Dosimetric characterization of the GammaClip™ ¹⁶⁹Yb low dose rate permanent implant brachytherapy source for the treatment of nonsmall cell lung cancer postwedge resection

Abstract

Purpose: A novel ¹⁶⁹Yb low dose rate permanent implant brachytherapy source, the GammaClip™, was developed by Source Production & Equipment Co. (New Orleans, LA) which is designed similar to a surgical staple while delivering therapeutic radiation. In this report, the brachytherapy source was characterized in terms of “Dose calculation for photon-emitting brachytherapy sources with average energy higher than 50 keV: Report of the AAPM and ESTRO” by Perez-Calatayud [Med. Phys. 39, 2904–2929 (2012)]10.1118/1.3703892 using the updated AAPM Task Group Report No. 43 formalism.

Methods: Monte Carlo calculations were performed using Monte Carlo N-Particle 5, version 1.6 in water and air, the in-air photon spectrum filtered to remove photon energies below 10 keV in accordance with TG-43U1 recommendations and previously reviewed ¹⁶⁹Yb energy cutoff levels [D. C. Medich, M. A. Tries, and J. M. Munro, “Monte Carlo characterization of an Ytterbium-169 high dose rate brachytherapy source with analysis of statistical uncertainty,” Med. Phys. 33, 163–172 (2006)]10.1118/1.2147767. TG-43U1 dosimetric data, including S_K, $\dot{D}(r,\theta )$, Λ, g_L(r), F(r, θ), ϕ_an(r), and ${\overline{\varphi }}_{an}$ were calculated along with their statistical uncertainties. Since the source is not axially symmetric, an additional set of calculations were performed to assess the resulting axial anisotropy.

Results: The brachytherapy source's dose rate constant was calculated to be (1.22 ± 0.03) cGy h⁻¹ U⁻¹. The uncertainty in the dose to water calculations, $\dot{D}(r,\theta )$, was determined to be 2.5%, dominated by the uncertainties in the cross sections. The anisotropy constant, ${\overline{\varphi }}_{an}$, was calculated to be 0.960 ± 0.011 and was obtained by integrating the anisotropy factor between 1 and 10 cm using a weighting factor proportional to r⁻². The radial dose function was calculated at distances between 0.5 and 12 cm, with a maximum value of 1.20 at 5.15 ± 0.03 cm. Radial dose values were fit to a fifth order polynomial and dual exponential regression. Since the source is not axially symmetric, angular Monte Carlo calculations were performed at 1 cm which determined that the maximum azimuthal anisotropy was less than 8%.

Conclusions: With a higher photon energy, shorter half-life and higher initial dose rate ¹⁶⁹Yb is an interesting alternative to ¹²⁵I for the treatment of nonsmall cell lung cancer.

INTRODUCTION

Nonsmall cell lung cancer (NSCLC) is a leading cause of cancer-related death occurring in the United States with an estimated 160 340 deaths estimated to occur in 2012.¹ While lobectomy is the most effective technique for preventing localized reoccurrence of NSCLC, patients with airway obstructions, preexisting lung complications, or poor pulmonary function are considered to be poor candidates for this procedure and have traditionally been treated with limited resection.² In these cases, limited resection alone has been shown to produce a three times higher rate of disease reoccurrence compared to lobectomy procedures.³ Intraoperative or permanently implanted placement of brachytherapy sources has shown promising results for reducing the risk of reoccurrence following limited surgical wedge resection.⁴

Clinically, the American College of Surgeons Oncology Group Z4302 (Refs. ⁵ and ⁶) is presently evaluating patients who are well suited for limited lobar resections and who can also be treated postresection with radioactive ¹²⁵Iodine (¹²⁵I). Although ¹²⁵I is the most commonly used radionuclide for limited resection procedures, the placement of these sources, either as a series of strands or woven into mesh that is attached to the resected lobe, is difficult and inaccurate due to lung motion during reinflation and regular breathing. To overcome these difficulties, a novel brachytherapy surgical staple-like source, called the GammaClip™, was developed by Source Production & Equipment Co. (SPEC; New Orleans, LA); this brachytherapy source consists of a ¹⁶⁹Yb isotopic active element encapsulated in a titanium tube with staple-like ends. ¹⁶⁹Yb is an interesting alternative to ¹²⁵I for the treatment of NSCLC because it has higher photon energy (providing a more uniform dose distribution), a shorter half-life, and is designed to have a higher initial dose rate. The GammaClip™ ¹⁶⁹Yb source was developed as a low dose rate (LDR) permanent implant brachytherapy source and can be characterized by its median photon energy of 57.5 keV, average photon energy of 92.7 keV, and half-life of (32.0147 ± 0.0093) days.⁷

The authors report their results from a Monte Carlo dosimetric analysis of a GammaClip™ LDR brachytherapy source. The data obtained were analyzed based on the Report of the AAPM and ESTRO (Perez-Calatayud et al.⁸), using the updated AAPM Task Group Report No. 43 [TG-43U1 (Ref. ⁹)] formalism, and the statistical uncertainties were calculated using the methodology described by Medich et al.¹⁰

MATERIALS AND METHODS

Brachytherapy source geometry and composition

The computational methods used in this investigation were similar to those used previously for the Monte Carlo analysis of the SPEC Model M-19 ¹⁹²Ir source,¹¹ SPEC Model M-42 ¹⁶⁹Yb source,¹² and Implant Sciences Model 4140.¹³ A GammaClip™ ¹⁶⁹Yb source was modeled using the Monte Carlo N-Particle 5, version 1.60 (MCNP5) transport code, based on specifications provided by SPEC and discussed in detail by Leonard et al.² A graphical depiction of the GammaClip™ is presented in Fig. 1 with the corresponding physical parameters listed in Table 1. The source construction is nonsymmetric about the long axis but symmetric about the transverse-plane.

