^{1,a),b)}, Dragan Mirkovic

^{2}, Luis A. Perles

^{2}, Narayan Sahoo

^{2}, X. Ron Zhu

^{2}, George Ciangaru

^{2}, Kazumichi Suzuki

^{2}, Michael T. Gillin

^{2}, Radhe Mohan

^{2}and Uwe Titt

^{2}

### Abstract

**Purpose:**

The purposes of this study were to validate a discrete spot scanning proton beam nozzle using the Monte Carlo (MC) codeMCNPX and use the MC validated model to investigate the effects of a low-dose envelope, which surrounds the beam’s central axis, on measurements of integral depth dose (IDD) profiles.

**Methods:**

An accurate model of the discrete spot scanning beam nozzle from The University of Texas M. D. Anderson Cancer Center (Houston, Texas) was developed on the basis of blueprints provided by the manufacturer of the nozzle. The authors performed simulations of single proton pencil beams of various energies using the standard multiple Coulomb scattering(MCS) algorithm within theMCNPX source code and a new MCS algorithm, which was implemented in the MCNPX source code. The MCmodels were validated by comparing calculated in-air and in-water lateral profiles and percentage depth dose profiles for single pencil beams with their corresponding measured values. The models were then further tested by comparing the calculated and measured three-dimensional (3-D) dose distributions. Finally, an IDD profile was calculated with different scoring radii to determine the limitations on the use of commercially available plane-parallel ionization chambers to measure IDD.

**Results:**

The distance to agreement, defined as the distance between the nearest positions of two equivalent distributions with the same value of dose, between measured and simulated ranges was within 0.13 cm for both MCS algorithms. For low and intermediate pencil beam energies, the MC simulations using the standard MCS algorithm were in better agreement with measurements. Conversely, the new MCS algorithm produced better results for high-energy single pencil beams. The IDD profile calculated with cylindrical tallies with an area equivalent to the area of the largest commercially available ionization chamber showed up to 7.8% underestimation of the integral dose in certain depths of the IDD profile.

**Conclusions:**

The authors conclude that a combination of MCS algorithms is required to accurately reproduce experimental data of single pencil beams and 3-D dose distributions for the scanning beam nozzle. In addition, the MC simulations showed that because of the low-dose envelope, ionization chambers with radii as large as 4.08 cm are insufficient to accurately measure IDD profiles for a 221.8 MeV pencil beam in the scanning beam nozzle.

The authors kindly thank Dr. Falk Poenisch and Dr. Martin Bues, M. D. Anderson Cancer Center for discussions; the staff of the information technology section of the Department of Radiation Physics, M. D. Anderson for technical support on issues related to the computer cluster; and Ann Sutton, Scientific Publications, M. D. Anderson for editing the manuscript. The authors also really appreciate the thorough review and recommendations provided by the referees and associate editor of this paper, which have helped the authors to significantly improve the presentation and quality of this work. This research was partially supported by Varian Medical Systems, Inc. Grant No. CS2005-00012856SP and National Institutes of Health Grant No. P01-CA21239.

I. INTRODUCTION

II. METHODS AND MATERIALS

II.A. Experimental details

II.B. MCmodel

II.B.1. MC system and transport parameters

II.B.2. Geometry

II.B.3. Particle source

II.B.4. 3-D dose distributions

II.B.5. Tallies

II.B.6. IDD profiles

III. RESULTS

III.A. Pencil beam PDD profiles

III.B. Pencil beam in-air lateral profiles

III.C. Pencil beam in-water lateral profiles as a function of depth

III.D. In-water 3-D dose distributions

III.E. Pencil beam IDD profiles

IV. DISCUSSION

V. CONCLUSIONS

### Key Topics

- Monte Carlo methods
- 58.0
- Optical microcavities
- 54.0
- Protons
- 32.0
- Dosimetry
- 24.0
- Ionization chambers
- 19.0

## Figures

Components of the PTCH proton scanning beam nozzle. The and magnets were not used in the MC model described in this study. The beam direction was parallel to the axis, propagating from positive to negative axis values. For simulations in water, the position in the beam direction was specified in terms of depth in the water phantom.

Components of the PTCH proton scanning beam nozzle. The and magnets were not used in the MC model described in this study. The beam direction was parallel to the axis, propagating from positive to negative axis values. For simulations in water, the position in the beam direction was specified in terms of depth in the water phantom.

