# Accelerating proton arc therapy delivery through dosimetry-guided energy
layer filtering

Sophie Wuyckens  Université catholique de Louvain, Institut de Recherche
Expérimentale et Clinique (IREC), Molecular Imaging, Radiotherapy and
Oncology, 1200 Woluwe-Saint-Lambert, Belgium  Viktor Wase  RaySearch
Laboratories AB, Stockholm, Sweden  Otte Marthin  RaySearch Laboratories AB,
Stockholm, Sweden  Johan Sundström  RaySearch Laboratories AB, Stockholm,
Sweden  Guillaume Janssens  Université catholique de Louvain, Institute of
Information and Communication Technologies (ICTEAM), Louvain-La-Neuve, 1348,
Belgium  Ion Beam Applications SA, Louvain-La-Neuve 1348, Belgium  Elena
Borderias-Villarroel  Université catholique de Louvain, Institut de Recherche
Expérimentale et Clinique (IREC), Molecular Imaging, Radiotherapy and
Oncology, 1200 Woluwe-Saint-Lambert, Belgium  Kevin Souris  Université
catholique de Louvain, Institut de Recherche Expérimentale et Clinique (IREC),
Molecular Imaging, Radiotherapy and Oncology, 1200 Woluwe-Saint-Lambert,
Belgium  Ion Beam Applications SA, Louvain-La-Neuve 1348, Belgium  Edmond
Sterpin  Université catholique de Louvain, Institut de Recherche Expérimentale
et Clinique (IREC), Molecular Imaging, Radiotherapy and Oncology, 1200 Woluwe-
Saint-Lambert, Belgium  KULeuven, Department of Oncology, Laboratory of
experimental radiotherapy, Leuven, 3000, Belgium  Particle Therapy
Interuniversity Center Leuven - PARTICLE, Leuven, 3000, Belgium  Erik Engwall
RaySearch Laboratories AB, Stockholm, Sweden  John A. Lee  Université
catholique de Louvain, Institut de Recherche Expérimentale et Clinique (IREC),
Molecular Imaging, Radiotherapy and Oncology, 1200 Woluwe-Saint-Lambert,
Belgium

(September 1, 2023)

###### Abstract

Introduction. Proton arc therapy has emerged as a promising approach for
faster treatment delivery in comparison to conventional proton treatments.
However, unexpected prolonged treatment times in several proton arc planning
studies have raised concerns. In this study, we aim to address the challenge
of minimizing delivery time through dosimetry-guided energy layer filtering,
comparing its performance to a baseline approach without filtering.
Approach. We developed three methods of energy layer (EL) filtering:
unrestricted, switch-up (SU), and switch-up gap (SU gap) filtering. The
unrestricted method filters the lowest weighted EL while the SU gap filtering
removes in priority the EL around a new SU to minimize the gantry rotation
braking. The SU filtering removes the lowest weighted group of EL that
includes a SU. These post-processing filters were used in conjunction with the
RayStation dynamic proton arc optimization framework (ELSA). Four bilateral
oropharyngeal cancer patients’ data were used for evaluation. Objective
function values, target coverage robustness, organ-at-risk doses and NTCP
evaluations, as well as comparisons to IMPT plans, were used to assess plan
quality.
Result. The SU gap filtering algorithm performed best in three out of the four
cases, maintaining plan quality within tolerance while significantly reducing
beam delivery time. It achieved up to approximately 22% reduction in delivery
time. The unrestricted filtering algorithm followed closely. In contrast, the
SU filtering showed limited improvement, suppressing hardly a few SU without
substantial delivery time shortening. Robust target coverage was kept within
1% of variation compared to the ELSA baseline plan while OAR doses slighlty
decreased in all four patients. Both arc plans present large reductions in
NTCP values for dysphagia and xerostomia compared to the reference IMPT plan.
Significance. This study provides insights to accelerate proton arc therapy
delivery without compromising plan quality. These advancements could enhance
treatment efficiency and patient throughput.

_Keywords_ Proton Therapy $\cdot$ Treatment Planning $\cdot$ Pareto $\cdot$
ELSA $\cdot$ Proton Arc Therapy $\cdot$ Optimization $\cdot$ Delivery time

##  1 Introduction

Over the past decade, proton arc therapy has raised significant attention in
the field of radiation oncology. This treatment technique involves continuous
rotation of the gantry while delivering radiation, similar to Volumetric
Modulated Arc Therapy (VMAT) in photon therapy [19]. The literature has
witnessed a substantial increase in publications related to proton arc therapy
between the first one in 1997 [21] and today, with a particular focus on
clinical proofs of concepts across various disease sites. Additionally,
researchers have been developing treatment planning algorithms to effectively
utilize the new degrees of freedom brought by the arc delivery.

One of the anticipated advantages of proton arc therapy is the potential for
faster treatment delivery compared to conventional proton treatments as was
seen with VMAT. Several studies have demonstrated that proton arc therapy can
reduce overall treatment time [4, 16, 9, 15]. Importantly, though, reported
delivery times are often estimated with rough approximations, relying solely
on the total energy layer switching time (ELST), without accounting for the
distinction between upward and downward energy switching, likely due to the
limitations of earlier delivery systems. The arc timing advantage was actually
only evident when ELST fell between 0.5 and 2 seconds, but this assumption for
upward energy switching is not realistic in most of the currently available
hardware. This makes it challenging to draw definitive conclusions based on
these estimates only. Furthermore, contradictory findings have also been
reported, where proton arc therapy exhibited prolonged treatment delivery
durations compared to Intensity-Modulated Proton Therapy (IMPT) [7, 25],
especially in the discrete arc mode where the delivery entails a large number
of static fields for which the gantry needs to come to a full stop at each
discrete direction to deliver a number of stacked energy layers [5]. In the
dynamic mode, the prolonged delivery times stem from a complex combination of
several factors, including energy layer switching time, spot irradiation,
gantry rotation, a large number of layers and spots, and the requirement for
precise delivery from the right directions. Consequently, the gantry needs to
undergo frequent deceleration and acceleration, contributing to the overall
prolonged delivery times.