Figure 1.

Configuration of the GammaClip™ ¹⁶⁹Yb brachytherapy source. This model consists of a 0.125 cm long ¹⁶⁹Yb source encapsulated in a 0.006 cm thick titanium shell.

Table 1.

The physical parameters of the GammaClip™ ¹⁶⁹Yb source used in the MCNP5 dosimetric simulations.

	Outside diameter	Inside diameter	Length	Density
Component	(mm)	(mm)	(mm)	(mg/mm3)	Remarks
Ytterbium	0.25	N.A.	1.25	6.90	Active element
Encapsulation	0.40	0.28	3.00	4.51	Titanium; 0.50 mm thick
					welded end; solid plug

Monte Carlo calculation techniques

Radiation transport calculations were performed using the MCNP5 code.¹⁴ MCNP5 is a general-purpose, continuous-energy time-dependent program designed to transport and tally coupled photon and electrons through materials. In this study, MCPLIB04 photoatomic cross-section tables were used as the bases of the photon transport calculations. This library is continually updated and maintained by the National Nuclear Data Center at Brookhaven National Laboratory. The library is derived from the EPDL97 dataset¹⁵ and offers superior representation of low energy photoelectric interactions in low Z materials when compared to EPDL datasets.^{16, 17, 18} Simulations were performed both in water and air, with a total of 2 × 10⁸ source photon histories processed for each simulation. ¹⁶⁹Yb has a very complex photon spectrum¹⁹ that includes 73 gamma ray and 5 x-ray emission lines. Based on recommendations made by Perez-Calatayud et al.⁹ and Medich et al.,¹¹ one gamma ray (8.41 keV) and one x-ray (7.18 keV) were omitted from the model. The final photon spectrum and corresponding uncertainty, obtained from Brookhaven National Laboratory²⁶ and used in this investigation, are presented in Table 2. MCNP5 was used to model a uniform activity ¹⁶⁹Yb distribution within the active element of the source. The uncertainty in photon yield for these simulations was evaluated as the average weighted (by yield) uncertainty of the individual photon energies in the spectrum.

Table 2.

¹⁶⁹Yb photon energy spectrum used in this Monte Carlo study was obtained from Brookhaven National Labs (Ref. ²⁶). The intensity weighted average energy of the spectrum is 93.7 keV, the median photon energy is 57.5 keV, and the total intensity is 3.319. The total uncertainty in the photon yield, 0.008 was determined using an intensity weighted average of the individual uncertainties presented below.

Energy (keV)	Intensity	Uncertainty	Energy (keV)	Intensity	Uncertainty
20.752	1.98 × 10−3	1.50 × 10−4	240.331	1.14 × 10−3	6.00 × 10−5
42.760	1.30 × 10−3	1.30 × 10−3	261.077	1.70 × 10−2	9.00 × 10−5
45.940	5.00 × 10−5	5.00 × 10−5	291.188	4.31 × 10−5	1.40 × 10−6
49.773	5.25 × 10−1	1.20 × 10−2	294.540	1.00 × 10−5	3.00 × 10−6
50.610	3.00 × 10−3	3.00 × 10−3	301.732	2.30 × 10−5	2.30 × 10−5
50.742	9.16 × 10−1	2.10 × 10−2	306.830	9.00 × 10−4	9.00 × 10−4
50.855	3.00 × 10−3	3.00 × 10−3	307.520	3.00 × 10−3	3.00 × 10−3
51.510	9.00 × 10−5	9.00 × 10−5	307.736	1.01 × 10−1	5.00 × 10−4
57.300	9.87 × 10−2	2.10 × 10−3	333.963	1.74 × 10−5	6.00 × 10−7
57.505	1.90 × 10−1	4.00 × 10−3	336.618	9.40 × 10−5	3.00 × 10−6
59.028	6.41 × 10−2	1.40 × 10−3	356.740	1.41 × 10−6	6.00 × 10−8
63.012	1.10 × 10−2	1.10 × 10−2	370.854	8.80 × 10−6	9.00 × 10−7
63.120	4.36 × 10−1	2.30 × 10−3	379.286	4.10 × 10−6	8.00 × 10−7
65.860	5.00 × 10−5	5.00 × 10−5	386.671	3.35 × 10−6	8.00 × 10−8
72.028	1.80 × 10−5	1.80 × 10−5	452.620	1.80 × 10−7	5.00 × 10−8
85.093	1.40 × 10−5	1.40 × 10−5	464.700	3.60 × 10−8	2.20 × 10−8
93.614	2.58 × 10−2	1.70 × 10−4	465.650	1.90 × 10−6	2.20 × 10−8
95.704	1.10 × 10−5	1.10 × 10−5	466.700	1.94 × 10−7	2.20 × 10−8
95.854	1.10 × 10−5	1.10 × 10−5	474.970	1.94 × 10−6	4.00 × 10−8
98.005	9.00 × 10−6	9.00 × 10−6	494.357	1.47 × 10−5	3.00 × 10−7
101.405	4.00 × 10−5	4.00 × 10−5	500.350	8.80 × 10−8	8.00 × 10−9
105.190	2.60 × 10−5	8.00 × 10−6	507.800	1.50 × 10−8	8.00 × 10−9
109.780	1.74 × 10−1	9.00 × 10−4	515.101	4.17 × 10−5	6.00 × 10−7
113.620	5.00 × 10−5	5.00 × 10−5	528.569	1.20 × 10−6	3.00 × 10−8
113.976	4.00 × 10−5	4.00 × 10−5	546.160	1.50 × 10−8	4.00 × 10−9
117.376	4.00 × 10−4	3.00 × 10−5	562.410	1.19 × 10−6	3.00 × 10−8
118.189	1.87 × 10−2	1.00 × 10−4	570.890	1.11 × 10−6	6.00 × 10−8
129.942	3.00 × 10−3	3.00 × 10−3	579.851	1.93 × 10−5	3.00 × 10−7
130.523	1.14 × 10−1	5.00 × 10−4	600.603	1.14 × 10−5	1.80 × 10−7
156.725	1.00 × 10−4	3.00 × 10−6	624.881	4.92 × 10−5	1.40 × 10−6
173.880	1.40 × 10−5	1.40 × 10−5	633.320	6.90 × 10−8	5.00 × 10−9
177.214	2.22 × 10−1	1.10 × 10−3	642.873	7.65 × 10−7	1.80 × 10−8
193.150	7.50 × 10−5	1.10 × 10−5	663.599	1.93 × 10−6	5.00 × 10−8
197.958	3.59 × 10−1	7.11 × 10−2	693.460	8.70 × 10−8	4.00 × 10−9
199.772	1.60 × 10−4	1.60 × 10−4	710.354	3.40 × 10−7	3.00 × 10−8
205.990	3.40 × 10−5	8.00 × 10−6	739.420	1.83 × 10−8	2.20 × 10−9
213.935	2.91 × 10−5	2.20 × 10−6	760.240	8.30 × 10−9	2.20 × 10−9
226.300	2.50 × 10−6	1.80 × 10−6	773.386	2.09 × 10−6	3.00 × 10−8
228.710	2.00 × 10−6	2.00 × 10−6	781.640	3.00 × 10−8	3.00 × 10−9

