Is an analytical dose engine sufficient for intensity modulated proton therapy in lung cancer?

Abstract

Objective:

To identify a subgroup of lung cancer plans where the analytical dose calculation (ADC) algorithm may be clinically acceptable compared to Monte Carlo (MC) dose calculation in intensity modulated proton therapy (IMPT).

Methods:

Robust-optimised IMPT plans were generated for 20 patients to a dose of 70 Gy (relative biological effectiveness) in 35 fractions in Raystation. For each case, four plans were generated: three with ADC optimisation using the pencil beam (PB) algorithm followed by a final dose calculation with the following algorithms: PB (PB-PB), MC (PB-MC) and MC normalised to prescription dose (PB-MC scaled). A fourth plan was generated where MC optimisation and final dose calculation was performed (MC-MC). Dose comparison and γ analysis (PB-PB vs PB-MC) at two dose thresholds were performed: 20% (D20) and 99% (D99) with PB-PB plans as reference.

Results:

Overestimation of the dose to 99% and mean dose of the clinical target volume was observed in all PB-MC compared to PB-PB plans (median: 3.7 Gy(RBE) (5%) (range: 2.3 to 6.9 Gy(RBE)) and 1.8 Gy(RBE) (3%) (0.5 to 4.6 Gy(RBE))). PB-MC scaled plans resulted in significantly higher CTVD2 compared to PB-PB (median difference: −4 Gy(RBE) (−6%) (-5.3 to −2.4 Gy(RBE)), p ≤ .001). The overall median γ pass rates (3%–3 mm) at D20 and D99 were 93.2% (range:62.2–97.5%) and 71.3 (15.4–92.0%). On multivariate analysis, presence of mediastinal disease and absence of range shifters were significantly associated with high γ pass rates. Median D20 and D99 pass rates with these predictors were 96.0% (95.3–97.5%) and 85.4% (75.1–92.0%). MC-MC achieved similar target coverage and doses to OAR compared to PB-PB plans.

Conclusion:

In the presence of mediastinal involvement and absence of range shifters Raystation ADC may be clinically acceptable in lung IMPT. Otherwise, MC algorithm would be recommended to ensure accuracy of treatment plans.

Advances in knowledge:

Although MC algorithm is more accurate compared to ADC in lung IMPT, ADC may be clinically acceptable where there is mediastinal involvement and absence of range shifters.

Introduction

Proton beam therapy (PBT) is increasingly used in the treatment of a number of non-conventional tumour sites such as lung, breast and head and neck both within and outside the context of clinical trials.^1,2 Unfortunately, PBT is prone to multiple uncertainties.³ One of these include the dose calculation algorithm within the treatment planning system (TPS). Currently, most proton therapy centres worldwide use a simplified analytical dose calculation (ADC) algorithm known as a pencil beam (PB) algorithm to generate clinical plans. The analytical dose engine has the advantage of being fast. However, in the presence of tissue heterogeneity its accuracy is debatable.^4,5 The issue largely arises due to the inaccuracy in modelling multiple Coulomb scattering as well as elastic and inelastic nuclear interactions.⁶ The TPS uses the so-called infinite slab approximation and therefore disregards lateral inhomogeneities for each individual ray traces. The inaccuracy is accentuated in lung cases as well as those with metal implants, bones or air cavities.^7,8 This error tends to increase with the magnitude of air gaps, use of range shifters for shallow targets and treatment of small volumes requiring small fields.^9–11

Monte Carlo (MC) dose calculation algorithm simulates transfer of particle through materials by random sampling of the various interactions. Provided that the physics process modelling is accurate and there is adequate number of particles simulated, MC should provide a more accurate dose estimation. The main disadvantage of MC simulations is its speed and complexity to implement. However, fast TPS-based MC algorithms have recently become available commercially. Compared to the general-purposed MC, not all physical interactions are considered.¹² It has been specifically optimised for speed but at the same time maintaining sufficient accuracy to the relevant physics processes.

A number of comparison studies have now been published assessing the accuracy of the ADC against MC simulations. Both Schuemann et al and Bednarz et al evaluated compared the ADC and MC in PBT delivered in the setting of passive scatter proton therapy.^8,10 In intensity modulated lung therapy (IMPT), a number of publications comparing the Raystation ADC and MC have been published in homogeneous, heterogeneous and anthropomorphic phantoms,^9,13 and in breast and lung clinical cases.^14,15 Yepes et al evaluated the Eclipse ADC against an in-house MC for IMPT in five different tumour sites in over 500 cases.¹⁶ The overall conclusion of these studies was that MC algorithm was found to be more accurate compared to ADC in particular for thoracic tumours.

