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A software tool for fabricating phantoms mimicking human tissues with designated dielectric properties and frequency

  • Xinyue Zhang , Guofang Xu , Qiaotian Zhang , Henghui Liu , Xiang Nan EMAIL logo and Jijun Han ORCID logo EMAIL logo
Published/Copyright: October 28, 2024
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Biomedical Engineering / Biomedizinische Technik
From the journal Biomedical Engineering / Biomedizinische Technik Volume 70 Issue 1

Abstract

Objectives

Dielectric materials play a crucial role in assessing and refining the measurement performance of dielectric properties for specific tasks. The availability of viable and standardized dielectric materials could greatly enhance medical applications related to dielectric properties. However, obtaining reliable phantoms with designated dielectric properties across a specified frequency range remains challenging. In this study, we propose software to easily determine the components of dielectric materials in the frequency range of 16 MHz to 3 GHz.

Methods

A total of 184 phantoms were fabricated and measured using open-ended coaxial probe method. The relationship among dielectric properties, frequency, and the components of dielectric materials was fitted through feedforward neural networks. Software was developed to quickly calculate the composition of dielectric materials.

Results

We performed validation experiments including blood, muscle, skin, and lung tissue phantoms at 128 MHz, 298 MHz, 915 MHz, and 2.45 GHz. Compared with literature values, the relative errors of dielectric properties are less than 15 %.

Conclusions

This study establishes a reliable method for fabricating dielectric materials with designated dielectric properties and frequency through the development of the software. This research holds significant importance in enhancing medical research and applications that rely on tissue simulation using dielectric phantoms.

Keywords: dielectric properties; open-ended coaxial probe; dielectric phantom; Android Studio

Introduction

Dielectric properties (DPs) are commonly known as electrical properties, including conductivity and relative permittivity [1], 2]. The DPs of human tissues are related to cellular composition, such as water content and ionic concentration which lead to changes in tissue physiology usually accompany alterations in DPs values [3]. Previous studies have confirmed a measurable deviation of DPs from normal values in many abnormal tissues such as liver cancer, glioma, skin cancer, and so on [4], 5]. These findings indicate DPs may serve as a promising biomarker for disease identification and diagnosis.

Recently, the rapid development of DPs measuring techniques such as magnetic resonance electrical properties tomography (MR-EPT) and microwave imaging makes it possible for DPs-based clinical diagnosis [6], [7], [8]. In DPs measuring techniques, a phantom with biologically equivalent tissue properties is widely used to test and evaluate the measurement performance for specific tasks [9]. It is also likewise desirable to characterize electromagnetic fields (such as B1 mapping techniques for MR-EPT in tissue-mimicking phantom) [10]. Additionally, safety regulations are a critical concern with DPs measuring techniques [11], 12]. Both the spatial distribution and intensity of the heating pattern associated with electromagnetic energy deposition are dependent on the DPs of the measured tissues. To ensure safe measurements, dielectric phantoms have been utilized to assess potential risks associated with measuring [13]. Moreover, a phantom-based quality assurance (QA) program has become a routine method for verifying measurement stability over time. The feasible and standardized dielectric phantom could facilitate the delivery of DPs measuring techniques to clinical applications.

The preparation of dielectric materials is a fundamental procedure in the fabrication of dielectric phantoms, which determines whether the phantom can accurately mimic the DPs of human tissues. Currently, materials based on sodium chloride-oil-gelatin dispersions are widely adopted in dielectric phantom fabrication due to their stability over a long time, easy accessibility of the components, and simple preparation process [14]. There, gelatin is used to provide mechanical strength and maintain the physical stability of the phantom. The conductivity of the phantom is determined by the concentration of sodium chloride (CNaCl), whereas the relative permittivity mainly depends on the volume percentage of oil (VPoil). Although one can readily prepare dielectric phantoms once CNaCl and VPoil are given, it is not a straightforward task to determine the amount of CNaCl and VPoil required to achieve the designated DPs of human tissues. The reason is that altering either of the two parameters, CNaCl and VPoil, leads to modifications in both the conductivity and relative permittivity.