The scientific community has therefore dedicated efforts to devise approaches
to minimize the delivery time of proton arc plans. One such approach is to
formulate additional objectives to be minimized, which are surrogate measures
of the delivery time, while simultaneously optimizing the spot weights within
an integrated framework [12, 27, 24, 29]. While the concept is elegant in
theory, this approach encounters practical challenges. These include the
requirement for simplified mathematical models to estimate beam delivery time,
the need for substantial computational resources and suitable solvers, as well
as the necessity for careful tuning of objective weights. These limitations
hinder its practical use and effectiveness in achieving significant time
savings in proton arc therapy planning and delivery. Another approach involves
the pre-selection of a user-defined number of energy layers using heuristics
based on dosimetry [8, 17] or on geometrical considerations [10], with the
intention of controlling the maximum number of upward energy switches. The
spot-scanning proton arc (SPArc) therapy algorithm has demonstrated efficacy
across various disease sites, primarily due to its dose-based approach.
However, its main drawbacks are long optimization times and limited
flexibility to select energy switch locations. On the other hand, ELSA has
been noted for its fast execution time but also exhibits limitations in terms
of flexibility, primarily stemming from its energy pre-selection based on
geometry only.

To bridge the gap between the dose-based and geometry-based approaches, we
propose a hybrid method that combines both strengths. Our hybrid approach
extends ELSA to create an initial set of energy layers, which are subsequently
filtered to a final set using dose-based objectives, thereby enabling
accelerated delivery. This approach is inspired by the Reverse Greedy
algorithm [1], originally proposed for discrete proton arcs, which
successively suppresses the energy layers contributing the least to the
solution according to a score. We have developed and compared three distinct
methods capable of energy layer filtering. These methods act as post-
processing tools that complement the spot weight optimization process. Through
the implementation of these filtering techniques, our aim is to enhance the
overall efficiency of proton arc therapy delivery.

##  2 Methods and Materials

###  2.1 Energy layer filtering algorithms

Unlike IMPT plans, where each beam angle is optimized to cover the target in
depth using a decreasing energy sequence, proton arc plans typically adopt a
sector-based approach. Arc beams are divided into sectors, with energy
decreasing within each sector and increasing only between sectors. This design
stem from the anticipated increased time required for upward energy switches.
Delivery occurs within fixed intervals (centered around a discrete direction)
known as control points across each sector. Although more than one energy
layer per discrete direction could be delivered in practice, doing so would
slow down gantry rotation and compromise treatment efficiency.

The number of sectors in a proton arc plan, which defines the number of
switch-ups (SU) between energy levels, is a carefully studied topic as it
directly correlates with the delivery time for most machines [12, 24, 27, 26].
Researchers have sought to develop methods of minimizing the number of SU in
these plans. The basic assumption of this conceptual model is that delivery
time is proportional to the irradiation time of each energy layer and the
number of switch-ups in the plan. Therefore, minimizing the delivery time can
be achieved by filtering energy layers and/or reducing the number of SU.

In this study, we developed and optimized proton arc plans in a modified
research build of the RayStation dynamic proton arc optimizer. While not
exactly the same as the one showcased in the original publication [10], our
approach still follows the ELSA framework for selecting energy layers based on
geometry followed by the classical spot weight optimization.

Considering an optimized arc plan as a starting point (fig. 1(a)), we have
developed three distinct methods that can filter energy layers and/or reduce
the number of SU as a post-processing step. Assuming $N$ initial energy layers
and $M$ initial SU in the plan, we aim at keeping at most $X$ energy layers or
$Y$ SU. The three methods are summarized below:

  1. 1.

Unrestricted filtering: This algorithm filters the $N-X$ energy layers with
the lowest corresponding monitor unit (MU) from the plan. By removing the
lowest MU energy layers, we aim to reduce the overall number of energy layers
in the plan while preserving the important dose contributions. In Fig. 1, from
(a) to (b) individual holes appear where the lowest ELs have been suppressed.

  2. 2.

SU filtering: This algorithm filters $M-Y$ SU by deactivating the partial
sectors with the lowest corresponding MU. It iterates through two nested loops
over the energy layers in the plan. It checks if at least one SU occurs
between the two indexed energy layers and verifies that the energy of the
second indexed angle is lower than the energy of the first indexed angle. When
these conditions are met, the algorithm accumulates the MUs of the energy
layers between the two indexes, forming a partial sector. These partial
sectors, containing SU, are then ordered based on increasing MU values. The
energy layers included in each partial sector are subsequently removed from
the plan. By eliminating the energy layers associated with partial sectors
containing SU and having the lowest MUs, the SU filter effectively reduces the
overall number of SU in the plan. Fig. 1(c) displays one large hole between
gantry angles $\sim$100° and 125°, effectively reducing from 5 to 4 SU in the
arc beam.

  3. 3.

