Sensitivity investigation of open-ended coaxial probe in skin cancer detection

Open-ended coaxial probe method is one of the most common modalities in measuring dielectric properties (DPs) of biological tissues. Due to the significant differences between the tumors and normal tissues in DPs, the technique can be used to detect skin cancer in the early stage. Although various studies have been reported, systematic assessment is in urgent need to advance it to clinical applications, for its parameters interactions and detecting limitations remained unclear. In this study, we aim to provide a comprehensive examination of this method, including the minimum detectable tumor size by using a three-layer skin model via simulation and demonstrated that open-ended coaxial probe method can be used for detection of early-stage skin cancer. The smallest detecting size are subject to different subtypes: for BCC, inside the skin is 0.5 mm radius × 0.1 mm height; for SCC, inside the skin is 1.4 mm × 1.3 mm in radius and height; the smallest distinguishing size of BCC is 0.6 mm × 0.7 mm in radius and height; for SCC is 1.0 mm × 1.0 mm in radius and height; for MM is 0.7 mm × 0.4 mm in radius and height. The experiment results showed that sensitivity was affected by tumor dimension, probe size, skin height, and cancer subtype. The probe is more sensitive to cylinder tumor radius than height growing on the surface of the skin while the smallest size probe is the most sensitive among the working probes. We provide a detailed systematic evaluation of the parameters employed in the method for further applications.


Introduction
Skin cancer is caused by abnormal growth of skin cells, which can be classified into two categories: melanoma (MM) and non-melanoma skin cancer (NMSC). MM is an aggressive skin cancer because it can spread to other organs rapidly. The latter category includes basal cell carcinoma (BCC) and squamous cell carcinoma (SCC) [1]. Different types display distinct growth characteristics and hazards: BCC is a slow-growing tumor that can be invasive but rarely metastasize, while SCC grows more rapidly and is more likely to invade and metastasize; these NMSC can result in significant disfigurement which jeopardize the physical and mental health of patients, MM is the most aggressive and the deadliest form of skin cancer. Early detection of skin cancer will help doctors adopt an appropriate treatment plan to improve prognosis.
The current diagnostic procedure to identify skin cancer is based on visual analysis involving full-body examination by a qualified physician using dermatoscope [2]. It allows a rapid observation of the skin surface [3]. The identification relies on dermatoscopic image characteristics caused by different lesion types. However, naked-eye observations have obvious drawbacks, with the main one being low accuracy and a risk of false-positive detections [4]. With computeraided techniques [5], the detection can be compromised due to imaging noises, shadows, and artifacts [6]. Thus, an accurate and objective method should be developed to detect early-stage skin cancer.

