Monte Carlo (MC) methods are considered one of the most powerful and precise approaches to study and solve medical physics issues. They, indeed, can be applied in all the situations where to use deterministic algorithms is infeasible or impossible. Surprising improvements in computer technology have promoted a wide diffusion of this technique, giving rise to the born of several Monte Carlo codes, such as the GEANT4 toolkit. In this paper we show some of the applications we developed using GEANT4. In particular, the simulation of two different radiotherapy

techniques, such as proton/ion therapy and stereotactic radiosurgery will be discussed. In the first case we show the main features of our last public version of the GEANT4 Hadrontherapy program, also discussing the issues related to the nuclear fragmentation. In the second case, we show the procedures followed for the simulation of a Gamma Knife device, in order to validate the Treatment Planning System (TPS) used for the dose computation

Cirrone, G. A. P.

Cuttone, G.

Di Rosa, F.

Mazzaglia, S. E.

Romano, Francesco

Sabini, M. G.

Sardina, D.

English

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2011-10810-5Colloquia: IFA 2010IL NUOVO CIMENTO Vol. 34 C, N. 1 Gennaio-Febbraio 2011Applications of Monte Carlo methods to special radiotherapeutictechniquesF. Romano(1)(∗), G. A. P. Cirrone(1), G. Cuttone(1), F. Di Rosa(1),S. E. Mazzaglia(1), M. G. Sabini(2) and D. Sardina(1)(1) INFN, Laboratori Nazionali del Sud - Catania, Italy(2) Department of Imaging, Cannizzaro Hospital - Catania, Italy(ricevuto il 26 Luglio 2010; approvato l’ 8 Settembre 2010; pubblicato online il 15 Febbraio 2011)Summary. — Monte Carlo (MC) methods are considered one of the most powerfuland precise approaches to study and solve medical physics issues. They, indeed, canbe applied in all the situations where to use deterministic algorithms is infeasibleor impossible. Surprising improvements in computer technology have promoted awide diffusion of this technique, giving rise to the born of several Monte Carlo codes,such as the GEANT4 toolkit. In this paper we show some of the applications wedeveloped using GEANT4. In particular, the simulation of two different radiother-apy techniques, such as proton/ion therapy and stereotactic radiosurgery will bediscussed. In the first case we show the main features of our last public versionof the GEANT4 Hadrontherapy program, also discussing the issues related to thenuclear fragmentation. In the second case, we show the procedures followed for thesimulation of a Gamma Knife device, in order to validate the Treatment PlanningSystem (TPS) used for the dose computation.PACS 87.55.K- – Monte Carlo methods.PACS 87.53.-j – Effects of ionizing radiation on biological systems.PACS 87.53.Ly – Stereotactic radiosurgery.1. – IntroductionWith the term “simulation” we mean the imitation of real things, states of affairsor processes. Monte Carlo (MC) simulations are used in many contexts, including Eco-nomics, Finance, Biology, Chemistry and, not last, Physical Sciences. In particular,medical physics applications have gained great benefits using MC methods. The highlevel of accuracy demanded for cancer treatment with ionizing radiation has led to a highdegree of complexity in the techniques used for the dose conformation to the tumourtarget. For this reason MC codes are today widely used in this field, representing a(∗) E-mail: francesco.romano@lns.infn.itc© Societa` Italiana di Fisica 167168 F. ROMANO, G. A. P. CIRRONE, G. CUTTONE, ETC.fundamental tool for the study of dosimetric systems, the reproduction of clinical beamline, the development and test of new kind of detectors and the verification of the Treat-ment Planning Systems (TPS). All the results presented and discussed in this paperhave been obtained with the GEANT4 (GEometry ANd Tracking) Monte Carlo toolkit,which is, among several codes today available, one of the most versatile and widespreadones.GEANT4 is a C++ object oriented toolkit permitting the simulation of particle inter-actions with matter [1]. It provides advanced functionalities for all the typical domains ofdetector simulation: geometry and material modeling, description of particle properties,physical processes, tracking, event and run management, user interface and visualiza-tion. Initially developed for High Energy Experiments (HEP) simulation, GEANT4 isnow widely used also for medical physics application [2]. It allows, indeed, the tracking ofany charged and uncharged particle relevant for radio diagnostics and radiation therapy.The possibility to allow geometry changes during a simulation is of particular interestfor the medical domain. This significantly facilitates the execution 4D Monte Carlo sim-ulations, where time-dependent information is involved. The applications described inthe following sections make use of this kind of features of the toolkit.Results shown in this paper have been performed with the 9.2 (patch 1) version ofGEANT4 [3].2. – GEANT4 simulations