Dosimetric consequences of pencil beam width variations in scanned beam particle therapy

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Phys. Med. Biol. 58 (2013) 3979–3993 doi:10.1088/0031-9155/58/12/3979

Dosimetric consequences of pencil beam widthvariations in scanned beam particle therapy

M A Chanrion1,2, F Ammazzalorso1, A Wittig1, R Engenhart-Cabillic1

and U Jelen1

1 Department of Radiotherapy and Radiation Oncology, University of Marburg, Marburg,Germany2 Universite Claude Bernard Lyon 1, Lyon, France

E-mail: Urszula.Jelen@med.uni-marburg.de

Received 4 December 2012, in final form 21 April 2013Published 17 May 2013Online at stacks.iop.org/PMB/58/3979

AbstractScanned ion beam delivery enables the highest degree of target doseconformation attainable in external beam radiotherapy. Nominal pencilbeam widths (spot sizes) are recorded during treatment planning systemcommissioning. Due to changes in the beam-line optics, the actual spot sizesmay differ from these commissioning values, leading to differences betweenplanned and delivered dose. The purpose of this study was to analyse thedosimetric consequences of spot size variations in particle therapy treatmentplans. For 12 patients with skull base tumours and 12 patients with prostatecarcinoma, scanned-beam carbon ion and proton treatment plans were preparedand recomputed simulating spot size changes of (1) ±10% to simulate thetypical magnitude of fluctuations, (2) ±25% representing the worst-casescenario and (3) ±50% as a part of a risk analysis in case of fault conditions.The primary effect of the spot size variation was a dose deterioration affectingthe target edge: loss of target coverage and broadening of the lateral penumbra(increased spot size) or overdosage and contraction of the lateral penumbra(reduced spot size). For changes �25%, the resulting planning target volumemean 95%-isodose line coverage (CI-95%) deterioration was ranging fromnegligible to moderate. In some cases changes in the dose to adjoining criticalstructures were observed.

(Some figures may appear in colour only in the online journal)

1. Introduction

The rationale behind the use of ion beams in high-precision radiation therapy lies in theirphysical property of depositing most of the dose at a well-defined depth, the Bragg peak.Additionally, for carbon ion beams, the enhanced biological effectiveness around their tracks(Amaldi and Kraft 2005) has to be considered. In order to irradiate an extended target volume,

0031-9155/13/123979+15$33.00 © 2013 Institute of Physics and Engineering in Medicine Printed in the UK & the USA 3979

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multiple individual Bragg peaks of single narrow mono-energetic beams need to be juxtaposed.To achieve the highest possible degree of target conformation, scanning delivery systems havebeen developed (Haberer et al 1993, Pedroni et al 1995, Furukawa et al 2010). In suchsystems the ion beam is deflected by magnetic fields to paint the tumour transversely in araster fashion, while in-depth Bragg peak placing is achieved by either active energy variationat the accelerator level or passive energy variation with range shifter plates.

In treatment planning systems (TPS), the lateral profiles of particle pencil beams aretypically described with a (single or double) 2D Gaussian function, characterized by its fullwidth at half maximum (FWHM), referred to in the following as a beam spot size. Energy-dependent multiple scattering in the treatment nozzle makes available spot sizes a functionof energy. During the commissioning phase, spot sizes measured in air are recorded in theTPS. In synchrotron-based facilities, libraries of several focus settings are typically predefined(Kramer et al 2000, Parodi et al 2012).

Spot size and spot spacing (raster pitch) determine the levels of dose homogeneity andinfluence the steepness of lateral dose fall-off (Weber 1996, Baumer and Farr 2011). In practice,the homogeneity of dose deposition from overlapping carbon ion pencil beams can be ensuredby rule of thumb that the raster pitch should be in the order of one-third of the beam spot size(Haberer et al 1993, Weber 1996, Kramer et al 2000), while optimal spot size and raster gridsettings for protons have been recently investigated by Widesott et al (2012).

