Modification of Source Strength in Low-Dose-Rate Lung Brachytherapy with 125I and 103Pd Seeds.

BACKGROUND: A new treatment approach for most patients who have undergone early stage non-small-cell lung carcinoma (NSCLC) is wedge resection plus permanent implant brachytherapy. However, the specification of dose to medium at low energies especially in heterogeneous lung is unclear yet.
OBJECTIVE: The present study aims to modify source strength for different configurations of 125I and 103Pd seeds used in lung permanent implant brachytherapy.
METHODS: Different arrays of 125I and 103Pd seeds were simulated by MCNPX code in protocol-based water vs. actual 3D lung environments. Absorbed dose was, then, scored in both mediums. Dose differences between both environments were calculated and source strength was modified for the prescription point. In addition, lung-to-water absorbed dose ratio was obtained and presented by precise equations.
RESULTS: Due to significant differences in prescription dose, source strength was modified 16%-19% and 37%-43% for different configurations of 125I and 103Pd seeds, respectively. In addition, depth-dependent dose differences were observed between the actual lung and protocol-based water mediums (dose difference as a function of depth).
CONCLUSION: Modification of source strength is essential for different arrangements of 125I and 103Pd seeds in lung implantation. Modified source strength and presented equations are recommended to be considered in future studies based on lung brachytherapy.

Introduction

Lung cancer has the highest rate of mortality among all cancers with more than 80% diagnosis of non-small-cell lung carcinoma (NSCLC) [1,2]. A new treatment approach for a wide range of high-risk patients with early-stage NSCLC who do not have proper respiratory conditions for lobectomy or pneumonectomy is wedge resection plus low-dose-rate (LDR) permanent implant brachytherapy [3,4,5]. In this technique, a wedge-shaped piece of lung is removed by segmentectomy, and an implant is created by weaving strands of LDR seeds (e.g. 125I or 103Pd) into a vicryl mesh which is then sutured over the resection staple line with the goal of delivering 100 to 120 Gy to the prescription point, 5 mm above the seeds plane [6,7]. The implants are prepared specifically for each patient under the supervision of treatment planning team in different configurations [8,9]. This technique was first used at the end of the 1990s and initially described by Chen et al. [9,10]. Chen et al. applied different configurations of 125I seeds (mostly 40, 50 and 60 seeds) for the mean target area of 48 cm2 with the mean total activity of 22 mCi and have reported this technique potentially effective and well tolerated with no increase in postoperative complications. Other researchers have also reported similar results and excellent local control rate; with seeds array as large as 50 cm2 [4,11]. Johnson et al. [8] have reported a monogram for different configurations of seeds with proper arrays. American Association of Physicists in Medicine Task Group number 43 (AAPM TG-43U1 protocol) recommends initial source strength (initial air-kerma strength) based on water-equivalent homogenous tissue [12,13] while lung heterogeneity and difference of lung-water electron densities (1:4) can cause significant dose change especially in case of multiple seeds [13]. Although, according to the recent multi-societal TG-186 report, assuming the patient as water being dosimetrically incorrect, AAPM TG-43 is still a commonly recommended protocol. Based on ICRU recommendation, the uncertainty of dose determination should not exceed 5% which only 2% can be due to calculations error [14]; and a study conducted by Van Dyk has reported 22% increase in the occurrence of radiation pneumonitis due to 5% increase in lung absorbed dose [15]. Sutherland [16] has studied breast and lung permanent brachytherapy using the BrachyDose algorithm and reported about 20% dose difference at the prescription point for different configurations of 125I seeds. Since the dosimetry in the actual lung is impractical, and accurate dose distribution is crucial for optimized treatment, in this study we intend to simulate water-equivalent and 3D lung environments and four configurations of 125I and 103Pd seeds in order to calculate the absorbed dose and dose difference caused by differences between protocol presumption and actual lung. Mentioned configurations were chosen based on previous studies conducted by Chen [8], Johnson [9] and Sutherland [16]. In the end, we present modified source strength (initial air-kerma strength) and precise equations in order to be considered in future studies based on lung permanent implant brachytherapy.

Material and Methods

Radiation Transport

In this study, a Monte Carlo N- Particle transport code (MCNPX, version 2.6.0) was used to simulate thorax phantom and four configurations of 125I and 103Pd seeds in order to calculate the lung absorbed dose and to modify seeds initial strength calculated by considering AAPM TG-43 U1 recommendations. With regard to the energy range of 125I and 103Pd sources and the voxels size (1 mm3 cubic voxel), electron equilibrium exists and collision kerma is a good estimation of absorbed dose. F6 track-length estimator was used to obtain dose per history and converted to total absorbed dose rate (for 40, 50 and 60 seeds) by equation 1 [16]. For permanent implant brachytherapy, the total absorbed dose at each voxel can be obtained by multiplying the total absorbed dose rate by mean lifetime (τ = 1.443 T1/2) of brachytherapy source.

