Effectiveness of microwave ablation using two simultaneous antennas for liver malignancy treatment

Nikola Bošković; Branislav Radjenović; Srdjan Nikolić; Marija Radmilović-Radjenović

doi:10.1515/phys-2024-0079

Article Open Access

Effectiveness of microwave ablation using two simultaneous antennas for liver malignancy treatment

Nikola Bošković , Branislav Radjenović , Srdjan Nikolić and Marija Radmilović-Radjenović

Published/Copyright: September 13, 2024

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From the journal Open Physics Volume 22 Issue 1

Abstract

Microwave ablation is becoming an increasingly important minimally invasive procedure that uses dielectric hysteresis to generate heat and destroy cancer cells. Tissue damage depends on the input power, procedure duration, and antenna position. Therefore, one of the essential problems is determining parameters that ensure the destruction of the tumor with the desired margins and minimal damage to the healthy tissue. In addition to experimental methods, computer modeling has been proven to be an effective approach for improving the performance of microwave ablation (MWA). Moreover, since the thermal spread in biological tissue is difficult to measure, the development of a predictive model from procedural planning to execution may have a great impact on patient care. This study focuses on determining the optimal parameters for MWA treatment of liver tumors using two identical parallel-positioned multi-slot coaxial antennas. The simulation results suggest that an input power of 20 W or 15 W per antenna suffices for complete tumor ablation with a sufficient safety margin for 600 and 900 s, respectively. In both cases, the created ablation zones were similar. The ablation zones for 15 W per antenna were more spherical, invading a smaller amount of healthy tissue than those for 20 W per antenna. This study may represent a step forward in planning MWA treatment for individual patients.

Keywords: microwave radiation; microwave ablation; necrotic tissue

1 Introduction

Liver cancer is one of the most common causes of cancer-related deaths worldwide, accounting for over 700,000 deaths annually [1,2,3,4]. Among the various therapeutic options used to treat liver cancer [5,6,7,8], microwave ablation (MWA) is a minimally invasive modality based on the destruction of cancer cells by microwave radiation-induced hyperthermia [9,10,11,12]. MWA can operate at different frequencies, but the most common frequency is 2.45 GHz, which allows the use of compact antennas and good radiation penetration into tissues [13]. In terms of efficiency and safety, high-temperature, short-duration MWA is the standard of care [14]. Assessing the distribution of heating damage is the most challenging task in MWA because it highly depends on the time, tissue type, and blood vessel distribution [15,16,17].

The antenna design responsible for the formation of ablation zones strongly affects the MWA efficiency. Over the years, various antenna designs have been developed to minimize thermal damage to healthy tissue [18,19,20]. A specially designed AngioDynamic Solero MWA system can rapidly ablate soft tissue, improving procedural outcomes [21]. MWA systems based on “thermosphere technology” create spherical ablation zones by adding small saline irrigation channels to the antennas [22]. However, the cooling system significantly increased the complexity and size of the probe. Novel compact multi-slot coaxial antennas are specially designed to work inside tissues without requiring a cooling system [23].

There are differences between ablation performed using a single probe and ablation performed using multiple probes simultaneously. In spite of some disadvantages, such as complication rates, multiple antenna configurations have been proposed for efficient ablation of large tumors [24,25]. This can be achieved by placing the same probe sequentially at multiple points or using multiple probes placed at multiple points simultaneously. Ablation performed using multiple probes is larger, more symmetrical and requires less treatment time [26,27]. In a multi-antenna configuration, the antennas usually have a parallel orientation; however, it is possible to change the ablation shape to a non-parallel orientation. The two-antenna configuration is the simplest, cheapest, and easiest to implement, producing more uniform thermal profiles and causing less damage to healthy tissues [28,29,30].

In addition to clinical studies, computational models have played a significant role in predicting MWA outcomes, especially three-dimensional (3D) models of an antenna and targeted tissue without assumptions of homogeneity [31,32,33]. This study aimed to provide optimal parameters for treating a real large tumor (from a database [34]) using two identical 10-slot coaxial antennas [17,23,35]. The simulations presented in this article were realized using an in-house developed SimSurgery simulation environment based on several open-source libraries widely used in scientific computing [35]. The obtained simulation results revealed that MWA treatment of large tumors using a two-antenna configuration causes less damage to the healthy tissue compared with using a single antenna. Furthermore, the two-antenna configurations produce more uniform thermal profiles and peripheral tissue temperatures.