SU gap filtering: This algorithm removes the energy layers with the lowest MU,
similarly to the unrestricted filtering algorithm. The difference is that this
algorithm is restricted to only choose from the energy layers that are located
just before or just after a SU. Note that after an energy layer is removed to
create a gap, the adjacent energy layers on either side of the gap become the
ones positioned just before and just after a SU. The rationale behind this
approach is that the gantry is often forced to decelerate to a rather low
velocity in conjunction with a SU and increasing the corresponding angular
span might mitigate this effect. The algorithm contains a maximum size of this
gap, since at a certain point the gantry will be able to keep a constant speed
and still perform a SU. We establish this maximum gap size, which is measured
in terms of the number of removed layers, as follows:

$\left\lfloor\frac{t_{\text{SU}}+t^{\text{mean}}_{\text{EL}}}{t_{\text{SD}}+t^{\text{mean}}_{\text{EL}}}\right\rfloor$
(1)

where $t_{\text{SU}}$ and $t_{\text{SD}}$ are the times to switch the energy
upward and downward respectively and $t^{\text{mean}}_{\text{EL}}$ is the
average irradiation time per energy layer. Which is to say, this is the ratio
between the delivery time of a layer with an SU and a layer with a SD. Note
that this means that different plans may have different maximum gap sizes.

(a)

(b)

(c)

(d)

Figure 1: Strategies to filter energy layers (EL) for a random generated case.
(a) Nominal arc plan used as starting point. (b) Unrestricted filtering
removes the 15 lowest MU (EL). (c) SU gap filters the 15 EL that reduce the
gantry time to break before each SU. (d) SU filters the lowest MU partial
sector that includes at least one SU.

Each algorithm, depicted in Fig. 1, is run multiple times, decreasing
monotonically the allotted budget of energy layers (for unrestricted and SU
gap filters) or switch-ups (for SU filtering) in the plan, hereinafter denoted
as the MaxBoundSequence. Following each filtering operation, we re-run the
spot weight optimization with a reduced number of iterations to compensate for
the loss of monitor units (MU) and to maintain plan quality. Each filtering
run is independent from the others and start from the initial optimized spot
weights of the optimized arc plan.

This strategy allows us to compute Pareto fronts, which then relate the
attainable dosimetric objective values to the necessary dynamic delivery
times. By examining the trade-off between these two sides of the problem, one
can select the most suitable trade-off plan from the Pareto front. Algorithm 1
summarizes the workflow of the methodology.

Algorithm 1 Filtering algorithm workflow

Input data: Optimized spot weight $\bm{x}^{*}$, $N$ EL, $M$ SU,
MaxBoundSequence $\bm{s}$, $R$ runs, filtering algorithm $\mathcal{A}$

1:$\\{s_{i}\\}_{i=1}^{R}:s_{i}\geq s_{i+1}\forall i\in\mathbb{N}$
$\triangleright$ Monotonic decreasing sequence

2:$\bm{x}=\bm{x}^{*}$

3:for i in range(R) do

4: if $\mathcal{A}$ is unrestricted or SU gap then

5: Filter $N-s_{i}$ EL

6: else if $\mathcal{A}$ is SU then

7: Filter $M-s_{i}$ SU

8: end if

9: for i in range(n_iter) do

10: $\bm{x}\leftarrow\text{spot\\_weights\\_optimizer}(\bm{x})$
$\triangleright$ Continue optimization

11: end for

12: save_spot_weights($\bm{x}$) $\triangleright$ Save plan properties

13: $\bm{x}\leftarrow\bm{x}^{*}$ $\triangleright$ Reset to initial optimized
spot weights

14:end for

###  2.2 Patient data and treatment planning

To demonstrate the efficiency of the algorithms, we selected four patients
with oropharyngeal cancer from an anonymized database obtained from Cliniques
Universitaires Saint-Luc in Brussels, Belgium. The local ethics committee
approved the retrospective use of this database. The choice of oropharyngeal
cancer as the disease site follows from the expectation that proton arc
therapy would benefit to those patients, as compared to conventional
treatments, with a lower integral dose, reduced doses to OARs, and overall
less toxicity [16, 5, 6]. Three out of the four patients were selected from
the database based on their higher NTCPs in the IMPT plans for the side
effects under consideration. Patient 1 showed the highest probability for
dysphagia grade 2, patient 2 had the highest probability for dysphagia grade
3, and patient 3 had the worst NTCPs for xerostomia grade 2 and 3. The fourth
patient was selected randomly from the database.

The patient database comprises IMPT plans manually generated by the same
experienced dosimetrist using a treatment planning protocol to ensure
consistency (see Table SM1 from [2]). These treatments were planned
retrospectively in the treatment planning system (TPS) RayStation 11B
(Raysearch Laboratories, AB). With the four selected patients being bilateral
cases, the proton plans were designed using a simultaneous integrated boost
IMPT technique using a constant relative biological effectiveness (RBE) factor
of 1.1. The prescribed dose was 70 Gy(RBE) to the high-risk clinical target
volume (CTV) and 54.25 Gy(RBE) to the low-risk CTV nodal regions, delivered in
35 fractions. The plan was designed with four beams at couch and gantry angles
of (10°, 60°), (10°, 120°), (350°, 240°), and (350°, 300°), respectively. A
range shifter was systematically used for each beam. Monte Carlo dose
calculation and robust worst-case optimization [11] were employed for the
proton plans, considering 21 scenarios (2.6% proton range error and 4 mm
systematic error in all three spatial directions) for the CTV volume, the
spinal cord and the brainstem.

The proton arc plans, referred to as ELSA plans according to [10], were
designed with a single full arc beam with one-degree spacing between each
control point, resulting in 360 initial energy layers available for
optimization. It’s worth noting that the version of ELSA used here is adapted
with a more predefined sector length, which also explains the consistency in
the number of SU across the four patients. They were planned for the study in
a research version of RayStation 2023B using a total of 250 iterations and
spot filtration iteration set at 150. Filtered ELSA plans, employ the same set
of objectives and robust settings as the original ELSA plans which were
intially obtained from the IMPT plans. However, in order to expedite the
planning process, the total number of iterations for optimization is reduced
to 50. All plans are normalized to the median dose (D50). The Monte Carlo (MC)
dose calculation was carried out until it reached an uncertainty of 0.5%.