FWHM of Gaussian distributions used to simulate the spatial distribution of the proton sources using the new MCS algorithm. The full and dashed lines represent the and FWHM, respectively. The dotted lines represent the pencil beam energies used to adjust the size of the sources.

FWHM of Gaussian distributions used to simulate the spatial distribution of the proton sources using the new MCS algorithm. The full and dashed lines represent the and FWHM, respectively. The dotted lines represent the pencil beam energies used to adjust the size of the sources.

(a) PDD profiles of pencil beams with energies ranging from 72.5 to 221.8 MeV. Simulations were performed using the new MCS algorithm. (b) Range as a function of pencil beam energy. The inset represents the DTA between the measured and simulated ranges (measured-MC). The error bars represent the experimental systematic uncertainty associated with the size of the sensitive volume of the ionization chamber. The circles and solid lines represent measured and simulated data, respectively. : Dose at depth in water ; : Dose at the Bragg peak; : Range; and : Beam energy.

(a) PDD profiles of pencil beams with energies ranging from 72.5 to 221.8 MeV. Simulations were performed using the new MCS algorithm. (b) Range as a function of pencil beam energy. The inset represents the DTA between the measured and simulated ranges (measured-MC). The error bars represent the experimental systematic uncertainty associated with the size of the sensitive volume of the ionization chamber. The circles and solid lines represent measured and simulated data, respectively. : Dose at depth in water ; : Dose at the Bragg peak; : Range; and : Beam energy.

(a) In-air lateral profiles of pencil beams at the isocenter plane for 72.5, 148.8, and 221.8 MeV. The circles and solid lines represent measured and simulated data, respectively. The lateral profiles are normalized to dose at the central axis . (b) FWHM, FW0.01M, and FW0.001M of in-air lateral profiles of pencil beams at the isocenter plane as a function of the pencil beam’s energy. The circles represent measured data, the squares and solid line represent simulated data, and the dashed lines represent fits of the standard MCS algorithm simulated data.

(a) In-air lateral profiles of pencil beams at the isocenter plane for 72.5, 148.8, and 221.8 MeV. The circles and solid lines represent measured and simulated data, respectively. The lateral profiles are normalized to dose at the central axis . (b) FWHM, FW0.01M, and FW0.001M of in-air lateral profiles of pencil beams at the isocenter plane as a function of the pencil beam’s energy. The circles represent measured data, the squares and solid line represent simulated data, and the dashed lines represent fits of the standard MCS algorithm simulated data.

(a) In-air FWHM, FW0.01M, and FW0.001M of pencil beams at positions upstream and downstream of the isocenter plane for 72.5 MeV (, 0.0, −3.7, and −19.5 cm), 148.8 MeV (, 0.0, and −19.5 cm), and 221.8 MeV (, 0.0, −12.5, and −19.5 cm). The circles and lines represent measured and simulated data, respectively.

(a) In-air FWHM, FW0.01M, and FW0.001M of pencil beams at positions upstream and downstream of the isocenter plane for 72.5 MeV (, 0.0, −3.7, and −19.5 cm), 148.8 MeV (, 0.0, and −19.5 cm), and 221.8 MeV (, 0.0, −12.5, and −19.5 cm). The circles and lines represent measured and simulated data, respectively.

(a) FWHM, (b) FW0.01M, and (c) FW0.001M for in-water lateral profiles of single pencil beams as a function of depth. The circles and lines represent measured and simulated data, respectively. For 148.8 MeV, the isocenter plane was at a depth of 20 cm in the water phantom, and for 72.5 and 221.8 MeV, the surface of the water phantom was located at the isocenter plane.

(a) FWHM, (b) FW0.01M, and (c) FW0.001M for in-water lateral profiles of single pencil beams as a function of depth. The circles and lines represent measured and simulated data, respectively. For 148.8 MeV, the isocenter plane was at a depth of 20 cm in the water phantom, and for 72.5 and 221.8 MeV, the surface of the water phantom was located at the isocenter plane.

PDD profiles of 3-D dose distributions with field sizes. The fields F1, F2, F3, and F4 used to create the dose distributions are given in Table I. The circles and lines represent measured and simulated data, respectively. The PDD profiles are normalized to the dose at the middle of the spread-out Bragg peak .

