Independent application of an analytical model for secondary neutron equivalent dose produced in a passive-scattering proton therapy treatment unit

Abstract

The purpose of this study was to independently apply an analytical model for equivalent dose from neutrons produced in a passive-scattering proton therapy treatment unit, H. To accomplish this objective, we applied the previously-published model to treatment plans of two pediatric patients. Their model accounted for neutrons generated by mono-energetic proton beams stopping in a closed aperture. To implement their model to a clinical setting, we adjusted it to account for the area of a collimating aperture, energy modulation, air gap between the treatment unit and patient, and radiation weighting factor. We used the adjusted model to estimate H per prescribed proton absorbed dose, D_Rx, for the passive-scattering proton therapy beams of two children, a 9-year-old girl and 10-year-old boy, who each received intracranial boost fields as part of their treatment. In organs and tissues at risk for radiation-induced subsequent malignant neoplasms, T, we calculated the mass-averaged H, H_T, per D_Rx. Finally, we compared H_T/D_Rx values to those of previously-published Monte Carlo (MC) simulations of these patients’ fields. H_T/D_Rx values of the adjusted model deviated from the MC result for each organ on average by 20.8 ± 10.0% and 44.2 ± 17.6% for the girl and boy, respectively. The adjusted model underestimated the MC result in all T of each patient, with the exception of the girl’s bladder, for which the adjusted model overestimated H_T/D_Rx by 3.1%. The adjusted model provided a better estimate of H_T/D_Rx than the unadjusted model. That is, between the two models, the adjusted model reduced the deviation from the MC result by approximately 37.0% and 46.7% for the girl and boy, respectively. We found that the previously-published analytical model, combined with adjustment factors to enhance its clinical applicability, predicted H_T/D_Rx in out-of-field organs and tissues at risk for subsequent malignant neoplasms with acceptable accuracy. This independent application demonstrated that the analytical model may be useful broadly for clinicians and researchers to calculate equivalent dose from neutrons produced externally to the patient in passive-scattering proton therapy.

1. Introduction

Nontherapeutic stray neutrons are produced in the delivery of proton therapy beams. These neutrons are of concern because of their high and uncertain relative biological effectiveness for late effects such as carcinogenesis (Grahn et al 1992, Wolf et al 2000, Hollander et al 2003, Kuhne et al 2009). Neutrons produced in the patient are unavoidable, but neutrons generated in the treatment unit, i.e. ‘external neutrons’, may be attenuated by simple modifications to the treatment unit (Taddei et al 2008, 2009b, Brenner et al 2009). In passive-scattering proton therapy (PSPT), the final collimating aperture is the chief source of patient exposures to external neutrons (Pérez-Andújar et al 2009, Matsumoto et al 2016). Because commercial treatment planning systems in proton therapy do not calculate the equivalent dose from external neutrons, H, a vast number of research studies into H have applied detailed Monte Carlo (MC) simulations (Fontenot et al 2005, Jiang et al 2005, Polf and Newhauser 2005, Polf et al 2005, Tayama et al 2006, Zheng et al 2007a, 2007b, 2008, Fontenot et al 2008, Moyers et al 2008, Newhauser et al 2008, Zacharatou Jarlskog et al 2008, Athar and Paganetti 2009, Fontenot et al 2009, Newhauser et al 2009, Taddei et al 2009a, Hultqvist and Gudowska 2010, Taddei et al 2010, Rechner et al 2012, Pérez-Andújar et al 2013a, De Smet et al 2014, Zhang et al 2013, Zhang et al 2014, Geng et al 2015, Taddei et al 2015, Matsumoto et al 2016, Homann et al 2016, De Smet et al 2017, Han et al 2017, Taddei et al 2018). However, MC simulations of this type are time consuming and, among other reasons, not currently used in a clinical setting. Analytical models, on the other hand, may offer faster computations of H with acceptable accuracy (Newhauser et al 2017).

One such model has been developed by Newhauser and co-workers over the past decade and is nonproprietary and straightforward to implement. Basic versions were developed between 2006 and 2010 at The University of Texas MD Anderson Cancer Center (Zhang et al 2010) and advanced versions between 2011 and 2017 at Louisiana State University with collaborators from Mary Bird Perkins Cancer Center and other institutions (Pérez-Andújar et al 2013b, Farah et al 2015, Schneider et al 2015, Eley et al 2015). For brevity, we shall refer to this model as the LSU-MDA model. The model estimates H per prescribed proton absorbed dose, D_Rx, in a water phantom. The version reported by Schneider et al (2015) was simpler to configure and use than previous versions and offered continuous applicability from 100 to 250 MeV in proton beam energy. Eley et al (2015) integrated the model into a proton therapy treatment planning system and extended the model to include range modulation and arbitrary collimator shapes. However, all of these studies were performed by the team who developed the LSU-MDA model, and, to date, an independent application had not been performed in a clinically relevant case.

