GEANT4 & GAMOS- A Particle Implementation of High Energy Simulation Toolkit to Oncology Therapy

Sonali Bhatnagar Department of Physics and Computer Science Dayalbagh Educational Institute, Agra-282110 deisonali.bhatnagar@gmail.com

S.N.L Sirisha Research Scholar

sirisha.dei@gmail.com

Abstract— Monte-Carlo simulation is an essential tool that assists in the design of new medical imaging devices; optimize the treatment planning in dose estimation to control tumors in oncology therapy. Geant4 and GAMOS (Geant4 based Application for Medicine Oriented Simulations) implements the optimized radiotherapy external beam application, the propagation through an accelerator geometry and the calculation of the dose in voxel phantoms. This paper gives an overview of the physical processes involved along with detailed description of the design and implementation to medical physics in Geant4 and GAMOS toolkits. We have calculated the dose deposition of a passive proton beam of 60 to 240 MeV in a human phantom geometry. The resulting Bragg peak, range, penumbra width has been calculated and verified with results of other groups. The applications of these systems in fields of nuclear fragmentation for carbon ion therapy, nuclear imaging and hadrontherapy for in vivo dose monitoring are also discussed. Keywords: Oncology therapy, Dose Estimation, GAMOS, GEANT4, Nuclear Fragmentation.

I. INTRODUCTION

In cancer treatment, one of the important approaches is radiotherapy which is applied after surgery. Protons and light nuclei are in use for irradiating tumors. Due to the finite range with precise ballistics and their maximum dose deposition at the end of the beam penetration with an improved biological effect efficiency in the Bragg Peak region make these heavy charged particles advantageous than X-rays in this treatment. One can target the heavy charged particles in curing tumors while preserving the healthy tissues. In case of carbon or heavier ions, the dose required is nearly 1/3rd of the dose delivered by X-rays due to the increased biological efficiency[1]. Light ion therapy is also much efficient in treating the radio—resistant tumors due to the low oxygenation rate of cancerous cells. This oxygen effect in case of ions helps is vanishing the radio resistance.

A. Present status of hadron therapy and its main advantages compared to conventional X-ray therapy:-

Initially for treating the cancers, the different therapeutic approaches developed are surgery, chemotherapy and X-ray therapy. But due to lack of control on tumor and also development of metastatic, these cancerous tissues are aimed to destroy by using ionizing particles while preserving the surrounding healthy tissues. The most crucial stage in this therapy is to accurately sight tumors which are deeply located in body while preserving simultaneous the surrounding tissues. This is not achieved in case of X-ray therapy due to its

ballistics. So the original 60Co source is replaced by a compact linear accelerator to deliver high energy X-rays undergoing bremstrahlung process induced by slowing down of high energy electrons in conversion target. The Intensity Modulated Radio Therapy (IMRT), the cyber knife and tomotherapy are different irradiation procedures developed to improve in efficiency. Unlike photons, charged particle beams have a well defined ballistics. For these projectiles, the maximum, dose deposition is located at the end of the path with a sharp peak defined as a Bragg Peak. This location of Bragg peak is also dependent on the particle incident energy. This feature can accurately sight the tumor with a weak dose deposition on the tissues located before Bragg Peak and with very weak dose deposition after Bragg Peak. Different energies are required for painting a tumor which results in a plateau spread from the combination of different energies. This plateau is termed as Spread Out in Bragg Peak (SOBP). This depends on the size of tumor and number of beams used to paint it. The biological effect induced by the charged particles also plays a crucial role in particle therapies. This biological response depends on radiation and tissue weighting factors of radiation protection. The radiation weighting factor / quality factor accounts for biological effect of different radiation qualities. For heavy ions, it is 20 whereas tissue weighting factor considers the radio-sensitivity of different organs. To determine the equivalent dose, both weighting factors are necessary to consider the radiation risk in the most conservative way. But this is entirely different from Relative Biological Efficiency (RBE) as it deals with the radiation quality and tissue specific response as well as biological end point and the dose level of radiation. RBE is the ratio of dose of the source radiation (e.g X-rays or γ-rays) to the dose of charged particle to produce an identical biological effect (iso effect),

