Cancer is the second cause of death worldwide, accounting for 18,078,957 cases and 9,555,027 deaths in 2018. The most common type is lung cancer, representing 11.6% of the total number of cases and accounting for the highest number of deaths due to cancer (18.4%). It is followed by breast cancer with 2,088,849 cases (11.6%) and 626,679 deaths (6.6%) [
An important correlation has been found between the presence of premalignant lesions (segmental and linear microcalcifications) and the development of cancer since most of the patients who present this type of lesion undergo surgery, chemotherapy, or radiotherapy [
Microwave ablation [
Analysis of different factors, such as the frequency-dependent reflection coefficient (also termed the
Equation (
To calculate the reflected power in percent, the following formula is used:
Additionally, the specific absorption rate [
In this equation,
The Pennes bioheat equation is based on the thermodynamic characteristics of the blood to calculate heat accumulation in perfused tissue. In this equation,
Previous research demonstrated the possibility of performing microwave ablation therapy for breast carcinoma tissue [
Breast calcifications are frequently observed through screening mammography in asymptomatic women. Most cases arise from benign processes, such as calcification of vascular structures, hyalinized fibroadenomas, cysts with apocrine changes, and ductal hyperplasia with or without atypia [
Calcifications of malignant origin result from central necrosis or secretions of malignant cells. They usually represent the only radiological sign of malignancy in asymptomatic patients, especially in those with calcifications that are not associated with the presence of a mass. Specifically, they are the only finding in most cases of ductal carcinoma
Mammography is the only imaging method capable of detecting malignant calcifications, far exceeding the ability of other methods for its detection in early breast cancer stages [
The Breast Imaging Reporting and Database System classifies calcifications according to their morphology and distribution. Regarding morphology, calcifications are categorized as typically benign, probably benign, and of suspicious morphology. With regard to distribution, calcifications are classified as diffuse, regional, grouped, linear, and segmental [
The aim of this study was to develop and compare a predictive computational model with a breast phantom, which emulates the dielectric properties of breast tissue with segmental microcalcifications. The frequency-dependent reflection coefficient and SWR factor were obtained to study the application of electromagnetic ablation to premalignant lesions in the breast, specifically segmental microcalcifications.
A phantom is an object typically used for the calibration of MRI equipment. Different substances are used during the manufacture of phantoms to emulate specific characteristics of human tissues. In the case of the breast phantom used in this study, the intention was to emulate the dielectric properties of the tissue (i.e., conductivity and permittivity) rather than the physical properties related to obtaining diagnostic images.
The materials used to produce this phantom were tridestiled water, agarose, corn oil, neutral detergent, and tricalcium phosphate Ca3(PO4)2. Tridestiled water does not contain minerals or residual material; thus, it was used as a solvent. Agarose was used as a binder for the substances that comprise the phantom. Corn oil was used to emulate the properties of breast adipose tissue. The neutral detergent was added to homogenize all the elements of the mixture. Tricalcium phosphate is present in breast microcalcifications [
Tricalcium phosphate for mimicking microcalcifications.
Random distribution of microcalcifications in the breast tissue phantom.
The phantom was produced according to the proportions shown in Table
Concentrations used for preparing the breast microcalcification phantom.
Materials | Concentration |
---|---|
Tridestilated water | 50 ml |
Agarose | 4.5 g |
Corn oil | 160 ml |
Neutral detergent | 30 ml |
Tricalcium phosphate | 2.14 g |
Measurements of the dielectric properties of isolated calcium phosphate (with a dielectric probe kit model 85070E) and SWR factor of the microcalcification phantom (with an open-ended coaxial probe model kit 5989-0222EN) were performed on an E5071B network analyzer ENA (Agilent, Colorado, USA). Measurements were taken at three different points with this probe using a support designed to keep the tip 70 mm away from the bottom of a 400 ml beaker (height: 107 mm)—this was the point where the highest concentration of tricalcium phosphate was found (see Figure
Microcalcification phantom with three measuring points and dielectric coaxial open probe.
Subsequently, in the same positioning, measurement of the SWR factor was performed using a coaxial double-slot antenna (see Figure
The coaxial double-slot antenna wrapped with polytetrafluoroethylene tape.
It was decided to use a coaxial double-slot cable antenna because the radiation lobe is ideal for the ablation zone to cover the cluster of segmental microcalcifications due to the distribution in which they occur; besides, it has shown better results in previous studies [
The antenna was wrapped with polytetrafluoroethylene tape to emulate the catheter, which would be introduced with a puncture to the breast during ablation therapy of biological tissue.
The microwave antenna used to perform the tests consisted of a microcoaxial cable with a diameter of 2,197 mm, which has an external copper conductor and an internal conductor of silver-plated copper separated by a polytetrafluoroethylene dielectric as shown in Figure
View of the axial cut of the double-slot antenna (measures are given in mm).