The purpose of this study was to independently apply and evaluate the LSU-MDA model for H in PSPT in clinically realistic circumstances. Using the model, we estimated the average H in organs and tissues, T, at risk for subsequent malignant neoplasms (SMNs), H_T, for two children who received PSPT to an intracranial target. To do so, we adjusted the LSU-MDA model to account for the patients’ treatment field parameters, namely, aperture size, range modulation, air gap, and radiation weighting factor, w_R. As a figure of merit for evaluation, we compared our estimated H_T values to those calculated by previously-published MC simulations.

2. Methods

2.1. Patient selection

Because MC simulations had already been performed, the boost treatment fields of the 10-year-old boy of Taddei et al (2009a) and the 9-year-old girl of Taddei et al (2010) were selected for this study. In each study, MC calculations were performed using the Monte Carlo N-Particle eXtended code version 2.6b (Pelowitz 2008) to estimate the absorbed dose from external neutrons in each voxel, D_v, of the patients’ simulated bodies. They applied the recommendations of the international commission on radiological protection (ICRP) in Publication 92 (2003) to estimate the radiation weighting factor, w_R. With these parameters, they determined H in each voxel, v, as:

$$H_v=w_R\cdot D_v.$$ (1)

Each patient’s plan included intracranial boost fields. These fields were similar in design to those of treatments for localized brain tumors, such as astrocytomas, ependymomas, and gliomas. Determining and minimizing out-of-field H for pediatric patients with brain tumors such as these is critical because they may have good long-term prognoses and are therefore at risk of developing late-effects of which SMNs are the chief concern (Armstrong et al 2010).

2.2. Patient diagnosis, prescription, and treatment planning

In the previous studies, treatment plans for a girl and a boy diagnosed with primitive neuroectodermal tumors were considered. Their treatments included intracranial boosts prescribed to deliver 21.3 Gy in the clinical target volume using PSPT. For the girl, the intracranial boosts comprised three fields of nominal energies (i.e. energies prior to beam shaping) at either 160 MeV or 180 MeV. The boy’s two PSPT intracranial boost fields were of slightly lower nominal energies of 140 MeV and 160 MeV. The beam characteristics of the intracranial boost fields for these two children are summarized in table 1. Further details of the computed tomography simulations, treatment plans, and MC techniques used for dose calculation can be found in the previous publications.

Table 1.

Treatment parameters for the intracranial proton boost fields of the girl and boy in this study and the previous MC studies (Taddei et al 2009a, 2010). Abbreviations: left posterior oblique (LPO), posterior–anterior (PA), right posterior oblique (RPO), and left lateral (LL).

	Girl			Boy
Beam	1	2	3	1	2
Beam orientation	LPO	PA	RPO	LPO	LL
Gantry angle (degree)	97	180	263	130	90
Nominal beam energy (MeV)	160	180	160	160	140
Maximum range in patient (cm H2O)	12.0	13.5	12.0	11.3	9.2
SOBP width (cm)	8.0	8.0	8.0	7.0	6.0
Collimated field, major axis (cm)	6.6	7.0	6.3	11.8	11.6
Collimated field, minor axis (cm)	6.3	6.3	6.3	5.5	5.4
Air gap (cm)	23.0	29.0	23.0	2.0	2.0
Aperture thickness (cm)	4	6	4	4	4

2.3. Translation of the analytical model to a clinical setting

The LSU-MDA analytical model for H considered four different external neutron energy regimes, contained 22 fitting parameters, and was continuous with proton beam energy from 100 to 250 MeV. We adjusted the model for translation to a clinical setting, accounting for w_R, spread-out Bragg peak (SOBP), aperture size, and air gap (the LSU-MDA model accounted for distance from the virtual neutron source but not for varying air gaps). We applied correction factors for each of these based on previous publications of generalized, detailed characterizations of the same PSPT treatment unit (Zheng et al 2007b, 2008). The equation for our adjusted model was the following:

$$\raisebox{1ex}{$H_v$}\!\left/ \!\raisebox{-1ex}{$D_{Rx}$}\right.=F_{wR}\cdot F_{SOBP}\cdot F_{as}\cdot F_g\cdot \raisebox{1ex}{$H_{LSU-MDA,v}$}\!\left/ \!\raisebox{-1ex}{$D_{Rx}$}\right.,$$ (2)

where F_wR, F_SOBP, F_as, and F_g were the adjustment factors for w_R, SOBP, aperture size, and air gap, respectively. H_LSU-MDA,v/D_Rx was the H_v/D_Rx values as calculated by the LSU-MDA model.