3
An alternative approach based on measuring dielectric properties (DPs) has been developed for tumor detection. The theory is that tumors, compared with normal tissues, exhibit significant differences in DPs. Since during tumor genesis, changes in cell membrane permeability, intracellular water content, and microenvironment lead to DPs variations [7]. Open-ended coaxial probe (OCP) method is used in DPs measurement. In this method, OCP is connected to one port of a vector network analyzer (VNA) through a transmission line. The reflection coefficients are measured at different frequencies by VNA and then resulting S11 parameters are used to retrieve DPs based on transmission line theory. OCP method is accurate and easy-to-use, so it has been widely used to measure DPs and distinguish tumors from normal tissues, such as breast [8], brain [9], liver [10], kidney [10], lung [11], colorectal [12], and lymph nodes [13].
OCP method has gained increasing attention for early detection and diagnosis of skin cancer. A recent study showed different sizes of skin cancer in simulation, and OCP method collected S-parameters with 2.2 mm open-ended coaxial probe; furthermore, it analyzed discrepancy between malignant tumor and healthy tissues [14]. Moreover, they demonstrated the possibility of identifying skin cancer from measured electrical properties and investigates the sensing depth of the 2.2 mm-diameter open-ended coaxial probe for skin mimicking phantom [15]. Aydinalp et al. [16] studied the effect of open-ended coaxial diameter on the depth of penetration and Porter et al. [17] highlighted the relationship between the volume of tissue and the contribution of that tissue to the measured DPs. Previous works reported the potential of skin cancer detection using OCP method. However, studies are scattered, and none provided the minimum detection limitation and systematic assessment needed for further clinical applications. It is crucial because the range of detectable DPs spectrum determines how early we can diagnose the cancer. Cancer progression stage is always the most important factor in an effective treatment, that is, the earlier the better.
In this work, the sensitivity of the probe, that is, how large skin cancer can be detected, was investigated. For BCC inside the skin, the smallest cancer detecting size is 0.5 mm radius and 0.1 mm height by using probe 1 to detect cylindrical target set at 25 µm away from 1.10 mm skin surface; for SCC inside the skin, the smallest identification radius and height is 1.4 mm and 1.3 mm by using probe 2 to detect cylindrical target set at 75 µm away from 2.23 mm skin surface. The smallest distinguishing size for BCC is 0.7 mm × 0.5 mm in radius and height with cylindrical target set at 2.23 mm skin surface by using probe 1; for SCC is 1.0 mm × 1.0 mm in radius and height with conical or cylindrical target set at 2.23 mm skin surface by using probe 1; for MM is 0.7 mm × 0.4 mm in radius and height with cylindrical target set at 2.23 mm skin surface by using probe 1. We also discuss multiple crucial parameters of this method. This work can provide details for DPs measurements for further clinical applications.

Methods
To investigate the minimal size of skin cancer tissues detected or distinguished by OCP, we use simulation for calculating electrical field distribution inside the skin tissues and reflection coefficients at the tissue/probe interface. Normal tissues and three types of skin cancer including BCC, SCC, and melanoma were discussed while modeling. Based on the obtained simulation data, we retrieved electrical properties including conductivity and relative permittivity by using the OCP reconstruction algorithm. Data analysis was performed to determine the minimal detectable and distinguishable size of skin cancer lesions. We verified the simulation results by phantom experiments. In this section, we provide a description of the skin cancer model, simulation setting, OCP reconstruction algorithm, data analysis, and phantom verification.

Skin cancer modeling
Human skin is a complex organ in structure and electromagnetic behavior. This complexity is a major challenge for the establishment of an accurate numerical model for simulating the interaction of electromagnetic fields with the skin tissue. Thus, a reasonable yet feasible model for numerical calculation of electromagnetic simulation should be established.
Here, we refer to the model in the G Mansutti's study and adopt a three-layer to describe the skin structure in Fig. 1: (1) the top layer, where the skin layer is modeled as a single uniform layer because the DPs measured from the single uniform layer and three layers including stratum corneum, epidermis, and dermis are similar; (2) the fat layer, with a thickness of 2. of 3 mm. These simplifications to the three-layer model can conform well to the physiological structure of human skin [18] for efficient numerical calculation. The thicknesses of the skin layers are set to 1.1 and 2.23 mm in simulations because the thickness of skin varies in different parts of the body. Considering that skin cancers generally start at the junction of the epidermis and dermis and grow up toward the skin's surface, we put the cancer starting position on the bottom of epidermis layer, i.e., the skin cancer is located at 0.02 and 0.075 mm away from the skin surface corresponding to thin skin and thick skin, respectively [19,20]. Skin ulcers are also under simulation by setting up the thickness of skin cancer target from the bottom of epidermis layer to the skin surface, which means that its thicknesses are 0.02 and 0.075 mm. The tests simulate the cancer growth with gradually increase sizes of tumor's geometry. As only the early stage of cancer is discussed in this work, the cancer model is limited in the epidermis and dermis and does not involve lymph nodes and cancer spread in all simulation episodes. We employ two geometric models that mimic tumor growth: cylindrical and conical shape [21]. The former represents tumors with longitudinal growth but little radial variation, while the latter describes tumors that grow radially. We simulate tumor growth by changing corresponding geometry parameters, i.e., H t and R t . The specified values of geometry parameters are shown in Tables 1 and 2.
To equip the model with electromagnetic responsive behavior, we assign electrical property values to corresponding part of the skin model. For normal, BCC, and SCC tissues, electrical properties are obtained via the Cole-Cole fitting expression as follows [22]: where, j = √ −1 , ω is the angular frequency, and ε ∞ , τ , Δε r ,σ i , and α are coefficients reported in previous works [23]. Considering that the Cole-Cloe coefficients of melanoma are unavailable, we assign electrical properties with regard to frequencies according to B.J. Mohammed's study via interpolation [24].

