Specific Absorption Rate and Temperature Distributions in the Human Head with Implanted Deep Brain Stimulation Subjected to Mobile Phone Electromagnetic Radiation

Abstract

Deep Brain Stimulation (DBS), also known as the brain pacemaker, has gradually evolved from a scientific experiment into an effective clinical treatment for movement disorders as a method of improving movement disorders. At present, there are few studies on the effects of 5G mobile phone antenna radiation on the heads of adult patients implanted with DBS. In this study, COMSOL Multiphysics was used to establish a mobile phone model with a 5G/4G patch antenna, a real human head, and the DBS models. Then, we calculated the specific absorption rate (SAR) of various layers of the head tissues with the mobile phone at different distances from the human head, as well as the temperature change rule of the head and the DBS irradiated by the antenna for 30 min. The simulation results showed that when the frequency is 3500 MHz, the electromagnetic radiation of the phone to the patient’s head is generally greater than that of the 2400 MHz. When at 3500 MHz, the distance between the phone and the head is inversely proportional to the SAR value; thus, when the distance between the phone and the head is 1 cm, the maximum SAR value—which is 1.132 W/kg—appeared in the skin layer of the head with implanted DBS. But it is worth noting that the largest temperature rise appeared in the brain layer at 2400 MHz and at a distance of 1 cm, which is 0.2148 °C. Although the SAR values and temperature rise obtained from all simulations are below the limits of 2 W/kg and +1 °C specified by the International Commission on Non-Ionizing Radiation Protection (ICNIRP), we still recommend that patients with implanted DBS maintain a distance when using the phones.

1. Introduction

Deep Brain Stimulation (DBS), also known as the brain pacemaker, is a new technology used to treat movement disorders through stereotactic surgery. Compared with traditional detrimental surgery, DBS has advantages such as a long therapeutic period, being non-destructive and adjustable, and having fewer side effects and complications [1]. It has clinical applications in the treatment of conditions such as tremors, Parkinson’s disease (PD), and dystonia. By 2030, the number of PD patients in China will reach 5 million, accounting for almost half of the global number of patients [2]. Currently, over 180,000 patients worldwide have undergone DBS implantation [3]. In modern society, wireless communication terminal equipment products in the form of phones have entered people’s lives, and the research of the impact on phone electromagnetic radiation on the human body has attracted people’s attention. Along with their yearning for a better life, people have begun to question whether the phone antenna will cause electromagnetic radiation safety issues, and whether the phone antenna will produce electromagnetic interference with many medical devices in use. The Institute of Electrical and Electronics Engineers (IEEE) and the International Commission on Non-Ionizing Radiation Protection (ICNIRP) have developed standards for human electromagnetic field exposure limits, which have been used in antenna electromagnetic exposure safety assessment studies [4,5].

