Supplementary material

for the paper

Combined proton-photon treatments - a new approach to proton therapy without a gantry

A. Treatment plan optimization details

In this section, we detail the treatment plan optimization for the three clinical cases with

malignancies of the nasopharynx, oropharynx, and larynx. We first consider the optimization of

the single-modality IMRT and IMPT plans. Combined proton-photon treatments are obtained by

simultaneously optimizing IMRT and IMPT plans based on their cumulative physical dose. Solutions

for all the optimization problems are found by using our own implementation of the L-BFGS quasi-

Newton method [1], together with an augmented Lagrangian method for handling constraints [2].

Dose influences matrices for photons are calculated with the open-source radiotherapy planning

research platform CERR [3], assuming a beamlet resolution of 5x5 mm2. Dose calculations for

protons are performed with the open-source radiation treatment planning toolkit matRad [4],

assuming a lateral spot spacing of 5 mm. The pencil beam sizes that are used represent a generic

proton machine. Assuming a Gaussian lateral profile, the initial sigma value at the patient surface

ranges from 5 to 2.3 mm for energies of 31.7-236.1 MeV.

A.1. Single-modality treatment plans optimization

A1.1. Nasopharyngeal cancer

For the NPC case, we solve optimization problems for the following choice of the objective

function:

f (d ) = 1N T 1

∑iϵT 1

❑

¿¿ (A.1

)

+ 1N T 2

∑iϵT 2

❑

¿¿ (A.2

)

+ 1N T 3

∑iϵT 3

❑

¿¿ (A.3

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)

+ 1N R

∑iϵR

❑

(di−d imax)+¿2¿

(A.4

)

+ 1N H

∑iϵH

d i(A.5

)

+ ( 1NP∑iϵP

d ip)1p (A.6

)

+ 1N C

∑iϵC

d i(A.7

)

+ 1N B

∑iϵB

d i(A.8

)

+ 1N PG

∑iϵPG

d i(A.9

)

and constraint function:

d imax≤26 ∀ i∈PG (A.10

)

where T1,2 and 3 denote the set of voxels in the three PTVs, R is the set of voxels in a 1cm

rim of normal tissues surrounding the PTV3; P, C, B and PG denote the set of voxels in the

PCM, cochlea, brainstem and parotid glands, and H is the set of voxels in the remaining

normal tissues. The exponent in the gEUD objective (Eq. A.6) for the PCM is set to p=5.

The maximum dose d imax in the conformity objective (Eq. A.4) is given by:

d imax≤54−zi(54−27) (A.11

)

where z i is the euclidian distance of a normal tissue voxel i from the PTV3 contour.

A1.2. Oropharyngeal cancer

For the OPC case, a complete list of the objective and constraint functions is as follows.

A dose of 70 Gy is prescribed to the PTV1. A dose exceeding 73.5 Gy is penalized

quadratically.

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A dose of 60 Gy is prescribed to the PTV2. A dose exceeding 70 Gy is penalized

quadratically.

A dose of 54 Gy is prescribed to the PTV3. A dose exceeding 60 Gy is penalized

quadratically.

The plan is to be conformal. A dose falloff to half the PTV3 prescription at 1 cm from

the PTV3 contour is aimed for.

The gEUD in the PCM is minimized (p=5).

The mean dose to the oral cavity and parotid glands is minimized.

The mean dose in the remaining healthy tissues is minimized.

The maximum mean dose to the union of the parotid glands is constrained to 26 Gy.

For the exact mathematical definition of the planning objectives see equations A.1-A.11.

A1.3. Laryngeal cancer

For the laryngeal cancer case we solve optimization problems for the following choice of

the objective function:

f (d ) = 1N T

∑iϵT

❑

¿¿ (A.12

)

+ 1N R

∑iϵR

❑

(di−d imax)+¿2 ¿

(A.13

)

+ 1N H

∑iϵH

d i(A.14

)

+ ( 1NP∑iϵP

d ip)1p (A.15

)

+ ( 1NL∑iϵL

d ip)1p (A.16

)

+ 1N C

∑iϵC

d i(A.17

)

where T, P, L, C and H denotes the set of voxels in the target volume, PCM, larynx,

arytenoid cartilage, and remaining normal tissues; and R is the set of voxels in a 1 cm rim of

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normal tissues surrounding the PTV. The exponents in the gEUD objectives (Eq. A.15 and

A.16) for the PCM and larynx are set to p=5 and p=0.8, respectively. The maximum dose

d imax in the conformity objective (Eq. A.13) is given by:

d imax≤68−zi(68−34) (A.18

)

A.2. Multi-modality treatment plans optimization

For each patient, the optimized combination is obtained by considering the same clinical goals

as for the single-modality IMRT and IMPT plans. A subset of objective functions is minimized

while the remaining ones are constrained to be no worse than in the IMRT plan. Thus, if f i

represents a single objective (e.g. target coverage or dose conformity) and f IMRT denote its

value in the IMRT plan, we add constraints of the form:

f i≤ f IMRT i(A.19

)

This is illustrated for the laryngeal cancer case where the objective is to minimize the weighted

sum of Eq. A.14-A.17 while all the remaining objectives (Eq. A.12 and A.13) are constrained to

their values in the IMRT plan.

