DPM as a radiation transport engine for PRIMO
Abstract
Background
PRIMO is a dose verification system based on the generalpurpose Monte Carlo radiation transport code penelope, which implements an accurate physics model of the interaction cross sections and the radiation transport process but with low computational efficiency as compared with fast Monte Carlo codes. One of these fast Monte Carlo codes is the Dose Planning Method (DPM). The purpose of this work is to describe the adaptation of DPM as an alternative PRIMO computation engine, to validate its performance against penelope and to validate it for some specific cases.
Methods
DPM was parallelized and modified to perform radiation transport in quadric geometries, which are used to describe linacs, thus allowing the simulation of dynamic treatments. To benchmark the new code versus penelope, both in terms of accuracy of results and simulation time, several tests were performed, namely, irradiation of a multilayer phantom, irradiation of a water phantom using a collimating pattern defined by the multileaf collimator (MLC), and four clinical cases. The gamma index, with passing criteria of 1 mm/1%, was used to compare the absorbed dose distributions. Clinical cases were compared using a 3D gamma analysis.
Results
The percentage of voxels passing the gamma criteria always exceeded 99% for the phantom cases, with the exception of the transport through air, for which dose differences between DPM and penelope were as large as 24%. The corresponding percentage for the clinical cases was larger than 99%. The speedup factor between DPM and penelope ranged from 2.5 ×, for the simulation of the radiation transport through a MLC and the subsequent dose estimation in a water phantom, up to 11.8 × for a lung treatment. A further increase of the computational speed, up to 25 ×, can be obtained in the clinical cases when a voxel size of (2.5 mm)^{3} is used.
Conclusions
DPM has been incorporated as an efficient and accurate Monte Carlo engine for dose estimation in PRIMO. It allows the concatenated simulation of the patientdependent part of the linac and the patient geometry in static and dynamic treatments. The discrepancy observed between DPM and penelope, which is due to an artifact of the cross section interpolation algorithm for low energy electrons in air, does not affect the results in other materials.
Keywords
Monte Carlo Radiation transport Linear acceleratorAbbreviations
 CT
Computerized tomography
 DTA
Distance to agreement
 GPU
Graphics processing unit
 OAR
Organatrisk
 PSF
Phasespace file
 PTV
Planning target volume
 VMAT
Volumetricmodulated arc therapy
Background
PRIMO [1, 2] is a computer software that simulates clinical linear accelerators (linacs) and estimates absorbed dose distributions in phantoms and computerized tomography (CT) studies. It combines a graphical user interface with the generalpurpose radiation transport Monte Carlo code PENELOPE (version 2011) [3]. It is freely distributed through the website https://www.primoproject.net since 2013.
PENELOPE implements an accurate physics model of the interaction cross sections and the radiation transport process but exhibits a relatively low computational performance compared with fast Monte Carlo codes specifically designed for radiotherapy problems [4]. One such code is the Dose Planning Method (DPM v1.1) [5] which simulates absorbed dose distributions deposited by electronphoton showers in external beam radiotherapy treatments. The opensource code is freely distributed through http://www.upc.es/inte/downloads. The present work describes the adaptation of DPM, hereafter identified as pDPM, to the PRIMO system and its subsequent validation.
pDPM includes a mixedgeometry model that allows the simulation in voxelized and quadric surface geometries. This capability allows the joined simulation of the linac patientdependent part and the patient, hence making possible the simulation of dynamic treatments. The scope of including pDPM as a simulation engine of PRIMO is to facilitate usage of the latter as a Monte Carlo dose verification system for the routine clinical practice.
Methods
The guidelines for reporting Monte Carlo simulations, provided by the AAPM Task Group 268 [6], have been followed in the preparation of this work.
Dose planning method

It uses simplified cross section models that are accurate for the energy range typically employed in conventional radiotherapy and for low atomic numbers, such as those encountered inside the patient body. For example, the KleinNishina differential cross section [7] is used to describe photon incoherent (Compton) scattering, thus neglecting Doppler broadening and binding effects, which are nonnegligible for high Z elements or low energies. Similarly, the Møller differential cross section [8] is used to describe electron inelastic collisions with atomic electrons, thus assuming that the target particle is free and at rest. This, again, is valid for low atomic numbers and high energies.

Photon transport is simulated detailedly using the delta scattering, or Woodcock tracking technique [9], which completely avoids the need to consider intersections with voxel walls.

For electrons, DPM employs the standard condensed history model, falling into what has been called a mixed scheme for the treatment of energy losses by Berger [10]. It treats large energy transfer collisions detailedly and uses the continuous slowing down approximation to describe the effect of small energy loss interactions. For condensing angular deflections, the code is based on a refinement of the Kawrakow and Bielajew [11] formulation of the Lewis multiplescattering theory [12], which allows fast random sampling of the scattering angle. The algorithm further relies on the small angle approximation, under which all materials can be characterized by means of a single scattering angle distribution.
