Introduction

According to the data published by the World Health Organization, the incidence of skin cancer has increased significantly in recent years. The most common types of skin cancer are melanoma, basal cell carcinoma （BCC） and squamous cell carcinoma （SCC）. Melanoma is one of the most dangerous types of skin cancer because it will metastasize and infect other organ ^[1]. Early diagnosis and treatment are essential to the survival of patients. The five-year survival rate of patients with skin cancer who are found and actively treated in the early stage was 98.3%, but the survival rate of patients with advanced multiple metastases was as low as 16% ^[2]. Currently, the diagnosis of skin cancer is mainly based on dermascopic detection. While the visual diagnosis is inaccurate and subjective, which can result in misdiagnosis. The accurate diagnosis of malignant melanoma requires rigorous training and experience, even for experienced dermatologists, the diagnostic accuracy of malignant melanoma is only 80%, and the early thinner melanoma is particularly hard to detect ^[3]. Although a variety of skin cancer diagnostic techniques have been developed, such as multispectral imaging, chaotic scanning laser microscopy, optical coherence tomography, ultrasound imaging, and impedance spectroscopy ^[4]-[5]. Since these methods do not have universal application value for assisted diagnosis in clinical practice. However, early diagnosis of melanoma and timely treatment can still achieve a five-year survival rate of nearly 100% ^[6]. Therefore, It is necessary to develop an effective and safe diagnosis method for detecting skin cancer in the early stages of tumor progression.

In the millimeter wave frequency range, tumor tissue can be distinguished from surrounding healthy tissue by its ' different dielectric properties（permittivity and loss factor）^[7]. This difference is dominated by water content , and the water content of malignant tissue is higher than that of healthy tissue by more than 20% ^[8,9], while the benign tumor has less water content than normal tissue. At the same time, the skin is in the outermost layer of the human body, which make it easy to measure the reflection parameters. The millimeter wave has a shorter wavelength than the radio frequency, so the higher resolution can be obtained. Moreover, the penetration depth of the millimeter wave in the human skin is close to the thickness of the skin. Therefore, millimeter waves become an ideal medium for skin tumor detection. It is known that the response of millimeter waves at frequencies of 35 GHz and 95 GHz are very sensitive to water content. Therefore, non-invasive detection of skin cancer can be performed based on the sensitivity of millimeter waves to the water content of malignant tissues ^[10]. In addition, since the tumor tissue contain more moisture than the healthy skin, the millimeter wave has more loss in the malignant tissue, so that the dielectric probe can detect the abnormality of the S₁₁ parameter between the malignant and normal tissue. This study used a 2D axisymmetric model to quickly analyze the radiation characteristics of circular wave-guide and tapered dielectric probes in the fundamental mode. At the same time, we also analyzed the skin temperature distribution and damage score under millimeter-wave irradiation, offering the safety input power and reasonable irradiation time, which will ensure that the millimeter wave-based skin cancer detection technology is safe, accurate and effective for clinical diagnosis.

1 Methods

1.1　Geometric model for millimeter wave skin cancer detection

The geometric of skin cancer detection model consists of a metal circular waveguide ,a tapered PTFE dielectric rod and a skin phantom as shown in Fig 1. The skin phantom consists of two parts: healthy skin and malignant tumor tissue. The entire model is enclosed by an air domain that is truncated at its outermost shell with perfectly matched layers（PML）to absorb any radiation directly from the rod or reflected from the skin model, which simulates the environment where the skin cancer screening is performed. One end of the waveguide is terminated with a circular port and excited using the dominant TE_1m mode, where m is the azimuthal number of this 2D axisymmetric model defined as 1 in the electromagnetic waves. The other end of the circular waveguide is connected to a tapered conical PTFE dielectric rod （ εr = 2.1）. The shape of the PTFE is a symmetrical tapered so the radius increases from the inside to the outside of the waveguide , then It is decreasing gradually for the impedance matching between the waveguide and the air domain. There is an ring structure in the middle of the dielectric rod for inserting the probe into the circular waveguide. The tip of the probe is in touch with the skin phantom. The entire probe model is simulated in a 2D axisymmetric space.