Relevant literature has shown that electromagnetic radiation from phones can cause neurasthenia, chest tightness, palpitations, and other diseases, and can accelerate glucose metabolism in the brain [6]. Keangin et al. calculated the SAR of liver tissue, as well as the effects of tissue temperature increase, using single-slit and double-slit coaxial antennas [7]. Wessapan et al. analyzed the SAR values and temperature distribution in the head under different frequencies of phone radiation, and the results were all lower than the ICNIRP limits [8]. Different researchers used different methods to calculate the effect of different antennas on human electromagnetic radiation, such as self-invented efficient algorithms and the FDTD method, and none of the results exceeded the ICNIRP limits [9,10]. Rashid T B et al. studied SAR values of different head and chest tissues using HFSS and wrote MATLAB scripts to calculate temperature distribution by using a solved bioheat equation [11]. Earlier, L. Hayes et al. studied the interference of phones on cardiac pacemakers, believing that this interference did not pose a health risk [12]. Some researchers proposed a method for electromagnetic interference impact estimation, which could accurately assess the impact of electromagnetic interference on implantable pacemakers [13]. Other researchers numerically calculated and experimentally measured the SAR distribution around a pacemaker model in a parallelepiped torso phantom when the phone was near the body [14]. Zhao Jun et al. investigated the electromagnetic compatibility and thermal effects of electric vehicle wireless charging systems on cardiac pacemakers in 2022, and the results showed that electric vehicle wireless charging systems do not cause electromagnetic interference to cardiac pacemakers [15]. Shah et al. investigated the SAR values when the human head has different implants in the context of the wireless power transfer (WPT) of an Alliance for Wireless Power (A4WP) charging system. These implants included skull plates, bone plates of different shapes, microplates, fixtures, and DBS, and the results showed that all these implants significantly affected the SAR values [16]. At this stage, we focused on evaluating electromagnetic exposure in the phone antenna environment with the head-implanted DBS. Therefore, this study used COMSOL Multiphysics to design a patch antenna operating in the 5G/4G frequency bands; the antenna adopted the commonly used input power of 0.125 W. We also established the corresponding phone model, the adult head, and the DBS models. Then, we calculated the distribution of the SAR values in the head, and the electric field intensity and temperature in the head and DBS. During the simulation, we considered two factors: different operating frequencies (3500 MHz and 2400 MHz) and the distance between the phone and the head (d = 1 cm, 2 cm, 3 cm).

2. Principles of Electromagnetic Radiation

2.1. Analytical Equations for Electromagnetic Wave Propagation

Based on Maxwell’s system of equations [17], the Helmholtz equations are derived to describe the propagation of electromagnetic waves. The Helmholtz equation for the plane electromagnetic wave in a conductor is shown below:

$$\nabla \times \frac{1}{{\mu }_{\mathrm{r}}}\left(\nabla \times \mathit{E}\right)-k_0^2\left({\epsilon }_{\mathrm{r}}-\frac{j\sigma }{\omega {\epsilon }_0}\right)\mathit{E}=0$$

(1)

here, $\mathit{E}$ is electric field intensity (V/m), ${\mu }_{\mathrm{r}}$ is the relative magnetic permeability, ${\epsilon }_{\mathrm{r}}$ is the relative dielectric constant, $j$ is the imaginary unit, $\sigma$ is the conductivity (S/m), and $k_0$ is the free space wave number (rad/m), and it is calculated in free space using the following equation:

$$k_0=\mathsf{\omega }\sqrt{{\mu }_0{\epsilon }_0}$$

(2)

here, $\mathsf{\omega }$ is the angular frequency of the electromagnetic wave (rad/s), ${\mu }_0$ is the vacuum magnetic permeability (H/m), and ${\epsilon }_0$ is the vacuum dielectric constant (F/m).

Meanwhile, in order to simplify the calculation, the following assumptions are made in this paper [8]:

• The boundary between the outermost skin of the head and the air domain meets the following conditions:

  $$E_{1T}=E_{2T}; J_{1N}=J_{2N}; H_{1T}=H_{2T}$$

  (3)
• The human head is directly exposed to the electromagnetic environment.
• Electromagnetic waves are completely absorbed by the head tissue.
• Free space is truncated using scattering boundary conditions.
• The dielectric properties of the head tissue are homogeneous.

2.2. SAR

The interaction of electromagnetic fields with biological tissues can be defined in terms of SAR values, expressed in W/kg [18], and it is usually expressed by the following equation:

$$\mathrm{SAR}=\frac{\sigma {\left|\mathit{E}\right|}^2}{\rho }$$

(4)

here, $\sigma$ is the conductivity (S/m), $\mathit{E}$ is the induced electric field of the biological tissue (V/m), and $\rho$ is the biological tissue density (kg/m³).

