Monte Carlo modeling of ⁶⁰Co HDR brachytherapy source in water and in different solid water phantom materials

Abstract

The reference medium for brachytherapy dose measurements is water. Accuracy of dose measurements of brachytherapy sources is critically dependent on precise measurement of the source–detector distance. A solid phantom can be precisely machined and hence source–detector distances can be accurately determined. In the present study, four different solid phantom materials such as polymethylmethacrylate (PMMA), polystyrene, Solid Water, and RW1 are modeled using the Monte Carlo methods to investigate the influence of phantom material on dose rate distributions of the new model of BEBIG ⁶⁰Co brachytherapy source. The calculated dose rate constant is 1.086 ± 0.06% cGy h⁻¹ U⁻¹ for water, PMMA, polystyrene, Solid Water, and RW1. The investigation suggests that the phantom materials RW1 and Solid Water represent water-equivalent up to 20 cm from the source. PMMA and polystyrene are water-equivalent up to 10 cm and 15 cm from the source, respectively, as the differences in the dose data obtained in these phantom materials are not significantly different from the corresponding data obtained in liquid water phantom. At a radial distance of 20 cm from the source, polystyrene overestimates the dose by 3% and PMMA underestimates it by about 8% when compared to the corresponding data obtained in water phantom.

Introduction

A high-dose-rate (HDR) ⁶⁰Co source is used for the treatment of gynecological cancers due to its longer half-life as compared with the more conventional ¹⁹²Ir source.[1–3] The AAPM (American Association of Physicists in Medicine) GEANT4-based Monte Carlo dosimetric parameters have been reported in the literature for the old and new designs of BEBIG ⁶⁰Co sources[1,2] using TG-43 protocol.[4,5] The accuracy in dosimetric measurement depends upon precise positioning of the detectors and maintaining correct distances between the source and detector. In order to achieve precision in the positioning of detectors, ease in machining in suitable designs, and convenience in handling, various Solid Water–equivalent phantoms are used. The accuracy in dosimetry data also depends upon the exact chemical composition of the solid materials and their radiation characteristics, i.e., attenuation and scattering in experimental measurement and cross-sectional data accuracy in Monte Carlo codes. There are many published dosimetric studies based on experimental and Monte Carlo methods for ¹²⁵I and ¹⁰³Pd brachytherapy sources in different phantom materials.[6–10] However, there is no such published data for the ⁶⁰Co HDR brachytherapy sources.

The objective of the present study is to investigate the influence of different solid phantom materials such as polymethylmethacrylate (common name: PMMA or Perspex or acrylic), polystyrene, Solid Water, and RW1 on dosimetric parameters of the new model of BEBIG ⁶⁰Co HDR source. We have employed the Monte Carlo-based MCNP code for this purpose.[11]

Materials and Methods

Radioactive source

The geometry of the new BEBIG ⁶⁰Co brachytherapy source[1] is slightly different from the old one.[2] The new BEBIG ⁶⁰Co source is composed of a cylindrical active core made of metallic⁶⁰Co, with 3.5 mm of active length and an active diameter of 0.5 mm (0.6 mm was the active diameter of the old source), covered by a 0.15-mm thick 316L stainless steel capsule. Note that there is an air gap of 0.1 mm around the active ⁶⁰Co pellet. A schematic view of the new BEBIG ⁶⁰Co source is shown in Figure 1. The technical details of the source were obtained from the manufacturer.

Figure 1.

Schematic diagram of the new BEBIG ⁶⁰Co HDR source in the Monte Carlo simulations. Dimensions shown are in millimeters (not to scale). (b) The co-ordinate system used in the Monte Carlo simulations.

The origin is chosen at the center of the active source

Monte Carlo simulations

Monte Carlo-based MCNP code[11] is used for modeling of the BEBIG new ⁶⁰Co source in different Solid Water phantom materials, including liquid water. The material, mass density data, and geometric details of the new BEBIG ⁶⁰Co source needed for Monte Carlo modeling are taken from Granero et al.[1] Tables 1 and 2 present the material description (density, composition, etc.) for the source and the investigated phantom materials, respectively.

Table 1.

