Active and Passive Antenna Sensor Signal for the Prediction of Breast Cancer Cell Size Below 3mm Using Bayesian Optimized Regression Analysis

Breast cancer is the second leading disease among women and causes more deaths, according to the World Health Organization (WHO) reports 2021. Breast cancer-based death rates have increased in every part of the world. However, the death rate is higher among women in industrialized nations. In the current scenario, women with age less than 40 years compulsorily need to do Breast Cancer screening. For initial screening, physicians advise mammography or MRI imaging for the early detection of breast cancer. Breast cancer patients must undergo multiple screening techniques during the breast cancer cell diagnosis, which affects the patient’s mental health.

MRI, PET, Ultrasound, and X-ray mammography are currently used for breast imaging. Minimal energy X-rays are used in X-ray mammography for breast cancer detection.

The above imaging modalities have certain limitations, such as exposure to ionizing radiation. Mammography shows 1/10th of the cases as false positives. X-ray mammography needs breast compression during the test, which causes severe discomfort. There is difficulty in detecting cancer cells in dense breast tissues. Moreover, frequent exposure to radiation at a young age causes tumours at a later age.

Ultrasound imaging has been reported as a painless method for detecting cancer cells at early stages compared to mammography. The resolution of ultrasound images is shallow, whereas MRI provides high-resolution images. A contrast liquid called gadolinium is injected during MRI scanning for a more explicit image. The adverse drug effect of gadolinium needs to be taken care of. MRI imaging is expensive and time-consuming. It will take 20-90 minutes to complete the procedure. MRI can never be used in pregnant women and patients with heart implants for breast cancer diagnosis [1].

Researchers are focusing on the development of an alternative imaging technique for breast cancer detection, which should be safe for women and solve the above limitations [2].

To solve the above drawbacks, scientists are focusing on microwave imaging. Microwave imaging differentiates the normal and cancerous tissue based on dielectric characteristics. Microwave imaging method never needs breast compression, ionization radiation, or contrast material. High-resolution 3D images are obtained using microwave imaging (MWI). MWI emits microwave radiation below the SAR limit of about 0.08 W/kg. The antennas used for microwave breast imaging must be in ultra-wide bands, which radiate in the range of frequencies with considerable gain and directivity [3]. The antenna must be small and fit around the breast region. Microwave imaging identifies minute signal fluctuations caused by cancer tissues. In Microwave Imaging, the breast tissue is exposed to microwave radiation. The breast tissue absorbs microwave energy while some energy is reflected. The dispersed microwave energy signals are recorded and processed for cancer detection. The features extracted from the microwave signal show the presence of the cancer [4].

Contributions: This paper uses a novel TAVA for the detection of cancer cells smaller than 3 mm in the intercoastal muscle region, lobules, nipple region, and the subcutaneous fat region of the breast phantom using active and passive TAVA as sensor. The above regions are dense breast tissues. The 3 mm cancer cell is detected by analyzing the S11 parameter and SAR values obtained from proposed ABCD devices and passive signal-based measurements in PBCD devices. Finally, Bayesian optimized multiple linear regression is applied to predict the size of the cancer cell. Multiple linear regression (MLR) effectively predicts the size of breast cancer cells, based on multiple features. Bayesian optimization of regression analysis enhances the performance by effective hyperparameter tuning, leading to accurate cancer cell size prediction. The main contributions of the proposed work are:

1. To detect the cancer cells of size below 3 mm located in the different dense regions of the breast, such as the intercoastal muscle region, lobules, nipple region, and the subcutaneous fat region of the breast phantom using active and passive TAVA as sensors.

2. To enhance cancer detection performance, external heat is applied to the breast region. The passive TAVA signals are analyzed with DWT, and statistical data for breast cancer detection are acquired.

3. To develop the ABCD device and PBCD device using TAVA as a sensor, Bayesian optimized linear regression (BO-LR), and Bayesian optimized multiple linear regression for breast cancer cell detection and prediction.

4. To compare the performance of the proposed devices (i) ABCD and (ii) PBCD using ground truth verification.

This paper uses a compact-sized TAVA as the sensor. The efficient design of the antenna can easily identify the minute signal variations caused by the cancer cells. For the proposed study, a heterogenous breast phantom is created, mimicking the dielectric characteristics of the woman's breast. The breast phantom is heated with the heating pad. The heating pad increases the cancer cell temperature, improving the SAR and differentiating the smaller cancer cells from normal cells. In this study, ABCD and PBCD devices were developed based on active sensing and passive sensing.

The heating pad in the experimental setup temporarily raises the surface temperature of the breast tissue, allowing for more accurate readings. The periodic temperature fluctuations significantly improve the precision of the methods mentioned earlier. Researchers can create a phase map showing the relationship between the thermal stimulation and the breast surface's temperature response by thermally stimulating the tissue at a specific rate and simultaneously recording the signals with a TAVA antenna. The signal's amplitude is directly related to the heat dissipated at the surface. This induced heating enables the detection of minimal temperature differences, even when obscured by background noise.

