Impact of spot charge inaccuracies in IMPT treatments

Transcription

1 Impact of spot charge inaccuracies in IMPT treatments Aafke C. Kraan a) Applications of Detectors and Accelerators to Medicine (ADAM SA), Geneva, Switzerland Nicolas Depauw and Ben Clasie Department of Physics, Massachusetts General Hospital, Boston, MA, USA Marina Giunta Applications of Detectors and Accelerators to Medicine (ADAM SA), Geneva, Switzerland Tom Madden and Hanne M. Kooy Department of Physics, Massachusetts General Hospital, Boston, MA, USA (Received 2 February 27; revised 8 April 27; accepted for publication 28 May 27; published 4 July 27) Background: Spot charge is one parameter of pencil-beam scanning dose delivery system whose accuracy is typically high but whose required value has not been investigated. In this work we quantify the dose impact of spot charge inaccuracies on the dose distribution in patients. Knowing the effect of charge errors is relevant for conventional proton machines, as well as for new generation proton machines, where ensuring accurate charge may be challenging. Methods: Through perturbation of spot charge in treatment plans for seven patients and a phantom, we evaluated the dose impact of absolute (up to 59 6 protons) and relative (up to %) charge errors. We investigated the dependence on beam width by studying scenarios with small, medium and large beam sizes. Treatment plan statistics included the passing rate, dose-volume-histograms and dose differences. Results: The allowable absolute charge error for small spot plans was about 29 6 protons. Larger limits would be allowed if larger spots were used. For relative errors, the maximum allowable error size for small, medium and large spots was about %, 8% and 6% for small, medium and large spots, respectively. Conclusions: Dose distributions turned out to be surprisingly robust against random spot charge perturbation. Our study suggests that ensuring spot charge errors as small as 2% as is commonly aimed at in conventional proton therapy machines, is clinically not strictly needed. 27 American Association of Physicists in Medicine [ Key words: dose delivery, IMPT, new technologies, spot charge, uncertainty. INTRODUCTION Intensity-modulated proton therapy (IMPT) delivers dose to the patient by combining the dose from numerous small proton beams (spots), combined in several fields, each with a certain energy, position, and number of protons. It is generally known that patient setup uncertainties, range uncertainties, and changes in patient anatomy can significantly change the dose distribution. Mitigation strategies include accurate patient setup methods, robust plan optimization, and adaptive proton therapy. Typically, the error on the spot charge or monitoring units, i.e., the number of protons per spot given to the patient in a treatment, is not considered. Current IMPT beam production systems based on cyclotrons, synchrotrons, or synchrocyclotrons have a spot charge uncertainty of about 2% which is no source of concern.,2 New-generation ion beam production systems may have spot charge errors significantly larger than current systems which may produce unacceptable dose deviations. Linear accelerators, for instance, produce protons in pulses. In the current systems, the beam is effectively DC and beam current monitoring and counting devices stop the beam as soon as the desired number of proton is reached. In pulsed machines, the beam pulse has a very short width (on the order of ls) and is produced in a duty cycle of typically a few hundred Hz. In this case the pulse charge is only controlled in the most upstream component of the accelerator complex: the proton source. Realizing fast changes in current intensity and/or pulse length, as required to modulate the pulse charge in IMPT, is thus challenging. Whether spot charge accuracy at the percent level is achievable is yet to be seen. Possible mitigation techniques to decrease the statistical error may be to rescan the tumor, or part of the tumor volume, several times which increases the treatment time. Apart from new-generation proton machines, knowing the effect of erroneous charge is important for conventional machines too. The goal of this study was to quantify the dose impact of charge uncertainties in patients through the analysis of comparative perturbation of the spot charge in treatment plans for different sites. In other words: what is the dose effect from possible charge errors and what charge errors are clinically tolerable without applying mitigation strategies? Moreover, 92 Med. Phys. 44 (8), August /27/44(8)/92/9 27 American Association of Physicists in Medicine 92