Atomic composition by weight and density of the new BEBIG ⁶⁰Co HDR source

Component	Source material	Atomic composition (%)	Density (g/cm3)
Active source	Cobalt	100 %	8.9
Encapsulation	Stainless steel (AISI 316L)	C(0.026%), Mn(1.4%), Si(0.42%), P(0.019%), S(0.003%), Cr(16.8%), Mo(2.11%), Ni(11.01%), Fe(68.21%)	7.8

Table 2.

Elemental composition, mass fraction, density and Z_eff. of water and water-substitute solid phantom materials. Densities are adapted from Hubbell and Seltzer (1995)

Element		Z	A	Water	Solid Water	RW1	PMMA	Polystyrene
Composition and mass fraction in %	H	1	1.008	0.112	0.081	0.132	0.081	0.077
	C	6	12.011		0.672	0.794	0.600	0.923
	N	7	14.007		0.024
	O	8	15.999	0.888	0.199	0.038	0.320
	Mg	12	24.305			0.009
	Cl	17	35.457		0.001	0.027
	Ca	20	40.078		0.023
Mass density (g/cm3)				0.998	1.015	0.970	1.190	1.060
Zeff. (Calculated)				7.416	7.294	7.210	6.096	5.584

In the Monte Carlo simulations, we have used 1.17 and 1.33 MeV gamma energy lines of ⁶⁰Co emission (yield: 2 photons/disintegration) in all calculations. The cutoff energy for photon transport in all calculations was 10 keV. Figure 1 shows the cross-sectional view of the new BEBIG ⁶⁰Co HDR source modeled in the Monte Carlo calculations. Also shown in this figure is the coordinate system used in the calculations. In the calculations, the origin coincided with the center of the active part of the sources [Figure 1]. In the Monte Carlo calculations, the length of the stainless steel cable considered is 2 mm.

Air-kerma strength

To estimate the value of air-kerma strength, S_k, the source was positioned at the center of a 5-m diameter air phantom. The photon fluence spectra at every 10 keV interval were scored along the transverse axis at y = 25, 50, 75, and 100 cm, using a point detector tally; this was subsequently converted into air-kerma per initial photon, k_air (Gy/initial photon) using the mass-energy-absorption coefficient of air.[12] The k_air (y) values were then converted to air-kerma rate per unit activity, ${\stackrel{.}{k}}_{air}\left(y\right)/A$ (in cGy h⁻¹ Bq⁻¹). The value of S_K is calculated using the linear equation fitting, i.e.,

$\left[{\stackrel{.}{k}}_{air}\left(y\right)/A\right]*y^2=S_k/A+b.y$

where S_k/A is S_K per unit source activity A (in cGy cm² h⁻¹ Bq⁻¹ or U Bq⁻¹) and b describes the build-up of scattered photons. The density of air is 1.2 × 10⁻³ g cm⁻³ and the elemental composition of air corresponds to 40% humidity. This is consistent with the updated TG-43U1 formalism.[4]

Water-kerma calculations in water and solid phantoms

Due to the high energy of the ⁶⁰Co gamma source, electronic disequilibrium exists up to 1 cm from the source.[2] A significant difference in dose and kerma values (up to 20% at 2 mm), was observed at distances less than 5 mm.[3] In our calculations, we have ignored transport of secondary electrons. In our calculations, we have scored collision kerma and, in the presence of charged particle equilibrium, collision kerma may be approximated to the absorbed dose.

Previous published studies suggest that spherical water phantom of 50-cm radius acts as an unbound phantom for BEBIG ⁶⁰Co sources up to a distance of 20 cm.[2,3] In order to calculate dose rate distribution in water as well as in solid phantom materials, the source was located in the center of a cylindrical phantom of 100-cm diameter and 100-cm height to get full scatter conditions up to a distance of 20 cm from the source. The density of water was taken 0.998 g cm⁻³ (at 22°C) as recommended in the TG-43 update.[4]

