Calculation of Temperature Rise Induced by Cellular Phones in the Human Head

Transcription

1 Journal of Microwaves and Optoelectronics, Vol. 6, No. 1, June Calculation of Temperature Rise Induced by Cellular Phones in the Human Head Ana O. Rodrigues, Juliano J. Viana Centro Universitário de Belo Horizonte (UNI-BH), Av. Prof. Mário Werneck, 1685, Estoril, Belo Horizonte, MG, , Brazil. Independent Computer Consultant Luiz O. C. Rodrigues and Jaime A. Ramirez Universidade Federal de Minas Gerais, Av. Antônio Carlos, 6627, Belo Horizonte, MG, , Brazil Abstract The problem associated with the calculation of temperature rise induced by cellular phones in the human head taking into account the effects of the thermoregulatory system (TS) is discussed in this work. The formulation uses the finite difference time domain method. The inclusion of the TS considered three modifications in the bioheat equation, which was solved dynamically: first, the convective heat transfer coefficient as a function of the gradient between the skin temperature and the environment temperature; second, the skin blood flow rate as a function of the energy absorved by the skin and by the brain; and third, the temperature in the brain constant at 36.8 o C. The bioheat equation was solved for a 3D anatomically based model of the human head composed of 15 tissues. The cellular phone was modeled as a half-wavelength dipole irradiating at 1.8GHz with a power of 120mW. The inclusion of the TS resulted in a maximum temperature rise of o C in the skin, a value considerably smaller than previously reported. These results suggest that modern cellular phones operating at full power would produce temperature rise in the human head within the basal temperature of these tissues. Index Terms Anatomic model of the head, temperature increase, cellular telephones, safety standards, thermoregulatory mechanisms. I.INTRODUCTION The rapid dissemination of wireless devices throughout our society, particularly cellular telephones, has raised public concern on whether the proximity of the cellular phone to the human head may cause any adverse health effects. There have been some contributions on the calculation of the specific absorption rate (SAR) and the induced temperature rise in the human head [1]-[6]. From the experimental and

2 Journal of Microwaves and Optoelectronics, Vol. 6, No. 1, June simulation results, many authors tend to a consensus that a cellular phone operating close to the human head at a frequency in the range 800MHz-1.9GHz and power of 120mW-600mW can produce maximum SAR values in the order of 4.0W/kg averaged over 1g of tissue, and maximum temperature rise values of 0.1 o C-0.2 o C in the brain and of 0.45 o C in the skin [1], [3], [4], [5]. The majority of the reported SAR values are within the limits suggested in the safety guidelines [18]-[19]. Previous studies indicate that a temperature rise of 0.1 o C is high enough to trigger intense thermoregulatory responses [12]. It is well stablished that under normal conditions, such a change in the head internal temperature should promote increased blood flow to the skin, increased sweat rate and behavioral responses, in order to dissipate the heat [13]. However, such a temperature rise is very improbable, due to the thermoregulatory mechanisms present in the brain. These mechanisms are specifically designed to maintain brain temperature constant through blood flow increase and heat exchange. Thus, if the electromagnetic waves from cellular telephones are able to dissipate a power that could induce an increase in the brain temperature of 0.1 o C-0.2 o C, the thermoregulatory mechanisms should also be considered in the temperature rise calculation. In this paper, we propose a mathematical formulation to consider the effects of the thermoregulatory system (TS) in the temperature rise induced by the SAR dissipation of cellular phones in the human head. The human head used is a 3D anatomically model composed of 15 tissues, as described in [8]. Emphasis is given to the bio-heat equation in order to describe its limitations and how the effects of the TS system were taken into account. The results are presented in terms of the temperature rise without the TS and with the TS. II.THE HUMAN HEAD MODEL The full model is a grid composed of 128 cells in x, 256 cells in y and 256 cells in z with cell size of 1.86mm x 1.11m x 1.11mm in x, y and z directions, respectively. The 3D model of the human head was built using semi-automatic image processing, which was performed on computed tomography scans of a real human head [9]. The 3D head model is composed of 15 tissues, namely: bone, brain (subdivided into general brain, hypothalamus and CSF), eye (subdivided into sclera, anterior chamber, cristalin, vitreous body, cornea and iris), fat, muscle and skin (subdivided into general skin, neck skin and skin with hair). Fig.1 shows a cut of the head model, illustrating the internal tissues. III.NUMERICAL SIMULATION The physical phenomena associated to a cellular phone operating close to a human head are simplified here to two coupled problems. First, the electromagnetic field irradiated from the antenna of the cellular phone that propagates through the human head, inducing eddy-currents and dissipating energy in the form of heat. The latter is calculated in terms of the specific absorption rate (SAR). Second, the heat dissipated in the human head, from the electromagnetic field, gives rise to a thermal problem which, in turn, accounts for the increase in the temperature. We discuss in this section the mathematical formulation employed to solve both problems.

