Integration and evaluation of automated Monte Carlo simulations in the clinical practice of scanned proton and carbon ion beam therapy

J Bauer; F Sommerer; A Mairani; D Unholtz; R Farook; J Handrack; K Frey; T Marcelos; T Tessonnier; S Ecker; B Ackermann; M Ellerbrock; J Debus; K Parodi

doi:10.1088/0031-9155/59/16/4635

1. Introduction

Ion beams exhibit favourable properties for highly conformal dose delivery to solid tumours, with excellent sparing of surrounding healthy tissue and critical structures. These ballistic advantages can be optimally exploited with state-of-the-art delivery such as three-dimensional intensity controlled raster scanning (Haberer et al 1993), which is the only beam application modality available at the Heidelberg Ion Beam Therapy Center (HIT, Haberer et al 2004) in Germany.

Inverse treatment planning of ion beam therapy is typically performed with analytical treatment planning systems (TPS) relying on fast-performing pencil-beam algorithms (Hong et al 1996, Krämer et al 2000). In this context, Monte Carlo (MC) simulations are increasingly considered essential tools to support and complement analytical TPS. In particular, vast application to passively scattered proton therapy has proven the value of MC in highlighting well-known shortcomings of analytical pencil-beam algorithms in the presence of severe tissue heterogeneities and metallic implants (Paganetti et al 2008). Beam scanning poses additional challenges due to the tighter conformation of the dose delivery and the additional degree of freedom of intensity modulation, making the treatment planning models more sensitive to the correct characterization and transport of the several thousand pencil beams forming the entire treatment field. However, MC experience for clinically used scanned ion beams, especially in the case of carbon ions, is still scarce.

At HIT MC simulations based on the particle transport and interaction code FLUKA (Fassó et al 2005, Battistoni et al 2007) have been thoroughly validated against pencil beam measurements in water and air (Parodi et al 2012, 2013). The code has also been used to create the physical basic data given as input to the commercial TPS (syngo^® RT Planning from Siemens), as well as to perform recalculations of treatment plans in water for comparison to the TPS calculations and the dosimetric measurements of plan verification (Parodi et al 2012, 2013). However, for clinical application it is also desirable to compare MC and TPS dose calculations in the heterogeneous patient anatomy as given by Computed Tomography (CT) data, where dosimetric verification is not accessible. To this aim, an easy-to-use computational framework has been developed to enable automated CT-based FLUKA MC calculations of physical and biological dose in the clinical routine.

This paper describes the implementation and systematic evaluation of the framework, aiming to provide recommendations on the required input settings for the different ion species. Moreover, it addresses a comparison of MC and TPS calculations obtained under different conditions, providing an insight on the extent of dosimetric and range uncertainties for different treatment sites and ion species, as well as highlighting the consequences of speed-up approximations of analytical TPSs.

2. Material and methods

2.1. Automated MC calculations

The automation of FLUKA MC calculations of patient treatment plans at HIT is realized via a graphical user interface developed within the MeVisLab environment (www.mevislab.de, Unholtz et al 2011) and a dedicated python library for the processing of the DICOM files and FLUKA data. In the standard workflow, the platform allows the user to pre-process the anonymised DICOM files exported from the TPS (e.g. by providing a CT-sub-image selection to minimize memory consumption when running the simulation, or by properly coding the Hounsfield Units HU of the stereotactic frame visible in the planning CT but not present at the time of irradiation), to create all the files and directories necessary for parallel FLUKA simulations on a high performance computing cluster, to start the FLUKA calculation and to monitor the simulation process. After completion, the program automatically merges the FLUKA outputs of parallel runs, calculates RBE (relative biological effectiveness)-weighted dose for the individual treatment fields and the entire fraction, using an RBE of 1.1 for protons and the LEM1 framework used by the TPS for carbon ions (Scholz et al 1997, Krämer et al 2010, Mairani et al 2010), and converts the MC results into a suitable format for visualization and analysis in the dedicated graphical interface (cf figure 1). On-the-fly conversion of dose-to-medium into dose-to-water is always performed during physical and biological calculations (cf appendix A), thus providing the results in both formalisms. Distributions of dose averaged LET (Linear Energy Transfer) can optionally be generated for proton beams (cf appendix A), and this feature has been recently exploited to address different LET-based biological dose calculations and resulting range variations in proton therapy, as will be reported in a separate contribution.

**Figure 1.** Schematic representation of the python-based framework for automated FLUKA calculations, including actions to be done either once ('General input') or for each patient and treatment field ('Patient-specific input, execution of MC simulation' and 'Post-processing'). The bold text refers to the operations performed by the dedicated visualisation platform, designed to properly prepare the DICOM input data extracted by the TPS and to visualise/analyse the MC results in comparison to the TPS.
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For consistency to the TPS, the FLUKA physics settings are the same as used for the generation of the TPS basic data in water (Parodi et al 2012, Parodi et al 2013), and the biological settings are based on the same RBE tables used by the TPS (cf appendix B, table 2). For CT-based calculations the MC patient model relies on the stoichiometric calibration of (Schneider et al 2000, Parodi et al 2007a, 2007b) with proper facility- and CT-number-dependent adjustments or 'correction factors' of the electromagnetic and nuclear processes as in (Jiang and Paganetti 2004), to provide consistency with the CT-range calibration curves used by the TPS for all the available CT protocols of different anatomical locations. This method, already described by (Parodi et al 2007a, 2007b) for protons in FLUKA, has been verified to result in sub-millimeter range agreement between MC and TPS in homogenous materials of different HU values for both ion beam species. The modeling of the scanning beam delivery is performed as described in (Parodi et al 2010), using the nominal beam width in air at isocentre and reducing the beam energy according to the water equivalent thickness of the beamline with the permanently installed beam monitor elements. The geometry of optional beamline elements such as the ripple filter (Weber and Kraft 1999) is explicitly implemented and rotated by the defined treatment angle around the isocenter and the CT geometry, which is kept fixed in the MC coordinate system.