Based on previous research, Deng et al. developed a robust method. At 128 MHz, the material composition is determined by specific relative permittivity and conductivity. They established a polynomial relationship between material composition and DPs [15]. However, the study focused on specific frequencies or specific tissue types and lacked a general method for accurately calculating arbitrary DPs for any frequency. At the same time, polynomial fitting has some limitations. First, establishing an equation process that includes additional factors is difficult and challenging. Second, due to the complexity of mapping DPs to material composition, polynomial fitting proved difficult to handle with a wide range of data sets, which required processing with more complex polynomials and a lot of computation [16].

For the past few years, models using neural networks as fitting, classification, clustering, and prediction tasks in numerous research fields have gained a viable popularity [17], [18], [19]. Feedforward neural network (FNN) is a type of neural networks which is a model of neurons that can be trained to perform a variety of tasks, including image recognition, speech recognition, and natural language processing [20], [21], [22]. As a machine learning (ML) model that goes beyond traditional regression and statistical methods, one of the key advantages of FNN is its ability to efficiently process large data sets, enabling efficient data analysis. This structure makes FNN suitable for many tasks, such as classification and regression. Therefore, by employing FNN, we can build powerful neural network models that can be applied to a variety of different domains and tasks. And in view of these benefits, we use the FNN to establish the relationship between DPs and phantom. FNN technology is briefly described in the following.

In this work, we present a method to easily determine the material composition of simulated human tissues in the frequency range of 16 MHz to 3 GHz. First, we made 184 sets of different phantoms based on CNaCl and VPoil. Then, we used the open-ended coaxial probe method to measure the correlation and obtain the experimental data of relative permittivity and conductivity of these phantoms. Next, the measurement data is fitted using FNN. Finally, by manufacturing phantoms at 128 MHz, we compared the accuracy of FNN fitting with polynomial fitting. The accuracy of FNN fitting at different frequencies was also verified at 298 MHz, 915 MHz, and 2.45 GHz. Nowadays, the popularity of smart phone devices has prompted many industries to rethink their marketing methods, compare costs and required application effects, and finally we have developed easy-to-use mobile software for phantom configuration using the above method as the core algorithm.

Materials and methods

Phantom fabrication

Common dielectric materials can be divided into liquid, solid, and gel, among which gel dielectric materials are the most widely used because of their physical similarity with human tissues and their ability to simulate a wider range of DPs. In this work, peanut oil, sodium chloride, gelatin, p-methylbenzoic acid, n-propanol, surfactant, deionized water and formaldehyde are used as raw gel-like dielectric materials. The specific steps for preparing biological tissue-mimicking materials are as follows, with the amounts of each material proportionally arranged:

Step 1: place 34 g of gelatin (Asia Pacific United Chemical Co. LTD) and 190 mL of deionized water into a 500 mL beaker. Seal the beaker with plastic wrap, secure it with a rubber band, and let it soak for 2 to 3 h.

Step 2: in a separate 100 mL beaker, add 0.2 g of p-methylbenzoic acid (Macklin AR, 98 %) and 10 mL of n-propanol (Macklin 99.5 %) (maintain a ratio of 1 g p-methylbenzoic acid to 50 mL n-propyl alcohol). Dissolve the mixture thoroughly and pour it into the 500 mL beaker from step 1.

Step 3: preheat the water bath half an hour in advance and set the temperature to 70 °C. Puncture several holes in the plastic wrap, place the 500 mL beaker in the water bath, and heat it. After 10 min, stir the solution thoroughly (using a magnetic mixer) until the gelatin is completely dissolved, yielding a gelatin solution.

