Study on the effective measurement area of an open-ended coaxial probe for the dielectric measurement of biological tissues

Abstract

BACKGROUND:

The dielectric properties of tissues are very important physical factors for the investigation and application of bio-electromagnetism. However, the size of the active sample tissue is usually limited in actual measurement, making it difficult to meet the requirements of the existing high-frequency measurement methods, thus influencing the measurement results.

OBJECTIVE:

The present study aimed to systematically investigate the various factors influencing the effective measurement area of the open-ended coaxial probe, including the design size of the probe and the dielectric properties of the object to be measured.

METHODS:

The simplified material mixing model, in which several types of materials were set as the material under test (MUT) and the perfect conductor (PEC) was set as the specific material, was used in the simulation to study the effective measurement area of eight types of probes with different sizes for the dielectric measurement of different MUTs. Different concentrations of NaCl solutions and three types of coaxial probes were used in the actual measurement to verify the simulation results.

RESULTS:

According to the simulation results, the effective measurement area, especially the effective measurement radius, was closely related to the outer conductor radius of the probe. The effective measurement area of the probe decreased when the outer conductor radius of the probe reduced. Moreover, the change in the effective measurement area of the probe was independent of the MUT when the cross-sectional size of the probe was smaller than a certain threshold value. The experimental results also confirmed this conclusion.

CONCLUSION:

According to the research results, the independent variable dimension could be effectively reduced and the modeling difficulty was reduced when the analysis model of the effective measurement area of the probe was established.

Keywords

Dielectric measurement effective measurement area coaxial probe bioelectromagnetism biological tissues

1. Introduction

Dielectric properties of biologically active tissues are related to not only the microstructure of the tissues [1, 2] but also various physiological activities inside the tissues [3]. Therefore, the dielectric property is an important factor for biophysical research on the impact of multiple electromagnetic radiation environment on organisms. It also has important applications in the study of biological electromagnetic effects, research and development of medical and health equipment, effectiveness evaluation of new military weapons, manned space engineering, and other fields. Since the beginning of the last century, people have carried out measurement research on the dielectric properties of tissues [4, 5, 6, 7]. At present, relevant technologies for measuring the dielectric properties of bioactive tissues in the middle and low frequency bands (10 KHz to 100 MHz) have been established [8, 9], but the high-frequency bands still have unresolved issues.

The main method for measuring the dielectric properties of high-frequency bands is the open-ended coaxial reflection method [6]. The dielectric properties of the tissue at the end of the probe were calculated by measuring the ratio of absorption and reflection of electromagnetic energy to biological tissue at the end of the probe and the change in the phase. The use of this method was mainly based on two assumptions: first, the measured tissue should be single and homogeneous. Second, the size of the measured tissue should be large enough to avoid the impact of tissue boundaries on the measurement results [6]. However, in the actual measurement, the size of active samples collected clinically for measurement was usually limited to keep the samples homogenous, and the tissue boundary had a significant impact on the measurement results [10, 11]. As a result, the actual measurement results were the equivalent dielectric properties of multiple substances mixed in the probe measurement area, rather than the dielectric properties of the target tissue itself, which is the main problem faced by the current measurement of dielectric properties of active tissues in the high-frequency band [12].