For proton beams, experimental validation of MC recalculated treatment plans in water has been reported in (Parodi et al 2012), showing very good agreement with mean deviations of up to 1% between MC dose calculation and multiple pin-point ionization chamber (IC) measurements. For carbon ion beams, we present in this work similar dosimetric investigations especially designed to be sensitive to the fragment contribution, in order to confirm the satisfactory performances of the code and of our dedicated fluence-based scoring (cf appendix A), thus supporting the reliability of the findings reported in section 3.3. In terms of tissue heterogeneities, additional MC validations have been performed in parallel to the TPS commissioning via multiple IC dose measurements in water after proton and carbon ion beam interaction in different inhomogeneous phantoms. In this work we show the dosimetric comparison for the most complex case of an anthropomorphic Alderson half-head phantom, which has been modeled in both the MC and the TPS on the basis of the CT image of the experimental set-up to account for the tissue heterogeneities in a similar way as for clinical scenarios.

2.2. Evaluation of the optimal configurable settings

Examples of clinical cases with tumours located in homogenous (brain: p_Hom_H, C_Hom_H), heterogenous (skull base: p_Het_H, upper spine: C_Het_HN) and deep seated (sacral: p_Het_B, C_Het_B) anatomical locations have been selected for both ion species. For target volume definition, the ICRU margin concept was used based on clinical target volume (CTV) and additional PTV margin of typically 3 mm in the head and neck and 5 to 7 mm in the body regions. The treatment plans were generated by the medical physics team using the latest version of our clinical TPS, including pencil beam splitting and a double Gaussian parametrization for multiple Coulomb scattering (MCS), a raster scan lateral spacing of 2 or 3 mm using the available beam size (FWHM) to ensure lateral dose homogeneity, a depth separation of 3 mm using the ripple filter for carbon ion beams, and inverse treatment planning with multi-field as well as biological optimization (based on RBE = 1.1 for protons and clinical RBE tables for carbon ions). Details are reported in table 1. For all the considered cases, simulations were first repeated keeping the geometry and dose scoring grid fixed to the native resolution of the planning CT, but varying the fraction of primary simulated particles as {0.1, 0.5, 1.0, 2.0, 3.0, 6.0, 10}% of the total planned ions for the carbon ion patients and as {0.1, 0.5, 1.0, 2.0, 3.0}% for the proton patients. In a second step the influence of resampling the CT image was investigated by increasing the lateral pixel size by a factor of {1.5, 2, 2.5, 3, 3.5} for a fixed native slice distance of 3 mm in both the MC geometry and scoring grids, as a coarser resolution reduces memory requirements and speeds up the calculation. Finally, we investigated the influence of the scoring grid alone by performing the simulations on the native CT resolution but calculating the dose on a coarser 2 x 2 x 2 mm³ grid, similar to the TPS approach. In the two latter scenarios, the simulations were performed either using a fixed number N of primaries (chosen according to the results of the statistical analysis for the native CT grid) or adjusting the number of primaries to compensate for the statistical changes in the scoring volumes, taking into account the Monte Carlo statistical dependence with √N. All the resulting biological or absorbed dose-to-water distributions of the carbon ion and proton patients, respectively, were evaluated in terms of Dose-Volume-Histogram (DVH) statistics.- For the planning target volume (PTV) the parameters D₅, D₉₅ and resulting Δ = D₅-D₉₅ were used to evaluate the DVH steepness, which was reported in (Paganetti et al 2008) to be highly dependent on the MC statistics. For the organs at risk (OAR) the parameters D₅, D_7.5 and D₁₀ were analyzed as relevant endpoints likely dependent on the choice of the scoring and transport grid. The chosen DVH thresholds were preferred over more extreme values, such as D₂ or D₉₈, due to their reduced dependence on the method used for DVH calculation. For all the analyses presented in this work (cf also section 2.3), DVHs were consistently processed from the 3 D dose distributions and DICOM structures using the same tools implemented in MeVisLab. The calculation is performed on a voxel basis, including voxels according to the midpoint decision, typically interpolated on a voxel grid of 0.5x0.5x1.5 mm³.

Table 1. Overview of considered clinical-like cases for scanned proton ('p') and carbon ion ('C') irradiation to homogeneous ('Hom') and heterogeneous ('Het') anatomical locations in the head ('H'), head and neck ('HN') and body ('B') regions, corresponding to the dose distributions of figures 7 and 8. Planning details include energy range, target volume, dose prescription, CT acquisition protocol and native resolution, number of planned ions ('#IonsTP'). Simulation details include the CT sub-volume used for the calculation, the number of parallel runs and the average CPU requirements per primary history. The last column depicts the suggested fraction of planned ions to be simulated, yielding stable DVH results with acceptable execution times.

ID	Energy [MeV/u]	Target volume [ml]	Prescribed Dose [Gy(RBE)]	CTprotocol	Native resolution [mm²]	MCSubvolume[#voxels]	#IonsTP	#runs	t_CPU/prim [s]	Reference statistics [%]
p_Hom_H	48–105	98.3	2	S4-Head	0.61×0.61	263×308×37	4.15E10	120	8.6E-03	0.5 (1*)
p_Het_H	81–133 (F1)80–136 (F2)	63.8	2	S4-Head	0.61×0.61	317×220×43	1.44E101.35E10	120	2.2E-02	0.5 (1*)
p_Het_B	54–178	1460.9	3	S4-Body	0.98×0.98	310×218×92	32.9E10	40	2.5E-02	0.1
C_Hom_H	89–208	67.6	3	S4-Head	0.61×0.61	322×155×32	0.53E09	120	6.8E-02	6
C_Het_HN	98–210	153.0	3	SO-Head/Neck	0.98×0.98	260×138×53	1.02E09	120	6.3E-02	3
C_Het_B	219–430	1772.1	3	S4-Body	0.98×0.98	363×166×89	8.40E09	80	2.3E-01	2 (1*)

2.3. Quantitative comparison between MC and TPS calculations under different conditions

In our facility we use a MC computational platform which is intrinsically consistent to the TPS pencil beam model in water, due to the usage of MC-generated basic data in the clinical TPS (cf section 2.1). These basic data in water include laterally integrated depth dose distributions and double Gaussian parametrization of lateral profiles for physical dose calculations, as well as fluence spectra and stopping power for all the fragments generated by primary carbon ion beams for LEM-based biological calculations (Parodi et al 2012, 2013). Furthermore, for CT-based calculations in materials different than water, we adjust on-the-fly the internal MC stopping power calculation to follow the same CT-range calibration curve of the TPS, using proper correction factors calculated for all the three CT protocols in clinical use (cf section 2.1).