The w_R used to determine H by the LSU-MDA model was considerably lower (approximately a factor of 1.7) than the w_R used in the previous MC datasets of the boy and girl, so we adjusted the w_R values to make a better comparison between the results of the analytical model and those of the MC simulations. We calculated F_wR in each voxel as the ratio of the MC studies’ w_R value to the value applied by the LSU-MDA model. The w_R values were not given by Schneider et al, so we approximated their values in each voxel by using an equation from their previous study (Pérez-Andújar et al 2013b). This equation calculated w_R as a function of depth and off-axis distance. In the MC studies, w_R was determined at isocenter for various proton beam energies based on ICRP Publication 92 (2003) (figure 5(a) of Zheng et al (2008)). The w_R for the respective proton beam energies of the intracranial boost fields were used to calculate F_wR.

An SOBP adjustment factor was created to account for the lack of modulation in the analytical model. F_SOBP values were taken directly from Zheng et al (2008). In these studies, Zheng et al performed MC simulations comparing the neutron ambient dose equivalent per therapeutic proton absorbed dose at isocenter, H*(10)/D_iso, from a nominal 250-MeV proton beam of various SOBP widths normalized to a pristine Bragg peak. We used the resulting values in their figure 9(a). The factor reflecting the relative increase in H*(10)/D_iso of the medium snout size for the respective SOBP width was directly used for F_SOBP (table 2) and applied to each intracranial boost field.

Table 2.

Adjustment factors used to translate the LSU-MDA model for use with clinical beams. F_wR, F_SOBP, F_as, and F_g were the adjustment factors for radiation weighting factor (w_R), spread-out Bragg peak, aperture size, and air gap, respectively. Because F_wR varied for each voxel, the average is reported. Additionally, mean w_R values for the fields of the girl and boy from the previous MC studies are listed (Taddei et al 2009a, 2010).

	Girl			Boy
Beam	1	2	3	1	2
Fas	0.930	0.930	0.930	0.900	0.890
FSOBP	1.800	1.800	1.800	1.750	1.690
Fg	0.680	0.550	0.680	2.220	2.220
FwR	1.710	1.750	1.710	1.730	1.700
Mean wR of MC studies	9.410	9.410	9.430	9.540	9.730

We adjusted the model for the varying size of the aperture in the clinical treatment fields in our study. We derived F_as based on the results of the previous MC studies. Similar to SOBP, Zheng et al performed MC simulations comparing H*(10)/D_iso for various aperture sizes and a closed-aperture in their figure 8 (Zheng et al 2008). However, this figure 8 was not normalized to a closed-aperture. Therefore, F_as was determined as the ratio of H*(10)/D_iso of the medium snout size of each aperture area to that of the medium snout size with a closed aperture (table 2).

To account for air gap, g, F_g was derived from the previous MC studies. Zheng et al (2007b) conducted MC simulations to study the effect of distance from the treatment snout on H per the therapeutic absorbed proton dose, D_p, for a 250 MeV proton beam with medium and large snout sizes (their figure 7). In our study of pediatric intracranial fields, the air gap was calculated as the difference of the snout position (i.e. distal portion of the treatment unit) and the surface of the patient along the central axis. In order to match this definition of air gap, we calculated air gap from Zheng et al’s study as the difference in the snout position and the isocenter minus the upstream radius of the tally volume. F_g was calculated from Zheng et al as the ratio of H/D_p that equated to the air gap of the intracranial fields and H/D_p that equated to the air gap used by Schneider et al to train their model, i.e. 15 cm. Thus, air gaps larger than 15 cm, e.g. those of the girl’s fields, would result in F_g values less than 1, and air gaps smaller than 15 cm, e.g. those of the boy’s fields, would result in F_g values greater than 1. The air gap of the boy’s fields was only 2 cm, which is very rare in clinical applications but was maintained in our study so that we could compare our results with those of the previous publications. Because 2 cm was less than the smallest air gap studied by Zheng et al, we extrapolated beyond the scope of their data using the following logarithmic function:

$$\raisebox{1ex}{$H_Z$}\!\left/ \!\raisebox{-1ex}{$D_P$}\right.=-11.81\text{ ln }g+50.767,$$ (3)

where H_Z/D_p was H/D_p as plotted in their figure 7 and g was the corresponding air gap (cm). To verify the fitted function, previous MC simulations estimating the neutron equivalent dose of the left posterior oblique (LPO) field of the girl were compared to the similar LPO field of the boy. The main difference between the two fields was the air gap–23 cm for the girl’s field and 2 cm for the boy’s field. The neutron equivalent dose decreased by a factor of 2.7 when increasing the air gap from 2 cm to 23 cm, which was consistent with the prediction of the above fitted function. Therefore, the fitted function was used to approximate the numerator of F_g for the boy.