When measuring the dielectric properties of tissues in vitro using the open-ended coaxial probe, the sample tissue size should be larger than the effective measurement area of the coaxial probe to avoid the influence of the tissue boundary. As a result, the determination of the measurement area of the probe is the primary prerequisite for the accurate measurement of high-frequency dielectric properties. Hagness believed that the size of the measured area varied with the design size of the probe, indicating that if the size of the probe was reduced, the measurement area would decrease accordingly [13]. However, Gabriel’s study showed that the design size was not the only factor affecting the measurement area. The working frequency and the dielectric properties of the measured object might affect the measurement area, so the probe size required to measure different biological tissues might also be different [14]. As no analytical model determining the measurement area is available, many research groups mainly determined the measurement area of their respective coaxial probes based on the actual measurement. Hagness et al. explored the measurement region of their 2.2-mm and 3.58-mm coaxial probes in the 1–20 GHz band based on the dielectric properties of salt solution. By comparing the measurement results of the probes at different positions in the salt solution, the measurement depth and breadth (the transverse measurement size of the probes) of the two probes were, respectively, 1.5 mm/5 mm and 3 mm/11 mm [13]. Meaney et al. compared the measurement results of the probe at different positions of the double-layer mixed substance composed of salt solution and poly tetra fluoroethylene (PTFE), and studied the measurement depth of the 2.2-mm coaxial probe at the 300-KHz to 8.5-GHz frequency band at 0.2–0.5 mm [15]. In the subsequent study, the measurement depths of several probes of different sizes were compared [16]. However, the experimental results were different from those of Hagness in terms of the depth measured by the probe. Porter’s team investigated the measurement depth and lateral size of a 2.2-mm probe in the 300-MHz to 8.5-GHz band based on simulation and verified it with a two-layer mixture of rubber, salt solution, and part of pig tissue. The measurement area of the probe was mainly affected by the surface material of the measured sample, but the probe measurement depth changed with the different frequencies and the measured materials [17, 18, 19]. Yonghong explored the induction range of the coaxial probe based on the layered model composed of various materials, such as ethanol, deionized water, and salt solution, and believed that it was affected by both the measurement parameters and the dielectric properties of the measured object, among which the measurement depth was greatly affected [20].

Most of the current researches on the probe measurement area were need based and explored only the measurement area of the probe with a specific size in the measurement object by experimental methods. Once the probe size or the measurement object changed, it could not be concluded whether the measurement area would change. Therefore, the conclusions of the existing studies are of limited use in practical measurement. A general analysis method or model for the effective measurement area of the probe is required. Therefore, this study systematically investigated the various factors influencing the effective measurement area of the open-ended coaxial probe. The design size of the probe and the dielectric properties of the object to be measured were discussed based on the simulation and measurement in the 100-MHz to the 3-GHz band to establish the analysis and calculation model of the effective measurement area of the coaxial probe.

2. Methods

2.1 Analysis method for measuring the area of the open-ended coaxial probe

The probe terminal was attached to the surface of the tissue and measured the reflection coefficient $\Gamma^{\ast}$ of electromagnetic energy reflected back by the tissue to measure the dielectric properties of biological tissues. Finally, the dielectric properties parameter $\varepsilon_{r}^{\ast}$ of the tissue, including dielectric coefficient $\varepsilon_{r}^{\ast}$ and electrical conductivity $\sigma$ , were obtained through the calculation of the established model [6]. For the convenience of model analysis, the reflection coefficient $\Gamma^{\ast}$ is usually converted to the equivalent input admittance of probe terminal $Y_{in}$ , and the relationship between the two is as follows:

$\displaystyle Y_{in}=Y_{C}\frac{1-\Gamma^{\ast}}{1+\Gamma^{\ast}}$ (1)

In Eq. (1), $Y_{C}$ is the characteristic admittance of the coaxial probe itself. General standard coaxial probe characteristic admittance is 0.02 S.

According to the previous research conclusion [21], the transverse sectional size of the measurement area of the coaxial probe in the tissue gradually decreased with the increase in the measurement depth. Therefore, the effective measurement area as a whole presented an approximate inverted conical shape, as shown in Fig. 1. The measurement radius $r$ and measurement depth $d$ are used to quantitatively describe the effective measurement area [20].

Figure 1.

Schematic diagram of the effective measurement area of the probe.

The equivalent input admittance of $Y_{in}$ at the probe terminal changes when substances other than the tissue are measured in the probe measurement area. Therefore, the range of the probe measurement area is determined according to the variation in $Y_{in}$ . The probe terminal equivalent input admittance measurement sensitivity $S_{p}$ is defined as follows:

$\displaystyle Re(S_{p})=\frac{Re(Y_{in})}{Re(Y^{\prime}_{in})}$ (2) $\displaystyle Im(S_{p})=\frac{Im(Y_{in})}{Im(Y^{\prime}_{in})}$

In Equ. (2.1), $Y^{\prime}_{in}$ is the terminal equivalent input admittance of the probe when only tissue is to be measured in the measurement area $Y_{in}$ is the terminal equivalent input admittance of the probe when the tissue and other substances are all present in the measurement area. $Re(S_{p})$ or $Im(S_{p})$ not equal to 1 indicates the presence of a specific substance in the probe measurement area. At this time, the effective measurement area parameters $r$ and $d$ of the probe can be determined according to the position of the specific substance.