Fluctuations in the beam transport and extraction systems may result in deviations of theactual spot sizes from the nominal values (Parodi et al 2010) and potentially lead to differencesbetween planned and delivered dose, including compromised target coverage or overdosage ofabutting critical structures. Such variations may exist among the treatment rooms, as well as beoccurring over time. For instance, during the irradiation blocks at the GSI Helmholtzzentrumfur Schwerionenforschung, in the framework of the German ion beam therapy pilot project,typical spot size variations within 10–20% with incidental maximum discrepancies of up to40% were observed for carbon ion beams (Schardt and Weber 2012). A similar range has beenrecently reported by Mirandola et al (2012) for proton beams at the CNAO (Centro Nazionaledi Adroterapia Oncologica) synchrotron-based facility. At the Particle Therapy Centre inMarburg, which is not yet in clinical operation, these variations have not been analysed so far,but are expected to be in the same range owing to the similar design of the accelerators. Thepurpose of this study was to analyse the dosimetric consequences of spot size variations onthe delivery of typical scanned beam particle therapy treatment plans.

2. Materials and methods

2.1. Patient data

Twelve patients with skull base tumours and 12 patients with prostate tumours were selectedfor this study. For both patient groups the clinical target volume (CTV), planning target volume(PTV) and the relevant organs at risk were delineated on the Pinnacle3 TPS (Philips Healthcare,Best, The Netherlands).

In the patient group with skull base tumours, cases were selected with tumour localizationtypical for established particle therapy indications (chordoma, chondrosarcoma, adenocysticcarcinoma). The planning computed tomographies (CT) had an in-slice pixel size and a slicethickness of respectively 0.98 and 3 mm for two patients, 0.59 and 3 mm for two patients and0.59 and 2.5 mm for the remaining eight patients. The mean CTV volume was 49.9 ± 24.1 cc(range: 15.6–90.7 cc). The PTV was defined by uniform 3D CTV expansion of 2 mm.

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In the patient group with prostate tumours, the planning CTs were acquired with a pixelsize of 0.98 and 3 mm slice thickness. The mean CTV volume was 67.8 ± 25.7 cc (range:30.9–108.0 cc). The PTV was defined by uniform 3D CTV expansion of 5 mm.

2.2. Treatment planning

For both patient groups, scanned beam proton treatment plans and biologically optimizedcarbon ion treatment plans were prepared using the TRiP98 TPS (Kramer et al 2000) whichemploys the local effect model (LEM) (Kramer and Scholz 2000). The conversion programdcm2trip, developed at our institution and distributed with TRiP98, was used to convert theDICOM data (CT images and structure sets) to the VOXELPLAN format used by TRiP98(Kramer 2011, TRiP online documentation). For carbon ion plans, the relative biologicaleffectiveness (RBE) of carbon ions was computed through the LEM I (αγ /βγ = 2 Gy, αγ =0.1 Gy−1, βγ = 0.05 Gy−2, threshold dose Dt = 30 Gy and nucleus radius r = 5 μm) (Kargeret al 2006, Schulz-Ertner et al 2007), employing the low-dose approximation (Kramer andScholz 2006). In proton plans, a constant RBE factor of 1.1 was used.

All plans used a two-lateral-opposed-beam setup, reflecting the geometry typicallyavailable at fixed-nozzle combined proton-carbon ion facilities. Isocentric table rotations wereused in some skull base cases, where deemed beneficial.

For skull base treatment plans the prescription dose was set to 60–63 Gy (RBE) deliveredin 20–21 fractions for carbon ion plans and 66–74 Gy (RBE) in 33–37 fractions for protonplans similarly to Nikoghosyan et al (2010a, 2010b) and Ares et al (2009). Also maximumdose constraints were derived from the protocols adopted in the above mentioned studies. Theprostate carbon ion treatment plans were optimized for a total dose of 60 Gy (RBE) deliveredin 20 fractions similarly to Akakura et al (2004) and the proton plans were optimized to 74 Gy(RBE) in 37 fractions. Treatment planning contained no formal constraints for the rectum,however the resulting plans were checked for V90% < 10%. For both tumour localizations, theminimum satisfactory planning objective was the delivery of at least 95% of the prescriptiondose to >95% of the PTV volume.

Realistic, clinically relevant optimization approaches were chosen for this planning study:for skull base cases, with the necessity of complex planning constraints coupled with thepossibility of accurate patient positioning, intensity modulation (IMPT) was used (Gemmelet al 2008), whereas for prostate cases, for which safety against intra-fraction movement is ofconcern, single field uniform dose optimization (SFUD) was employed.