Fig.1 Three-dimensional geometric structure of millimeter wave skin cancer detection model

图1 毫米波皮肤癌检测模型三维几何结构

1.2　Governing equation of electromagnetic field

Based on the finite element method（FEM）, the electromagnetic field was solved in the simulation domain. The electromagnetic field changes sinusoidally with time, and all the properties of the material change linearly with respect to the field strength. The electromagnetic field distribution in the circular waveguide and the tapered dielectric rod under millimeter wave excitation can be described by Maxwell equation ^[11]. The 2D Maxwell governing equation can be simplified to the equation（1）:

Where  μr is relative magnetic permeability, ω is angular frequency,  εr is relative dielectric constant,  σ is electrical conductivity, E is electric field strength, and c0 is velocity of light in vaccum . For a two-dimensional axisymmetric model, the electric field governing equation can be expressed as follow:

Where m is the out-of-plane wave number.

1.3　Dielectric properties model of skin tissue

For human skin tissue, there are abundant blood vessels, lymph, nerves and muscles in addition to various appendages （e.g. hair, sebaceous glands, sweat glands and nails）. The dielectric properties of multi-layer skin tissue can be estimated using the effective medium theory （e.g. the hybrid dielectric model）^[12]. There are many different hybrid dielectric models, the Bruggeman model is a simple but effective model for calculating the dielectric properties of human skin tissue^[13].

The complex permittivity of biological tissue consists of two parts, the real part and the imaginary part, where the real part represents the ability of the tissue to store energy of the electromagnetic wave, and the imaginary part represents the energy absorption capacity of the electromagnetic wave. When considering the dielectric constant of free space, it is called the relative dielectric constant and represented by εr .

Where  εr' is the real part of the complex permittivity of the tissue, εr'' is the imaginary part of the relative dielectric constant of the structure, and the imaginary part εr'' is related to the conductivity σ , which can be obtained according to the formula（4）^[14]:

Where f is the frequency of the millimeter wave, its unit is Hz, ε0 is the dielectric constant in vacuum state, and σi is the dielectric constant under direct current condition.

The skin tissue is composed of water and other living biological materials. The water within the skin exists in two states, one is bulk water and the other is hydration water. The dielectric properties of skin tissue under the millimeter wave range are mainly determined by the content of bulk water, and the dielectric constant of the hydration water is not related to the frequency, and its value is similar to the biomass, so that the skin tissue can be considered as a binary mixture which consists of free water and biological materials, the dielectric properties of skin tissue can be described using the Bruggeman model :

Where φ represents the content of biological materials, 1-  φ is the content of bulk water. εreff represents the relative effective dielectric constant of the tissue. εrw and εrd represent the complex dielectric constants of bulk water and dry biological materials in skin tissue, respectively. The dielectric constant of dry biological materials is εrd =2.5 according to the literature[15].

The dielectric constant of bulk water is related to the frequency, temperature and pressure of electromagnetic waves. It is calculated according to the double Debye complex permittivity model in the millimeter wave band and is described as follows ^[10]:

where  ε∞ 、 εs 、 ε2 、 τ1 and τ2 are temperature-dependent dielectric constant、static dielectric constant, intermediate frequency limit, slow relaxation time and fast relaxation time, respectively. The real and imaginary parts can be expressed as follows^[16]:

According to the formula proposed by Hamelin et al, εs can be accurately calculated. The formula is as follows^[17]:

Where T is the Celsius temperature of water, Ellison et al showed that the relaxation time of water can be obtained by the following model which is a function of temperature ^[18]:

Studies have shown that SCC （squamous cell carcinoma） has a dielectric permeability 97% higher than normal tissue under millimeter waves near 40 GHz^[19]. Therefore, the dielectric properties of malignant skin tissue can be inferred based on the dielectric properties of normal skin tissue according to the above hybrid model.

1.4　Heat transfer model of skin tissue

In living state, the skin tissue undergoes a complex heat and mass transfer process, the skin surface is in contact with the air for convective heat transfer, and there are also various heat transfer activities inside the skin, such as cell metabolic heat production, the cooling effect of blood perfusion et al ,those process happen simultaneously . Therefore ,in order to describe the heat transfer in skin tissue we will use the pennes equation, which was derived from the measurement of human forearm temperature at rest. The model is described as follow ^[20]：

Where ρ is the density of the tissue,  c is the specific heat of the tissue, k is the thermal conductivity of the tissue, wb is the blood perfusion rate , cb is the specific heat of the blood, qm is the metabolic heat production rate of the skin tissue, qr is the heat produced by the electric field, depending on the tissue conductivity . In this study, we regard the blood temperature and metabolic production rate as constant, they are Tb =36.5 ℃ , qm =420 J∙s-1∙m-3 respectively.