Despite the availability of a fast commercial MC algorithm, ADC remains the most widely used for treatment planning in PBT. Furthermore, although the commercial MC algorithm is faster than a general purpose MC algorithms, optimisation and dose calculations time is still longer compared to ADC algorithms. Given our understanding of the limitations and advantages of ADC, we aimed to identify if there are any clinical lung cases where the ADC would be acceptable for lung IMPT.

Methods and materials

Patients

20 patients with locally advanced non-small cell lung cancer (NSCLC) previously treated with photon radiotherapy were selected based on varying tumour sizes and locations (10/20 patients had left-sided primary tumour and 11 had middle/lower lobe primary tumours). Most cases had nodal/mediastinal involvement as the main cohort of patients receiving radical chemoradiotherapy are stage III NSCLC (16/20). Of 20 cases, 14 were previously treated with photon radiotherapy at the Oxford Cancer Centre between August 2013 and March 2017. The planning study was registered and approved by the NHS Health Research Agency and conducted under the auspices of Oxford University Clinical Trials (research ethics committee reference: 16/LO/1324). The other six patients were provided by Hugo et al¹⁷ through the cancer imaging archive (TCIA).¹⁸

Four-dimensional (4D) CT simulation (Optima CT580RT, GE Healthcare, WI) were acquired for all patients. Each 4DCT dataset was acquired under free breathing conditions and recorded using the real-time position management system (Varian Medical Systems, Palo Alto, CA). The entire thorax and upper abdomen were scanned with 2.5 mm slice thickness. Each breathing period was phase-binned into 10 bins. Unweighted averaged-intensity projection (Ave-CT) datasets were generated for treatment planning.

Contouring

Target and normal anatomy delineation were done by a radiation oncologist (ST) following the RTOG 1308 trial protocol.^19,20

Dose specifications and constraints

The target prescription was 70 Gy (relative biological effectiveness (RBE)) in 35 fractions. RTOG 1308 trial dose specifications and constraints were used.¹⁵ All plans were robust-optimised using the minimax robust optimisation method.²¹ The minimax optimisation minimised the objective function in the worst-case scenario. An estimate of the effects of the errors was obtained by recalculating a set of dose distributions based on the scenarios. The TPS would then expand the CTV based on this. The optimisation parameters for setup error was 3 mm based on the institutions threshold for online shifts and 3.5% for range uncertainty as recommended by Paganetti.³ Proton RBE was assumed to be 1.1. Plans were normalised such that the prescribed dose covered 99% of the CTV.

Plan design

All plans used coplanar beams. A summary of the beam arrangements and whether range shifters were used for each plan could be found in Supplementary Material 1.

Raystation MC algorithm

We considered the Raystation MC algorithm to be the gold-standard. Comparison between the Raystation TPS ADC and MC algorithms has been previously validated in water and lung phantoms.^9,13 Saini et al compared the Raystation ADC vs MC algorithms vs GATE as well as Raystation MC vs measurements in homogeneous, heterogeneous and anthropomorphic phantoms.⁹ Taylor et al compared ADC vs MC vs measurements in heterogeneous anthropomorphic moving lung phantom.¹³ In both studies, the Raystation MC algorithm was observed to have higher accuracy over the Raystation PB algorithm. Saini et al reported γ pass rates of greater than 90% in six of seven planes using the Raystation MC algorithm (dose tolerance (DT) = 3%, distance-to-agreement (DTA) = 3 mm).⁹ When Raystation MC algorithm was validated against GATE in a water phantom, the Raystation MC and GATE MC were always within 3% of the measurement.⁹ In addition, Raystation MC has been validated against GATE⁹ and FLUKA (Fiorini et al, unpublished work) MC software packages. When Raystation MC algorithm was compared against FLUKA in different tumour sites (thoracic, CNS, pelvic tumours), the γ analysis passing rates were all above 85% (global 3%–3 mm, median: 98%, range: 87–100%)). However, when the Raystation ADC was compared against FLUKA, the median pass rate was 79% (57–100%).

Treatment plans

For each case, four plans were created. In the first three plans, optimisation of plans were executed using the analytical PB algorithm within Raystation TPS (v6.99, Raysearch Laboratories, Stockholm). This was followed by three final dose calculations:

• PB (PB-PB) algorithm. Pencil-beam dose engine (v4.2).

• MC algorithm (PB-MC). MC dose engine (v4.1) with 1% statistical uncertainty.

• MC algorithm normalised to prescription dose (PB-MC scaled).

The fourth plan was generated using MC optimisation (10,000 ions/spot) and final dose calculations (MC-MC) in Raystation.