The DPM code has been extensively benchmarked and validated by a group from the University of Michigan [13, 14]. It should be noticed that the bulk of the DPM development effort was focused on the electron transport algorithm. There is still room for improvement regarding the application of variancereduction techniques for photon transport. Despite this fact, the code has been shown to reproduce dose distributions estimated with highaccuracy generalpurpose Monte Carlo codes within an error of the order of 1.5% of the maximum dose with a significant increase in computational efficiency [15].
DPM has been employed as a dose distribution calculation engine by other authors. For example, version 3 beta of the ADAC Pinnacle treatment planning system was based on a C++ port of DPM. ADAC was subsequently acquired by Philips Medical Systems in 2000 but the Pinnacle version based on DPM was never released [4]. The code was also integrated into the University of Michigan’s inhouse treatment planning system (UMPlan) [15]. Additionally, a prototype of a new treatment planning system based on DPM was also developed by Técnicas Radiofísicas (Zaragoza, Spain) [16].
Some researchers have devoted efforts to further accelerate the code. Thus, for instance, Tyagy and coworkers [17] used the Message Passing Interface (MPI) library to parallelize the algorithm, Weng et al. [18] aimed at vectorizing the code and Jia et al. [19] adapted it to the graphics processing unit (GPU) architecture.
DPM improvements
Parallelization of DPM
One of the limitations of DPM is its lack of support for phasespace files or other sources of particles needed for linac simulation. Furthermore, its sequential code cannot fully exploit the capabilities of parallel processors. These capabilities have been added to pDPM as explained in a previous work [20].
Mixed geometry model
The developed mixed geometry model combines bodies defined by quadric surfaces and voxels. The aim is to merge the patientdependent region of the linac, which is modeled by quadrics, and the patient, represented by the voxelized geometry. Therefore, in simulations of dynamic treatments, the transport through both regions can be performed in a single simulation step.
In the mixed model the patient dependent region of the linac is defined according to the rules of PENGEOM, the PENELOPE geometry package, while the voxelized geometry uses the model currently implemented in DPM. To combine both models we rely on an approach that has been used before by Sempau and collaborators in the PENEASY code [2]. Transport in the voxelized geometry proceeds as in the original version of DPM [21] while in the quadric geometry it is performed using the routines included in PENELOPE.
Dynamic geometry
Dynamic geometry uses our mixed geometry model to simulate dynamic irradiations, thus allowing changing the positions of multileaf collimators, jaws, gantry, collimator and couch at execution time. To this purpose the simulation is divided into control points, each one defined by a fixed configuration of the aforementioned movable elements. The fraction of the total number of histories that is simulated for each control point equals the fraction of monitor units as specified in the cumulative meterset weight of the DICOMRTPLAN file.
Variancereduction techniques
Two variancereduction techniques [22] were implemented in pDPM, namely simple particle splitting in the patient and rangerejection of electrons in the internal regions of the MLC and the jaws. Range rejection was implemented through the movableskins technique [23].
pDPM benchmarks
Simulations presented in this article considered a 6 MV beam of a ClinaciX linear accelerator equipped with a Varian Millennium 120 MLC. The particle source employed was a phasespace file (PSF) tallied from the simulation of the patientindependent part of the linac using PENELOPE with initial beam parameters E=6.2 MeV, FWHM_{E}=0.186 MeV, FWHM_{focal spot size}=0.15 cm and a beam divergence of 2.5 degrees. The PSF produces a dose distribution in water that reproduces well the measured dose profiles.
The assessment of the agreement between dose distributions was done using gamma analysis. The reference data sets were those obtained with PENELOPE while the evaluated data sets were those obtained with pDPM. Local gamma analysis was performed with a search volume established according to the distance to agreement (DTA) criterion. The maximum search distance from the reference point to the volume border is calculated as 1.2 DTA. Therefore, any evaluated dose point outside the local volume cannot pass the gamma analysis as it would not comply with the DTA criterion. The search step inside the local volume is set such that at least 5 points are sampled in each spatial direction inside the volume and it is required to be at least half the minimum spatial resolution of both dose distributions. Dose sampling inside the local volume is made by trilinear interpolation. Reference dose values less than 1% of the maximum dose or with uncertainties (2 σ) larger than 10% were not included in the analysis. Gamma pass rate (Γ_{d,DTA}), i.e. the fraction of points passing gamma analysis with a dose difference d (in %) and distance DTA (in mm) criteria was evaluated in all cases. For clinical cases, Γ_{1,1}, Γ_{2,1} and Γ_{2,2} were evaluated in the region inside the patient’s body, in planning target volumes (PTVs) and in selected organsatrisk (OARs).