The temperature of the skin will increase under millimeter wave irradiation, and the skin will be damaged under the continuous action of heat .There are usually two methods to determine the thermal damage degree of the skin: one is based on the isotherm method ,once the temperature exceeds the a certain threshold, it is considered as irreversible damage to the tissue; The other is to consider the cumulative effect of temperature and time, and introduce the concept of thermal dose according to the Arrhenius model^[21]. The calculation formula is described as follow:

where Ωt is a dimensionless damage parameter, A is frequency factor （ S-1 ）, Ea is energy barrier （ J/mol ）, indicating that the activated molecule contains the minimum energy that can participate in the chemical reaction, R is gas constant （8.3143 [ J/mol∙℃ ]）, Tt represents the temperature of skin tissue and τ is the total time exceeding the threshold temperature. The proceeding in the electromagnetic field and heat transfer problem solving is shown in Fig 2.

Fig 2 The procedure of calculation in the computational model

图2 数值计算模型的求解步骤

2 Results and discussions

2.1　Study on the effectiveness of conical dielectric probes

To analyze the validity of the probe design, we firstly observe the electromagnetic properties of the circular waveguide and dielectric probe without the skin phantom. the electromagnetic properties of the conical dielectric probe were analyzed without skin phantom to verify the effectiveness of the waveguide and dielectric probe. Next, increase the complexity of the model by adding a healthy skin phantom and then increasing the tumor tissue in healthy skin phantom. The distribution of the electric field Er generated by excitation at one end of the waveguide was investigated. From the simulation results, Fig 3 （a） shows the electric field energy distribution of the millimeter wave metal waveguide when the skin model was not included. Fig 3（b） shows the distribution of the electric field when it contains skin tissue . Due to the skin's reflection on the radiation, and the electric field energy concentrate on the tip of the conical dielectric probe, From the simulation results, we found the design of conical dielectric probe to be functional.

Fig 3 the electric field distribution of a circular waveguide (a)the electric field distribution of the circular waveguide without skin,（b） the electric field distribution of the circular waveguide including skinthe electric field distribution of the circular waveguide without skin

图3 圆形波导电场分布（a）不包含皮肤影响（b）包含皮肤影响

The circular boundary condition was placed on the interior boundary where the reflection and transmission characteristics are computed automatically in terms of S-parameters. the interior port boundary with PEC backing for one-way excitation requires the slit condition. The port orientation is specified to define the inward direction for the S-parameter calculation. The spatial distribution characteristics of the electric field of the conical dielectric probe can be clearly seen from the polar coordinate pattern of Fig 4 and Fig 5 The main lobes of the probe are narrow, the side lobes are small, the gain is relatively high, and the directionality is relatively well. Therefore, the design validity of the waveguide and dielectric rod was checked.

Fig.4 Polar coordinate pattern of the conical dielectric probe

图4 介电探针极坐标方向图

Fig.5 Three-dimensional near-field pattern of the conical dielectric probe

图5 圆锥介电探针三维近场方向图

According to the hybrid dielectric model, the real part of the dielectric constant of healthy skin tissue is 15.421,At the same frequency, the real part of the dielectric constant of the malignant tissue is 30.379.The dielectric properties of normal tissue and malignant tumor tissue are set to（15.421±10%）and 30.379±10% respectively.The results are shown in Fig 6. When only healthy skin tissue was included, the S₁₁ parameter detected by the conical dielectric probe was among -8.998∼-8.445 dB.While in the case of malignant tissue, the detected S₁₁ parameter was between -8.120 dB and -7.651 dB. These values indicate that more reflection occurs when the probe contacts the skin phantom with malignant tissue. We can expect such a result, as tumor have higher moisture content than healthy skin, the S₁₁ parameters of the probe in healthy skin tissue and malignant skin tissue are significantly different. It can be used as the basis for the auxiliary diagnosis of skin cancer, and the purpose of early detection of skin cancer without damage was achieved.

Fig.6 S₁₁ parameters detected by the dielectric probe

图6 基于介电探针检测到的皮肤组织S11参数

2.2　Study on safety of skin tissue under millimeter wave irradiation

While we found the S-parameter approach to be functional, we also want to ensure that it is safe. To do so, we study the temperature distribution over the skin phantom surface in order to find the fraction of necrotic （damaged due to heat） tissue.

The transmission depth of the millimeter wave to the skin is about 1 mm; At the same time, the transmission of millimeter waves in the skin has a pyrogenic effect on the skin. Therefore, it is necessary to study the safety of applying the millimeter wave to detect the skin cancer technology, and to determine the safe irradiation time and input power of the millimeter wave for detection.