Despite the consistency of the beam model in water and of the stopping power calculation in materials relative to water, radiation transport in matter is handled in a completely different way by the stochastic MC approach and the deterministic analytical pencil beam calculation. Thus, we investigated the different performances of the MC explicit particle transport and interaction with respect to the analytical TPS solution for clinical-like treatment fields in heterogeneous CT patient geometries. For all the plans reported in table 1, TPS and MC (with the optimized settings of section 2.2) dose distributions have been quantitatively compared in terms of DVH (for the entire treatment fraction) and distal range (for individual treatment fields). For the latter comparison, range difference maps were obtained by analyzing different fall-off positions of the dose distribution along the beam penetration depth in beam eye view (BEV) within the projected region of the PTV. Results presented here are based on the distal 90% dose threshold of the extended treatment field, with positive range difference values indicating a larger range of the TPS dose distribution. For the identified case showing the largest deviations, the treatment plan was additionally recalculated with MC in pure water and compared to the plan verification calculation of the TPS in water, in order to eliminate effects due to the handling of tissue heterogeneities in the CT geometry. Additional comparisons were performed for different approximations of the TPS pencil beam algorithms, which can provide improvements in computational speed at the expense of accuracy. The investigated approximations featured (i) neglecting pencil beam splitting (i.e. the subdivision of individual pencil-beams into several beamlets) for proton beams and (ii) disregarding lateral beam scattering for carbon ion beams, which were the simplifications used by a first pre-clinical TPS version at our facility. The crude ray-tracing approximation without pencil beam splitting could be reproduced in the MC calculation as follows. The coordinates of the primary beam particles were first randomly sampled according to the usual approach based on the nominal Gaussian beam profile at isocenter (Parodi et al 2010), but then laterally displaced to the central beam axis for starting beam transport. During beam transport, the opposite lateral displacement was applied to the scoring positions every time a dose deposition was generated. Lateral broadening due to electromagnetic interaction could be easily disregarded by using the possibility to switch-off multiple Coulomb scattering in FLUKA. Since angular emission of nuclear fragments plays also an important role but cannot be easily suppressed, additional simulations were performed to score the individual particle fluence of ions (1 ≤ Z ≤ 6) and neutrons, in order to assess their spatial distribution and impact on the dose delivery. Finally, we investigated the impact of considering a single virtual source of the beam, which may be assumed in planning systems for simplicity, with respect to the correct implementation of the scanning process with about 70 cm distance between the horizontal and vertical scanning magnet in the horizontal beamlines of our facility.

3. Results and discussion

3.1. Automated MC calculations

The developed software framework enables automated MC recalculation of patient treatment plans with only a minimum number of straightforward user interactions with the dedicated graphical user interface (e.g. for selection of the patient identifier), without requiring a-priori MC knowledge. Figure 2 illustrates an example of calculated fraction dose distribution with related dose-averaged LET maps, which appear to be smeared-out for the considered multi-field proton irradiation of a skull-base tumour.

**Figure 2.** TPS-optimised (top) and FLUKA recalculated absorbed dose-to-water (middle) with corresponding dose-averaged LET maps (bottom) for an exemplary proton treatment field delivered to a skull base tumor. The sagittal (left), coronal (middle) and axial (right) dose and LET views are shown as color wash display overlaid onto the gray-scale planning CT used for the calculation. In the display of dose, the clinical target volume is encompassed by a green contour, while the relevant critical structures are encompassed by magenta contours. In the display of LET (without structures), values below a 10% threshold of the maximum have been omitted to suppress statistical fluctuations.
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In terms of the experimental validation carried out prior to clinical evaluation, figure 3 illustrates the MC calculation of a scanned carbon ion Spread-Out-Bragg-Peak (SOBP) in water. In the high dose region, an agreement with the measured data better than 2% was found, which is below the 3% uncertainty of the dose-to-water calibration of the used air-filled ICs (IAEA 2000). A remarkable agreement was also observed for the more critical measurement positions which are sensitive to the fragment contribution, such as in the distal tail of the depth dose profile (panels a–b) and at large out-of-axis distance in the lateral dose profiles (panels c–f). This investigation in the presence of a pronounced mixed radiation field also demonstrates the consistency of the intrinsic dose scoring of FLUKA, which is based on energy deposition events, with the approach based on track-length fluence estimator and mass stopping power, which has been implemented and used throughout this work to perform the on-the-fly dose-to-water conversion and the dose-averaged LET calculations (cf appendix A). Figure 4 depicts the dosimetric evaluation of two treatment fields designed to place a proton and carbon ion SOBP in water (where the ICs were placed), after traversal of a heterogeneous Alderson half-head phantom. Relative dose deviations ΔD between the measured and MC calculated absorbed doses normalized to the dose maximum (as done for the dosimetric treatment plan verification in our facility) were found to be on average below 1%, thus supporting the reliability of the developed computational framework. The shown data also suggest an improved performance of MC both in the presence of large dose gradients distal to the target volume (left, protons, ΔD_p = −0.7 ± 4.3 %) as well as in the more homogeneous central dose region (right, ¹² C, Δ D₁₂ _C = 0.1 ± 1.4 %) in comparison to the TPS (ΔD_p = 0.5 ± 8.4 %; Δ D₁₂ _C = −2.8 ± 1.3). However, the observed differences remain below the already mentioned dose-to-water calibration uncertainties of 2% (p) and 3% (¹² C) for dosimetry with air-filled ICs, as well as the 3% MC statistical uncertainties in the high dose region, besides additional unavoidable experimental uncertainties in the measuring process (beam delivery, monitor calibration, positioning of the ICs and of the heterogeneous phantom), especially in the presence of large dose gradients.

