctly stage images with high accuracy at stage III. Suitable method(s) to evaluate tumour areas near the boundaries such as Fuzzy classification using Z-numbers may be able to improve the staging result.