2 Methodology

2.1 Physics of the MWA procedure

The equations governing the calculation of the electric-field distribution through the tissue and heat generated by the electromagnetic field during the MWA procedure have already been described in previous publications [11,33,35], so only the main equations are listed here. The first part is the wave equation for the electric field in the frequency domain:

(1) ∇ 2 E → − μ r k 0 2 ε r − j σ ω ε 0 E → = 0 ,

where μ r is the relative permeability (its value is 1 for a non-magnetic environment), ω = 2 π f is the angular frequency, E → is the electric field vector generated by the antenna, σ is the electric conductivity, ε ₀ is the permittivity of the vacuum, and k 0 is the vacuum propagation constant.

The change in temperature over time can be calculated using Pennes’ bio-heat equation [33,36,37]:

(2) ρ c ∂ T ∂ t = ∇ ⋅ ( k ∇ T ) + ρ b ω b c b ( T b − T ) + Q ext + Q met ,

where t is the time, ρ , c , and T are the density, specific heat capacity, and temperature of tissue, respectively. ρ b , c b , and ω b are the density, specific heat capacity, and perfusion rate of blood, respectively. T b = 37°C denotes the arterial blood temperature, Q met is the metabolic heat, and Q ext represents the external heat source generated from MWA, and Q ext ≫ Q met , Q met can be neglected. The bio-heat equation must be solved in the time domain.

Soft tissues, such as the liver, have a very high water concentration. At steady state, the water content of liver tissue is ∼78% water by mass, whereas at temperatures >100°C, the tissue water content may decrease to 20% by mass due to evaporation. An increase in temperature leads to a significant change in water content, affecting tissue parameters [15]. The temperature dependence of the water content can be mathematically expressed as follows [33,35,38]:

(3) W ( T ) = 0.778 ⋅ 1 − e T − 106 3.42 , 70 ° C ≤ T ≤ 100 ° C 7.053 − 0.064096 ⋅ T , 1 0 0 ° C ≤ T ≤ 104 ° C 0.778 ⋅ e − T − 80 34.37 , T > 104 ° C .

This function can be implemented into the specific heat capacity c in Eq. (2) as effective specific heat capacity c′ = c – ∂ W ∂ T [36]. The material parameters of the tissues used in this study are summarized in Table 1.

Table 1

Thermophysiological parameters corresponding to tumor tissues, healthy tissues, and blood used in this study

Parameter	Tissue
	Liver	Tumor	Blood
Density (kg/m³)	1,079	1,040	1,060
Specific heat (J/kg/°C)	3,540	3,960	3,600
Thermal conductivity (W/m/°C)	0.52	0.57	0.5

The dielectric constant of the tissue ε r and electrical conductivity σ are considered temperature-dependent functions [17,33,35]:

(4) ε r = a 1 ⋅ 1 − 1 1 + e ( a 2 − a 3 T ) ,

(5) σ = b 1 ⋅ 1 − 1 1 + e ( b 2 − b 3 T ) ,

with coefficients listed in Table 2.

Table 2

Values of the coefficients used in the calculation of ε r and σ for the liver tissue and tumors

Coefficients	Tissue
	Liver	Tumor
a 1	44.3	54.8
a 2	5.223	5.223
a 3	0.0524	0.0524
b 1	1.69	2
b 2	6.583	6.583
b 3	0.0598	0.0598

The blood perfusion ω _b also depends on the temperature T [17]:

(6) ω b = 2.1 × 10 − 5 T + 3.5 × 10 − 3 .

The difference in temperature between blood and tissue results in convective heat transfer.

The specific absorption rate (SAR) is a measure of the radiation absorbed by the tissue [33,35]:

(7) SAR = σ 2 ρ ∣ E → ∣ 2 ,

where E → is the electric field vector, σ is the electric conductivity, and ρ is the density of the observed domain. It can identify the tissue that is most affected by radiation and how the electric field propagation interacts with the tissue. The total power loss in the targeted tissue can be estimated from the SAR as follows [39]:

(8) P LOSS = ∫ V ρ SAR d V = 1 2 ∫ V σ ∣ E → ∣ 2 d V .

