A particle track-repeating algorithm for proton beam dose calculation

Department of Radiation Oncology, Fox Chase Cancer Center, Philadelphia, PA 19111, USA.
Physics in Medicine and Biology (Impact Factor: 2.76). 04/2005; 50(5):1001-10. DOI: 10.1088/0031-9155/50/5/022
Source: PubMed


A particle track-repeating algorithm has been developed for proton beam dose calculation for radiotherapy. Monoenergetic protons with 250 MeV kinetic energy were simulated in an infinite water phantom using the GEANT3 Monte Carlo code. The changes in location, angle and energy for every transport step and the energy deposition along the track were recorded for the primary protons and all secondary particles. When calculating dose for a patient with a realistic proton beam, the pre-generated particle tracks were repeated in the patient geometry consisting of air, soft tissue and bone. The medium and density for each dose scoring voxel in the patient geometry were derived from patient CT data. The starting point, at which a proton track was repeated, was determined according to the incident proton energy. Thus, any protons with kinetic energy less than 250 MeV can be simulated. Based on the direction of the incident proton, the tracks were first rotated and for the subsequent steps, the scattering angles were simply repeated for air and soft tissue but adjusted properly based on the scattering power for bone. The particle step lengths were adjusted based on the density for air and soft tissue and also on the stopping powers for bone while keeping the energy deposition unchanged in each step. The difference in nuclear interactions and secondary particle generation between water and these materials was ignored. The algorithm has been validated by comparing the dose distributions in uniform water and layered heterogeneous phantoms with those calculated using the GEANT3 code for 120, 150, 180 and 250 MeV proton beams. The differences between them were within 2%. The new algorithm was about 13 times faster than the GEANT3 Monte Carlo code for a uniform phantom geometry and over 700 times faster for a heterogeneous phantom geometry.