**Figure 4.** Dosimetric comparison between MC and TPS calculations of dose-to-water against multiple IC measurements, calibrated in dose-to-water. The selected test irradiation consisted of a cubic SOBP delivered to a water tank (where the ICs were placed) after traversal of a half-head Alderon phantom in the beam path, to mimic a patient-like situation with heterogeneities. Exemplary 24 chamber positions are shown for irradiation with protons (left) and carbon ions (right). These positions were selected to include steep dose gradients (from 50 mGy/mm to 150 mGy/mm for the last 9 chambers) distal to the target volume (a and c) and in a more homogeneous central dose region (b and d). Both absolute dose values (top row) and percentage differences relative to the global maximum dose Dmax (bottom row) are depicted.
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3.2. Evaluation of the optimal configurable settings

The dosimetric impact of variations in the number of simulated primary beam particles, the voxel size of the CT geometry and the dose scoring grid has been studied for all six considered clinical cases (cf table 1). Concerning the impact of simulation statistics, the steepness of the target volume DVH was analysed in terms of Δ=D₅-D₉₅. For all cases we observed a decrease in Δ with increasing particle statistics, as illustrated in the DVH comparison in figure 5 for the PTV of two exemplary treatment plans. In order to derive a recommendation for a sufficient simulation statistics with reasonable computational time, we considered those runs, where the change in Δ between two subsequent simulation scenarios with increasing statistics was below 2%.

**Figure 5.** Exemplary results of the sensitivity study for the PTV DVH variations depending on the fraction of MC simulated primaries with respect to the total planned number of ions for two considered carbon ion (top) and proton (bottom) treatment plans (cf table 1).
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The resulting suggested statistics is reported in the last column of table 1, referred to as 'reference statistics'. We found significantly lower values for the proton simulations (below 1%), compared to the carbon ion simulations which required at least 1% (up to 6%) of the total planned ions to fulfil the defined DVH criteria.

For the subsequent investigation of the dosimetric dependency on the voxel size, simulations were performed with the respective reference statistics, except for the two proton cases p_Hom_H and p_Het_H, where it was feasible to enhance the statistics by a factor of two at an acceptable computing time, and the carbon ion case C_Het_B, for which we decided to reduce the reference statistics by a factor of two in order to perform the full set of simulations on a reasonable time scale. These modified reference values are marked in table 1 by a star.

For the simulations with varied voxel size (both CT geometry and dose scoring detector) we investigated changes in D₅ and D₉₅ for the target volume and in D₅, D_7.5 and D₁₀ for OARs.

Variations in the DVH parameters for the target volume with respect to the reference simulation were found to be below 0.5% for both ion species cases (except 2% for C_Het_HN with the distal part of the treatment field located in the heterogeneous bony structure of the spine, cf figures 6 and 7) and are therefore considered negligible. Concerning the OAR parameters, we found a systematic dependency for the spinal cord structure of C_Het_HN, which can be attributed to its particular location downstream the treatment beam right behind the distal dose fall-off (cf figures 6 and 7). Deviations of the DVH parameters D₅, D_7.5 and D₁₀ are increasing with the voxel size, up to about 10% compared to the reference value, with largest deviations observed for D₅. For the evaluated OARs of the other patient cases no such systematic dependency could be observed. Changes were below 1% for the rectum and uterus structure of C_Het_B, and below 1.5% for brain stem, left and right optical nerve of p_Het_H. Due to the very long processing time for case p_Het_B we simulated only the scenario of a voxel rescaling by a factor of 3.5 (figure 6). Findings for the target volume were consistent with the results of the other cases. The DVH parameters of the evaluated OARs showed minor deviations of up to 3.5% with respect to the reference run for distal structures like the rectum (figure 6 and 8) and the left ovary, and even smaller deviations of below 1% for laterally adjacent structures like the left femur.

**Figure 6.** Exemplary results of the MC sensitivity study for the PTV and OAR DVH variations depending on the voxel size of the CT and scoring grid ('Voxel') as well as the fixed scoring grid of 2x2x2 mm³ ('TPS-like') using the standard ('high stat') or reduced ('low stat', to compensate for the enlarged scoring grid) simulation statistics for the carbon ion (top, C_Het_HN) and proton (bottom, p_Het_B) treatment plans in heterogeneous anatomical locations (cf table 1). The DVHs from the TPS are additionally shown for comparison.
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**Figure 7.** Overview of clinical-like carbon ion treatment fields for the considered homogenous and heterogeneous sites in the head, head & neck and body (cf details in table 1), reporting MC-recalculated RBE-weighted dose-to-medium (left) and dose-to-water (middle) in comparison to the TPS-optimised plan (right). The PTV (contoured by the green line) is shown for all cases, while critically located OARs (red line: spinal cord of C_Het_HN) are only shown for cases that are in particular discussed in the analysis.
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**Figure 8.** Overview of clinical-like proton treatment fields for the considered homogenous and heterogeneous sites in the head, head & neck and body (cf details in table 1), including MC-recalculated absorbed dose-to-medium (left) and dose-to-water (middle) in comparison to the TPS-optimised plan (right). The PTV (contoured by the green line) is shown for all cases, while critically located OARs (red line: brain stem of p_Het_H, rectum and left ovary of p_Het_B) are only shown for cases that are in particular discussed in the analysis.
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The DVH parameter analysis of the TPS-like simulation scenario (i.e. native CT resolution but coarser scoring grid of ca. 2x2x2 mm³) did not show a significant impact: the observed variations for the target volumes were negligible (up to (0.5–1.0)%), largest deviations of up to 4% with respect to the reference simulation were found for the distal OARs of cases C_Het_HN (spinal cord, figure 6 and 7) and p_Het_B (left ovary and rectum, cf figure 6 and 8) and about 2.4% for the lateral-distal brain stem structure of case p_Het_H. These deviations in the dosimetric parameters observed for the TPS-like simulation scenario could be mitigated by adapting the simulation statistics in order to compensate for the enlarged voxel size, considering the √N dependence of the MC statistical uncertainty as explained in section 2.2 (figure 6).

3.3. Quantitative comparison between MC and TPS calculations under different conditions

Figures 7 and 8 present an overview of TPS plans (dose-to-water) with corresponding MC recalculations (dose-to-water and dose-to-medium, obtained with the reference settings discussed in section 3.2) for the exemplary carbon and proton ion clinical indications summarized in table 1.