The high sensitivity of the radiation reduces the signal strength in regular tissue areas, while large temperature gradients affect the breast tissue's thermal properties, such as blood flow. Furthermore, if the thermal modulation frequency is high, the TAVA antenna signal can be used to identify small breast cancer cells emitting a signal.

The proposed TAVA antenna is connected to a microwave radar sensor in active sensing that transmits microwave signals at 10 GHz. TAVA antenna is placed on breast phantom with cancer cells. The TAVA antenna transmits signal at the resonant frequency to the breast phantom. The reflected signals from the cancer cells are analyzed for the Specific Absorption Rate (SAR). It has been observed that cancer cells have the highest SAR value.

In passive sensing, the signals radiated from cancer cells, without transmitting signals, are processed using the MATLAB acquisition toolbox software, and the signal is analyzed through the discrete wavelet transform. The size of the tumour is predicted using the extracted features from DWT and the machine learning algorithm. Based on the active sensing of the TAVA antenna, the ABCD device is developed, and based on the passive sensing of the TAVA antenna, the PBCD device is developed. Figure 1 shows the block diagram of the proposed system.

The proposed study consists of five main sections. Section 1 delves into the discussion of the Proposed TAVA design, while Section 2 elaborates on the design of the breast phantom model. The SAR analysis using CST simulation is discussed for different locations of cancer cells in the breast phantom model in Section 3. Experimental analysis of tumour detection, i.e., both ABCD and PBCD device measurements, is elaborated in section 4. Section 5 explains cancer cell size prediction using a machine learning algorithm.

1.png

Figure 1. Block diagram of the proposed system

3.1 Proposed TAVA design

The TAVA design spans a frequency range of 1.63 GHz to 13.8 GHz. TAVA is fabricated with FR-4 as the substrate with a relative permittivity of 4.3 and a thickness of 0.6 mm. The substrate [8] features low permittivity and tangent loss to minimize power loss in the antenna. The antenna length (L) is determined by combining major radii of ellipse1 (r_s1) and the feeder height.

The substrate thickness (h) is also a key parameter. The Input Impedance of the antenna (Zo) is set at 50 Ω. Table 2 shows the details on the antenna specifications.

The TAVA antenna is shown in Figure 2, which consists of slots and directors. The dimensions of the TAVA are 53.07 × 46.07 × 0.6 mm³. The exponential arms of the antenna are made of copper, and the thickness is about 0.036 mm - a tree-shaped slot increases stepwise on the front and back sides of the antenna. Directors in the rectangle are used in the AVA's front side, enhance metrics such as Return loss, Gain, and Directivity.

The detailed dimensions of the front and back views of the proposed AVA are illustrated in Figure 2.

2.png

Figure 2. Proposed TAVA design

Table 2. Proposed TAVA antenna parameters

3.2 Design of breast phantom model

For this study, the developed breast phantom model, which consists of four layers, is used and is illustrated in Figure 3. The layers include skin layer, adipose Layer, fibro glandular layer, and a tumor. The skin layer has a radius of 50 mm, the adipose layer has a radius of 48 mm. Different sizes of cancer cells such as 3 mm, 4 mm, and 5 mm in radius are placed inside the phantom.

The various layers of the breast phantom model are created with dielectric properties which mimic the human breast [26] as shown in Table 3.

3.png

Figure 3. Breast phantom model design

Table 3. Dielectric properties of various layers of developed breast phantom model

Breast Phantom with multiple tumors of size, such as 3 mm, 4 mm, and 5 mm, placed at the dense breast regions, such as the intercoastal muscle region, lobules, nipple region, and the subcutaneous fat region, as shown in Figure 4. The developed heterogeneous breast phantom model has three layers: the skin layer, the adipose layer, and the tumour.

4.png

Figure 4. Real time breast phantom model with multiple tumor

3.3 SAR analysis using CST simulation

In this section, SAR analysis is measured using the CST software to identify the cancer cell location. The Specific Absorption Rate determines the electromagnetic field exposure in living tissues. SAR value varies based on tissue density, measured in kilograms per cubic meter, and its electrical conductivity is measured in Siemens per meter. The SAR level is influenced by the strength of the electric field generated by the radiated energy, measured in volts per meter. The SAR level for a tissue with a mass of 1 gram should not exceed 1.6 watts per kilogram. The SAR value decreases from the Skin Layer. Women aged 50 to 55 have breast layers with the highest SAR values.