TG-43U1 calculations

As defined by TG-43U1, the dose rate, $\dot{D}(r,\theta )$, for each dosimetric point of interest in a water phantom is

$${\dot{D}}_{\mathrm{TG}-43}(r,\theta )=S_K·\Lambda ·\frac{G(r,\theta )}{G(r_0,{\theta }_0)}·F(r,\theta )·g\left(r\right).$$ (1)

The dose rate, $\dot{D}(r,\theta )$, is computed from the Monte Carlo tally output, R_tally(r, θ), based on Eq. 2:

$$\dot{D}(r,\theta )=R_{\mathrm{tally}}(r,\theta )·I_{\gamma }.$$ (2)

In this equation, I_γ is the ¹⁶⁹Yb photon intensity in units of photons per disintegration (3.319 photons Bq⁻¹ s⁻¹). For convenience, $\dot{D}(r,\theta )$ was converted into more conventional units through the relationship 1 MeV g⁻¹ Bq⁻¹ s⁻¹ equals 2.13 × 10³ cGy mCi⁻¹ h⁻¹.

Values for $\dot{D}(r,\theta )$, the radial dose function, (g_L(r)), the 2D anisotropy function, (F(r, θ)), 1D anisotropy function, (ϕ_an(r)), and anisotropy constant, (${\overline{\varphi }}_{\mathrm{an}}$), were calculated from the output of an MCNP5 model consisting of a GammaClip™ source placed at the center of a 100 cm radius spherical water phantom. This phantom size was selected to approximate an infinite water phantom because it is also appropriate as an infinite phantom for the more energetic photon spectrum of Ir-192.²⁰ Dosimetric data were calculated at radial distances ranging from 0.5 to 10 cm in 0.5 cm increments over angles in 10° increments ranging from 0° to 180° using an F6 energy deposition tally. The tally output reported results of energy deposition averaged over the mass of the tallied region per starting photon, R_tally(r, θ), in units of MeV g⁻¹ photon⁻¹.

The uncertainty for $\dot{D}(r,\theta )$ was derived using Eq. 3, where ${\sigma }_{\mathrm{tally}}^{\mathrm{relative}}(r,\theta )$ is the propagated uncertainty for the relative uncertainties in the Monte Carlo output tallies, ${\sigma }_{\mathrm{crosssection}}^{\mathrm{relative}}\left(r,\theta \right)$ is the relative uncertainty in cross section data, and ${\sigma }_{I_y}^{\mathrm{relative}}\left(r,\theta \right)$ is the relative uncertainty in the photon yields.¹⁰ Contributions from the uncertainty in the photon energy spectrum were ignored since these values (≤0.1%) do not contribute significantly to the total uncertainty in the dose rate. A detailed derivation for the statistical uncertainties in all dosimetric variables is discussed by Medich et al:¹⁰

$$\begin{array}{c}\hfill {\sigma }_{\dot{D}}^{\mathrm{relative}}\left(r,\theta \right)=\sqrt{{\left({\sigma }_{\mathrm{tally}}^{\mathrm{relative}}\left(r,\theta \right)\right)}^2+{\left({\sigma }_{\mathrm{crosssection}}^{\mathrm{relative}}\left(r,\theta \right)\right)}^2+{\left({\sigma }_{I_y}^{\mathrm{relative}}\left(r,\theta \right)\right)}^2}.\end{array}$$ (3)