In terms of dosimetric (dose-to-water) comparisons in the target volume, D₉₅ was found to agree within 1% for carbon ion cases and within 2% for proton cases, hence indicating a reasonable consistency between the two dose calculation engines (cf figure 6). However, local dose deviations of up to 5% within the target volume were observed for proton treatments in heterogeneous anatomy (e.g. p_Het_H) or in the presence of heterogeneities in the beam entrance due to previous skull surgery (e.g. p_Hom_H) and up to 10% for the deep seated carbon ion treatment of C_Het_B. In the latter case, the enhancement of MC simulated dose was only restricted to the biological effective dose (cf figure 7) and is reduced in the absorbed dose distribution (cf figure 9). This can be attributed to the explicit transport in the MC of light target recoils, which were not included in the fragment spectra used by the TPS and whose biological contribution is known to be overestimated by the LEM1 model version (Elsässer et al 2011) used by the TPS.

**Figure 9.** MC recalculations of absorbed dose-to-medium (left) and dose-to-water (middle) in comparison to the TPS plan (right) for the same carbon ion treatment field of figure 7, shown there in terms of RBE-weighted biological dose.
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Examples of range difference maps are reported in figure 10. In terms of range analysis, a very good agreement with an average BEV range deviation in the projected PTV area of -0.4 (-0.2) mm and a RMS of 2.3 (1.6) mm was observed for subject p_Hom_H (C_Hom_H) with homogenous target area. For the C_Het_HN subject treated with carbon ions in a heterogeneous site a range deviation of (0.1 ± 1.1) mm was found between TPS and MC, while the heterogeneous proton case p_Het_H yielded slightly higher deviations of (1.1 ± 4.0) mm for the first and (0.7 ± 3.6) mm for the second field. For the two irradiation plans covering the lower abdominal region we observed severe range differences in the boundary region of the treatment field which were ascribed to artifacts in the dose distribution near the treatment table position, and were therefore suppressed in the range analysis by restricting the considered area to the inner part of the treatment field projection in BEV. Resulting range differences were (-0.2 ± 4.8) mm for p_Het_B and (1.5 ± 5.9) mm for C_Het_B.

For the proton case showing the largest deviations in the range analysis for the dose calculated in the CT geometry, p_Het_H, a MC recalculation of the treatment plan in water was found to be consistent with dosimetric pin-point IC measurements in the same order of magnitude (1–2% deviation normalized to the dose maximum) as the dosimetric verification prediction of the TPS. This confirms that the larger deviations observed in the patient anatomy mostly originate from differences due to the particle transport in the highly heterogeneous CT geometry and not in pure water as approximated by the TPS. The largest range deviations for the carbon ion case C_Het_B were ascribed to the already outlined quantitative differences in the biological dose calculation, and might be improved in future studies by using more robust range estimators than the 90% dose fall-off position. In fact, range estimation from distal fall-off levels is more suited to the case of smooth TPS distributions, but can become more sensitive to dose level fluctuations (beyond statistics) when using MC simulations, which indeed exhibit increased dose heterogeneity due the more realistic description of electromagnetic and nuclear interactions in tissue.

In terms of possible speed-up approximations in analytical TPSs, figure 11 demonstrates the impact of pencil beam splitting for the broad and highly scattering proton beams. In particular, the special MC implementation emulating the simple ray-tracing approximation without splitting yielded an impressive agreement with the simplified calculation of a premature pre-clinical TPS prototype, which we had received for testing as a precursor of the finally delivered clinical version. In the clinical TPS, the dosimetric depth of each dose calculation point is computed via ray tracing, starting from the virtual beam source and ending in this point. Thus, pencil beam splitting is performed on the scale of the dose grid resolution that is typically 2 and 3 mm in the head and body region, respectively. Indeed, subdividing the proton pencil-beams into several beamlets provides a much better agreement with the standard MC calculation of the same original plan (i.e. optimised by the early pre-clinical prototype). Remaining differences between the standard MC approach and the current clinical TPS version are due to range mixing effects, meaning that the TPS calculations are performed along a straight line for each beamlet, while the MC calculation accounts for mixing contributions from neighbouring areas due to scattering. This results in an enhancement of spiky distal dose edges after large density gradients lateral to the beam direction in the analytical calculation (cf figure 11 right panel). Although our investigation was restricted to the more extreme case of completely neglecting pencil beam splitting, we have introduced an original computational method for emulating TPS analytical ray-tracing in a MC engine. A similar approach could also be used to simulate the TPS subdivision of each scanned beam in several beamlets to be transported with ray-tracing, simply by changing accordingly the lateral displacement of the sampled particles and of the dose scoring. This could offer an independent MC method to validate different TPS implementations of pencil-beam splitting.

In terms of approximations owing to the reduced scattering of carbon ion beams (Krämer et al 2000a), figure 12 illustrates MC calculations including ('MCS') and excluding ('noMCS') multiple Coulomb scattering for a lateral profile sampled in the center of the target volume of a carbon ion spinal indication similar to patient C_Het_HN (figure 7 of section 3.3). The MC calculations are compared to the original TPS plan taking into account lateral beam broadening in depth according to the double Gaussian parametrization ('DG'), as well as its forward TPS re-calculation completely neglecting the broadening ('noDG'). This comparison clearly shows a non-negligible influence of scattering on the lateral extension of the field, confirming the improved performances of planning systems which do account for this effect, such as the later release of the TPS in clinical use at our facility. In particular, a good correspondence is pairwise observed in the high dose region between the two different calculation approaches with (MC: 'MCS', TPS: 'DG') and without (MC: 'noMCS', TPS: 'noDG') scattering. Remaining differences between the MC and TPS calculations in the low dose region are attributed to the angular emission of the nuclear fragments, which is still handled by the MC even when switching off multiple Coulomb scattering, but is never perfectly reproduced by the TPS. Specifically, the halo induced by secondary particles is completely neglected by the TPS when using a single constant Gaussian lateral beam profile in depth ('noDG'), or can only marginally be reproduced by the used double Gaussian parameterization ('DG', Schwaab et al 2011). For a deeper understanding, figure 13 depicts the MC calculated fluence of ions (1 ≤ Z ≤ 6) and neutrons along the same lateral profile. This analysis highlights the laterally varying abundance of the light and heavy components of the mixed radiation field, which due to the different charge exhibit a different sensitivity to multiple Coulomb scattering, as well as a different LET likely resulting in a different biological contribution. In particular, the dominant abundance of carbon ions in the tumour region is evident, qualitatively explaining the enhancement in the biological dose due to the higher RBE values of carbon ions compared to lighter fragments. Our findings are consistent with the observations of Lühr et al 2012 on the radiobiological impact of nuclear fragmentation for carbon ion SOBPs in water, suggesting a weak dependence of radiobiology on the detailed composition of the mixed radiation field as long as the physical distribution (dominated by carbon ions) is correctly reproduced. Nevertheless, fragments and neutrons reduce the quality of the dose deposition outside the target volume, producing a halo which can only be properly modeled when taking into account the lateral broadening of the depth dose distribution with its spectral components.