For all plans a minimum reference beam width of 5 mm was requested from theplanning system, which selected effective sizes (in air, at isocentre) available in a synchrotronlibrary compatible with the GSI facility during the German ion beam therapy pilot projectand representative of modern combined-beam facilities, like the Particle Therapy Centre inMarburg. This resulted in carbon ion beam widths of 5.0–7.5 mm for skull base cases and5.4–5.7 mm for prostate cases (similarly to Kosaki et al 2012, Jelen et al 2012). For protons therespective values were 6.1–13.5 mm and 7.3–10.5 mm (in air, at isocentre) and were enabledby treatment planning and delivery with shorter nozzle-to-patient distance than for carbon ions(Bubula et al 2012).

These planning settings enabled comparability of some effects, as they resulted in protonspot sizes, measured at patient surface, as close as possible to the corresponding ones ofcarbon ions. The irradiation raster pitch was set to 2 mm for carbon ion plans and to 3 mm forproton plans. Approximately equal values were used for the so-called lateral target extension,a tolerance allowing the TPS to place additional spots outside the target volume projection,transversely to the beam, to ensure PTV coverage without the need for spots with excessive

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fluence at the target border. The in-depth peak positioning step was set to 3 mm for carbon ionplans, through use of a ripple filter (Kramer et al 2000), and to 2 mm for proton plans.

For dose calculation, the multiplescatter (ms) algorithm was used, which employs adouble-Gaussian pencil beam parametrization, taking into account the angular distributionof fragments after nuclear interactions and multiple Coulomb scattering of charged particlesthrough matter (Kramer et al 2000, Iancu et al 2009). The dose grid resolution was the sameas the planning CT.

2.3. Simulation of spot size variations

The characteristics of all scanned pencil beams in an optimized plan (spot size and pitch,energy, particle count) are recorded by the TPS. These data were edited and the FWHM ofeach spot modified by (1) ±10% to simulate the typical magnitude of fluctuations, (2) ±25%to simulate the worst-case scenario and (3) ±50% as a part of treatment risk analysis in case offault conditions and to verify suitability of interlock thresholds. The modified plans were fedback into the planning system and the dose distributions recomputed without re-optimization.

2.4. Evaluation

The treatment plans were compared in terms of dose distribution and dose–volume histograms(DVH). For a quantitative assessment the mean dose (Dmean), coverage index (CI), conformityindex (CN), homogeneity index (HI) and near-maximum/near-minimum dose (Dnear-max,Dnear-min) were used. The CI was defined as the volume percentage encompassed by a selectedisodose line. The CN index was calculated as proposed by Paddick (2000). The Dnear-min andDnear-max were defined at the 98% and 2% volume levels respectively (ICRU 2007) and theHI index was calculated as the difference Dnear-max − Dnear-min normalized to the prescriptiondose.

For statistical comparison of selected indices, a non-parametric, paired-sample sign testwas performed with a significance level of 0.05 using the R statistical environment (R CoreTeam 2012). A 3 pp (percentage point) deviation from the clinical objective was deemedclinically relevant.

3. Results

3.1. Dosimetric quality of the optimized treatment plans

For the original plans, with no FWHM modifications, the mean PTV and CTV coverage wasadequate for both groups of patients as presented in tables 1 and 2 for skull base cases andtables 3 and 4 for prostate cases (denoted as ‘nominal’). For skull base cases the constraintsdefined for critical structures were fulfilled to a clinically satisfactory level in all plans. Instead,in 1 of 12 prostate cases rectum dose exceeded the planning constraint (V90% = 17.5% for bothion species), but was deemed acceptable in consideration of a complex anatomical situation.

3.2. Dosimetric effects of spot size variations

The primary effect of the spot size variations was a dose deterioration around the targetedge. For larger deviations, visible loss of coverage and broadening of the lateral penumbra(increased spot size) or overdosage and contraction of the lateral penumbra (reduced spot size)occurred.

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Table 1. Mean (±1 sd) of selected dosimetric indices of the original (nominal FWHM) andrecomputed (modified FWHM) carbon ion skull base treatment plans.

