COMSOL 6.4 - Specific Absorption Rate (SAR) in the Human Brain

Specific Absorption Rate (SAR) in the Human Brain

Scientists use the SAR (specific absorption rate) to determine the amount of radiation that human tissue absorbs. This measurement is especially important for mobile telephones, which radiate close to the brain. The model studies how a human head absorbs a radiated wave from an antenna and the temperature increase that the absorbed radiation causes.

This example requires the RF Module and the Heat Transfer Module.

The increasing use of wireless equipment has also increased the amount of radiation energy to which human bodies are exposed, and it is particularly important to avoid radiation into the brain. Experts continue to debate how dangerous this radiation might be. Almost everyone agrees, however, that it is important to minimize exposure to radiation. A common property that measures absorbed energy is the SAR value, calculated as

where σ is the conductivity of human brain tissue, ρ is the density, and |E| is the norm of the electric field (RMS). The SAR value is an average over a region of either 10 g or 1 g of brain tissue, depending on national rules. This example does not calculate the average value and so it refers to the local SAR value. The maximum local SAR value is always higher than the maximum SAR value.

Model Definition

The human head geometry is the same geometry (SAM Phantom) provided by IEEE, IEC, and CENELEC from their standard specification of SAR value measurements. The original geometry was imported into COMSOL Multiphysics after minor adjustments of the original geometry.

In addition, the model samples some material parameters with a volumetric interpolation function that estimates the variation of tissue type inside the head. The source data for this function comes directly from a file named sar_in_human_head_interp.txt. That data file was created from a magnetic-resonance image (MRI) of a human head; these images contain 109 slices, each with 256-by-256 voxels (Ref. 2). The use of the variation of the data in this file on the tissue material parameters has no scientific background, and this example simply implements it to illustrate a variation in conductivity, permittivity (Figure 1), and perfusion rate as a function of the position inside the head. The model reduces the resolution of the volumetric data to 55-by-50-by-50 interpolation points, which matches the mesh-element density inside the head. Prior to generating the data file, the modeler in this case scaled, translated, and rotated the 3D MRI data to match the form of the imported head geometry in COMSOL Multiphysics.

Figure 1: This plot shows how the average relative permittivity varies inside the head. The permittivity is calculated from the imported MRI image data.

Wave Propagation

The radiation comes from a patch antenna placed on the left side of the head. The patch antenna is excited by a lumped port. To absorb the scattered radiation, the model makes use of a PML; see the section Perfectly Matched Layer in the COMSOL Multiphysics Reference Manual for details. The model solves the vector-Helmholtz equation everywhere in the domain for a certain frequency

where μr is the relative permeability, k0 is the free-space wave vector, and εr is the permittivity.

For wave-propagation problems such as this one, you must limit the mesh size according to the problem’s minimum wavelength. Typically you need about five elements per wavelength to properly resolve the wave.

This example takes material properties for the human brain from a presentation by G. Schmid (Ref. 1). The following table reviews some important frequency-dependent properties in this publication. The interpolation function samples these values to create a realistic variation.


Parameter	Frequency	Value	description
σ	835 MHz	1.15 S/m	Conductivity
εr	835 MHz	58.13	Relative permittivity

Heating of the Head

The bioheat equation models the heating of the head with a heating loss due to the blood flow. This heat loss depends on the heat capacity and density of the blood, and on the blood perfusion rate. The perfusion rate varies significantly in different parts of the human body, and the table below presents the values used here.


Part	perfusion rate
Brain	2·10-3 (ml/s)/ml
Bone	3·10-4 (ml/s)/ml
Skin	3·10-4 (ml/s)/ml

The same interpolation function used for the electric parameters also models the difference in perfusion rate between the brain tissue inside the head and the outer parts of skin and bone. Note again that the use of the interpolation function does not have any physical relevance; it is just to show a realistic effect of a varying material parameter.

Figure 2: Log-scale slice plot of the local SAR value.

Results and Discussion

The model studies the local SAR value in the head using the formula described earlier for the frequency 835 MHz. The SAR value is highest close to the surface of the head facing the incident wave. The differences in electrical properties become visible if you plot the local SAR value on a log scale (Figure 1).

The bioheat equation produces a similar plot for the heating of the head, which is highest closest to the antenna. The maximum temperature increase (from 37°C) is about 0.15°C, and drops rapidly inside the head.

Figure 3: The local increase in temperature at the surface has the maximum right beneath the antenna.

References

1. G. Schmid, G. Neubauer, and P.R. Mazal, “Dielectric properties of human brain tissue measured less than 10 h postmortem at frequencies from 800 to 2450 MHz,” Bioelectromagnetics, vol. 24, pp 423–430, 2003.

2. M. Levoy, MRI data originally from Univ. of North Carolina (downloaded from the Stanford volume data archive at graphics.stanford.edu/data/voldata/).

RF_Module/Microwave_Heating/sar_in_human_head

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > .

Click .

In the text field, type dT.

In the tree, select > .

Click .

Wait with adding the study until the multiphysics coupling has been added. Then the study sequence will be automatically configured for the right interfaces.

