Improved power steering with double and triple ring waveguide systems: The impact of the operating frequency

Figures & data

Figure 1. Model cross-sections of an elliptical phantom in the single-ring 70-MHz AMC-4 system and two and three-ring waveguide systems at 70 and 130 MHz, respectively.

Table I.  Modelled waveguide aperture sizes and depths for different operating frequencies.

	70 MHz	100 MHz	120 MHz	130 MHz	140 MHz	150 MHz
Single ring 8.5 × 34.25 cm^2	*
Two rings 8.5 × 34.25 cm^2	*
8.5 × 30.25 cm^2	*	*
8.5 × 25.25 cm^2	*	*	*
8.5 × 20.25 cm^2		*	*	*	*	*
Three rings 8.5 × 20.25 cm^2		*	*	*	*	*
Waveguide depth (cm)	12	8.5	7	6.5	6	5.5

*Specific combination of frequency and waveguide configuration was modelled.

Table II.  Values of the dielectric properties for different tissue types at the frequencies applied in the simulations; conductivity (σ [S m⁻¹]), relative permittivity (ε_r [-]).

	70 MHz	100 MHz	120 MHz	130 MHz	140 MHz	150 MHz
Air σ (S m^−1)	0	0	0	0	0	0
εr (-)	1	1	1	1	1	1
Bone σ (S m^−1)	0.05	0.05	0.06	0.06	0.06	0.06
εr (-)	10	9	9	9	9	9
Fatty tissue σ (S m^−1)	0.06	0.06	0.06	0.06	0.06	0.06
εr (-)	10	9	9	9	9	9
Lung σ (S m^−1)	0.2	0.21	0.21	0.22	0.22	0.22
εr (-)	20	18	17	16	16	16
Muscle σ (S m^−1)	0.75	0.77	0.78	0.78	0.78	0.79
εr (-)	75	70	68	67	66	66
Phantom σ (S m^−1)	0.55	0.55	0.55	0.55	0.55	0.55
εr (-)	75	75	75	75	75	75
Tumour σ (S m^−1)	0.74	0.78	0.80	0.81	0.82	0.83
εr (-)	65	58	55	54	53	52

Table III.  Values of the thermal properties for different tissue types used in the simulations; density (ρ [kg m⁻³]), specific heat capacity (c [J kg⁻¹°C⁻¹]), thermal conductivity (k [W m⁻¹°C⁻¹]) and perfusion (W_b [kg m⁻³s⁻¹]).

	(ρ [kgm^−3])	(c [J kg^−1°C^−1])	(k [Wm^−1°C ^−1])	(Wb [kgm^−3s^−1])
Air	1.29	10000*	0.024	0.0
Bone	1595	1420	0.65	0.12
Fatty tissue	888	2387	0.22	1.1
Lung	750	3000	0.25	3.6
Muscle	1050	3639	0.56	3.6
Tumour	1050	3639	0.56	1.8

*The value of c used for air was ten times too high in order to allow larger time steps in thermal computations. This has a negligible effect on the steady-state temperature distribution.

Table IV.  Values of the S_ratio (i.e. the ratio between the maximum SAR in the phantom and the SAR in the central target) for both the homogeneous and the fat-muscle phantom after SAR optimisation. Constraints were set to the output power of each waveguide: an antenna of the single-ring AMC-4 system should deliver at least 10% and at most 40% of the total applied power; for a two-ring system this was at least 5% and at most 25%. For a three-ring system the minimum and maximum output power of each waveguide was constrained to 3% and 15% of the total power, respectively.

