Comments on the FCC Approval of Finite Element Method for Biomedical Transmitters

Juliano F. Mologni and Leandro A. Percebon ESSS – Engineering Simulation & Scientific Software

São Paulo, Brazil juliano.mologni@esss.com.br

Marco A. R. Alves and Edmundo Braga Unicamp

Campinas, Brazil edmundo@fee.unicamp.br

Abstract—The Federal Communications Commission (FCC) ruled on February 1st 2011 that the finite element method (FEM) is a valid technique to simulate transmitters that are placed inside, on the surface, or near the human body. This paper investigates how FEM can be employed on biomedical engineering. A complete high fidelity human body model including frequency dependent materials and complex geometries was used. Three examples are described including a magnetic resonance imaging (MRI) system, a human body on a substation environment and specific absorption rate (SAR) simulations on a human head due to a cell phone radiation. Advanced multiphysics technology coupling electromagnetic and thermal simulations are also addressed. A very good agreement between FEM simulations and measurement data was achieved for SAR calculations.

Keywords-finite element method, biomedical transmitter, radiation, multiphysics, specific absorption ratio.

I. INTRODUCTION With the Federal Communications Commission (FCC)

supportting the use of FEM as a computational procedure equivalent to the finite-difference time-domain (FDTD) technique [1], engineers now have more options to design biomedical devices. Moreover, enhanced graphical user interfaces and adaptive mesh techniques available on FEM solvers like Ansys HFSS [2] provides an accurate way to evaluate biomedical devices. Additional studies have stated that FEM simulations converge much faster than FDTD [3] enabling a speed up on the development time of biomedical products. Examples including FEM analysis of specific absorption rate (SAR) following procedures described on IEEE P1528-2002 [4] are shown. The simulated SAR values are compared to measurement data yelding similar results. A full human body including frequency dependent materials and more than 380 solids are used for our FEM simulations. Three examples are presented: The first example is a magnetic resonance imaging (MRI) system. The second example concerns the Brazillian Normative Resolution 398, from the National Agency of Electrical Energy / Agencia Nacional de Energia Elétrica (ANEEL) [5], which determines the maximum levels of magnetic and electric fields which a human body can be exposed to. The third example is a SAR study of a cell phone near the human head. A further multiphysics analysis to determine the temperature profiles on the human head and the brain is also addressed.

II. FINITE ELEMENT METHOD SAR CALCULATION In order to verify the accuracy of FEM as a valid technique

for biomedical transmitters, SAR calculations are performed on a flat phantom model covered with a shell due to a dipole antenna radiation. The parameters for the lossless phantom shell, shell thickness, frequency dependent permittivity and the distance between the reference dipole and liquid were obtained from IEEE P1528-2002 [4]. In Ansys HFSS, SAR values are calculated according to (1):

(1)

where ρ is the mass density of the dielectric material in mass/unit volume, � is the material´s conductivity, E is the electric field and � is the permittivity. The comparison between FEM simulations and measurements data from [4] is shown in fig. 1. The inset displays the dipole on the top part and local SAR field inside the phantom at 900MHz. Stronger SAR is observed on the surface of the phantom near the center of the dipole.

Fig. 1. Comparison between FEM results from HFSS and measurement data.

( )[ ]rbulk

ESARεωεσσρσ

0

2 2/+=

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III. BIOMEDICAL SIMULATIONS USING FEM A comparison between a simulation of a head model using

FDTD and FEM was presented in [3] resulting on very close results. Comparison of SAR values using FEM with published measurement data from [4] was also demonstrated in fig 1. These are factors that inclined FCC to rule that FEM is a sound engineering technique that can be used for biomedical projects [1]. In order to understand the capabilities of FEM, three examples are shown:

A. Magnetic Ressonance Imaging Example There are numerous challenges in a MRI design, including

but not limited to resonance at the correct operating frequency, compliance with SAR regulations, electromagnetic field distribution and rotating magnetic field with proper polarization [6-8]. In order to simulate a MRI system, a high fidelity human body model needs to be used. Fig. 2 shows the human body model used for the FEM simulations including frequency dependent electromagnetic material properties. The MRI system, including the RF coil with 18 excitations is shown in fig. 3 as well as the electric field plot and the human body. The frequency was set to 300MHz and each of the 18 excitations was set to 5W. Muscles and tissue are hided in the plot of fig.3 for clarity. The intensity of the electric field is very strong (region in red) near the coils and weak outside the cylindrical shield structure that surrounds the RF coil and the body. The electric field distribution inside the human body is visualized in fig. 4, indicating lower values (blue region) inside the lungs due to the lungs permittivity. In order to

Fig. 2. Human body model: a) front view, b) without muscles and tissues andc) cross sectional lateral view.