To calculate the air-kerma strength in free space, S_K, a 1.3 m void (in vacuo) was modeled in the MCNP5 environment. TG-43U1 requires that the air-kerma rate, $\dot{K}(\mathrm{d},\theta )$, a precursor to S_K, be calculated along the perpendicular bisector, θ₀ = 90°, at the reference distance of 100 cm in a model of negligible photon scatter.⁸ In our model, a tally volume was generated, consisting of a 5 cm thick spherical shell located at a distance of 100 cm, with an inner radius of 97.5 cm and outer radius of 102.5 cm, constrained between 88° and 92° from the source axis, for calculating the air-kerma rate at 100 cm from the source at an angle of 90° [$\dot{K}\left({100\mathrm{cm},90}^{\circ }\right)$]. Here, volumetric averaging within the 4° tally area contributed an uncertainty of less than 0.1% to the dose calculation. This geometric uncertainty in the air-kerma rate was calculated using Eq (4), where a and b are the inner and out radius distances specified:

$$\begin{array}{ccc}& & \frac{1}{\left(b-a\right)}\underset{a}{\overset{b}{\int }}\frac{1}{r^2}dr\hfill \\ & & =\frac{1}{\left(b-a\right)}\times {\left[-\frac{1}{x}\right]}_a^b=\frac{1}{\left(b-a\right)}\left[\frac{1}{a}-\frac{1}{b}\right].\hfill \end{array}$$ (4)

The tally volume was filled with air at standard temperature and pressure to allow for photon energy-transfer and deposition calculations; all regions outside the tally volume were maintained as vacuum.

A GammaClip™ ¹⁶⁹Yb source was centered at the origin of the above model and the resulting air-kerma rate within the tally volume was calculated using the MCNP5 *F4 tally. This is a track-length tally (MeV/cm²) designed to compute the energy-flux, Ψ (E), averaged in the target volume.

The *F4 tally was further modified to aggregate photons entering the tally volume into energy bins of 1 keV increments to obtain an energy spectral distribution of air kerma rate. Using this method, the energy flux and corresponding air kerma attributable to photons with energies of 10 keV and lower (δ = 10 keV) were subtracted from the results, in accordance with the Report of the AAPM and ESTRO (Section V.D.1).⁸ The contribution to the air-kerma rate of photons with energies less than 10 keV represented less than 0.02% of the total.

Each energy binned *F4 tally output (MeV cm⁻²) was further multiplied by its respective mass-energy transfer coefficient [μ_tr/ρ (cm² g⁻¹)] to obtain the air kerma per source photon (MeV g⁻¹ photon⁻¹) at each energy bin in the tally volume. An equivalence is assumed between μ_tr/ρ and the mass-energy absorption coefficients [μ_en/ρ (cm² g⁻¹)] for the middle to low energy photons emitted by a brachytherapy source in water.²¹

The air-kerma per source photon for photon energies greater than δ were summed and expressed as $R_{\mathrm{air}-\mathrm{kerma}}^{\delta =10\mathrm{keV}}\left(r,\theta \right)$. This value was multiplied by the total ¹⁶⁹Yb photon yield to obtain the air-kerma rate, ${\dot{K}}_{\delta =10\mathrm{keV}}(100\mathrm{cm},{90}^{\circ })$, measured in the tally volume.¹ Finally, the air-kerma strength in free space, S_K, was calculated, as recommended in TG-43U1,⁸ through the relationship:

$$S_K={\dot{K}}_{\delta }(100\mathrm{cm},{90}^{\circ })·d^2,$$ (5)

where d is the radial distance of the tally volume and is equal to 100 cm.

Using the air-kerma strength, the Monte Carlo calculated reference dose rate in water, $\dot{D}\left(r_0,{\theta }_0\right)$, was determined, where $\dot{D}\left(r_0,{\theta }_0\right)$ is the dose rate in water at reference position and P(r₀, θ₀), 1 cm from the source along the plane.

The dose rate constant, Λ, was calculated by dividing the reference dose rate to water, $\dot{D}\left(r_0,{\theta }_0\right)$, by the brachytherapy source's air-kerma strength in free space, S_K, in units of cGy h⁻¹ U⁻¹. The uncertainty in the dose rate constant was calculated by multiplying its relative uncertainty, by the dose rate constant, Λ, as shown in Eq. 6:

$${\sigma }_{\Lambda }^{\mathrm{relative}}=\frac{{\sigma }_{\Lambda }}{\Lambda }=\sqrt{{\left({\sigma }_{R_{\mathrm{tally}}}^{\mathrm{relative}}\left(r_0,{\theta }_0\right)\right)}^2+{\left({\sigma }_{R_{\mathrm{air}\mathrm{kerma}}^{\delta =10}}^{\mathrm{relative}}\right)}^2}.$$ (6)

The geometry function, G_L(r, θ), which provides an effective inverse square-law correction in the dose rate distribution equation, was calculated using the AAPM Task Group 43 approximation of a line source of length L equals 1.25 mm and angle, β, subtended by the tip of the line source with respect to P(r₀, θ₀):

$$G_L(r,\theta )=\frac{\beta }{L·r·\sin \left(\theta \right)}.$$ (7)

The radial dose function, g(r), accounts for dose fall-off along the transverse axis of the source. The GammaClip™ radial dose function was computed for distances ranging from 0.5 to 10 cm, at 0.5 cm increments. The subscript L denotes that a line source approximation was performed in this study:

$$g_L\left(r\right)=\frac{\dot{D}(r,{\theta }_0)·G_L(r_0,{\theta }_0)}{\dot{D}(r_0,{\theta }_0)·G_L(r,{\theta }_0)}.$$ (8)

For clinical implementation, the computed g(r) values were fit to a fifth order polynomial in accordance with AAPM TG-43U1 (Section III.4) and because the behavior of a polynomial function outside the limits of the data can be unreliable,¹⁸ an alternative model of the radial dose function is also presented. This model, originally proposed by Furhang,²² takes the form of a dual exponential:

$$g_L\left(r\right)=C_1·e^{{\mu }_1·r}+C_2·e^{{\mu }_2·r}.$$ (9)