B. NTCP models

The NTCP models used in this paper are selected from literature and have in parts been proposed

for model-based patient selection in the Netherlands [5]. These are based on three different

formulas:

1. Lyman-Kutcher-Burman (LKB) model with parameters m, n, and TD50:

NTCP=Φ( gEUD (n )−TD50

m ∙TD50) (B.1)

where Φ is the cumulative distribution function of the standard normal distribution.

2. Logistic regression model (LM) with parameters TD50 and k :

NTCP=(1+(TD50

D )k

)−1 (B.2)

3. Multivariable logistic regression model (MV) with parameters a, b, and c:

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NTCP=(1+ea−b ∙ X 1−c∙ X 2 )−1 (B.3)

Details regarding the different NTCP models are provided in Table B.1.

C. Proton gantry treatments

In this section, the IMPT plans that could be delivered with a gantry will be discussed. When

designing the gantry-based IMPT plans, several beam arrangements were tested and the best one

was chosen. For all the patients, the gantry treatment uses 5 equispaced beams on a transversal

plane (gantry angles of 36°, 108°, 180°, 252°, and 324°). For optimizing the gantry-based IMPT

plans, Table B.1: Details of the NTCP models used in the present study. Considered toxicities, impacted organs, and used NTCP models with corresponding coefficients are listed.

the same objective functions were used as for generating the IMRT and fixed beamline IMPT plans

(Appendix A).

C.1. Nasopharyngeal cancer

5

Toxicity Model type Impacted organ(s) Model coefficients Mean

Xerostomia [6, 7] MV Parotid gland abX1

1.5070.052Dmean controlat parotid

Dysphagia [6, 7] MV Oral mucosa and PCM

abX1cX2

3.3030.024Dmean oral cavity

0.024Dmean sup-PCM

Oral mucositis [8] LM Oral mucosa kTD50 (Gy)

151

Aspiration [9] LKB Larynx TD50 (Gy)nm

46.510.5

LKB PCM TD50 (Gy)nm

64.50.20.09

Laryngeal edema [10] LKB Larynx TD50 (Gy)nm

47.31.170.23

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858687

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Figure 2b of the main manuscript compares the DVHs for the IMPT plans with and without a

gantry. The DVHs for the IMRT plan and the optimal combination are also shown. It can be

seen that all plans are similar in terms of target coverage with the main differences observed

in the OARs. The use of a proton gantry improves the sparing of the parotid glands compared

to single-modality fixed beamline IMPT. In fact, if a gantry is used the mean dose can be

reduced from 23 to 14 Gy in the parotid glands and from 32 to 27 Gy in the PCM. On the other

hand, the oral cavity can be spared to a lesser extent due to the use of the anterior beams

(mean dose of 17 Gy). The gantry treatment has a 11% lower risk for xerostomia compared to

the IMRT plan, while no benefit is expected from the IMPT plan with the fixed beam line

(NTCP=0). Since the superior PCM is part of the target volume, both the IMPT plans have no

benefit for the risk of aspiration versus the IMRT plan. Small differences are observed in the

risk assessment of dysphagia for both the IMPT treatments compared to the IMRT plan

(NTCP=4% for the FBL treatment and NTCP=2% for the gantry treatment). The benefit in

oral mucositis versus the IMRT plan is smaller for the gantry treatment than for the FBL

treatment but a moderate NTCP-value reduction is still observed (NTCP=5% for the gantry

treatment and NTCP=12% for the FBL treatment).

C.2. Oropharyngeal cancer

Figure C.1a shows the DVHs for the IMPT plans with and without a gantry as well as for the

optimal combination and the IMRT plan. Note that if a FBL is used, the IMPT plan is suboptimal

for the parotids and PCM whereas the oral cavity can be better spared. The mean dose of 6 Gy

that can be obtained with the gantry treatment in the contralateral parotid gland translates

into a 6% lower risk for xerostomia compared to the IMRT plan. The IMPT plan with a FBL is

instead associated with a higher risk for this toxicity (NTCP=-13%). The benefits for the risk of

dysphagia and oral mucositis versus the IMRT plan are the same for both the IMPT plans

(NTCP=3% for dysphagia and NTCP=4% for oral mucositis). Finally, a NTCP=2% is seen with

regard to aspiration when using a gantry whereas no favourable result is observed with a FBL.