	70 MHz	100 MHz	120 MHz	130 MHz	140 MHz	150 MHz
Homogeneous muscle
Single ring 8.5 × 34.25 cm^2	1.62
Two rings 8.5 × 34.25 cm^2	1.4
8.5 × 30.25 cm^2	1.5	1.53
8.5 × 25.25 cm^2	1.78	1.64	1.49
8.5 × 20.25 cm^2		1.98	1.78	1.54	1.45	1.81
Three rings 8.5 × 20.25 cm^2		1.58	1.5	1.33	1.19	1.65
Fat-muscle
Single ring 8.5 × 34.25 cm^2	1.63
Two rings 8.5 × 34.25 cm^2	1.47
8.5 × 30.25 cm^2	1.62	1.72
8.5 × 25.25 cm^2	1.75	1.22	1.5
8.5 × 20.25 cm^2		1.26	1.8	1.55	1.37	1.59
Three rings 8.5 × 20.25 cm^2		1.1	1.03	1.02	1.04	1.36

The lowest S_ratio values for the three-ring systems are written in bold type.

Figure 2. Optimised SAR distributions in the homogeneous muscle-equivalent phantom for the 2D single-ring 70 MHz AMC-4 system and 3D double-ring and triple-ring systems at different operating frequencies. Slices were taken in the central xz-plane. For frequencies and configurations for which multiple aperture sizes were simulated, results for the largest aperture size are shown.

Table V.  Optimised indexed tumour temperatures for five cervical cancer patients and the total absorbed power at 70 MHz for aperture sizes 8.5 × 34.25 cm², 8.5 × 30.25 cm² and 8.5 × 25.25 cm². The last column lists the amount of power and the gain in temperature with respect to the single-ring 70-MHz AMC-4 system averaged over the five patients.

70 MHz	Patient 1	Patient 2	Patient 3	Patient 4	Patient 5	Average gain (°C) w.r.t. AMC-4/average power (W)
34.25 cm T90 (°C)	40.3	40.3	40.9	41.0	41.0	0.4
T50 (°C)	41.1	41.8	41.6	42.0	43.0	0.6
T10 (°C)	41.9	42.8	42.4	43.8	44.2	0.7
Power (W)	803	681	635	662	674	691
30.25 cm T90 (°C)	40.2	40.3	40.8	41.0	40.6	0.3
T50 (°C)	41.0	41.8	41.6	42.0	42.5	0.5
T10 (°C)	41.9	42.9	42.3	43.7	43.8	0.6
Power (W)	808	694	620	647	669	688
25.25 cm T90 (°C)	40.2	40.3	40.7	40.9	40.8	0.3
T50 (°C)	41.0	41.7	41.5	41.9	42.6	0.4
T10 (°C)	41.8	42.7	42.2	43.8	44.1	0.6
Power (W)	759	657	588	617	675	659

Table VI.  Optimised indexed tumour temperatures for five cervical cancer patients and the total absorbed power at 100 MHz for aperture sizes 8.5 × 30.25 cm², 8.5 × 25.25 cm² and 8.5 × 20.25 cm². The last column lists the amount of power and the gain in temperature with respect to the single-ring 70-MHz AMC-4 system averaged over the five patients.

100 MHz	Patient 1	Patient 2	Patient 3	Patient 4	Patient 5	Average gain (°C) with respect to AMC-4/average power (W)
30.25 cm T90 (°C)	40.6	40.7	41.7	41.5	41.1	0.8
T50 (°C)	41.6	42.4	42.4	42.7	43.1	1.1
T10 (°C)	42.6	43.6	43.1	44.5	44.6	1.3
Power (W)	746	702	609	616	642	663
25.25 cm T90 (°C)	40.8	40.6	41.7	41.3	41.2	0.8
T50 (°C)	41.9	42.4	42.5	42.5	43.4	1.2
T10 (°C)	42.9	43.7	43.3	44.0	45.0	1.4
Power (W)	770	665	594	610	715	671
20.25 cm T90 (°C)	40.8	40.6	41.7	41.2	41.2	0.8
T50 (°C)	41.9	42.4	42.4	42.4	43.4	1.2
T10 (°C)	42.9	43.6	43.2	44.1	45.1	1.4
Power (W)	793	683	581	615	692	673

Table VII.  Optimised indexed tumour temperatures for five cervical cancer patients and the total absorbed power at 120 MHz for aperture sizes 8.5 × 25.25 cm² and 8.5 × 20.25 cm². The last column lists the amount of power and the gain in temperature with respect to the single-ring 70-MHz AMC-4 system averaged over the five patients.