in hadrontherapy2.1. The Hadrontherapy application. – Hadrontherapy is a free and open source appli-cation created, regularly maintained and improved by some of the authors of this paper.It has been initially developed for the simulation of the CATANA (Centro di AdroTer-apia ed Applivazioni Nucleari Avanzate) beam line of the Laboratori Nazionali del Sud(LNS) of INFN in Catania, where ocular tumours are treated using 62 MeV protonbeams accelerated by a Superconducting Cyclotron (CS) [4]. Hadrontherapy permits thesimulation, via simple macro commands, of a typical beam line for proton/ion therapyincluding all the necessary transport elements: diffusion and modulation systems for theparticles spatial and energy distribution, collimators, transmission detectors as well asdetectors for the dose distribution measurements [5]. Since the beginning of its devel-opment, Hadrontherapy has undergone many changes and its capabilities have grown tosuch an extent that in 2009 the authors decided to release a specific version separatedfrom the one included in the GEANT4 Advanced Example. This full version offers manyadds in comparison to the basic one, such as the modularization of the geometry and ofthe implemented physical models, the possibility to easily calculate stopping powers andranges for any couple of ion-material combinations, the implementation of specific algo-rithms for the calculation of the average 3-dimensional LET (Linear Energy Transfer)and a new graphical user interface, based on the QT libraries. Moreover, next versionsof the application will include the possibility to use DICOM interfaces in order to takeinto account the different tissue densities.Figure 1 shows the Hadrontherapy graphic output when LNS proton therapy beamline is simulated. Each beam transport element is exactly reproduced and the simulatedprimary beam (blue tracks) together with secondary particles produced (green and redtracks) are also shown. The red cubic box (on the right) is the volume where dose, fluenceand any useful parameter can be stored.APPLICATIONS OF MONTE CARLO METHODS ETC. 169Fig. 1. – Graphic view of the CATANA proton beam line simulated in the Hadrontherapyapplication.2.2. Carbon ion therapy and related studies. – Besides protons, heavier ions havebeen also investigated in the past for therapeutic purposes, because of their enhancedbiological effects [6]. After many years of studies about the effects of different kind ofions, the scientific community has finally accepted carbon ions as the best compromisebetween local control of the tumour and negative side effects for healthy tissues. Carbonion therapy is now performed in Europe and Japan. Many new hadrontherapy centreshave been recently built or planned [7]. Carbon ions show a higher spatial conformation,thanks to a smaller lateral scattering and an enhanced biological effect at the end of theirpath, where the Bragg peak overlaps the tumour target.On the other hand, the nuclear interactions with the atomic nuclei of the traversedtissues produce charged fragments. This last aspect represents the main drawback comingfrom the use of carbon ion beams. A mixed radiation field is present in the target volume,where both primary and secondary particles travel through the matter with differentbiological effects. For an accurate calculation of the final biological dose, each singlecontribution has to be considered and weighted depending on the respective biologicalefficiency. Monte Carlo simulations represent a powerful tool to reproduce such a complexconfiguration. Using Hadrontherapy we have obtained the depth dose distributions (i.e.,Bragg peaks) of carbon ion incident beams inside a PMMA cubic phantom. It has beendivided into 4000 slices, 10μm of thickness, orthogonal to the beam direction, where thetotal dose is retrieved (fig. 2, left). In order to have reasonable statistical fluctuations(less than 3%) without huge calculation time, a production cut of 0.01mm and a maxStepof 0.01mm have been defined as simulation transport parameters. The data obtainedby the simulation have been compared with data acquired at INFN-LNS of Catania inorder to verify the developed code. An experiment has been performed for this purposewith carbon ions accelerated at 62AMeV. The dose distributions have been measuredwith a parallel plate ionization chamber, having an active volume of 0.055 cm3, polarizedwith an electric field of 300V and coupled with a dedicated electrometer. The chamber,placed in a cubic phantom, is able to measure the depth dose distribution with a spatialresolution of 50μm by means of a motorized system. Figure 2 (right) shows a comparisonbetween experimental and Geant4 Bragg peaks. The good agreement demonstrates theaccuracy of the GEANT4 simulation in the dose reconstruction.For a complete characterization of the clinical beam, dose, fluence, and LET distri-butions of fragments produced at different depths have to be known. We calculated170 F. ROMANO, G. A. P. CIRRONE, G. CUTTONE, ETC.Fig. 2. – Left: