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Computation of the Cell Phone-Induced SAR Distribution in a 3D Multi-Layered

Model of the Human Head/Brain Using ANSYS HFSS

Deniz Celik

Engineering Intern

Ozen Engineering, Inc.

Abstract

Since their first commercial debut in 1983, mobile phones have quickly become an integral part of

modern society, providing instant communication over long distances and allowing for the world to

grow closer as a whole. Recently, a debate has been raging about the safety of the electromagnetic

waves produced by cell phones so close to the brain, one of our most critical organs. While many

studies, including the massive INTERPHONE project [5], attempt to experimentally determine the

dangers of long term exposure, using FEA simulation for such problems is still a nascent idea among

scientists. While the software may not be ready to handle the biological implications of mobile phone

use, it is more than capable of analyzing realistic and complex models to determine their Specific

Absorption Rate (SAR), the standard unit for determining safety of devices. In lieu of these abilities, a

complex, 3D, multi-layered, homogeneous model was created and analyzed using ANSYS HFSS software

in an attempt to determine the SAR distribution on the human brain due to exposure to cell phone

radiation.

1. Introduction

As we enter the 21st century, many scientists have begun investigating the negative effects of cell

phones, particularly those associated with the powerful electromagnetic emissions created [8]. As is the

case with most research, studies have come out supporting both the harmless nature of such radiation

[11] and the dangerous biological effects on the brain [1, 11]. Because of the lack of long-term studies,

there has been no concrete evidence to prove either side right/wrong. However, the 13-nation

INTERPHONE study [5] showed no conclusive evidence of brain tumors.

One systematic way of determining the impact of electromagnetic waves on the body is to define the

absorbed energy in terms of specific absorption rate (SAR). SAR is defined by the FCC as being “a

measure of the amount of radio frequency energy absorbed by the body when using a mobile phone”

[21]. SAR is evaluated as


where σ is the electrical conductivity of the sample, E is the RMS electric field, and ρ is the sample

density; SAR has units of W/kg. SAR is the standard for determining safe levels of operation for cell

phones, with a value of 1.6 W/Kg being accepted as the uppermost safe limit for phones in the U.S.

While most companies utilize experimental data from special testing companies to determine the SAR

rating for their phone(s), some have begun to explore using the field of FEA (Finite Element Analysis)

simulation as a viable alternative. To date, the most advanced simulations still utilize one piece

"phantoms" to model the head [7,8,11], a phantom being defined by the OED “ A physical or computer-

generated model used to calculate radiation doses, evaluate or enhance imaging techniques, etc.”.

However, it is clear that this approximation can be improved upon considerably. Using a suite of ANSYS

products, including DesignModeler and HFSS, it is possible to create more realistic 3D models in order to

provide quick and efficient data for the debate over cell phone safety.

For the 3D multi-layered model used here, the human head is comprised of multiple tissue types:

Brain

Cerebellum and Cerebrum

CSF (Cerebro-Spinal Fluid)

Bone (Skull)

Skin

2. Problem Setup

For any FEA simulation, including one using ANSYS HFSS, one must define four main components of the

simulation:

1. boundary conditions,

2. excitations,

3. material properties, and

4. geometry (or geometries).

Each of these is discussed below in a separate subsection.

2.1 Boundary Conditions

For models that deal with radiation sources and electromagnetic wave propagation, HFSS requires the

use of a boundary condition, an artificial absorbing layer that restricts waves from exciting a user

defined region. The two most commonly used conditions for antenna problems are the Finite Element

Boundary Integral (FEBI) and the Perfectly Matched Layer (PML).

Initially, a box of air was placed around the entire geometry. Next, a "radiation boundary," the HFSS

term for a FEBI, was specified on each of the external faces of this air region. This set-up was tested

using a basic dipole antenna model in order to validate its efficiency. While this formulation provided


adequate absorption, some reflected waves were noted at the corners of the air region, prompting an

investigation of a better boundary condition.

A solution was found in the form of a PML boundary, a method in which the layer changes the

properties of incoming waves to decay exponentially in the surrounding material, resulting in little to no

reflection as the waves are still propagated to a PML material outside the region. Setting up a PML was a

trivial task as a result of the use of the PML Setup Wizard found within the HFSS interface, and in the

end a plethora of PML boundary boxes were placed on all the outside faces and edges of the indicated

region. These were much more effective in absorbing the radiation, showing no signs of wave-form

reflection. This desired quality combined with the ease of creation established the PML as the best

boundary condition to use.