Interestingly, the optimal combination improves on the single-modality plans for the parotids

and oral cavity and achieves most of the integral dose reduction in the PCM that is possible

with the gantry IMPT plan. The target coverage remains similar for all the plans.

C.3. Laryngeal cancer

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Figures C.1b shows the DVHs for the IMPT plans, the IMRT plan, and the optimal combination.

In this case, the IMPT plans deliver similar doses to the larynx. Therefore, both plans are

associated with the same risk for larynx-based aspiration (NTCP=4%) and laryngeal edema

(NTCP=1%) with respect to the IMRT plan. The cartilage and PCM cannot be better spared by

using a gantry. Interestingly, the optimal combination reduces the dose to the larynx and

arytenoid cartilage with respect to the single-modality plans. The PCM can be spared to a

lesser extent, however, the optimal combination maintains most of the integral dose reduction

that is possible with the FBL protons-only plan.

Figure C.1: DVHs compared for the IMPT plans with and without a gantry, the IMRT plan and the optimal combination for: (a) the OPC case; and (b) the laryngeal cancer case.

D. Robustness of combined treatment plans against proton range uncertainties

One of the main concerns in cancer treatment with protons is the uncertainty in the range of a

proton beam within the patient. The dose distribution delivered to the patient may highly degrade

compared to the planned one if the true range of protons is uncertain. This uncertainty may

originate from several sources including the conversion of CT Hounsfield units to stopping power

values [11], artefacts in the CT image [12], delivery uncertainties and changes in the patient’s

geometry. Therefore, in this section, we address the issue of the robustness of combined

treatment plans against proton range uncertainties. Range errors are modelled via three error

scenarios (nominal scenario, range overshoot and undershoot) by uniformly scaling the CT

Hounsfield units by 3.5%, such that all proton pencil beams penetrate further or less within the

patient. The stochastic programming approach [13] is used to incorporate the set of error

scenarios into the planning of combined treatments while safety margins are applied to account

for other potential sources of uncertainty including setup errors. The method minimizes a

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weighted sum of objective functions for cumulative dose evaluated for all error scenarios.

Formally, the optimization problem is:

minimizex γ , xp

❑∑s

ps f [ (dγ+d p )s ] (D.1)

where the parameter ps represents an importance weight for error scenario s and is chosen as 0.5

for the nominal scenario and 0.25 for the overshoot and undershoot scenarios [14, 15].

Figure D.1a shows the results of a sensitivity analysis of the non-robust combined treatment plan

for the NPC case. The undershoot of protons yields inhomogeneous dose distributions within the

target volumes whereas if the range of protons is larger than expected, higher doses are delivered

to the main OARs. Consequently, the benefit of the combined treatment over the single-modality

IMRT plan is reduced (Table D.1). Figure D.1b shows that proton range uncertainties can be

efficiently accounted for through stochastic optimization, with the robustly optimized combined

plan being less affected by uncertainties. Robustness is achieved by increasing the photon

component as shown in Figure D.2 for the nominal scenario. The price to pay for robustness is a

lower benefit over the single-modality IMRT plan (Table D.1). However, a substantial clinical

benefit remains.

Table D.1: NTCP-value reductions for the nasopharyngeal cancer case using non-robust and robust combined treatment plans versus IMRT plan.

NTCP in %Non-robust plan Robust plan

Toxicity nominal undershoot overshoot nominal undershoot overshoot

Xerostomia 10 13 7 9 11 7Dysphagia 3 3 2 2 2 2Mucositis 9 11 8 6 7 5

Figure D.1: DVHs from the non-robust (a) and robust (b) combined proton-photon treatment plans for the nasopharyngeal cancer case for the nominal condition (no range errors) and for scenarios in which the proton range is underestimated (overshoot) or overestimated (undershoot).

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Figure D.2: Proton-photon combinations for the nasopharyngeal cancer case. Top row: non-robust plan. Bottom row: robust plan. (a) and (d) photon dose contributions; (b) and (e) proton dose contributions; (c) and (f) cumulative doses. The contours show the high-risk PTV (red), the elective PTV (blue), the parotid glands (green), the mandible (magenta), and the oral cavity (orange).

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