Modeling of interstitial microwave hyperthermia for hepatic tumors using floating sleeve antenna

Microwave hyperthermia is a treatment modality that uses microwaves to destroy cancer cells by increasing their temperature to 41–45 °C. This study aims to design, model, and simulate a microwave sleeve antenna for hepatic (liver) hyperthermia. A floating sleeve antenna with 0.5 w input power was designed to resonate at 2.45 GHz. The antenna was tested in six different 3D liver models. The models were varied from a very simple model without a tumor and blood vessels to complex models that contain realistic tumors and blood vessels. To test the capability of the proposed antenna for heating the interstitial tumors, the size, shape, and location of the tumor were changed. The specific absorption rate (SAR) and temperature were calculated for each model. The tumors’ temperature was elevated between 43 and 45 °C, while the temperature of the surrounding tissues was below 41 °C. The Specific Absorption Rate (SAR) was between 29 and 30 W/kg in the tumors and below 24 W/Kg in the surrounding tissues. The return loss of the antenna varied from − 45 to − 25 dB for the six models. The antenna could heat hepatic tumors with different sizes and locations. The heating process was performed in a short time by using a very low input power compared to all previous studies.


Introduction
According to the American Cancer Society, liver (Hepatic) cancer had an estimated 42,230 new cases in 2021, and about 30,230 cases are expected to die of this cancer. Approximately 80% of these cases occur in developing countries [1]. Currently, surgical resection is the standard treatment for liver cancer since it provides survival benefits. Patients refuse chemotherapy and radiotherapy because of their side effects [2]. Only 5-15% of hepatic tumors could undergo such curative surgery [2] because of: multifocal disease, tumor size, and location around key blood vessels. For these reasons, there is an emergent need for interstitial techniques to treat hepatic tumors, such as microwave hyperthermia (MWH).
Microwave hyperthermia involves inserting an applicator into the tumor to elevate its temperature to 41-45 °C without damaging the surrounding normal tissues [3,4]. This microwave-generated heat could shrink or destroy tumors [2]. The simple devices to perform interstitial microwave hyperthermia comprise a microwave generator, a microwave applicator/antenna, and a flexible coaxial cable (to connect the antenna to the microwave generator) [4]. Using these thin microwave hyperthermia devices has many advantages: avoiding the possible damage of surrounding tissues and reducing the procedural risks [5].
Many studies designed antennas to perform hepatic microwave hyperthermia [6][7][8][9] and microwave ablation [5,[10][11][12][13]. However, the modeling procedure involves simple structures for the liver and tumor. This leads to less localization of the microwave pattern in the tumor's exact location because anatomical structures and blood circulation directly influence temperature distribution Clinical applications of microwave hyperthermia consider whether the tumor is superficial or interstitial [14]; as such, taking into account tumor position and size helps for the accurate evaluation of the designed antenna. This study aims to design a floating sleeve antenna capable of performing microwave

Antenna design
The designed antenna was 3.4 mm in diameter from a 50 Ω coaxial cable with inner and outer conductors made of copper. Teflon was used as: a dielectric material between the conductors; a catheter for easy antenna insertion and removal. The choice of antenna geometry parameters, slot spacing, and floating sleeve length is mainly based on the effective wavelength in human liver tissue at 2.45 GHz. For calculations, Eq. 1 was used [10]: where c is the speed of light in free space, f is the operating frequency of the microwave generator (2.45 GHz), and ε r = 43.03 is the relative permittivity of human liver tissue at 2.45 GHz; this yielded the effective wavelength of approximately 18.667 mm.
In this study, slot spacing and floating sleeve length correspond to 0.25 λ ef f , and λ ef f respectively; the design started by choosing the initial values and then optimizing them to achieve localized power deposition near the distal tip of the antenna. Figure 1 shows the schematic diagram of the designed floating sleeve antenna (dimensions in mm), and Table 1 shows the layers' dimensions.
In the antenna design, the pattern of a linear dipole with an overall length less than the half-wavelength (L < λ/2) is insensitive to the frequency [15]. Thus, the dipole length chose to be greater than the half-wavelength according to Eq. 2.
where c is the speed of light in free space and f is the operating frequency of the microwave generator (2.45 GHz), this resulted in a half-wavelength of 61.18 mm. The Computer Simulation Technology (CST) software [16] was the main platform to simulate antenna with 0.5 W stimulation power at the excitation port.

