COMSOL 6.4 - Microwave Heating of a Cancer Tumor

Electromagnetic heating appears in a wide range of engineering problems and is ideally suited for modeling in COMSOL Multiphysics because of its multiphysics capabilities. This example comes from the area of hyperthermic oncology and it models the electromagnetic field coupled to the bioheat equation. The modeling issues and techniques are generally applicable to any problem involving electromagnetic heating.

In hyperthermic oncology, cancer is treated by applying localized heating to the tumor tissue, often in combination with chemotherapy or radiotherapy. Some of the challenges associated with the selective heating of deep-seated tumors without damaging surrounding tissue are:

•

Control of heating power and spatial distribution

•

Design and placement of temperature sensors

Among possible heating techniques, RF and microwave heating have attracted much attention from clinical researchers. Microwave coagulation therapy is one such technique where a thin microwave antenna is inserted into the tumor. The microwaves heat up the tumor, producing a coagulated region where the cancer cells are killed.

This model computes the temperature field, the radiation field, and the specific absorption rate (SAR) — defined as the ratio of absorbed heat power and tissue density — in liver tissue when using a thin coaxial slot antenna for microwave coagulation therapy. It closely follows the analysis found in Ref. 1. It computes the temperature distribution in the tissue using the bioheat equation.

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

Model Definition

Figure 1 shows the antenna geometry. It consists of a thin coaxial cable with a ring-shaped slot measuring 1 mm cut on the outer conductor 5 mm from the short-circuited tip. For hygienic purposes, the antenna is enclosed in a sleeve (catheter) made of PTFE (polytetrafluoroethylene). The following tables give the relevant geometrical dimensions and material data. The antenna operates at 2.45 GHz, a frequency widely used in microwave coagulation therapy.

Table 1: Dimensions of the coaxial slot antenna.
Property	Value
Diameter of the central conductor	0.29 mm
Inner diameter of the outer conductor	0.94 mm
Outer diameter of the outer conductor	1.19 mm
Diameter of catheter	1.79 mm

Table 2: Material Properties.
Property	Inner dielectric of the coaxial cable	Catheter	Liver tissue
Relative permittivity	2.03	2.60	43.03
Conductivity			1.69 S/m

Figure 1: Antenna geometry for microwave coagulation therapy. A coaxial cable with a ring-shaped slot cut on the outer conductor is short-circuited at the tip. A plastic catheter surrounds the antenna.

The model takes advantage of the problem’s rotational symmetry, which allows modeling in 2D using cylindrical coordinates as indicated in Figure 2. When modeling in 2D, you can select a fine mesh and achieve excellent accuracy. The model uses a frequency-domain problem formulation with the complex-valued azimuthal component of the magnetic field as the unknown.

Figure 2: The computational domain appears as a rectangle in the rz-plane.

The radial and axial extent of the computational domain is in reality larger than indicated in Figure 2. This problem does not model the interior of the metallic conductors, and it models metallic parts using boundary conditions, setting the tangential component of the electric field to zero.

Domain and Boundary Equations — Electromagnetics

An electromagnetic wave propagating in a coaxial cable is characterized by transverse electromagnetic fields (TEM). Assuming time-harmonic fields with complex amplitudes containing the phase information, the appropriate equations are

where z is the direction of propagation, and r, φ, and z are cylindrical coordinates centered on the axis of the coaxial cable. Pav is the time-averaged power flow in the cable, Z is the wave impedance in the dielectric of the cable, while rinner and router are the dielectric’s inner and outer radii, respectively. Further, ω denotes the angular frequency. The propagation constant, k, relates to the wavelength in the medium, λ, as

In the tissue, the electric field also has a finite axial component whereas the magnetic field is purely in the azimuthal direction. Thus, you can model the antenna using an axisymmetric transverse magnetic (TM) formulation. The wave equation then becomes scalar in Hφ:

The boundary conditions for the metallic surfaces are

The feed point is modeled using a port boundary condition with a power level set to 10 W. This is essentially a first-order low-reflecting boundary condition with an input field Hφ0:

where

for an input power of Pav deduced from the time-average power flow.

The antenna radiates into the tissue where a damped wave propagates. Because you can discretize only a finite region, you must truncate the geometry some distance from the antenna using a similar absorbing boundary condition without excitation. Apply this boundary condition to all exterior boundaries.

Domain and Boundary Equations — Heat Transfer

The bioheat equation describes the time-dependent heat transfer problem as

where k is the liver’s thermal conductivity (W/(m·K)), ρb represents the blood density (kg/m3), Cb is the blood’s specific heat capacity (J/(kg·K)), ωb denotes the blood perfusion rate (1/s), and Tb is the arterial blood temperature (K). Further, Qmet is the heat source from metabolism, and Qext is an external heat source, both measured in W/m3.