Total Absorbed Dose Rate (cGy/h) = MC output (MeV/gr per photon) × (cm2.MeV/gr per photon)-1 × Sk (U/seed) × Ns

where MC output is the F6 tally output (dose per history), S is air-kerma strength per history obtained from Monte Carlo calculations, S is the initial air-kerma strength of each source in the treatment [17] and N is the total number of seeds in each particular configuration. The calculation of air kerma strength per history (S) for a particular seed is thoroughly described by Taylor et al. [18]. The photon and electron cut-off energies were set to 5 and 10 keV, respectively. In order to reach maximum accuracy (max error 1%), 1.5 × 109 photon histories were considered.

Simulated Thorax Phantom

Using quadric equations, anthropomorphic QRM thorax phantom including lung, heart and vertebral column was simulated by MCNPX 2.6.0 considering their constituent compositions and densities. These phantoms are generally made in the form of elliptical cylinders as thorax with a cross-section of 20×30 cm2 including two symmetric elliptical cylinders as lungs with a cross-section of 12×16 cm2. Heart and vertebral column were simulated as circular cylinders with proper constituent compositions. A part of the right lung with 50 cm2 cross-section was removed as the resected volume, and the seeds’ plane was simulated on it. The composition and densities of thorax organs are mentioned in Table 1 [19,20]. Figure 1 illustrates the cross-section of simulated anthropomorphic QRM thorax phantom.

Table 1

Mass densities and elemental compositions of thorax tissues used in our simulations [19,20]

Material	Composition (mass %)					ρ (g/cm3)
	H	C	N	O	Elements with Z > 8
Lung	10.3	10.5	3.1	74.9	Na(0.2), P(0.2), S(0.3), Cl(0.3), K(0.2)	0.26
Heart	10.3	12.1	3.2	73.4	Na(0.1), P(0.1), S(0.2), Cl(0.3), K(0.2), Fe(0.1)	1.06
Vertebrae	3.4	15.5	4.2	43.5	Na(0.1), Mg(0.2), P(10.3), S(0.3), Ca(22.5)	1.92
Soft Tissue	10.2	11.2	3.0	74.5	Na(0.1), P(0.2), S(0.3), Cl(0.1), K(0.4)	1.05
Water	11.22	0.0	0.0	88.78	_	0.998
Air(TG-43)	0.07	0.01	75.03	23.61	Ar(1.27)	0.0012

Figure1

a. Cross section of anthropomorphic QRM thorax phantom. b. Thorax Phantom Simulated in this study by MCNPX code.

125I Seed (Amersham, model 6711)

In this study, 125I source (model 6711) was used. This source was benchmarked by Monte Carlo simulation in our previous study and was simulated thoroughly based on 3D actual source [21]. In designing the source, one silver cylindrical marker was used by 10.5 g/cm3 density, 2.8 mm length and 0.254 mm radius covered with Br5I2 compound with 2 µm thickness and 6.245 g/cm3 density. Source effective length was 2.8 mm and the end of the source was curved by 0.045 mm under 45-degree angles. This composition was located at one titanium capsule with 4.54 g/cm3 density filled by Argon gas with 1.784 g/cm3 density. The average energy, half-life and mean life-time of 125I source are 28.37 keV, 59.4 and 85.7 days, respectively [22,23].

103Pd Seed (Theragenics, model 200)

103Pd seed (Theragenics, model 200) includes two cylindrical graphite rods with 2.22 g/cm3 density, 0.56 mm diameter and 0.890 mm length. These rods are coated with a thin layer of radioactive palladium with 12.03g/cm3 density and 2.2 µm thickness. The graphite cylinders are separated by a lead marker with 11.4 g/cm3 density, 0.5 mm diameter and 1.09 mm length. Mentioned components are capsulated inside a cylindrical titanium capsule with 4.51 g/cm3 density, 0.826 mm external diameter and 0.056 mm thickness. Both ends of the capsules are closed with cylindrical titanium cups as shields. These cups have 0.306 mm internal diameter and 0.04 mm thickness. The total length of this source is 4.5 mm with 4.23 mm effective length. The average energy, half-life and mean life-time of the103Pd source are 20.74 keV, 16.99 and 24.5 days, respectively. 103Pd seed (Theragenics, model 200) was benchmarked and its dosimetric parameters have been reported by the present authors previously [24].