The original liver model
The original model is a realistic 3D model (from the 3D-IRCADb-01 database) of a man's liver with blood vessels and a tumor (2 × 3 cm) [17]. This model was used to generate six models.

Assigning material properties
The electrical and thermal properties for liver tissues were assigned according to the literature and the CST material library [10,11,[18][19][20][21][22][23][24][25][26][27]. Assigning the metabolic properties was one of the significant challenges because of lacking reported values for the basal metabolic rate (BMR) of hepatic tumors. The literature cites the changing of tumors' metabolic activities compared to the normal cells. These changes support the acquisition and maintenance of malignant properties [28]. Gorbach et al. reported that brain tumors have 0.5 to 2 °C higher temperatures than surrounding tissues [29]. In addition, Mital et al. measured the elevation of skin temperature over breast tumors to 2-3 °C above the normal skin temperatures [20]. The liver has a higher metabolic rate than the breast and brain [30]; based on this, the BMR of the tumor was set to be 10 times the surrounding tissues (120,000 W/m 3 ), with 3400 W/(K*m 3 ) as a perfusion rate. Table 2 presents assigned material properties.
The temperature elevation in this study was based on Pennes' suggestion (Eq. 3)  where T = T(x, y, z, t) is the temperature elevation ( • C ), ρ the physical density of the tissue ( kg∕m 3 ), c the specific heat of the tissue ( J∕kg∕ • C ), k the tissue thermal conductivity ( W∕m • C ), w b the blood volumetric perfusion rate ( kg∕m 3 ∕s ), c b the specific heat of blood ( J∕kg∕ • C ), and T a = T a (x, y, z, t) the average temperature elevation of the arteries ( • C ). Q m is the mechanism for modeling physiological heat generation ( W∕m 3 ) and Q r the regional heat delivered by the source ( W∕m 3 ). The term w b c b T a − T , which is the perfusion heat loss ( W∕m 3 ), is always considered in tissues with a high degree of perfusion, such as a liver. In general, w b is assumed to be uniform throughout the tissue. However, its value may increase with heating time because of vasodilation and capillary recruitment [2].

The complete system (antenna and liver) simulation
The antenna was designed in CST MICROWAVE STU-DIO, then the liver model was imported, and the materials' properties were assigned. The transient solver of CST MICROWAVE STUDIO was used to calculate the antenna parameters and the Specific Absorption Rate (SAR). Finally, the thermal solver in CST MPHYSICS STUDIO was used to solve the Pennes' bio-heat equation. For both solvers, open boundary conditions were adjusted. The initial setting of the temperature was 25 • C and 37 • C for the surrounding ambient and tissues, respectively with 10 min simulation time. Figure 2 shows the complete system with different models. The designed antenna was first tested in a liver model without a tumor or blood vessels (Model A), then in a model with a tumor of about 2 × 3 cm and without blood vessels (Model B). After that, blood vessels were added to model B to get a complete model (Model C). To evaluate the effect of both size and location of the tumor, the location of the original tumor was changed (Model D) and scaled down to (1.5 × 1.5 cm) (Model E). Finally, a spherical tumor of 1.5 cm diameter was created to test the designed antenna on a simple-shape tumor model (Model F). Return loss, SAR, and temperature were calculated for all models.

Results
The results show the potential of the designed antenna in raising the temperature of hepatic tumors to above 41 °C, while the temperature of the surrounding tissues was below 41 °C. Return loss, SAR, and temperature were calculated for each simulation model.

Return loss
Values of the return loss at 2.45 GHz vary from − 45 to − 27 dB (Fig. 3). It could be observed that the maximum value (− 45 dB) was obtained in model F (model with spherical tumor), and the minimum value (− 27 dB) was obtained in model A (model without tumor and blood vessels).

Specific absorption rate (SAR)
The SAR value for the model without tumor and blood vessels was 30.2 W/Kg (Fig. 4a), where the values varied from 31.4 to 29.4 W/Kg for others models with tumors ( Fig. 4b-e). In these models, the high value of SAR was observed in model B (without blood vessels) (Fig. 4b).