3 Journal of Microwaves and Optoelectronics, Vol. 6, No. 1, June Fig. 1. Cut of the model of the head A. Electromagnetic Field Calculation Maxwell s time-dependent curl equations (1) to (4) are solved using the finite difference time domain (FD-TD) method. The formulation discussed here is based on [7]. H = D t + J e (1) E = B t (2) B = 0 (3) D = ρ (4) where E is the electric field vector in volts per meter, H is the magnetic field vector in amperes per meter, B is the magnetic flux density vector in weber per square meter, D is the electric flux density vector in coulombs per square meter, J e is the electric conduction current density in amperes per square meter, and ρ is the electric charge density in coulomb per cubic meter. In linear, isotropic nondispersive materials, we can relate B to H and D to E using (5) and (6). B = µh (5) D = εe (6) where ε is the electric permittivity in farads per meter, µ is the magnetic permeability in henrys per meter. The FD-TD method is based on the Yee algorithm, that solves for both electric and magnetic fields in time and space using the coupled Maxwell s curl equations rather than solving for the electric of magnetic field alone with a wave equation. As illustrated in Fig. A., Yee algorithm center its E and H components in three-dimensional space so that every E component is surrounded by four circulating H components. Also, Yee algorithm centers its E and H components in time in what is termed a leapfrog arrangement. All of the E computations in the three-dimensional space of interest are completed and stored in memory for a particular time

4 Journal of Microwaves and Optoelectronics, Vol. 6, No. 1, June Fig. 2. Position of the E and H components about a cubic unit cell of the Yee space lattice point using H data previously stored in the memory. Then, all of the H computation in the modeled space are completed and stored in memory using the E data just computed. The cycle begin again until time-stepping is concluded. Defining the notation for the H component in x direction in point x = i, y = j and z = k at the time-step t = n as H x n+1/2 i,j,k and using finite differences in (1) to (4) it is possible to obtain the desired explicit time-stepping relation for this component, presented in (7). H x n+1/2 i,j,k ( ) ( t E = H x n+1/2 y n i,j,k+1/2 i,j,k + E y n i,j,k 1/2 E z n i,j+1/2,k E ) z n i,j 1/2,k µ i,j,k z y where n is the time instant, i, j, k is the coordinate positions in x, y and z directions, t is the time step, and y and z are the size of the Yee cell in y and z directions. Equivalent relations can be derived for E x, E y, E z, H y and H z. A software in C++ was developed to implement these equations [8]. First, the head model is loaded into the software, specifying the material in each cell and its electromagnetic, thermal and physical properties. The next step is to set all fields in the domain to zero. At each time step the value of the source of electromagnetic fields are calculated and fed in the appropriate point in space, originating a propagating wave. Once the steady state electric field is computed, it is possible to calculate the specific absorption rate (SAR) in watt per kilogram in each cell using (8): (7) SAR = σ E 2 2ρ (8) where σ is the electric conductivity in Siemens per meter, and ρ is the density in kilograms per cubic meter. The value of SAR in each cube is then used to calculate the electromagnetic energy accumulated in each cell, h EMi,j,k, using (9), that will be used in the bio-heat equation to calculate the temperature rise, also dynamically, as presented in the next section. h EMi,j,k = ρ.sar (9)