Mesh Including 40, 50 and 60 Seeds

Lung mesh seed implants can be used to cover a target area of about 50 cm2 [4,9,11]. Four configurations of 125I and 103Pd seeds considered in this study are mentioned in Table 2. These configurations were chosen based on previous studies done by Chen et al. [8], Johnson et al. [9] and Sutherland et al. [16]. Ten seeds were put in each row with 1 cm center-to-center distance but with various row spacing (RS) due to row numbers. Row spacing was 0.8, 1, 1.3 and 1.5 cm for 60, 50, 40(I) and 40(II) seeds configurations, respectively. Figure 2 shows configurations II and IV with 40 and 60 seeds, both on a 5×10 cm2 plane but with different row spacing. Using equation 1, initial source strength was calculated in the water-equivalent environment (based on AAPM TG-43U1 protocol) to deliver 100 Gy to the prescription point. In this study, the plane with 5×10 cm2 cross-section was considered as the resected volume of the lung.

Table 2

Initial air-kerma strength per seed (U/seed) per prescription dose (100 Gy) for different configurations of 125I and 103Pd seeds. (TG-43)sim is calculated source strength based on AAPM TG-43 U1 protocol (in water environment) versus source strength modified by authors based on actual 3D lung environment.

Configuration		Row Spacing (cm)	Initial source strength (U/prescription dose)
			103Pd (200)			125I (6711)
			(TG-43)Sim	Modified by Authors	%Diff (Rounded)	(TG-43)Sim	Modified by Authors	%Diff (Rounded)
I	(4 × 10)	1.5	5.04	2.88	-42 %	0.75	0.61	-18 %
II	(4 × 10)	1.3	4.24	2.53	-40 %	0.67	0.56	-16 %
III	(5 × 10)	1.0	3.03	1.90	-37 %	0.48	0.41	-15 %
IV	(6 × 10)	0.8	2.50	1.58	-36 %	0.39	0.33	-16 %

Figure2

Configuration II (40 seeds) versus configuration IV (60 seeds). All configurations are simulated on a 5×10 cm2 plane; ten seeds in each row with 1 cm center-to-center distance but with various row spacing.

Absorbed Dose & Dose Difference

The purpose of putting mesh including LDR seeds is to deliver 100 to 120 Gy dose to the prescription point 5 mm above center, perpendicular to the plane. This point is illustrated in Figure 3. Since the treatment time in permanent implant brachytherapy is the same for different cases (source mean lifetime) the comparison of absorbed dose rate and absorbed dose is equivalent. To obtain depth dose with high resolution, 50 cubic voxels with 1 mm3 volume were considered on the central axis in a 5 cm depth. Using equation 1 and F6 tally outputs in a water environment initial strength per seed was calculated for each configuration in order to deliver 100 Gy to the prescription point. Mentioned source strength was used to calculate prescription dose in lung environment (using MC output in lung environment). Due to significant differences, source initial strength was modified by authors so that prescription dose difference between water and lung environments became almost zero (<0.5%). DW(TG-43) and DL(TG-43) are absorbed dose rates in water-equivalent and actual lung tissues by application of seed strength based on TG-43U1 protocol, respectively. DL(Mod) is lung absorbed dose rate considering modified source strength presented in this study. The maximum error in dose calculation was below 0.5% at the first 2 cm and below 1% between 2 to 5 cm. The percentage dose differences between two cases were calculated as below:

Figure3

Prescription point at the center of red cube (voxel) at 0.5 cm along central axis of seeds’ plane. The voxel dimension is 1×1×1 mm3.

%Diff = [(DL - DW) / DW] × 100 = [(DL / DW) - 1] × 100

where DL and DW are the absorbed dose rates of a particular voxel in lung and water-equivalent tissues, respectively. The percentage dose difference in lung between two situations (water-based vs. modified source strength) is calculated with a similar equation.

Results and Discussion

Multiple MCNP programs were programmed and implemented for different cases mentioned in the article. Different configurations of 125I and 103Pd seeds were simulated in protocol-based water-equivalent vs. actual lung environments and F6 tally outputs were obtained from 50 cubic voxels along central axis up to 5 cm depth. Using equation 1 and specific treatment time, the prescription dose was considered as 100 Gy in water environment (based on protocol) and source initial strength was obtained for 40, 50 and 60 seeds configurations. Protocol-based source strength is shown in Table 2 (labeled as AAPM TG-43) for various configurations of 125I and 103Pd seeds.