**Figure 13.** Lateral fluence of ions (1 ≤ Z ≤ 6) and neutrons, sampled along the same profile of figure 12. The different contribution of neutrons and heavy and light fragments is illustrated with different colours and linestyles. In particular, the out-of-field contribution of neutrons and light fragments is evident.
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Finally, for a reasonably small (~ 70 cm) separation of the scanning magnets with respect to their typical several meters long distance to the isocenter (~ 6.8 m in our facility), no significant difference was observed between a trustful MC implementation and an approximation placing the origin of the beam at the geometrical center of the scanning magnets. For example, for a 1 Gy delivery to a cubic target voume of about 6 cm side placed at 20 cm penetration depth in water, mean and maximum dose differences of 3.9 (5.4) mGy and 21.5 (29.9) mGy were found in the SOBP region for protons (carbon ions) simulations at less than 1% statistical uncertainty, respectively. Hence, in this beamline configuration the approximation of a single virtual source can be considered fully adequate, but special care should be taken in the case of different beamlines arrangements, such as gantries with large separation of the scanning magnets.

4. Discussion and conclusion

MC calculations are a powerful tool to validate and support ion therapy treatment planning and, especially, for introducing new treatment techniques, indications and ion species in the clinical practice. In this work we have developed a dedicated computational framework to provide automated FLUKA CT-based calculations of clinical treatment plans for scanned proton and carbon ion beams in a workflow efficient way, i.e. with few interactions for non-experienced MC users. For a consistent comparison between TPS and MC calculations, a dose to water conversion scheme has been introduced not only in terms of absorbed dose, but also of RBE-weighted dose (cf appendix B). Extensive characterization of the framework allowed us identifying initial recommendations on the optimal fraction of primaries in dependence of the ion species and tumor location for reliable results within acceptable execution times, i.e. enabling completion of the MC calculation of the total fraction dose within one day, which is typically before the plan is dosimetrically verified and approved for delivery. In particular, our findings suggest that the largely reported MC experience in passively scattered proton therapy cannot be directly translated to scanned carbon ion fields, which is attributed to the different relevance of nuclear reaction processes. In fact, the increased loss of primary carbon ions from nuclear interactions results in a different recommendation on counting statistics for similar performances in terms of DVH stability, as well as in a high sensitivity to the correct description of the mixed radiation field and, particularly, to the impact of low energy recoils on RBE-weighted dose (cf figures 7 and 13). On the other hand, the reduced role of scattering results in a reduced sensitivity of carbon ions to the influence of heterogeneity on the beam range in contrast to protons (cf the standard deviations of the range histograms in figure 10).

Moreover, our results indicate a minor dependency of the evaluated DVH parameters on the size of the transport and scoring grid within the studied variations, with larger effects apparently depending on the location of the OAR (i.e. largest variations were observed in the case of distal OARs). Preservation of the statistical uncertainty per scoring volume by reduction of the statistics N in simulations with a coarser scoring grid generally showed a mitigation of the dosimetric differences (cf figure 6). Moreover, changes in the studied OAR DVH parameters always showed a dose overestimation tendency with increasing scoring grid size, i.e. lower spatial resolution, which would imply a conservative estimate for treatment planning. All these observations suggest that increasing the scoring grid (while preserving the natural CT resolution for transport) and reducing accordingly the simulation statistics could be a viable approach for optimizing execution times. However, further investigations addressing a more systematic evaluation in a larger population study will be needed to confirm our initial findings and devise general recommendations on the clinical use of MC.

In our implementation, the MC and TPS engines share the same beam model in water (being the TPS input basic data generated by the same MC code) and are adjusted to reproduce the same range in materials of different HU values (via proper on-the-fly adjustment of the stopping power calculations relative to water). Thus, while results in water are largely agreeing as long as the known shortcomings of the double Gaussian parameterization are negligible, results in realistic patient geometries may show local dosimetric deviations up to 5% for protons (absorbed dose) and 10% for carbon ions (biological dose) and range differences up to a few millimeters. These deviations are ascribed to the shown limitations of the pencil beam algorithms in the handling of scattering and range mixing effects for proton beams, and in the modeling of light fragments and their lateral broadening in carbon ion beams. Consequently, the discrepancies are found to be more pronounced in heterogeneous as well as deep seated treatment volumes, which can be considered eligible indications most likely profiting from MC recalculations of treatment plans based on analytical approaches.

Our experience also supports the usefulness of reliable, experimentally validated MC tools in the pre-clinical phase of an ion beam therapy facility. In fact, our work has provided improved understanding of the consequences of speed-up approximations implemented in a pre-clinical TPS prototype, thus considerably supporting the algorithmic developments which resulted in the currently clinically used TPS version.

The developed computational platform currently builds the basis for further research activities at our facility, including the extension to the simulation of irradiation induced β⁺-activity for PET-based treatment monitoring (Bauer et al 2013a, 2013b) and the study on the impact of different RBE models in proton therapy, which will be soon reported. Moreover, it is being coupled to a novel approach proposed by (Böhlen et al 2013, Mairani et al 2013), opening the perspectives of MC-based treatment planning with multiple ion species for the envisioned application to biologically adaptive ion beam therapy.

Although the reported results were specific to our MC and TPS systems, the methodology of this work can be generalized to other facilities using different MC and TPS engines. In particular, due to the scarce literature on the use of MC for scanned ion beams, especially carbon ions, we believe that this contribution can be of general interest to the rapidly growing community going to introduce pencil beam scanning with protons and heavier ions in the clinical practice.