A grid system was set up with cells defined as symmetrical rings around z-axis with rectangular cross-section δy – δz (δy = δz = 0.5 mm) in the y–z plane. Initially, photon energy fluence spectra were calculated as functions of Cartesian coordinates y and z (z is distance along source axis, y is distance away from the source) for all the investigated phantom materials. We used the F4 tallying feature of the MCNP code for this purpose. The photon spectrum at each position (y,z) was subsequently converted to collision kerma by using the mass-energy-absorption coefficients of water.[12] Using the collision kerma values scored in the phantom materials, dose rate constant (λ) and radial dose function [g_L(r)] were calculated. We used the line source–based geometry function, G_L(r,θ), for calculating g_L(r). This is consistent with the TG-43 update.[4]

Depending upon the simulation, up to 5 × 10⁷ primary photon histories are simulated. The simulations are run on a Dual-core CPU, 3.4 GHz machine. Depending upon the scoring regions positioned with respect to the origin of the coordinate system used, the 1 σ statistical uncertainties on collision kerma values vary between 0.04% and 2%.

Results and Discussion

Photon energy spectrum

Figure 2 presents the normalized photon fluence spectra calculated for the BEBIG new HDR ⁶⁰Co source at 1 cm, 5 cm, and 20 cm along the transverse axis of the source in the spherical water phantom with dimensions of 100-cm radius. Also presented in Figure 2 is the spectrum obtained at 50 cm along the transverse axis of the source in a 500-cm radius air and vacuum sphere. In the Monte Carlo calculations, the photon fluence spectra were scored in a 20 keV energy bin. The bin width at ⁶⁰Co energies, 1.17 MeV and 1.33 MeV, was chosen at 2 keV. The photon fluence in each energy bin was normalized to the total photon fluence. Figure 2 demonstrates the influence of the water medium on the photon fluence spectrum. As the distance increases, the relative fluence of low-energy photons increases due to multiple scattering of photons in the water medium.

Figure 2.

Energy spectra of the new BEBIG ⁶⁰Co HDR source at 1, 5, and 20 cm in water and at 50 cm in air and in vacuum. The radii of the sphere considered are 500 cm for air and vacuum and 100 cm for water

Following is the analysis of the distribution of the energy spectrum of photons exiting the source capsule in a vacuum. The predominant mode of photon interaction at ⁶⁰Co energies (average energy = 1.25 MeV) is through Compton scattering. In normal circumstances, all scattering angles will occur in the detector, yielding a continuum of scattered photons with energies ranging from 1.25 MeV down to the minimum possible energy, $h{v}_{\min }^{/}$, which occurs when an incident photon is backscattered through an angle of 180°; this is given by, $h{v}_{\min }^{/}=\frac{hv}{1+2\alpha }$ where hv is the energy of the incident primary photon, $\alpha =\raisebox{1ex}{$hv$}\!\left/ \!\raisebox{-1ex}{$m_0{c}^2$}\right.$, and m_oc² is the rest mass energy of the electron (511 keV). For a primary photon of energy 1.25 MeV, the $h{v}_{\min }^{/}$ is 212 keV, which is consistent with Figure 2, with the drop-off in the number of photons below the 210 keV energy bin.

Air-kerma strength and dose rate constant

The calculated value of S_K/A for the BEBIG ⁶⁰Co source is found to be 3.04 × 10⁻⁷ ± 0.05% cGy cm² h⁻¹ Bq⁻¹. The source is also simulated at the center of a 5-m diameter vacuum sphere and the values of S_k obtained is found to be same as that obtained in air.

The value of λ is 1.086 ± 0.06% cGy h⁻¹ U⁻¹ for water, PMMA, polystyrene, Solid Water, and RW1 phantom materials. This is in good agreement with GEANT Monte Carlo-based published value 1.087 ± 0.011 cGy h⁻¹ U⁻¹ in the water medium.[1]

It has been shown by Papagiannis et al,[3] that λ, for any source design of ⁶⁰Co, can be accurately determined using the corresponding point source–based dose rate constant, λ_point, (λ_point = 1.094 cGy h⁻¹ U⁻¹). The λ of real source is dictated by the spatial distribution of radioactivity addressed by the exact geometry factor and, at 1 cm along transverse axis from the source, the line source based geometry factor may well be approximated to the exact geometry factor. The value of λ obtained for the BEBIG ⁶⁰Co source, using the equation λ = λ_point × G_L (r = 1 cm, θ = 90°) is 1.083 cGy h⁻¹ U⁻¹.