By using mentioned source strength, the total absorbed dose rate of each voxel (depth) was calculated by equation 1 in water (DW(TG-43)) and lung (DL(TG-43)) up to 5 cm depth. Significant differences in prescription dose were observed for different cases so that lung prescription dose (DL(TG-43) at d = 0.5 cm) was 23.2%, 20.8%, 18.2% and 18.6% higher than protocol recommendation (DW(TG-43) at d = 0.5 cm) for configurations I, II, III and IV of 125I seeds , respectively. Mentioned differences were 75.7%, 67.4%, 58.2% and 58.6% for configurations I, II, III and IV of 103Pd seeds, respectively. Therefore, protocol-based initial strength was modified by the present authors to new figures (Table 2) so that prescription dose differences between water and lung environments reached almost zero (< 0.5%) in all cases. Lung absorbed dose rate was also calculated with modified source strength, DL(Mod). Table 3 and Table 4 illustrate total absorbed dose rates (cGy.h-1) as function of distance for different configurations of 125I and 103Pd seeds calculated by using TG-43 protocol-based and modified source strength. In a study conducted by Chen [9], the mean radioactivity per seed were 0.48, 0.52, 0.44 and 0.39 mCi / seed for configurations I, II, III and IV of 125I seeds, respectively. The differences between modified source strength presented in this study and Chen’s study are 0%, -15.4%, -27.3% and -33.4% for mentioned arrangements, respectively. Another study conducted by Sutherland has reported modified radioactivities of 0.47, 0.43, 0.34 and 0.27 mCi / seed for configurations I, II, III and IV of 125I seeds, respectively. The differences between modified source strength presented in this study and Sutherland’s study [16] are 2.1%, 2.3%, -5.9% and -3.7% for mentioned configurations of 125I seeds, respectively. In the following, dose differences at other depths in water and lung environments were calculated by equation 2 and were compared to each other in a 5 cm distance. As it is seen in Table 5, if modified source strength were used in lung environment, the lung absorbed dose would modify -18.64%, -16.98%, -15.79% and -16.13% for configurations I, II, III and IV of 125I seeds, respectively. For 103Pd sources, this reduction is -42.82%, -40.24%, -37.18% and -36.79% for mentioned configurations, respectively (in the case of 103Pd, the modification of prescription dose is almost 2 times more than 125I). DL(TG-43) vs. DW(TG-43) and DL(Mod) vs. DW(TG-43) were compared at further depths (beyond the prescription point) and the ratio of DL/DW was obtained at different depths. It is seen that the ratio of DL/DW is a quadratic function of depth (DL/DW = a1(d)2 + a2(d) + a3). This ratio is greater when protocol-based source strength is used for both environments and becomes less in the case of using modified source strength for lung. However, this ratio is constantly a quadratic function of depth for all configurations of 125I and 103Pd seeds. All equations presented in Table 5 were obtained by curve fitting with R2>0.99. Because the equations of each column (Table 5) had close coefficients, the average of coefficients was used to obtain one equation for four configurations of seeds. Hence, for different configurations of 125I seeds, DL(TG-43) / DW(TG-43) gives a polynomial equation of grade two with a1 = 0.045, a2 = 0.13 and a3 = 1.13. The ratio DL(Mod) / DW(TG-43) gives another depth-dependent quadratic equation with a1 = 0.037, a2 = 0.11 and a3 = 0.94. These equations are shown in Figure 4. In addition, for different configurations of 103Pd seeds, DL(TG-43) / DW(TG-43) gives a polynomial equation of grade two with a1 = 0.43, a2 = -0.24 and a3 = 1.85 and DL(Mod) / DW(TG-43) gives similar equation with a1 = 0.26, a2 = -0.14 and a3 = 1.01, as well. These equations are shown in Figure 5.

Table 3

Total absorbed dose rate (cGy.h-1) as function of distance for different configurations of 125I seeds in water and lung environments calculated by equation 1.