Dosimetric evaluation

For each plan, the hot spot dose received by 2% of the volume (D2%), the minimum dose received by 99% of the volume (D99%) and the mean dose (D_mean) to the CTV were recorded. Wilcoxon signed-rank test was used for testing the differences between any two types of plans. Doses to OAR were evaluated for the oesophagus, heart, lungs and spinal cord.

γ-analysis

Dose distributions from PB-PB (reference dose) were compared to PB-MC through a global γ index analysis²² with DT/DTA 3%/3 mm. γ analyses were performed in MATLAB (R2017a, Mathworks, MA). Two low-dose threshold were chosen: 20% (D20) and 99% (D99) of the prescribed dose. The former to evaluate the dose agreement of the entire treatment plan and the latter to evaluate the dose agreement within the CTV.

Statistical analysis

Wilcoxon signed-rank test was used to compared the dose metrics. Univariate and backward elimination multivariate linear regression analysis were undertaken to evaluate if any variable was predictive of high correlation in the γ-analysis between ADC and MC dose engines. GTV, CTV and average CTV HU were considered as continuous variable. The following variables were treated as binary variables: presence of mediastinal disease and use of range shifter. In order for plans to be categorised as no range shifter used, all beams within the plan must not utilise a range shifter. If one or more beams required a range shifter in order to achieve an optimal dose distribution, the plan would be classified as requiring range shifter. Statistical significance was defined as p < 0.05. All statistics were performed in IBM SPSS Statistics v20 (IBM Corp, Armonk, NY).

Results

Patient and plan characteristics

A summary of the patient characteristics along with the result of the γ analysis can be found in Table 1. gross tumour volume (GTV-primary and nodes) ranged from 15-404cc. The overall median pass rates of γ analysis for D20 and D99 at DT/DTA 3%/3 mm were 93.2% (range: 62.2–97.5%) and 71.3 (15.4%–92.0%).

Table 1.

Summary of tumour characteristics, use of range shifter and γ analyses pass rates. (HU hounsfield units)

Patient	GTV (cc)	CTV (cc)	TNM 8 staging	Average HU of CTV	Range shifter	Mediastinal disease	γ-pass rates, %
							D20	D99
1	15	82	TxN2	−142.93	no	yes	96.02	48.39
2	261	502	T4N2	−135.03	no	yes	93.15	48.39
3	106	296	T2N0	−522.80	yes	no	89.72	47.40
4	25	96	TxN2	−319.72	no	yes	96.16	80.97
5	404	715	T4N0	−518.43	no	yes	86.02	60.91
6	50	194	T2N2	−378.60	no	yes	96.89	85.39
7	21	78	T4N0	−169.25	no	no	62.16	15.40
8	28	152	T1N2	−344.52	yes	yes	94.15	78.13
9	127	335	T2N2	−33.68	yes	yes	95.81	92.02
10	56	170	T3N0	−106.04	yes	no	95.26	91.42
11	46	295	T3N2	−78.28	yes	yes	97.50	91.62
12	50	238	T3N2	−377.44	no	yes	95.56	81.19
13	48	180	T2N3	−220.04	yes	yes	97.30	87.26
14	32	159	T3N0	−279.68	yes	no	84.40	42.84
15	115	252	T3/4 N1	−212.58	yes	yes	85.51	53.57
16	33	175	T2N1	−525.07	yes	yes	80.10	29.72
17	175	542	T3N2	−443.06	yes	yes	87.96	27.08
18	27	130	T2N0* T1N0*	−294.21	yes	no	94.52	67.53
									19	306	603	T4N0	−206.26	no	yes	91.20	41.56
20	68	317	T4N3	−252.29	yes	yes	92.28	60.07

Dose to target

Overestimation of CTV D99 and CTV mean was observed in all PB-MC compared to PB-PB plans. Both overestimation and underestimation were found for CTV D2 metric when PB-PB were compared with PB-MC plans. Median and range values of CTV coverage in the different plans can be found in Table 2. There were highly statistically significant differences in CTV D99 coverage between PB-PB and PB-MC plans and PB-PB and PB-MC scaled plans (both p ≤ 0.001, see Figure 1). The overall median overestimation of CTV D99 and CTV mean was 3.7 Gy(RBE) (5%) (range: 2.3 to 6.9 Gy(RBE) (3 to 10%)) and 1.8 Gy(RBE) (3.1%) (0.5 to 4.6 Gy(RBE) (1 to 7%), see Table 3). Simple scaling of PB-MC plans resulted in significantly higher CTVD2 compared to PB-PB or PB-MC plans (median difference: 4 Gy(RBE) (6%), range: 2.4 to 5.3 Gy(RBE) (3–8%), p ≤ .001, see Table 3).