RBEiso = It requires both the specification of reference radiation and the level of biological effect. The biological dose quantifies the dose of conventional radiation which yields same biological effect as the applied radiation. It can also be used for many biological end points such as DNA strand breaks, mutations or transformation. The treatment of hypoxic tumor also poses a significant challenge in this field. When tumor grows in its size, there is a need of new blood vessels to supply oxygen to the cells in the tumor core. They are of minor quality and also result in lower oxygen level as compared to healthy cells. In

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case of large tumors, this hypoxic condition is centered and also leads to a larger radio resistance. This effect is explained by oxygen enhancement ratio :

(OER) = Dhypoxic & Daerobic are doses with reduced & normal oxygen supply which results in same biological and clinical effect. It is quite different from RBE i.e. OER is a dose-modifying factor and is independent of dose. The RBE value increases with size of ion & ORE decreases with size of ion. OER=1, for ions heavier than neons i.e. the oxygen effect almost disappears.

B. Treatment Planning System (TPS):

TPS is software developed to compute the accelerator parameters to develop 3D dose map in it. It includes the clinical images, graphical software for organs identification, to irradiate the contouring area. At Heidelberg Ion therapy (HIT), a local effect model (LEM) is used to compute the biological effects from physical dose. A simplified version of TPS is explained in 1 dimension. Let us assume to irradiate an l cm long segment in water. Its proximal points are set at 8 cm. For an incident energy Ei, there exists a corresponding depth dose profile Di (x). The dose at depth x for different energies D(x) = Σi Ni Di (x). Biological dose D(x) = Σi Ni Di (x) BF(x). Here BF(x) is the biological factor. Now we want to determine Ni to deposit a wanted biological dose Dwanted (x) at depth x. so.

For biological dose computation:

Here the RBE depends on the linear energy transfer (LET) of particle. In next section, we can see that LET is close to stopping power dE/dx of the particle in material. The LET values for proton ranges from 0.5 MeV/mm to 3 MeV/mm and RBE =1 where biological dose is equal to physical dose. Whereas for carbon ions it ranges from 20 MeV/mm. to 250 MeV/mm. where RBE varies between 1.3 and 3 [2]. The use of this biological model leads to a different weights distribution & to a different physical SOBP. TPS also has its extended applications in order to deliver a 3D dose map.

C. Beam Delivery System

In order to transport the particle beam to the treatment area and distribute the beam over planned target volume accurately and uniformly with desired dose distribution we require a treatment planning system in this radiotherapy. It has two basic strategies ie fully passive systems with fixed beam modulation or fully active beam scanning system. For passive beam system, the particle beam is adapted in three dimensions to target volume by passive non variable field shaping elements. In case of active beam system, a target

volume is dissected in voxel and a pencil beam is used to fill the voxel with appropriate dose. The passive beam when delivered from accelerator is first broadened by a double scattering system which generates a flat transversal profile in most efficient way. A range modulator is used to spread out the mono energetic Bragg Peak to cover the entire length of target volume. The resulting SOBP is shifted in depth by absorber plates (“range shifter”). A collimator is used to present the particle defection from the field. The distal depth pattern is adjusted by range compensator. But the fixed width of the SOBP is the major limitation of the system. For active beam delivery system, the dose is sequentially delivered to the voxelised region of target volume. Even an irregular volume can be exactly determined without any need of neither field specific nor patient specific hardware. The production of secondary particles, beam losses can be minimized. But it needs a stable and reproducibility of beam position in a accelerator. This technique is been in use for tumor therapy at the proton therapy facility at PSI (Switzerland) and carbon ion facility GSI. The broad beam method is also employed at two clinical carbon-ion facilities i.e. Heavy Ion Medical Accelerator (HIMAC) in Chiba and Hyogo Ion Beam Medical Centre (HIBMC) in Japan. Nearly 36 hadron therapy centers are already in operation for both proton and carbon ions. The National French Hadrontherapy Centre (ETOILE) project, a treatment centre is located in Lyon and Advance Research Center for Hadrontherapy in Europe (ARCHADE) project for hadron therapy research is located in Caen. The depth dose profile of the SOBP generated by ridge filters is designed to produce a constant biological effect while considering the variation of RBE as function of depth.