Depth (cm)	Total Absorbed Dose Rate (cGy/h)
	DW(TG-43)				DL(TG-43)				DL(Mod)
	I	II	III	IV	I	II	III	IV	I	II	III	IV
0.1	5.74	5.93	5.01	6.12	7.07	7.14	5.64	7.06	5.75	5.93	4.75	5.92
0.2	5.63	5.77	5.70	5.99	6.81	6.85	6.43	6.87	5.54	5.69	5.41	5.76
0.3	5.38	5.54	5.66	5.64	6.49	6.56	6.47	6.55	5.28	5.45	5.45	5.49
0.4	5.12	5.20	5.35	5.26	6.27	6.22	6.20	6.14	5.10	5.16	5.22	5.15
0.5	4.82	4.89	4.90	4.84	5.94	5.91	5.79	5.74	4.83	4.90	4.88	4.82
0.6	4.53	4.54	4.48	4.43	5.65	5.57	5.40	5.33	4.59	4.63	4.54	4.47
0.7	4.23	4.21	4.07	4.07	5.34	5.25	5.00	4.97	4.35	4.36	4.21	4.17
0.8	3.93	3.90	3.70	3.70	5.02	4.92	4.64	4.65	4.08	4.09	3.91	3.90
0.9	3.62	3.58	3.39	3.39	4.74	4.62	4.34	4.29	3.86	3.84	3.65	3.60
1.0	3.39	3.31	3.10	3.15	4.48	4.33	4.03	4.03	3.64	3.59	3.39	3.38
1.1	3.14	3.07	2.86	2.87	4.23	4.08	3.80	3.80	3.44	3.38	3.20	3.19
1.2	2.91	2.83	2.63	2.64	3.99	3.84	3.56	3.57	3.25	3.19	3.00	2.99
1.3	2.71	2.60	2.43	2.44	3.78	3.59	3.36	3.35	3.08	2.98	2.83	2.81
1.4	2.51	2.44	2.25	2.26	3.58	3.42	3.14	3.17	2.91	2.84	2.64	2.66
1.5	2.33	2.24	2.08	2.06	3.41	3.22	2.97	2.95	2.78	2.67	2.50	2.48
1.6	2.15	2.09	1.93	1.91	3.25	3.07	2.82	2.78	2.64	2.55	2.37	2.34
1.7	2.00	1.95	1.79	1.78	3.06	2.89	2.67	2.63	2.49	2.40	2.25	2.21
1.8	1.89	1.82	1.67	1.66	2.93	2.74	2.53	2.49	2.38	2.28	2.13	2.09
1.9	1.77	1.70	1.54	1.55	2.77	2.61	2.40	2.35	2.25	2.17	2.02	1.97
2.0	1.65	1.58	1.45	1.43	2.65	2.46	2.28	2.23	2.15	2.05	1.92	1.87
2.1	1.53	1.47	1.34	1.33	2.50	2.35	2.14	2.13	2.03	1.95	1.80	1.79
2.2	1.44	1.36	1.24	1.25	2.38	2.24	2.04	2.04	1.94	1.86	1.72	1.71
2.3	1.35	1.28	1.16	1.17	2.28	2.14	1.93	1.94	1.85	1.78	1.63	1.63
2.4	1.26	1.19	1.08	1.10	2.18	2.05	1.85	1.85	1.77	1.70	1.55	1.55
2.5	1.18	1.11	1.03	1.01	2.09	1.94	1.77	1.75	1.70	1.61	1.49	1.47
2.6	1.12	1.05	0.95	0.95	2.00	1.87	1.69	1.67	1.63	1.56	1.42	1.40
2.7	1.04	0.98	0.90	0.88	1.91	1.79	1.61	1.59	1.55	1.48	1.35	1.33
2.8	0.99	0.93	0.84	0.82	1.84	1.69	1.55	1.53	1.50	1.41	1.31	1.28
2.9	0.92	0.87	0.78	0.78	1.74	1.63	1.47	1.47	1.42	1.36	1.24	1.23
3.0	0.86	0.80	0.72	0.73	1.66	1.56	1.40	1.40	1.35	1.29	1.18	1.17
3.1	0.79	0.75	0.68	0.67	1.59	1.50	1.35	1.33	1.29	1.24	1.14	1.11
3.2	0.73	0.69	0.64	0.63	1.53	1.41	1.29	1.27	1.24	1.17	1.09	1.06
3.3	0.69	0.66	0.60	0.60	1.47	1.35	1.24	1.22	1.20	1.12	1.04	1.02
3.4	0.66	0.62	0.58	0.56	1.42	1.30	1.18	1.16	1.15	1.08	0.99	0.97
3.5	0.63	0.59	0.53	0.52	1.36	1.25	1.13	1.11	1.11	1.04	0.95	0.92
3.6	0.60	0.55	0.50	0.49	1.32	1.21	1.10	1.08	1.07	1.01	0.92	0.90
3.7	0.55	0.50	0.46	0.47	1.25	1.15	1.05	1.04	1.02	0.95	0.88	0.86
3.8	0.51	0.47	0.43	0.43	1.21	1.10	1.00	0.98	0.98	0.91	0.84	0.82
3.9	0.50	0.46	0.41	0.40	1.15	1.08	0.96	0.95	0.93	0.89	0.81	0.80
4.0	0.47	0.43	0.39	0.38	1.11	1.04	0.92	0.91	0.90	0.86	0.78	0.76
4.1	0.43	0.41	0.37	0.36	1.08	0.99	0.89	0.87	0.87	0.82	0.75	0.73
4.2	0.40	0.38	0.35	0.34	1.03	0.96	0.88	0.83	0.83	0.80	0.74	0.69
4.3	0.38	0.35	0.33	0.32	1.01	0.92	0.83	0.81	0.82	0.76	0.70	0.67
4.4	0.36	0.34	0.31	0.29	0.97	0.88	0.80	0.78	0.79	0.73	0.67	0.66
4.5	0.34	0.32	0.29	0.28	0.92	0.85	0.76	0.75	0.75	0.71	0.64	0.63
4.6	0.32	0.30	0.27	0.27	0.90	0.81	0.72	0.72	0.73	0.67	0.61	0.60
4.7	0.31	0.28	0.26	0.25	0.86	0.80	0.70	0.69	0.70	0.66	0.59	0.58
4.8	0.29	0.27	0.25	0.24	0.83	0.76	0.68	0.67	0.67	0.63	0.57	0.56
4.9	0.27	0.25	0.23	0.22	0.79	0.72	0.65	0.64	0.64	0.60	0.55	0.54
5.0	0.26	0.24	0.22	0.21	0.76	0.70	0.64	0.62	0.62	0.58	0.54	0.52