Radial dose function, g_L (r)

The Monte Carlo calculated values of g_L (r) for the new BEBIG ⁶⁰Co source are presented in Table 3 for water, PMMA, polystyrene, Solid Water, and RW1 phantom materials. In Figure 3, these g_L(r) results are plotted vs radial distance, r. The values of g_L(r) in water has been fitted to a third-order polynomial for r = 0.2 cm to 20 cm. The co-efficients obtained as a₀ = 1.0118, a₁ = −0.01225 cm⁻¹, a₂ = −3.39297 × 10⁻⁴ cm⁻², and a₃ = 3.9995 × 10⁻⁶ cm⁻³. The fitted values of g_L(r) agree with the corresponding Monte Carlo calculated values obtained in the present work as well as with the published values.[1]

Table 3.

Comparison of radial dose function g_L(r) of the new BEBIG ⁶⁰Co HDR source in water and four water-equivalent solid phantom materials. The dimensions of cylindrical phantom are 100 cm diameter × 100 cm height

Distance r(cm)	gL(r)
	Water	PMMA	Polystyrene	RW1	Solid Water
0.2	1.014	1.016	1.014	1.014	1.014
0.3	1.010	1.012	1.010	1.010	1.010
0.4	1.008	1.010	1.009	1.008	1.009
0.5	1.007	1.008	1.007	1.007	1.007
0.6	1.003	1.004	1.004	1.004	1.003
0.7	1.002	1.003	1.002	1.002	1.002
0.8	1.001	1.002	1.001	1.001	1.001
0.9	1.001	1.002	1.001	1.001	1.001
1	1.000	1.000	1.000	1.000	1.000
1.2	0.996	0.996	0.996	0.997	0.996
1.4	0.992	0.992	0.992	0.993	0.992
1.5	0.992	0.992	0.992	0.993	0.992
1.8	0.987	0.985	0.986	0.987	0.987
2	0.985	0.983	0.986	0.985	0.985
2.5	0.979	0.976	0.979	0.979	0.979
3	0.972	0.965	0.970	0.972	0.971
3.5	0.960	0.957	0.962	0.961	0.961
4	0.957	0.946	0.957	0.957	0.957
4.5	0.947	0.939	0.948	0.949	0.948
5	0.940	0.932	0.941	0.940	0.940
6	0.926	0.919	0.928	0.926	0.927
7	0.918	0.905	0.920	0.918	0.918
8	0.900	0.880	0.905	0.900	0.901
9	0.882	0.866	0.883	0.883	0.882
10	0.860	0.840	0.871	0.862	0.863
11	0.841	0.818	0.852	0.845	0.844
12	0.820	0.799	0.830	0.822	0.821
13	0.799	0.770	0.809	0.802	0.801
14	0.788	0.749	0.796	0.789	0.786
15	0.759	0.732	0.772	0.763	0.760
18	0.708	0.665	0.716	0.705	0.703
20	0.663	0.625	0.681	0.658	0.657

The radial dose function of BEBIG new HDR ⁶⁰Co source in water has been fitted to a 3^rd order polynomial between r = 0.2 − 20 cm. The co-efficients obtained as a₀ = 1.0118, a₁ = −0.01225 cm⁻¹, a₂ = −3.39297 × 10⁻⁴ cm⁻² and a₃ = 3.9995 × 10⁻⁶ cm⁻³.

Figure 3.

Radial dose function of the new BEBIG HDR ⁶⁰Co source in water and in solid phantom materials such as PMMA, polystyrene, RW1, and Solid Water

Dose variation in different phantoms

Tables 4–6 present dose rate distributions in the Cartesian format (in cGy h⁻¹ U⁻¹) around the BEBIG new ⁶⁰Co source in water, PMMA, and polystyrene phantom materials, respectively. The dosimetric data in RW1 and Solid Water is not presented because these two phantoms produced the same dose results as that of water. For radial distances up to 10 cm, PMMA is water-equivalent as PMMA underestimates dose by about only 3% at 10 cm. At radial distances 15 cm and 20 cm, PMMA underestimates the dose by about 5% and 8%, respectively. A similar comparison of dose values in the polystyrene phantom suggests that polystyrene is water-equivalent up to a radial distance of 10 cm from the source. At radial distances 15 cm and 20 cm, polystyrene overestimates the dose by less than 2% and 3%, respectively.