Fig. 3. MRI system with the human body.

Fig. 4. Electric field plot.

Fig. 5. Electric field on the probe line.

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quantify the electric field, a line crossing the human body was used as a probe. Figure 5 shows the electric field along the probe line and the inset shows the position of the line in the model. As expected, the electric field is weaker inside the human body varying according to the organs. In regions of high electric fields, discomfort to the patient and tissue damage can occur.

When using FEM, there is a tradeoff between accuracy and computational time. The MRI model was solved in 112 minutes using a model resolution of 2mm, which means that all geometries bigger than 2mm in any dimension is considered. Solving time can be improved if the model resolution is increased, on the other hand, accuracy of the results will decrease.

B. Power Distribution Substation Example ANEEL released the Brazilian Normative Resolution 398

that defines the limits of human exposure to magnetic and electric time-varying fields. This rule applies to all installations operating over 138kV. Table 1 shows the electric and magnetic field maximum limits that the occupational public can be exposed to [5]. Occupational public includes people that are normally exposed to electric and magnetic fields in known conditions due to their occupational duties.

TABLE I. ELECTRIC AND MAGNETIC FIELD LIMITS

Electric Field (kV/m)

Magnetic Field (μT)

Occupational public 8.33 416.67

The flexibility of grid sizing in FEM leads to an order of

magnitude in time savings compared to FDTD [9]. This feature is very suitable for very large models like a power distribution substation shown in fig. 6, having the following physical dimensions: 35m x 29m x 65m. The flexible mesh in FEM uses small elements on small and complex geometries, like the human body, and larger elements on region like air. The flexible adaptive mesh generation is done automatically

by the FEM solver, leading to an accurate result with less solving time.

Fig. 6 also shows the electric field plot limited to 8.33 kV/m (red region). Without the human body, the electric field limits of the power distribution substation are in compliance the Resolution Normative 398. Nevertheless, when a human model is placed under a high voltage cable, the electric field above its head overcomes the 8.33kV/m limit as shown in the inset in figure 1. This demonstrates that in order to evaluate any facility that operates over 138kV under the Brazilian Normative Resolution 398, a human body needs to be included in the model so accurate electromagnetic fields are calculated, representing the real world environment.

C. SAR Multiphysics Simulation Example This example intends to show how a generic cell phone,

including a complete print circuit board (PCB) with antennas and electronics components can be modeled within Ansys HFSS together with a human head. Fig 7 shows the cell phone model, including the electric field distribution over the PCB. The cell phone model and the PCB are not related to any commercial product available today and they were modeled

Fig. 6. Electric field plot on a power distribution substation.

Fig. 7. a) Generic cell phone model and b) electric field plot.

Fig. 8. a) Isometric view of the cell phone model and the head and b) lateral view with skull and tissues removed.

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for the unique purpose to show how a multiphysics simulation can be carried out on a FEM environment. Nevertheless, real parameters for excitation of the PCB traces and the transmitting antenna were used. The cell phone transmitting power was set to 500mW at 900MHz, which is the maximum output of power class 2 mobile phones [10]. The complete 3D model is shown in figure 8, where the cell phone is placed close to the right ear of the human head.

The far field radiation pattern from the phone and the electric field distribution is shown in figure 9. It is clearly noticeable that the electric field inside the human head decreases due to the skull. Local SAR values are calculated over the human head and inside of all internal organs. As shown in figure 10, SAR values are higher near the right ear, where the cell phone is placed. In order to quantify local SAR

values, a line is used as a probe once again. The line crosses the human head from the right ear to the left ear as detailed in the inset of fig. 11. Local SAR values are plotted as a function of the line distance in fig. 11, showing very high local SAR values on the right surface of the human head (right ear). Local SAR values strongly decrease as the line goes toward the inner side of the head.