The 2D anisotropy function, F(r, θ), describes the variation in dose relative to the transverse plane and was calculated using Eq. 10. Measurements were taken at distances of 0.5 cm and between 1 and 10 cm in 1 cm increments, and at 10° angular increments between 0° and 180°:

$$F(r,\theta )=\frac{\dot{D}(r,\theta )·G_L(r,{\theta }_0)}{\dot{D}(r,{\theta }_0)·G_L(r,\theta )}.$$ (10)

Similarly, the anisotropy factor or 1D anisotropy function, ϕ_an(r), is the ratio of the sold angle-weighted dose obtained by integrating from 0° to 180°, as illustrated in Eq. 11. Measurements were taken in identical distances and increments as the 2D anisotropy function calculations:

$${\varphi }_{an}\left(r\right)=\frac{\underset{0}{\overset{\pi }{\int }}\dot{D}(r,\theta )·\sin \left(\theta \right)d\theta }{2·\dot{D}(r,{\theta }_0)}.$$ (11)

The resulting anisotropy constant, ${\overline{\varphi }}_{an}$, was calculated by integrating the anisotropy factor between 1 and 10 cm using a weighting factor proportional to r⁻².

Finally, because this source is not axially symmetric, Monte Carlo calculations were performed to assess the spatial asymmetry in the absorbed dose distribution at a distance of 1 cm in both the polar and azimuthal anisotropy directions. The results of these simulations and the attenuation effects of the titanium encapsulation were analyzed at a distance of 1 cm.

RESULTS AND DISCUSSION

Results for the normalized dose rate in water are presented in Table 3 and graphically represented in Fig. 2. Calculated from the MCNP5 output file, it was determined that generating 2 × 10⁸ photon histories leads to an uncertainty in the MCNP output, ${\sigma }_{\mathrm{tally}}^{\mathrm{relative}}(r,\theta )$, that was less than 0.5% at each tallied volume. The total uncertainty in $\dot{D}(r,\theta )$, ${\sigma }_{\dot{D}}^{\mathrm{relative}}(r,\theta )$, calculated using Eq. 3, was determined to be 2.5%. This indicated that ${\sigma }_{\dot{D}}^{\mathrm{relative}}(r,\theta )$ was dominated by the uncertainty in the cross-section tables, ${\sigma }_{\underset{\mathrm{section}}{\mathrm{cross}}}$ and the ¹⁶⁹Yb photon yields, ${\sigma }_{I_{\gamma }}$.

Table 3.

Monte Carlo calculated GammaClip™ ¹⁶⁹Yb normalized dose distribution in water, ${\dot{D}}_N=[\dot{D}(r,\theta )·r^2]/\dot{D}(r_0,{\theta }_0)$. These data are normalized to the dose rate at 1 cm and 90° from source center with geometrical effects effectively removed by multiplying the dose rate by the radial distance squared. These data may be un-normalized by multiplying them by $\dot{D}(r_0,{\theta }_0)$ (1.67 ± 0.03) cGy mCi⁻¹ h⁻¹ and dividing by the square of their radial distances. Calculated total uncertainty, ${\sigma }_{{\dot{D}}_N}$, was normalized to the dose distribution in water, ${\dot{D}}_N$, by multiplying the fractional uncertainty, Eq. 7, by the value of the normalized dose rate.