Step 4: allow the gelatin solution to cool to 60 °C for reserve. Simultaneously, heat the oil (Golden Arowana) to 60 °C. Add gelatin solution and oil into another 250 mL beaker according to the VPoil (VPoil ranges from 0 to 80 %. Within the range of 0–60 %, the interval is 5 %. Within the range of 60–80 %, the interval is 2 %). The combination of dielectric materials is shown in Table 1. For example, when the VPoil is 40 %, 40 mL peanut oil and 60 mL gelatin aqueous solution were added. Then, add the sodium chloride according to the CNaCl and maintain the solution temperature at 50 °C (CNaCl ranges from 0 to 1.4 g, with a unit of g/100 mL, and an interval of 0.2 g). For example, when the CNaCl is 0.80 g/100 mL, add 0.80 g sodium chloride per 100 mL of oil-gelatin dispersion.

Table 1:

Detailed composition of dielectric materials used in the fabrication of phantoms for mimicking biological tissues, including variations in oil volume percentage and NaCl concentration.

Phantom NaCl concentration (g/100 mL oil in‐gelatin dispersion) Oil volume concentration (%)
P1-P104 0–1.4 (in 0.2 increments) 0–60 (in 5 increments)
P105-184 0–1.4 (in 0.2 increments) 62–80 (in 2 increments)

Step 5: stir thoroughly until the oil dissolves into small droplets, dispersing in the solution. Add 0–5.6 mL of surfactant (1 mL of oil to 0.07 mL of surfactant), and stir thoroughly until the solution reaches approximately 37 °C.

Step 6: finally, introduce 1.1 mL of formaldehyde solution into the container and stir continuously until uniform, completing the sample preparation (refer to Figure 1).

Figure 1: Fabrication process of a dielectric phantom for mimicking tissue properties, including the preparation of a gelatin solution, incorporation of oil and sodium chloride, and final adjustments with surfactant and formaldehyde.
Figure 1:

Fabrication process of a dielectric phantom for mimicking tissue properties, including the preparation of a gelatin solution, incorporation of oil and sodium chloride, and final adjustments with surfactant and formaldehyde.

Dielectric properties acquisition

Following the procedures described in the phantom fabrication section, a total of 184 sets of dielectric phantoms were fabricated. Subsequently, the open-ended coaxial probe method was used to measure the reflection coefficients of the phantoms at the frequency 16 MHz to 3 GHz, with a frequency step of 4 MHz [23], [24], [25]. The experiments were conducted at room temperature (25 ± 0.3 °C). The measuring system consists of a vector network analyzer (VNA, E5071C, Keysight), open-ended coaxial probe, semi-rigid transmission line, and thermometer (VC6801, Victor) as shown in Figure 2. The end of the coaxial line is placed on the surface of the fabricated phantom, and the probe is connected to the VNA through a transmission line. After the Smith chart is completely stabilized, the reflection coefficients are obtained and recorded. In order to evaluate the measurement error, the DPs of ethanol solution were obtained and compared to the literature values.

Figure 2: The measurement system consists of a vector network analyzer, open-ended coaxial probe, semi-rigid transmission line and thermometer. Reflection coefficients were measured from 16 MHz to 3 GHz at room temperature (25 ± 0.3 °C) with a frequency step of 4 MHz.
Figure 2:

The measurement system consists of a vector network analyzer, open-ended coaxial probe, semi-rigid transmission line and thermometer. Reflection coefficients were measured from 16 MHz to 3 GHz at room temperature (25 ± 0.3 °C) with a frequency step of 4 MHz.

Then, the DPs were reconstructed based on transmission line theory. The relationship between the properties of the tissue and the reflection coefficient is [26], 27]:

(1) ε r − j σ e ω ε 0 = A 2 − A 1 ρ m ρ m − A 3

where εr and σe are the relative permittivity and conductivity of the tissue, ρm is the reflection coefficient, and A1, A2, and A3 can be determined by calibration with the open circuit, short-circuit, and deionized water.