Temperature results
Considering that the SAR values alone are insufficient to access the hyperthermia effect, it is essential to calculate the temperature of the tumor and surrounding tissues. Figure 5 shows the temperature pattern in all models. It is clear that for model A, without tumor; the highest temperature was 39.7 °C which is below the hyperthermia range. For the other models, the temperature elevation in the tumors was within the therapeutic range (41-45 °C). Compared to other models with tumors ( Fig. 5b-e), the temperature pattern in the model with the spherical tumor (Fig. 5f) showed a uniform distribution. Model C (Fig. 5c) showed the best results with the temperature reaching 45.6 • C and uniform distribution within the tumor.

Discussion
This study introduced a design of a sleeve antenna for microwave hyperthermia of hepatic tumors. The proposed design is shown to be capable of effectively heating interstitial hepatic tumors without harming the surrounded liver tissues. In addition, using realistic 3D liver and tumor models affirms that the tumor shape and the internal structure of the liver directly affect the temperature distribution within the tumor and surrounding tissues. The antenna achieves the  same results when using tumors of different sizes and locations; this shows its high potentiality in treating the interstitial hepatic tumors. The simulations involved various realistic liver models (Fig. 2). Based on the model results without tumor (Fig. 5a), the temperature is uniform in the complete model with a slight increase (1 • C ) around the tip of the antenna. It is reported that basal metabolic rate plays a fundamental role in raising the tumor temperature [31]; however, many studies neglected its effect and used only SAR patterns to evaluate the efficiency of the designed applicator [9,32]. Considering the assumptions of increasing tumor temperature from 0.5 to 3 • C [20,29], the designed antenna elevates the tumor temperature to about 6 • C (Fig. 5b-e). Such an increase in temperature required higher power (up to 50 W) and longer excitation time, as reported in several attempts [7,8,33]. The presence of blood vessels showed a direct effect on the temperature distribution (Fig. 5a, b) since the temperature decreased in the upper side of the tumor close to the lateral blood vessel.
For the models with tumors, the highest SAR values were observed in the model without blood vessels (Fig. 4b).
Compared to the other models ( Fig. 4c-f), this interprets the presence of blood vessels and its effect on microwaves absorption. On the other hand, Model A (in which the antenna has a similar position as Model B but without tumor) shows smaller SAR values (Fig. 4a) compared to Model B; because of the high conductivity of the tumor. Considering the effect of the realistic model on the amount of absorbed microwaves (energy focusing and overheating) [34], it is clear that the model with the spherical tumor (Fig. 4e) shows uniform temperature distribution and lower SAR values compared to the realistic tumors.
The value of the return loss at a frequency of 2.45 GHz (Fig. 3) varies by changing tumor size and location (− 45 dB to − 27 dB). Other antennas designed for microwave ablation had achieved return loss ranging between − 13 and − 25 dB at 2.45 GHz using a higher excitation power (1 to 15 W) [5,12,13,27] compared to only 0.5 W used in this study. As the antenna's efficiency mainly depends on its return loss, small values show greater output power coupled to a tumor. This result shows the efficiency of our antenna, which is comparable to microwave ablation antennas designed to provide a higher heating effect. The current design needs to be tested in different models by varying tumor size and insertion depth. Furthermore, future design optimization to a smaller size with experimental validation will show the applicability of this floating sleeve antenna for microwave hyperthermia. The introduced design achieved the required temperature for heating hepatic tumors while keeping adjacent tissues at a temperature less than 41 ºC. This heating is performed in only 10 min, which is more comfortable for the patients. Moreover, low excitation power (0.5 W) was used compared to previous studies for microwave hyperthermia and microwave ablation.

Conclusion
In summary, we designed a floating sleeve antenna for interstitial microwave hyperthermia of hepatic tumors. The antenna was able to heat hepatic tumors of different sizes and locations. The heating process was performed in a short time by using a very low input power. By conducting more optimizations, the proposed antenna may form the basis for a variety of clinical applications of microwave hyperthermia.
Author contributions FE and SA carried out the concept, design of the study, interpreted the data, and wrote the first manuscript. MA and MY provided critical revision of the manuscript.
Funding This research did not receive any type of grant.

Data availability
The used datasets are available from the corresponding author on reasonable request.

Conflict of interest
The authors declare that they have no competing interests.

Consent for publication
The participants acknowledged their consent to publish the acquired data.
Ethical approval Not applicable.