2.2 Simulation research method for an effective measurement area of the probe

According to the analysis method of the measurement area of the probe, the effective measurement area parameters $r$ and $d$ can be determined by changing the position parameters of the specific substance introduced into the measured tissue. Therefore, the research on effective measurement area of the probe can be carried out based on simulation.

Figure 2.

Schematic diagram of simulation model structure: (a) $d$ is the simulation setting of the effective measurement depth of the probe and (b) $r$ is the simulation setting of the effective measurement radius of the probe.

2.2.1 Simulation model setting

As shown in Fig. 2, the object measured in the simulation was mainly composed of two parts: one was the target material under test (MUT), and the other was the specific material. The perfect conductor (PEC) was adopted to highlight the difference. In Fig. 2a, the transverse section size of PEC was consistent with that of the MUT. In the depth direction, the effective measurement depth $d$ of the probe could be determined by observing the change in the simulation results when the depth $d$ of the probe at the upper boundary of PEC was changed. Similarly, in Fig. 2b, the longitudinal depth of PEC was consistent with the MUT, and the position $r$ of the PEC distance from the probe was changed in the transverse direction. The effective measurement radius $r$ of the probe could be determined by observing the change in the simulation results.

The simulation working frequency was set as 100 MHz to 3 GHz. The dielectric parameters of the MUT were set directly according to the research needs. In the simulation study, when the MUT was identified as the biological tissue, its dielectric properties could be analyzed and calculated using Gabriel’s fourth-order Cole–Cole equation, as shown in Eq. (3), and imported into the model [4]:

$\displaystyle\hat{\varepsilon}=\varepsilon_{\infty}+\sum\limits_{i=1}^{4}{% \frac{\Delta\varepsilon_{i}}{1+(j\omega\tau_{i})^{(1-\alpha_{i})}}}+\frac{% \sigma_{s}}{j\omega\varepsilon_{0}}$ (3)

where $\varepsilon_{\infty}$ is the high-frequency permittivity and $\varepsilon_{s}$ is the static permittivity; $\tau$ is the relaxation time; $\alpha$ is the relaxation factor; and $\sigma$ is the static conductivity.

2.2.2 Setting of factors affecting the effective measurement area

Table 1
Coaxial probes with an open terminal in different design sizes

Probe type	$b$ (mm)	$a$ (mm)	Filling medium	$Z_{c}$ ( $\Omega$ )
Type A	3	1.303	Air	50
Type B	4.55	1.303	Air	75
Type C	6	1.303	Air	91.56
Type D	6	2.61	Air	50
Type E	10	4.343	Air	50
Type F	6	1.95	Air	67.38
Type G	0.77	0.35	Air	50
Type H	30	13.03	Air	50

The main factors affecting the effective measurement area of the probe were the design size of the probe and the dielectric properties of the measured materials. The probe design size mainly included the probe inner radius $a$ and the probe outer radius $b$ , which also determined the probe characteristic impedance $Z_{c}$ . Table 1 lists the setting of the probe size in the simulation. The dielectric parameters mainly included the dielectric coefficient $\varepsilon_{r}$ and conductivity $\sigma$ . In the simulation study of the influence of probe design size on the effective measurement area, the dielectric parameters of the MUT were set according to Gabriel’s fourth-order Cole–Cole model of skin tissue [4]. When studying the influence of the dielectric parameters of the MUT on the effective measurement area, the dielectric parameters of the MUT were randomly set within the range of dielectric parameters of biological tissues in the simulation frequency band [4]. The combination of dielectric coefficient and conductivity was also random in order to ensure the objectivity of the study. The dielectric parameters of the MUT in our simulation were shown in Table 2.