The establishment and fitting of the FNN model

In this work, the establishment and fitting of FNN model were implemented in MATLAB software through feedforwardnet function. The input data include relative permittivity, conductivity, and frequency, while the outputs are CNaCl and VPoil. Before fitting, the input data were normalized to ensure balanced weights of the input values and to prevent the result from being numerically dominated by a particular input value while ignoring other input values using [28]:

(2) y = y min + ( y max − y min ) * ( x − x min ) x max − x min

where y max =1, y min =−1, and x is the input data. The training data were split to train, validation, and test sets with a ratio of 0.7:0.15:0.15. Levenberg-Marquardt algorithm was used to establish the optimal parameters. The number of epochs was set to 1,000, the minimal performance gradient was set to 1e-7. The model consists of an input layer, three hidden layers, and an output layer to fit the measured data. In the input layer, three neurons are created, representing three inputs, including relative permittivity, conductivity, and frequency. The mapping between the input layer and the first hidden layer is calculated by the following equation:

(3) y = ω x + b

The ω and b indicate the weights and biases in training model, x is the input data. The number of ω is the multiplication of the number of neurons in the input layer and the first hidden layer, in this work, the first hidden layer has 100 neurons, and the number of b equals to the number of neurons in first hidden layer. The activation function is used to process the mapping data, which is logsig function:

(4) y = 1 1 + e − x

The processed data are entered into the second layer with 50 neurons through the trained weights and biases. Then poslin function is employed to calculate the data which are processed with weights and biases and expressed as follows:

(5) y = max ( 0 , x )

The last hidden layer contains 30 neurons and the activity function is purelin function which is:

(6) y = x

Finally, the data calculated with weights and biases are entered into the output layer, and the activation function is also the purelin function. In this work, the correspondences between the measured DPs and CNaCl, as well as between the measured DPs and VPoil, were fitted separately, leading to one neuron in the output layer.

Software design and function realization

According to the obtained parametric formula, we developed this mobile software using Android Studio based on the Android system (Figure 3) [29], 30].

Figure 3: Workflow from feedforward neural network (FNN) development to mobile software design using Android Studio. On the left: FNN model development in MATLAB, including input data (frequency, relative permittivity, and conductivity), output parameters (sodium chloride and oil volume percentage), and training using the Levenberg-Marquardt algorithm. On the right: mobile software design in Android Studio, featuring two calculation methods: (1) selecting an organization by tissue library and (2) manually entering frequency, conductivity, and relative permittivity.
Figure 3:

Workflow from feedforward neural network (FNN) development to mobile software design using Android Studio. On the left: FNN model development in MATLAB, including input data (frequency, relative permittivity, and conductivity), output parameters (sodium chloride and oil volume percentage), and training using the Levenberg-Marquardt algorithm. On the right: mobile software design in Android Studio, featuring two calculation methods: (1) selecting an organization by tissue library and (2) manually entering frequency, conductivity, and relative permittivity.

Verification and comparison of calculation results

In order to ensure the reliability and accuracy of the calculation results of the phantom configuration software constructed with the obtained parameterized formulas, we compare the FNN fitting results with polynomial fitting results [15]. This comparison involved the use of eight different phantoms representing blood, muscle, skin, and lung tissue at 128 MHz (for MRI at 3T). Additionally, the phantoms of blood, muscle, skin, and lung tissue were fabricated and verified at 298 MHz, 915 MHz, and 2.45 GHz through FNN fitting method. The DPs of these tissues at 128 MHz, 298 MHz, 915 MHz, and 2.45 GHz are listed in Table 2, and the compositions of the phantoms are listed in Table 3.

Table 2:

The literature values of prepared phantoms representing blood, muscle, skin, and lung tissue at 128 MHz, 298 MHz, 915 MHz, and 2.45 GHza.

Tissue 128 MHz [15] 298 MHz [31] 915 MHz [31] 2.45 GHz [31]
εr σe (S/m) εr σe (S/m) εr σe (S/m) εr σe (S/m)
Blood 73.2 1.25 65.7 1.32 61.3 1.54 58.3 2.55
Muscle 63.5 0.72 58.2 0.67 55.0 0.85 52.7 1.64
Skin 65.4 0.52 49.9 0.64 41.3 0.87 38.0 1.46
Lung 29.5 0.32 24.8 0.31 22.0 0.41 20.5 0.76

  1. aεr and σe are the relative permittivity and conductivity.

Table 3:

The ingredients of prepared phantoms representing blood, muscle, skin, and lung tissue obtained through polynomial fitting and feedforward neural network (FNN) fittinga.