2.3. Theory of Biological Heat Transfer

To describe the heat transfer of tissues within the human head using the Pennes transient bio-heat equation [19], which is shown by:

$$\rho c_{\mathrm{p}}\frac{\partial T}{\partial t}+\nabla ·\left(-k\nabla T\right)=\rho ·\mathrm{SAR}+{\rho }_{\mathrm{b}}{c}_{\mathrm{p}}{\omega }_{\mathrm{b}}\left(T_{\mathrm{b}}-dT\right)+Q_{\mathrm{met}}$$

(5)

here, $\rho$ is the material density (kg/m³), $k$ is the thermal conductivity of the tissues (W/(m·K)), ${\rho }_{\mathrm{b}}$ is the blood density (kg/m³), ${\omega }_{\mathrm{b}}$ is the blood perfusion rate (1/s), $c_{\mathrm{p}}$ is the specific heat capacity of blood (J/(kg·K)), $T_{\mathrm{b}}$ is the temperature of the arterial blood (K), and $Q_{\mathrm{met}}$ is a metabolic heat source (W/m³).

When performing heat transfer analysis, we assume that the human tissue is a biomaterial with constant thermal properties, and the initial temperature is set to 309.65 K. The external boundary condition of the human body is set as the thermal insulation boundary condition, regardless of the heat scattering from the head tissue into the surrounding free space.

3. Verification of the Model Validity

Before researching the effects of phone electromagnetic radiation on the heads of implanted DBS patients, a preliminary validation was needed to check the accuracy of this study’s methods. Therefore, we established a model of the literature [20] and compared it with the numerical results of the literature [20], as shown in Figure 1.

The calculation results are shown in

Table 1. Simulation of SARpeak values and temperature rise of different tissues and their errors: 900 MHz/1800 MHz, 2 W.

Operating Frequency	Tissue	Literature [20] SARpeak (W/kg)	Validation	% Errors	Literature [20] $\mathbf{\Delta }\mathit{T}$ (K)	Validation	% Errors
900 MHz	scrotum	6.745	6.681	0.95%	1.21	1.155	4.55%
	penis	5.414	5.127	5.30%	1.18	1.243	5.34%
	testis	2.707	2.752	1.66%	0.339	0.341	0.59%
	skin	3.99	3.808	4.56%	0.428	0.445	3.97%
	fat	0.417	0.403	3.36%	0.432	0.417	3.47%
	muscle	2.389	2.444	2.30%	0.438	0.461	5.25%
1800 MHz	scrotum	7.856	7.816	0.51%	1.452	1.506	3.72%
	penis	7.124	7.133	0.13%	1.39	1.451	4.39%
	testis	1.953	1.948	0.26%	0.34	0.356	4.71%
	skin	5.317	5.393	1.43%	0.523	0.5228	0.04%
	fat	0.697	0.702	0.72%	0.515	0.5049	1.96%
	muscle	2.947	2.979	1.09%	0.498	0.524	5.22%

. The SAR values and the temperature rise of the different tissues in the validation model are in agreement with the literature [20], with average errors of 3.43% and 6.65%, respectively. The results show that our method is accurate and feasible.

4. Electromagnetic Model Establishment

4.1. DBS Model

In this study, the real size and material parameters of the Medtronic 3387 electrode, which is commonly used in electrodes for DBS, are established by COMSOL Multiphysics. The implantable DBS system mainly consists of two parts: the in vivo device and the extracorporeal control device. The in vivo device includes three main parts: the electrical stimulator, the extension lead, and the electrode. The electrode is implanted in the subthalamic nucleus (STN) of the PD patients, and the electrical stimulator is implanted in the patient’s subcutaneous area of chest with a lead connected. The electrical stimulator sends out electrical impulses that stimulate the nerve nuclei in the human brain, thus acting to control the symptoms of PD [21]. In this study, the patient’s head is subjected to electromagnetic radiation from the phones, so we only established an electrode model implanted in the brain, which is shown in Figure 2. The materials for the relevant parts of the Model 3387 electrodes are shown in

Table 2. Material description of Model 3387 electrode-related parts.