2 924 Kraan et al.: Spot charge inaccuracies in IMPT 924 we identify which factors contribute to the sensitivity of dose to charge uncertainties, and we propose charge uncertainty mitigation strategies. 2. METHODS AND MATERIALS 2.A. Charge error simulation We define two independent sources of charge errors: DQ ¼ Gð; Þ () Gð; ÞQ S where G(,) is a Gaussian centered on with a r =, is an absolute charge error magnitude, e is a relative error value of the spot charge Q S expressed in %. We separately simulated values of ¼ :5; ; :5; 2; and 5 Mp ( 6 protons) and e = 2, 4, 6,, 6, 22, and %. These values are very large for conventional machines but may not be unrealistic for new-generation proton therapy machines. The random charge error DQ for each spot was added to its spot charge value Q S in a fraction. The nominal, i.e., without any error, fraction dose matrix was D Fx, which is the same for each fraction i. The perturbed fraction spotlist yielded a perturbed fraction dose matrix D Fx;i for fraction i of the total fractions N Fx. We compared the individual fraction doses D Fx;i and the mean dose over all fractions hd Fx i¼ R id Fx;i (2) N Fx with D Fx. We used a set of seven patients and one phantom, irradiated to individual prescription dose values D T, delivered over N fx fractions. The patients differ in target volume, number of fractions, dose per fraction D Rx, and number of fields N F per fraction. The latter affected the average spot charge which, in turn, affects the consequences of charge errors, especially for absolute charge errors. The Astroid treatment planning system developed at MGH 4 6 was used for plan creation. For each patient, plans were created using three different spot widths (r = 2.5, 5, and mm at high energy at the iso-center in air, also referred to as small, medium and large spots, respectively. The longitudinal distance between the spots was equal to the distal Bragg peak width at % of its maximum value, w%. The lateral spacing, d, between the spots was.5r. We aimed at V95% > 98% and V7% < 5%. We allowed more flexibility for the spinal sarcoma and cardiac patient, in order to better spare the organs-at-risk. All plans were clinically validated. We repeated the simulation N Fx times for each error value, for a total of about simulations: 8 (7 patients + phantom) 9 (beam widths) 9 4 (nominal plan + 6 absolute + 7 relative error values) N Fx, with the latter depending on the patient, see Table I. 2.B. Analysis We analyzed differences between fractions and over fractions based on a comparison of the perturbed dose matrix D Fx;i and hd Fx i, respectively, against the nominal dose matrix D Fx. The analysis was restricted to voxels v above a particular dose threshold T = % of D Fx, to identify voxels within and close to the target. This threshold was chosen to avoid that the plan statistics are influenced by the size of the dose matrix and to avoid statistics to be dominated by a large low-dose region. We analyzed the following plan statistics. The dose volume histograms (DVH) and associated dose parameters like V95% and V7%. We considered V95% > 98% and V7% < % acceptable for perfraction results, and V95% > 99% and V7% < 5% acceptable for fraction-averaged results. TABLE I. Summary of patients and the water phantom studied: site, target names, target volumes, prescribed dose D T, number of fractions N fx, prescribed dose per fraction D Rx, number of fields N F, and median spot charge Q med. and HR refer to clinical target volume and clinical target volume high risk, respectively, where the latter is the part of the receiving a boost dose. Q med ð 6 protonsþ Site Target name Target volume [cc] D T [Gy(RBE)] N fx D Rx [Gy(RBE)] N F Large Medium Small Pelvis Chest wall HR Rectum HR Chordoma Cardiac HR Retro- HR peritoneal,98.8 Spinal sarcoma Phantom Medical Physics, 44 (8), August 27