Table 2.

CTV coverage of all plans with ADC compared to MC. (D_pres – dose relative to the prescribed dose of 70 Gy (RBE))

Metric	PB-PB	PB-MC	PB-MC scaled	MC-MC
CTV D99
Median, Gy (%Dpres)	70.0 (100)	66.3 (95)	70.0 (100)	70.0 (100)
Range, Gy	70.0–70.0	63.1–67.7	70.0–70.0	70.0–70.0
CTV mean
Median, Gy (%Dpres)	72.2 (103)	70.3 (100)	74.4 (106)	72.4 (104)
Range, Gy	71.2–73.6	67.6–71.8	71.1–75.6	71.8–73.8
CTV D2
Median, Gy (%Dpres)	74.5 (106)	74.0 (106)	78.5 (112)	74.7 (107)
Range, Gy	72.4–76.3	70.5–77.0	75.9–80.7	73.4–75.9

Figure 1.

Boxplots of CTV coverage of all plans. (* - p < 0.05, *** - p < 0.001, n.s. – not statistically significant). There was no statistically significant difference in CTVD99 of PB-PB, PB-MC scaled and MC-MC plans as plans were by definition normalised such that the prescribed dose covered 99% of the CTV.

Table 3.

Absolute and relative difference in dose between PB-PB and PB-MC, and PB-MC scaled plans. (D_pres – dose relative to the prescribed dose of 70 Gy (RBE))

Metric, Gy (RBE) (%Dpres)	Difference in dose
	PB-PB – PB-MC	PB-PB – PB-MC (scaled)	PB-PB – MC-MC
Overall
CTV D99
Median	3.7 (5)	0.0 (0)	0.0 (0)
Range,	2.3 to 6.9 (3 to 10)	0.0 to 0.0 (0 to 0)	0.0 to 0.0 (0 to 0)
CTV mean
Median,	1.8 (3)	−2.2 (-3)	−0.5 (-1)
Range,	0.5 to 4.6 (1 to 7)	−3.2 to 1.4 (-5 to 2)	−0.8 to 0.6 (-1 to 1)
CTV D2
Median,	0.3 (0.4)	−4.0 (-6)	−0.3 (0)
Range,	−1.6 to 3.1 (-2 to 4)	−5.3 to -2.4 (-8 to -3)	−1.4 to 1.0 (-2 to 1)
With predictors, n = 7
CTV D99
Median,	2.9 (4)	0.0 (0)	0.0 (0)
Range,	2.3 to 4.1 (3 to 6)	0.0 to 0.0 (0 to 0)	0.0 to 0.0 (0 to 0)
CTV mean
Median,	0.7 (1)	−2.1 (-3)	−0.3 (0)
Range,	0.5 to 1.7 (1 to 2)	−2.9 to -1.6 (-4 to -2)	−0.7 to 0.0 (-1 to 0)
CTV D2
Median,	−0.4 (-1)	−3.5 (-5)	−0.2 (0)
Range,	−1.6 to 0.8 (-2 to 1)	−5.2 to -2.4 (-7 to -3)	−1.4 to 0.4 (-2 to 1)
The rest, n = 13
CTV D99
Median,	4.4 (6)	0.0 (0)	0.0 (0)
Range,	3.2 to 6.9 (5 to 10)	0.0 to 0.0 (0 to 0)	0.0 to 0.0 (0 to 0)
CTV mean
Median,	2.5 (4)	−2.1 (-3)	−0.5 (-1)
Range,	1.4 to 4.6 (2 to 7)	−3.2 to 1.4 (-5 to 2)	−0.8 to 0.6 (-1 to 1)
CTV D2
Median,	0.9 (1)	−3.9 (-6)	−0.4 (1)
Range,	−1.5 to 3.1 (-2 to 4)	−5.3 to -3.2 (-8 to -5)	−1.3 to 1.0 (-2 to 1)

When PB-PB plans were compared to MC-MC plans, no statistically significant difference was found in CTV D99 coverage. Statistically, CTVD2 and mean dose to CTV were found to be significantly higher with MC-MC plans compared to PB-PB plans (CTV mean: median: −0.5 Gy(RBE) (−1%) (range: −0.8 to 0.6 Gy(RBE) (-1 to 1%), CTVD2: −0.3 Gy(RBE) (0%) (-1.4 to 1.0 Gy(RBE) (-2 to 1%)).