Table 4

Total absorbed dose rate (cGy.h-1) as function of distance for different configurations of 103Pd seeds in water and lung environments calculated by equation 1.

Depth (cm)	Total Absorbed Dose Rate (cGy/h)
	DW(TG-43)				DL(TG-43)				DL(Mod)
	I	II	III	IV	I	II	III	IV	I	II	III	IV
0.1	21.4	21.0	17.8	22.5	36.9	35.0	27.0	33.8	21.1	20.9	17.0	21.4
0.2	21.0	20.8	19.2	22.1	34.7	33.4	28.3	32.7	19.8	19.9	17.8	20.6
0.3	19.7	19.7	20.1	20.9	33.4	31.5	29.8	31.9	19.1	18.8	18.7	20.2
0.4	18.7	18.2	18.6	18.8	31.6	29.9	28.8	29.5	18.1	17.8	18.1	18.6
0.5	16.9	16.9	17.0	16.9	29.7	28.3	26.9	26.8	16.9	16.9	16.9	16.9
0.6	15.5	15.2	15.0	15.1	27.7	26.5	25.3	25.7	15.8	15.8	15.9	16.2
0.7	14.3	13.8	13.4	13.5	26.9	25.16	23.3	23.7	15.4	15.0	14.6	14.9
0.8	12.6	12.5	11.9	12.1	25.1	23.3	21.6	22.1	14.3	13.9	13.6	14.0
0.9	11.5	10.9	10.6	10.6	23.0	21.2	20.2	19.6	13.1	12.6	12.7	12.3
1.0	10.2	9.85	9.35	9.46	21.7	19.8	18.5	18.6	12.4	11.8	11.6	11.7
1.1	9.41	8.83	8.19	8.42	20.3	18.5	17.3	16.9	11.6	11.0	10.9	10.7
1.2	8.37	7.82	7.36	7.58	19.2	17.4	15.9	16.2	11.0	10.4	10.0	10.2
1.3	7.50	6.95	6.67	6.56	18.1	16.0	15.0	15.1	10.3	9.61	9.45	9.55
1.4	6.88	6.28	5.98	5.90	17.1	15.5	14.1	14.1	9.80	9.29	8.85	8.94
1.5	6.22	5.74	5.28	5.26	16.1	14.6	13.3	13.2	9.21	8.76	8.41	8.35
1.6	5.52	5.14	4.69	4.72	15.2	13.9	12.2	12.4	8.74	8.32	7.69	7.84
1.7	5.08	4.70	4.15	4.28	14.2	12.9	11.5	11.6	8.15	7.71	7.24	7.35
1.8	4.57	4.22	3.82	3.87	13.7	12.1	10.8	10.8	7.87	7.26	6.84	6.88
1.9	3.92	3.79	3.50	3.40	12.7	11.5	10.3	10.5	7.28	6.88	6.51	6.65
2.0	3.58	3.44	3.09	3.11	12.0	10.9	9.53	9.63	6.89	6.52	5.98	6.09
2.1	3.29	3.07	2.75	2.90	11.2	10.2	9.01	9.26	6.44	6.11	5.66	5.85
2.2	3.04	2.77	2.50	2.62	10.7	9.63	8.73	8.95	6.16	5.75	5.48	5.65
2.3	2.82	2.55	2.25	2.30	10.0	9.34	8.10	8.16	5.73	5.58	5.08	5.15
2.4	2.54	2.30	2.02	2.08	9.65	8.53	7.59	7.67	5.51	5.10	4.77	4.85
2.5	2.12	2.10	1.83	1.90	9.15	8.31	7.32	7.25	5.23	4.96	4.60	4.58