Acknowledgments

The authors would like to thank the Medical Physics team headed by Oliver Jäkel and the HIT colleagues headed by Thomas Haberer, especially Bernd Hasch and Stephan Brons, for the constant support with the TPS data and the IT infrastructure, as well as fruitful discussions. Furthermore, the support of the FLUKA collaboration is gratefully acknowledged. Parts of this work have been supported by the European FP7 project PARTNER (grant agreement number 215840–2) and the BMBF project DOTMOBI (grant agreement number 01IB08002F). Thomas Tessonnier and Tiago Marcelos acknowledge funding from DFG (Klinische Forschergruppe Schwerionentherapie 214) and EU (ERASMUS exchange program), respectively.

Appendix A: The calculation of dose-to-water and dose-averaged LET maps

TPSs traditionally calculate dose-to-water (D_w) distributions while MC codes report dose-to-medium (D_m). For conversion of MC D_m into D_w (Paganetti 2009) we follow an approach which intentionally conserves the mixed radiation field produced by proton and carbon ions beams. This means that the primary beam and the secondary particles and fragments are transported and undergo nuclear interactions in the patient geoemetry as given by the CT image (i.e. medium). The dose-to-water is calculated on-the-fly as:

$\begin{eqnarray}&&{{\tilde{D}}_{w}}=\underset{i}{\sum} {\int}{{\Phi}_{\text{m,i}}}\left(E\right)\left({{S}_{w,i}}\left(E\right)/{{\rho}_{w}}\right)dE\end{eqnarray} \tag{ 3 }$

where ${{\Phi}_{\text{m,i}}}\left(E\right)$ is the particle fluence spectrum in medium for all the fragment species i at kinetic energy E, and ${{S}_{w,i}}\left(E\right)/{{\rho}_{w}}$ is the corresponding mass stopping power in water. The latter quantity is consistent to the values used in FLUKA for generation of the TPS basic data as well as for performing biologically-based calculations (cf appendix B).

For proton beams we can additionally calculate the dose-averaged LET in water $LE{{T}_{w}}$ :

$\begin{eqnarray}&&LE{{T}_{w}}=\frac{\underset{i}{\sum} {\int}^{}\frac{{{\Phi}_{m,i}}}{{{\rho}_{w}}}\left(E\right){{\left({{S}_{w,i}}\left(E\right)\right)}^{2}}dE}{{{{\tilde{D}}}_{w}}}\end{eqnarray} \tag{ 4 }$

where the mixed radiation field is limited to charge contributions with Z=1, similar to the approach of (Grassberger and Paganetti 2011) for heavy charged particles, i.e. neglecting the contributions from electrons and photons.

Appendix B: The RBE-weighted dose calculation according to the LEM formalism

In the Local Effect Model (LEM), the biological effect, defined in terms of the logarithm of the cell survival –ln(S),can be related to the traversals of particles of a particular type, having a certain charge (Z) and mass (A), and energy per nucleon (E_k/n):

$\begin{eqnarray}&&- \ln (S({{z}_{\text{cn}}}))=\alpha _{z}^{\text{ion}}{{z}_{\text{cn}}}+\beta _{z}^{\text{ion}}z_{\text{cn}}^{2}\end{eqnarray} \tag{ 1A }$

where ${{z}_{\text{cn}}}$ is the specific energy deposited by the particle in the cell nucleus. The coefficients $\alpha _{z}^{\text{ion}}$ and $\beta _{z}^{\text{ion}}$ of the linear and quadratic terms, respectively, are calculated by means of LEM, as described in detail in (Scholz et al 1997), and then stored in an external database for both primary beam and secondary fragments as a function of ${{E}_{k}}/n,$ particle type and cell line. The input parameters of the LEM for generating the $\alpha _{z}^{\text{ion}}$ and $\beta _{z}^{\text{ion}}$ tables applied in this work are reported in table 2.

Table 2. Input parameters of the original version of the LEM (Scholz et al 1997, Krämer and Scholz 2000 b) used in the MC calculation. 𝛼_X and ${{\beta}_{X}}$ represent the coefficients of the linear and quadratic terms for x-rays irradiation while ${{D}_{t}}$ represents the transition dose at which the survival curve for x-rays is assumed to have an exponential shape with the maximum slope ${{S}_{\max}}={{\alpha}_{X}}+2{{\beta}_{X}}{{D}_{t}}$ .

Input parameter	Value
${{\alpha}_{X}}(G{{y}^{-1}})$	0.1
${{\beta}_{X}}(G{{y}^{-2}})$	0.05
${s_{\max }}(G{y^{ - 1}})$	3.1
${{D}_{t}}\left(Gy\right)$	30

The low dose approximation approach, presented by (Krämer and Scholz 2006), describes how to link the LEM calculated intrinsic microscopic parameters, $\alpha _{z}^{\text{ion}}$ and $\beta _{z}^{\text{ion}}$ , to the macroscopic dose ones, $\alpha _{D}^{\text{ion}}$ and $\beta _{D}^{\text{ion}}$ which are used both in the analytical TPS and in FLUKA for performing biological calculations. The initial slope $\alpha _{D}^{\text{ion}}$ is calculated as:

$\begin{eqnarray}&&\alpha _{D}^{\text{ion}}=\frac{\left(1-{{S}_{1}}\right)}{{{d}_{1}}}\end{eqnarray} \tag{ 2A }$

where ${{d}_{1}}=CLET_{\infty}^{w}/{{A}_{\text{nucl}}}$ and ${{S}_{1}}=\exp (-\alpha _{z}^{\text{ion}}{{d}_{1}})$ are, respectively, the dose deposited and the surviving fraction due to a single particle traversal in the cell nucleus. $LET_{\infty}^{w}$ is the unrestricted LET in water while C is a constant as reported in (Krämer and Scholz 2006). For calculating the quadratic term, the following expression is adopted:

$\begin{eqnarray}&&\beta _{D}^{\text{ion}}=\left(\frac{1-{{S}_{1}}}{\alpha _{z}^{\text{ion}}{{d}_{1}}}\right)\cdot \beta _{z}^{\text{ion}}\end{eqnarray} \tag{ 3A }$