The relative to the input power ratio (in %) is (P _LOSS/P _IN)·100%.

Estimation of the temperature damage Ω as a function of time can be performed using the Arrhenius equation [33,40]:

(9) ∂ Ω ∂ t = A e − Δ E RT ,

where A = 7.39 × 10³⁹ 1/s and ΔE = 2.577 × 10⁵ J/mol represent the frequency factor and activation energy for the irreversible damage reaction, respectively, T is the temperature, and R is the universal gas constant. The most common parameter for the expression of tissue necrosis caused by MWA is the fraction of necrotic tissue [33,35]:

(10) θ d = 1 − e − Ω ,

ranging from 0 (no damage) to 1 (total tissue necrosis). Numerical values of θ _d > 0.99 are acceptable as the total tissue necrosis.

The extent of damage to healthy tissue during MWA should be minimal relative to tumor size. Volumetric damage (VD) is defined as the ratio of the volume of damaged healthy tissue (V _DAMAGED) to that of tumor tissue [41]:

(11) VD = V DAMAGED V TUMOR ⋅ 100 % .

The amount of damaged healthy tissue (DT) was calculated as the ratio of the volume of the damaged healthy tissue to the total volume of the liver (V _LIVER) without tumor tissue (V _TUMOR) [42,43]. The mean volume of the human liver is approximately 1,750 cm³ [44]. V _TUMOR = 13 cm³.

(12) DT = V DAMAGED V LIVER − V TUMOR ⋅ 100 % .

The total delivered energy (TDE) is associated with the input power and duration of the MWA: TDE = Time · P _in [45]. A higher TDE can result in higher temperatures and ablation zones.

2.2 Geometric model

As the first step in modeling, it is necessary to determine the optimal number and position of antennas, depending on the tumor shape. The use of a single antenna in MWA is recommended for the treatment of tumors up to 3 cm in diameter, whereas multiple antenna designs are more useful for larger tumors. Figure 1 illustrates two identical parallel antennas that create spherical ablation zones approximately 3 cm in diameter with a mutual spacing of 3 cm, leading to complete tumor ablation. Although the part of the tumor between the red circles is outside the ablation zones, with the simultaneous use of multiple antennas, closely spaced ablation zones tend to merge, making the overall combined ablation larger than a simple combination of the two ablation zones.

Figure 1

Stereolithography (STL) representation of the liver tumor (taken from a database [34]) from different perspectives. The dimensions of the tumor were 56.8 mm × 27.6 mm × 22.4 mm, with a total volume of approximately 13 cm³. Red circles denote 30 mm in diameter.

Figure 2a shows a 3D simulation model of the tumor (56.8 mm × 27.6 mm × 22.4 mm) (red surface), which was acquired from a 54-year-old male [34], and its position in the liver (gray surface). The 3D-IRCADb-01 database [34] contains enhanced 3D CT images of 10 women and 10 men with hepatic tumors in 75% of cases. The 3D medical images and masks of the segmented structures of interest are available as DICOM files, and the representation of segmented zones is provided as surface meshes in the VTK format, which can be converted to the STL format. The STL surface representation of the tumor was then used to co-create the solid geometry volume in STEP format, which could be directly used in our 3D finite-element method (FEM) simulation. In this study, a configuration of two coaxial antennas with 10 slots was used. As mentioned in previous publications, a 10-slot antenna offers higher heating efficiency for tissues and more near-spherical ablation zones than a 1-slot antenna [11,23].

Figure 2

A schematic view of (a) 3D model of the liver (gray surface) and tumor (red surface) [34] and (b) planar cross-section of the 3D geometry of the problem with two multi-slot antennas with control points.