D. Physics for Hadron Therapy.

In therapeutic use of charged particles, the Bragg Peak location has to be within 1 mm. and the dose in tumor has to be delivered within 3%. For conventional therapy, the initial dose buildup by high energy photons is caused by forward scattered Compton electron which shifts the peak dose by a few centimeters away from the surface of patient’s body. In contrast to photons, the position of this peak can be precisely adjusted to a desired value in depth of incident ions. But protons and heavier ions also differ in two features essentially: Protons have a similar biological effect as photons (at the same absorbed dose) while heavy ions show high effectiveness, ranging from low RBE values in plateau region to a significant enhancement in Bragg Peak. Unlike proton, heavy ions exhibit a characteristic dose tail behind the Bragg peak, which is caused by secondary fragments produced in nuclear reactions along the stopping path of the ions, resulting in a complex radiation field. The dose deposited in tissue is the most important physical quantity in radio therapy. The absorbed dose (Gray Gy) as the mean energy deposited by ionizing radiation in a mass

element due If the fluency and material’s density are known then physical

dose can be computed from

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N/dS is fluency of the beam, dE/dx is Stopping power of the particle, ρ is material’s density.

1) Stopping Power The physical processes responsible for dose deposition are necessary to be understood for computing the stopping power for a particle. Inelastic is the significant process which results in collision of nuclei on the electrons of atoms present in target matter. Thus the projectile of kinetic energy Ec looses energy.

where ec is energy of out coming electron and I is Ionization potential of that electron. Linear energy transfer is the energy transferred by the material to material per unit length

where is total kinetic energy of δ electrons having energy above a given threshold. If some δ electrons are coming from an elementary volume depositing their energy in the volume consideration. This can balance the energy of δ electrons produced in that volume. Also in first approximation we can identify the stopping power, LET and absorbed energy in elementary volume of thickness dx, dE/dx = LET = Edep/dx. To compute the stopping power induced by collision on electrons, Beth Bloch formula used:

Zt is target atomic number, Zp is projectile atomic number, e is electron charge , me is electron mass, ν is projectile velocity, β = ν/c, c is light velocity, C is shell correction factor, δ density effect correction, < I > is mean ionization energy

Zi & Ai : charge & mass numbers for elements , ωi mass ratio of element i in the material, Ii: ionization energy of element i from Janni tables. Elastic Coloumb Scattering is another process which can slow down particle penetration in matter. It induces range end lateral spreading. The elastic collision with target nuclei is significant at low energies Ec< 10 keV/u. But this process is neglected for hadron therapy applications. Electron capture leads to an effective charge of projectile. The term Zp is replaced by Zeff = Zp [ 1 - exp (- 125β Zp

-2/3)]. This is important at Ec< 10MeV/u. Bremstrahlung process is also neglected in hadron therapy application. The nucleus-nucleus collisions which produce secondary particles with longer ranges than the projectiles range. For protons, the inelastic collision on electrons is the most dominant one for all energies. For carbon ion this process is dominant except for last few µm in path.

2) Particle Range & Particle energy: For a given energy per nucleon, the range of a projectile is proportional to the ratio A/Z2 where A is projectile number of charges. The corresponding energy range for protons is 0 to 220 MeV and from 0 to 425 MeV/υ for 12C ions [2].

3) Range & Angular Straggling: The inelastic collisions leads to an energy straggling which can be parameterized the following way

Where σ

E = 4π Zeff Zt e2 N ∆x

Where Zt is target number of charges, Zeff is projectile effective charge, β is the projectile velocity in (units E projectile kinetic energy.)