Electrode-Related Parts	Material	Conductivity (S/m)	Relative Dielectric Constant
Electrode contacts	Platinum–iridium (Pt-Ir)	1.4 × 107	1
Probe insulation layer	Polyurethane (PU)	0	2.5

.

4.2. Human Head Model

This study established a three-dimensional realistic human head model based on the literature [8], which consists of four tissues—skin, fat, skull, and brain—and defined their material properties in layers. The dielectric and thermal properties of each head tissue are shown in

Table 3. Dielectric properties of human head tissues.

Tissue	2400 MHz		3500 MHz
	Conductivity (S/m)	Relative Dielectric	Conductivity (S/m)	Relative Dielectric
Skin	1.441	38.063	2.025	37.005
Fat	0.102	5.285	1.810	35.003
Skull	0.385	11.410	0.615	10.793
White matter	1.190	36.226	1.810	35.003
Gray matter	1.773	48.994	2.636	47.305
Cerebrospinal fluid	3.412	66.319	4.571	64.577
Brain	2.125	50.513	3.006	48.962

and

Table 4. Thermal properties of human head tissues.

Tissue	$\mathit{\rho }$ (kg/m3)	$\mathit{k}$ (W/m °C)	${\mathit{C}}_{\mathit{p}}$ (J/kg °C)	${\mathit{Q}}_{\mathit{m}\mathit{e}\mathit{t}}$ (W/m3)	${\mathit{\omega }}_{\mathit{b}}$ (1/s)
Skin	1125	0.420	3600	1620	0.02
Fat	916	0.250	3000	300	4.58 × 10−4
Skull	1990	0.370	3100	610	4.36 × 10−4
Brain	1038	0.535	3650	7100	8.83 × 10−3
Blood	1050	0.520	3617	-	-

, respectively.

The dielectric parameters of each tissue in the head at the frequencies of 3500 MHz and 2400 MHz are calculated according to the Cole–Cole model, in which the brain tissue is taken as the average of the three tissues: white matter, gray matter, and cerebrospinal fluid. The thermal performance parameters of the tissue are taken from references [8,20]. Since this study mainly considers the influence of electromagnetic radiation generated by 5G antenna on the part of DBS systems in the brain, only the electrode part model is established. The head model implanted with DBS is shown in Figure 3.

4.3. Antenna and Mobile Phone Model

At higher 5G applications, the antenna with high directivity is required, but in this study we designed a sub-6G antenna, which has a frequency range of 0.45–6 GHz. The 5G/4G mobile phone model which we designed consists of an FR4 dielectric plate, a composite silicone substrate, a glass layer, and an ABS shell. To simulate the electromagnetic radiation environment of 5G phones more realistically, this study designed an antenna model that could cover the main operating frequencies of 5G and 4G. The detailed parameters of the mobile phone are shown in Figure 4. The material properties, such as their relative dielectric constant, electrical conductivity, and magnetic permeability, are shown in detail in

Table 5. Material properties of mobile phone model.

Material	Conductivity (S/m)	Relative Dielectric Constant	Relative Magnetic Permeability
FR4 dielectric plate	0.004	4.5	1
composite silicone substrate	1 × 10−12	11.7	1
Glass layer	1 × 10−14	4.2	1
ABS shell	0	2.1	1

.

Whereas the patch antenna serves as a near-field radiation source, as can be seen from the S₁₁ resonance curve diagram of the patch antenna (Figure 5), the phone antenna designed in this study has a return loss bandwidth (−6 dB) (VSWR 3:1) [22]. This could cover the 5G/4G mobile phone work center frequency and the 5G phone operating center frequency of 3500 MHz and LTE-2300/2500 bands, meeting its operation in the 5G network frequency band and the requirement for downward compatibility in the 4G frequency band.

To discuss the thermal effect of the antenna on DBS more precisely, the representative frequency bands of 5G/4G phones were selected to research the effect of the electromagnetic environment generated by the phone antenna at the frequencies of 2400 MHz and 3500 MHz.