r (cm)
θ (deg)	0.5	1	2	3	4	5	6	7	10
0	0.61 ± 0.04	0.67 ± 0.02	0.79 ± 0.02	0.88 ± 0.02	0.94 ± 0.02	0.98 ± 0.03	0.99 ± 0.03	1.00 ± 0.03	0.93 ± 0.03
10	0.69 ± 0.02	0.75 ± 0.02	0.86 ± 0.02	0.94 ± 0.02	0.99 ± 0.03	1.02 ± 0.03	1.03 ± 0.03	1.03 ± 0.03	0.96 ± 0.03
20	0.79 ± 0.02	0.84 ± 0.02	0.94 ± 0.02	1.01 ± 0.03	1.05 ± 0.03	1.08 ± 0.03	1.08 ± 0.03	1.07 ± 0.03	0.99 ± 0.03
30	0.85 ± 0.03	0.9 ± 0.02	0.99 ± 0.03	1.06 ± 0.03	1.10 ± 0.03	1.12 ± 0.03	1.12 ± 0.03	1.11 ± 0.03	1.01 ± 0.03
40	0.89 ± 0.03	0.94 ± 0.03	1.03 ± 0.03	1.09 ± 0.03	1.13 ± 0.03	1.15 ± 0.03	1.15 ± 0.03	1.13 ± 0.03	1.03 ± 0.03
50	0.91 ± 0.03	0.97 ± 0.03	1.06 ± 0.03	1.12 ± 0.03	1.15 ± 0.03	1.17 ± 0.03	1.17 ± 0.03	1.15 ± 0.03	1.04 ± 0.03
60	0.93 ± 0.03	0.98 ± 0.03	1.07 ± 0.03	1.13 ± 0.03	1.17 ± 0.03	1.18 ± 0.03	1.18 ± 0.03	1.16 ± 0.03	1.05 ± 0.03
70	0.94 ± 0.03	1.00 ± 0.03	1.08 ± 0.03	1.14 ± 0.03	1.18 ± 0.03	1.19 ± 0.03	1.19 ± 0.03	1.17 ± 0.03	1.06 ± 0.03
80	0.94 ± 0.03	1.00 ± 0.03	1.09 ± 0.03	1.15 ± 0.03	1.18 ± 0.03	1.20 ± 0.03	1.19 ± 0.03	1.18 ± 0.03	1.06 ± 0.03
90	0.94 ± 0.03	1.00 ± 0.03	1.09 ± 0.03	1.15 ± 0.03	1.19 ± 0.03	1.20 ± 0.03	1.19 ± 0.03	1.18 ± 0.03	1.07 ± 0.03
100	0.94 ± 0.03	1.00 ± 0.03	1.09 ± 0.03	1.15 ± 0.03	1.18 ± 0.03	1.20 ± 0.03	1.19 ± 0.03	1.18 ± 0.03	1.06 ± 0.03
110	0.94 ± 0.03	1.00 ± 0.03	1.08 ± 0.03	1.14 ± 0.03	1.18 ± 0.03	1.19 ± 0.03	1.19 ± 0.03	1.17 ± 0.03	1.06 ± 0.03
120	0.93 ± 0.03	0.98 ± 0.03	1.07 ± 0.03	1.13 ± 0.03	1.17 ± 0.03	1.18 ± 0.03	1.18 ± 0.03	1.16 ± 0.03	1.05 ± 0.03
130	0.91 ± 0.03	0.97 ± 0.03	1.06 ± 0.03	1.12 ± 0.03	1.15 ± 0.03	1.17 ± 0.03	1.17 ± 0.03	1.15 ± 0.03	1.04 ± 0.03
140	0.89 ± 0.03	0.94 ± 0.03	1.03 ± 0.03	1.09 ± 0.03	1.13 ± 0.03	1.15 ± 0.03	1.15 ± 0.03	1.13 ± 0.03	1.03 ± 0.03
150	0.85 ± 0.03	0.9 ± 0.02	0.99 ± 0.03	1.06 ± 0.03	1.10 ± 0.03	1.12 ± 0.03	1.12 ± 0.03	1.11 ± 0.03	1.01 ± 0.03
160	0.79 ± 0.02	0.84 ± 0.02	0.94 ± 0.02	1.01 ± 0.03	1.05 ± 0.03	1.08 ± 0.03	1.08 ± 0.03	1.07 ± 0.03	0.99 ± 0.03
170	0.69 ± 0.02	0.75 ± 0.02	0.86 ± 0.02	0.94 ± 0.02	0.99 ± 0.02	1.02 ± 0.03	1.03 ± 0.03	1.03 ± 0.03	0.96 ± 0.02
180	0.61 ± 0.03	0.67 ± 0.03	0.79 ± 0.02	0.88 ± 0.02	0.94 ± 0.02	0.98 ± 0.02	0.99 ± 0.02	1.00 ± 0.02	0.93 ± 0.02

Figure 2.

Resulting GammaClip™ ¹⁶⁹Yb brachytherapy source dose rate distribution based on the Monte Carlo program output. For easier comparison between radial distances, geometry effects are effectively removed by multiplying the dose rate, $\dot{D}(r,\theta )$, by the radial distance squared, r². Once corrected, the dose rate is then normalized to the dose rate at 1 cm along the seed's transverse axis, $\dot{D}(r_0,{\theta }_0)$, (1.67 ± 0.03) cGy mCi⁻¹ h⁻¹, to obtain the normalized dose rate distribution.

The GammaClip™ radial dose function, g(r), and the calculated statistical uncertainty in each datum are presented in Table 4. As described in Sec. 2, g(r) values were fit to a fifth order polynomial and dual exponential regression as shown in Fig. 3.

Table 4.

Monte Carlo calculated radial dose function, g_L(r), for the GammaClip™ ¹⁶⁹Yb source with calculated total uncertainty, ${\sigma }_{g_L}\left(r\right)$.

r (cm)	$g_L\left(r\right)\pm {\sigma }_{g_L}\left(r\right)$
0.5	0.94 ± 0.03
1.0	1.00
1.5	1.05 ± 0.03
2.0	1.09 ± 0.03
2.5	1.12 ± 0.03
3.0	1.15 ± 0.03
3.5	1.17 ± 0.03
4.0	1.18 ± 0.03
4.5	1.19 ± 0.03
5.0	1.20 ± 0.03
5.5	1.20 ± 0.03
6.0	1.19 ± 0.03
6.5	1.19 ± 0.03
7.0	1.17 ± 0.03
8.0	1.15 ± 0.03
9.0	1.11 ± 0.03
10.0	1.06 ± 0.03
11.0	1.02 ± 0.03
12.0	0.97 ± 0.03

Figure 3.

Calculated GammaClip™ ¹⁶⁹Yb brachytherapy source radial dose function, g_L(r), at distances between 0.5 and 12 cm with the predicted maximum for g_L(r) at 5.15 cm. These data were fit to a fifth order polynomial function, g_L(r) = a₀+ a₁·r + a₂·r² + a₃·r³ + a₄·r⁴ + a₅·r⁵, and a dual exponential function $g_L\left(r\right)=C_1·e^{-{\mu }_1·r}+C_2·e^{-{\mu }_2·r}$ with both resulting fits displayed. Error bars in g_L(r) reflect calculated uncertainties at ±1 standard deviation.

Values for the resulting geometry function, G_L(r, θ), are presented in Table 5. Geometric uncertainty, due to source movement was not accounted for because of the small 0.03 mm distance of separation between the single ¹⁶⁹Yb source and surrounding titanium shield. In cases where sources consisted of multiple cores and larger space within the capsule, similar to MED3631-A/M I-125,²³ results have been shown to have high geometric uncertainties at distances less than 5 mm.

Table 5.