Table 4.

Dose rate per unit air-kerma strength (in cGy h⁻¹ U⁻¹) in an unbounded water phantom for the new BEBIG ⁶⁰Co HDR source

Away distance, y (cm)
Along distance, z(cm)	0	0.5	0.75	1	1.5	2	2.5	3	4	5	6	8	10	15
−15	0.00347	0.00346	0.00346	0.00342	0.00344	0.00341	0.00341	0.00342	0.00334	0.00321	0.00305	0.00270	0.00236	0.00156
−10	0.00839	0.00847	0.00843	0.00855	0.00871	0.00863	0.00836	0.00829	0.00783	0.00720	0.00658	0.00535	0.00424	0.00238
−8	0.0137	0.0137	0.0137	0.0141	0.0140	0.0137	0.0134	0.0129	0.0118	0.0105	0.00928	0.00708	0.00534	0.00273
−6	0.0251	0.0253	0.0258	0.0256	0.0253	0.0245	0.0234	0.0218	0.0189	0.0159	0.0133	0.00934	0.00663	0.00311
−5	0.0365	0.0371	0.0379	0.0381	0.0364	0.0346	0.0320	0.0296	0.0244	0.0198	0.0159	0.0106	0.00725	0.00326
−4	0.0584	0.0596	0.0599	0.0592	0.0559	0.0510	0.0460	0.0410	0.0317	0.0243	0.0190	0.0119	0.00789	0.00341
−3	0.104	0.109	0.108	0.104	0.0927	0.0806	0.0682	0.0576	0.0410	0.0297	0.0221	0.0132	0.00848	0.00354
−2.5	0.151	0.158	0.153	0.146	0.124	0.103	0.0841	0.0686	0.0465	0.0324	0.0237	0.0138	0.00877	0.00359
−2	0.239	0.246	0.233	0.213	0.171	0.133	0.103	0.0806	0.0516	0.0352	0.0251	0.0143	0.00895	0.00363
−1.5	0.431	0.429	0.384	0.333	0.240	0.171	0.125	0.0937	0.0570	0.0375	0.0263	0.0147	0.00913	0.00365
−1	0.995	0.881	0.702	0.546	0.333	0.215	0.147	0.106	0.0614	0.0395	0.0272	0.0150	0.00920	0.00368
−0.75	1.83	1.37	0.978	0.700	0.385	0.235	0.157	0.111	0.0628	0.0402	0.0276	0.0150	0.00930	0.00368
−0.5	4.52	2.24	1.35	0.873	0.433	0.253	0.164	0.115	0.0641	0.0405	0.0278	0.0151	0.00932	0.00368
−0.25	-	3.50	1.74	1.02	0.468	0.265	0.169	0.117	0.0650	0.0410	0.0280	0.0152	0.00935	0.00372
0	-	4.26	1.92	1.09	0.482	0.269	0.171	0.118	0.0653	0.0411	0.0281	0.0153	0.00939	0.00370
0.25	-	3.50	1.74	1.02	0.469	0.265	0.169	0.117	0.0650	0.0411	0.0279	0.0151	0.00935	0.00371
0.5	4.76	2.24	1.35	0.874	0.433	0.253	0.165	0.115	0.0641	0.0407	0.0279	0.0151	0.00930	0.00372
0.75	1.95	1.37	0.979	0.698	0.385	0.235	0.157	0.111	0.0631	0.0402	0.0276	0.0151	0.00927	0.00368
1	1.06	0.881	0.703	0.546	0.333	0.215	0.147	0.106	0.0612	0.0394	0.0272	0.0150	0.00924	0.00370
1.5	0.460	0.429	0.385	0.333	0.239	0.171	0.125	0.0939	0.0570	0.0375	0.0263	0.0147	0.00915	0.00368
2	0.255	0.247	0.233	0.214	0.171	0.133	0.103	0.0809	0.0518	0.0352	0.0251	0.0143	0.00896	0.00363
2.5	0.162	0.160	0.153	0.145	0.124	0.103	0.0841	0.0683	0.0463	0.0325	0.0237	0.0137	0.00878	0.00359
3	0.111	0.111	0.108	0.104	0.0930	0.0805	0.0684	0.0578	0.0410	0.0298	0.0221	0.0132	0.00847	0.00355
4	0.0615	0.0609	0.0604	0.0596	0.0563	0.0512	0.0461	0.0408	0.0316	0.0244	0.0190	0.0119	0.00794	0.00343
5	0.0387	0.0391	0.0385	0.0382	0.0366	0.0348	0.0323	0.0296	0.0244	0.0198	0.0160	0.0106	0.00726	0.00327
6	0.0265	0.0264	0.0261	0.0261	0.0254	0.0248	0.0232	0.0220	0.0189	0.0159	0.0134	0.00937	0.00664	0.00311
8	0.0144	0.0147	0.0145	0.0142	0.0142	0.0138	0.0134	0.0130	0.0117	0.0106	0.00930	0.00707	0.00535	0.00274
10	0.00882	0.00863	0.00891	0.00890	0.00884	0.00869	0.00847	0.00826	0.00783	0.00715	0.00657	0.00533	0.00424	0.00239
15	0.0035	0.00362	0.00353	0.00349	0.00355	0.00351	0.00344	0.00342	0.00336	0.00322	0.00307	0.00273	0.00235	0.00156