5 Journal of Microwaves and Optoelectronics, Vol. 6, No. 1, June B. Temperature Rise Calculation Bio-Heat Equation The temperature at point x = i, y = j and z = k at the time-step t = n is represented by Ti,j,k n. In the first time-step (n = 0), we set initial temperatures for the tissue and the environment, i.e., Ti,j,k 0 = T init. The following equation, which is based on [3], accounts for internal differences in temperature inside the materials and heat losses to the environment: T n i,j,k = T n 1 i,j,k + t {V i,j,k [ (K i,j,k T) + C i,j,k m i,j,k +h mi,j,k + h EMi,j,k + b fi,j,k C blood (T blood T n 1 i,j,k )] + h RADi,j,k h CONVi,j,k h Ei,j,k } (10) In (10), the heat losses of the voxels at the surface of the model include radiative, convective and evaporative losses. The radiative heat loss is represented by the Stefan-Boltzmann formula: h RAD = ε δ A eff [(T skin + 273) 4 (T air + 273) 4 ] (11) where δ = (W/(m 2 K 4 )) is the Stefan-Boltzmann constant; ε is the emissivity of the tissue; A eff is the area of the head that is effective in radiating heat (m 2 ); T skin is the temperature of the skin ( o C) and T air is the ambient air temperature, assumed to be 25 o C. The convective heat losses from the body and the evaporative heat loss due to insensible perspiration from the surface voxels are given by (12) and (13), respectively: h CONV = h c A eff (T skin T air ) (12) h E = k evap A N (P w,skin P w,air ) (13) where h c = 2.7(W/(m 2 oc)) is the convective heat transfer coefficient; k evap = 0.35(W/(m 2 mmhg)) is the evaporative coefficient; P w,skin, P w,air are the vapor pressures of water at skin and in air, respectively, in (mmhg); and A N is the area of the voxel exposed to air (m 2 ). Thermal Properties The thermal properties of each tissue are presented in Table I, where C is the specific heat, k the heat conductivity, b f the blood flow rate, h m the basal metabolic rate. For the general skin and the skin with hair, ε (emissivity of the tissue for radiation losses) is 0.98 and k evap (evaporation coefficient) is 0.35 W/(m 2 mmhg). For all other tissues, ε and k evap are considered 0.

6 Journal of Microwaves and Optoelectronics, Vol. 6, No. 1, June TABLE I. THERMAL PROPERTIES OF THE TISSUES [3], [10], [11] Material C k b f h m ( W.h kg. o C ( W ) m. o C ( kg ) m 3.h (W) kg Air Bone Brain: General CSF Hypot Copper Eye: Sclera Ant.Chamb Cristalin Vit.Body Cornea Iris Fat Muscle Skin: General Neck Skin Skin with Hair IV.THE THERMOREGULATORY SYSTEM The main cooling mechanism of the brain is the heat exchange with the blood that flows through its tissue [13]. The blood that flows through the brain absorbs the heat dissipated by the SAR, bringing this thermal energy to the circulation. The circulation of the blood takes the thermal energy to the skin, where it is dissipated to the environment. The following section presents how the thermoregulatory system was included in the temperature rise calculation. A. Implementation in the Temperature Rise Calculation The model proposed here includes the thermoregulatory system in the following way: The term h c presented in (12) that regulates the losses by convection to the environment is suggested by [3] to have a constant value of 2.7W/m 2. o C. It will be replaced by an equation that is dependent of the temperature gradient between the skin and the environment ( ). This change in the model, suggested by [14], accounts also for the changes in local sweat. h c = (14) Local rises in the skin temperature will result in a local rise in the blood flow. A similar approach accounting for temperature rises due to muscular activities (exercises) is described in [12]. The rise

7 Journal of Microwaves and Optoelectronics, Vol. 6, No. 1, June in the local blood flow will be calculated using (15), where h mi is the metabolic heat generation per unit volume (W/m 3 ) and h EMi is the EM energy deposition per unit volume (W/m 3 ), presented in (10). rise in b fskin (%) = (h m i h EMi ) h mi (15) The brain temperature is set at 36.8 o C until steady state is reached dynamically. All the energy absorbed from the electromagnetic waves will be dissipated through heat exchange with the blood that flows through the brain. The blood flow in the skin will be increased proportionally to the energy dissipated in the brain, according to the relationship presented in Fig. 3, i.e. the relationship between the internal temperature (T int ) and the skin conductance is considered linear. Fig. 3. Quantitative relationships in the human body between the temperature inside the head (internal temperature) and the blood flow in the skin (indirectly measured through the conductance of the skin, squares, legend at right) and sweat rate (triangles, legend at left). The arrow shows the point where these parameters shoot up. In this individual, the cutting point was at 36.9 o C. (Adapted from [15] and [16]) The rise in the skin conductance is a direct result of the increase in the blood flow, consequently, the blood flow in the skin may be expressed by: b fskin = [kg/m 3 h] if T int 36.8 o C (16) b fskin = T int [kg/m 3 h] if 36.8 o C < T int 37.4 o C (17) b fskin = [kg/m 3 h] if T int > 36.8 o C (18) In this way, the blood with increased temperature will circulate in the external tissues, raising the