4) Relative Range Straggling,

M is projectile mass; f is varying function depends on absorber. But this relative range straggling is smaller for heavier particles. Lateral spreading of beam is mainly due to multiple Coulomb Scattering. This is smaller for heavy ions than for protons. For small deflections, the angular distribution of projectile after passing through a distance‘d’ of absorber can be described by Gaussian distribution

Lrad is radiation light parameter of absorber material. Although there are many papers discussing the physical aspects of radiotherapy, but there are individual tools developed in optimizing the treatment planning systems used in therapeutic use. In this paper we have given a detailed outline of how the architecture of Geant4 has evolved according to requirements of the users. In Section II and III, we discuss the flexibility in architecture, models and physics processes required by the user of Geant4 and GAMOS. The applications of these toolkits in field of oncology therapy also presented. In this paper we have also presented a basic study of the Bragg peak and further parameters like Bragg peak position, range and penumbra width for the passive proton beam in a human phantom represented by a homogeneous medium. The simulated data was then compared with the work done by ASO et. al and the values matched. Thus we can now extend this work to the more realistic studies of dose deposition in organs of the human body and its effect on its surrounding tissues.

II. GEANT4 – ITS APPLICATIONS TO ONCOLOGY

THERAPY:

Now-a-days the treatment planning systems used in the radiotherapy are optimized using Monte-Carlo techniques. There is a real time opportunity for wide spread use of analogue Monte Carlo interfaced to commercial treatment planning systems in this area. Geant4 is a Monte-Carlo Simulation toolkit developed for applications in high energy physics experiments using an object-oriented methodology with applications in medical science and astrophysics experiments [3]. It provides a wide set of tools for medical physics applications such as accurate and flexible geometry and material description; particles tracking within any geometry,

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material and field; an ample variety of physics processes, interface to powerful visualisation, GUI and analysis tools. Particularly relevant to medical applications are the physics functionalities provided by Geant4, such as extensions of electromagnetic interactions down to low energies and a powerful hadronic physics toolkit, suitable for particle cancer treatments such as Boron Neutron Capture Therapy or Hadrontherapy.

Figure 1: Hierarchy System in Object Oriented toolkits [3]

Simulation of nano-scale effects of radiation at the DNA level in various scientific domains involved medical, biology, genetics, physics, software engineering. Multiple approaches can be implemented with Geant4 RBE parameterisation, detailed biochemical processes, etc. Research in nano dosimetry, nanotechnology-based detectors, radiation effects on components in space and at high luminosity colliders, nuclear power, plasma physics etc. would profit not only of new Geant4 physics functionality, but also of new methodological approaches to radiation transport simulation. Radioactive Decay developed to evaluate the interaction of hadronic and electromagnetic physics domains at the software design level. Physics processes at the nano-scale in various materials: a first step towards co-working micro-macro scale simulation. The proton beam deposits its maximum dose located at the end of the path. This results in a Bragg peak curve where its location depends on the biological effects induced by the charged particles. The proton beam gradually slows down by energy loss undergoing multiple coulomb scattering with material. The consistency of dose deposition may also be influenced by inhomogeneous materials present in path of beam direction. These inhomogenities results in degradation of Bragg peak and its range. This uncertainty in dose distribution can be determined from Full Width Half Maximum which has a large impact on treatment system because maximum dose of proton may be delivered to normal tissue. The distance between the entrance surface of beam and distal point of 80% of energy deposition results in particle range during beam irradiation. Another parameter, penumbra width gives the resultant absorbed dose in distal region of Bragg peak. So, initially the effect of proton Bragg peak in a homogeneous medium is studied. The Geant4 toolkit, version 4.9.4.p04 was chosen to simulate a homogeneous medium depicting the human phantom of dimension 100x100x100 cm3. The proton beam penetrates along x-direction perpendicular to human phantom as shown in Figure 2.

Figure 2: Homogeneous Medium used in study of Energy deposition of proton beam.

Physics models used for study of Electromagnetic and Hadronic Interactions are given in Table 1.

TABLE 1: THEORETICAL MODELS USED:

The Bragg peak of proton beam within the energy range of 60-240 MeV was studied and is shown in Figure 3.