The simulated three-dimensional radiation pattern is shown in Figure 6. It can be seen that the antenna designed in this study has good omnidirectionality.

As Figure 6 shows, we discovered that the head tissues could impact the resonant frequency. In this study, we focused on the safety assessment of electromagnetic exposure of human head tissue.

4.4. Patient Head Model and Air Domain Model Establishment

A joint integration of the head model of patients with implanted DBS and the 5G phone model was performed by the COMSOL. This study researched the electromagnetic environment generated by the 5G antenna, and the radiation source was next to the head. Therefore, the model was wrapped in an air domain. A spherical air domain with a radius of 400 mm was established. The overall model establishment and boundary condition settings are shown in Figure 7.

Combining the initial conditions and boundary conditions, the overall model was finely meshed. Finally, the degree of freedom of the meshed model was 6,176,376, and the calculation was carried out with a 64 G memory computer. The simulation time was 6 h. Figure 8 shows the grid partition of the overall geometric model.

5. Analysis of Simulation Results

Based on the above designed 5G patch antenna, this study simulated the SAR values of head tissues. The electric field intensity and temperature in the head and DBS were exposed to input power of 0.125 W at different distances (d = 1 cm, 2 cm, 3 cm) from the head at different frequencies. Finally, this study compared the SAR values and temperature rise with the ICNIRP standard limits (2 W/kg and +1 °C, respectively).

5.1. Electric Field Intensity of Head and DBS

5.1.1. Electric Field Intensity of DBS

According to the requirements of the immunity of the relevant standards for implantable neurostimulators, the maximum requirement of the immunity for DBS systems complying with ISO 14708-3 [23] is 61 V/m for external devices operating at frequencies from 2000 to 6000 MHz [24]. Figure 9 shows the distribution of the DBS electric field intensity for each case.

As Figure 9 shows, at 2400 MHz, the electric field intensity of DBS decreases as the distance from the phone increases, and the maximum value appears near the metal electrode when the distance is shorter. However, at 3500 MHz, the larger the distance, the greater the electric field intensity, and the maximum values all occur near the end of the insulation layer. In all cases, the research results indicate that the electric field intensity values of DBS are less than the maximum immunity required by DBS could withstand.

5.1.2. Electric Field Intensity of the Human Head

Figure 10 shows the distribution of electric field intensity in the head at the same horizontal cross-section when the d = 1 cm.

As Figure 10 shows, the largest electric field values of all tissues appear on the side near the phone. At different frequencies, the maximum electric field intensity values of the horizontal cross-section of the head appear in the skin layer.

As Figure 11 shows, we also obtained the electric field distribution of the skin, fat, skull, and brain layers in the head at frequencies of 2400 MHz and 3500 MHz, with distances from 1 cm to 3 cm.

By comparison, the induced electric field corresponding to the head tissue also varies with different operating frequencies of the antenna. At 2400 MHz, the maximum electric field intensity of each tissue is generally higher than that at 3500 MHz. When at 2400 MHz, the maximum electric field intensity is 41.089 V/m, located at the skin layer. When at 3500 MHz, the maximum electric field intensity is 35.444 V/m, located at the skin layer. The research shows that as the penetration of electromagnetic waves gradually extends from the skin layer to the brain layer, the electric field gradually decreases.

5.2. SAR Value of the Head

To better observe the SAR value distribution of various tissues inside the patient’s head, Figure 12 is used to represent the local SAR value distribution of the patient’s head model in all cases in this study.

From the figures, it can be seen that in all research cases, the maximum SAR value of the patient’s head appears in the skin layer. As shown in Figure 12, we learned that the SAR values are inversely proportional to the distance between the radiation source and the head. Figure 13 provides a detailed histogram showing the maximum SAR values of each layer of the patient’s head tissue in all cases.