8 Journal of Microwaves and Optoelectronics, Vol. 6, No. 1, June skin temperature and dissipating this energy in exchange with the environment. V.RESULTS AND DISCUSSION We present in this section the numerical results of a cellular phone with power of 120mW, modeled as a half-wavelength dipole, irradiating at 1.8GHz the head model describe in section II. A. Steady State Temperature The average steady state temperature was calculated in the head model without and with the thermoregulatory system (TS). The results are presented in Table II. T av indicates the change in the average steady state temperature for each tissue due to the TS. TABLE II. AVERAGE STEADY STATE TEMPERATURE WITHOUT AND WITH THE THERMOREGULATORY SYSTEM (TS) Material T av ( o C) T av without TS with TS Bone Brain: General CSF Hypothalamus Eye: Cornea Vit.Body Cristalin Sclera Ant.Chamber Iris Fat Muscle Skin: General Neck Skin Skin with Hair The general brain and the hypothalamus presented a smaller steady state T av, o C and o C, respectively. All the other tissues presented an increased T av, except the temperature of the CSF that was held constant at 36.8 o C. The increased T av in the head is expected since the heat in the brain must be dissipated to maintain the internal temperature constant at 36.8 o C, as discussed in Section IV. The steady state temperatures without the TS were compared with [3]. Table III indicates the good agreement between the results calculated with our model and [3]. The differences in these results are probably due to the different head models used. TABLE III. COMPARISON WITH [3] STEADY STATE TEMPERATURE WITHOUT THE THERMOREGULATORY SYSTEM

9 Journal of Microwaves and Optoelectronics, Vol. 6, No. 1, June Material T av ( o C) This Work( o C) [3]( o C) Error( o C) Brain Eye Skin (Pinna) B. SAR Validation The specific absorption rate (SAR) results, calculated for peak 1-voxel SAR and peak 1g SAR, show good agreement when compared to with [2], as illustrated by Table IV. The rather large difference observed in the brain is probably due to differences in skin modeling. The CT scans from which our head model was developed presented a thick layer of skin, due to wave diffraction in the border of the head. For this reason, in our model the electromagnetic wave is more absorbed by the skin, resulting in a smaller SAR in the internal tissues that are more distant from the source, such as the brain and the eye. Another source of error, though small - considering that the electrical parameters do not alter significantly, is the difference in the frequency used in the simulations, 1.8GHz in this work and 1.9GHz by [2]. TABLE IV. SAR RESULTS SAR values This Work [2] Peak 1-voxel (W/kg) Peak 1g SAR (W/kg) Peak 1g SAR for brain (W/kg) Peak 1-voxel for brain max (W/kg) C. Temperature Distributions The temperature rise (T rise ) induced by a cellular phone in the human head was calculated for a exposure time of 60 minutes. Table V compares the temperature rise observed without the thermoregulatory system with temperature rises presented by [3]. A significant difference in the temperature rise was expected, as slightly different models usually present very large differences in local SAR values [17]. No significant temperature rise was observed in the eye in our model due to the low SAR present in its tissues. Table VI shows the maximum temperature rise in each tissue of the head model not considering the thermoregulatory system (without TS), and considering the thermoregulatory system (with TS). The bold values show the maximum temperature rise for each case. shows the rate of decrease of the maximum temperature rise due to the inclusion of the TS.