Figure 3: Energy Deposition of proton beam in Homogeneous Medium.

From Figure 3 we infer that on increasing the proton beam incident energy, the energy deposition with respect to depth in phantom also gradually increased. The parameters obtained with respect to different proton energies are listed in Table 2.

TABLE 2: BRAGG PEAK PARAMETERS OF PROTON BEAM FOR ENERGY RANGE 60-240MeV.

Energy (MeV)

Bragg Peak Pos (mm)

Range (mm)

Penumbra (mm) (20%) Penumbra Width

60 24.37 28.92 38.6 -9.68

80 44.43 51.34 61.02 -9.68

100 73.76 78.31 82.65 -4.34

120 103.86 108.39 112.16 -3.77

140 134.04 139.32 144.6 -5.28

160 174.09 178.54 182.31 -3.77

180 214.05 219.18 222.45 -3.27

200 254.1 259.11 266.15 -7.04

220 304.13 309.31 311.25 -1.94

240 352.27 358.89 364.08 -5.19

Our simulation results obtained from the present study of energy deposition of proton beam penetrating through a water phantom is also comparable with available NIST [6] data and ASO et.al [7] at different energies i.e. 150 MeV, 190 MeV and 230 MeV. The proton range at different energies in water is given in Table 3.

Electromagnetic standardem_opt3

Hadronic Elastic G4HadronElastic (0-500GeV)

Hadronic Inelastic Binary -Pre Compound(<100MeV)

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TABLE 3: PROTON RANGE COMPARISON WITHIN SIMULATION AND NIST [4] DATA, ASO et.al [5].

Energy (MeV)

Depth (mm)

NIST ASO et.al (GEANT4.6.0)

Present sim. (GEANT4.9.4.p04)

150 157.7 157.6 158.933 190 237.7 237.6 239.07 230 329.1 329.4 329.443

A human phantom is handled through the builder design pattern. The 3D representation of the geometrical model and trajectories, etc; is generated using HepRepFile visualization driver and also shown in Figure 3. It generates files in the HepRep format, suitable for viewing with WIRED frame.

An electron beam of 50 MeV is incident on phantom. Charged particles removed from beam after the target. The energy deposit can be calculated in the organs of the human phantom. Brachytherapy – another application developed for precise evaluation of the effects of source anisotropy in the dose distribution. A thin volume is placed to score gamma beam properties. The radial radiation dose distribution can be determined inside the phantom.

Figure 4: Geant4 Brachytherapy Application

III. GAMOS: APPLICATIONS TO ONCOLOGY

THERAPY:

GAMOS (Geant4 based Application for Medicine Oriented Simulations) is also a simulation framework which facilitates the use of Geant4 by avoiding the need to use C++ coding while compared to other codes based on Geant4 such as MULASSIS (MUlti-LAyered Shielding SImulation Software), GRAS (Geant4 Radiation Analysis Software), PTSIM (Particle Therapy Simulation) and TOPAS (Tool for Particle Simulation). It is used as an interface to minimize the problems arising in other simulation codes such as peculiar

volume shape, a novel primary generator, and position distribution in physics processes [6]. All Monte Carlo codes have further sub systems such as random number generator, rules to sample probability distributions and sets of probability density functions. In the field of radiotherapy, the Monte-Carlo simulation codes such as GAMOS are also in use to perform realistic simulations where the dose and imaging systems have been optimized.

Figure 5: Application of GAMOS toolkit.

PET & SPECT applications in GAMOS contain two phases. In first phase, a simple ring detector is defined in the Geometry. The general setup is shown in Figure 6.