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FWMH CI-98%a CI-95%a CN-95% Dmean (%) Dnear-min (%) Dnear-max (%) HI (%)

−50% 91.7 ± 4.5b,c 98.7 ± 0.5 77.3 ± 3.6 101.7 ± 0.3 95.9 ± 0.9 112.0 ± 2.6 16.1 ± 3.4−25% 96.6 ± 1.6b 99.3 ± 0.3b 82.6 ± 2.9 101.1 ± 0.2 97.0 ± 0.5 106.9 ± 1.3 9.9 ± 1.4−10% 98.1 ± 0.7b 99.0 ± 0.4b 85.2 ± 2.7 100.5 ± 0.1 96.5 ± 0.7 104.3 ± 0.7 7.7 ± 0.9Nominal 98.0 ± 0.9 98.2 ± 0.4 86.6 ± 2.6 100.1 ± 0.2 95.3 ± 0.7 103.1 ± 0.4 7.8 ± 0.9+10% 96.5 ± 1.5b 96.8 ± 0.6b 87.1 ± 2.6 99.7 ± 0.2 93.8 ± 0.6 102.3 ± 0.3 8.6 ± 0.8+25% 91.0 ± 2.3b,c 92.3 ± 1.7b,c 85.0 ± 2.8 99.0 ± 0.3 91.1 ± 0.8 101.7 ± 0.3 10.6 ± 0.9+50% 77.2 ± 4.9b,c 81.9 ± 3.4b,c 77.2 ± 4.2 97.7 ± 0.5 86.8 ± 1.2 101.3 ± 0.3 14.5 ± 1.1a Differences tested statistically (sign test).b Statistically significant (p < 0.05) difference with respect to the nominal plan.c Clinically relevant (3 pp) deviation from the clinical objective.

Table 2. Mean (±1 sd) of selected dosimetric indices of the original (nominal FWHM) andrecomputed (modified FWHM) proton skull base treatment plans.

CTV PTV

FWMH CI-98%a CI-95%a CN-95% Dmean (%) Dnear-min (%) Dnear-max (%) HI (%)

−50% 87.6 ± 3.8b,c 97.8 ± 0.8b 75.7 ± 5.2 101.3 ± 0.4 94.8 ± 0.8 109.2 ± 1.8 14.4 ± 1.5−25% 94.1 ± 2.1b 97.7 ± 0.7b 77.5 ± 5.2 101.3 ± 0.3 94.6 ± 0.9 107.7 ± 1.2 13.1 ± 1.0−10% 94.7 ± 2.0b 96.7 ± 0.7b 78.6 ± 5.1 100.8 ± 0.2 93.4 ± 0.8 106.5 ± 0.9 13.1 ± 0.9Nominal 94.2 ± 2.1 95.5 ± 0.7 79.0 ± 4.9 100.5 ± 0.2 92.3 ± 0.7 105.7 ± 0.7 13.4 ± 0.9+10% 93.3 ± 2.2b 93.9 ± 0.9b 78.9 ± 4.8 100.1 ± 0.2 91.1 ± 0.8 105.0 ± 0.5 13.9 ± 0.9+25% 90.2 ± 2.5b,c 90.3 ± 1.5b,c 77.7 ± 4.5 99.4 ± 0.2 89.1 ± 0.9 104.2 ± 0.5 15.0 ± 1.0+50% 78.0 ± 7.1b,c 80.6 ± 6.2b,c 71.5 ± 7.6 95.8 ± 8.2 78.2 ± 24.7 103.2 ± 0.5 25.0 ± 24.5a Differences tested statistically (sign test).b Statistically significant (p < 0.05) difference with respect to the nominal plan.c Clinically relevant (3 pp) deviation from the clinical objective.

Table 3. Mean (±1 sd) of selected dosimetric indices of the original (nominal FWHM) andrecomputed (modified FWHM) carbon ion prostate treatment plans.

CTV PTV

FWMH CI-98%a CI-95%a CN-95% Dmean(%) Dnear-min (%) Dnear-max (%) HI (%)

−50% 81.7 ± 9.4b,c 98.0 ± 1.1b 85.0 ± 3.0 100.2 ± 0.2 95.0 ± 0.7 109.5 ± 0.9 14.6 ± 1.5−25% 96.3 ± 1.8 99.8 ± 0.1b 88.7 ± 2.0 100.5 ± 0.1 97.4 ± 0.4 105.5 ± 0.4 8.1 ± 0.7−10% 99.0 ± 0.6b 99.8 ± 0.1b 90.5 ± 1.7 100.4 ± 0.1 98.1 ± 0.3 103.4 ± 0.2 5.3 ± 0.5Nominal 99.7 ± 0.2 99.6 ± 0.3 91.6 ± 1.5 100.2 ± 0.1 97.9 ± 0.5 102.5 ± 0.3 4.6 ± 0.6+10% 99.9 ± 0.1b 99.2 ± 0.4b 92.6 ± 1.3 100.0 ± 0.2 96.7 ± 0.7 102.0 ± 0.2 5.3 ± 0.7+25% 99.9 ± 0.1b 97.3 ± 0.8b 92.6 ± 1.3 99.6 ± 0.2 94.3 ± 0.7 101.6 ± 0.2 7.2 ± 0.7+50% 99.6 ± 0.6b 87.5 ± 4.0b,c 84.7 ± 3.9 98.8 ± 0.4 90.5 ± 0.9 101.3 ± 0.2 10.8 ± 0.8a Differences tested statistically (sign test).b Statistically significant (p < 0.05) difference with respect to the nominal plan.c Clinically relevant (3 pp) deviation from the clinical objective.

