Modeling a Conical Dielectric Probe for Skin Cancer Diagnosis

The response of a millimeter wave with frequencies of 35 GHz and 95 GHz is known to be very sensitive to water content. This model utilizes a low-power 35 GHz Ka-band millimeter wave and its reflectivity to moisture for non-invasive cancer diagnosis. Since skin tumors contain more moisture than healthy skin, it leads to stronger reflections on this frequency band. Hence the probe detects abnormalities in terms of S-parameters at the tumor locations. A circular waveguide at the dominant mode and a conically tapered dielectric probe are quickly analyzed, along with the probe’s radiation characteristics, using a 2D axisymmetric model. Temperature variation of the skin and the fraction of necrotic tissue analysis are also performed as well.

Figure 1: 3D visualization of the 2D axisymmetric model. The probe consists of a circular waveguide and a tapered dielectric rod.

Model Definition

The model consists of a metallic circular waveguide, a tapered PTFE dielectric rod, and a phantom of skin chunk shown in Figure 1. The entire model is enclosed by an air domain which is truncated at its outermost shell with perfectly matched layers (PML) to absorb any radiation directly from the rod or reflected from the skin phantom. One end of the waveguide is terminated with a circular port and excited using the dominant TE1m mode, where m is the azimuthal mode number of this 2D axisymmetric model defined as 1 in the Electromagnetic Waves, Frequency Domain physics interface settings. The other end is connected to a tapered conical PTFE dielectric (εr = 2.1) rod. The shape of the rod is symmetrically tapered so the radius is increasing from the inside to the outside of the waveguide, then it is decreasing gradually for the impedance matching between the waveguide and the air domain. There is a ring structure in the middle to support the rod on the rim of the waveguide. The tip of the rod is touching the skin phantom.

The conductivity of the metallic waveguide is assumed to be high enough to neglect any loss and is modeled as perfect electric conductor (PEC). With the given radius of the waveguide and excited TE mode, the cutoff frequency is around 29.3 GHz, which is calculated by

where c0 is the speed of light, p′nm are the roots of the derivative of the Bessel functions Jn(x), m and n are the mode indices, and a is the radius of the waveguide. The value of p′11 is approximately 1.841. The operating frequency of the probe, 35 GHz, is higher than the waveguide cutoff frequency. The excited wave is propagating along the waveguide.

The circular port boundary condition is placed on the interior boundary where the reflection and transmission characteristics are computed automatically in terms of S-parameters. The interior port boundary with PEC backing for one-way excitation requires the slit condition. The port orientation is specified to define the inward direction for the S-parameter calculation.

First, the electromagnetic properties of the model are analyzed without a phantom to check the design validity of the waveguide and dielectric rod. Then, complexity is added, first with a healthy phantom, then a phantom with a skin tumor. See Table 1.

Table 1: Material property variation.
Property	Probe only	with a healthy phantom	tumor added
Relative permittivity (imaginary part)	0	10	15
Relative permittivity (real part)	1	5	8

Figure 2: Zoomed 3D visualization of the skin tumor area. The entire probe model is simulated in a 2D axisymmetric space dimension. The measured S-parameters vary due to the different moisture content in each skin phantom.

Though the waveguide excited by low power is expected to be harmless, its effect on necrotic tissue is reviewed by studying Bioheat Transfer as well as temperature, over a 10 minute period.

Results and Discussion

Figure 3 shows the real part of the electric field Er excited from one end of the waveguide without a phantom. Its radiation pattern is visualized in the Modeling Instructions section.

Figure 3: Wave propagation from the dielectric rod plotted with the Er component of the E-field (probe-only case without a phantom).

Temperature change on the surface of the phantom with the tumor is plotted in Figure 4. Since the input power from the waveguide port is low, 1 mW, the temperature change is within 0.06 K even after 10 minutes of millimeter wave exposure. The color difference shows the relatively hotter spot where the temperature is still very close to the initial temperature, 34°C. Though the temperature analysis for the healthy phantom case is not included, it is easily expected that the temperature variation is less than the case with the tumor because the resistive loss should be lower due to the smaller imaginary part of the permittivity of the healthy skin. So the visualized temperature profile is the worst-case scenario of temperature increase among all three cases. The damaged tissue ratio is visualized in Figure 5. It shows that the effect of the low-power millimeter wave is negligible.

The computed S-parameters indicate more reflection when touching the skin with the tumor due to its higher moisture content, and they are approximately summarized below:

Table 2: S-parameter response of the probe.
	Probe only	with a healthy phantom	tumor added
S11	-29.4 dB	-9.83 dB	-8.97 dB

Figure 4: The temperature after 10 minutes. The variation compared to the initial temperature is negligible in the case where the tumor is added at the center of the center top of skin surface.

The modeling instructions show how to access the data plotted in Figure 6 which is not the dependent variable of the Electromagnetic Waves, Frequency Domain, by tweaking the solver settings.

Figure 5: Fraction of necrotic (damaged) tissue is extremely low even after 10 minutes of millimeter wave exposure in the case where the tumor is added in contact with the probe, at the surface of the skin.

Figure 6: The resistive losses in the case where the tumor is added in contact with the probe, at the surface of the skin.

Notes About the COMSOL Implementation

The electromagnetic material properties of skin and tumor at 35 GHz are approximated to show the feasibility of the S-parameter method by detecting the areas with higher moisture content. For any further research, extracting accurate data in the given frequency range is recommended.