Table 2

Dielectric properties of different measurement objects

MUT	$\varepsilon_{r}$	$\sigma$ (S/m)
Material 1	30	0.3
Material 2	140	1.2
Material 3	80	0.01
Material 4	50	0.64
Material 5	20	0.15
Material 6	70	0.39
Material 7	110	1.31
Material 8	400	1.68

2.3 Test verification method for the effective measurement area of the probe

Three types of coaxial probes with different sectional sizes were used to test and verify the effective measurement area of the probe. The design sizes of the three probes were as follows: probe 1 (PTFE filled, internal and external diameter 0.29/1.19 mm), probe 2 (PTFE filled, internal and external diameter 0.53/2.15 mm), and probe 3 (PTFE filled, internal and external diameter 1.2/4.5 mm). The vector network analyzer NanovNA-F V2, which had its own open circuit, short circuit, and matching load accessories for calibration was used for measuring the frequency range of 100 MHz to 3 GHz. The NaCl solutions at different concentrations (0.005M, 0.01M, 0.03M, 0.05M, and 0.15M) were used as the MUT.

According to the simulation settings in Fig. 2, the 100 ml beaker with the diameter 5.7 cm and height 7.3 cm containing NaCl solution was placed on a metal base to form a longitudinal layered measured object model. The probe terminal was placed at the bottom of the beaker for initial measurement. The probe terminal position was continuously raised to observe and record the measurement results and the probe terminal height, and the effective measurement depth $d$ of the probe was determined according to the changes in the measurement results. In the same way, the aluminum foil and the test paper soaked in the NaCl solution were spliced to form a lateral layered model. The distance between the probe terminal and the splicing place was changed, and the effective measurement radius $r$ of the probe could be determined according to the change in the measurement results. Figure 3 shows the measurement system and measurement setup.

Figure 3.

Schematic diagram of simulation model structure: (a) probe measurement depth measurement setting (the NaCl solution was 4.8 cm in diameter and 5.0 cm in height), (b) probe measurement breadth measurement setting, (c) the measurement system combination.

3. Results

3.1 Study of the probes featuring different openings of the outer conductor b

The radius of the outer conductor $b$ was examined in this section. Therefore, the type A, type B, and type C probes listed in Table 1 were used for the simulation. Figure 4 shows the real part of the measurement sensitivity $Re(S_{p})$ of each probe. As shown in Fig. 4a, the $Re(S_{p})$ of the type A probe was not 1 when the parameter $r$ was $<$ 4 mm. This indicated the presence of PEC in the effective measurement area. As a result, the measurement radius $r$ of the type A probe was determined to be 4 mm. The measurement depth $d$ of the type A probe was determined to be 9 mm according to Fig. 4b. By the same method, the measurement radius $r$ and measurement depth $d$ of the type B and C probes were $r=$ 5 mm and 7 mm and $d=$ 9 mm and 9 mm respectively, according to Fig. 4c–f.

Comparing Fig. 4a, c, and e, it was seen that the effective measuring radius $r$ of the probe increased with the increase in the outer radius $b$ of the probe. As a result, the measured radius $r$ of the type C probe ( $r=$ 7 mm) was larger than that of the other two probes. On the contrary, the radius of the outer conductor could not increase the effective detected depth of the probe for the measurement as shown in Fig. 4b, d, and f. Therefore, the effective detected depth of these probes was $d=$ 9 mm. However, the measurement sensitivity $Re(S_{p})$ of the probe in the depth direction increased with the increase in the outer radius $b$ of the probe. Therefore, a larger radius of the outer conductor $b$ could increase the effective measured radius $r$ of the probe and improve the measurement sensitivity of the probe in the depth direction a little.

Figure 4.

Real part of the measurement sensitivity $Re(S_{p})$ of each probe. (a) $Re(S_{p})$ of the type A probe in the direction of cross section. (b) $Re(S_{p})$ of the type A probe in the depth direction. (c) $Re(S_{p})$ of the type B probe in the direction of cross section. (d) $Re(S_{p})$ of the type B probe in the depth direction. (e) $Re(S_{p})$ of the type C probe in the direction of cross section. (f) $Re(S_{p})$ of the type C probe in the depth direction.