Figure 6: Simple Ring Detector designed in GAMOS The parameters used to build the utility are number of crystals per block, no. of blocks of crystals per ring, number of rings of blocks, crystal size, trans-axial, crystal size, axial radial and diameter of detector ring. In second phase, it contains the PET event classifier, and a couple of histogram classes. It counts the reconstructed hits having 511 keV of within a precision of minimum energy 0.7* 511 keV and maximum energy of 1.3*511 keV. The output includes the origin positron and secondaries created with respect to the range (mm) during annihilation process. Angle between the secondaries when created and hit the sensitive detector can be studied. Further the conversion of incident photons to photoelectrons undergoing photoelectric effect, Compton, Rayleigh process and energy lost by them at different positions also defined as a desired output. There is also a utility available for image construction of the PET/SPECT output. Compton Camera is a another application which contains a utility to build a compton camera composed of either rings of detectors or a stack of parallel detectors. It is defined as scattered detector where Compton scattering is the ideal interaction of incident gamma rays and absorber detectors where photoelectric absorption is the ideal gamma ray interaction. Stochastic Origin Ensemble (SOE) is an algorithm developed for image reconstruction studied in this toolkit. In Compton camera application [7], the coincidence of a scatter

Figure 3: Geant4 Human Phantom

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and absorber detector is tending to store in data files using SOE. This is done for construction of Compton camera. A medical gamma or electron linear accelerator is designed for transportation of initial beam of particles. The utilities available in this application can also satisfy the use of dose computation in brachytherapy, X-ray CT, hadrontherapy or dosimetry. The dose from the same accelerator is calculated for several voxelised phantoms. The real movement of an accelerator head, the phase space can be displaced or rotated in this framework. IV. DISCUSSION AND FUTURE WORK: Monte Carlo methods are extensively used in field of radiotherapy applications for optimizing the treatment planning systems. The interfacing approach in the Geant4 toolkit developed for nuclear medicine and radiotherapy was studied. There are also ample choices of Physics models available in the toolkit to exploit the user for study of electromagnetic and hadronic physics interactions in different applications. The Monte Carlo simulation systems i.e. GAMOS because of its specific features such as voxelised phantom, advanced visualization tools, dose estimation maps allow these systems to be used for different applications such as realistic simulations in field of hadrontherapy, complicated 3D sources, emission tomography systems. Further the Geant4 studies also can be extended for different organs depicted as inhomogeneous volumes inside the human phantom. The study will include the shift in the Bragg Peak and other parameters such as Bragg Peak Position, Range, and Penumbra Width with respect to the homogeneous water phantom. This study is presently being done and shall be submitted for publication soon. We are also aiming to compute the amount of dose necessary to deposit using proton and carbon ion beams for different ages of human in soft and bone tissues.

References: [1] Dieter Schardt, “Heavy-ion tumor therapy: Physical and

radiobiological benefits”, Review of Modern Physics, Volume 82, January-March 2010.

[2] Daniel Cussol, “Nuclear Physics and Hadrontherapy”, LPC Caen, ENSICAEN, Universite de Caen Basse-Normandie, IN2P3/CNRS, 2011.

[3] S. Agostinelli, J. Allison, K.Amako, J.Apostolakis, H.Araujo, P.Arce et.al, “Geant4-A Simulation Toolkit”, Nucl. Instrum. Meth. A, 2003; vol. 506: 250-303.

[4] M.J Berger, J.S Coursey, M.A Zucker, J.Chang, “Stopping Power and Range Tables for electrons, protons and helium ions”, NIST-Physics Measurement Laboratory [cited October 2009]. Available from: http://www.nist.gov/pml/data/star/

[5] T.ASO, A. Kimura, S.Tanaka, H.Yoshida, N.Kanematsu, T.Sasaki et.al “Verification of Distributions with Geant4 Simulation for Proton therapy”, IEEE Transc. Nucl. Sci, 2005; Vol. 52: No. 4 896-901.

[6] Pedro Arce, Juan I. Lagares, Laura harkness, Laurent Desorgher, Gainluca de Lorenzo, Yamiel Abrue, et.al “GAMOS: an easy and flexible way to use Geant4”, 978-1-4673-0120-6, IEEE Trans. Nucl. Sci., 2011; 978-1-4673-0120-6/11 (2230-2237).

[7] Luca Christopher Stackhausen, “Evaluation of Compton Camera Imagingduringboron neutron capture therapy”, May 2012.

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