Tissue Polynomial fitting [15] FNN fitting
128 MHz 128 MHz 298 MHz 915 MHz 2.45 GHz
NaCl Oil NaCl Oil NaCl Oil NaCl Oil NaCl Oil
Blood 1.21 1.9 0.959 0.63 0.959 0.99 0.859 2.27 0.890 2.14
Muscle 0.67 11 0.501 7.17 0.340 6.41 0.320 9.31 0.190 6.22
Skin 0.46 5 0.297 4.96 0.433 11.03 0.567 18.69 0.583 20.55
Lung 0.27 56 0.457 49.78 0.130 53.20 0.171 56.00 0.178 54.37

  1. aThe unit of NaCl concentration is g/100 mL oil‐in‐gelatin dispersion and the unit of oil volume concentration is %.

We measured the DPs of these phantoms and compared them to the literature values. All phantoms were manufactured under consistent conditions to ensure uniformity, and measurements were recorded at controlled temperatures. This comprehensive comparative analysis allows us to fully assess and evaluate the performance and effectiveness of the methods covered in this study.

Results

The measured error of measurement system

We performed a characterization of the measurement error by measuring ethanol solutions before measurements. The DPs of the ethanol solution were then calculated and compared with literature values to assess the accuracy. The results are shown in Figure 4 and the mean measurement uncertainty for relative permittivity was determined to be 2.11 %, while the mean measurement uncertainty for conductivity was found to be 3.84 %. These values provide an indication of the reliability and precision of our measurement system in determining the DPs of the materials [32], 33].

Figure 4: Measurement uncertainty analysis of the system: A is relative permittivity and B is conductivity, based on comparisons with literature values. The analysis was based on comparisons with literature values for ethanol solutions, revealing a mean measurement uncertainty of 2.11 % for permittivity and 3.84 % for conductivity.
Figure 4:

Measurement uncertainty analysis of the system: A is relative permittivity and B is conductivity, based on comparisons with literature values. The analysis was based on comparisons with literature values for ethanol solutions, revealing a mean measurement uncertainty of 2.11 % for permittivity and 3.84 % for conductivity.

The dielectric properties of phantoms and FNN fitting results

The fabricated phantoms are shown in Figure 5. The DPs of phantoms were measured around 27 ± 2 °C in the range of 16 MHz to 3 GHz and the results of 128 MHz are presented in Figure 6. These observations highlight the complex and interconnected nature of the relationships between material concentration and DPs.

Figure 5: A displays a variety of the fabricated phantoms. B illustrates the preparation process prior to measurement, while C provides detailed information about the measurement setup. The dielectric properties were measured under controlled conditions at approximately 27 ± 2 °C across the 16 MHz to 3 GHz frequency range.
Figure 5:

A displays a variety of the fabricated phantoms. B illustrates the preparation process prior to measurement, while C provides detailed information about the measurement setup. The dielectric properties were measured under controlled conditions at approximately 27 ± 2 °C across the 16 MHz to 3 GHz frequency range.

Figure 6: Dielectric properties of the phantoms measured around 27 ± 2 °C at 128 MHz. A shows the conductivity changes with the concentration of sodium chloride when the volume percentage of oil is 50 %, B depicts the relative permittivity changes with the volume percentage of oil when the concentration of sodium chloride is 1 g.
Figure 6:

Dielectric properties of the phantoms measured around 27 ± 2 °C at 128 MHz. A shows the conductivity changes with the concentration of sodium chloride when the volume percentage of oil is 50 %, B depicts the relative permittivity changes with the volume percentage of oil when the concentration of sodium chloride is 1 g.

Due to fabrication errors, the data from two phantoms was removed, resulting in a total of 135,954 sets of DPs (182 phantoms × 747 frequencies) used for fitting. The constructed neural network model is in good agreement with the measured data. To evaluate the performance of the FNN model, the mean squared errors (MSEs) were calculated. The MSE for CNaCl fitting was 0.0121, while the MSE for VPoil fitting was 0.0018. These small MSE values indicate its effectiveness in fitting the relationship between the input parameters and the output.