The liver is typically much larger than the tumor and antenna setup. Modeling and simulation of the entire liver create an extremely large computational model. Using a portion of the liver as a computational domain in a given setup can create a suitable model that is much faster to compute [33,35]. This domain is composed of material parameters corresponding to the liver, and it is limited by the absorbing boundary, which prevents wave reflection, thus imitating a much larger volume (Figure 2b). The number, quality, and size of the finite elements are the second factors after domain size, and they have a large influence on the overall simulation. To capture the behavior of electromagnetic waves, the general rule is that the size of the element should be within a 1/10 of a guided wavelength at 2.45 GHz, which is approximately 2 mm for liver tissue. Some parameters were calculated at control points A, B, C, and D. Point A was in the center of the tumor 15 mm from each antenna, whereas point D was located 15 mm from the first antenna. Therefore, these points can be used to determine the radiation contribution of a single antenna relative to the combined contribution of two antennas. Point B was located 10 mm from the first antenna, and point C was located 13.2 mm from the first antenna, away from the tumor.

Our study focused on the creation and analysis of a complete MWA model using an in-house developed SimSurgery simulation framework. The graphic user interface and 3D visualizations of the framework are based on the Qt [46] and VTK [47] libraries, which are currently the standard for scientific calculations. The geometry module, which can create and manipulate complex model geometries, is based on the OpenCASCADE computer-aided design engine [48]. Meshing operations are performed using the Gmsh package [49]. The details of our strategy of using Gmsh to generate meshes for MWA analysis can be found in Bošković et al. [35]. In this study, we used mixed meshing for the geometry segmentation. The tumor has an irregular geometry and is meshed with unstructured meshing using tetrahedrons. The mesh of the probe with the antenna and computational domain is composed of standard geometric cylinders and hexahedrons, which can be easily represented by structured meshing with hexahedrons. The transition between structured and unstructured meshing was made using the pyramid layer. There is a great advantage in using hexahedrons in FEM simulations, as regular structures can be represented with substantially smaller numbers of elements compared with standard unstructured representations, and the equilateral hexahedron (cube) is the perfect element for FEM analyses, providing the most accurate results. The maximum size of the FEM element is 1/10 of the guided wavelength, and smaller sizes yield negligible differences in the results. The time step size check is incorporated into the time loop. There are four control points in the proposed domain. If the temperature difference between successive time steps is greater than 1°C at any point, the time loop is repeated with a smaller time step, thus ensuring the stability of the results. The model equations were solved using the FEM implemented in the open-source package GetDP [50–52]. The GetDP function in SimSurgery is optional, and other FEM solvers can also be used.

3 Results and discussions

The SAR radiation at a power of 20 W per antenna is shown in Figures 3a–c. The highest level (above 40 dBW/kg) was observed around the antenna slots. Zones >30 dBW/kg are practically guaranteed to be ablated within a short period, whereas zones <30 dBW/kg indicate MWA progression over a longer period. The tumor mass was positioned along the x-axis; therefore, the ablation zone grew in the direction of the x-axis (Figure 3a). There is also an ablation zone along the z-axis in the form of a comet tail along the probe structure toward the power source. Figures 3d–f show SAR radiation at a power of 15 W for each antenna. As expected, high-intensity zones above 30 dBW/kg were smaller. The zone between the antennas can be problematic because the x–z plane radiation intensity may not necessarily be sufficient to encompass the entire tumor. Based on the presented spatial and power distributions, we can conclude that a power of 20 W per antenna can provide complete tumor ablation, whereas a power of 15 W per antenna would require an extended duration of MWA.

Figure 3

SAR calculation for two 10-slot antennas with 30-mm separation and power of 20 W per antenna (a) x–z cut plane, (b) y–z cut plane, (c) x–y cut plane, and 15 W per antenna (d) x–z cut plane, (e) y–z cut plane, and (f) x–y cut plane. White curves represent the tumors.

Temperature-dependent material parameters influence the temperature distribution of the MWA [16]. The locations with the highest temperatures were always near the antenna slot. Moving away from the slots, the electromagnetic wave travels through the tissue, and the effect of radiation on the temperature strongly depends on the material parameters. Blood perfusion dictates bio-heat transfer in tissues. Below 60°C, blood perfusion has a significant effect on the temperature distribution [17,23,35]. Above 60°C, the tissue is completely ablated, and there is no more blood perfusion in the ablated tissue [17,23,35]. Lower conductivity and permittivity of the tissue affect the electromagnetic wave passing through the ablated tissue. With a certain power, the temperature increases to a certain level and then saturates.