Going back to Algorithm 1, given $R=10$ runs, the 360 initial EL and the 16
initial SU in each ELSA plan, we chose the MaxBoundSequence to be 10 evenly
spaced numbers over the interval $\left[350,200\right]$ for the maximum number
of allowed energy layers (Method 1 & 3) and the sequence of numbers
decremented by 1 over the interval $\left[15,5\right]$ for the maximum number
of allowed SU (Method 2). These specific numbers were chosen intentionally to
ensure a smooth transition towards the number of energy layers present in the
IMPT plans, which is approximately 160 energy layers.

###  2.3 Treatment plan evaluation

####  2.3.1 Delivery time

Since the objective of this study is to achieve faster delivery rather than
improving plan quality, it is noteworthy that suppressing energy layers from
the initial set of energy layers is not expected to enhance plan quality. The
aim is merely to minimize the delivery time with precautions to ensure that
plan quality remains comparable to the ELSA baseline plan.

Dynamic beam delivery time (BDT) was calculated using the ATOM (Arc Trajectory
Optimization Method) algorithm, an open-source tool [20] published by
RaySearch Laboratories. ATOM is designed to determine a fast plan delivery
while adhering to the mechanical constraints specified by the user. The
machine parameters utilized in this study are detailed in Table 1. The maximum
window size specifies the angular safety tolerance around each irradiation
direction. The selection of ATOM was driven by its utility, given that no
proton arc machine has yet been established and commissioned in clinical
settings; ATOM serves as a reliable estimator at present.

Maximum gantry velocity | 5°/s
---|---
Maximum gantry acceleration | 0.5 °/s2
Maximum gantry jerk | 0.5 °/s3
Downward energy switching time | 0.5 s
Upward energy switching time | 5 s
Spot switching time | 2 ms
Spot delivery time (per MU) | 5 ms
Maximum window size | 1.99°
Table 1: Machine constraints parameters used for BDT estimation.

####  2.3.2 Dosimetry

In addition to our primary objective of achieving faster delivery, we have
included a comprehensive dosimetric evaluation to consider the selected trade-
off from the generated Pareto front. Target coverage is evaluated in the IMPT,
ELSA, and filtered ELSA plans employing the worst-case scenario robustness
evaluation approach. This approach considers 14 different isocenter shifts,
comprising 6 points along the main axes and 8 points along the diagonals,
which are defined by the setup uncertainty. Additionally, three density shifts
were taken into account, resulting in a total of 42 scenarios. The assessment
of robust target coverage was based on the criterion of achieving a minimum
dose of at least 95% of the prescribed dose at 98% of the target volumes in a
worst-case scenario dose distribution (D98$\%\geq 95$% Dp). This criterion was
applied to both the high-risk and prophylactic lymph nodal regions, ensuring
sufficient dose coverage for these target areas. Both arc plans (ELSA and
filtered ELSA) are compared by evaluating the deviations in target coverage
from the values achieved by the IMPT plan in the nominal and worst-case
scenarios. We also assess the nominal average doses received by organs-at-risk
in the head-and-neck region using the same comparative approach. Finally, we
have incorporated the evaluation of NTCPs for xerostomia and dysphagia using
the models from the Dutch model-based approach [14]. The $\Delta$NTCP is
calculated by taking the difference between the arc plans and the IMPT plan in
the nominal scenario for each patient.

##  3 Results

###  3.1 Energy layer filtering algorithms comparison

The plan quality of the three algorithms is compared for each of the four
patients, using the objective function value as a global scalar surrogate of
the plan quality. Fig. 2 illustrates the evolution of the objective value with
respect to the remaining number of energy layers in the plan, where the
maximum number of allowed EL or SU decreases linearly from right to left. The
red star represents the optimized plan from which EL or SU are filtered. The
filtering process is performed independently for each run, starting from the
red star (i.e. the baseline ELSA plan). The multiple runs for each algorithm
form a front, with a pink band denoting the tolerance range around the initial
objective value that should not be exceeded (above). A tolerance value of 10%
is employed.

From the plotted data, it looks like that the unrestricted filtering algorithm
performs better compared to others, with a majority of data points falling
within the tolerance band compared to the other two methods. The SU gap
filtering also shows favorable results, closely following the unrestricted
filtering, for patient 1 & 2, with a behavior indicating the importance of
preserving energy layers for optimal plan quality. SU filtering struggles
more, as it experiences a rapid increase in the objective function value.
Notably, SU filtering suppresses many more layers than the other two filters.

(a)

(b)

(c)

(d)

Figure 2: Objective function value versus number of energy layers for three
energy layers filtering methods for the four oropharyngeal patients. Plan
quality is deteriorating as more energy layers are filtered from right to
left.

Interestingly, the assumption that suppressing more energy layers at once
would lead to a stronger decrease in BDT is proven incorrect in Fig. 3, that
illustrates the true Pareto front. The SU filtering, despite suppressing more
energy layers simultaneously, actually exhibits the smallest reduction in
delivery time. On the contrary, the SU gap filtering effectively reduces the
beam delivery time with just a small number of suppressed energy layers. For
instance, in patient 1, implementing the SU gap filtering and suppressing 44
energy layers in the third run resulted in a significant reduction of the BDT
from 422 seconds to 330 seconds. In contrast, the unrestricted filter required
77 energy layers to be suppressed in the fifth run to achieve a comparable
decrease in BDT (336 seconds). We also observe a decrease of approximately 30
seconds by only filtering 10 energy layers with the SU gap method in patient
4.

(a)

(b)

(c)

(d)

Figure 3: Pareto front comparing the objective function value versus dynamic
beam delivery for three energy layers filtering methods for the four
oropharyngeal patients. Best compromise is circled in red showing the shortest
delivery time with reasonable objective value.