Additionally, the method proposed by Kawrakow and Fippel [24] was used to compare the dose distributions estimated with PENELOPE and pDPM. This method allows to discern systematic differences from those resulting from statistical fluctuations. In all clinical cases, the dose threshold applied was 50% of the maximum dose and only voxels inside the patient’s body region were considered. For simulations in phantoms the dose threshold applied was 20% of the maximum dose.
Photon transport in a MLC
Photon transport in a multilayer phantom
Dose distributions produced by a 6 MV photon beam were estimated in a slab phantom consisting of seven 5cmthick layers. The phantom dimensions were 40×40×35 cm^{3} with a bin size of 0.5×0.5×0.25 cm^{3}. An open field of 10×10 cm^{2} with a SSD = 100 cm was used. The layer materials were (starting from the upstream phantom surface): muscle skeletal (ρ=1.04 g/cm^{3}), air, lung (ρ=0.3 g/cm^{3}), muscle skeletal, compact bone (ρ=1.85 g/cm^{3}), lung and muscle skeletal [26].
Simulation of photon beams in clinical cases
Three volumetricmodulated arc therapy (VMAT) clinical cases of head and neck, brain and lung were considered in this work. The head and neck plan consisted of two coplanar hemiarcs, covering from 0 to 179 degrees. Each arc had 96 control points. Two PTVs were delineated in the left side of the patient neck (see Fig. 4). The prescribed dose were 40 Gy and 44 Gy in 20 fractions to PTV_{1} and PTV_{2}, respectively. Two OARs were selected for dose comparison, the left parotid gland and the spinal cord. The lung plan also had two hemiarcs, from 181 to 0 degrees with 96 control points each. The PTV was a relatively small region with a volume of 6.9 cm^{3} located in the posterior lung wall near the diaphragm. The prescribed dose to that PTV was 52 Gy in 8 fractions. The brain case is a post surgery irradiation of a brain tumor. Two PTV regions were delimited PTV_{1} and PTV_{2} with prescribed doses of 50 Gy and 60 Gy in 25 fractions, respectively. The plan consisted of two coplanar full arcs with 177 control points each. The brain stem OAR was selected for dose comparison. Additionally, a prostate IMRT plan consisting of five fields distributed at angles of 255, 315, 45, 105 and 180 degrees was included in this study. The total number of control points was 621. The prescribed dose to the prostate PTV was 76 Gy in 39 fractions. The bladder and rectum OARs were selected for dose comparison.
The voxelized geometry generated by PRIMO uses the voxel size provided in the CT scan. However, PRIMO allows to set a fixed spatial resolution of the simulation geometry of 0.25 cm^{3}. This is done by averaging HU in neighbor voxels, each weighted by the fraction of the volume included in the destination voxel. At the end of the simulation the original CT resolution is recovered by interpolating the dose obtained for the coarser voxel size.
Dose distributions were obtained with pDPM, both using the original voxel size and the coarse option, and with PENELOPE only using the original size. The dose distribution obtained with the original CT resolution was used for comparison with PENELOPE. Gamma analysis was applied to all voxels inside the body region.
Simulation times
Simulation times obtained with pDPM were reported in a previous work [20]. However, that article considered only voxelized geometries. For the present study all simulations were carried out in two Xeon E52670V3 CPUs with 12 cores each, and hyperthreading. The compiler used was Intel Fortran v16 for Windows with compilation options /O2 /Qipo /QxP for PENELOPE and /Qopenmp for pDPM. PENELOPE is a serial code, hence, simulations were carried out by simultaneously running 32 instances of the code (each one with different initial random number seeds) and letting the operating system (Windows Server 2016) deal with the task assignment to the CPU cores. In order to provide a source of particles for each PENELOPE instance, the source phasespace file must be partitioned prior to starting the simulation. For the phase space used in this work this partitioning process took approximately 15 min. This time was not taken into account in the benchmark. Conversely, pDPM genuinely runs in parallel, hence, partitioning of the phasespace file is not necessary. The simulations with pDPM used 32 threads. In all cases the simulation time reported corresponds to that required to reach an average standard statistical uncertainty of 1%. The reported dose statistical uncertainties are computed using voxels that score more than 50% of the maximum dose.
