
Figure 2: Nozzle components in a Geant4 model of Mevion S250 scattering pro-
ton system.
tion of the RMW superposes the modulated proton beams with
different energies. The result is a spread-out Bragg peak (SOBP),
with a uniform proton dose curve, inside the water phantom.
Broadening of the proton beam in the model is achieved
through the second scatterer. The unwanted part of the beam is
trimmed by the collimation system which is modeled by highly
attenuating materials such as stainless steel and brass with large
stopping power. The collimation system is modeled with a
stainless-steel cylinder with a 3 cm thickness, 9.75 cm inner ra-
dius, and 36 cm height. A similar structure with a thickness of 2
cm, 15 cm inner radius, and 52.5 cm height was used for the col-
limator with the same material. In addition to the outer cylinder,
the collimator contains two inner rings at its entrance and exit
sides. Each ring has an inner radius of 12.5 cm with the same
material as the outer collimator. A brass aperture with a thick-
ness of 6.84 cm is placed next to the collimator. The center of
the brass aperture contains a square opening.
During the actual treatment, the fine-tuning of the output
beam energy is done by a patient-specific lucite compensator that
varies the depths of the beam at different positions to shield the
healthy tissues from the proton beam. The compensator is mod-
eled with a lucite cylinder of 5 cm height placed as the last step
of the nozzle.
2.2 Geant4 Monte Carlo simulation toolkit
Geant4 (GEometry ANd Tracking) has been developed by CERN
as a general-purpose Monte Carlo (MC) simulation software for
particle transport through matter. Two fundamental aspects of
Geant4 are handling the geometrical shapes and tracking various
particles through objects made of different materials. Detailed ra-
diation transport calculations are performed by the toolkit for that
purpose. The building blocks of Geant4 simulations are G4Step
objects from which information can be stored. Particle transport
involves a 3D simulation of the interactions of particles irradi-
ated through materials with specific geometries. In this work,
the primary particle source is protons.
3 Results and discussion
The proton PDDs and neutron spectra are benchmarked with
measured data. The neutron fluence spectra calculated by Geant4
form the basis of the presented analysis. The properties of the
spectra are described based on the neutron cross-section data ob-
tained from ENDF datasets [1].
Protons form a well-defined dose deposition peak as they
travel through matter, due to the stopping power. The simula-
tion PDD is obtained by emitting a primary proton beam with
250 MeV energy, 2 MeV energy bandwidth, and 1 mm spot size.
Figure 3: Matching the Geant4-calculated pristine percentage depth dose to the
experimental data. Both PDDs correspond to the first step of the range mod-
ulation wheel. The benchmarked parameters include the thickness of the range
shifter (affecting the range in water), the energy width of the primary proton beam
(affecting the range straggling), and the spot size of the initial beam (affecting the
entrance dose height).
Each range modulation step delivers a specific proton beam
energy to the isocenter with a corresponding pristine peak depth.
Rotation of the range modulation wheel leads to a simultane-
ous superposition of the proton beams with various energies, and
depending on the design of the angular extent of each step that
corresponds to their weights, leads to a spread-out Bragg peak or
SOBP.
The main characteristics of an SOBP are range and modula-
tion. The range is defined as the distance from the surface of
the water phantom to the distal 90% proton dose. Modulation is
defined as the distance from the proximal 95% dose to the distal
90% [2]. Specifically, for the treatment setup of the whole brain
the range of 17 cm and modulation of 16 cm has been used in the
work of Howell et al. [2]. The same SOBP has been simulated
in this work for benchmarking the neutron calculations.
Simulation of an SOBP requires a linear combination of sev-
eral pristine peaks with different ranges. Each pristine peak is
obtained by positioning a step of the range modulation wheel in
the primary proton beam path. The final SOBP has a 17 cm range
and 16 cm modulation. The first 15 pristine peaks delivered by
the 15 are used as the base functions in a singular value decompo-
sition (SVD) method to obtain the composition weights. Figures
4 and 5 show the normalized pristine peaks and the SOBP with a
range of 17 cm, respectively.
Figure 4: Normalized proton pristine peaks corresponding to 15 steps of RMW.
To obtain the agreement between the transverse proton dose
profiles, the parameters that define the shape of the second scat-
2