3 925 Kraan et al.: Spot charge inaccuracies in IMPT 925 Pass Rate. We defined a pass rate for the c function, 7 with tolerances of 2 mm and 2% (of prescribed dose) for per fraction results and mm and % (of global max dose) for fraction-averaged results. We considered > 95% acceptable for per fraction results, and > 99% for fraction-averaged results. We calculated for each fraction and charge error value. For each error value, we determined for the N Fx fractions the minimum, 25%, median, 75% and maximum values. The 25% values were interpolated, and we determined the value ;P and P for absolute and relative charge errors which still had an acceptable between D Fx and D Fx;i. We chose to not take the minimum Gamma value of all the fractions, because it is very subject to fluctuations and would result in an over conservative estimate of ;P and P. In a similar way, we determined the values hpi and hpi, which still have an acceptable fraction-averaged result for the mean dose (per fraction) hd Fx i compared to D Fx. Dose differences. The dose difference statistics were per fraction i: P v2t R Fx;i ¼ % ðd Fx D Fx;i Þ () N v2t D Rx and the mean over all fractions P v2t R Fx ¼ % ðd Fx hd Fx iþ (4) N v2t D Rx where N v2t was the number of voxels passing the % threshold. We consider a R Fx;i \ 5% acceptable for per fraction results, and R Fx \ 2% for fraction-averaged results.. RESULTS.A. Spot charge Table I displays the median spot charge in a fraction for all treatment plans. The median spot charge is approximately proportional to d 2 (we used d =.5r) and thus proportional to r 2. Furthermore, it is proportional to the prescribed dose, and inversely proportional to the number of fields..b. Absolute charge errors Figure gives the results of the for the perturbed plans for small spots. The black whisker plots at each simulated represent the minimum, 25%, %, 75%, and maximum (2 mm/2% tolerance) for the N Fx simulations. The 25% values, chosen as a worse-case scenario that lowers the allowable charge error, are interpolated with a smooth function, and the value ;P was determined at = 95% (dashed black line). The ( mm/% tolerance) of the mean dose matrix over all fractions is displayed in red. An interpolation with a smooth curve was done as well and the value hpi was determined at = 99% (dashed red line). Note that the different tolerances of (2%, 2 mm) and (%, mm) causes the mean dose and fraction dose curves to switch order between sites. If the Pelvis σσ CW σσ Rectum σσ CD σσ Cardiac σ = 2.5 mm, d =.5σ RP σσ Spine σσ Water σσ (g) (h) FIG.. Gamma passing rates for various patients, spot size 2.5 mm. Effects for fractional dose are displayed in black (tolerance 2%, 2 mm), and effects for fraction averaged dose (tolerance %, mm) in red. The dashed lines indicate how the value of ;P (black dashed line) and hpi (red dashed line) were determined through interpolation between simulation values of. [Color figure can be viewed at wileyonlinelibrary.com] Medical Physics, 44 (8), August 27

4 926 Kraan et al.: Spot charge inaccuracies in IMPT 926 same tolerance criteria are used, the of the mean fractional dose matrix was in all cases better than the individual fractions, so a partial cancelation of the effects occurs when considering all fractions together. We investigated the relationship between ;P and the median spot charge in the small spot plans, and found a moderate positive correlation (correlation coefficient.). A stronger correlation was found between ;P and tumor volume (correlation coefficient.8). Only weak correlations were found between hpi and median charge (correlation coefficient ) and between hpi and tumor volume (correlation coefficient 5). Absolute charge errors up to 5 6 protons were seen to have negligible impact on medium and large spot plans; in all cases we found from the values that ;P [ 5 6 protons..c. Relative charge errors We determined for small, medium, and large size spots, the value P at which 25% of the fractions had an unacceptable value, as above in Fig.. The same was done for hpi. The whisker plots for small, medium, and large size spots are displayed in Figs. 2 4, respectively. In most cases, P was smaller than hpi, demonstrating that dose effects are typically canceled when considering all fractions together. For all spot sizes together, we investigated the correlation between P and the median charge, as well as between P and the tumor volume. While a weak negative correlation was seen between P and the median charge (correlation coefficient.64), there was no correlation between P and tumor volume (correlation coefficient.). Weak negative correlations were found between hpi and median charge (correlation coefficient.6) and between hpi and tumor volume (correlation coefficient.7)..d. Charge error limits From Fig., we can estimate the maximum allowable absolute charge error in a proton accelerator providing beam sizes of 2.5 mm by looking at the minimum value of ;P and hpi. Based on the, the allowable absolute charge error for our eight patient cases is about 2 6 protons in the small spot plans, where the worse case is the chordoma case. From Table I, we can deduce that this value corresponds to about % (chordoma) to % (water phantom) of the