Programming results of software

The software interface for phantom configuration includes input, output, calculation, exit, and drop-down boxes. In the input data, the units of conductivity and frequency are S/m and MHz, respectively; in the output data, the units of NaCl concentration and oil volume percentage ratio are g/100 mL and %, respectively. Optional tissues are displayed in the drop-down box and click the specific tissue you want to use. The software can be used in two ways to obtain the CNaCl and VPoil required for phantom production. The first way is to click the drop-down box to select the organization you want, and the interface pops up to select the organization. Enter the frequency, and then click “OK” after selecting the tissue. The second method is to manually input the frequency, relative permittivity, and conductivity then click “Calculate” and the software will quickly and automatically output the required CNaCl and VPoil.

The software is user-friendly. The required composition of phantoms can be obtained within seconds by inputting DPs and frequency according to the text prompts. We present the calculated CNaCl and VPoil of muscle tissue here, as shown in Figure 7.

Figure 7: The calculated concentration of sodium chloride and the volume percentage of oil in the muscle tissue phantom at 915 MHz, determined using the software. The relative permittivity and conductivity of the muscle tissue at this frequency were found to be 55.0 and 0.85 S/m, respectively. The NaCl concentration was calculated as 0.320 g per 100 mL of oil‐in‐gelatin dispersion, with an oil volume concentration of 9.31 %.
Figure 7:

The calculated concentration of sodium chloride and the volume percentage of oil in the muscle tissue phantom at 915 MHz, determined using the software. The relative permittivity and conductivity of the muscle tissue at this frequency were found to be 55.0 and 0.85 S/m, respectively. The NaCl concentration was calculated as 0.320 g per 100 mL of oil‐in‐gelatin dispersion, with an oil volume concentration of 9.31 %.

Verification results

At first, the DPs of the verification phantoms at 128 MHz were measured at 25 ± 1 °C, and then comparison results between polynomial fitting and FNN fitting are shown in Table 4. It is evident that the relative error between the measured DPs obtained from the verification phantoms of FNN fitting and the literature values is within the range of 15 % from Table 4. In addition, we constructed 12 additional phantoms at 298 MHz, 915 MHz, and 2.45 GHz using FNN fitting. The measurement results are listed in Table 5 and the relative errors were kept in the range of 15 %.

Table 4:

Comparison of dielectric properties for verification phantoms representing blood, muscle, skin, and lung tissue, using polynomial fitting and feedforward neural network (FNN) fitting at 128 MHz. The phantoms were measured at 25 ± 1 °C, with relative errors between FNN fitting results and literature values maintained within 15%a.

Tissue Literature values FNN fitting Polynomial fitting
εr εr Relative error εr Relative error
Blood 73.2 73.3 0.14 % 72.3 1.23 %
Muscle 63.5 62.2 2.05 % 61.6 2.99 %
Skin 65.4 59.8 8.56 % 60.6 7.34 %
Lung 29.5 30.4 3.05 % 27.5 6.78 %
Tissue Literature values FNN fitting Polynomial fitting
σe (S/m) σe (S/m) Relative error σe (S/m) Relative error
Blood 1.25 1.20 4.00 % 1.35 8.00 %
Muscle 0.72 0.66 8.33 % 0.74 2.78 %
Skin 0.52 0.50 3.85 % 0.59 13.46 %
Lung 0.32 0.30 6.25 % 0.34 6.25 %

  1. aεr and σe are the relative permittivity and conductivity.

Table 5:

The dielectric properties of verification phantoms representing blood, muscle, skin, and lung tissue were measured  at 298 MHz, 915 MHz, and 2.45 GHz. The dielectric properties obtained using feedforward neural network fitting are compared with literature values, with relative errors maintained within 15%a.