2.6	1.99	1.91	1.69	1.74	8.82	7.94	6.86	6.98	5.04	4.75	4.31	4.41
2.7	1.93	1.64	1.61	1.59	8.17	7.27	6.71	6.69	4.67	4.34	4.21	4.23
2.8	1.61	1.56	1.42	1.49	7.63	6.92	6.27	6.35	4.36	4.14	3.93	4.01
2.9	1.47	1.43	1.25	1.28	7.30	6.60	5.87	5.83	4.17	3.94	3.68	3.68
3.0	1.34	1.29	1.12	1.15	6.90	6.35	5.60	5.57	3.94	3.79	3.51	3.52
3.1	1.26	1.12	1.07	1.04	6.66	6.00	5.33	5.17	3.81	3.58	3.34	3.27
3.2	1.18	1.00	0.93	0.97	6.28	5.78	4.94	5.11	3.59	3.45	3.10	3.23
3.3	1.04	0.93	0.83	0.90	6.13	5.41	4.77	4.83	3.50	3.23	2.99	3.05
3.4	0.95	0.85	0.81	0.80	5.96	5.07	4.66	4.62	3.41	3.03	2.93	2.92
3.5	0.90	0.78	0.72	0.73	5.78	4.93	4.50	4.48	3.30	2.94	2.83	2.83
3.6	0.79	0.76	0.65	0.70	5.39	4.73	4.36	4.14	3.08	2.83	2.74	2.61
3.7	0.71	0.67	0.62	0.58	5.12	4.56	4.02	4.04	2.93	2.72	2.52	2.55
3.8	0.65	0.61	0.54	0.52	4.91	4.23	3.83	3.82	2.80	2.52	2.40	2.41
3.9	0.62	0.57	0.51	0.46	4.74	4.16	3.74	3.56	2.71	2.48	2.35	2.25
4.0	0.59	0.49	0.48	0.42	4.53	4.00	3.52	3.21	2.59	2.39	2.21	2.03
4.1	0.54	0.48	0.45	0.41	4.20	3.87	3.39	3.11	2.40	2.31	2.13	1.97
4.2	0.44	0.43	0.39	0.42	4.06	3.56	3.18	3.04	2.32	2.13	2.00	1.92
4.3	0.44	0.36	0.38	0.37	3.98	3.39	3.03	3.08	2.27	2.02	1.90	1.95
4.4	0.45	0.34	0.34	0.32	3.77	3.21	2.91	2.84	2.15	1.91	1.82	1.79
4.5	0.43	0.30	0.30	0.30	3.57	3.06	2.74	2.89	2.04	1.83	1.72	1.83
4.6	0.36	0.29	0.27	0.27	3.43	3.00	2.57	2.62	1.96	1.79	1.61	1.65
4.7	0.29	0.28	0.24	0.22	3.26	2.85	2.49	2.65	1.86	1.70	1.56	1.67
4.8	0.28	0.23	0.22	0.21	2.98	2.75	2.47	2.44	1.70	1.64	1.55	1.54
4.9	0.27	0.22	0.23	0.20	2.92	2.64	2.22	2.16	1.67	1.58	1.40	1.37
5.0	0.22	0.20	0.22	0.19	2.87	2.49	2.22	2.08	1.64	1.49	1.39	1.31

Table 5

Percentage dose difference in lung (%Diff [DL(Mod) : DL(TG-43)]) due to modification of source strength; and the ratio of lung-water absorbed dose (DL/DW) in cases of using protocol and modified source strength for different configurations of 125I and 103Pd seeds.