Results
Photon transport in a MLC
Systematic differences between the dose distributions estimated with PENELOPE and pDPM for the photon test cases included in this work
Test case  α [%]  Δ[%]  α[%]  Δ[%] 

Described in section Photon transport in a multilayer phantom  
(all voxels)  14.2  5.0  17.0  0.2 
(in the air layer)  97.0  5.3  0  0 
(excluding the air layer)  32.1  0.2  20.4  0.2 
Described in “Photon transport in a MLC” section  26.0  0.4  13.3  0.3 
Head&Neck  32.4  0.8  17.8  0.7 
Lung  36.6  0.8  11.7  0.5 
Brain  30.5  0.6  7.0  0.7 
Prostate  28.1  0.4  18.2  0.4 
Photon transport in a multilayer phantom
Simulation of photon beams in clinical cases
Fraction of points passing gamma analysis with criteria 1%,1 mm (Γ_{1,1}) and 2%,1 mm (Γ_{2,1}) in the region delimited by the body contour, the PTVs and the OARs
Region  Γ_{1,1} [%]  Γ_{2,1} [%] 

Prostate  
Body  99.8  100 
PTV  99.6  100 
Rectum  99.7  100 
Bladder  100  100 
H&N  
Body  99.6  100 
PTV_{1}  98.0  100 
PTV_{2}  96.2  100 
Spine  100  100 
Left Parotid  99.2  99.9 
Brain  
Body  99.7  100 
PTV_{1}  99.4  100 
PTV_{2}  99.1  100 
Brain stem  99.6  100 
Lung  
Body  99.6  100 
PTV  99.2  100 
Simulation times
Simulation times in minutes for PENELOPE and pDPM to obtain a dose distribution with 1% standard statistical uncertainty for some single field cases and dynamic treatments
Simulation time [min]  Speedup  

pDPM  
Test case  Voxel size [cm^{3}]  penelope  Original voxel  Coarse voxel  Original voxel  Coarse voxel 
Described in “Photon transport in a multilayer phantom” section  0.5×0.5×0.25  37  9.5    3.9×   
Described in “Photon transport in a MLC” section  0.2×0.2×0.5  324  129    2.5×   
Head&Neck VMAT, 194 CP  0.19×0.15×0.19  1061  140  42  7.6×  25.3× 
Lung VMAT, 194 CP  0.19×0.14×0.19  331  28  14  11.8×  23.6× 
Brain VMAT, 354 CP  0.11×0.2×0.11  687  117  34  5.8×  20.2× 
Prostate IMRT, 621 CP  0.18×0.25×0.18  472  64  45  7.3×  10.5× 
Discussion and conclusions
DPM has been incorporated as an efficient Monte Carlo engine for photon dose estimation in PRIMO since version 0.3.1.1600. It allows the joined simulation of the patientdependent part of the linac and the patient geometry, thus facilitating dose estimation of dynamic treatments. The version of PRIMO used for this article has been 0.3.1.1681.
PENELOPE and DPM use different physics models. Generally speaking, DPM cross section models are simpler albeit accurate enough for the dynamical range for which the code was designed, that is, low Z materials and high energies. In this work, however, we have used pDPM to simulate the transport in some of the tungsten elements of the linac head. Despite this fact, the comparisons between PENELOPE and pDPM made in this work have not shown a substantial impact on the dose accuracy of DPM physics models simplifications. Thus, a good agreement between the results obtained with PENELOPE and pDPM was obtained for the studied clinical cases, in which 99.9% or more of points passed the 3D gamma analysis with criteria 2%, 1 mm and systematic differences were within ±0.8% of the maximum dose. The discrepancy observed in the multilayer phantom, related to the transport in air, is due to an artifact of the cross section interpolation algorithm for low energy electrons in air. The dose is not biased in any other material, nor at the interfaces with air. Investigations to correct this artifact are currently in progress.
The speedup factor obtained with pDPM with respect to PENELOPE was in all clinical cases between 6 and 12. This speedup factor is further increased when voxels are grouped using the “coarse” option, attaining values in the order of 20. These factors are reached although the transport in the linac geometry hinders the overall efficiency of pDPM owing to the use of the PENELOPE geometry model.
Notes
Acknowledgments
Not applicable.
Funding
The authors acknowledge support by the Open Access Publication Fund of the University of DuisburgEssen.
The authors acknowledge funding by Deutsche Forschungsgemeinschaft project BR 4043/31.
J Sempau was also funded by H2020 EJP Concert, project 0032017PODIUM and the Spanish Networking Research Center CIBERBBN.
Availability of data and materials
The implementation of pDPM in PRIMO is available in https://www.primoproject.net. DPM can be downloaded from http://www.upc.es/inte/downloads. penelope is distributed by the Nuclear Energy Agency.
Authors’ contributions
MR coded pDPM, run the simulations, participated in the conception of the work and writing the manuscript. JS studied the origin of the discrepancy in air, contributed to coding pDPM, participated in the conception of the work and writing the manuscript. CB carried out the statistical analysis and helped to draft the manuscript. BT designed the clinical cases and helped to draft the manuscript. LB coded the linac geometry files and adapted them for dynamic treatments, participated in the conception of the work and writing the manuscript. All authors read and approved the final manuscript.
Ethics approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Competing interests
L Brualla, M Rodriguez and J Sempau declare that they have authored the PRIMO system. J Sempau is coauthor of DPM and penelope.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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