^{1}, D. Granero

^{2}, J. Pérez-Calatayud

^{2}, Ali. S. Meigooni

^{3}and F. Ballester

^{4,a)}

### Abstract

Ir-192 wires have been used in low-dose-rate brachytherapy for many years. Commercially available treatment planning systems approximate the dose rate distribution of the straight or curved wires applying the superposition principle using one of the following methods: (i) The wire is modeled as a set of point sources, (ii) the wire is modeled as a set of small straight segment wires, (iii) the values of the parameters and functions of the American Association of Physicists in Medicine (AAPM) Task Group 43 protocol are obtained for wire lengths between 3 and assuming some simplifications. The dose rate distributions obtained using these methods for linear wires of different lengths and U-shaped wires present significant deviations compared to those obtained by Monte Carlo. In the present study we propose a new method to model wires of any length and shape, named the Two Lengths based Segmented method. This method uses the formalism stated in the AAPM Task Group 43 protocol for two straight wires only, 0.5 and , to obtain the dose rate distribution around wires of any length (down to and up to ) improving on the results of the aforementioned ones. This method can easily be applied to dose calculations around other wires, such as Pd-103 ones.

This study was supported in part by the Generalitat Valenciana [Projects No. GVEMP06/15)], by the Ministerio de Educación y Ciencia (Spain) (Project Nos. DPI2004-04268-C02-01, FPA2003-07581-C02-00, and FIS2004-05713).

I. INTRODUCTION

II. MATERIAL AND METHODS

II.A. Brachytherapysources

II.B. Dosimetry procedure

II.C. The two lengths based linear source segmented method (TLS)

III. RESULTS AND DISCUSSION

III.A. Dose rate distribution of and straight wires

III.B. Comparison of the PSS, LSS, Karaiskos’ methods and TLS models for the straight wire

III.C. Comparison of the PSS, LSS, Karaiskos’ and TLS models for the U-shape wire

IV. CONCLUSIONS

### Key Topics

- Dosimetry
- 22.0
- Monte Carlo methods
- 20.0
- Anisotropy
- 14.0
- Interpolation
- 8.0
- Infrared sources
- 5.0

## Figures

Schematic view of the hairpin of total length. All dimensions are in cm. The coordinate system is also shown.

Schematic view of the hairpin of total length. All dimensions are in cm. The coordinate system is also shown.

A comparison between the MC simulated and theoretically calculated isodose lines for the Ir-192 wire. Isodose curves obtained with the MC simulation (black lines) are compared with: (Upper left side, red line) those obtained superimposing wires; (upper right side, red line) those obtained superimposing wires; (lower left side, red line) those applying the PSS model; (lower right, red line) and those obtained applying the TLS model. Different color coded shades in the background of the figure represent the ratio of the dose obtained directly from the MC simulation and that obtained using the superposition principle with each one of the four models.

A comparison between the MC simulated and theoretically calculated isodose lines for the Ir-192 wire. Isodose curves obtained with the MC simulation (black lines) are compared with: (Upper left side, red line) those obtained superimposing wires; (upper right side, red line) those obtained superimposing wires; (lower left side, red line) those applying the PSS model; (lower right, red line) and those obtained applying the TLS model. Different color coded shades in the background of the figure represent the ratio of the dose obtained directly from the MC simulation and that obtained using the superposition principle with each one of the four models.

Isodose curves for the Ir-192 wire obtained with the MC simulation (black lines) are compared with those obtained applying the Karaiskos’ method. Different color coded shades in the background of the figure represent the ratio of the dose obtained directly from the MC simulation and that obtained using the Karaiskos’ method.

Isodose curves for the Ir-192 wire obtained with the MC simulation (black lines) are compared with those obtained applying the Karaiskos’ method. Different color coded shades in the background of the figure represent the ratio of the dose obtained directly from the MC simulation and that obtained using the Karaiskos’ method.

A comparison between the MC simulated and theoretically calculated isodose lines in the yz plane, for the U-shaped wire. The plane shown is . Isodose curves obtained with the MC simulation of the hairpin (black line) are compared with those obtained applying the TLS model (left side, red line) and those applying the PSS model (right side, red line). Different color coded shades in the background of the figure represents the ratio between the dose obtained directly from the MC simulation and that obtained using the superposition principle.

A comparison between the MC simulated and theoretically calculated isodose lines in the yz plane, for the U-shaped wire. The plane shown is . Isodose curves obtained with the MC simulation of the hairpin (black line) are compared with those obtained applying the TLS model (left side, red line) and those applying the PSS model (right side, red line). Different color coded shades in the background of the figure represents the ratio between the dose obtained directly from the MC simulation and that obtained using the superposition principle.

## Tables

Radial dose function for the 0.5 and straight wires. (Note: The radical dose function of wires has been fitted to a fifth order polynomial between 0.25 and with coefficients: (a) For the length wire , , , , and . (b) For the wire , , , , and ).

Radial dose function for the 0.5 and straight wires. (Note: The radical dose function of wires has been fitted to a fifth order polynomial between 0.25 and with coefficients: (a) For the length wire , , , , and . (b) For the wire , , , , and ).

Anisotropy function for the wire. The origin is taken at the geometrical center of the wire.

Anisotropy function for the wire. The origin is taken at the geometrical center of the wire.

Anisotropy function for the wire. The origin is taken at the geometrical center of the wire.

Anisotropy function for the wire. The origin is taken at the geometrical center of the wire.

Dose rate in water per unit air-kerma strength around the wire. axis is the longitudinal source axis with its origin located at the geometrical center of the wire.

Dose rate in water per unit air-kerma strength around the wire. axis is the longitudinal source axis with its origin located at the geometrical center of the wire.

Dose rate in water per unit air kerma strength around the wire.

Dose rate in water per unit air kerma strength around the wire.

Dose rate in water per unit air-kerma strength around the wire.

Dose rate in water per unit air-kerma strength around the wire.

Dose rate in water per unit air-kerma strength as a function of the superposition method. Dose points are set transverse to the source axis at from the outer end of a wire on the source axis. The dose rate in point (0, 1.0 cm, 0), i.e., the dose rate constant , is also given. The wire setup is according to Fig. 2. Between brackets is given the percentage error relative to the Monte Carlo (MC) dose rate in the same point, obtained from Table IV. LSS-a uses the linear source of Table II, with anisotropy correction. LSS-i is the same as LSS-a but without the anisotropy correction.

Dose rate in water per unit air-kerma strength as a function of the superposition method. Dose points are set transverse to the source axis at from the outer end of a wire on the source axis. The dose rate in point (0, 1.0 cm, 0), i.e., the dose rate constant , is also given. The wire setup is according to Fig. 2. Between brackets is given the percentage error relative to the Monte Carlo (MC) dose rate in the same point, obtained from Table IV. LSS-a uses the linear source of Table II, with anisotropy correction. LSS-i is the same as LSS-a but without the anisotropy correction.

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