cubic phantom used in the simulation to store the released dose at differentdepths. Right: comparison between experimental and simulated carbon ions Bragg peaks at62AMeV on PMMA, normalized at the entrance.these quantities using the Hadrontherapy application, both for primary and secondaryparticles. In fig. 3 an example of secondary particles contribution on the total dose distri-bution is shown. It can be distinguished, in semi-logarithmic scale, the dose contributionfor each atomic number Z and the sum of the secondary particle contributions, whichare responsible of a typical tail just after the Bragg peak. As expected, the main contri-bution in the distal part of the peak is essentially due to α-particles and, partially, alsoto hydrogen isotopes (p, d, t).Fig. 3. – (Colour on-line) Total depth dose distribution (Bragg curve, in black) and contributionsof charged fragments (coloured lines) in PMMA. Dotted line represents the sum of contributionsreleased by secondary particles.APPLICATIONS OF MONTE CARLO METHODS ETC. 171Fig. 4. – (Colour on-line) One of the 60Co sources with the respective collimation system and thespherical phantom. Left: schematic representation of the source and beam channel. Right: vi-sualization of the geometrical elements and trajectories simulated with GEANT4 (photons ingreen, electrons in red).3. – GEANT4 simulation of a Gamma Knife deviceThe Leksell Gamma Knife is a radio-surgical device manufactured by Elekta Instru-ments Inc. and used to treat brain disorders, such as benign or malignant tumours,which are often inaccessible to conventional surgery [8]. In Stereotactic Radiosurgeryhigh doses with sharp dose gradients are delivered in a single session in order to mini-mize undesired effects on critical brain structures adjacent to the target. Since 2005 aGamma Knife unit (model C) has been installed at Cannizzaro Hospital of Catania andseveral patients have been treated so far.Gamma radiation, emitted by 201 60Co sources arranged in a hemispherical shape,focuses on the isocentre, where the target volume has to be located. The radiation beamis collimated by means of fixed and mobile collimation systems in order to obtain fourpossible beam diameters at the isocentre: 4, 8, 14 and 18mm. Using an AutomaticPosition System it is possible to combine different “shots” to cover complex shapes oftumour. Calculations of the delivered dose are performed by the TPS Leksell GammaPlan(LGP) [9]. It includes some approximations related to the gamma-rays energy and thetarget material in order to compute the prescribed dose in a reasonable time.We simulated the GammaKnife device installed in Catania for the purpose of verifyingthe accuracy of the TPS and to check if the simplifications used in its algorithms canaffect the planned dose distributions. Similar studies have been already carried outwith the Monte Carlo codes EGS4 [10], PENELOPE [11] and MCNP [12], where all theradioactive sources have been fully simulated. Our application has been developed usingthe GEANT4 toolkit, with original solutions involving time-dependent geometries.3.1. Monte Carlo simulation and comparison with the TPS . – The Gamma KnifeUnit consists of a cast-iron body containing the 60Co sources and the collimation system.Sources are displaced along five parallel rings at the same distance from the isocentre.Depending on the specific ring, sources are located with a different spacing, respectivelywith an angle of 7.6◦, 8◦, 9◦, 9◦ and 10◦. Photons of 1.17 and 1.33MeV are emitted andcollimated by cylindrical and conical lead elements. A spherical phantom is placed atthe isocentre for routinely measurements of dose distributions at different depths.We have simulated this device considering a different approach respect to the pre-viously mentioned works. Indeed, exploiting the geometrical symmetry of the sourceswe decided to simulate only one single source (with the respective collimators) rotatingthe spherical phantom, rather than reproduce 201 sources with a fixed phantom (fig. 4).In such a way, the final dose distribution is due to the integration of the contributions172 F. ROMANO, G. A. P. CIRRONE, G. CUTTONE, ETC.Fig. 5. – (Colour on-line) Comparison between GEANT4 results and LGP predictions in thecentral plane (axial) of the spherical phantom, for the 14mm collimator. Left: X profiles andgamma index (line on the top). Right: isodose curves and gamma index (in grey levels).related to 201 different angular positions. This solution permits a simpler code develop-ment and higher flexibility for further modifications of the sources location (dependingon the specific Unit model). The absorbed dose in the phantom has been stored usinga voxelized geometry similar to the Hadrontherapy application (see subsect. 