Figure 2.1: Final PML/Airbox Boundaries Surrounding Final Head model

2.2 Excitations

In order to evaluate this problem, a radiation source, or in HFSS terms an "excitation," had to be

created. The development process can be separated into 3 distinct steps; step one revolved around

creating a virtual point emission source near the brain, the second dealt with creating a dipole antenna,

and the final attempted to create a modern cell phone antenna.

Initially, it seemed that using a single point as a center of the cell phone emissions would be an easy yet

realistic solution to portray the cell phone antenna. However, after multiple tests of the electromagnetic

emission patterns and magnitude, many discrepancies were found between the simulation results and

the desired patterns.


In response, time was spent learning about antenna design and space requirements before a simple

dipole tuned for 900 MHz was built using the HFSS Antenna Design Kit to mimic the antenna used in cell

phones. This, unfortunately, was a crude approximation of circa 1980's technology, an antenna as long

as the head and much larger than modern phones. Accordingly, this dipole was used to test out the

head geometry and boundary conditions, but its bulky nature and single band attributes left it

inadequate to be used as our final antenna.

After additional research on modern antenna designs and many failed attempts at creating slot,

monopole, and planar devices, a realistic, feasible and commonly used blueprint was found, the Planar

Inverted F Antenna (PIFA). This design allowed for the use of multi-band technology to improve accuracy

and produced electric field patterns in line with expected results. To achieve the most realism for our

design, a multi-band PIFA was used; in order to create such an antenna, studies concerning such multi-

band designs were consulted [5,13,18,20], until one was decided upon [18]. This final design was then

placed inside a box with dimensions corresponding to those of the iPhone 4S, one of the most wildly

popular phones currently on the market, and about the size of most smart phones currently in use.

Figure 2.2: Final multi-band PIFA design.

2.3 Material Properties

Material properties are required for each of the constituents of the overall model; these constituents

are listed in the first column of Table 1 below. Fortunately, an entire data bank of frequency-dependent

human tissue properties was compiled by the "Nello Carrara" Institute of Applied Physics [2], and this

plethora of information was used to create frequency-dependent curves for each tissue type for the

three material properties of primary interest: permittivity, conductivity, and loss tangent. The range of


these values across a frequency range of 0.824 GHz to 2.155 GHz for each material in the model is

tabulated in below in Table 1. These frequency-dependent material properties are graphed in Figures 1-

3 for each of the tissue types in the model.

Tissue Permittivity (F/m) Loss Tangent (dB) Conductivity (S/m)

Cerebrum 48.473-45.127 0.355-0.263 0.796-1.430

Cerebellum 49.968-45.353 0.536-0.352 1.229-1.916

CSF 68.811-66.683 0.755-0.400 2.383-3.199

Skull 15.338-14.004 0.268-0.266 0.197-0.460

Muscle 55.221-53.094 0.363-0.243 0.918-1.547

Fat 5.474-5.311 0.196-0.145 0.049-0.092

Skin 41.829-38.359 0.439-0.289 0.842-1.331

Bulk Skin 32.841-31.060 0.322-0.220 0.572-0.943

Table 2.1. Range of values of the primary material properties for each tissue type across the frequency range 0.824 - 2.155 GHz.

Figure 2.1: Frequency-dependent permittivity.

0

10

20

30

40

50

60

70

80

8.0E+08 1.0E+09 1.2E+09 1.4E+09 1.6E+09 1.8E+09 2.0E+09

Pe

rmit

tivi

ty (F

/m)

Frequency (Hz)

Permittivity (F/m) vs. Frequency (Hz)

Brain

Cerebellum

CSF

Skull

Muscle

Fat

Skin

Bulk Skin


Figure 2.2: Frequency-dependent loss tangent.

Figure 2.3: Frequency-dependent conductivity.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

8.0E+08 1.0E+09 1.2E+09 1.4E+09 1.6E+09 1.8E+09 2.0E+09

Loss

Tan

gen

t (d

B)

Frequency(Hz)

Loss Tangent (dB) vs. Frequency (Hz)

Brain

Cerebellum

CSF

Skull

Muscle

Fat

Skin

Bulk Skin

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

8.0E+08 1.0E+09 1.2E+09 1.4E+09 1.6E+09 1.8E+09 2.0E+09

Co

nd

uct

ivit

y (S

/m)

Frequency (Hz)

Conductivity (S/m) vs. Frequency (Hz)

Brain

Cerebellum

CSF

Skull

Muscle

Fat

Skin

Bulk Skin


In addition to the material properties for the tissues in the model, material properties are also required

for the cell phone itself. Here, the cell phone cover's material was taken to be polycarbonate, a form of

plastic commonly used in such applications. The antenna was assumed to be comprised of a

combination of tin and bronze, and a single volume-averaged value was used for each property of

interest.