Dose to OAR

When comparing PB-PB and PB-MC plans, similar to the target, both over and under estimation is observed outside the target. A summary of the absolute dose to OAR and observed differences can be found in Table 4. There were a few cases where underestimation of dose occurred immediately distal to the target. For example, in patient 14, dose to the area distal to the target (Figure 2E, pink arrow) was underestimated by at least 15 Gy, PB-PB vs PB-MC plans point dose from 25.8 to 44.8 Gy(RBE)). A separate area (red arrow) was underestimated by 9 Gy(RBE) (point dose: 58.2 to 67.6 Gy(RBE)).

Table 4.

Absolute doses and difference in OAR doses between ADC and MC. (PB-MC (s)–PB-MC scaled)

Metric	PB-PB	PB-MC	PB-MC (s)	MC-MC	P-values
median (range)					PB-PB– PB-MC	PB-PB– PB-MC (s)	PB-MC– PB-MC (s)	PB-PB– MC-MC
MHD (Gy (RBE))	4.5	4.3	4.6	4.7	0.001	<0.001	<0.001	0.765
	(0.1–14.2)	(0.1–13.5)	(0.1–15.0)	(0.1–14.1)
MLD (Gy (RBE))	10.9	10.8	11.5	11.8	0.057	<0.001	<0.001	0.37
	(5.1–16.6)	(5.1–16.2)	(5.4–17.7)	(5.7–17.9)
Lung V20 (%)	19.4	19.3	20.4	20.4	0.55	<0.001	<0.001	0.411
	(10.4–29.7)	(10.5–29.4)	(10.9–30.3)	(10.5–32.5)
Lung V5 (%)	27.8	28	28.4	30.7	0.001	<0.001	<0.001	0.411
	(17.4–45.4)	(17.6–45.9)	(17.8–46.3)	(17.8–46.3)
Oesophagus D1.5cc (Gy (RBE))	56.2	54.7	57.4	55.7	0.023	0.001	<0.001	0.185
	(0.0–71.5)	(0.0–71.7)	(0.1–75.8)	(0.1–73.6)
Spinal cord Dmax (Gy (RBE))	22.1	21.3	22.3	25.9	0.108	<0.001	<0.001	0.737
	(0.5–45.2)	(0.5–46.1)	(0.5–49.5)	(0.7–46.8)
Difference Median (range)	Absolute difference
	PB-PB–PB-MC			PB-PB–PB-MC (s)		PB-PB–MC-MC
MHD (Gy (RBE))	0.1 (-0.1 to 0.7)			−0.2 (-0.8 to 0.0)		−0.5 (-1.4 to 2.7)
MLD (Gy (RBE))	0.1 (-0.2 to 0.6)			−0.6 (-1.2 to -0.3)		−0.9 (-2.2 to 0.9)
Lung V20 (%)	0.0 (-0.3 to 0.7)			−0.5 (-1.2 to 0.0)		−1.1 (-3.1 to 2.4)
Lung V5 (%)	−0.4 (-2.0 to 0.3)			−0.7 (-2.8 to 0.0)		−1.8 (-7.3 to 0.3)
Oesophagus D1.5cc (Gy (RBE))	0.7 (-2.7 to 3.1)			−2.1 (-6.1 to 1.4)		−0.2 (-5.3 to 6.7)
Spinal cord Dmax (Gy (RBE))	−0.4 (-9.2 to 2.9)			−2.0 (-10.2 to 1.9)		−1.0 (-8.5 to 2.9)

Figure 2.

Axial dose colour map and DVH of PB-PB vs PB-MC plan of patient 14. The GTV was 32cc, stage T3N0 with range shifter used. A- PB-PB, B- PB-MC, C- PB-MC scaled, D- MC-MC plans. E- Dose difference between PB-PB and PB-MC (A minus B). In PB-MC plan, dose overestimation observed in CTV. F- DVH of all four plans. Red and pink arrows indicate area of underestimation by PB-PB plan compared to PB-MC plan. (Red region of interest (ROI) - CTV, Cyan ROI - heart, Orange ROI - oesophagus).

In all cases, apart from one (patient 4), the OAR dose constraints were met in all the plan modalities. In patient 4, the oesophageal D1.5cc constraint was not met (PB-PB: 69.4 Gy(RBE), PB-MC: 72.1 Gy(RBE), PB-MC scaled 75.5 Gy(RBE), RTOG 1308 dose constraint oesophagus max dose: 74 Gy(RBE)<1.5 cc). In patient 8, although the spinal cord Dmax constraint was met in all the plans, PB-PB plan underestimated the Dmax dose by 9.2 Gy(RBE) compared to PB-MC plan (Cord Dmax, PB-PB: 12.0 Gy(RBE), PB-MC: 21.3 Gy(RBE), PB-MC scaled: 22.3 Gy(RBE), MC-MC: 18.5 Gy(RBE)). A table summarising the absolute dose to the OAR for each plan can be found in the Supplementary Material 2.