Heat_Transfer_Module/Medical_Technology/conical_dielectric_probe

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

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
r1	0.003[m]	0.003 m	Waveguide radius
fc	1.841*c_const/2/pi/r1	2.928E10 1/s	Cutoff frequency
f0	35[GHz]	3.5E10 Hz	Frequency
lda0	c_const/f0	0.0085655 m	Wavelength, free space
l_probe	12.8[mm]	0.0128 m	Tapered probe length
w1_probe	3[mm]	0.003 m	Tapered probe width1
w2_probe	0.58[mm]	5.8E-4 m	Tapered probe width2
T0	34[degC]	307.15 K	Initial skin temperature

Study 1

Step 1: Frequency Domain

In the window, under click .

In the window for , locate the section.

In the text field, type f0.

Geometry 1

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In the window for , locate the section.

From the list, choose .

Circle 1 (c1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 75.

In the text field, type 180.

Locate the section. In the text field, type 270.

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


Layer name	Thickness (mm)
Layer 1	lda0

Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type r1.

In the text field, type 50.

Rectangle 2 (r2)

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In the window for , locate the section.

In the text field, type 50.

Locate the section. In the text field, type 3.

Polygon 1 (pol1)

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In the window for , locate the section.

From the list, choose .

In the text field, type 0 w2_probe w2_probe w1_probe w1_probe 0 0 0.

In the text field, type -l_probe -l_probe -l_probe 0 0 0 0 -l_probe.

Click

Mirror 1 (mir1)

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and choose .

Select the object only.

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Select the check box.

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In the text field, type 1.

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Rectangle 3 (r3)

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In the text field, type 4.

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Fillet 1 (fil1)

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On the object , select Point 2 only.

It might be easier to select the correct point by using the window. To open this window, in the toolbar click and choose . (If you are running the cross-platform desktop, you find in the main menu.)

In the window for , locate the section.

In the text field, type 0.5.

Rectangle 4 (r4)

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In the window for , locate the section.

In the text field, type 35.

In the text field, type 32.2.

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Fillet 2 (fil2)

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On the object , select Points 2 and 3 only.

In the window for , locate the section.

In the text field, type 10.

Rectangle 5 (r5)

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In the text field, type 6.5.

In the text field, type 0.7.

Locate the section. In the text field, type -13.5.

Click

Definitions

Perfectly Matched Layer 1 (pml1)

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Select Domains 1 and 9 only.

Add Material

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to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Materials

PTFE

In the toolbar, click

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

Select Domains 5–7 and 10 only.

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	2.1	1	Basic
Relative permeability	mur_iso ; murii = mur_iso, murij = 0	1	1	Basic
Electrical conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	0	S/m	Basic

Electromagnetic Waves, Frequency Domain (emw)

In the window, under click .

In the window for , locate the section.

In the m text field, type 1.

Perfect Electric Conductor 2

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and choose .

Select Boundaries 23–25 and 27 only.

Port 1

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and choose .

Select Boundary 16 only.

In the window for , locate the section.

From the list, choose .

In the Pin text field, type 1[mW].

The input power is 0 dBm.

Select the check box.

Click .

Far-Field Domain 1

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and choose .

Mesh 1

In the window, under right-click and choose .

Study 1

Step 1: Frequency Domain

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Results

Surface

In the window, expand the node, then click .

In the window for , locate the section.

In the text field, type emw.Er.

Locate the section. From the list, choose .

In the toolbar, click

See Figure 3 for the plot of the real part of Er, showing wave propagation from the input port to the air domain via the tapered dielectric probe.

Radiation Pattern, Polar

In the window, expand the node, then click .

In the window for , type Radiation Pattern, Polar in the text field.

Radiation Pattern 1

In the window, click .

In the window for , locate the section.

Find the subsection. In the text field, type 1.

In the text field, type 0.

Find the subsection. In the text field, type 1.

In the text field, type 0.

In the toolbar, click

The Far-field pattern on the yz-plane shows the radiation from the tapered probe toward the bottom side.

Radiation Pattern, 3D

In the window, expand the node, then click .

In the window for , type Radiation Pattern, 3D in the text field.

The 3D far-field pattern is directed along the z-axis.

S-parameter (emw)

In the window, expand the node, then click .

In the window for , click

The evaluated S-parameter is the input matching property of the circular waveguide without a human body phantom when the dominant mode is excited.

Electromagnetic Waves, Frequency Domain (emw)

Add another Wave Equation which describe the human body phantom in term of dielectric loss using a complex permittivity.

Wave Equation, Electric 2

In the toolbar, click

and choose .

Select Domains 3 and 4 only.

In the window for , locate the section.

From the list, choose .

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Materials

Skin (mat3)

Select Domains 3 and 4 only.

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Relative permittivity (imaginary part)	epsilonBis_iso ; epsilonBisii = epsilonBis_iso, epsilonBisij = 0	10	1	Dielectric losses
Relative permittivity (real part)	epsilonPrim_iso ; epsilonPrimii = epsilonPrim_iso, epsilonPrimij = 0	5	1	Dielectric losses
Relative permeability	mur_iso ; murii = mur_iso, murij = 0	1	1	Basic
Electrical conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	0	S/m	Basic

In the toolbar, click

Results

S-parameter (emw)

Evaluate the S-parameter assuming the probe is touching a phantom representing a healthy body.

In the window, under click .

In the window for , click

Radiation Pattern, 3D

Click the

button in the toolbar.

Due to the body, the radiation is reflected back.

Materials

Skin (mat3)

Now, add a tip of tumor skin.

Skin Tumor

In the window, under right-click and choose .

In the window for , type Skin Tumor in the text field.

Locate the section. Click

Select Domain 4 only.

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


Property	Variable	Value	Unit	Property group
Relative permittivity (imaginary part)	epsilonBis_iso ; epsilonBisii = epsilonBis_iso, epsilonBisij = 0	15	1	Dielectric losses
Relative permittivity (real part)	epsilonPrim_iso ; epsilonPrimii = epsilonPrim_iso, epsilonPrimij = 0	8	1	Dielectric losses