Geometry factor, G_L(r, θ), used for the GammaClip™ ¹⁶⁹Yb brachytherapy source. The calculations assume an active source length, L, of 0.125 cm.

r (cm)
θ (deg)	0.5	1.0	2.0	3.0	4.0	5.0	6.0	7.0	8.0	9.0	10.0
0	4.0635	1.0039	0.2502	0.1112	0.0625	0.0400	0.0278	0.0204	0.0156	0.0123	0.0100
10	4.0609	1.0038	0.2502	0.1112	0.0625	0.0400	0.0278	0.0204	0.0156	0.0123	0.0100
20	4.0533	1.0033	0.2502	0.1112	0.0625	0.0400	0.0278	0.0204	0.0156	0.0123	0.0100
30	4.0419	1.0026	0.2502	0.1111	0.0625	0.0400	0.0278	0.0204	0.0156	0.0123	0.0100
40	4.0280	1.0018	0.2501	0.1111	0.0625	0.0400	0.0278	0.0204	0.0156	0.0123	0.0100
50	4.0134	1.0008	0.2501	0.1111	0.0625	0.0400	0.0278	0.0204	0.0156	0.0123	0.0100
60	3.9998	1.0000	0.2500	0.1111	0.0625	0.0400	0.0278	0.0204	0.0156	0.0123	0.0100
70	3.9889	0.9993	0.2500	0.1111	0.0625	0.0400	0.0278	0.0204	0.0156	0.0123	0.0100
80	3.9818	0.9989	0.2499	0.1111	0.0625	0.0400	0.0278	0.0204	0.0156	0.0123	0.0100
90	3.9794	0.9987	0.2499	0.1111	0.0625	0.0400	0.0278	0.0204	0.0156	0.0123	0.0100

The calculated values for the anisotropy function, F(r, θ), and anisotropy factor, ϕ_an(r), including the relative uncertainties in these measurements are presented in Table 6. From the anisotropy factor, the resulting anisotropy constant, ${\overline{\varphi }}_{an}$, was determined to be 0.96 ± 0.011.

Table 6.

MCNP5 calculated anisotropy function, F(r, θ), and anisotropy factors, ϕ_an(r), for the GammaClip™ ¹⁶⁹Yb brachytherapy source, at radial distances between 0.5 and 10 cm with angles between 0° and 180°. Total uncertainty in the anisotropy function, F(r, θ), and anisotropy factor, ϕ_an(r), for the GammaClip™ ¹⁶⁹Yb brachytherapy source were calculated using methods described by Medich et al. (Ref. ¹⁰).

r (cm)
θ (deg)	0.5	1	2	3	4	5	6	7	10
0	0.63 ± 0.03	0.67 ± 0.02	0.73 ± 0.02	0.77 ± 0.02	0.79 ± 0.02	0.82 ± 0.02	0.83 ± 0.02	0.85 ± 0.02	0.87 ± 0.02
10	0.72 ± 0.02	0.75 ± 0.02	0.79 ± 0.02	0.82 ± 0.02	0.83 ± 0.02	0.85 ± 0.02	0.87 ± 0.02	0.87 ± 0.02	0.90 ± 0.02
20	0.82 ± 0.02	0.84 ± 0.02	0.86 ± 0.02	0.88 ± 0.02	0.89 ± 0.02	0.90 ± 0.02	0.91 ± 0.02	0.91 ± 0.02	0.92 ± 0.02
30	0.89 ± 0.02	0.90 ± 0.02	0.91 ± 0.02	0.92 ± 0.02	0.93 ± 0.02	0.93 ± 0.02	0.94 ± 0.02	0.94 ± 0.03	0.95 ± 0.03
40	0.93 ± 0.03	0.94 ± 0.03	0.94 ± 0.03	0.95 ± 0.03	0.95 ± 0.03	0.96 ± 0.03	0.96 ± 0.03	0.96 ± 0.03	0.97 ± 0.03
50	0.96 ± 0.03	0.96 ± 0.03	0.97 ± 0.03	0.97 ± 0.03	0.97 ± 0.03	0.98 ± 0.03	0.98 ± 0.03	0.98 ± 0.03	0.98 ± 0.03
60	0.98 ± 0.03	0.98 ± 0.03	0.98 ± 0.03	0.99 ± 0.03	0.99 ± 0.03	0.99 ± 0.03	0.99 ± 0.03	0.99 ± 0.03	0.99 ± 0.03
70	0.99 ± 0.03	0.99 ± 0.03	0.99 ± 0.03	0.99 ± 0.03	1.00 ± 0.03	0.99 ± 0.03	1.00 ± 0.03	0.99 ± 0.03	1.00 ± 0.03
80	1.00 ± 0.03	1.00 ± 0.03	1.00 ± 0.03	1.00 ± 0.03	1.00 ± 0.03	1.00 ± 0.03	1.00 ± 0.03	1.00 ± 0.03	1.00 ± 0.03
90	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
100	1.00 ± 0.03	1.00 ± 0.03	1.00 ± 0.03	1.00 ± 0.03	1.00 ± 0.03	1.00 ± 0.03	1.00 ± 0.03	1.00 ± 0.03	1.00 ± 0.03
110	0.99 ± 0.03	0.99 ± 0.03	0.99 ± 0.03	0.99 ± 0.03	1.00 ± 0.03	0.99 ± 0.03	1.00 ± 0.03	0.99 ± 0.03	1.00 ± 0.03
120	0.98 ± 0.03	0.98 ± 0.03	0.98 ± 0.03	0.99 ± 0.03	0.99 ± 0.03	0.99 ± 0.03	0.99 ± 0.03	0.99 ± 0.03	0.99 ± 0.03
130	0.96 ± 0.03	0.96 ± 0.03	0.97 ± 0.03	0.97 ± 0.03	0.97 ± 0.03	0.98 ± 0.03	0.98 ± 0.03	0.98 ± 0.03	0.98 ± 0.03
140	0.93 ± 0.03	0.94 ± 0.02	0.94 ± 0.03	0.95 ± 0.03	0.95 ± 0.03	0.96 ± 0.03	0.96 ± 0.03	0.96 ± 0.03	0.97 ± 0.03
150	0.89 ± 0.02	0.90 ± 0.02	0.91 ± 0.02	0.92 ± 0.02	0.93 ± 0.02	0.93 ± 0.02	0.94 ± 0.02	0.94 ± 0.03	0.95 ± 0.03
160	0.82 ± 0.02	0.84 ± 0.02	0.86 ± 0.02	0.88 ± 0.02	0.89 ± 0.02	0.90 ± 0.02	0.91 ± 0.02	0.91 ± 0.02	0.92 ± 0.02
170	0.72 ± 0.02	0.75 ± 0.02	0.79 ± 0.02	0.82 ± 0.02	0.83 ± 0.02	0.85 ± 0.02	0.87 ± 0.02	0.87 ± 0.02	0.90 ± 0.02
180	0.63 ± 0.03	0.67 ± 0.02	0.73 ± 0.02	0.77 ± 0.02	0.79 ± 0.02	0.82 ± 0.02	0.83 ± 0.02	0.85 ± 0.02	0.87 ± 0.02
${\varphi }_{an}\left(r\right)\pm {\sigma }_{{\varphi }_{an}}\left(r\right)$		0.96 ± 0.02	0.96 ± 0.02	0.97 ± 0.02	0.97 ± 0.02	0.97 ± 0.02	0.97 ± 0.02	0.97 ± 0.02	0.98 ± 0.02