Upon closer look at the Pareto front data points within the tolerance band in
Fig. 3, the optimal trade-off between plan quality and delivery time can be
determined for each of the four patients. The SU gap filter proves to be the
most efficient for patients 1 and 2, achieving an effective reduction of
approximately 22% in beam delivery time by suppressing 44 energy layers in the
third run, while still maintaining plan quality within the tolerance band. It
is closely followed by the simplistic unrestricted filter, which reduces beam
delivery time by up to 18% and 15% for patients 1 and 2, respectively. SU gap
filtering was also the best compromise found for patient 4 although it could
only decrease the BDT by 6%. Conversely, the SU filter demonstrates limited
improvement, as it could only suppress 1, 2, 1 and 1 SU for patients 1, 2, 3
and 4, respectively, without exceeding the tolerance zone for plan quality.
Consequently, the SU filter shows the smallest gain in beam delivery time.
Patient 3 presented a bigger overal CTV, compared to the three other cases and
raised tougher planning challenges. The filtering for this patient exhibited
better results with the unrestricted filtering method. It achieved a 10%
reduction in beam delivery time in the third run. This smaller reduction in
beam delivery time, as the one observed for patient 4, compared to the two
first patients may indicate that more energy layers are required to meet the
clinical goals effectively for these particular patients. Nevertheless, SU gap
Pareto front in patient 4 looks like we could have had filtered a few more
energy layers while staying in the tolerance band. The final best compromises
for each patient were circled in red in Fig. 2-3.

Figure 4 provides an illustration of the energy layers retained after
determining the best trade-offs for each filtering method, compared to the
ELSA baseline plan. Additionally, relevant metrics are presented to assess the
timing results. Notably, the SU filtering demonstrates a consistent pattern of
energy layers suppression around 270° for all four patients. Furthermore, the
removal of the second SU for patient 2 appears to be symmetrically suppressed
relative to the first SU. One possible explanation for this behavior is that
the optimizer tends to avoid shooting through the shoulders, which may require
higher energy levels and deliver higher dose to the body. Another explanation
could be related to the position of the primary tumor and also the relative
position of the OARs to the tumor. The primary tumor is centrally located for
the first three patients while it slightly shifted to the right for patient 4.
In contrast, the unrestricted filter sporadically suppresses energy layers,
resulting in holes across each sector. Moreover, this filter tends to remove
high energy layers. On the other hand, the SU gap filtering displays a cleaner
pattern by sequentially removing energy layers around the SU points. This
method generates gaps primarily in between sector transitions.

Figure 4: Comparison of energy layers kept in the plan after best filtering
compromise found for the different algorithms. Rows display each patient
whereas columns showcase the filtering algorithm.

After optimizing filtered proton arc plans (filtered ELSA plans) for each
patient and keeping the best compromise found, the next question that arises
is whether these plans can be delivered more rapidly than IMPT plans. In the
case of the IMPT plans, the delivery time is computed for each beam
individually, resulting in what we refer to as static delivery time, as
opposed to the dynamic delivery time of proton arc plans. To enable a fair
comparison between static and dynamic delivery timings, one should consider
the manual interventions required between each beam delivery in the control
room and/or treatment room. This includes beam loading in the console,
rotation of the gantry and/or the couch with potential re-imaging step.
Moreover, given that range shifters are used for each IMPT beam, extra caution
is needed for the sake of collision. After consulting with two separate proton
centers, we introduce therefore a simulated delay of 60 seconds between each
beam plus a unique additional time of 120 seconds required for the couch-kick
for each of the IMPT plans. Figure 5 illustrates this comparison.

Figure 5: Comparison of beam delivery times between IMPT, ELSA and filtered
ELSA plans for the best compromises found for each patient. Filtered ELSA
employed the SU gap filtering algorithm for patients 1, 2 and 4 whereas
unrestricted filtering was applied for patient 3.

Including the simulated delay, all arc plans are faster to be delivered than
the IMPT plans. The filtered ELSA plans lead to significant improvement
compared to the IMPT delivery time. The biggest improvement is observed for
patient 1 and 2 where the filtered ELSA plans speed-up the delivery by 25% and
31% respectively compared to IMPT. Regarding ELSA baseline plans, they were
only able to speed-up the delivery by 5% and 9% for these patients. Patient 3
and 4 show more resistance for the delivery speed-up but filtered ELSA plans
still show an improvement of 15% and 6% compared to IMPT.

###  3.2 Treatment plan evaluation

The previous results can be complemented with a detailed dosimetric evaluation
for each of the best compromises found for each patient and a comparison with
the ELSA baseline plan and the IMPT plan.

Figure 6 reports the evaluation results for the CTV targets in terms of D98 in
the nominal and worst-case scenario for each patient. The D98 is slightly
reduced in the filtered ELSA plans compared to the ELSA baseline, although the
deviation is minimal, not exceeding 1% for all targets in nominal and worst-
case (corresponding to at most 0.6 Gy). These small reductions is therefore
not considered significant. Both ELSA plans yield comparable or better results
compared to the IMPT plans with most of the data points displayed on the
right-hand side of the plot, bringing higher CTV coverage for arc plans.

Figure 6: Differences in target coverage (D98 - dose received by 98% of the
CTV) between the evaluated arc plans and the IMPT plan in nominal and worst-
case scenarios. Negative differences imply that the IMPT plan was better than
the arc plan for that metric.

The clinical goals for target coverage (i.e., D98$\%\geq 95$% Dp) in both
high-dose and low-dose CTVs were met for all the patients in the nominal
scenario and the worst-case scenario.