median spot charge in their small spot treatment plans. Larger limits would be allowed if larger spots were used. The values for ;P and hpi for small spot plans for all patients are summarized in the second and third column in Table II. For relative errors, the maximum allowable error size for small, medium, and large spots can be determined by looking at the smallest value of P and hpi found in Figs. 2 4: about %, 8%, and 6% for small, medium, and large spots, respectively. The worse case is the water phantom. The values for P and hpi obtained for each patient are summarized in the fourth and fifth column of Table II for large spots, the scenario allowing smallest errors. Thus, for a machine delivering spots with variable sizes from 2.5 to mm (at isocenter in air at high energy), the required accuracy on spot charge is about 2 6 protons or 6% per spot, whichever is larger. The absolute number is based on small spots and has negligible impact on medium and large spots, and the relative number is relevant for medium and large spots and has negligible impact on small spots. If a single spot size is offered, values can be estimated from Figs. 4 by looking at the individual spot sizes. We checked the other plan statistics at the above determined charge tolerances. For absolute charge errors, the V95% was always satisfactory up to ¼ 2 6 protons. The V7% was for all patients satisfactory, apart from the chordoma case, where in one fraction it was 2% at ¼ 2 5 protons. As the fraction-averaged V7% was zero, we see that effects cancel, and we believe that an error of ¼ 2 5 can safely be tolerated. Concerning the other dose statistics, R Fx;i was below % for all fractions and all patients at an absolute charge error of 2 6 protons, and R Fx was always below %, i.e., well acceptable. For relative errors, an error of 6% had a negligible impact on all plan statistics of small and medium spot plans, demonstrating that dose distributions are not influenced by errors of this size. For large spot plans, the V95% was unmodified at e = 6%. The V7% was satisfactory for all patients apart from the chordoma patient, where we noticed that a large V7% (%) occurred at this error in single fraction. However, again the fraction-averaged V7% was zero, showing that a cancelation of hot spots takes place. Thus, we believe that a relative error of 6% can be safely tolerated..e. Dose volume histograms Concerning the DVH parameters, in Fig. 5 we display the DVHs of all patients at an absolute charge error of 2 6, for small spot plans. As mentioned above, the Chordoma patient is clearly most sensitive. This is both due to the small volume and the small spot charge, resulting from the four beam directions in a single fraction. In clinical practice, it is more common to use two beam directions per fraction in alternation. The spot charge would thus increase and the sensitivity would decrease. The sensitivity of our chordoma patient plans with small spots to the absolute error size is also demonstrated in Fig. 6. For relative charge errors, a few example DVHs are displayed in Fig. 7 for the pelvis patient. 4. DISCUSSION In the above studies, we evaluated for eight patients to what extend charge errors can modify dose distributions. Different statistics were used to quantify the dose impact. The sensitivity to charge errors turned out to be patient dependent, and correlations with tumor volume and spot charge were found. We extracted rough limits of tolerable charge errors in proton machines. Medical Physics, 44 (8), August 27

5 927 Kraan et al.: Spot charge inaccuracies in IMPT 927 Pelvis σσ CW σσ Rectum σσ CD σσ Cardiac σ σ RP σσ Spine σσ Water σσ (g) (h) FIG. 2. Gamma passing rates for various patients, spot size 2.5 mm. Effects for fractional dose are displayed in black (tolerance 2%, 2 mm), and effects for fraction averaged dose (tolerance %, mm) in red. The dashed lines indicate how the value of P (black dashed line) and hpi (red dashed line) were determined through interpolation between simulation values of e. [Color figure can be viewed at wileyonlinelibrary.com] Pelvis σ=5. mm, d=.5σ CW σ=5. mm, d=.5σ Rectum σ=5. mm, d=.5σ CD σ=5. mm, d=.5σ Cardiac σ=5. mm, d=.5σ RP σ=5. mm, d=.5σ Spine σ=5. mm, d=.5σ Water σ=5. mm, d=.5σ (g) (h) FIG.. Gamma passing rates for various patients, spot size 5 mm. Whiskers and lines as in Fig. 2. [Color figure can be viewed at wileyonlinelibrary.com] Medical Physics, 44 (8), August 27