3.2.1. Skull base cases. For a selected patient, the exemplary dose distributions of theoriginal plan and of recomputations with beam spot size modifications, are presented infigure 1 for carbon ion plans and in figure 2 for proton plans. The corresponding doseprofiles, demonstrating the influence of spot size modifications on dose homogeneity andlateral penumbra, are shown in figure 3. These effects are noticeable in the prolonged tails andthe shallower shoulders of the PTV and CTV DVHs (figure 4).

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Figure 1. Carbon ion dose distributions of an exemplary skull base case with original (nominal)and modified spot FWHM, in the transversal (T), coronal (C) and sagittal (S) planes. In transversalview: PTV—white, brainstem—blue.

Table 4. Mean (±1 sd) of selected dosimetric indices of the original (nominal FWHM) andrecomputed (modified FWHM) proton prostate treatment plans.

CTV PTV

FWMH CI-98%a CI-95%a CN-95% Dmean (%) Dnear-min(%) Dnear-max (%) HI (%)

−50% 78.3 ± 5.6b,c 98.6 ± 0.8b 86.4 ± 3.0 101.4 ± 0.3 95.4 ± 0.5 109.0 ± 0.7 13.6 ± 1.1−25% 88.1 ± 4.4b,c 98.9 ± 0.5b 88.5 ± 2.4 101.2 ± 0.2 95.9 ± 0.6 107.3 ± 0.7 11.4 ± 1.2−10% 92.0 ± 3.5 98.3 ± 0.8b 89.5 ± 2.0 100.8 ± 0.1 95.3 ± 1.0 106.1 ± 0.6 10.7 ± 1.5nominal 94.6 ± 2.9 97.4 ± 1.0 89.7 ± 1.9 100.4 ± 0.1 94.4 ± 1.0 105.2 ± 0.6 10.8 ± 1.5+10% 96.7 ± 2.1b 95.9 ± 1.3b 89.3 ± 1.8 100.1 ± 0.2 93.2 ± 1.0 104.4 ± 0.6 11.2 ± 1.5+25% 98.7 ± 1.1b 91.6 ± 2.0b,c 86.3 ± 2.1 99.6 ± 0.2 91.3 ± 0.9 103.4 ± 0.5 12.1 ± 1.3+50% 98.9 ± 1.1b 85.0 ± 3.5b,c 81.4 ± 3.8 98.5 ± 0.3 87.8 ± 0.8 102.2 ± 0.4 14.4 ± 1.1a Differences tested statistically (sign test).b Statistically significant (p < 0.05) difference with respect to the nominal plan.c Clinically relevant (3 pp) deviation from the clinical objective.

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Figure 2. Proton dose distributions of an exemplary skull base case with original (nominal) andmodified spot FWHM, in the transversal (T), coronal (C) and sagittal (S) planes. In transversalview: PTV—white, brainstem—blue.

The mean dosimetric indices of treatment plans, both with nominal and modified FWHMvalues, are presented in table 1 for carbon ion and table 2 for proton plans. Spot size variationsdid not induce relevant change in mean target dose. In terms of PTV coverage, for bothparticle species, the plans recomputed with reduced spot sizes or with spot size increase of10% showed only minor changes and continued to fulfill the initial clinical objectives, while aFWHM increase by 25% and 50% resulted in a statistically significant and clinically relevantreduction of the mean CIPTV-95%. This was reduced respectively to 92.3 ± 1.7% and 81.9 ±3.4% in carbon ion plans and to 90.3 ± 1.5% and 80.6 ± 6.2% in proton plans.