3.2 Study of the probes featuring different radii of the inner conductor a

The radius of the inner conductor $a$ was examined in this section, considering the type C, type D, and type F probes in Table 1. Figure 5 shows the real part of the measurement sensitivity $Re(S_{p})$ of each probe. As shown in Fig. 5, the measurement radius $r$ and depth $d$ of each probe were the same, which were determined to be 7 mm and 9 mm, respectively. As a result, the type D probe with the largest radius of the inner conductor could not increase the measurement radius and depth of the probe for the measurement. However, the measurement sensitivity $Re(S_{p})$ of the type D probe in the direction of cross section and depth was larger than that of the other two probes especially in the high-frequency band. Therefore, it was demonstrated that the larger radius of the inner conductor could improve the sensitivity of the probe to the target in heterogeneous tissues, especially in the high-frequency band. However, it could not increase the effective measurement area obviously.

Figure 5.

Real part of the measurement sensitivity $Re(S_{p})$ of each probe. (a) $Re(S_{p})$ of the type C probe in the direction of cross section. (b) $Re(S_{p})$ of the type C probe in the depth direction. (c) $Re(S_{p})$ of the type D probe in the direction of cross section. (d) $Re(S_{p})$ of the type D probe in the depth direction. (e) $Re(S_{p})$ of the type F probe in the direction of cross section. (f) $Re(S_{p})$ of the type F probe in the depth direction.

3.3 Study of the probes with the same characteristic impedance

Z_{c}

In the previous section, the main factors influencing the dimension of the probe were examined for the dielectric measurement. However, the characteristic impedance $Z_{c}$ of the probe might also have an influence on the measurement. However, it could be changed when the dimension of the probe was changed. Therefore, in this section, the type A, type D, and type E probes with the same characteristic impedance $Z_{c}$ in Table 1 were used to validate the influence of probes with different dimensions in the dielectric measurement. As shown in Fig. 6e and f, the probe with the largest dimension (type E) had a larger effective measurement area than that of the other two probes whose measurement radius $r$ and depth $d$ were 9 mm and 10 mm, respectively.

On the contrary, Fig. 6 shows that the increase in the inner and outer radius of the probe could significantly improve the effective measuring radius $r$ , while the increase in the effective measuring depth $d$ was relatively small, which was consistent with the research results in the previous section.

3.4 Study of the probes with different MUTs

The effect of dielectric properties on the effective measurement area of the probe was discussed in this section. The type A, type G, and type H probes in Table 1 and different measurement objects in Table 2 were used for the simulation. Table 3 shows the results of simulation.

Table 3
Effective measurement area parameters of the probe under different MUTs

MUT	Type A		Type G		Type H
	$d$ (mm)	$r$ (mm)	$d$ (mm)	$r$ (mm)	$d$ (mm)	$r$ (mm)
Material 1	2	3	1	1	40	30
Material 2	4	4	1	1	70	30
Material 3	1	3	1	1	70	50
Material 4	2	3	1	1	40	30
Material 5	4	3	2	1	70	50
Material 6	3	3	2	1	70	50
Material 7	5	3	2	1	50	30
Material 8	6	5	2	1	70	30

Figure 6.

Real part of the measurement sensitivity $Re(S_{p})$ of each probe. (a) $Re(S_{p})$ of the type A probe in the direction of cross section. (b) $Re(S_{p})$ of the type A probe in the depth direction. (c) $Re(S_{p})$ of the type D probe in the direction of cross section. (d) $Re(S_{p})$ of the type D probe in the depth direction. (e) $Re(S_{p})$ of the type E probe in the direction of cross section. (f) $Re(S_{p})$ of the type E probe in the depth direction.

As shown in Table 3, the effective measurement radius $r$ of the type G probe with the minimum dimension was not changed with the dielectric properties of the MUT. As the dimension of the probe increased, the effective measuring radius $r$ gradually changed with the dielectric properties of the MUT, such as that of the type A and H probes in Table 3. This suggested that the effective measuring radius of the probe did not change with the dielectric properties of the MUT when the cross-section dimension of the probe was small enough. Therefore, when the effective measurement radius parameter of a sufficiently small probe was modeled, the influence of the dielectric properties of the MUT could be ignored and the number of model-independent variables was reduced On the contrary, Table 3 shows that the effective measuring depth $d$ of the three probes changed with the dielectric properties of the MUT, but the effective measuring depth of the probe with small cross-section dimension (type C) was the least affected by the MUT.

3.5 Test verification results

Figure 7 shows the real part of the measurement sensitivity $Re(S_{p})$ of the probe 3 when measuring the 0.03M NaCl solution, which was the part of the experiment results. Table 4 shows the effective measurement area parameters of the three probes measuring different NaCl solutions.