6 928 Kraan et al.: Spot charge inaccuracies in IMPT 928 Pelvis σ=. mm, d=.5σ CW σ=. mm, d=.5σ Rectum σ=. mm, d=.5σ CD σ=. mm, d=.5σ Cardiac σ=. mm, d=.5σ RP σ=. mm, d=.5σ Spine σ=. mm, d=.5σ Water σ=. mm, d=.5σ (g) (h) FIG. 4. Gamma passing rates for various patients, spot size mm. Whiskers and lines as in Fig. 2. [Color figure can be viewed at wileyonlinelibrary.com] TABLE II. Summary of ;P, hpi, P and hpi obtained for each patient. Here ;P ð P Þ and hpi ð hpi Þ are the maximum allowed absolute (relative) charge errors determined per fraction and fraction-summed, respectively. The values for ;P and hpi are based on small spot plans, and the values for P and hpi are based on large spot plans, both representing the most conservative estimate. Site ;P ½ 6 protonsš hpi ½ 6 protonsš P ½%Š hpi ½%Š Pelvis Chest wall > 5. > Rectum > Chordoma Cardiac Retroperitoneal > > > Spinal sarcoma Phantom Absolute errors of up to 5 6 protons had a negligible impact on medium and large size spot plans. The impact on small spot plans was instead more significant, and in that case absolute charge errors should be kept below about 2 6 protons to avoid significant dose modifications, based on the chordoma case. Compared to the median spot charge for small spots plans for that case, 6:2 6 (Table I), we see that this is about %. It must be noted that 2 6 protons is only a very small fraction of the total number of protons delivered, which is :4 in this case, in about 2 spots. The impact of random relative errors was also evaluated. For small spot plans, relative errors up to % do not cause significant dose modifications. For medium and large spot plans, the relative error should stay below about 8% and 6% of the spot charge, respectively. These numbers were based on the worse case, which was the water phantom. For small spot plans, it is surprising that there are patients where even a % error does not have significant dose impact, like the retro-peritoneal and the rectum patient (Fig. 2). The reason why treatment plans are generally robust against random relative charge errors is that there is a large amount of statistical smearing naturally occurring, due to lateral and longitudinal pencil beam overlap, as well as multiple Coulomb scattering of protons in the patient. As long as errors are random, relative errors do not easily perturb the dose distributions. The numbers extracted above strongly suggest that a charge accuracy as high as %, as is commonly aimed for in circular machines, is clinically not strictly needed. For most proton machines, errors are naturally neither purely absolute nor purely relative, and a different behavior Note that when normalized to target volume, the number of delivered protons for the chordoma case is more than the general rule-ofthumb number of about protons to deliver Gy to a liter target: the target is very small and many protons are delivered in the beam penumbra. Medical Physics, 44 (8), August 27

7 929 Kraan et al.: Spot charge inaccuracies in IMPT 929 Pelvis.8 Spinal_cord Bladder R_kidney Liver CW.8 CW+IMN Lung_L esophagus thyroid_n.8 Rectum SmallBowel IliacWings Bladder IliacWings.8 CD Brain BRAINSTEM CHIASM LTOPTNRV Cardiac.8 SpinalCord Esophagus Liver Ventricles Bronchus.8 RP HighRisk SpinalCord Heart Esophagus Liver_Avg Spine.8 _Postop SpinalCord Heart_Postop Esophagus_Post.8 Water reference_cube skin 6l 6s FIG. 5. DVHs of the eight patients for small spot plans. Each thin colored line corresponding to the N Fx simulations when applying an absolute charge error of 2. 6 protons. The black solid lines are the DVHs of the nominal plan, and the black dashed lines are the DVHs corresponding to the dose of all fractions averaged. [Color figure can be viewed at wileyonlinelibrary.com].8 CD Brain BRAINSTEM CHIASM LTOPTNRV.8 CD Brain BRAINSTEM CHIASM LTOPTNRV.8 CD Brain BRAINSTEM CHIASM LTOPTNRV FIG. 6. DVHs of the chordoma patient for error sizes of :5 6, 2: 6, and 5: 6 protons. Each thin colored line corresponding to the N Fx simulations. The black solid lines are the DVHs of the nominal plan, and the black dashed lines are the DVHs corresponding to the dose of all fractions averaged. [Color figure can be viewed at wileyonlinelibrary.com] Medical Physics, 44 (8), August 27

8 9 Kraan et al.: Spot charge inaccuracies in IMPT 9 FIG. 7. Example DVHs for the pelvis patient for small (a and b), medium (c and d), and large spots (e and f), for various values of rel. The colored bands are the result of N Fx individual DVH lines. The solid line is the nominal DVHs. The dashed lines, largely overlaying with the solid lines, are the DVHs of the averaged effect over all fractions, divided by the number of fraction. The left plots all have acceptable C and the right plots have unacceptable C. [Color figure can be viewed at wileyonlinelibrary.com] Medical Physics, 44 (8), August 27