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
epsilonr_pcb	5.23	5.23	Permittivity for the patch antenna board
epsilonr0_brain	58.13	58.13	Permittivity for the brain tissue
sigma0_brain	1.15[S/m]	1.15 S/m	Conductivity for the brain tissue
rho_brain	1.03e3[kg/m^3]	1030 kg/m³	Density of brain tissue
sdamping	2e-4	2E-4	Sampling parameter
edamping	4e-4	4E-4	Sampling parameter
soffset	-1.0[S/m]	-1 S/m	Sampling parameter
eoffset	-50	-50	Sampling parameter
c_blood	3639[J/(kg*K)]	3639 J/(kg·K)	Heat capacity of blood
rho_blood	1000[kg/m^3]	1000 kg/m³	Density of blood
odamping	1.08e-6[1/s]	1.08E-6 1/s	Sampling parameter
ooffset	7.8e-4[1/s]	7.8E-4 1/s	Sampling parameter
f0	835[MHz]	8.35E8 Hz	Frequency

Geometry 1

The head geometry has been created outside COMSOL Multiphysics, so you import it from an MPHBIN-file. Then create the surrounding domains of PML, air, and antenna manually.

Import 1 (imp1)

In the toolbar, click

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file sar_in_human_head.mphbin.

Click

Block 1 (blk1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 0.004.

In the text field, type 0.08.

Locate the section. From the list, choose .

In the text field, type 0.1.

In the text field, type 0.05.

Click

Work Plane 1 (wp1)

In the toolbar, click

In the window for , locate the section.

From the list, choose .

In the text field, type 0.098.

Click

Work Plane 1 (wp1) > Square 1 (sq1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 0.06.

Locate the section. From the list, choose .

In the text field, type 0.05.

Click

Work Plane 1 (wp1) > Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 0.005.

In the text field, type 0.01.

Locate the section. From the list, choose .

In the text field, type 0.015.

Click

Work Plane 1 (wp1) > Union 1 (uni1)

In the toolbar, click

and choose .

Click in the window and then press Ctrl+A to select both objects.

In the window for , locate the section.

Clear the checkbox.

In the toolbar, click

Work Plane 2 (wp2)

In the window, right-click and choose .

In the window for , locate the section.

In the text field, type 0.01.

Click

Work Plane 2 (wp2) > Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

From the list, choose .

In the text field, type 0.1.

Locate the section. In the text field, type 0.004.

In the text field, type 0.005.

Click

Form Union (fin)

In the toolbar, click

You have now created the patch antenna close to the head. Continue with the surrounding air and the PML regions.

In the window, under > click .

Sphere 1 (sph1)

In the window, right-click and choose .

In the window for , locate the section.

In the text field, type 0.35.

Click to expand the section. In the table, enter the following settings:


Layer name	Thickness (m)
Layer 1	0.1

Click

Click the

button in the toolbar.

Click the

button in the toolbar.

Form Union (fin)

In the window, click .

In the window for , locate the section.

From the list, choose .

In the text field, type 1E-5.

This completes the model geometry.

Definitions

To get a better view, you can use the mouse to rotate the plot. Furthermore, by assigning the resulting settings to a View node, you can easily return to the same view later.

In the window, under right-click and choose .

In the window for , click to expand the section.

Select the checkbox.

Rotate the geometry to get a good view.

The view can also be set manually.

Camera

In the window, expand the node, then click .

In the window for , locate the section.

In the text field, type 3.

Locate the section. In the text field, type 4.62.

In the text field, type -8.28.

In the text field, type 5.4.

Locate the section. In the text field, type 4.2.

In the text field, type -7.5.

In the text field, type 4.9.

Locate the section. In the text field, type -0.25.

In the text field, type 0.425.

In the text field, type 0.86.

Locate the section. In the text field, type 0.06.

In the text field, type -0.04.

In the text field, type 0.05.

Locate the section. In the text field, type 0.26.

In the text field, type 0.19.

Click

In the window, click .

In the window for , locate the section.

Select the checkbox.

This action locks the camera settings you just applied for this View node. Suppress some of the boundaries to simplify the domain selection.

Hide for Physics 1

Right-click and choose .

In the window for , click

Select Domains 1, 2, 5, 7, and 8 only.

To return to this view after rotating, translating, or zooming the geometry in the window, click the button in the toolbar.

Click the

button in the toolbar.

Create the selections to simplify the model specification.

PML

In the toolbar, click

In the window for , type PML in the text field.

Click the button in the toolbar.

Select Domains 1–4 and 7–10 only.

Head

In the toolbar, click

In the window for , type Head in the text field.

Click the button in the toolbar.

Select Domain 6 only.

PCB

In the toolbar, click

In the window for , type PCB in the text field.

Select Domain 11 only.

Interpolation 1 (int1)

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Click

Browse to the model’s Application Libraries folder and double-click the file sar_in_human_head_interp.txt.

Click

Find the subsection. In the table, enter the following settings:


Function name	Position in file
fbrain	1

Variables 1

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Locate the section. In the table, enter the following settings:


Name	Expression	Unit	Description
epsilonr_brain	epsilonr0_brain(1+fbrain(x[1/m],y[1/m],z[1/m])edamping)+eoffset		Relative permittivity of the brain
sigma_brain	sigma0_brain(1+fbrain(x[1/m],y[1/m],z[1/m])sdamping)+soffset	S/m	Conductivity of the brain
omega_head	odamping*fbrain(x[1/m],y[1/m],z[1/m])+ooffset	1/s	Blood perfusion rate

Bioheat Transfer (ht)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Materials

Material 1 (mat1)

In the window, under right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	epsilonr_pcb	1	Basic
Relative permeability	mur_iso ; murii = mur_iso, murij = 0	1	1	Basic
Electric conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	0	S/m	Basic

Material 2 (mat2)

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	0.5	W/(m·K)	Basic
Density	rho	1050	kg/m³	Basic
Heat capacity at constant pressure	Cp	3700	J/(kg·K)	Basic
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	epsilonr_brain	1	Basic
Relative permeability	mur_iso ; murii = mur_iso, murij = 0	1	1	Basic
Electric conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	sigma_brain	S/m	Basic