In the CTV, for FWHM modifications of +25%, +50% and −50%, a statisticallysignificant and clinically relevant CICTV-98% reduction to respectively 91.0 ± 2.3%,77.2 ± 4.9% and 91.7 ± 4.5% was observed for carbon ion plans. Consistently, for protonplans, a mean CICTV-98% reduction to 90.2 ± 2.5%, 78.0 ± 7.1% and 87.6 ± 3.8% wasobserved for the same FWHM modifications. The appearance of overdosed and underdosed

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Figure 3. Exemplary dose cross-profiles for a skull base case, at the isocentre along the mediolateral(left), superoinferior (middle) and anteroposterior (right) directions, of the original (nominalFWHM) and recomputed (modified FWHM) plans. Plans prepared with: (a) with carbon ions(b) with protons. Shaded area represents the extension of the PTV.

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regions was reflected by changes in the Dnear-max and Dnear-min and, consequently, by increase(i.e. worsening) of the HI.

A modification of the lateral beam gradients, visible in the profile plots in figure 3lead, in some cases, to a change in the dose delivered to the critical structures in closeproximity of the target. An example of this effect is shown in one patient in figure 4, where thelow-to-medium-dose and high-dose regions of the brainstem DVH are affected by the FWHMvariations.

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Figure 5. Carbon ion dose distributions of an exemplary prostate case with original (nominal) andmodified spot FWHM, in the transversal (T), coronal (C) and sagittal (S) planes. In transversalview: PTV—white, rectum—blue.

Over the entire patient cohort and for both ion species, the Dnear-max to the brainstemincreased with the decrease of the spot size. For carbon ion plans the maximum increase ofDnear-max to the brainstem, observed in an individual patient, was 1.0 pp for 10%, 2.5 for 25%and 5.4 pp for 50% spot size reduction. For proton plans, respectively for the same spot sizemodifications, brainstem Dnear-max increases by 1.1, 2.6 and 4.4 pp were observed, also in anindividual patient.

3.2.2. Prostate cases. The dose distributions of the original and recomputed plans of anexemplary prostate patient are shown in figure 5 for carbon ion and in figure 6 for proton plans,while the corresponding dose cross-profiles are presented in figure 7. For both carbon ionsand protons, plans behaved in general similarly to those of skull base cases: with a decreasingspot FWHM, overdosage areas appeared in the dose distributions, while an increasing spot

3988 M A Chanrion et al

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Figure 6. Proton dose distributions of an exemplary prostate case with original (nominal) andmodified spot FWHM, in the transversal (T), coronal (C) and sagittal (S) planes. In transversalview: PTV—white, rectum—blue.

size led to underdosage effects, also reflected in the prolonged tails and shallower shouldersof the DVH of the PTV (figure 8).

The mean dosimetric indices for prostate treatment plans, both original and recomputed,are presented in tables 3 and 4 for carbon ion plans and proton plans respectively. No clinicallyrelevant changes were observed in the mean PTV doses. Dose distribution deteriorationsvisible in figures 5 and 6 were reflected in homogeneity and coverage indices. In carbonion plans, changes of the spot size by ±10% and ±25% did not induce a clinically relevantdeterioration of the CTV and PTV coverage. For a beam spot size variation of +50%, themean CIPTV-95% was reduced significantly to 87.5 ± 4.0%, while for a spot size reduction by50% the CICTV-98% was reduced to 81.7 ± 9.4%.

Similarly, in proton plans, all tested spot size reductions, together with the spot sizeincrease by 10%, did not induce a clinically relevant deterioration of the PTV coverage.Instead further spot size increase affected the PTV coverage, reducing it to 91.6 ± 2.0%and to 85.0 ± 3.5%. Contrary to carbon ion plans, the spot size decrease always resulted in

Dosimetric consequences of pencil beam width variations in particle therapy 3989

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Figure 7. Dose cross-profiles for an exemplary prostate case, at the isocentre along the mediolateral(left), superoinferior (middle) and anteroposterior (right) directions, of the original (nominalFWHM) and recomputed (modified FWHM) plans. Plans prepared with: (a) with carbon ions(b) with protons. Shaded area represents the extension of the PTV.

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Figure 8. DVH for the PTV (left), CTV (middle) and rectum (right) for an exemplary prostatecase. Plans prepared with: (a) with carbon ions (b) with protons.

pronounced reduction of CICTV-98% to 92.0 ± 3.5%, 88.1 ± 4.4% and 78.3 ± 5.6% for −10,−25% and −50%. The spot size increase caused instead a slight CICTV-98% enhancement.