9 9 Kraan et al.: Spot charge inaccuracies in IMPT 9 may apply. To estimate the exact impact of error sources, it is very important to understand the source of charge errors, so appropriate mitigation strategies in dose delivery could be applied. If the error is mostly relative, mitigation techniques to avoid dose errors include rescanning (repeatedly scanning the tumor, or part of it) or reducing the inter-spot distance (lateral or longitudinal). The latter reduces the average spot charge, and thereby the effect of charge errors. On the other hand, if errors are mostly absolute, rescanning could lead to an unnecessary increase of dose errors, and an average spot charge should be assured that is safely above the absolute error size. Our limits were based on dose prescriptions around 2 Gy. For hypofractionation schemes, where spot charges are larger, we expect the impact of the absolute error to be even smaller. Results for relative errors are not expected to change. There are several shortcomings in this work. Absolute and relative errors were considered separately and not simultaneously. We chose to keep the results as generally applicable as possible. It would make sense to perform detailed simulations of combined effects only when the error sources are precisely knows. Moreover, the simulated charge error was random as dictated by the Gaussian function, and results probably do not apply to nonrandom errors. Furthermore, the number of patients was limited to eight. Considering a larger patient group could help in understanding better why some patients are more sensitive to charge errors than other patients, for instance by also analyzing tumor shape or depth. Only errors with sizes of up to 5 6 and % were studied and results were not extended to higher error values. The reason is that these error sizes are already large, and even larger errors seem improbable for most new-generation proton machines. Finally, our plans were IMPT plans. The effect on single field optimization plans is part of a future study. 5. CONCLUSION A potential source of errors typically not considered in treatment uncertainty studies are spot charge uncertainties. This is justified if charge errors are of the order 2%, as the effects from setup, range, and anatomical uncertainties are typically much larger (see for instance 8 ). For new-generation machines, sources to spot charge errors may be very different and much larger errors may need to be considered. In this work, we quantified the dose effect of charge errors up to % (relative error) and up to 5 6 protons (absolute error). Dose distributions turned out to be surprisingly robust against spot charge perturbation. Our study suggests that ensuring spot charge errors as small as 2% as is commonly aimed at in conventional proton therapy machines, is clinically not strictly needed. ACKNOWLEDGMENTS We thank Ugo Amaldi for valuable discussions about mitigation strategies of statistical charge errors. Furthermore, we are grateful for input from Alberto Degiovanni about pulse generation in linear accelerators. CONFLICTS OF INTEREST The authors have no conflicts of interest to disclose. a) Author to whom correspondence should be addressed. Electronic mail: Aafke.Kraan@cern.ch. REFERENCES. Gillin MT, Sahoo N, Bues M, et al. Commissioning of the discrete spot scanning proton beam delivery system at the University of Texas M.D. Anderson Cancer Center, Proton Therapy Center, Houston. Med Phys. 2;7: Giordanengo S, Garella MA, Marchetto F. The CNAO dose delivery system for modulated scanning beam radiotherapy. Med Phys. 25; 42:26.. Amaldi U, Braccini S, Puggioni P. High frequency linacs for hadrontherapy. Rev Accelerator Sci Technol. 29;2:. 4. Kooy HM, Clasie BM, Lu H-M, et al. A case study in proton pencil beam scanning delivery. Int J Radiat Onc Biol Phys. 2;76: Hong L, Goitein M, Bucciolini M, et al. A pencil beam algorithm for proton dose calculations. Phys Med Biol. 996;4:5. 6. Chen W, Craft D, Madden TM, Kooy HM. A fast optimization algorithm for multicriteria intensity modulated proton therapy planning. Med Phys. 2;7: Clasie BM, Sharp GC, Seco J, Flanz JB, Kooy HM. Numerical solutions of the c-index in two and three dimensions. Phys Med Biol. 22;57: Kraan AC, van de Water S, Teguh DN, et al. Dose uncertainties in IMPT for oropharyngeal cancer in the presence of anatomical, range, and setup errors. Int J Radiat Oncol Biol Phys. 2;;87: Medical Physics, 44 (8), August 27