PDD profiles of 3-D dose distributions with field sizes. The fields F1, F2, F3, and F4 used to create the dose distributions are given in Table I. The circles and lines represent measured and simulated data, respectively. The PDD profiles are normalized to the dose at the middle of the spread-out Bragg peak .

Normalized in-water lateral profiles of 3-D dose distributions. The fields F1, F2, F3, and F4 used to create the 3-D dose distributions, with PDD profiles shown in Fig. 7, are given in Table I. The lateral profiles were measured and simulated at depths corresponding to the center of the volumes. F1: Depth of 6.0 cm; F2: Depth of 10.0 cm; F3: Depth of 15.5 cm; and F4: Depth of 25.6 cm. The circles and lines represent measured and simulated data, respectively. The measurements in F1 and F2 were obtained from EBT films and in F3 and F4 from ionization chambers.

Normalized in-water lateral profiles of 3-D dose distributions. The fields F1, F2, F3, and F4 used to create the 3-D dose distributions, with PDD profiles shown in Fig. 7, are given in Table I. The lateral profiles were measured and simulated at depths corresponding to the center of the volumes. F1: Depth of 6.0 cm; F2: Depth of 10.0 cm; F3: Depth of 15.5 cm; and F4: Depth of 25.6 cm. The circles and lines represent measured and simulated data, respectively. The measurements in F1 and F2 were obtained from EBT films and in F3 and F4 from ionization chambers.

Energy deposition per particle as a function of depth in water simulated using the new MCS algorithm for the 221.8 MeV pencil beam. The solid, dashed, and dotted lines represent the integral energy deposition and the energy deposition in cylindrical tallies with radii 4.08 and 10 cm, respectively. The circles represent measurements using a commercially available ionization chamber with radius 4.08 cm. The inset represents the percentage deviation between the integral energy deposition and the energy deposition in the cylindrical tallies with radii 4.08 and 10 cm, respectively.

Energy deposition per particle as a function of depth in water simulated using the new MCS algorithm for the 221.8 MeV pencil beam. The solid, dashed, and dotted lines represent the integral energy deposition and the energy deposition in cylindrical tallies with radii 4.08 and 10 cm, respectively. The circles represent measurements using a commercially available ionization chamber with radius 4.08 cm. The inset represents the percentage deviation between the integral energy deposition and the energy deposition in the cylindrical tallies with radii 4.08 and 10 cm, respectively.

## Tables

Fields used to create the 3-D dose distributions used in this study. The lateral extent of the fields was and the lateral spacing between the centers of adjacent spots at the isocenter plane was 0.5 cm. : Location of the 90% proximal dose level relative to the Bragg peak dose; : Location of the 90% distal dose level relative to the Bragg peak dose; : Lowest pencil beam energy; and : Highest pencil beam energy.

Fields used to create the 3-D dose distributions used in this study. The lateral extent of the fields was and the lateral spacing between the centers of adjacent spots at the isocenter plane was 0.5 cm. : Location of the 90% proximal dose level relative to the Bragg peak dose; : Location of the 90% distal dose level relative to the Bragg peak dose; : Lowest pencil beam energy; and : Highest pencil beam energy.

Differences between measure and simulated FWHM, FW0.01M, and FW0.001M for in-air lateral profiles at the isocenter plane.

Differences between measure and simulated FWHM, FW0.01M, and FW0.001M for in-air lateral profiles at the isocenter plane.

Differences between measured and simulated FWHM, FW0.01M, and FW0.001M for in-air lateral profiles at positions downstream and upstream of the isocenter plane. The differences were obtained from the data represented in Fig. 5. See caption of Fig. 5 for positions.

Differences between measured and simulated FWHM, FW0.01M, and FW0.001M for in-air lateral profiles at positions downstream and upstream of the isocenter plane. The differences were obtained from the data represented in Fig. 5. See caption of Fig. 5 for positions.

Differences between measured and simulated FWHM, FW0.01M, and FW0.001M for in-water lateral profiles at five depths for 72.5 and 148.8 MeV pencil beams and seven depths for the 221.8 MeV pencil beam. The differences were obtained from the data represented in Fig. 6.

Differences between measured and simulated FWHM, FW0.01M, and FW0.001M for in-water lateral profiles at five depths for 72.5 and 148.8 MeV pencil beams and seven depths for the 221.8 MeV pencil beam. The differences were obtained from the data represented in Fig. 6.

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