Conversely, PB-MC scaled plans had significantly higher OAR doses compared to PB-PB plans (all p < 0.05). There were no statistically significant difference in dose to OAR between PB-PB and MC-MC plans for the following OAR dose metrics: MHD, MLD, lung V5, lung V20, oesophagus D1.5cc and maximum dose to the spinal cord. Figure 2 shows a representative axial dose colour map of the four different treatment plans and DVHs. Simple scaling of PB-MC plan resulted in considerable hot spots within the CTV (Figure 2C).

Predictors of high γ pass rates

Presence of disease in the mediastinum followed by absence of a range shifter were consistently the largest predictors for good agreement in the γ analysis between PB-PB and PB-MC plans in both univariate and multivariate analysis for D20 and D99 (Table 5. The average CTV HU were marginally significant in the univariate analysis for D99 (p = .059).

Table 5.

Univariate and multivariate analysis for γ pass rates with D99 dose at DT/DTA 3%/3 mm. PBPB plans (reference dose) were compared to PB-MC (SE- standard error of β, 95% CI - 95% confidence interval, HU - hounsfield unit)

Variables	Co-efficient (ß)	SE	95% CI	P value
Univariate analysis - D20 3%/3 mm
GTV	0.01	0.02	−0.03 to 0.05	0.624
CTV	0.01	0.01	−0.02 to 0.03	0.729
Mediastinal disease	11.47	3.48	4.17 to 18.78	0.004
Range shifter	−8.51	3.34	−15.52 to −1.50	0.02
Average CTV HU	0.01	0.01	−0.15 to 0.04	0.373
Multivariate analysis - D20 3%/3 mm
Mediastinal disease	9.75	3.22	2.95 to 16.55	0.008
Range shifter	−6.48	2.85	−12.48 to −0.47	0.036
Univariate analysis - D99 3%/3 mm
GTV	0.08	0.05	−0.02 to 0.18	0.102
CTV	0.04	0.03	−0.02 to 0.10	0.156
Mediastinal disease	33.66	9.72	13.24 to 54.07	0.003
Range shifter	−26.2	9.21	−45.55 to −6.85	0.011
Average CTV HU	0.07	0.03	−0.00 to 0.138	0.059
Multivariate analysis - D99 3%/3 mm
Mediastinal disease	28.24	7.65	9.99 to 46.49	0.005
Range shifter	−20.31	8.65	−36.45 to −4.18	0.017

High collinearity was observed between GTV and CTV (Pearson correlation r = 0.95), hence only GTV was included in the multivariate model. On multivariate analysis, presence of mediastinal involvement and absence of range shifter were significantly associated with higher γ pass rates for D20 (β = 9.75, 95% CI = 2.95 to 16.55 and β = −6.48, 95% CI = −12.48 to −.47, respectively, both p < .05, see Table 5). Similarly for D99, presence of mediastinal involvement and absence of range shifter were significantly associated with higher γ pass rates (β = 28.24, 95% CI = 9.99 to 46.49 and β = −20.31, 95% CI = -36.45 to -4.18, respectively, both p < .05).

Figure 3 shows that plans with mediastinal involvement and absence of range shifters were found to have higher D20 and D99 γ pass rates compared to those without these two predictors. Median D20 and D99 pass rates with these predictors were 96.0% (range 95.397.5%) and 85.4% (75.1–92.0%). Similarly, CTV coverage in PB-MC plans was observed to be superior when these predictors were present in a treatment plan (Table 6). A summary of the absolute differences in CTV D99, mean and D2 coverage between the different plans with and without the predictors is found in Table 3. For comparison between PB-PB and PB-MC plans, the median difference in CTV D99 with predictors vs the rest of the plans were 2.9 Gy(RBE) (4%), (range: 2.3 to 4.1 Gy (RBE) vs 4.4 Gy(RBE) (6%), (3.2 to 6.9 Gy(RBE) and CTV mean 0.7 Gy(RBE) (1%) (0.5 to 1.7 Gy(RBE) vs 2.5 Gy(RBE) (4%) (1.4 to 4.6 Gy(RBE)). The median difference in CTV mean between PB-PB and PB-MC scaled plans with predictors vs the rest of the plans were −2.1 Gy(RBE) (−3%) (-2.9 to −1.6 Gy(RBE) vs −2.1 Gy(RBE) (−3%) (-3.2 to 1.4 Gy(RBE)). Figures 4 and 2 illustrate the difference between ADC and MC dose calculations depending on whether plans have the associated predictors. In the absence of both mediastinal disease and use of range shifters, larger discrepancies were observed between the two dose distributions.