	Seeds	%Diff [DL(Mod) : DL(TG-43)]	DL(TG-43) / DW(TG-43)	DL(Mod) / DW(TG-43)
	125I
I	40	- 18.64 %	= 0.046 (d)2 + 0.13 (d) + 1.16	= 0.038 (d)2 + 0.10 (d) + 0.94
II	40	- 16.98 %	= 0.045 (d)2 + 0.13 (d) + 1.13	= 0.038 (d)2 + 0.11 (d) + 0.94
III	50	- 15.79 %	= 0.041 (d)2 + 0.14 (d) + 1.11	= 0.035 (d)2 + 0.12 (d) + 0.94
IV	60	- 16.13 %	= 0.047 (d)2 + 0.12 (d) + 1.12	= 0.039 (d)2 + 0.10 (d) + 0.94
	103Pd
I	40	- 42.82 %	= 0.41 (d)2 - 0.13 (d) + 1.84	= 0.23 (d)2 - 0.07 (d) + 1.05
II	40	- 40.24 %	= 0.51 (d)2 - 0.58 (d) + 2.12	= 0.30 (d)2 - 0.34 (d) - 1.26
III	50	- 37.18 %	= 0.33 (d)2 + 0.14 (d) + 1.50	= 0.21 (d)2 + 0.09 (d) + 0.94
IV	60	- 36.79 %	= 0.47 (d)2 - 0.41 (d) + 1.94	= 0.30 (d)2 - 0.26 (d) + 1.23

Figure4

The ratio of DL/DW as function of depth for different configurations of 125I seeds. The average of coefficients in Table 5 were used to obtain a single equation for each case.

Figure5

The ratio of DL/DW as function of depth for different configurations of 103Pd seeds. The average of coefficients in table 5 were used to obtain a single equation for each case.

Based on results, it is obvious that a simple change (modification) in source strength for the prescription point cannot eliminate the depth-dependent differences between lung and water absorbed doses at other depths. Therefore, in addition to modified strength, the equations presented in Figure 4 and Figure 5 should also be considered. Due to the impossibility of dosimetry in actual lung and protocol-based calculation limitations, lung absorbed dose at different depths can be obtained directly from DW(TG-43) by mentioned equations. Dose differences between two environments result from particle transport and dose scoring. Due to the difference of water-lung electron densities (4:1), photon energy fluence is higher at deeper distances in lung environment. Energy absorbed per unit energy fluence and Roentgen-to-Rad conversion factors are other factors that cause differences between lung and water. Roentgen-to-Rad conversion factor is a function of material composition and photon energy. As regards to the results, it seems that the coincidence of these factors leads to a depth-dependent quadratic difference. It is necessary to point that these results are based on plane phantom geometry considering no deformation; while in reality there is sometimes seeds disarrangement or mesh deformation which can lead to asymmetric dose distribution and hot spots. In addition, although each single source was validated and benchmarked by the authors, inaccessibility to realistic patient data set restricts us to see how the presence of artifacts or tissue density (e.g. ribs) affects the dose distribution. On the other hand, at low energies like this, it is not clear yet how to specify dose to a medium (as dose to water in the medium). Therefore, Monte Carlo method is a unique way to calculate the absorbed dose with high accuracy in lung LDR brachytherapy. Another point is that using Monte Carlo method with accurate simulation of brachytherapy seeds can take some missing into consideration; interested effects and attenuation/changing of initially emitted photon that would not be considered through protocol-based point/line source calculations.

Conclusion

Different configurations of 125I and 103Pd brachytherapy sources which are used in lung permanent implantation were studied by Monte Carlo method in this research. Using AAPM TG-43U1 recommendations, protocol-based source strength was calculated to deliver recommended prescription dose in the water-equivalent environment. Lung absorbed dose was also calculated by mentioned source strength. Due to significant differences, protocol-based initial source strengths (initial air-kerma strength) were modified by the present authors for different configurations of 125I and 103Pd seeds so that prescription dose differences reached almost zero. However, further calculations at other depths indicated depth-dependent differences between lung and water environments in spite of prescription dose modifications. Therefore, several quadratic equations were obtained for different cases in form of DL/DW = a1(d)2 + a2(d) + a3 where D and d are absorbed dose and depth, respectively. Since the specification of dose to medium at low energies is not clear yet, and dosimetry in the actual lung is impractical, Monte Carlo method is a unique way of calculating absorbed dose, especially in LDR brachytherapy. Modified source strength and quadratic equations presented in this study are recommended to be considered in future studies based on lung permanent implant brachytherapy.