Tissue Frequency Literature values Measurement values Relative error
εr σe (S/m) εr σe (S/m) εr σe (S/m)
Blood 298 MHz 65.7 1.32 68.4 1.47 4.11 % 11.36 %
Muscle 58.2 0.67 58.8 0.75 1.03 % 11.94 %
Skin 49.9 0.64 47.1 0.61 5.61 % 4.69 %
Lung 24.8 0.31 26.4 0.29 6.45 % 6.45 %
Blood 915 MHz 61.3 1.54 61.9 1.73 0.98 % 10.98 %
Muscle 55.0 0.85 49.7 0.92 9.64 % 8.24 %
Skin 41.3 0.87 40.3 0.98 2.42 % 12.64 %
Lung 22.0 0.41 23.0 0.47 4.55 % 14.63 %
Blood 2.45 GHz 58.3 2.55 56.0 2.54 3.95 % 0.39 %
Muscle 52.7 1.64 57.0 1.71 8.16 % 4.27 %
Skin 38.0 1.46 38.6 1.59 1.58 % 8.90 %
Lung 20.5 0.76 19.5 0.73 4.88 % 3.95 %

  1. aεr and σe are the relative permittivity and conductivity.

Discussion

In this study, we developed software to determine the CNaCl and VPoil of dielectric material, corresponding to desired values of DPs across the frequency range of 16 MHz to 3 GHz. This software is easy to use and will provide great convenience and efficiency for the most DPs-related research, which can be found at https://github.com/XinyueZhang02/software. Additionally, the dielectric material fabricated in this work has lots of advantages like simplicity in fabrication, long-term stability, and high reliability [15]. It is important to note that the DPs are also influenced by temperature, and therefore, the fabricated phantom, prepared according to the software, should be measured at the same temperatures [34], 35].

The dielectric materials can better assist the conduct of experiments. The scarcity of human tissue makes it very difficult to perform accurate dielectric experiments, therefore hindering the conduct of research and verification of conclusions. By phantoms, the physical properties of human tissue can be easily obtained, resulting in more reliable and repeatable experimental results. Besides, the use of dielectric materials can simplify the operation and process of research. The fabricated phantoms can be more readily available and can be stored for a long enough time. In conclusion, dielectric materials can mimic the physical properties of human tissues with designated DPs and frequency.

FNN model provides flexibility and accuracy in modeling dielectric materials with designated DPs. The relative permittivity and conductivity of dielectric materials are determined by the amount of CNaCl and VPoil in this work. Though it is simple to obtain the CNaCl and VPoil in a specified frequency, achieving the desired relative permittivity and conductivity at designated frequency reliably remains difficult. Therefore, an accurate and robust relationship among the materials composition, DPs, and frequency is required. To do this, a total of 184 phantoms were fabricated and measured. Then, we introduced the FNN model to establish the relationship. In previous work, Deng et al. established the relationship between the compositions of the dielectric materials and DPs at 128 MHz through polynomial fitting [15]. This fitting method is simple and reliable while it does have some limitations such as difficulty in representing highly complex data. Unlike their work, we aim to link the DPs with the compositions of the materials in a frequency range which leads to a large amount of data. Compared to the polynomial fitting, FNN has many advantages like powerful fitting capabilities and suitable for multiply data. Therefore, FNN is used in this work. According to the evaluation indicators, the FNN shows a good acquisition ability for CNaCl and VPoil with designated DPs and frequencies.

This work develops a comprehensive and simple model to obtain the accurate material amounts with desired DPs values and frequency. With an accuracy model, it is still inconvenient to for researchers to use. The acquisition of material amounts involves obtaining the established FNN model, inquiring DPs of human tissue, and calculating the CNaCl and VPoil. This process is time-consuming, especially inquiring DPs of human tissue. Hence, software was proposed to calculate the CNaCl and VPoil over a wide frequency range from 16 MHz to 3 GHz. The software can help users skip the complicated calculation process through simple operations, just input the relevant data or select the specified organization to quickly output the required formula amount. The software’s operability and ease of use are very friendly to users with non-engineering backgrounds, and combined with its advanced algorithms, it can become an efficient, convenient, and accurate tool in the phantom production process.