Figure 3.

Boxplots of γ analyses pass rates showing higher pass rates in plans with mediastinal involvement and absence of range shifter. PB-PB (reference dose) was compared to PB-MC through a global γ index analysis with DT/DTA 3%/3 mm.

Table 6.

CTV coverage with ADC compared to MC in plans stratified according to number of associated predictors based on multivariate analysis for high γ passing rates are absence of range shifter and presence of mediastinal involvement. (D_pres – dose relative to the prescribed dose of 70 Gy(RBE))

Metric 2Gy (RBE) (%Dpres)	PB-PB	PB-MC	PB-MC (scaled)
Absence of RS + mediastinal disease, n = 7
CTV D99
Median	70.0 (100)	67.1 (96)	70.0 (100)
Range	70.0–70.0	66.0–67.7	70.0–70.0
CTV mean
Median	72.0 (103)	71.2 (101)	74.5 (106)
Range	71.8–72.4	70.4–71.7	73.6–74.7
CTV D2
Median	74.0 (106)	74.5 (106)	78.1 (112)
Range	73.6–75.2	73.7–75.6	76.9–78.8
The rest, n = 13
CTV D99
Median	70.0 (100)	65.4 (93)	70.0 (100)
Range	70.0–70.0	63.1–66.5	70.0–70.0
CTV mean
Median	72.4 (103)	69.4 (99)	74.4 (106)
Range	71.2–73.6	67.6–71.1	71.1–75.6
CTV D2
Median	74.7 (107)	73.0 (104)	78.8 (113)
Range	72.4–76.3	70.5–75.1	75.9–79.8

Figure 4.

Coronal dose colour map and DVH of PB-PB vs PB-MC plan of patient 2. The GTV was 261cc, stage T4N2 and no range shifter was used. A & B coronal dose colour maps of PB-PB and PB-MC plans, respectively, C- DVH of both plans, D- Difference dose colour map between PB-PB and PB-MC plans (PB-PB minus PB-MC plan).

Discussion

Outcome of patients with locally advanced lung cancer is poor and PBT increasingly used due to the potential clinical benefit.^23–25 However, accuracy of treatment delivery is at the heart of radiotherapy and a number of reports have recently emerged regarding the limitations of the ADC algorithm especially in thoracic cancers.^9,13–15,26 Comparison studies between measurements in heterogeneous and anthropomorphic phantoms showed systematic overestimation of dose to parts of the target with ADC algorithm by up to 30%.^9,13 Both Saini et al and Taylor et al found improved agreement with MC algorithm.^9,13 Similarly, in 10 clinical lung cases, Maes et al found a median decrease in CTV V95% of 10% when ADC plans were recalculated using MC algorithm (Raystation 6 PB v4.0, MC v6.0, 0.5% statistical uncertainty, 10,000 ions/spot).¹⁵ Their reported median dose discrepancy in CTV coverage was higher compared to our study. This is likely to be due to differences in the individual patient cohort included in the studies (i.e., proportion of plans where range shifters were used and patients with mediastinal disease). In our case, 15 of 20 had mediastinal disease and eight plans did not utilise a range shifter. As well as overestimation, we observed underestimation within and outside the target. Although, the degree of underestimation tended to be small, we observed in one of the cases (patient 8), an underestimation of the Dmax to the spinal cord of up to 9 Gy(RBE).

Our analysis showed that although overestimation was observed in all cases, there was a subgroup of lung cancer plans where the difference between PB-PB and PB-MC plans may be clinically acceptable. In this group of patients,>95% of pixels passed the γ analysis (DT/DTA 3%/3 mm - D20) with an average difference in CTV D99 coverage of 3.2% (maximum 6%). At DT/DTA 2%/2 mm - D20, pass rates were >85% in these six plans (data not shown). Predictors found to be significantly associated with high γ pass rates on univariate and multivariate analyses that include: plans requiring no range shifter with mediastinal involvement (Table 5). On univariate analysis, higher CTV HU was marginally associated with higher γ pass rates at D99%. Our findings on the dose discrepancy between ADC and MC when range shifter is used is consistent with that of Widesott et al (Raystation 6, PB v4.0, MC v6.0, 0.5% statistical uncertainty).¹¹