Table 4
Effective measurement area parameters of the probe for different NaCl solutions

MUT	Probe 1		Probe 2		Probe 3
	$d$ (mm)	$r$ (mm)	$d$ (mm)	$r$ (mm)	$d$ (mm)	$r$ (mm)
0.15M NaCl	1	$<$ 0.5	2	1	4	5
0.05M NaCl	1	$<$ 0.5	2	1	3	5
0.03M NaCl	1	$<$ 0.5	2	1	3	5
0.01M NaCl	1	$<$ 0.5	2	1	3	5
0.005M NaCl	1	$<$ 0.5	2	1	2	5

Figure 7.

Real part of the measurement sensitivity $Re(S_{p})$ of the probe 3 measuring the 0.03M NaCl solution. (a) $Re(S_{p})$ in the direction of cross section. (b) $Re(S_{p})$ in the depth direction.

As shown in Fig. 7, when the probe 3 was used for measuring 0.03M NaCl solution, the effective measuring radius $r$ and depth $d$ of the probe were 5 mm and 3 mm, respectively. Table 4 shows that the effective measurement area of the probe, especially the effective measurement radius, increased with the increase in the probe section dimension. Moreover, the effective measuring radius of the three probes did not change with the MUT, indicating that the effective measurement radius of the probe had no correlation with the dielectric properties of the MUT when the cross-sectional dimension of the probe was small enough. The test results were consistent with the simulation conclusions in the previous section.

4. Discussion

The measurement of dielectric properties of biological tissues has always been a concern for the researchers. The final research goal of this study was to explore a method to accurately measure the dielectric properties of biological tissues based on the principle of coaxial probe measurement. In this study, we focused on the methodologies for in vitro measurement of the effective area with coaxial probes.

Although the structure of biological tissue is complex, the homogeneity of the samples can be ensured by controlling the measurement of the sample size in vitro. As a result, the tissue samples measured in vitro using the open-ended coaxial probe in this study were considered to be homogeneous. However, the tissue boundary had a significant impact on the measurement results when the size of the samples was smaller than that of the probe measurement area. At this time, the actual measurement results were the equivalent dielectric properties of the target tissue mixed with the air in the probe measurement area, rather than the dielectric properties of the target tissue itself. Therefore, the measurement area of the probe in in vitro measurement was investigated in this study for the analysis and modeling to determine the measured sample size required to ensure that the measured tissue size was larger than the probe measurement area.

According to the results of simulation and experimental tests in the previous section, the increase in the outer conductor radius $b$ could observably improve not only the sensitivity but also the effective measurement area of the coaxial probe for the dielectric measurement of the MUT. This might be because the electromagnetic field in the MUT was expanded by increasing the outer conductor radius of the probe. This meant that the larger dimension probe might not be suitable to be used for the actual dielectric measurement in vitro. The size of tissue samples in actual measurements was usually not too large to keep the samples homogenous. Thus, the probe with a smaller cross-sectional dimension was more suitable for in vitro measurement of tissue dielectric properties. On the contrary, the effective measurement radius of the probe had no correlation with the dielectric properties of the MUT when the cross-sectional dimension of the probe was small enough. It meant that when the size of the probe was determined, the effective measurement radius of the probe was also determined. Moreover, we could sample biological tissues according to the effective measurement radius size of the probe to ensure that the sample was homogeneous, as well as the transverse cross-sectional sizes of the tested tissues were greater than the effective measurement radius of the probe. At the same time, the effective measurement depth size of the probe with the smaller dimension was also usually small ( $d=$ 1 mm or 2 mm) as shown in Table 4, which was smaller than that of most homogeneous samples. The threshold of the probe cross-section size $b$ should be explored to determine which type of probe could satisfy the sufficiently small condition.