The breast phantom model has 3 mm, 4 mm, and 5 mm cancer cells in various positions for experimentation. The designed phantom model has a depth of 40 mm. The breast phantom is kept near the antenna. The maximum SAR of 1.32 W/ Kg is obtained for a 4 mm cancer inserted in the position (0,0,25) in the phantom., as shown in Figure 5(a). In CST simulation, to view the field distribution, the model is cut along the YZ plane using a cutting plane. Similarly, a 5mm sized spherical cancer cell has maximum SAR value of 1.52 W/Kg, shown in Figure 5(b).

5a.png

(a) Tumor of 4 mm radius placed at (0,0,25)

5b.png

(b) Tumor of 5 mm radius placed at (3,-5,21)

Figure 5. Field distribution in SAR analysis of single tumor

The field radiation of SAR analyzed for multiple cancer cells is shown in Figure 6.

In CST, for experimental validation of multiple tumor identification, a 4 mm sized tumor is placed at (0.0,25) and a 5 mm sized tumor is placed at (3,-5,21). The two tumors listed are placed at various depths. The maximum SAR value is 0.27 W/Kg at (-0.26,-0.5,29.5).

Table 4 shows the detected cancer location for cancer sizes 3 mm, 4 mm and 5 mm using SAR values. Maximum radiation is obtained nearer to the cancer location.

6.png

Figure 6. Field distribution of SAR analysis of multiple tumors, a 4 mm tumor placed at (0,0,30) and a 5 mm tumor placed at (-4,2,20)

Table 4. SAR analysis of 3 mm, 4 mm and 5 mm cancer cells using CST simulation

3.4 Proposed ABCD device for breast cancer detection

In active sensing, the antenna is connected to the VNA to transmit and receive the microwave signal. The directional antenna is kept in the direction of maximum radiation near the skin surface and measures backscattered signal S11 as in Figure 7.

The S11 value at resonant frequency without cancer cells is obtained as -25.91 dB and with cancer cells as -29.54 dB. The proposed ABCD devices replace the VNA with an HB100 microwave IC of 10.25 GHz for transmitting and receiving the signal. The received signal is connected to the microcontroller and is measured using node MCU. The block diagram of ABCD is shown in Figure 8(a), and the experimental setup is shown in Figure 8(b). Table 5 shows the S11 and SAR obtained for the cancer cells of sizes 3 mm, 4 mm, and 5 mm placed at the subcutaneous region. SAR value increases with the cancer size. Reflection is more for breast phantoms with cancer cells than without cancer cells because of the high moisture content in the tumor.

7.png

Figure 7. Measurement of S11 with and without tumor using VNA

Table 5. S11 and SAR values for cancer cells of sizes 3 mm/4 mm and 5 mm

8a.png

(a) Block diagram of ABCD device

8b.png

(b) Experimental set up using ABCD

Figure 8. Proposed ABCD device

3.5 Experimental analysis of proposed PBCD device

In passive sensing-based cancer cell detection, the antenna absorbs radiation from cancer cells. TAVA antenna acts as a sensor and acquires radiation from the cancer cells. The radiation signal from the cancer cell is acquired using SigView software via a DAQ card. The signal acquired is shown in Figure 9. The signals are obtained by placing the antenna at different positions from the breast phantom with and without cancer cells. The acquired signals are further analyzed using MATLAB.

9.png

Figure 9. Radiated Signals from 3 mm cancer cells acquired using SigView software

10a.png

(a) Block diagram of PBCD

10b.png

(b) Experimental set up using PBCD

Figure 10. Proposed PBCD device

In the PBCD, the radiated signal from the cancer cells acquired through the proposed TAVA is processed using the SigView software, which is shown in Figure 10(a) and Figure 10(b). The radiated signals are acquired from the breast without tumors and with tumors of different sizes. The antenna is placed in various locations, and the strength of the phantom signal is measured. From signal acquisition, the signal strength is maximum when the antenna is kept near the cancer cells.

The acquired signal is processed using a discrete wavelet transform. Discrete Wavelet Transform (DWT) preprocesses the signal and extracts the signal's features such as mean, standard deviation, median and variance. Figure 11 shows the histogram of the synthesized signal.

11.png

Figure 11. Features extracted using discrete wavelet transform for 3 mm cancer cell signal

The DWT is defined as:

$W_{\emptyset}\left(j_0, k\right)=\frac{1}{\sqrt{M}} \sum_x f(x) \emptyset_{j 0 . k}(x)$         (1)

$W_{\varphi}(j, k)=\frac{1}{\sqrt{M}} \sum_x f(x) \varphi_{j . k}(x)$           (2)

For j>j₀

Inverse DWT is defined as:

$\begin{gathered}f(x)=\frac{1}{\sqrt{M}} \sum_x W_{\emptyset}\left(j_0, k\right) \emptyset_{j 0 . k}(x)+ \frac{1}{\sqrt{M}} \sum_{j-j 0}^{\infty} \sum_k W_{\emptyset}(j, k) \emptyset_{j, k}(x)\end{gathered}$          (3)

where, $f(x), \emptyset(x)$ are functions of discrete variable.