3. Geometry and Mesh

A multi-step process was used to develop the final model. First, a lengthy literature survey was carried

out in order to understand the work that had already been done in the simulation aspect of cell phones.

A large model search was then performed and approximately three dozen models including skulls,

brains, and skin bodies that were edited for accuracy using ANSYS DesignModeler and SpaceClaim.

At first, an extremely basic model was created using a sphere and a virtual point excitation. This model

failed to achieve any plausible results and was refined significantly with the replacement of the virtual

point with a dipole and the sphere with a 6-layered sphere. These adjustments lead to the correct

radiation pattern and allowed for tests to be run on the material properties given to each layer. Two

problems were discovered with this model; firstly, it was a far cry from the accurate geometry desired

and, secondly, the antenna was bulky and not realistic for the problem posed.

The final model improved upon both of those concerns, replacing the spheres with an anatomically

accurate, 4-layer head model and the dipole with a modern multi-band PIFA encased within a plastic

phone body. Building such a complex multi-layered model required multiple steps to achieve both

realism in scale and shape. To begin, the brain model had to be resized to realistic proportions; the skull

was then translated and scaled to fit over the brain with the correct cranium thickness throughout. After

removing a brain cavity from the skull, the brain was copied and subsequently scaled outwards in

preparation for the next layer. By subtracting the brain from this slightly larger version, a thin layer

mimicking the shape of the brain was formed around the cerebrum, yielding the cerebro-spinal fluid

(CSF) layer. Originally, it was surmised that individual layers of fat, skin and muscle would be created to

cover the entire skull. Because of geometric limitations and varying thicknesses, this was scrapped in

favor of a bulk skin layer with each layer's material properties blended in volumetric proportions. After

some minor edits to the skin's overall shape, cavities were made within the skin to ensure that the

solver would work correctly when analyzing each layer. Figures 3.1 through 3.6 display each of the parts

individually and then a sliced version of the final model.


Figure 3.1: Skin Geometry Figure 3.2: Skull Geometry

Figure 3.3: CSF Geometry Figure 3.4: Brain Geometry

Figure 3.5: Cerebellum Geometry Figure 3.6: Sliced view of all bodies

This final model was highly detailed, satisfying the need for a realistic model. In Table 2 are shown the

number of elements in each of the layers of the final head model; all values were taken from mesh

statistics for the 2.1 GHz simulation, the most complex mesh of all the cases. This complexity is due to

the element size needing to be a certain fraction of the wavelength; therefore, as the wavelength gets


smaller, the element size decreases as well, leading to a larger number of elements being required to

cover the entire geometry.

Tissue Brain Cerebellum CSF Skull Skin

# of Tetrahedra 87,923 40,552 236,298 152,798 233,269

Table 3.1. Number of elements for each tissue-type region of the head model.

Geometry Cell Phone Air Box PML Boxes

# of Tetrahedra 59,865 409,419 54,533

Table 3.2. Number of elements for the other regions of the overall model.

Figures 3.7 through 3.11 show the final adaptive pass mesh from the 2.1 GHz case for each of the

geometries.

Figure 3.7: 2.1GHz Final Skin Mesh Figure 3.8: 2.1GHz Final Skull Mesh

Figure 3.9: 2.1GHz Final CSF Mesh Figure 3.10: 2.1GHz Final Brain Mesh


Figure 3.11: 2.1GHz Final Cerebellum Mesh Figure 3.12: 2.1GHz Final Antenna Mesh

Figure 3.13: 2.1GHz Final PML/Airbox Mesh

4. Results

The model was run at three different frequencies: 0.9 GHz, 1.7 GHz, and 2.1 GHz. Each of these

corresponds to the median value for each of the most common cellphone frequencies, GSM 900/1800

and UMTS 2100. Each frequency was calculated using at the maximum transmission power instead of

the average power under the IEEE guidelines [8]: the power levels were 2W, 1W, 0.5W, respectively. For

each of these frequencies, four contour plots were created:

Electric field across each plane,

Average SAR across each plane,

SAR for the brain region, and

SAR for the skin region.

While SAR plots could be created for each individual layer, the SAR for the brain and skin regions were

recognized to be the most important - the brain because of its critical functions for survival and the skin

because of its close proximity to the phone.

The 0.9GHz case yielded both the highest SAR values on the brain and skin, 0.145 and 4.259 W/kg

respectively. This is in part due to the high wattage, 2W, used at 0.9GHz and to the deeper penetration

achieved by the longer wavelength. Figures 1 through 5 are taken from the 0.9GHz case.