As in the skull base cases, dose modifications in structures abutting the target volumewere observed for both particle species, as shown by the DVH (figure 8). In carbon ion plans,the maximum increase of Dnear-max observed in one patient was 1.8, 4.8 and 10.4 pp, for spotsize reduction by 10%, 25% and 50% respectively, while for proton plans the maximumincrease was respectively 1.1, 2.5 and 4.1 pp.

3990 M A Chanrion et al

4. Discussion

The consequences of variations in the delivered spot sizes, with respect to the nominal valuesused for planning, on target coverage and on sparing of abutting critical structures wereinvestigated, for scanned beam particle therapy with protons and carbon ions. In the onlypublished study known to the authors addressing this topic, Parodi et al (2010) simulatedfor proton and carbon ion beams, horizontal profile width changes of 50%, 100% and 150%,as well as extreme situations of narrow rectangular or truncated profiles, on treatment plansprepared for a spherical target of 50 mm in diameter, placed at a 50 mm depth in water, withno contiguous critical structures. Such geometry represents a worst-case scenario, where in-depth beam broadening and the compensating effects of numerous overlapping pencil beamsunlikely manage to counteract the effects of spot size deviations. Additionally, as the focusof this work was risk assessment and definition of threshold settings for the beam monitoringsystem, the FWHM variations that were tested all fall in the upper range of expected values.Instead in our study spot size variations were simulated on realistic clinical treatment plans.The simulated values of the FWHM deviations, ±10, ±25 and ±50%, reflect respectivelytypical fluctuations, peak fluctuations and fault conditions, for synchrotron-based particletherapy facilities (Schardt and Weber 2012, Mirandola et al 2012). Moreover, the patientcohorts represent realistic clinical scenarios: extent and localization of target volumes areconsistent with typical particle therapy indications, treatment plans were prepared accordingto clinical guidelines (e.g. use of planning constraints, IMPT for skull base cases) and RBE ofcarbon ions, as calculated by the LEM model, was taken into account.

The primary effect of the spot size variations on both particle species was a loss ofconformity and homogeneity in the delivered dose mainly in proximity of the target edges. Forlarger deviations, visible dose deterioration occurred, with loss of coverage and broadeningof the lateral penumbra (increased spot size) or overdosage and contraction of the lateralpenumbra (reduced spot size) (figures 3 and 7). In the first approximation, the differing patientgeometries (tumour volume and location, tissue inhomogeneity), within each patient cohort,did not introduce significant variability in the dosimetric results. Instead, these appeared moredependent on the indication and optimization approach of choice: the skull base cases, withshallower penetration depths and more modulated original rasters (IMPT), were more affectedby spot size changes as compared to the prostatic tumour cases, with deeper localization andsmoother original fluences (SFUD-optimization on a regular volume).

For decreasing spot sizes, an overdosage trend appeared with both carbon ions and protons,compatible with the delivery of the fluence planned for each pencil beam to a smaller area. Thenarrowing of the lateral penumbra, combined with the unmodified raster pitch, qualitativelyresulted in a modulation or rippling of the delivered dose, visible in the notched cross-profiles(figures 3 and 7), especially nearby the edge and for larger variations (−50%). The ripplingeffect introduced dose minima below the clinical CTV reference dose (98% of the prescription)causing decrease of mean CICTV-98%, both in skull base and prostatic tumour localization.No relevant change on either the mean PTV dose or the CIPTV-95% was associated with it, asthe dose oscillations remained above 95% and cancelled out. On the target edges the fluenceboost caused by spot reduction is the dominating effect, with the appearance of overdosages.

The spot size increase resulted in dose smearing and gradient softening induced by thedelivery, by each pencil beam, of the same fluence over a larger surface. With larger spot sizedeviations (�25%), this phenomenon affected the PTV coverage and the underdosage involvedalmost the entire inner PTV rim (figures 1 and 2). For the head cases, where a CTV-to-PTVmargin of 2 mm was employed, the edge underdosage affected even the CTV coverage with adecrease of the CICTV-98%, which can potentially be clinically relevant. For the largest spot

Dosimetric consequences of pencil beam width variations in particle therapy 3991

size increase (50%) applied on skull base cases, the underdosage affected such a large relativevolume (by expanding from the edge inside the target) to induce a reduction of the mean PTVdose, a parameter else virtually unaffected in all other scenarios considered in this study. Inprostate cases, with a CTV-to-PTV margin of 5 mm, the CTV coverage was not affected.