Figure 13 shows that, with the increase in distance from the phone, the SAR value of each tissue layer decreased rapidly; this change is consistent with the change rule in Figure 11. In all cases, the SAR maximums occur on the side near the phone. Combined with Figure 12 and Figure 13, at the frequency of 3500 MHz, the SAR values of each tissue in the head are generally higher than those at 2400 MHz. But it is worth noting that in the brain tissue, the calculations were contrary to the above findings. Fortunately, compared with the SAR value limit of ICNIRP (2 W/kg), none of the SAR values obtained in this study exceed the limit value.

5.3. Temperature Rise of the Head and DBS

5.3.1. Temperature Rise of DBS

We also determined the temperature distribution of the DBS for all cases, as shown in Figure 14.

As Figure 14 shows, the temperature rise of the DBS at 2400 MHz is generally higher than at 3500 MHz. When d = 1 cm, the largest value of the temperature rise appears on the insulating layer of the DBS, which increases by 0.0058 °C.

Considering that the electromagnetic wavelength at 2400 MHz is longer than the electromagnetic wavelength at 3500 MHz, the penetration of electromagnetic energy in the head is deeper at 2400 MHz. However, as the distance between the phone and the head model increases, the temperature rise gradually decreases.

5.3.2. Temperature-Rise of the Head

We also obtained the temperature rise after 30 min of radiation exposure to the head under different circumstances. Figure 15 depicts cross-sectional plots of the temperature field distribution of the head model.

We also observed the largest temperature rise values of various tissues in the head when irradiated for 30 min at different distances and frequencies, as shown in Figure 16.

As Figure 15 and Figure 16 show, in the above cases, the temperature rise in the head shows a gradual decrease from the brain tissue to the sides. It is worth noting that this is different from the distribution of SAR values shown in Figure 13. The reason could be that, in the weak electric field intensity region, metabolic heat production and blood perfusion become the main heat transfer mechanisms; the blood perfusion rate of brain tissue is higher than that of other tissues, so the temperature of brain tissue is larger than that of other tissues.

The relevant standards stipulate that the temperature rise in the body does not exceed 1 °C [4], while the temperature rise of the active implanted medical devices does not exceed 2 °C [23,24]. Therefore, the temperature rise of patients with implanted DBS is within the safe range when using the phone in all cases.

6. Conclusions

In this study, we calculated the SAR deposition, the electric field intensity and temperature rise in the head, as well as the electric field intensity and temperature rise in the DBS, which contained different frequencies and distances. The results lead us to draw the following conclusions:

• For the head tissues, we found that the distribution of the electric field intensity at 2400 MHz is greater than that at 3500 MHz. When d = 1 cm, the electric field intensity has the maximum value, which is 41.089 V/m. But the SAR values at 3500 MHz are greater than those at 2400 MHz, and when d = 1 cm, the SAR value has the maximum value, which is 1.132 W/kg. None of the SAR values exceed the ICNIRP standard of 2 W/kg.
• For the head tissues, we found that the temperature rise at 2400 MHz is greater than that at 3500 MHz. Meanwhile, the temperature of brain tissue is higher than that of other tissues. When d = 1 cm, the temperature rise has the maximum value, which is 0.2148 °C. None of the temperature rise values exceed the ICNIRP standard of 1 °C.
• For the DBS, we found that the electric field intensity and temperature rise of DBS at 2400 MHz are greater than those at 3500 MHz. When d = 1 cm, the electric field intensity and the temperature rise have the maximum values, which are 6.535 V/m and 0.0058 °C. The temperature rise of DBS is less than the ISO standard of 2 °C.

In summary, the electromagnetic exposure of patients with implanted DBS is within safe limits when using 5G/4G phones. However, we still recommend that when patients use these phones, they should keep their devices at a larger distance as often as possible and do not spend too much time on the phone.

The focus of this research is on the electromagnetic exposure assessment of the DBS from 5G/4G phone antennas. Other members of our research group are working on the safety assessment of electromagnetic exposure from active implantable medical devices such as cardiac pacemaker, cochlear implants, and so on.