Table 6.

Dose rate per unit air-kerma strength (in cGy h⁻¹ U⁻¹) in an unbounded polystyrene phantom for the new BEBIG ⁶⁰Co HDR source

Away distance, y (cm)
Along distance, z(cm)	0	0.5	0.75	1	1.5	2	2.5	3	4	5	6	8	10	15
−15	0.00349	0.00350	0.00350	0.00351	0.00352	0.00347	0.00348	0.00349	0.00341	0.00327	0.00310	0.00276	0.00241	0.00160
−10	0.00856	0.00854	0.00848	0.00862	0.00874	0.00872	0.00845	0.00835	0.00791	0.00727	0.00664	0.00541	0.00430	0.00243
−8	0.0138	0.0138	0.0138	0.0142	0.0141	0.0138	0.0134	0.0130	0.0119	0.0106	0.00935	0.00713	0.00541	0.00278
−6	0.0250	0.0254	0.0258	0.0257	0.0254	0.0246	0.0235	0.0219	0.0190	0.0160	0.0134	0.00942	0.00669	0.00316
−5	0.0365	0.0372	0.0380	0.0381	0.0365	0.0347	0.0321	0.0297	0.0244	0.0199	0.0160	0.0107	0.00733	0.00332
−4	0.0580	0.0597	0.0600	0.0592	0.0560	0.0510	0.0460	0.0411	0.0318	0.0244	0.0190	0.0120	0.00795	0.00347
−3	0.104	0.109	0.108	0.104	0.093	0.081	0.0683	0.0576	0.0411	0.0298	0.0221	0.0132	0.00855	0.00359
−2.5	0.152	0.158	0.153	0.146	0.124	0.103	0.0841	0.0687	0.0465	0.0324	0.0238	0.0138	0.00884	0.00365
−2	0.239	0.246	0.233	0.213	0.170	0.133	0.103	0.0807	0.0516	0.0353	0.0252	0.0143	0.00900	0.00368
−1.5	0.431	0.429	0.384	0.333	0.239	0.171	0.125	0.0937	0.0570	0.0376	0.0264	0.0147	0.00920	0.00371
−1	0.995	0.881	0.702	0.546	0.332	0.215	0.147	0.106	0.0615	0.0395	0.0273	0.0150	0.00926	0.00375
−0.75	1.830	1.37	0.978	0.699	0.385	0.235	0.157	0.111	0.0629	0.0402	0.0276	0.0151	0.00937	0.00375
−0.5	4.52	2.24	1.35	0.873	0.433	0.253	0.164	0.115	0.0641	0.0406	0.0279	0.0152	0.00939	0.00373
−0.25	-	3.50	1.74	1.02	0.468	0.265	0.169	0.117	0.0651	0.0410	0.0280	0.0152	0.00941	0.00377
0	-	4.26	1.92	1.09	0.482	0.269	0.171	0.118	0.0654	0.0412	0.0282	0.0153	0.00946	0.00377
0.25	-	3.50	1.74	1.02	0.469	0.265	0.169	0.117	0.0651	0.0411	0.0280	0.0152	0.00942	0.00377
0.5	4.76	2.24	1.35	0.874	0.433	0.253	0.165	0.115	0.0641	0.0407	0.0279	0.0152	0.00937	0.00377
0.75	1.95	1.37	0.979	0.698	0.385	0.235	0.157	0.111	0.0632	0.0402	0.0277	0.0152	0.00934	0.00374
1	1.06	0.881	0.703	0.546	0.333	0.215	0.147	0.106	0.0613	0.0394	0.0272	0.0150	0.00932	0.00375
1.5	0.460	0.429	0.385	0.333	0.239	0.171	0.125	0.0939	0.0571	0.0376	0.0263	0.0147	0.00922	0.00373
2	0.255	0.248	0.233	0.214	0.171	0.133	0.103	0.0809	0.0518	0.0353	0.0252	0.0143	0.00901	0.00370
2.5	0.162	0.160	0.153	0.145	0.124	0.103	0.084	0.0684	0.0463	0.0326	0.0238	0.0138	0.00884	0.00365
3	0.111	0.111	0.108	0.104	0.0931	0.0805	0.0684	0.0578	0.0410	0.0298	0.0222	0.0133	0.00855	0.00361
4	0.0618	0.0610	0.0605	0.0597	0.0564	0.0513	0.0462	0.0409	0.0317	0.0245	0.0191	0.0120	0.00801	0.00348
5	0.0387	0.0391	0.0387	0.0382	0.0366	0.0349	0.0323	0.0297	0.0245	0.0199	0.0161	0.0107	0.00733	0.00332
6	0.0265	0.0266	0.0263	0.0261	0.0255	0.0248	0.0233	0.0220	0.0189	0.0160	0.0134	0.00943	0.00670	0.00317
8	0.0144	0.0147	0.0146	0.0143	0.0143	0.0139	0.0134	0.0131	0.0118	0.0107	0.0094	0.00715	0.00541	0.00280
10	0.00889	0.00867	0.00901	0.00901	0.00893	0.00875	0.00853	0.00834	0.00790	0.00724	0.00664	0.00539	0.00431	0.00244
15	0.00366	0.00366	0.00358	0.00360	0.00362	0.00357	0.00350	0.00350	0.00342	0.00328	0.00312	0.00279	0.00241	0.00160