Figure 7 illustrates the DVH metrics differences with respect to the IMPT plan
for the OARs included in the clinical goals. Comparing ELSA and its faster
delivered version, it is good that we can maintain OAR sparing and similar
target coverage while reducing the number of energy layers. In the transition
from IMPT to proton arc modality, only patient 3 shows a slight increase in
doses to the spinal cord and brain stem but still under the limit. However,
average doses in organs generally decrease (85% of all data points lie on the
left-side of the plot), which is highly favorable for arc modality in
oropharyngeal patients.

Figure 7: Differences in terms of clinical planning criteria for the OARs
between arc plans and the IMPT plan. Negative differences imply that the arc
plan was better than the IMPT plan for that metric (i.e., less dose to the
OARs). SMG, submandibular gland; PCM, pharyngeal constrictor muscle.

Figure 8 displays the difference in NTCP relative to the IMPT plan
($\Delta$NTCP = NTCP${}_{\text{arc}}$ \- NTCP${}_{\text{IMPT}}$). The arc
modality significantly decreases the NTCPs for all reported side effects,
including grade 2 and 3 xerostomia and dysphagia. This finding further
supports the adoption of proton arc therapy for the treatment of this
particular cancer site. Moreover, patients 1 and 2, selected for their high
NTCPs in the IMPT plan, show a reduction of approximately 5 and 7.5 percentage
points (p.p.) in NTCPs for dysphagia grade 2 and 3, respectively. Similarly,
patient 3, chosen for its elevated xerostomia NTCP value, demonstrates a
decrease of around 2.5 p.p. in NTCP for the proton arc plans, further
highlighting the advantages of proton arc therapy.

Figure 8: Differences in terms of NTCP between arc plans and the IMPT plan.
Negative differences imply that the arc plan was better than the IMPT plan for
that metric (i.e., reduced probability to develop the side-effect). IMPT NTCP
values for the ordered four patients: Grade 2 xerostomia = [43.5, 48.7, 53.1,
2.1], grade 3 xerostomia = [12.1, 14.1, 16.1, 11.6], grade 2 dysphagia =
[44.2, 43,8, 19.3, 17.2], grade 2 dysphagia = [22.6, 24.4, 3.2, 7.1].

##  4 Discussion

In this study, we presented three post-processing energy layer filters to
accelerate the delivery of proton arc treatment plans for oropharyngeal
cancers. These filters were designed to suppress the low-weighted energy
layers or partial sectors in the arc plans optimized with ELSA. Among the
three methods, the SU gap filter was proved to be highly efficient in reducing
the dynamic delivery time by suppressing a minimal number of energy layers.
The unrestricted filter also achieved similar results, although it required
more energy layers to be suppressed for the same reduction in BDT. On the
other hand, the SU filter, despite removing a significant number of energy
layers (partial sectors), was the least effective in reducing the BDT.

Pareto plots, showcasing the objective value against the BDT, revealed that
the SU gap filtering algorithm, which suppressed 44 energy layers out of 360
for patients 1 and 2, provided the best trade-off between plan quality and
delivery time, accelerating the delivery by $\sim$100 s. Further removal of
energy layers resulted in a significant increase in the objective value,
correlating with a degradation in plan quality. ELSA plans for patient 3 and 4
were harder to accelerate where the best speed-up gain was about 50 and 30
seconds but removing as few as 44 and 10 energy layers respectively. Both
patients had much higher initial number of spots, attesting for their more
complex tumor geometry. Energy layers could therefore hardly be filtered.
Although the choice of a 10% tolerance criterion for the objective values was
arbitrary, further investigation might determine the actual threshold passed
which plan degradation becomes unacceptable. Moreover, additional iterations
may be necessary after the post-processing filter, depending on the number of
energy layers removed from the plan. Ultimately, the Pareto graphs could be
used for MCO-like optimization and thus help the treating physician to find
the best trade-off for each patient.

For the patients treated with IMPT plans, four beams were used with about 40
energy layers each, resulting in a total of 160 energy layers. In comparison,
the ELSA baseline proton arc plans needed 360 energy layers, one for each beam
direction, to achieve a comparable plan quality. This discrepancy might arise
because it’s more challenging to combine beamlets from each energy layer in
the arc, ensuring an adequately spread-out Bragg Peak to cover the targets.
It’s also important to understand that both the plan quality and BDT heavily
rely on the preliminary energy selection. The angular sampling and sectors
count may not be optimal and could potentially benefit from adjustments that
aren’t purely geometry-driven. Yet, incorporating dose-based objectives into
the initial energy layers choice can be complex due to the size of the proton
arc problem [24]. Hence, dose-based filtering methods paired with rapid energy
layer selection become pivotal to address the shortcomings of purely geometry-
based energy layer choices.

Despite the proton arc plans using a significantly higher number of energy
layers than the IMPT plans, they still achieved shorter BDT for the four
evaluated patients. This outcome was reached based on certain assumptions
regarding the IMPT beams delivery. We factored in extra time between each
static beam delivery to ensure a more fair comparison. After consulting with
two separate proton centers about this additional time, we chose the lowest
values (i.e. faster IMPT delivery). This suggests that the difference in BDT
between IMPT and arc plans could be even more pronounced. Moreover, the
filtered arc plans further reduced the BDT, attaining up to a 30% speed-up in
comparison to IMPT, emphasizing the utility of the proposed method.

The plan evaluation and robustness analysis demonstrated that the filtered
ELSA plans maintained target coverage with insignificant deviations from the
ELSA baseline plans in both nominal and worst-case scenarios. Comparisons with
the ‘clinical’ IMPT plans, generated by an experienced dosimetrist, showed
that both the non-filtered and filtered ELSA plans outperformed the IMPT plans
in most clinical goals, as observed across all four patients. Additionally,
the study of NTCPs for dysphagia and xerostomia further supported the
superiority of proton arc therapy for oropharyngeal cancer. These findings
concur with existing publications on proton arc therapy in this target region
[16, 6].