H_T/D_Rx was determined for each component of the adjusted model and for all adjustments. First, we implemented the LSU-MDA model with the adjustment factors using in-house codes and commercial software (version R2014a, MATLAB, The MathWorks, Inc., Natick, Massachusetts) to calculate H_v/D_Rx. Second, we recycled the same contours for organs and tissues, T, from the previous publications for the girl and boy to compute mass-averaged H_T/D_Rx. We selected out-of-field T associated with site-specific SMN risk, including the esophagus, thyroid, heart, lungs, liver, small bowel, colon, stomach, kidneys, bladder, breast tissue, ovaries, testicles, and prostate. Finally, our values for H_T/D_Rx were compared to those of the previous MC studies of the girl and boy.

3. Results

3.1. Validation of the previous analytical model

The adjustment factors we found to account for SOBP, aperture area, air gap, and w_R of each intracranial beam are listed in table 2. Only F_g differed considerably between the girl’s fields and the boy’s fields. F_g, the largest adjustment factor for the boy’s fields, increased H_v/D_Rx by a factor of 2.22 for the boy’s fields but decreased H_v/D_Rx by 36.3% for the girl’s fields. The largest adjustment factors for the girl’s fields were F_SOBP and F_wR. Unlike the other adjustment factors, F_wR varied for each voxel and therefore, the average F_wR was reported. The w_R for each field of the MC dataset of the girl and boy are also included in table 2. Although the w_R approximated from Zheng et al are not explicitly shown in table 2, these values of w_R were within 3% on average of the previous MC dataset of the girl and boy.

Figure 1 shows all H_T/D_Rx values from the girl’s fields of the adjusted model compared to those of the previous MC studies. Before we applied any adjustment factors to the model, H_T/D_Rx calculated by the model was less than the MC results for all organs, on average by 57.4% ± 4.8%, i.e. approximately within a factor of 2. After applying all corrections, H_T/D_Rx calculated by the model was less than the MC results for all organs, on average by 20.8% ± 10.0%, with the exception of the bladder for which the model overestimated H_T/D_Rx by 3.0%. The maximum deviation of the model from the MC result was in the breast tissue, for which H_T/D_Rx calculated by the fully adjusted model underestimated the MC result by 39.0%.

Figure 1.

H_T/D_Rx from external neutrons for the composite of the intracranial boost fields of the girl. The mean organ doses were estimated by MC simulations (blue), the model with all adjustments (red), the model with no adjustments (green).

Figure 2 shows all H_T/D_Rx values from the boy’s fields of our adjusted model compared to those of the previous MC studies. Similar to the girl’s fields, H_T/D_Rx of the unadjusted model was less than those of the MC for all organs. However, unlike the girl’s fields, the unadjusted model grossly underestimated the MC results, on average by 91.4% ± 2.9%. After applying all adjustments, H_T/D_Rx calculated by the model underestimated the MC H_T/D_Rx by less than a factor of 2, at 44.2% ± 17.6% on average for all the organs. Unlike the girl’s fields, the analytical model’s dose estimation of the boy’s fields diverged from the MC results with distance from the field edge. For example, H_T/D_Rx estimated in organs near the treatment field, i.e. esophagus, thyroid, heart, lungs, stomach, liver, and kidneys, were on average 31.7% ± 10.8% lower than the MC result whereas H_T/D_Rx estimated by the model in organs far from the treatment field, i.e. prostate, bladder, colon, rectum, and testicles, were 61.7% ± 5.1% on average lower than the MC result. The model’s maximum deviation from the MC result was in the rectum, for which H_T/D_Rx estimated by the model underestimated that of the MC by 65.9%.

Figure 2.

H_T/D_Rx from external neutrons for the composite of the intracranial boost fields of the boy. The mean organ doses were estimated by MC simulations (blue), the model with all adjustments (red), the model with no adjustments (green).