The temperature distribution with time for two 10-slot antennas with 30-mm separation and 20 W per antenna is displayed in Figure 4a. Evidently, high temperatures are near the antenna slots and decrease as the antennas move away from the antennas. The temperature rapidly rose until 120 s, after which it became much subtler. As observed from Figures 4b–d (temperature distribution at 600 s at different cross-sections), the bulk of the tumor was inside the area with temperatures of and above 60°C, which ensured instantaneous cell death. Figure 4b clearly shows that a region with a temperature greater than 60°C has a comet-like shape, implying the destruction of a substantial amount of healthy tissue.

Figure 4

Temperature distribution for two 10-slot antennas with 30-mm separation and 20 W per antenna: (a) x–z cut plane during 600 s; at 600 s for (b) x–z cut plane, (c) y–z cut plane, and (d) x–y cut planes. The tumor is plotted on a green surface.

For 15 W of the antenna, a similar effect was achieved over a longer time than 600 s, as shown in Figure 5. During the entire 900 s period, the temperature rises slowly (Figure 5a). At 900 s, the larger part of the tumor was practically inside the zones at temperatures of 60°C or higher (Figures 5b–d), thereby guaranteeing immediate cell death, but the shape of the zones was much more spherical.

Figure 5

Temperature distribution for two 10-slot antennas with 30-mm separation and 15 W per antenna: (a) x–z cut plane during 900 s; at 900 s for (b) x–z cut plane, (c) y–z cut plane, and (d) x–y cut planes. The tumor is plotted on a green triangulated surface.

Figure 6 illustrates the tumor’s complete ablation after 600 s using a total power of 20 W per antenna. Both antennas form ablation zones that merge into a single zone. Until 180 s, the necrotic zones were spherical, but after that, they became the shape of a comet with the tail oriented toward the power source. Figure 6 indicates that 20 W per antenna for 600 s is sufficient for complete tumor necrosis with the desired ablation margin. For 15 W per antenna (Figure 7a), however, the ablation zone encompasses two highly spherical zones for up to 600 s. Practically, no margins are observed, so additional time is needed. After 900 s, the necrotic zone became larger, encompassing not only the tumor but also the proper ablation margin. Figures 7b–d show that the damage caused to the healthy tissue was much smaller than that caused by the use of 20 W per antenna for 600 s.

Figure 6

Fraction of necrotic tissue for two 10-slot antennas with 30-mm separation and 20 W per antenna: (a) x–z cut plane during 600 s; at 600 s for (b) x–z cut plane, (c) y–z cut plane, and (d) x–y cut planes. The white surface represents the tumor.

Figure 7

Fraction of necrotic tissue for two 10-slot antennas with 30-mm separation and 15 W per antenna: (a) x–z cut plane during 900 s; at 900 s for (b) x–z cut plane, (c) y–z cut plane, and (d) x–y cut planes. The tumor is plotted on a white surface.

Figure 8 depicts the temporal evolution of (a) the temperature and (b) the fraction of necrotic tissue calculated at the control points plotted in Figure 2b. As seen in Figure 8a, at point A, for 20 W per antenna, the temperature rises rapidly at approximately 120 s and then remains almost constant for up to 300 s. At 450 s, there was an abrupt change in the slope owing to the cessation of blood perfusion. For 15 W per antenna, the temperature first increased and then reached saturation at around 62°C after 540 s. At point B, for 20 W per antenna, the temperature dependence is similar to that observed at point A. For 15 W per antenna, saturation occurs at approximately 61°C after 570 s. At point C, for 20 W per antenna, the temperature exhibited a small change in the slope around 150 s and reached 56.8°C after 600 s. Similarly, for 15 W per antenna, the temperature reached 51.3°C after 900 s. For 20 and 15 W per antenna, the temperature recorded at point D exhibits a very stable change over time, with a maximum value of 50.5°C at 600 s and 46.8°C at 900 s. Figure 8b shows that, during the observation period, 100% of the fraction of necrotic tissue was not achieved only at point D, which can be attributed to the fact that this point is outside the tumor. Complete ablation was achieved at points B, A, and C after 150, 200, and 450 s, respectively, using 20 W per antenna and after 300, 320, and 750 s, respectively, using 15 W per antenna.

$Figure 8 The time dependence of (a) the temperature distribution and (b) the fraction of necrotic tissue at the points shown in Figure 2b for antennas with 15 or 20 W.$

Figure 8

The time dependence of (a) the temperature distribution and (b) the fraction of necrotic tissue at the points shown in Figure 2b for antennas with 15 or 20 W.