10 Journal of Microwaves and Optoelectronics, Vol. 6, No. 1, June TABLE V. MAXIMUM ONE-VOXEL TEMPERATURE RISE WITHOUT THERMOREGULATORY SYSTEM COMPARISON WITH [3] Material T ( o C) This Work( o C) [3]( o C) Error( o C) Brain: Eye: Skin: TABLE VI. MAXIMUM TEMPERATURE RISE Material T rise ( o C) ( o C) without TS with TS Bone Brain: General CSF Hypothalamus Eye: Cornea Vit.Body Cristalin Sclera Ant.Chamber Iris Fat Muscle Skin: General Neck Skin Skin with Hair The inclusion of the TS resulted in a maximum temperature rise of o C in the skin with hair. In the model without the TS the maximum temperature rise occured in the CSF (0.041 o C). The change in the tissue in which the maximum value is observed was expected, as the temperature rise in the CSF is now controlled by the TS. A decrease of o C is observed in the skin with hair, and more significant decreases in the temperature rise are observed in the fat, muscle and bone. This effect is a consequence of the smaller propagation of heat from the external tissues as the brain and the skin with hair are cooler with TS than without TS, therefore, the tissues in contact with them will also present a smaller temperature. Fig. 4 and Fig. 5 show the T rise as a function of exposure time for some tissues of the model without TS and with TS, respectively. The choice of the tissues presented, bone, CSF, brain, general skin, muscle, fat and skin with hair was based on the fact that a significant temperature rise was observed on them. The steady state is reached faster for the model with TS than for the model without TS. In the model without TS it takes approximately 20 minutes for all tissues to reach steady state. This result is very similar to the value of minutes presented in [3]. In the model with TS this time is approximately 10 minutes. It is an evidence that the inclusion of the TS resulted in more efficient and faster response of the body to a external heat source, which is exactly the main purpose of the TS. The temperature rise distribution in the 3D model is presented in Fig.6 without the TS and in Fig.7 with

11 Journal of Microwaves and Optoelectronics, Vol. 6, No. 1, June Temperature Rise [oc] Bone CSF General Brain General Skin Muscle Fat Skin with Hair Time [min] 0.03 Fig. 4. T rise in time, without TS Temperature Rise [oc] Bone CSF General Brain General Skin Muscle Fat Skin with Hair Time [min] Fig. 5. T rise in time, with TS the TS. These results allow a detailed visualization of the fast decay of the temperature rise distribution and, as expected, a temperature rise distribution more concentrated in the surface of the model. VI.CONCLUSION This work has proposed a mathematical formulation to consider the effects of the thermoregulatory system (TS) in the temperature rise induced by cellular phones in the human head. The new formulation has considered three modifications in the bioheat equation: first, the convective heat transfer coefficient is a function of the gradient between the skin temperature and the environment temperature; second, the skin blood flow rate is a function of the energy absorved by the skin and by the brain; and third, the temperature in the brain is considered constant (36.8 o C). The bio-heat was subsequetly solved dynamically for a 3D anatomically based model of the human head, being irradiated by the antenna of a cellular phone operating at 1.8GHz with a power of 120mW. The results regarding the steady state temperature, specific absorption rate and temperature rise with-

12 Journal of Microwaves and Optoelectronics, Vol. 6, No. 1, June Fig. 6. Final T rise without TS Fig. 7. Final T rise with TS out the TS were compared and validated with the literature. The inclusion of the TS resulted in a maximum temperature rise of o C in the skin, a value considerably smaller than previously reported. The temperature rise distribution is significantly affected by this change, resulting in a more superficial heat distribution. Finally, the consideration of the TS suggest that modern cellular phones operating at full power would produce SAR dissipation within the limits of the safety guidelines and temperature rise in the human head in the same order or magnitude of the basal temperature of these tissues. AKNOWLEDGMENT This work was supported by CNPq (grants n / and n /2003-1), Brazil. REFERENCES [1] P.J. Dymbylow and S.M. Mann, SAR Calculations in an anatomically realistic model of the head for mobile communication transceivers at 900MHz and 1.8GHz, Phys. Med. Biol., vol.39, pp , [2] O.P. Gandhi, G. Lazzi and C.M. Furse, Electromagnetic Absorption in the Human Head and Neck for Mobile Telephones at 835 and 1900 MHz, IEEE Trans. on Microwave Theory and Techniques, vol.44, no.10, pp , [3] O.P. Gandhi, Q-X. Li and G. Kang, Temperature Rise for the Human Head for Cellular Telephones and for Peak SARs Prescribed in Safety Guidelines, IEEE Trans. on Microwave Theory and Techniques, vol.49, no.9, pp , [4] J. Wang and O. Fujiwara, FDTD Computation of Temperature Rise in the Human Head for Portable Telephones, IEEE Trans. on Microwave Theory and Techniques, vol.47, no.8, pp , [5] P. Bernardi, M. Cavagnaro, S. Pisa and E. Piuzzi, Specific Absorption Rate and Temperature Increases in the Head of a Cellular-Phone User, IEEE Trans. on Microwave Theory and Techniques, vol.48, no.7,

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