From MCNP5, $\dot{D}(r_0,{\theta }_0)$ was determined to be (1.67 ± 0.03) cGy mCi⁻¹ h⁻¹ and the air-kerma rate, ${\dot{K}}_{\delta =10\mathrm{keV}}(100\mathrm{cm},{90}^{\circ })$, was calculated as [(1.37 ± 0.03) × 10⁻⁴] cGy mCi⁻¹ h⁻¹. From these results, the free space air-kerma strength, S_K, and dose rate constant, Λ, were calculated to be (1.37 ± 0.03) cGy mCi⁻¹ h⁻¹ and (1.22 ± 0.03) cGy h⁻¹ U⁻¹, respectively.

The results of these simulations and the attenuation effects of the titanium encapsulation are presented in Fig. 4. On the left, the broken line represents the anisotropy in a plane through the axis of the active element perpendicular to the titanium leg. The solid line represents the anisotropy in a plane through the axis of the active element which contains the legs. On the right, the various lines represent the anisotropy at a distance of 1 cm from the center of the active element at the polar angles indicated. It is clearly shown that the maximum anisotropy occurs near the equatorial direction (θ = 90°) and is far less severe (0.92) than the nonazimuthal anisotropy in the polar direction (0.65). From this analysis, it was determined that the maximum reduction of absorbed dose in the direction of the titanium legs was less than 8.0%.

Figure 4.

Polar plot results of the GammaClip™ ¹⁶⁹Yb brachytherapy source anisotropy and azimuthal anisotropy absorbed dose calculations.

CONCLUSIONS

The application of a GammaClip™ LDR permanent brachytherapy implant used congruently with limited wedge resection surgery has two distinct advantages over other previously developed brachytherapy sources including improved positional accuracy, which is currently limited by uncertain lobe contact from lung motion, and reduction of physician hand doses, due to the delivery method described in detail by Leonard et al.² In this study, TG-43U1 dosimetric calculations for the GammaClip™ ¹⁶⁹Yb brachytherapy source were performed using the MCNP5 radiation transport code.⁹ From these calculations, the dose rate constant, radial dose function, anisotropy function, anisotropy factor, and anisotropy constant were determined along with their respective statistical uncertainty using the method described in detail by Medich et al.¹⁰

To provide a relative basis of validation for the GammaClip™ source, we made a comparison of the results to published radial dose function results for other ¹⁶⁹Yb sources (Fig. 5). Four other sources were chosen:

• Amersham Type 4 (Ref. ²⁴)

• Amersham Type 5 (Ref. ²⁴)

• Implant Sciences Model 4141 (Ref. ²⁵)

• SPEC Model M42 (Ref. ²⁶)

Figure 5.

Comparing the GammaClip™ radial dose function to those of other published ¹⁶⁹Yb sources.

The data for the Amersham Type 4 and Type 5 predated the AAPM TG43 report. Therefore, we extracted the radial dose function for these two sources from the reported dose rates at various distances at 90° from the source axis.

Additionally, we calculated the radial dose function for a non-self-absorbing point source of ¹⁶⁹Yb using the Monte Carlo results of Luxton et al.²⁵ and interpolating for the spectrum of ¹⁶⁹Yb. The maximum differences between the variations of these radial dose functions compared to the GammaClip™ were determined to be

Amersham Type 4	2.62%
Amersham Type 5	6.86%
Model 4141	3.58%
SPEC Model M42	2.50%
Luxton Point Source	2.48%

These differences can be attributed to two factors: (1) differences in Monte Carlo cross section data and (2) the specific design of each source's active element (size, composition, density) and encapsulation system.

With a higher photon energy, shorter half-life and higher initial dose rate ¹⁶⁹Yb is a good alternative to ¹²⁵I for the treatment of nonsmall cell lung cancer. The results presented in this work can be used toward the development of treatment planning software for clinical use of the GammaClip™ source.