Simulation setting
In OCP method, an open-ended coaxial probe transmits an electromagnetic field, which generates an electric field distribution inside the tested medium. The reflection coefficient at the medium/probe interface was calculated to obtain electrical properties with a specific reconstruction algorithm. We used the commercial finite element software COMSOL Multiphysics to calculate the electric field induced inside the medium of the skin tissue as well as the reflection coefficients at the tissue/probe interface. Considering the influence of coaxial open-ended probe size on the detection performance [25] and in the pre-test, six probes are used; meanwhile, the two larger size probes are unsuitable for 2.23 mm skin thickness and the four larger size probes are unsuitable for 1.10 mm skin thickness because increasing detection depth as the probe size increases would lead to measurements affected by the fat layer and the muscle layer. Thus, in a formal experiment, we examined four commercially available probes (UT-047-M17, RG-405, RG-402, and customed-probe) in following simulation ( Table 3). The dielectric between the inner and outer conductor was assigned to PTFE (UT-047-M17), PTFE (RG-405), PTFE (RG-405), and Teflon (customed-probe) for 50 Ω impedance matching. The open-ended port of the probe was attached to the skin model, while another port was the feed point used to provide the electromagnetic signal source. The simulations were performed within the frequency range of 300 MHz to 6 GHz with 30 MHz increments to mimic the frequency spectrum sweep of the network analyzer. Given that electrical properties depend on frequency, we obtain its value of the current examined frequency according to Eq. (1) by MATLAB (Mathworks, Natick, MA, USA) and then enter it into the simulation via COMSOL/MATLAB interface. In the simulations, the perfectly matched layer was set to a sphere with a radius of 500 mm. Electric field was calculated by the combination of Maxwell ampere law and Faraday's law, and reflection coefficient was calculated through the energy input and output of various ports. The reflection coefficients of 0.9% sodium chloride solution, ethanol solution, and methanol solution medium were measured for calibration [26]. We then measured the reflection coefficient of normal skin, BCC, SCC, and MM tissues for subsequent analysis. All of numerical simulations were implemented on the Medical Big Data Supercomputing Center System of Anhui Medical University.

OCP reconstruction algorithm
According to electromagnetic theory, the transverse electromagnetic wave can propagate in a uniform transmission line, such as a coaxial cable [27]. Reflection would occur on medium/probe interface once the impedance of the OCP does not match the medium's impedance. The equivalent impedance model of the probe tip can be expressed as [28] where C f and C 0 are two parallel shunt capacitors, ε 0 is the permittivity of free space, σ dc is dc conductivity, and � r ( ) = � − j �� is the relative permittivity of the material.
Hence, we can reconstruct electrical properties by measuring reflection coefficient. The relationship between the properties of the medium and reflection coefficient is: is the real parts of the dielectric permittivity which denoted as ε r , in the following work, we called the � r ( ) , ,i.e., ε r as "relative permittivity", �� r ( ) is the imaginary parts of the dielectric permittivity, σ(ω) is electrical conductivity of the medium, ρ m is the reflection coefficient; and A1, A2, and A3 can be determined by calibration:

Data analysis
In this research, Mann-Whitney U test was employed as a statistical test on relative permittivity and conductivity for verification. We programmed this test for MATLAB rank sum test function, and the significance level, denoted as alpha, was set to 0.01. The input of this tool is the measured DPs and the calculated DPs through the Cole-Cole model; and the outputs are p-value and h-value. The p-value of Mann-Whitney U test reflects the difference between the simulated values and literature values, h-value equals 1 indicates a rejection of the null hypothesis, and h-value equals 0 indicates a failure to reject the null hypothesis at the 1% significance level [29]. The statistical differences of measured DPs compared to healthy and unhealthy tissues are obtained by Mann-Whitney U test. The criteria that the measured DPs is diagnosed as malignant is when the results of statistical differences satisfy the requirements which the measured DPs have no statistical difference with malignant skin and it is statistically different from normal skin at the same time.