The temperature response of tumor-containing skin tissue to millimeter waves is a complex process and is subject to a variety of key influencing factors, including millimeter wave power, frequency, irradiation time, blood perfusion rate of skin tissue, thermal conductivity and others. Therefore, the temperature distribution of skin tissue under millimeter wave irradiation is studied. It is necessary to analyze the influence of thermal physical factors on tissue temperature and damage distribution.

Firstly, temperature distribution of skin tissue at low input power was studied. The temperature change on the surface of the tumor model is shown in Fig 7. When the input power was 1 mW, after 10 minutes under millimeter wave irradiation, the temperature change was within 0.06 ℃ . The color difference shows a relatively hot spot, while the temperature was still close to the initial temperature of 34 ℃ . Although the temperature of the healthy skin phantom was not analyzed, it is easy to predict that the temperature change should be less than that of the tumor-containing condition, because the imaginary part of the dielectric constant of healthy skin is small, which results in less resistance loss. Set two temperature probe at the site where the skin was in contact with the dielectric probe and at the edge of the tumor, respectively. The temperature at point 1 and point 2 are shown in Fig 8 （a）. The temperature at point 1 has changed slightly. while the temperature of point 2 is substantially consistent with the initial temperature. When considering the blood perfusion, as shown in Fig 8 （b）, the input power was 1mW, the temperatures of points 1 and 2 are basically the same. The temperature distribution of the entire skin is uniform. The results show that the heat effects of low power millimeter waves are negligible.

Fig.7 Changes in skin temperature for 10 minutes of continuous irradiation at input power of 1 mW

图7 输入功率1mW 持续辐照10min皮肤表面温度分布

Fig.8 Temperature change at the point where the probe contact with the skin and at the edge of the tumor with input power 1 mW （a）Input power 1 mW（not contain blood perfusion），（b） Input power 1 mW （contains blood perfusion）

图8 在输入1mW时探针与皮肤接触点和肿瘤边缘处温度变化

When the input power was 100 mW, 300 mW, 500 mW, 600 mW, 700 mW, 900 mW, respectively. The temperature distribution of skin tissue is shown in Fig 9. When the input power was 100 mW and 300 mW. The temperature increment of the skin was 5.5 ℃ and 16 ℃ , respectively. Temperature changes are still within the safe threshold. While the input power was among 500 mW and 900 mW, the temperature increment of the skin had risen by 25 and 50 ℃ respectively, which indicates that the millimeter wave has already exerted a strong thermal effect on the skin, those temperature have been far beyond the thermal damage threshold.

Fig.9 （a） （b） （c） （d） （e） （f） skin temperature distribution at input power of 100 mW, 300 mW, 500 mW, 600 mW, 700 mW, 900 mW

图9 （a） （b） （c） （d） （e） （f）分别为在输入功率为100 mW, 300 mW, 500 mW, 600 mW, 700 mW, 900 mW时皮肤温度分布

Study the temperature changes of these two temperature detection points with different input powers. As shown in Fig 10, the temperature increment at point 1 was greater than in point 2 in each of those cases. The temperature at which the probe contacts with the skin increases significantly with increasing input power, when the input power was 100 mW for 10 minutes, the temperature of the point 1could reach 39.85 ℃ , and the temperature at 6.5 mm from the probe was 35.83 ℃ , which does not cause any damage to skin tissue. When the input was 300 mW, the temperature at point1 can reach 51 ℃ ,and the temperature of point 2 only reached 40 ℃ . In the case of input power was 500 mW for 10 minutes, the highest temperature at point 1 was 63 ℃ , which exceeds the tissue thermal damage threshold, and the temperature at the edge of the tumor was 45 ℃ . With the input power 600-900 mW, the maximum temperature of point 1 was 68.9 ℃ , 74.85 ℃ , and 86.3°C , respectively, which is far beyond the skin thermal damage threshold value.

Fig.10 Temperature changes at the different input powers at temperature detection ponts （a）Temperature change at the point of the probe contact with the skin,（b）Temperature change at the edge of the tumor

图10 探针与皮肤接触点的温度变化和肿瘤边缘处温度变化

The skin tissue suffer necrosis and solidification under the cumulative action of heat. According to the Arrhenius model, the damage score of the skin tissue with different input power was calculated as shown in Fig 11. The red part indicates the irreversible damage area. When the input power was less than 300mW, and the irradiation time lasts for 10min, the damage fraction of the tissue was10^-5-10^-3, It can be considered that the skin was not irreversibly damaged and completely safe. When the input power exceeds 300mW, skin tissue （including tumors and healthy tissues） will suffer different degrees of damage. As shown in Fig 11（f）, the tissue with a radius of 6.5 mm around the probe was completely necrotic when the input power was 900 mW.