120 MHz	Patient 1	Patient 2	Patient 3	Patient 4	Patient 5	Average gain (°C) with respect to AMC-4/average power (W)
25.25 cm T90 (°C)	41.0	41.1	42.0	41.8	41.8	1.2
T50 (°C)	42.2	42.6	42.8	43.1	43.5	1.5
T10 (°C)	43.3	43.8	43.6	44.6	44.8	1.7
Power (W)	832	707	611	585	814	710
20.25 cm T90 (°C)	41.0	41.1	42.1	41.8	41.2	1.1
T50 (°C)	42.0	42.7	43.0	43.1	43.1	1.5
T10 (°C)	43.0	43.9	43.7	44.6	44.2	1.5
Power (W)	840	679	624	637	740	704

Figure 3. Gain in optimised indexed temperatures T₁₀, T₅₀ and T₉₀ (left) with respect to the single-ring 70-MHz AMC-4 system and the corresponding total amount of absorbed power (right) for two-ring waveguide systems at different operating frequencies. Results are averaged over the five patients.

Table VIII.  Optimised indexed tumour temperatures for five cervical cancer patients and the total absorbed power using the single-ring AMC-4 system and two-ring waveguide systems at different frequencies. At frequencies for which multiple aperture sizes were simulated, results for the largest aperture size are shown (70 MHz: 8.5 × 34.25 cm², 100 MHz: 8.5 × 30.25 cm², 120 MHz: 8.5 × 25.25 cm²). The highest T₉₀ for each patient is written in bold type.

	Patient 1	Patient 2	Patient 3	Patient 4	Patient 5
AMC-4 T90 (°C)	39.8	40.1	40.7	40.6	40.3
70 MHz T50 (°C)	40.5	41.3	41.3	41.6	41.9
T10 (°C)	41.3	42.3	42.0	43.3	42.9
Power (W)	606	552	549	527	494
Two-ring systems
70 MHz T90 (°C)	40.3	40.3	40.9	41.0	41.0
T50 (°C)	41.1	41.8	41.6	42.0	43.0
T10 (°C)	41.9	42.8	42.4	43.8	44.2
Power (W)	803	681	635	662	674
100 MHz T90 (°C)	40.6	40.7	41.7	41.5	41.1
T50 (°C)	41.6	42.4	42.4	42.7	43.1
T10 (°C)	42.6	43.6	43.1	44.5	44.6
Power (W)	746	702	609	616	642
120 MHz T90 (°C)	41.0	41.1	42.0	41.8	41.8
T50 (°C)	42.2	42.6	42.8	43.1	43.5
T10 (°C)	43.3	43.8	43.6	44.6	44.8
Power (W)	832	707	611	585	814
130 MHz T90 (°C)	40.9	41.2	42.3	41.9	42.2
T50 (°C)	41.9	42.7	43.2	43.3	43.7
T10 (°C)	42.9	43.9	44.0	44.9	44.9
Power (W)	932	747	620	628	755
140 MHz T90 (°C)	39.4	40.6	42.1	41.8	41.7
T50 (°C)	40.0	42.0	43.1	43.3	43.9
T10 (°C)	40.9	43.2	44.1	45.1	45.5
Power (W)	750	688	650	637	705
150 MHz T90 (°C)	40.5	40.6	40.3	41.7	41.5
T50 (°C)	41.2	42.2	41.3	43.1	44.1
T10 (°C)	42.4	43.7	42.3	44.9	45.8
Power (W)	778	637	565	641	655

Figure 4. Coronal (top), sagittal (centre) and transversal (bottom) slices of the anatomy of patient 3 (left column). Red corresponds to muscle tissue, fat tissue is yellow, bone is green and inner air is blue. The tumour is represented by the black spot in the centre. The other three columns show the temperature distributions optimised for the 70-MHz AMC-4 system and double-ring systems at 70 and 130 MHz. Left and right of the patient correspond with right and left in these pictures, respectively. The orthogonal slices run through the centre of gravity of the tumour.