Phantom verification
To validate the accuracy of simulation, we conducted a phantom experiment. A skin phantom modeled as a single uniform layer because of the similar water content of epidermis and dermis was fabricated according to the recipe [30]. It was fabricated by dissolving 0.3 g of p-toluic acid and 15 ml of n-propanol with 51 g of gelatin and 285 ml of deionized water. The mixture was sealed for at least 3 h and gradually heated to 70 °C under stirring to become uniform. About 5 ml of oil and 0.46 g of sodium chloride were added to 95 ml of the mixture under stirring, and 2.8 ml of the surfactant and 1.1 ml of the formalin solution were mixed. When the mixture cooled down to 34 °C, it is poured in a mold.
The resulting phantom is depicted in Fig. 6, and the measurement experiment is as follows. The measurement system contains a VNA (AV3680A), a laptop, a thermometer, a semi-rigid coaxial line (UT-141), an iron stand, a lifting table, and a customed probe. Before measurement, the probe was calibrated by measuring sodium chloride solution, ethanol solution, and methanol solution. The probe was then fixed by iron stand, while the phantom was placed on the lifting table. By operating the lifting table, the skin phantom was connected to the probe without pressure. At this time, the acquisition of the data began. Five positions were selected, and data were collected at each point by more than 10 s. To protect the skin phantom, it was lowered after measurement before shifting the probe to a new position.
Five measurements were conducted, and the results were averaged. The data were then imported into simulation software as DPs of skin, and the rest of the simulation sets remained unchanged. After simulation calculation, the simulated data were compared with the resulting data. The difference was used to validate the accuracy of the simulation.

Results
In the first subsection, the numerical curves of normal skin, BCC, SCC, and MM are reported. In the second subsection, the sensitivity of each probe, the height of the skin, and the types, shapes, and location of skin cancer are discussed. In the third subsection, the electric field is analyzed. At last, the results of skin phantom verification are described.

Comparison
At the beginning of the simulations, normal skin, BCC, SCC, and MM were compared. In Fig. 2, the conductivity and permittivity of normal skin, BCC, SCC, and MM show a big difference, with frequency ranging from 300 MHz to 6 GHz, except for the conductivity of normal skin and MM.

Sensitivity
When detecting the DPs of a multiple-layer tissues, the reflection coefficients are affected by the area probe. Sensitivity will vary due to alterations in the size and type of cancer target and numerous simulations performed. When the detecting cancer target is on the skin surface ( d t =0 mm), the DPs measurement can distinguish normal and malignant type, further can identify cancer subtypes; but when it used to detect beneath skin target ( d t =0.02 mm, d t =0.075 mm), DPs measurement can only distinguish normal or malignant but failed to identify specific cancer type. Thus, Tables4 and 6 present the detecting size, while Tables 5 and 7 present the distinguishing size. As long as the cancer size is larger than the sizes in the tables, it could be detected or distinguished. In Table 6   size probes are included in the simulations because of the thin skin and that the result would be affected by fat layer or muscle layer if the probe size is too large. Due to simulation error and similar DPs, some tests could not determine the cancer size. For example, when skin cancer is set to BCC with probe 1, the electrical conductivity is almost indistinguishable from the skin's, so that result of rank sum test shows no significant difference. Similarly, the electrical conductivity of normal skin and MM have no significant difference. Figure 3 shows the difference when the SCC cylinder target is set on the surface of the skin by using probe 2 (p < 0.01). The differences from Fig. 3 shows that the probe completely diagnose cancer when the SCC target's size is larger than 1.50 mm × 1.90 mm. Consequently, DPs measurement and significantly different p values are 0.6944 and 0.1164 compared with SCC cancer, and the h values are 0 and 0 corresponding to when the target's size is 1.50 mm × 1.90 mm.
In Fig. 4, the thickness of the skin layer was simulated at 1.10 mm and the cancer type is set to 1 mm radius BCC with the detecting frequency of 3 GHz. The results from Fig. 4 depict that the measured conductivity with probe 2 is higher than that obtained using probe 1, while the measured permittivity with probe 2 is lower than that by probe 1. The measured conductivity with the cylinder is lower than that that with the cone, while the measured permittivity with the cylinder is higher.