The antenna measurements according to the manufacturer and its dielectric properties are shown in Tables
Dimensions of the antenna elements [
Component | Diameter (mm) |
---|---|
External conductor |
|
Dielectric |
|
Internal conductor |
|
Catheter |
|
Dielectric properties of the antenna [
Material | Relative permittivity ( |
---|---|
Dielectric | 2.03 |
Catheter | 2.60 |
For both simulation and experimentation, the antenna operating frequency of 2.45 GHz was considered the frequency of interest. This frequency is part of the industrial, scientific, and medical band provided by the International Telecommunication Union, which is available worldwide for medical applications. Using this frequency, the effective wavelength in the tissue was calculated by means of the following equation [
In this equation,
Effective wavelength of phantom materials.
Material |
|
---|---|
Breast tissue | 66.57 |
Tricalcium phosphate | 60.99 |
Average | 63.78 |
With these wavelength values, the maximum element size for the electromagnetic simulation can be obtained since it should be smaller than 1/8 of the effective wavelength; however, they should only be considered an approximation since the tissue properties are heterogeneous.
The simulation was performed using the COMSOL Multiphysics® 5.4 software [
3D geometric model of the antenna and breast tissue.
All empty space inside the sphere was considered breast tissue, while everything outside the sphere was considered air. The mesh of the geometry for the FEM analysis had a maximum element size of 24.47 mm, a minimum element size of 0.1191 mm, 470,396 vertices, 47,556 edges, 277,0381 elements, and a total volume computational domain equal to 1,392,000 mm3 (see Figure
Mesh of the model of the antenna, breast, and microcalcifications.
Table
Parameters used in the FEM simulation.
Parameter | Value | Reference |
---|---|---|
Input power, |
12 W | — |
Frequency, |
2.45 GHz | — |
Electrical conductivity of breast tissue, |
0.137 S·m−1 | [ |
Thermal conductivity of breast tissue, |
0.42 W·m−1·K−1 | [ |
Relative permittivity of breast tissue, |
5.1467 | [ |
Relative permeability of breast tissue, |
1 | — |
Blood density, |
1040 kg·m−3 | [ |
Specific heat of blood, |
3639 J·kg−1·K−1 | [ |
Blood perfusion rate, |
0.0036 s−1 | [ |
Heat capacity of tricalcium phosphate at constant pressure, |
227.8 J·mol-1·K-1 | [ |
Density of tricalcium phosphate, |
3140 kg·m-3 | [ |
Thermal conductivity of tricalcium phosphate, |
0.612 W· m-1·K-1 | [ |
Relative permittivity of tricalcium phosphate, |
4.0296 | Measured |
Electrical conductivity of tricalcium phosphate, |
0.1394 S·m-1 | Measured |
Relative permeability of tricalcium phosphate, |
1 | — |
Figure
Temperature at the tip of the antenna of both computational models with and without blood perfusion.
Comparison of temperature distributions of the breast model including microcalcification considering (b) and without considering (a) energy loss due to blood flow for different time moments (100 s, 200 s, 300 s, 400 s, and 500 s).
The blood perfusion rate, the specific heat of the blood, and the density of the blood were considered to analyze the difference in the temperature reached compared with the control simulation and the experiment using the tissue-mimicking phantom.
In the model, where blood perfusion is considered, the area of ablation was notably reduced. The maximum temperature between the two simulations achieved a level of 28.7°C. The SWR values obtained for the simulations and the experiment with the phantom are shown in Table
Comparison of
|
SWR |
| |
---|---|---|---|
Measurement 1 | –12.64 | 1.609 | 5.4 |
Measurement 2 | –10.88 | 1.800 | 8.2 |
Measurement 3 | –11.68 | 1.705 | 6.8 |
Simulated without blood | –12.30 | 1.641 | 5.9 |
Simulated with blood | –12.30 | 1.641 | 5.9 |
Measurement average | –11.68 | 1.705 | 6.8 |
Abbreviations:
Figure
The
Figure
The
The SWR values in the three measurements exhibited a change of 0.191 between the minimum and maximum SWR and –1.76 in
This comparison allows us to determine the accuracy of the simulations performed using the COMSOL Multiphysics software. Blood perfusion is depreciated, as the phantom does not include this characteristic.
In conclusion, both experimentation using the phantom and simulations demonstrated that ablation therapy can be performed using this antenna; however, further investigation focusing on antenna optimization is warranted to reach the maximum possible efficiency and reduce the power reflection below the acceptable value of 1% before we can perform heating tests with biological tissue. It is also important to perform
The data used to support the findings of this study are included within the article.
The authors declare that there is no conflict of interest regarding the publication of this paper.