With $\beta _{z}^{\text{ion}}\approx ({{S}_{\max}}-\alpha _{z}^{\text{ion}})/{{(2{{D}_{t}})}^{}}$ (Kraemer and Scholz 2006) ${{D}_{t}}$ represents the transition dose at which the survival curve for x-rays is assumed to have an exponential shape with the maximum slope ${{s}_{\max}}={{\alpha}_{X}}+2{{\beta}_{X}}{{D}_{t}}$ The terms ${{\alpha}_{X}}$ and ${{\beta}_{X}}$ represent the linear and quadratic coefficients for x-rays irradiation. The $\alpha _{D}^{\text{ion}}$ and $\beta _{D}^{\text{ion}}$ tables are calculated off-line, prior the start of the simulation, using the LEM based $\alpha _{z}^{\text{ion}}$ and $\beta _{z}^{\text{ion}}$ tables for the chordoma cell, the equations (2A) and (3A) and the FLUKA calculated $LET_{\infty}^{w}$ for a certain ion (Z,A) at an certain ${{E}_{k}}/n$ .

The coupling of the FLUKA code with the LEM (Mairani et al 2010) has been performed following the theory of dual radiation action (Kellerer et al 1978) calculating the $\alpha _{D}^{\text{mixed}}$ and $\beta _{D}^{\text{mixed}},$ i.e. the linear and quadratic term of the mixed radiation field:

$\begin{eqnarray}&&\alpha _{D}^{\text{mixed}}=\frac{\underset{i=1}{\overset{\text{Ndep}}{\sum}} \alpha _{D,i}^{\text{ion}}{{D}_{i}}}{\underset{i=1}{\overset{\text{Ndep}}{\sum}} {{D}_{i}}}\end{eqnarray} \tag{ 4A }$

$\begin{eqnarray}&&\beta _{D}^{\text{mixed}}={{\left(\frac{\underset{i=1}{\overset{\text{Ndep}}{\sum}} \sqrt{\beta _{D,i}^{\text{ion}}}{{D}_{i}}}{\underset{i=1}{\overset{\text{Ndep}}{\sum}} {{D}_{i}}}\right)}^{2}}\end{eqnarray} \tag{ 5A }$

where N_dep is the total number of energy deposition events composing the mixed radiation field. In the simulation, similarly to (Ballarini et al 2003), whenever energy is deposited by a certain radiation type, the following two quantities, in addition to the absorbed dose D (to medium or to water, cf appendix A), are stored using 'USRBIN' cards: $\alpha _{D}^{\text{ion}}D$ and $\sqrt{\beta _{D,i}^{\text{ion}}}\cdot D$ . By characterizing each energy deposition event, i.e. determining charge, mass and E_k/n of each particle, we are able to interpolate the correct values of $\alpha _{D}^{\text{ion}}$ and $\beta _{D}^{\text{ion}}$ _.

At the end of the simulation we obtain the dose-weighted averages $\alpha _{D}^{\text{mixed}}$ and $\beta _{D}^{\text{mixed}}$ for the mixed radiation field using equations (4A) and (5A), respectively. Finally the number of lethal lesions, the RBE-weighted dose ${{D}_{\text{RBE}}}$ and the RBE values are calculated using the same formalism introduced in Krämer and Scholz 2006:

$\begin{eqnarray}&&\begin{array}{*{35}{l}} - \ln \left(S\right)=\left\{\begin{array}{*{35}{l}} \alpha _{D}^{\text{mixed}}D+\beta _{D}^{\text{mixed}}{{D}^{2}} \quad D\leqslant {{D}_{t}} \\ \alpha _{D}^{\text{mixed}}{{D}_{t}}+\beta _{D}^{\text{mixed}}D_{t}^{2}+\left(D-{{D}_{t}}\right){{S}_{\max}}\quad D>{{D}_{t}} \\ \end{array} \right.\\ \nonumber {{D}_{\text{RBE}}}=\left\{\begin{array}{*{35}{l}} \sqrt{-\ln \left(S\right)/{{\beta}_{X}}+{{\left({{\alpha}_{X}}/\left(2{{\beta}_{X}}\right)\right)}^{2}}}-\left({{\alpha}_{X}}/\left(2{{\beta}_{X}}\right)\right)\quad -\ln \left(S\right)\leqslant -\ln \left({{S}_{t}}\right) \\ \left(-\ln \left(S\right)+\ln \left({{S}_{t}}\right)\right)/{{S}_{\max}}+{{D}_{t}}\quad -\ln \left(S\right)>-\ln \left({{S}_{t}}\right) \\ \end{array} \right.\\ \nonumber \text{RBE=}{{D}_{\text{RBE}}}/D \\ \end{array}\end{eqnarray} \tag{ 6A }$

where D is the total absorbed dose (to medium or to water) and $- \ln \left({{S}_{t}}\right)={{\alpha}_{X}}{{D}_{t}}+{{\beta}_{X}}D_{t}^{2}$

Integration and evaluation of automated Monte Carlo simulations in the clinical practice of scanned proton and carbon ion beam therapy

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Dates

Abstract

1. Introduction

2. Material and methods

2.1. Automated MC calculations

2.2. Evaluation of the optimal configurable settings

2.3. Quantitative comparison between MC and TPS calculations under different conditions

3. Results and discussion

3.1. Automated MC calculations

3.2. Evaluation of the optimal configurable settings

3.3. Quantitative comparison between MC and TPS calculations under different conditions

4. Discussion and conclusion

Acknowledgments

Appendix A: The calculation of dose-to-water and dose-averaged LET maps

Appendix B: The RBE-weighted dose calculation according to the LEM formalism

Integration and evaluation of automated Monte Carlo simulations in the clinical practice of scanned proton and carbon ion beam therapy

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Share this article

Author e-mails

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Dates

Abstract

1. Introduction

2. Material and methods

2.1. Automated MC calculations

2.2. Evaluation of the optimal configurable settings

2.3. Quantitative comparison between MC and TPS calculations under different conditions

3. Results and discussion

3.1. Automated MC calculations

3.2. Evaluation of the optimal configurable settings

3.3. Quantitative comparison between MC and TPS calculations under different conditions

4. Discussion and conclusion

Acknowledgments

Appendix A: The calculation of dose-to-water and dose-averaged LET maps

Appendix B: The RBE-weighted dose calculation according to the LEM formalism