Fig.11 Tissue damage （necrosis） score at different input powers

图11 在不同输入功率下皮肤组织的损伤

When considering the effect of blood perfusion in skin tissue on the temperature distribution, the results are shown in Fig 12. Observing the temperature change of point 2, when input power was100 mW, adding blood perfusion item to the heat transfer model, which will increase the temperature of the skin surface. This is because the temperature of the skin tissue is lower than of the blood under low power millimeter irradiation, and convective heat transfer happened between the venous vascular network plexus in the dermis layer and the surrounding skin tissue, resulting in temperature increment of the skin tissue by the blood. When the input power exceeded 300 mW, the skin temperature was higher than the blood ,and the blood in the vascular plexus will take away part of the heat. When the input contact power was less than 300mW, the maximum temperature of the tip of the probe was 41.85 ℃ , which was significantly lower than the maximum temperature of 50.85 ℃ . when the blood perfusion item was not included. It can be seen that blood perfusion has a great influence on the temperature distribution under low power millimeter wave irradiation. At the edge of the tumor, the intensity of the millimeter wave was attenuated due to the distance from the center of the probe, which causes the temperature to be greatly affected by blood perfusion. When considering the blood perfusion item, due to the cooling effect of blood perfusion, the skin temperature will not increase continually after a period of millimeter wave irradiation, and the dynamic balance of heat conduction will be achieved. When the blood perfusion was not considered, the skin temperature will continue to increase during irradiation time, but the temperature growth rate will slow down significantly.

Fig.12 Temperature changes of two temperature detection point （including blood perfusion item） with different input powers（a） Temperature change at the point where the probe contact with the skin,（b） Temperature change at the edge of the tumor

图12 探针与皮肤接触点的温度变化和肿瘤边缘处温度变化（考虑血液灌注项）

2.3　Verification of the numerical method

In order to verify the correctness of the results, the analysis method and results of conical millimeter wave dielectric probe were compared to the results adopted from the previous studies [20],[22], as are shown in Fig 13. To verify the heat generated by electronic field and the heat transfer model in skin tissue during the millimeter wave radiation, the calculated results of conical millimeter wave dielectric probe was verified against the experimental results offered by Hu et al. Fig 13 （a） （b） shows the results of the validation model adopted from Ref [20]. Under the same experimental conditions, compare the skin tissue temperature distribution at input powers of 474 mW and 853 mW. The result was shown in Figure 13（a） （b）, the simulated results are consistent closely with the experimental results, and the uncertainty and difference is less than 5%. Cheng et al[22] used millimeter wave with a power of 22W at a frequency of 35GHz for skin heating. The parameters of the validation model are adopted from Ref [22]. Fig13（c） shows the validation results of the skin tissue temperature during the same heating process, The solution based on above methods is corresponded closely with the Ref[22]. And calculated results are consistent closely to previously work in Ref[22], and the maximum error is not more than 1 ℃ . Especially under high power irradiation conditions, the theoretical calculation value is basically consistent with the experimental value.

Fig.13 Calculated temperature changes with power densities at 474 mW ,853mW and 22 W, respectively

图13 皮肤组织在功率密度为474 mW ,853mW and 22 W下温度变化

3 conclusion

In this paper, a conical millimeter wave dielectric probe for auxiliary detection of skin cancer was studied. The results showed that there were significant differences in S₁₁ parameters between healthy skin tissue and malignant skin tissue. The conical millimeter wave dielectric probe can be effectively used in the diagnosis of early skin cancer. At the same time, the safety of millimeter wave detection technology was analyzed. Based on the pennes heat transfer equation, the temperature distribution of skin tissue under millimeter wave irradiation was studied, and the effect of blood perfusion in dermis on skin temperature was also considered. when the input excitation power was less than 300mW with the irradiation time lasts 10min, the temperature of the skin tissue was always in a safe range, and no tissue damage is caused. When the input power exceeds 500mW, the probe will have excessive temperature. If the temperature exceeds the skin pain threshold, the skin will have a burning sensation. According to the Arrhenius thermal injury model, the tissue has different damage scores under different input powers. Therefore, in the process of skin cancer detection with millimeter wave, it is necessary to strictly control the input power, monitor and control the temperature of the irradiation area, so as to avoid causing damage to the patients in the process of diagnosis. So that the skin cancer detection technology based on millimeter wave can be safely and effectively applied in clinic practice.

References