For the thermal simulation, the loss densities are mapped from the Ansys HFSS analysis to ANSYS Mechanical and take the role of heat load. The heat spreads through the entire human head at a rate dependent on the thermal conductivities of the materials. Also, blood perfusion is taken into account since it removes heat from the organs. A natural convection (stagnant air model) was used as a boundary condition for the thermal analysis. Fig. 12 shows the temperature plot over the surface of the head. As expected, temperatures are higher near the cell phone antenna, while the PCB traces also generate a moderate quantity of heat. Since the ambient temperature was considered 22o C, a temperature rise of only 0.892 o C occurred due to cell phone radiation. Figure 13 shows the heat flux vectors on the human surface. This analysis does not

Fig. 9. Radiation far field pattern and electric field plot [V/m] at 900MHz.

Fig. 10.SAR field plot over the human head.

Fig. 11. Local SAR values [W/Kg] on a probe line crossing the human head.

Fig. 12. Temperature distribution on the surface of the human head due to the cell phone radiation.

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consider the cell phone in contact with the human head, so conduction between the phone and the head are not considered. Also, the simulation neglects the heat caused by the phone battery which can also interfere in the results. These assumptions were made to speed up the simulation, even though they can be included in future works since this application is not limited by the software.

Since the temperature rise was relatively low, a new simulation changing the cell phone transmitting power to 1W was performed. With this value, a temperature rise in the brain can be observed. Fig. 14 shows only a 0.006 o C temperature rise on the brain.

SUMMARY

This paper shows the potential use of FEM on biomedical applications. Since February 1st,2011 when FCC approved the use of FEM for biomedical transmitters, engineers have more options to numerically evaluate biomedical designs using the advantages of FEM. SAR calculations using FEM and measurement data were compared, yelding a very good agreement. Three examples including a complete MRI system, a substation with a human body and a multiphhysics approach of a cell phone radiation on a human head were presented. The accuracy and connectivity between the various FEM solvers for electromagnetic and thermal analyses enable the fast evaluation of biomedical applications under real-world multiphysics conditions.

REFERENCES [1] FCC- DA11-192. http://fjallfoss.fcc.gov/edocs_public/attachmatch/DA-

11-192A1.pdf. February 2011. [2] D. K. Sun, Z. Cendes, J.-Fa Lee, “Adaptive mesh refinement, h-version,

for solving multiport microwave devices in three dimensions,” IEEE Trans. Magnetics, pp 1596-1599, Vol. 36, N.4, July 2000.

[3] M. Kozlov and R. Turner, “A comparison of Ansoft HFSS and CST microwave studio simulation software for multi-channel coil design and SAR Estimation at 7T MRI,” PIERS Online, vol. 6, no. 4, pp.395-399, 2010.

[4] IEEE P1528-2002, “Recommended practice for determining the peak spatial-average specific absorption rate (SAR) in the human head from wireless communications devices: measurement techniques,” December 2002.

[5] ANEEL, “Normative Resolution 398 / Resolução Normativa 398,” March 2010.

[6] M. Kozlov and R. Turner, “Fast MRI coil analysis based on 3-D electromagnetic and RF circuit co-simulation," Journal of Magnetic Resonance, vol. 200 147-152, 2009.

[7] R. S. Menon, J. S. Gati, B. G. Goodyear, D. C. Luknowsky, and C. G.Thomas, “Spatial and temporal resolution of functional magnetic resonanceimaging,” Biochem, Cell Biol., vol. 76, pp. 560–571, 1998.

[8] E. A. Disbrow, D. A. Slutsky, T. P. L. Roberts, and L. A. Krubitzer, “Functional MRI at 1.5 tesla: A comparison of the blood oxygenation level-dependent signal and electrophysiology,” in Proc. Natl. Acad. Sci., vol. 97, pp. 9718–9723, 2000.

[9] Feng Huang, Sathya Vijayakumar, Shahed Reza, Mark Limkeman, Randy Duensing, “A self-calibration method for radial GRAPPA/k-tGRAPPA,” Magnetic Resonance in Medicine, vol.14, 2006.

[10] K. Shrier and C. Jiaa, “Cell phone GaAs power amplifiers: ESD, TLP, and PVS devices,” Electrical Overstress/Electrostatic Discharge Symposium, Print ISBN: 978-1-58537-069-6, INSPEC Accession Number: 10915258 ,pp. 1-10, September 2005.

Fig. 13. Total heat flux on the human head.

Fig. 14. Temperature on the brain.

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