Methods of layer filtering have already been extensively studied in the
context of IMPT [22, 3, 23, 13]. However, recent advancements in beam energy
layer selection hardware have significantly reduced the impact of suppressing
energy layers in IMPT plans. This raises the question of whether this would
also apply to proton arc plans. Proton arc plans actually involve more energy
jumps and they must be dynamically delivered. Most machine capabilities face
challenges with achieving the same efficiency for upward energy switching as
they do for downward energy switching. This is due to physical constraints of
the magnet [28], a common limitation seen in many proton therapy machines.
However, there is potential for future improvements in energy layer systems
[18]. Such advancements would simplify proton arc optimization by reducing the
burden of dealing with costly SU in the plan, which is currently a major
bottleneck in proton arc treatment planning.

Nevertheless, despite the complexity of proton arc plans, the implementation
of a post-processing algorithm that filters out the least significant energy
layers can still have a positive impact on treatment delivery. Even a small
reduction in BDT could potentially enhance patient throughput in clinical
settings. Furthermore, the integration of delivery-accelerating strategies
could be seamlessly implemented into existing treatment planning systems. It
is noteworthy that post-processing filter, including the subsequent short re-
optimization, only takes around 10 minutes for the patients evaluated in this
study (with 5 minutes dedicated to pre-dose calculation which could be
cached). This relatively short running time might fall within an acceptable
range of delay for proton treatment planning.

This study selected oropharyngeal cancer patients to showcase the filtering
algorithms, as these patients appear to benefit significantly in terms of plan
quality, even though the delivery time remains long. However, the proposed
post-processing filters could potentially be applied to other treatment sites
with long treatment times, such as esophageal cancer that has shown very large
difference compared to its IMPT plan counterpart in a recent institutional
study [25]. It is important to acknowledge the limitations of this study,
including the small sample size of four patients and the absence of
statistical analysis. Nevertheless, this study provides a proof of concept and
lays the groundwork for future investigations.

##  5 Conclusion

In conclusion, this study introduces energy layer filters as a post-processing
to accelerate the delivery of proton arc treatment plans. The results
demonstrate that these filters effectively reduce beam delivery times while
maintaining plan quality. The findings support the use of proton arc therapy
in reducing organ-at-risk toxicity and improving local tumor control in
oropharyngeal cancers. Further research is needed to optimize proton arc
planning and understand the underlying requirements for energy layer
selection. The proposed filters have the potential to enhance clinic
efficiency and patient throughput without compromising treatment quality.

##  6 Acknowledgments

Sophie Wuyckens is funded by the Walloon Region as part of the Arc Proton
Therapy convention (Pôles Mecatech et Biowin). Computational resources have
been provided by the supercomputing facilities of the Université catholique de
Louvain (CISM/UCL) and the Consortium des Équipements de Calcul Intensif en
Fédération Wallonie Bruxelles (CÉCI) funded by the F.R.S.-FNRS under
convention 2.5020.11. John A. Lee is a Research Director with the F.R.S.-FNRS.

