-We use machine learning technologies and neural networks to improve the efficiency of medical diagnostics based on the microwave radiometry. Originality of our approach is that we use the results of computer modeling temperature fields in multicomponent biological tissues to build training and test data sets. We investigate limits of applicability of the method for diagnosing breast cancer using microwave radiometry data. Task of determining diagnostic quality for different sizes of tumors seems promising to us.
I. INTRODUCTION
Early diagnosis of breast cancer is an important issue in
modern medicine. Incidence of breast cancer is increasing
worldwide and is one of the most common types of cancer.
At the moment, there is no effective means to prevent breast
cancer. Probability of successful treatment and full recovery of
the patient depends entirely on early detection and diagnosis.
Breast cancer is a curable disease with a probability of
97% with early detection [
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medicine [
Mathematical models and numerical methods that we use
to construct a sample of temperature data are described in [
Fig. 1. Distribution of thermodynamic temperature at a depth 4 cm obtained by computer simulation. On the left is a model with a tumor of radius R = 0.5 cm.
To do this, we need to build samples data from computer modeling of breast temperatures, volume which will allow for machine learning, as well as binary classification of test data (healthy-sick). When building a large volume of models, it is necessary to take into account the fact that most often malignant tumors appear in the upper outer quadrant. We present results of numerical simulation thermal dynamics in the biological tissues of the mammary gland (Fig. 1.).
III. MACHINE LEARNING METHODS AND TOOLS The following methods are used for binary classification of computer modeling data: support vector machines (SVM), k-nearest neighbors, (KNN) and the naive Bayesian classifier (NBC). These methods are implemented in the Scikit-learn Python library. In addition to the classification task, this library allows you to build regressions, perform clusterization, and so on.
The training set is a temperature data set at points of the
breast (according to the survey method [
2 T01 T11 : : : T118 3 2 y1 3 X = 664: T::2: : : : : : : : : : : : : : : : T::12:8:775 ; Y = 664: y:2: :775 ;
0 T12 : : : where T0i; : : : ; T8i are internal temperature at the points 0; : : : ; 8, T9i; : : : ; T1i8 are temperature of the skin at points 0; : : : ; 8 and yi 2 fHealth, R=0.5, R=0.75, R=1.0g is label i model.
Ratio of cancer and healthy models in the training and test sets is assumed to be equal, in order to preserve data uniformity. We conducted a statistical analysis of the data at the first stage. It showed general differences between the data sets.
Qualitative analysis of large amounts of data is particularly difficult. Statistical analysis confirms reliable differences in temperature data at certain points of the breast (Fig. 3.).
1 0 1 0 0 where Mj is the average value of the samples, and Sj is the standard deviation of the samples.
a b 100 200 300 400 500 100 200
300 epoch 400 500
We solve binary classification problem, so number of neurons in the output layer is two. The softmax function is selected as the activation function for last layer. This function converts the network output vector to another vector. The coordinate of this vector is located in range [0; 1]. The sum of the coordinates is 1. We define patient class by the largest coordinate in output vector. Parameters of the layers and their number were selected empirically. We were based on the results of testing.
To train a neural network, the original sample consisting of 160 numerical simulation results was randomly mixed and divided into two parts, the first p art c ontaining 1 20 survey results, the second part containing 40. Gradient optimization methods were used to train neural networks.
In order for the model not to be retrained, the number of epochs was set to 500. The Fig.4. shows the accuracy of model and model loss in learning process.
G = pL S ; (3)
To determine dependence of the effectiveness diagnostics on size of the tumor, we used binary classification “Healthy” and “Cancer”. This is due to the fact that most important, in our opinion, is correct detection of malignant neoplasms.
A measure of the effectiveness of medical diagnostics is considered to be the geometric mean of sensitivity and specificity
MP thanks RFBR (project number 19-37-90142) for the financial support. AK acknowledges the Ministry of Science and Higher Education of the Russian Federation (government task, project No.0633-2020-0003) for the financial support of the development of the software. EE is grateful to RFBR and the government of Volgograd region according to the research project No. 19-47-343008 for the financial support.
The support vector method gave the best result in relation to other machine learning methods (Table 1), which indicates that this method is better applicable to this type of tasks and to this structure of training data set. The SVM method’s gain in relation to the NBC is 10% for a data set with a tumor R=0.5 cm. Which is significant for the task of medical diagnostics. Ratio of correctly classified models to volume of test sample was used as a measure of efficiency for comparing methods. E = F! , where ! is number of correctly recognized models, and F is volume of test data set.
0.8 0.75 0.7 0.65 E 0.6 0.55 0.5 0.45 0.5 0.6 0.7 0.8 0.9
1
R, cm
The calculated sensitivity and specificity indicators (Table 2) are quite high. At the same time, we should note characteristic space limited only by temperatures and rather small training data set.
Neural network testing results show comparable results with machine learning methods (Table 3). Structure of neural network significantly affects the accuracy of diagnostics. Effectiveness of diagnostics increases with increase in radius of tumor (Fig. 5.). Even for small tumors of radius R=0.5 cm with a probability of 57.5%, it is possible to correctly determine the class. We can expect a successful application of microwave radiometry method for smaller tumors, with an expansion of feature space, an increase in sample size, and the use of heuristics.