The characteristic impedance $Z_{c}$ would also have an influence on the effective measuring area of the probe. However, the characteristic impedance of the probe was closely related to the design dimension parameters of the probe. The characteristic impedance of the probe was calculated as follows:

$\displaystyle Z_{c}=\frac{60\ln\left(\raise 3.01pt\hbox{$b$}\!\mathord{\left/{% \vphantom{ba}}\right.\kern-1.2pt}\!\lower 3.01pt\hbox{$a$}\right)}{\sqrt{% \varepsilon_{r}}}$ (4)

where $\varepsilon_{r}$ is the relative permittivity of the material filled in the probe; and $a$ and $b$ are the probe inner and outer radius, respectively. Therefore, the characteristic impedance $Z_{c}$ of the probe was considered in Section 3.3 to confirm that the design dimension parameters of the probe were the main factors affecting its effective measurement area. In practical measurement, the standard coaxial probe was usually used to measure the dielectric properties whose characteristic impedance was 50 $\Omega$ . As a result, the parameter $b$ was the only dimensional variable to be considered

Figures 4–7 show that the measurement sensitivity $S_{p}$ of the probe changed at different frequencies, but it did not affect the discrimination of the effective measurement radius $r$ and depth $d$ of the probe. This suggested that we could study and determine the effective measurement parameters of the probe without considering the influence of frequency factors on the operating frequency band.

The effective measurement area of the probe was firstly studied based on simulation in this paper. Then the simulation results were verified by actual measurement. As a result, a discussion of the metrological aspects of measurement is very important for actual measurement [22, 23]. The room temperature was constant at 26 ${}^{\circ}$ C during the measurement. The humidity was not necessary to be considered, mainly because the front part of the probe was soaked in solution during measurement. The incubator with a humidifier can be used for the measurement of the non-liquid substances, such as biological tissue in order to maintain the temperature and humidity of the measurement environment. The calibration process mainly consists of two parts. First, the calibration was performed by the open circuit, short circuit, and matching load accessories according to network analyzer NanovNA-F V2 calibration function, which determined the port of the analyzer as the referenced plane for measurement. Then the reflection coefficient that was measured when the probe was opening was used to decrease the systemic error by the phase offset method.

5. Conclusion

In this study, the key factors influencing the effective measurement area of the open-ended coaxial probe, including the probe design dimension and the dielectric properties of the MUT, were studied in the frequency ranging from 100 MHz to 3 GHz based on simulation and measurement. The simplified material mixing model, in which several types of materials were set as the MUT and the PEC was set to be the specific material, was used in the simulation to study the effective measurement area of eight types of probes of different sizes for the dielectric measurement of different MUTs. The NaCl solutions with different concentrations and three types of coaxial probes were used in the actual measurement to verify the simulation results. According to the results, the effective measurement area, especially the effective measurement radius, was closely related to the outer conductor radius of the probe. The effective measurement area of the probe decreased when the outer conductor radius of the probe was reduced. Further, the change in the effective measurement area of the probe was independent of the MUT when the cross-sectional size of the probe was smaller than a certain threshold value. As a result, the change in the effective measurement area of the probe whose cross-sectional size was smaller than 2.15 mm was independent of the MUT in the frequency ranging from 100 MHz to 3 GHz according to the results in this paper. This conclusion is very important to establish the analysis model of the effective measurement are of the open-ended coaxial probe. The independent variable dimension can be effectively reduced and the modeling difficulty can be reduced when the analysis model of the effective measurement area of the probe is established.

Footnotes

Acknowledgments

This research was supported by the National Key R&D Program of China (2019YFC0119103) and the NSFC (31900978).

Conflict of interest

None to report.

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Study on the effective measurement area of an open-ended coaxial probe for the dielectric measurement of biological tissues

Abstract

BACKGROUND:

OBJECTIVE:

METHODS:

RESULTS:

CONCLUSION:

Keywords

1. Introduction

2. Methods

2.1 Analysis method for measuring the area of the open-ended coaxial probe

Table 1 Coaxial probes with an open terminal in different design sizes

3.1 Study of the probes featuring different openings of the outer conductor b

3.4 Study of the probes with different MUTs

Table 3 Effective measurement area parameters of the probe under different MUTs

Table 4 Effective measurement area parameters of the probe for different NaCl solutions

Footnotes

Acknowledgments

Conflict of interest

References

Table 1
Coaxial probes with an open terminal in different design sizes

Table 3
Effective measurement area parameters of the probe under different MUTs

Table 4
Effective measurement area parameters of the probe for different NaCl solutions