2.2), withcubic voxels of 1 mm of side. In order to achieve acceptable statistical fluctuations (lessthan 3%), a huge number of primary events must been sampled; hence, the simulationhas been split into 20 jobs and submitted to a Linux cluster installed at LNS-INFN.In order to verify the reliability of the Gamma Knife application, a set of experimentalmeasurements has been carried out at Cannizzaro Hospital. GafChromic films have beenirradiated inside a spherical phantom with all the available collimators. Digital imagesof the films have been acquired with a transmission scanner and analyzed in one and twodimensions. Experimental and simulated dose distributions have been compared withthe GEANT4 results, with a good agreement.Once the application has been validated, it has been used to study and verify thedose distributions predicted by the LGP, which computes the released dose in a 3D arrayof 31 × 31 × 31 elements arranged in a cubic shape, considering the phantom entirelycomposed by water. X-Y profiles and isodose curves respectively of the GEANT4 ap-plication and LGP have been superimposed. For a quantitative comparison between thetwo dose distributions we have used the gamma index method, which combines togetherthe “dose-difference (DD)” and “distance-to-agreement (DTA)” [13]. This method allowsto compare point by point two dose distributions and to show their level of agreementaccording to the acceptance criteria which characterize the specific radiotherapeutic tech-nique. In fig. 5 (left) a comparison between GEANT4 and LGP X profiles is shown forthe 14mm collimator. Points not passing the gamma index test cross the straight line onthe top of the graph. In the same figure (right) the isodose curves for both the two dis-tributions are represented; points with an acceptable agreement are visualized in white,while points which do not pass the gamma index test are in grey levels. The comparisons,executed for each available collimator, demonstrate as the dose analytically calculatedby LGP is in agreement with the Monte Carlo predictions. Therefore, we can concludeAPPLICATIONS OF MONTE CARLO METHODS ETC. 173that LGP compute the dose to be delivered to the tumour target with a good level ofaccuracy. On the other hand, LGP predictions get worse when different density materialsare considered in the dose calculation. The presence of inhomogeneities, indeed, causesuncertainties in the LGP computations because of the approximations included in thealgorithm [14].4. – Conclusions and perspectivesMonte Carlo methods play an important role in medical physics applications, in par-ticular in case of complex methodologies and devices, representing the best approachwhen also different tissue densities have to be taken into account.The results presented in this work show how the GEANT4 Hadrontherapy applicationis able to simulate in detail each element of a proton/ion beam, well reproducing themeasured depth dose distributions. Moreover, it permits to study the issues relatedto the carbon ions fragmentation, considering the single contributions of the producedisotopes. These results together with the knowledge of the LET distributions are usefulto link radiobiological data with physical ones. On this regard we plan to include newinteresting features in the future versions of the application, such as the implementationof a radiobiological model for the evaluation of the biological damage.The simulation of the Gamma Knife demonstrates how the use of interesting featuresof GEANT4 allows to reproduce in a simple way also the most complex geometries, evenmaintaining high level of accuracy. The Gamma Knife application, still in a privateversion, has been recently proposed and accepted by the GEANT4 international collab-oration as a public example; it will be included among the Advanced Examples categoryfor the future releases of the toolkit.The topics discussed in this paper clearly show as the Monte Carlo techniques repre-sent a powerful tool which medical physics community has been more and more widelyusing.REFERENCES[1] Agostinelli G. et al., Nucl. Instrum. Methods A, 506 (2004) 250.[2] Allison J. et al., IEEE Trans. Nucl. Sci., 53 (2006) 270.[3] The GEANT4 website, http://geant4.cern.ch.[4] Cirrone G. A. P. et al., IEEE Trans. Nucl. Sci., 51 (2004) 860.[5] Cirrone G. A. P. et al., IEEE Trans. Nucl. Sci., 52 (2005) 262.[6] Amaldi U. et al., Riv. Med., 14 (2008) 7.[7] Cuttone G. and Calabretta L., Riv. Med., 14 (2008) 43.[8] Elekta, Leksell Gamma Unit - User’s Manual (Elekta Instrument, Stockholm) 2003.[9] Elekta, Reference Manual for Leksell GamaPlan (Elekta Instrument, Stockholm) 2003.[10] Cheung J. Y. C. et al., Med. Phys., 25 (1998) 1673.[11] Moskvin V. et al., Phys. Med. Biol., 47 (2002) 1995.[12] Trnka J. et al., Med. Phys., 34 (2006) 63.[13] Low D. et al., Med. Phys., 25 (1998) 656.[14] Romano F. et al., Proceedings of the 2007 IEEE Nuclear Science Symposium and MedicalImaging Conference, Honolulu, Hawaii, U.S.A., 27 October - 3 November 2007 (2007),p. 2581.

Applications of Monte Carlo methods to special radiotherapeutic techniques

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Applications of Monte Carlo methods to special radiotherapeutic techniques

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