Table 5.

Dose rate per unit air-kerma strength (in cGy h⁻¹ U⁻¹) in an unbounded PMMA phantom for the new BEBIG ⁶⁰Co HDR source

Away distance, y (cm)
Along distance, z(cm)	0	0.5	0.75	1	1.5	2	2.5	3	4	5	6	8	10	15
−15	0.00329	0.00328	0.00330	0.00331	0.00330	0.00329	0.00327	0.00328	0.00321	0.00304	0.00290	0.00256	0.00223	0.00144
−10	0.00821	0.00830	0.00826	0.00833	0.00847	0.00844	0.00816	0.00808	0.00761	0.00698	0.00638	0.00515	0.00406	0.00224
−8	0.0135	0.0135	0.0136	0.0138	0.0137	0.0134	0.0131	0.0127	0.0116	0.0103	0.00903	0.00686	0.00516	0.00258
−6	0.0249	0.0251	0.0255	0.0254	0.0250	0.0242	0.0231	0.0215	0.0186	0.0156	0.0131	0.00910	0.00642	0.00295
−5	0.0363	0.0369	0.0376	0.0377	0.0361	0.0342	0.0316	0.0292	0.0240	0.0194	0.0156	0.0104	0.00705	0.00310
−4	0.0575	0.0592	0.0595	0.0587	0.0554	0.0506	0.0456	0.0405	0.0313	0.0240	0.0186	0.0116	0.00767	0.00326
−3	0.104	0.108	0.107	0.103	0.0920	0.0799	0.0677	0.0570	0.0405	0.0293	0.0217	0.0129	0.00827	0.00337
−2.5	0.151	0.158	0.152	0.145	0.124	0.102	0.0833	0.0681	0.0459	0.0320	0.0233	0.0134	0.00852	0.00342
−2	0.239	0.245	0.232	0.212	0.170	0.132	0.102	0.0800	0.0511	0.0347	0.0247	0.0140	0.00870	0.00346
−1.5	0.432	0.428	0.383	0.331	0.238	0.171	0.124	0.0930	0.0565	0.0371	0.0259	0.0144	0.00889	0.00349
−1	0.997	0.880	0.700	0.544	0.331	0.214	0.146	0.105	0.0608	0.0391	0.0268	0.0147	0.00897	0.00352
−0.75	1.83	1.37	0.977	0.697	0.384	0.234	0.156	0.110	0.0623	0.0397	0.0272	0.0147	0.00906	0.00352
−0.5	4.52	2.23	1.35	0.871	0.432	0.252	0.163	0.114	0.0635	0.0400	0.0275	0.0149	0.00908	0.00351
−0.25	-	3.50	1.74	1.02	0.466	0.264	0.168	0.116	0.0644	0.0405	0.0276	0.0149	0.00909	0.00355
0	-	4.25	1.92	1.09	0.480	0.268	0.170	0.117	0.0647	0.0406	0.0277	0.0150	0.00912	0.00354
0.25	-	3.50	1.74	1.02	0.468	0.264	0.168	0.116	0.0645	0.0406	0.0276	0.0149	0.00912	0.00354
0.5	4.76	2.24	1.35	0.872	0.432	0.252	0.164	0.114	0.0635	0.0402	0.0275	0.0148	0.00910	0.00355