Furthermore, dose increase caused by spot size reduction can occur partially outside ofthe target volume and involve abutting critical structures. In our study, for carbon ion plans,this resulted in an increase of the Dnear-max by up to 2.5 pp in the brainstem for skull base casesand 4.8 pp in the rectum for prostate cases, for spot size reduction by 25%, and respectivelyby 5.4 pp and 10.4 pp, for spot size reduction by 50%. For proton plans, the correspondingvalues were: 2.6 pp and 2.5 pp for spot size reduction by 25% and 4.4 pp and 4.1 pp for spotsize reduction by 50%.

An attempt at a direct comparison between carbon ions and protons based on the dosimetricresponse of treatment plans in the presence of spot size modifications, is confounded byinherent differences in the dose conformity the two species enable. However, some qualitativeobservations can be made considering the dosimetric indexes obtained in case of extremespot size modifications (±50%) relatively to the original values for each species. While thechanges in CI were comparable, some distinct patterns could be observed for the HI. For skullbase cases the HI was affected more by spot size reduction in carbon ion plans and more byspot size increase in proton plans. This observation can be easily explained by the reducedcompensating effect from scattering in carbon ion plans as compared with proton plans,especially for very narrow spot sizes. In contrary, the effects of beam spot size increase aremore severe for protons, as they accumulate with the more pronounced scattering in tissue. Forprostate cases, a stronger homogeneity degradation in carbon ion plans with reduced spot sizeswas also present, while the effects of spot size increase were similar for both ion species. Thelatter demonstrates how, at depths corresponding to prostate localization, scattering becomesrelevant also for carbon ions, making the effects comparable.

When assessing the potential impact of these results on patient treatment, somesimplifications potentially affecting the interpretation of this study should not be neglected.In our investigation identical modifications were simulated for all energy layers of eachplan and along both transversal beam axes. In practice, fluctuations of variable magnitudeshould be expected at each extraction cycle and with one transversal direction (horizontal)larger than the other, as a consequence of the extraction septum construction (Parodi et al2010), presumably reducing the total effect on dose distributions. Furthermore, as previouslymentioned, according to the technical data of different facilities, a variation of ±25% should beconsidered as the worst-case scenario under normal operation conditions. Excessive deviationscould be prevented, employing the beam monitoring system coupled with an interlock, stronglylimiting, in practice, possible dose distribution deterioration.

Finally, the application of the total therapeutic dose is often divided into fractions, typicallyover the course of several weeks, causing delivery uncertainties, like spot size discrepancies,to be statistically smoothed, provided that they are not systematic. Still, it is advisable that,for a thorough clinical assessment, a similar study be repeated in the future, employing e.g.the on-line beam monitoring system log as input, in order to consider the real number ofparticles delivered per spot, spot size and spot position, which are all subject to delivery-timefluctuations.

5. Conclusion

In actively scanned particle beam radiotherapy, differences in the width of pencil beamsbetween commissioning data and actual beam extraction have dosimetric influence on

3992 M A Chanrion et al

treatment plans. Although for realistic spot size variation (�25% FWHM), the observed targetcoverage deterioration was ranging from negligible to moderate, this should be considered withcaution. In particular, in some cases spot size variations are associated with relevant changesin the dose to adjoining critical structures. Some of the negative effects can be mitigatede.g. with the application of treatment planning margins. Finally, spot size variations are onlyone of many potential delivery-time uncertainties that can affect the final dose distribution,like positioning errors, anatomy changes, range uncertainties etc. For novel techniques, likecarbon ion scanned-beam radiotherapy, the relevance of such uncertainties and of their interplayremain mostly to be quantified.

Acknowledgments

This work has been supported by a Research Grant of the University Medical Center Giessenand Marburg (UKGM) 35/2010 MR. The development of the data conversion and visualisationtools was supported by the ULICE project co-funded by the European Commission under FP7grant agreement number 228436. The authors are grateful to Dr M Kramer for enabling theTRiP98 computations, to Dr G Iancu and Dr U Weber for providing the proton base data andto Dr U Weber for providing technical information on the beam spot size variations and hisvaluable comments on the manuscript.

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