With the software, a set of validation dielectric materials was fabricated including blood, muscle, skin, and lung tissue as listed in the Table 3. The results show a good fitting effect with the relative errors of measured and literature DPs within 15 %. Through comparing the eight phantoms fabricated at 128 MHz using FNN fitting and polynomial fitting, and by constructing 12 additional phantoms at 298 MHz, 915 MHz, and 2.45 GHz using FNN fitting, we further validated the accuracy of the FNN fitting method.

However, the verification results indicate some discrepancies between the DPs of fabricated phantoms and literature values, which we attribute to manufacturing processes, measurement errors, or fitting flaws. Another concern is that the measurement temperature is not consistent. Since DPs are temperature-dependent, potential temperature perturbations will affect the measured DPs and the experimental results. To address these issues, we plan to improve our future work as follows. First, increasing the mapping between artificial material and DPs would enhance FNN fitting. Second, redesigning the FNN model to include temperature as an input parameter during fitting would be beneficial. We expect these limitations to be effectively addressed in future work.

Conclusions

The aim of this study is to develop concise and efficient software that can quickly calculate the composition of dielectric materials with the required DPs in the frequency range from 16 MHz to 3 GHz. The key to realizing this software lies in establishing the relationship among DPs, material concentrations, and frequency. We used FNN to fit the relationship. This software has several significant advantages. First of all, the software is easy-to-use and the calculations are simple. Additionally, the dielectric phantoms produced in this study exhibit long-term stability. However, it is essential to acknowledge the temperature dependency of phantom DPs, thus, the temperature of the measured phantom should align with the conditions used in this study. Adhering to consistent temperature conditions ensures the reliability and validity of the obtained data. In the future work, our goal is to incorporate temperature considerations into the relationship between DPs and material concentrations. We anticipate that our efforts will contribute to streamlining the fabrication process of dielectric materials.

Corresponding authors: Xiang Nan, Basic Medical School, Anhui Medical University, No. 81 Meishan Road, Shushan District, Hefei, Anhui, China, E-mail: ; and Jijun Han, School of Biomedical Engineering, Anhui Medical University, Tanghe Road, Xinzhan High-tech Industrial Development Zone, Hefei, Anhui, China, E-mail:

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 62271007

Award Identifier / Grant number: 82102742

Acknowledgments

The authors thank the Center for Scientific Research of School of Biomedical Engineering, Anhui Medical University for valuable help in our experiment. This work is supported by the National Natural Science Foundation of China (Grant No. 62271007, 82102742).

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: The AI was used to improve the language and clarity of the manuscript.

  5. Conflict of interest: The authors state no conflict of interest.

  6. Research funding: The National Natural Science Foundation of China (Grant No. 62271007, 82102742).

  7. Data availability: The raw data can be obtained at https://github.com/XinyueZhang02/software.

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Received: 2024-01-30
Accepted: 2024-10-07
Published Online: 2024-10-28
Published in Print: 2025-02-25

© 2024 the author(s), published by De Gruyter, Berlin/Boston

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/bmt-2024-0043
Keywords for this article
dielectric properties; open-ended coaxial probe; dielectric phantom; Android Studio
Creative Commons
BY 4.0

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. Change of publication model for Biomedical Engineering/Biomedizinische Technik
  4. Research Articles
  5. Mechano-responses of quadriceps muscles evoked by transcranial magnetic stimulation
  6. A type-2 fuzzy inference-based approach enables walking speed estimation that adapts to inter-individual gait patterns
  7. DeepCOVIDNet-CXR: deep learning strategies for identifying COVID-19 on enhanced chest X-rays
  8. Prediction of muscular-invasive bladder cancer using multi-view fusion self-distillation model based on 3D T2-Weighted images
  9. Evaluation of the RF depositions at 3T in routine clinical scans with respect to the SAR safety to improve efficiency of MRI utilization
  10. A software tool for fabricating phantoms mimicking human tissues with designated dielectric properties and frequency
  11. MedShapeNet – a large-scale dataset of 3D medical shapes for computer vision
  12. Concept and development of a telemedical supervision system for anesthesiology in operating rooms using the interoperable communication standard ISO/IEEE 11073 SDC
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