The initial temperature equals Tb in all domains.

This model neglects the heat source from metabolism. The external heat source is equal to the resistive heat generated by the electromagnetic field:

The model assumes that the blood perfusion rate is ωb = 0.0036 s−1, and that the blood enters the liver at the body temperature Tb = 37°C and is heated to a temperature, T. The blood’s specific heat capacity is Cb = 3639 J/(kg·K).

For a more realistic model, you might consider letting ωb be a function of the temperature. At least for external body parts such as hands and feet, it is evident that a temperature increase results in an increased blood flow.

This example models the heat transfer problem only in the liver domain. Where this domain is truncated, it uses insulation, that is

In addition to the heat transfer equation, this model computes the tissue damage integral. This gives an idea about the degree of tissue injury α during the process, based on the Arrhenius equation

where A is the frequency factor (s−1) and ΔE is the activation energy for irreversible damage reaction (J/mol). These two parameters are dependent on the type of tissue. The fraction of necrotic tissue, θd, is then expressed by

Results and Discussion

Figure 3 shows the resulting steady-state temperature distribution in the liver tissue for an input microwave power of 10 W. The temperature is highest near the antenna. It then decreases with distance from the antenna and reaches 37°C closer to the outer boundaries of the computational domain. The perfusion of relatively cold blood seems to limit the extent of the area that is heated.

Figure 3: Temperature in the liver tissue.

Figure 4 shows the distribution of the microwave heat source. Clearly the temperature field follows the heat source distribution quite well. That is, near the antenna the heat source is strong, which leads to high temperatures, while far from the antenna, the heat source is weaker and the blood manages to keep the tissue at normal body temperature.

Figure 4: The computed microwave heat-source density takes on its highest values near the tip and the slot. The scale is cut off at 1 W/cm3.

Figure 5 plots the specific absorption rate (SAR) along a line parallel to the antenna and at a distance of 2.5 mm from the antenna axis. The results are in good agreement with those found in Ref. 1.

Figure 5: SAR in W/kg along a line parallel to the antenna and at a distance 2.5 mm from the antenna axis. The tip of the antenna is located at 70 mm, and the slot is at 65 mm.

You can visualize the fraction of necrotic tissue in the surface plot of Figure 6.

Figure 6: Fraction of necrotic tissue.

Figure 7 shows the fraction of necrotic tissue at four different point of the domain. Observe that necrosis happens faster near the antenna.

Figure 7: Fraction of necrotic tissue at four points of the domain.

Reference

1. K. Saito, T. Taniguchi, H. Yoshimura, and K. Ito, “Estimation of SAR Distribution of a Tip-Split Array Applicator for Microwave Coagulation Therapy Using the Finite Element Method,” IEICE Trans. Electronics, vol. E84-C, no. 7, pp. 948–954, 2001.

Heat_Transfer_Module/Medical_Technology/microwave_cancer_therapy

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > .

Click .

In the tree, select > .

Click .

Do not add the study right now, as it will be easier to define it once the multiphysics coupling has been added.

Click

Multiphysics

Electromagnetic Heating 1 (emh1)

In the toolbar, click

and choose > .

This brings the heat created by the electromagnetic waves to the heat transfer simulation.

Now add a study sequence that first adds a study for the electromagnetic part and then adds a study for the heat transfer part.

Add Study

In the toolbar, click

to open the window.

Go to the window.

Find the subsection. In the tree, select > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Geometry 1

The geometry sequence for the model is available in a file. If you want to create it from scratch by yourself, you can follow the instructions in the Geometry Modeling Instructions section. Otherwise, insert the geometry sequence as follows:

In the toolbar, click and choose .

Browse to the model’s Application Libraries folder and double-click the file microwave_cancer_therapy_geom_sequence.mph.

In the toolbar, click

Click the

button in the toolbar.

In the window, under click .

You should now see the geometry shown above.

Global Definitions

Parameters 1

The relevant material properties and other model data are provided in a text file.

In the window, under click .

In the window for , locate the section.

Click

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

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select > .

Click the button in the window toolbar.

Materials

Liver (human) (mat1)

Select Domain 1 only.

In the window for , 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	eps_liver	1	Basic
Relative permeability	mur_iso ; murii = mur_iso, murij = 0	1	1	Basic
Electric conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	sigma_liver	S/m	Basic

The remaining materials take part only in the RF simulation, making any definitions of their thermal properties redundant.

Catheter

In the toolbar, click

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

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	eps_cat	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]	S/m	Basic

Dielectric

In the toolbar, click

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

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	eps_diel	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]	S/m	Basic