Figure 4.1: 0.9GHz Brain SAR with Brain only Figure 4.2: 0.9GHz Brian SAR with Full Body

Figure 4.3: 0.9GHz Electric Field with Brain only Figure 4.4: 0.9GHz Electric Field with Full Body

Figure 4.5: 0.9GHz Skin SAR with Full Body

The 1.8GHz case displayed much lower SAR values when compared to the 0.9GHz case and also

displayed a different absorption pattern. The pattern difference is caused by the shape of the antenna,

which utilizes different parts of the antenna for each frequency, leading to separate spots of high


absorption for each frequency. Figures 6 through 10 are taken from the 1.8GHz case.

Figure 4.6 : 1.8GHz Brain SAR with Brain only Figure 4.7: 1.8GHz Brian SAR with Full Body


Figure 4.10: 1.8GHz Skin SAR with Full Body

The 2.1 GHz case displayed the lowest SAR values of the three and an interesting radiation pattern,

mimicking parts from both the 0.9 and 1.8 GHz cases. This similarity is due to the antenna using a

separate branch for high frequencies. This branch, when activated also makes the lower frequency

branch next to it activate at a much lower strength. This creates the overall similarity while also keeping

a level of uniqueness from the others. Figures 11 through 15 are taken from the 2.1GHz case.


Figure 4.11: 2.1GHz Brain SAR with Brain only Figure 4.12: 2.1GHz Brian SAR with Full Body


Figure 4. 15: 2.1GHz Skin SAR with Full Body

The peak values for each of the cases for the Brain and Skin are displayed in table 4.1.

Measurement Location Brain Skin

0.9GHz 0.145 W/kg 4.259 W/kg

1.8GHz 0.018 W/kg 0.615 W/kg

2.1GHz 0.011 W/kg 0.506 W/kg

Table 4.1: Peak SAR values in Brain and Skin for simulated frequencies


The U.S. identifies the safety limit to be 1.6 W/kg while the EU uses 2.0 W/kg as the limit. These values

are the maximum SAR points when averaged over 1g of tissue for the U.S. limit and averaged over 10g

of tissue for the EU limit. For all of the designs considered here, the maximum SAR was found to be

located on the skin, a logical deduction because of its close proximity to the source; the overall

maximum value was 4.02 W/kg for the 0.9 GHz simulation. This was found to be higher than the SAR

limit set forth by both the U.S. and the EU. However, it is critical to note that while this is a realistic

simulation, without perfect models for the head - and all its concomitant layers - as well as the

cellphone, this result can only be used as a weak indicator. In addition, instead of using the actual inner

working of a cellphone, a singular arbitrary antenna was created, making our results only relevant to

that antenna and setup. For this reason, our results cannot be applied universally to all phones, as each

separate geometry, antenna and cover material could have dramatic effects on the SAR values.

However, if certain improvements were completed, more realistic and more useful results could be

obtained. Nevertheless, this is another step on the path toward the integration of FEA simulations as a

reliable and accurate tool for biological simulations.

5. Summary and Conclusion(s)

5.1 Improvements

Although this model is significantly realistic and detailed, it still lacks the polish to be considered a final,

end-all model. Instead of using 3d models acquired from a variety of sources, it would be much more

accurate if CT scans could be converted to 3d models in order to eliminate some small measurement

errors. In addition, if the field of biological electromagnetic simulation is to be expanded, a standardized

table of frequency-dependent material properties must be compiled. While such tables exist, they differ

slightly from study to study, further complicating the design process of such models. Finally, the use of

an arbitrary phone model, instead of a detailed, singular phone design means that such a result can only

be used as a generalized validation of the process, rather than real life application of such results. If such

a head model was developed, 3d phone designs provided by the actual producers of said products

would allow for pinpoint solutions for each phone design. These accurate solutions for each phone

would be in line with the original idea, a head model that could be quickly yet realistically solved in

order to help settle the debate on cellphone safety.

5.2 Future Work

Some areas of interest are obviously the refinement and polishing of the model geometry and packaging

such a model to be used commercially. If such a model could be designed to meet IEEE standards and

material properties, the packaging of this with a phone model import system could create a

commercially viable alternative to the expensive manual results obtained by experiment. In addition, the

use of simulation technology brings with it intrinsic benefits, such as testing before reaching the

prototype stage, saving thousands of dollars and hours on product creation and design by receiving

feedback on the design of phones stages in advance of current technology. Such ideas are 100 percent


plausible with current software, computing power and knowledge, providing a more efficient pathway

for analyzing such problems.

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