From Table 6, the mean and median values are lower for signal without cancer cells and higher for cancer cells of size 5 mm and 3 mm. Similar readings were taken from different angle for the prediction of cancer size.

3.6 ML approach on cancer size prediction

The data are acquired for different cancer cells from ABCD and PBCD devices and are shown in Tables 6 and 7. The data are processed using the Bayesian optimization method. The cancer size is predicted using the machine learning algorithm. This paper proposes cancer size prediction using Bayesian optimized and multiple linear regression. Linear regression is a statistical technique that analyses the relationship between a dependent variable and one or more independent variables. Linear regression is limited to one independent variable, while multiple linear regression includes two or more independent variables.

Table 6. Features of discrete wavelet transform

Table 7. Evaluation measures of cancer size prediction using active antenna as sensor

The R-squared method is used to assess the model's performance.

In linear regression, the equation is as follows:

$y=\beta_0+\beta_1 x$           (4)

where, y is the dependent variable and x is the independent variable.

Bayesian optimized regression is a preferable alternative when the assumptions of linear regression, such as normality of data and linearity of predictor variables, are not met. This method integrates prior knowledge or beliefs about the data, leading to better understanding and accuracy in predictions. Bayesian optimization is beneficial for complex or unclear datasets, as it considers the uncertainty of refined estimates. This method is based on Bayes, given the observed data.

3.6.1 BO-linear regression – ABCD devices

In this measurement, cancer size is the dependent variable, and the SAR coefficients obtained from the phantom with an active TAVA antenna as the sensor are the independent variables.

Bayesian optimization seeks to identify the most accurate values for the parameters that define a linear model, which captures the underlying connection between predictor variables and a response variable. This linear relationship can be mathematically expressed as a function of the dependent variable Y and the independent feature set X, as follows:

$Y=f(x, w)+\varepsilon$             (5)

The regression coefficients w represent the connections between the independent variables and the dependent variable. These errors, ε, are independent and follow a normal distribution with a mean of 0 and a variance of σ².

Given the predictors x, target Y follows a normal distribution with mean µ=f(x,w) = w₀ + w₁x₁ +w₂x₂+ …+w_px_p and variance σ².

The conditional probability density function (PDF) of Y given the predictor variables is shown in Eq. (6).

$P\left(y \mid x, w, \sigma^2\right)=\frac{1}{\sqrt{2 \pi \sigma^2}} e^{-\frac{(y-f(x, w))^2}{2 \sigma^2}}$            (6)

Eq. (7) shows the ABCD device predictor equation:

Cancer size =0.448 × SAR -8.624            (7)

From the analysis, Correlation, r= 0.953.

R- squared, r² = 0.909.

Table 7 shows the accuracy of the predicted cancer cell size with the actual cancer cell size. It is observed that cancer cells can be predicted with TAVA up to a distance of 2 cm from the skin surface. For a 3 mm tumor the machine learning algorithm has predicted the cancer cell size as 2.99.

3.6.2 BO-multiple regression approach on PBCD and prediction of cancer cell

In this approach, cancer size is the dependent variable and the mean value obtained after performing discrete wavelet transform is the independent variable.

Cancer size=0.234 × mean value of the DWT - 22.1655           (8)   

From the analysis, Correlation, r= 0.9618.

R- squared, r² = 0.925.

In cancer size prediction, multiple linear regression is optimized with Bayesian optimization (BO).

The BO- multiple linear regression for PBCD is as given below:

$\begin{aligned} y= & \beta_0+\beta_1 x_1+\beta_2 x_2+\beta_{1,1} x_1 \times x_1 +\beta_{1,2} x_1 \times x_2+\beta_{2,2} x_2 \times x_2\end{aligned}$   (9)

Cancer size is predicted using the following equation:

Cancer size= 34.345 – 1.4591 mean + 5.564 standard deviation + 0.0063 mean × mean + 0.0164 mean × standard deviation – 0.2518. standard deviation × standard deviation     (10)

Overall fit is given by R – squared, r² = 0.9965

Table 8 shows the evaluation measures for predicting the cancer cell size. It is observed that prediction of the cancer size is more accurate for BO multiple linear regression than BO linear regression. Cancer size of 3 mm can be predicted using this approach.

Table 8. Evaluation measures of cancer size prediction using regression analysis

The proposed system gave the best results for tumors present in subcutaneous region. But the tumors present in intercoastal muscle region were not able to detect accurately. The proposed devices can be updated with a Digital signal processor to detect cancer cell sizes below 2mm to 1mm, and generative artificial intelligence signals can be used to detect cancer cells.