Electric field distribution
To intuitively represent the simulations, we exported an electric field diagram of a 1.90 mm × 0.90 mm BCC cylinder cancer target set at 2.23 mm skin surface by using probe 4 for detecting 2.23 mm skin. The electric field is exported at 3 and 6 GHz.     Figure 5 shows a simplified 2D axisymmetric image with abscissa and ordinate in millimeters. The inner conductor has a greater influence in the detection area, and the insulator also affects the electric field distribution. When the electric field is close to the probe tip, the electric field intensity also increases. Probe 4 has an outer conductor inner radii of 3.02 mm, as shown in Fig. 5a and b. The electric field intensity with 3 GHz is significantly higher than the intensity with 6 GHz.

Phantom verification
The skin phantom in Fig. 6 was used to verify the accuracy of the simulation (Fig. 6). The elasticity of the phantom allows detection for many times with the probe on the surface; five points in this area are measured, and the average value is inputted for simulation. After obtaining the reflection coefficient, the DPs are calculated using the same configuration mentioned above, and the curves are shown in Fig. 6. The simulation results are compared with the measured results through rank sum test. The difference is not statistically significant since the p values are 0.9786 and 0.9010 and the h values are 0 and 0, respectively, for conductivity and permittivity.

Discussions
In this section, several factors that affect the detecting size or distinguishing size are analyzed. The sensitivity of cancer detection is the focus of discussion.
As shown in Fig. 7a and b, when probe 1 is used to detect conical SCC tumor set at 2.23 mm skin surface with target height changing, the larger tumor size with radius and height of 1.00 mm and 1.00 mm is more sensitive, wherein the p values of permittivity and conductivity are greater than 0.01 compared with the DPs of SCC. Similarly, when the target radius changes under the same conditions, only the radius is greater than 1.00 mm, and both p values are greater than 0.01. The change in the p-value when the target radius increases from 0.50 to 0.70 mm with fixed height is larger than that target height increasing from 0.50 to 0.70 mm with fixed radius. In summary, the probe is more sensitive to tumor radius than height. From Fig. 8a and b, different shapes of MM tumor with radius of 1.00 mm and height of 0.60 mm at 1.10 mm skin surface are detected by probe 1. The p values of cylindrical target are greater than 0.01 compared with the DPs of MM, while the p value of conical tumor's permittivity does not reach 0.01. As depicted in Fig. 8c and b, when probe 1 is used to detect different shapes of BCC tumor at 1.10 mm skin surface and the BCC tumor's size is 1.00 mm radius and 1.00 mm height, the p values of cylindrical target exceed 0.01 compared with the DPs of BCC, while the p value of conical tumor's permittivity does not. The conclusion is that detecting cancer in cylinder is more sensitive than in cone.
As depicted in Fig. 9a and b, probe 2 is used to detect cylindrical SCC tumor at different locations and the tumor target radius and height are set to 1.00 and 1.00 mm, respectively, in 2.23 mm skin. The p values of cylindrical SCC tumor on the skin surface are larger than the target set at 0.075 mm away from skin surface when compared with the DPs of SCC. When detecting cylindrical BCC tumor with 1.00 mm height and 1.00 mm radius at different locations of 2.23 mm skin by probe 2 (Fig. 9c and d), the p values of cylindrical SCC tumor on the skin surface are larger than the target set at 0.075 mm away from skin surface when compared with the DPs of BCC. In conclusion, probes are more sensitive to tumor target set on the skin surface.
In Fig. 10a and b, when detecting different skin thickness by probe 1 and conical MM tumor with 1.00 mm height and 1.00 mm radius located on the skin surface, the p values of 2.23 mm skin are larger than 0.01 compared with the DPs of MM, while the p value of 1.10 mm skin's permittivity has not reached 0.01. Thus, detecting thicker skin is more sensitive if the cancer target is located on the skin surface.