These findings are relevant as currently most proton therapy centres around the world still rely on ADC algorithm for treatment planning. ADC has the benefit of being fast compared to MC dose engines. Although, fast commercial MC TPS are becoming available, optimisation and dose calculation times are still longer compared to ADC. When tested on different tumour sites, with 1% statistical uncertainty, the final dose calculation times with Raystation MC could take as much as four times that of the PB algorithm.⁹ When MC robust-optimisation is done, depending on the number of scenarios considered, the time taken for optimisation and dose calculation is even longer. Liang et al reported the time taken to generate an MC robust-optimised plan with 147 scenarios for a breast and regional lymph node case was ∼20 h (200 iterations with 50,000 ions/spot). The PB plan took $\frac{1}{4}$ of the time.¹⁴ In our case, as an example, it took 50 min to optimise an MCMC robust-optimised plan for patient two with PB-PB plans taking only half the time (200 iterations with 10,000 ions/spot, 21 scenarios). Furthermore, although this study specifically reports on lung cancer cases, the findings could be applied to other tumour sites such as oesophagus where tumours tend to be located deep within the mediastinum and use of range shifters could be avoided.

As previously described, simple scaling of dose to correct the underestimation of dose by PB-PB plans within the target would result in significant hotspots generated within the target as well as OAR (Figure 2).¹⁴ Of all the cohort of patients included in the study, the maximum dose constraints to the target were met with the scaled plan. For OAR, as PBT was able to significantly reduce dose to surrounding organs compared to photon,²⁴ there was only one patient where the oesophagus D1.5cc was exceeded with the scaled plan (patient 4). If these hotspots were located in serial organs, such as the spinal cord, they could potentially be detrimental. For other organs such as the heart, there is increasing evidence to show that exposure of high doses to small volumes could contribute to cardiac toxicity.²⁷ As it is difficult to predict where these hotspots might occur, solving the issue of overestimation by simple scaling would not be advisable. We note that although, statistically, CTVD2 and mean dose to CTV were found to be significantly higher with MC-MC plans compared to PB-PB plans, these differences were not clinically relevant (Table 2 for median and range values of CTV coverage). Doses to OAR were generally over estimated by the ADC algorithm, however, we observed that there were a number of cases where underestimation of dose occurred at potentially clinically relevant dose levels. Figure 2E showed an area of underestimation of at least 15 Gy distal to the target (pink arrow, PB-PB vs PB-MC plans point dose from 25.8 to 44.8 Gy (RBE)). The potential biological effect of the dose underestimation would need to be considered individually as it is dependent on which OAR the dose is deposited. For this particular case, dose to the right atrium was markedly underestimated which could increase risk of cardiac toxicity.²⁴ In view of this, caution needs to be taken when using ADC when an OAR is immediately distal to the target as the dose underestimation could then be of clinical relevance.

There are a number of limitations to our study. First, only 20 cases were evaluated. However, despite the number, we were able to identify statistical significance in both the univariate and multivariate analysis for predicting high agreement between PB-PB plans and PB-MC plans. This was due to the large effect of the predictors. These predictors are consistent with what is known to be limitations of the ADC algorithm.

Another limitation to our study is that these findings are specific to the Raystation PB algorithm investigated and as such is not generalisable to other ADC algorithms. Therefore, validation of other ADC dose engines would need to be performed. Interestingly, although overestimation of up to 10% was observed by Yepes et al, dependence on presence of range shifter was not observed when the Eclipse ADC algorithm was evaluated.¹⁶ Similarly, Winterhalter et al did not see dependence when using a pre-absorber when evaluating their PB or ray-casting algorithms.²⁸

Our evaluation has specifically focused on the uncertainties based on the dose calculation algorithm. We recognise that this is only one aspect of thoracic PBT plan that needs to be considered. Careful considerations to the robustness of a lung plan against the interplay effect, setup and range uncertainties also need to be accounted for. While robust optimisation would reduce most of the plan sensitivities against setup and range uncertainties, the interplay effect would need to be mitigated by strategies such as rescanning.²⁹ Furthermore, it is known that the limited spatial resolution of current clinical planning CT could impact the dose predicted by the TPS especially in highly heterogeneous lung tissue.³⁰ However, as both dose algorithms rely on the same planning CT, the magnitude of error is likely to be the same in both algorithms.

In conclusion, we have identified a subgroup of lung cases where the Raystation ADC may be clinically acceptable for treatment planing in thoracic PBT. Key to this is understanding the limitations of the ADC algorithm used. In the presence of mediastinal involvement and absence of range shifters ADC maybe clinically acceptable for treatment planning in lung IMPT. Without these features, the Raystation MC algorithm would be recommended to ensure accuracy of treatment plans.