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    • "2- Neutrons: Since the energy of the neutron is deposited far from the initial point (as illustrated in Figure 1) and their contribution in total dose is less than 0.1%, they can be neglected. This assumption is verified by several groups,[293044] and it is the case for most of the fast MC codes for proton transport. "
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    ABSTRACT: An important requirement for proton therapy is a software for dose calculation. Monte Carlo is the most accurate method for dose calculation, but it is very slow. In this work, a method is developed to improve the speed of dose calculation. The method is based on pre-generated tracks for particle transport. The MCNPX code has been used for generation of tracks. A set of data including the track of the particle was produced in each particular material (water, air, lung tissue, bone, and soft tissue). This code can transport protons in wide range of energies (up to 200 MeV for proton). The validity of the fast Monte Carlo (MC) code is evaluated with data MCNPX as a reference code. While analytical pencil beam algorithm transport shows great errors (up to 10%) near small high density heterogeneities, there was less than 2% deviation of MCNPX results in our dose calculation and isodose distribution. In terms of speed, the code runs 200 times faster than MCNPX. In the Fast MC code which is developed in this work, it takes the system less than 2 minutes to calculate dose for 10(6) particles in an Intel Core 2 Duo 2.66 GHZ desktop computer.
    Journal of Medical Physics 07/2014; 39(3):156-63. DOI:10.4103/0971-6203.139004
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    • "As a statistical method, the total number of particles simulated determines the accuracy of an MC dose calculation and an enormously large number of particles are usually necessary to yield a desired level of precision. Over the years, despite the great efforts devoted to accelerating the MC dose calculation process, such as using large-scale computational hardware and developing simplified algorithms (Kohno et al 2003, Fippel and Soukup 2004, Li et al 2005, Yepes et al 2009), the available proton MC dose calculation methods still cannot meet the clinically acceptable efficiency. The unsatisfactory efficiency also prohibits the development of advanced treatment techniques for proton therapy, e.g. "
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    ABSTRACT: Accurate radiation dose calculation is essential for successful proton radiotherapy. Monte Carlo (MC) simulation is considered to be the most accurate method. However, the long computation time limits it from routine clinical applications. Recently, graphics processing units (GPUs) have been widely used to accelerate computationally intensive tasks in radiotherapy. We have developed a fast MC dose calculation package, gPMC, for proton dose calculation on a GPU. In gPMC, proton transport is modeled by the class II condensed history simulation scheme with a continuous slowing down approximation. Ionization, elastic and inelastic proton nucleus interactions are considered. Energy straggling and multiple scattering are modeled. Secondary electrons are not transported and their energies are locally deposited. After an inelastic nuclear interaction event, a variety of products are generated using an empirical model. Among them, charged nuclear fragments are terminated with energy locally deposited. Secondary protons are stored in a stack and transported after finishing transport of the primary protons, while secondary neutral particles are neglected. gPMC is implemented on the GPU under the CUDA platform. We have validated gPMC using the TOPAS/Geant4 MC code as the gold standard. For various cases including homogeneous and inhomogeneous phantoms as well as a patient case, good agreements between gPMC and TOPAS/Geant4 are observed. The gamma passing rate for the 2%/2 mm criterion is over 98.7% in the region with dose greater than 10% maximum dose in all cases, excluding low-density air regions. With gPMC it takes only 6-22 s to simulate 10 million source protons to achieve ∼1% relative statistical uncertainty, depending on the phantoms and energy. This is an extremely high efficiency compared to the computational time of tens of CPU hours for TOPAS/Geant4. Our fast GPU-based code can thus facilitate the routine use of MC dose calculation in proton therapy.
    Physics in Medicine and Biology 11/2012; 57(23):7783-7797. DOI:10.1088/0031-9155/57/23/7783 · 2.76 Impact Factor
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    • "To fully exploit the potential advantages of IMPT, one must have a fast and accurate dose calculation algorithm. In recent years, a number of such algorithms have been proposed (Deasy 1998, Li et al 2005, 2008, Petti 1992, 1996, Russell et al 2000, Schaffner et al 1999, Soukup et al 2005, Szymanowski and Oelfke 2002), most of which are of the pencil beam type. For most pencil beam algorithms, the doses deposited from the pencil beams are described as the product of a central axis term, which is basically the depth–dose distribution 'Bragg curve' of a broad beam (or scanning pencil beam), and an off-axis term, which describes the lateral dose distribution. "
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    ABSTRACT: Although Bortfeld's analytical formula is useful for describing Bragg curves, measured data can deviate from the values predicted by the model. Thus, we sought to determine the parameters of a closed analytical expression of multiple Bragg curves for scanning proton pencil beams using a simultaneous optimization algorithm and to determine the minimum number of energies that need to be measured in treatment planning so that complete Bragg curves required by the treatment planning system (TPS) can be accurately predicted. We modified Bortfeld's original analytical expression of Bragg curves to accurately describe the dose deposition resulting from secondary particles. The parameters of the modified analytical expression were expressed as the parabolic cylinder function of the ranges of the proton pencil beams in water. Thirty-nine discrete Bragg curves were measured in our center using a PTW Bragg Peak chamber during acceptance and commission of the scanning beam proton delivery system. The coefficients of parabolic function were fitted by applying a simultaneous optimization algorithm to seven measured curves. The required Bragg curves for 45 energies in the TPS were calculated using our parameterized analytical expression. Finally, the 10 cm width of spread-out Bragg peaks (SOBPs) of beams with maximum energies of 221.8 and 121.2 MeV were then calculated in the TPS and compared with measured data. Compared with Bortfeld's original formula, our modified formula improved fitting of the measured depth dose curves at depths around three-quarters of the maximum range and in the beam entrance region. The parabolic function described the relationship between the parameters of the analytic expression of different energies. The predicted Bragg curves based on the parameters fitted using the seven measured curves accurately described the Bragg curves of proton pencil beams of 45 energies configured in our TPS. When we used the calculated Bragg curves as the input to TPS, the standard deviations of the measured and calculated data points along the 10 cm SOBPs created with proton pencil beams with maximum energies of 221.8 and 121.2 MeV were 1.19% and 1.18%, respectively, using curves predicted by the algorithm generated from the seven measured curves. Our method would be a valuable tool to analyze measured Bragg curves without the need for time-consuming measurements and correctly describe multiple Bragg curves using a closed analytical expression.
    Physics in Medicine and Biology 11/2011; 56(24):7725-35. DOI:10.1088/0031-9155/56/24/003 · 2.76 Impact Factor
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