In Fig. 11a and b, four probes are used to detect conical MM tumor with 1.00 mm height and 1.00 mm radius set at 2.23 mm skin surface. The results of the comparison show that probe 1 is more sensitive because the p values are larger than 0.01 compared with the DPs of MM. In Fig. 11c   0.60 mm height and 1.00 mm radius set at 1.10 mm skin surface. The p values of probe 1 are larger than the probe 2 when compared with the DPs of BCC. If the probe is too large, for example as probe 5 and 6 shown in Fig.S1, then the simulation will not work. In conclusion, among the four working probes, the smallest size is the most sensitive.
The crucial factors that affect the detectable size are discussed above. In the previous studies, such as in Aydinalp's study [16], they proposed a protocol for charactering the skin depth and discussed the probe sensitivity for utilizing EP in skin cancer detection. Another work reported the effect of probe size on sensing depth by Meaney [25]. These research results provided limited information for EP in skin cancer detection. None has mentioned the sensitivity of probe on skin cancer which is very important factor may affect further clinical applications. Therefore, in this work, we confirmed the possibility of early cancer diagnosis with OCP through numerical study and investigates the sensitivity of the probes with different sizes in different situations to mimic realworld scenario.
However, this work also has some limitations. First, the models used in simulations is simplified while clinical trial would face many challenges. On the other hand, this work focuses on the early detection of skin cancer, neglects the research on other tumors which the sensitivity of the probe is a little different for other tumors. At last, Mann Whitney U Test is used to identify tumors with malignant potential. In simulation, measurement error can be ignored so that the Mann Whitney U Test is appropriate to distinguish between healthy and unhealthy tissues, but, in actual measurement error is inevitable which makes the identify ability of Mann Whitney U Test is limited. To address these limitations, we need to optimize simulation models and collected clinical data to cope with challenges. At same time, the research on other tumors would be carried out. Finally, machine learning which is the first choice to solve the problem of binary classification will be used to distinguish between healthy and unhealthy tissues.
This work indicate that open-ended coaxial probe method can be used for early detection of skin cancer. However,

Conclusions
In this work, numerical simulations were conducted to investigate the sensitivity of the probes with different  sizes in different situations. The significant factors which can affect DPs measurements are discussed. It was found that the sensitivity limitation for DPs measurements is very diverse and varies according to different types. The probe is more sensitive to cylinder tumor radius than height growing on the surface of the skin. And among the four working probes, the smallest size probe is the most sensitive.
In summary, this study investigated the minimum detectable size of skin cancer and discussed the factors that can affect detectable size. These findings are the basis for early diagnosis of skin cancer. Further investigation on inhomogeneous and deeper skin tumors needs to be conducted. Our work provides a discussion with multiple parameters based on a model mimicking the anatomy of human skin cancer. We expect to contribute useful insights to prepare tumor DPs detection technology for clinical applications.

Acknowledgements
The numerical calculations in this paper have been done on the Medical Big Data Supercomputing Center System of Anhui Medical University. This work is supported by the National Natural Science Foundation of China (Grant No. 62271007, 82102742).
Author contributions All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by GX, HL, and QH. The first draft of the manuscript was written by GX and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
Funding This work was supported by the National Natural Science Foundation of China (Grant No. 62271007, 82102742).
Data availability All data referred to and underpinning this publication are openly avaliable on Github and can be found at https:// github. com/ shell tink/ data.

Declarations
Competing interests The authors have no relevant financial or nonfinancial interests to disclose.
Ethical approval This article does not contain any studies with human participants or animals performed by any of the authors.