In Figure 9, the difference between the use of a single antenna and two identical antennas under the same conditions is shown. We can see that with the same input power and duration of the MWA, in the case of the two antennas, there are two connected ablation zones that are slightly larger than the simple sum of the ablation zones originating from the single antennas. This is in accordance with the conclusions of [24].

Figure 9

Fraction of necrotic tissue for a single 10-slot antenna at x–z plane: (a) 20 W after 600 s, (b) 15 s after 600 s, and (c) 15 W after 900 s. The triangulated surface represents the tumor. The black curves represent the shape of the ablation for the cases with the two antennas shown in Figures 6b and 7b under the same parameters.

VD and DT can be calculated using Eqs. (11) and (12). Both increase with time and power (Table 3). The least damage to the healthy tissue was observed after 600 s at 15 W, with a VD of 46.9% and a DT of 0.4%. After 900 s, the volume of damaged healthy tissue increased more than twice, with a VD of 113.1% and a DT of 1%. The highest damage occurred for the case with 20 W after 600 s, with a VD of 166.2% and a DT of 1.5%. Higher power and longer durations of MWA increase TDE, but tissue necrosis is not a simple linear function. Depending on the radiation pattern of the MWA system and system configuration, the power distribution among multiple antennas can produce a targeted ablation shape, thereby minimizing unwanted damage to healthy tissue [32]. The largest TDE was observed for the case with 15 W per antenna after 900 s; however, due to more spherical ablation zones, the damage was confined in the area around the tumor, thus producing a lower amount of damage to healthy tissue compared with the case with 20 W per antenna after 600 s.

Table 3

VD, DT, and TDE after MWA for 15 and 20 W per antenna

MWA	V _DAMAGED (cm³)	VD (%)	DT (%)	TDE (kJ)
15 W after 600 s	7.5	46.9	0.4	18
15 W after 900 s	18.1	113.1	1.0	27
20 W after 600 s	26.6	166.2	1.5	24

4 Conclusion

In this study, we simulated MWA treatment of a real large elongated tumor from the database [34] using two identical parallel-positioned multi-slot coaxial antennas. The obtained simulation results show that the fastest temperature rise occurs near the radiating slots. For 20 W per antenna, tumor ablation was completed in 600 s, the temperature rapidly increased, and the two connected comet-shaped ablation zones led to excessive damage to the healthy tissue. Ablation can also be achieved using 15 W per antenna for 600 s without margins between the healthy tissue and tumor. Prolonging MWA to 900 s resulted in larger spherical ablation zones with significantly less damage to the healthy tissue. Our results indicate that using a two-antenna configuration with lower power and longer MWA duration provides complete ablation of large tumors with a sufficient safety margin. A comparison of the ablation created with 20 W per antenna during 600 s and 15 W per antenna during 900 s showed that volumetric damage was significantly higher in the first case (166.2 vs 113.1%). On the other hand, the total delivered power was larger in the second case as a direct consequence of the more spherical ablation zones. The calculation results showed that 25.7 and 24.8% of the input energy was converted into thermal energy for heating the tumor tissue for the 15 and 20 W per antenna, respectively. The remaining energy is converted into thermal energy for heating the liver tissue and losses in the device itself. These results agree well with those published in [53].

Funding information: N.B., B.R., and M.R.-R. acknowledge that this research was supported by the Science Fund of the Republic of Serbia, The Program IDEAS, GRANT No. 7739583, SimSurgery.
Author contributions: Conceptualization: N.B., S.N., and M.R.-R.; methodology: B.R., N.B., and M.R.-R.; software: N.B. and B.R.; investigation and data interpretation: all of the authors; original draft preparation: N.B. and M.R.-R.; writing – review, and editing: all of the authors; supervision: B.R., S.N., and M.R.-R. All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
Conflict of interest: The authors state no conflict of interest.
Data availability statement: The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Received: 2024-04-17

Revised: 2024-07-03

Accepted: 2024-08-01

Published Online: 2024-09-13

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/phys-2024-0079

Keywords for this article

microwave radiation; microwave ablation; necrotic tissue

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