0.75	1.95	1.37	0.977	0.696	0.384	0.234	0.156	0.110	0.0626	0.0397	0.0272	0.0148	0.00904	0.00353
1	1.060	0.879	0.702	0.544	0.331	0.214	0.146	0.105	0.0606	0.0390	0.0268	0.0147	0.00902	0.00352
1.5	0.459	0.428	0.384	0.331	0.238	0.170	0.124	0.093	0.0564	0.0371	0.0259	0.0144	0.00892	0.00349
2	0.255	0.247	0.232	0.213	0.170	0.132	0.103	0.0800	0.0513	0.0348	0.0247	0.0140	0.00872	0.00346
2.5	0.161	0.159	0.153	0.144	0.124	0.102	0.0830	0.0680	0.0458	0.0321	0.0233	0.0135	0.00851	0.00342
3	0.111	0.110	0.107	0.104	0.0924	0.0798	0.0678	0.0573	0.0405	0.0293	0.0218	0.0130	0.00825	0.00337
4	0.0610	0.0604	0.0600	0.0592	0.0558	0.0507	0.0456	0.0404	0.0313	0.0241	0.0187	0.0117	0.00773	0.00326
5	0.0388	0.0388	0.0383	0.0378	0.0362	0.0344	0.0319	0.0292	0.0240	0.0195	0.0157	0.0104	0.00707	0.00311
6	0.0269	0.0262	0.0259	0.0258	0.0250	0.0245	0.0229	0.0216	0.0185	0.0157	0.0131	0.00913	0.00643	0.00296
8	0.0164	0.0144	0.0142	0.0139	0.0139	0.0135	0.0131	0.0127	0.0115	0.0103	0.00906	0.00687	0.00515	0.00259
10	0.00863	0.00847	0.00871	0.00872	0.00863	0.00847	0.00823	0.00805	0.00761	0.00695	0.00637	0.00513	0.00408	0.00225
15	0.00335	0.00352	0.00336	0.00336	0.00337	0.00338	0.00331	0.00329	0.00322	0.00307	0.00291	0.00259	0.00221	0.00145

Conclusions

The dose rate per unit air-kerma strength around the new BEBIG HDR ⁶⁰Co source in water, PMMA, and polystyrene materials are calculated using the Monte Carlo methods. The investigation suggests that the phantom materials RW1 and Solid Water represent water-equivalent at all distances from the source. PMMA and polystyrene are water-equivalent up to 10 cm and 15 cm from the source, respectively, as the differences in the dose data obtained in these phantom materials are not significant when compared to the corresponding data in water. In general, all the investigated phantom materials are water-equivalent up to 10 cm from the source.