4. Discussion

In this study, we applied an analytical model for estimating equivalent dose from neutrons produced in a PSPT treatment unit and confirmed its ability to reproduce organ doses with accuracy similar to that of MC simulations for two pediatric patients with intracranial tumors. We performed this study independently of the team who developed the model. However, we made adjustments for clinical realism. Specifically, we attuned the model to account for SOBP, aperture area, air gap, and w_R.

Our aim was to test the feasibility of using a fast and simple analytical model to estimate external neutron equivalent dose with an acceptable level of accuracy but without the computational overhead and complexity of MC. After adjusting the model for clinical realism, we achieved this with similar accuracy to what was attained when validating MC results against measurements (Fontenot et al 2005, Wroe et al 2007, Howell and Burgett 2014). To estimate organ doses from external neutrons to within a factor of 2 using a simple analytical model is especially noteworthy considering the large uncertainties in w_R for neutrons, a radiological protection quantity that attempts to take into account the relative biological effectiveness of neutrons for carcinogenesis (Grahn et al 1992, Wolf et al 2000, Hollander et al 2003, Kuhne et al 2009). An adjusted analytical model gives clinicians the opportunity to routinely calculate equivalent dose from external neutrons for PSPT treatment units as well as researchers performing retrospective studies involving stray neutron equivalent dose, with the goal of lowering the risk of SMNs or other toxicities in survivors (Newhauser et al 2016, Berrington de González et al 2017, Stokkevåg et al 2017).

The impacts of adjusting the model differed between the two test cases. H_T/D_Rx of the unadjusted model adequately estimated the external neutron dose for the girl’s fields (by a factor of 2–2.5) but underestimated the external neutron dose for the boy’s fields (by a factor of 13). However, after our adjustments, H_T/D_Rx estimated by the model was generally within a factor of two of the MC result for both patients. One cause of the underestimation for the boy’s was a very small 2 cm air gap between the treatment unit and the patient. A 2 cm air gap is rarely used in proton therapy and it was much smaller than the 15 cm air gap used to train the LSU-MDA model, and our F_g values for this small air gap were extrapolated far beyond the data of Zheng et al. The considerable deviation in the length of the air gap at treatment compared to the training data created an F_g of 2.22 for each of the boy’s fields, deviating farther from 1 than F_g of the girl’s fields, which were 0.64 ± 0.08 on average.

The H_T values after our adjustments to the LSU-MDA model, especially for the girl’s fields, were even closer to the H_T values of the MC than those of Eley et al (2015) for a patient with Hodgkin’s Lymphoma. However, they accounted for different factors—range modulation, aperture area, and anatomical heterogeneities—than we did. For example, the application of the model by Eley et al reproduced H_thyroid to within 39% of the MC result while our application of the model estimated H_thyroid to within 13% and 34% of the MC for the girl and boy, respectively. In either case, within or independent of the LSU-MDA team, the model has been demonstrated in clinical cases to estimate H_T with accuracy comparable to that of MC or measurements (Agosteo et al 1998, Polf et al 2005, Farah et al 2014) and with greatly lessened computational overhead.

Our study had the following limitations. First, we applied the LSU-MDA model to two patients’ treatments only. However, the realism of our work is notable. Second, we did not consider other reasonable adjustments to the model. For example, unlike Eley et al, we did not account for water equivalent thickness of heterogeneous tissue nor did we consider their nuclear cross sections. Considering actual tissue compositions may affect neutron production by up to 40% (Moffitt et al 2018). Thus, accounting for tissue heterogeneities is another avenue for a potentially major improvement in the model. Another possible improvement over our adjustments may be to compensate for further complexities, such as the lateral dimensions of the proton beams incident on the aperture, the self-shielding of the aperture block, and integrating over a 3D distribution of secondary neutron generation points in the aperture block rather than assuming a single point source. Although these omissions may have contributed to the general underestimation of H_T/D_Rx values from our adjusted model, we would expect their affects to be minor compared to the adjustments made in this study and in the study by Eley et al. Future developments of a more generalized analytical model may test and, if necessary, account for the effects of these and various other physical aspects of a modern clinical proton beam.

In conclusion, we independently applied and evaluated a fast and simple analytical model to estimate equivalent dose from neutrons generated in a PSPT treatment unit. We found its accuracy to be sufficient, for example, for the purpose of estimating the risks of radiogenic cancers. In particular, after applying clinically-relevant adjustment factors, the model provided satisfactory estimates of equivalent dose from external neutrons in out-of-field organs and tissues for two pediatric intracranial therapy treatment plans. This independent testing advocates for further validation of analytical models for neutron doses in proton therapy, with the goal of understanding and minimizing neutron exposures and SMN risks.