Figure 5. Optimised T₉₀ for each patient simulated with three-ring systems at different operating frequencies. For comparison the optimised T₉₀ with the 70-MHz AMC-4 system and with a two-ring system at 130 MHz (optimum of the two-ring systems) are plotted as well.

Figure 6. Gain in optimised indexed temperatures T₁₀, T₅₀ and T₉₀ (left) with respect to the single-ring 70-MHz AMC-4 system and the corresponding total amount of absorbed power (right) for three-ring waveguide systems at different operating frequencies. Results are averaged over the five patients. For comparison, the results for the optimal double-ring system at 130 MHz are plotted as well.

Table IX.  Optimised indexed tumour temperatures for five cervical cancer patients and the total absorbed power using three-ring waveguide systems at different frequencies. For reference the optimised results for the single-ring AMC-4 system are repeated here as well as for the optimal frequency for a two-ring system (130 MHz).

	Patient 1	Patient 2	Patient 3	Patient 4	Patient 5
AMC-4 T90 (°C)	39.8	40.1	40.7	40.6	40.3
70 MHz T50 (°C)	40.5	41.3	41.3	41.6	41.9
T10 (°C)	41.3	42.3	42.0	43.3	42.9
Power (W)	606	552	549	527	494
Two-ring system
130 MHz T90 (°C)	40.9	41.2	42.3	41.9	42.2
T50 (°C)	41.9	42.7	43.2	43.3	43.7
T10 (°C)	42.9	43.9	44.0	44.9	44.9
Power (W)	932	747	620	628	755
Three-ring systems
100 MHz T90 (°C)	41.5	41.0	42.3	41.7	42.2
T50 (°C)	42.6	42.6	43.3	42.9	43.9
T10 (°C)	43.7	43.8	44.2	43.8	45.3
Power (W)	871	762	742	719	842
120 MHz T90 (°C)	42.0	41.4	42.9	42.0	42.5
T50 (°C)	43.2	43.2	43.9	43.3	44.1
T10 (°C)	44.5	44.5	44.9	44.8	45.5
Power (W)	1059	885	735	779	838
130 MHz T90 (°C)	41.9	41.5	43.2	41.9	42.5
T50 (°C)	43.1	43.4	44.3	43.4	44.1
T10 (°C)	44.3	44.9	45.3	45.0	45.5
Power (W)	1147	914	784	749	984
140 MHz T90 (°C)	41.9	41.7	42.9	42.1	42.5
T50 (°C)	42.8	43.5	43.9	43.6	44.3
T10 (°C)	44.1	45.0	44.9	45.3	45.7
Power (W)	1178	905	729	787	1021
150 MHz T90 (°C)	41.8	41.7	42.0	42.1	42.6
T50 (°C)	43.1	43.7	43.0	43.7	44.3
T10 (°C)	44.6	45.2	44.0	45.4	45.8
Power (W)	1109	866	857	724	886

Figure 7. Coronal (top), sagittal (centre) and transversal (bottom) slices of the anatomy of patient 1 (left column). Red corresponds to muscle tissue, fat tissue is yellow, bone is green and inner air is blue. The tumour is represented by the black spot in the centre. The other three columns show the temperature distributions optimised for double-ring systems at 70 and 130 MHz and a three-ring system at 130 MHz. Left and right of the patient correspond with right and left in these pictures, respectively. The orthogonal slices run through the centre of gravity of the tumour.

Figure 8. The number of equivalent min at 43°C for the T₉₀ of each patient according to Equation 6 plotted against the operating frequency. The left picture shows the improvement with a two-ring system at higher frequencies and the right picture with a three-ring system. The grey dotted line represents the result for the T₉₀ averaged over all five patients. A log-scale was used on the vertical axis. This graph emphasises the significant improvement in thermal dose delivery that can be achieved by increasing the operating frequency from 70 to 130 MHz.