## References

  * [1] Cecilia Battinelli.  Proton Arc Therapy Optimization.  2019\.
  * [2] Elena Borderias‐Villarroel, Margerie Huet Dastarac, Ana María Barragán‐Montero, Rasmus Helander, Mats Holmstrom, Xavier Geets, and Edmond Sterpin.  Machine learning‐based automatic proton therapy planning: Impact of post‐processing and dose‐mimicking in plan robustness.  Medical Physics, 50(7):4480–4490, July 2023.  Number: 7.
  * [3] Wenhua Cao, Gino Lim, Li Liao, Yupeng Li, Shengpeng Jiang, Xiaoqiang Li, Heng Li, Kazumichi Suzuki, X Ronald Zhu, Daniel Gomez, and Xiaodong Zhang.  Proton energy optimization and reduction for intensity-modulated proton therapy.  Physics in Medicine and Biology, 59(21):6341–6354, October 2014\.  Number: 21.
  * [4] Sheng Chang, Gang Liu, Lewei Zhao, Joshua T. Dilworth, Weili Zheng, Saada Jawad, Di Yan, Peter Chen, Craig Stevens, Peyman Kabolizadeh, Xiaoqiang Li, and Xuanfeng Ding.  Feasibility study: spot-scanning proton arc therapy (SPArc) for left-sided whole breast radiotherapy.  Radiation Oncology, 15(1):232, December 2020.  Number: 1.
  * [5] Bas A. De Jong, Cecilia Battinelli, Jeffrey Free, Dirk Wagenaar, Erik Engwall, Guillaume Janssens, Johannes A. Langendijk, Erik W. Korevaar, and Stefan Both.  Spot scanning proton arc therapy reduces toxicity in oropharyngeal cancer patients.  Medical Physics, 50(3):1305–1317, March 2023.  Number: 3.
  * [6] Bas A. De Jong, Erik W. Korevaar, Anneke Maring, Chimène I. Werkman, Daniel Scandurra, Guillaume Janssens, Stefan Both, and Johannes A. Langendijk.  Proton arc therapy increases the benefit of proton therapy for oropharyngeal cancer patients in the model based clinic.  Radiotherapy and Oncology, 184:109670, July 2023.
  * [7] Xuanfeng Ding, Xiaoqiang Li, An Qin, Jun Zhou, Di Yan, Craig Stevens, Daniel Krauss, and Peyman Kabolizadeh.  Have we reached proton beam therapy dosimetric limitations? – A novel robust, delivery-efficient and continuous spot-scanning proton arc (SPArc) therapy is to improve the dosimetric outcome in treating prostate cancer.  Acta Oncologica, 57(3):435–437, March 2018.  Number: 3.
  * [8] Xuanfeng Ding, Xiaoqiang Li, J. Michele Zhang, Peyman Kabolizadeh, Craig Stevens, and Di Yan.  Spot-Scanning Proton Arc (SPArc) Therapy: The First Robust and Delivery-Efficient Spot-Scanning Proton Arc Therapy.  International Journal of Radiation Oncology*Biology*Physics, 96(5):1107–1116, December 2016.  Number: 5.
  * [9] Xuanfeng Ding, Jun Zhou, Xiaoqiang Li, Kevin Blas, Gang Liu, Yinan Wang, An Qin, Prakash Chinnaiyan, Di Yan, Craig Stevens, Inga Grills, and Peyman Kabolizadeh.  Improving dosimetric outcome for hippocampus and cochlea sparing whole brain radiotherapy using spot-scanning proton arc therapy.  Acta Oncologica, 58(4):483–490, April 2019.  Number: 4.
  * [10] Erik Engwall, Cecilia Battinelli, Viktor Wase, Otte Marthin, Lars Glimelius, Rasmus Bokrantz, Björn Andersson, and Albin Fredriksson.  Fast robust optimization of proton PBS arc therapy plans using early energy layer selection and spot assignment.  Physics in Medicine & Biology, 67(6):065010, March 2022.  Number: 6.
  * [11] Albin Fredriksson, Anders Forsgren, and Björn Hårdemark.  Minimax optimization for handling range and setup uncertainties in proton therapy: Minimax optimization for handling uncertainties in proton therapy.  Medical Physics, 38(3):1672–1684, March 2011.  Number: 3.
  * [12] Wenbo Gu, Dan Ruan, Qihui Lyu, Wei Zou, Lei Dong, and Ke Sheng.  A novel energy layer optimization framework for spot‐scanning proton arc therapy.  Medical Physics, 47(5):2072–2084, May 2020.  Number: 5.
  * [13] M. Fuglsang Jensen, L. Hoffmann, J. B. B. Petersen, D. S. Møller, and M. Alber.  Energy layer optimization strategies for intensity-modulated proton therapy of lung cancer patients.  Medical Physics, 45(10):4355–4363, October 2018.  Number: 10.
  * [14] JA Langendijk, MS Hoogeman, R Monshouwer, and M Verheij.  Indicatie Protocol Protonen Therapie (versie 2.2) HOOFD-HALSTU- MOREN.  Technical report, 2019.
  * [15] Xiaoqiang Li, Peyman Kabolizadeh, Di Yan, An Qin, Jun Zhou, Ye Hong, Thomas Guerrero, Inga Grills, Craig Stevens, and Xuanfeng Ding.  Improve dosimetric outcome in stage III non-small-cell lung cancer treatment using spot-scanning proton arc (SPArc) therapy.  Radiation Oncology, 13(1):35, December 2018.
  * [16] Gang Liu, Xiaoqiang Li, An Qin, Weili Zheng, Di Yan, Sheng Zhang, Craig Stevens, Peyman Kabolizadeh, and Xuanfeng Ding.  Improve the dosimetric outcome in bilateral head and neck cancer (HNC) treatment using spot-scanning proton arc (SPArc) therapy: a feasibility study.  Radiation Oncology, 15(1):21, December 2020.  Number: 1.
  * [17] Gang Liu, Xiaoqiang Li, Lewei Zhao, Weili Zheng, An Qin, Sheng Zhang, Craig Stevens, Di Yan, Peyman Kabolizadeh, and Xuanfeng Ding.  A novel energy sequence optimization algorithm for efficient spot-scanning proton arc (SPArc) treatment delivery.  Acta Oncologica, 59(10):1178–1185, October 2020.  Number: 10.
  * [18] Vivek Maradia, Anna Chiara Giovannelli, David Meer, Damien Charles Weber, Antony John Lomax, Jacobus Maarten Schippers, and Serena Psoroulas.  Increase of the transmission and emittance acceptance through a cyclotron‐based proton therapy gantry.  Medical Physics, 49(4):2183–2192, April 2022.
  * [19] Karl Otto.  Volumetric modulated arc therapy: IMRT in a single gantry arc: Single arc radiation therapy.  Medical Physics, 35(1):310–317, December 2007.
  * [20] RaySearch Laboratories AB.  Arc Trajectory Optimization Method, July 2023.  Programmers: _:n319 original-date: 2023-05-23T08:45:51Z.
  * [21] G.A. Sandison, E. Papiez, C. Bloch, and J. Morphis.  Phantom assessment of lung dose from proton arc therapy.  International Journal of Radiation Oncology*Biology*Physics, 38(4):891–897, July 1997.
  * [22] S Van De Water, A C Kraan, S Breedveld, W Schillemans, D N Teguh, H M Kooy, T M Madden, B J M Heijmen, and M S Hoogeman.  Improved efficiency of multi-criteria IMPT treatment planning using iterative resampling of randomly placed pencil beams.  Physics in Medicine and Biology, 58(19):6969–6983, October 2013\.  Number: 19.
  * [23] Steven Van De Water, Maria F Belosi, Francesca Albertini, Carla Winterhalter, Damien C Weber, and Antony J Lomax.  Shortening delivery times for intensity-modulated proton therapy by reducing the number of proton spots: an experimental verification.  Physics in Medicine & Biology, 65(9):095008, May 2020.  Number: 9.
  * [24] Sophie Wuyckens, Michael Saint-Guillain, Guillaume Janssens, Lewei Zhao, Xiaoqiang Li, Xuanfeng Ding, Edmond Sterpin, John A. Lee, and Kevin Souris.  Treatment planning in arc proton therapy: Comparison of several optimization problem statements and their corresponding solvers.  Computers in Biology and Medicine, 148:105609, September 2022.
  * [25] Anne-Catherine Wéra, Macarena Chocan Vera, Hamdiye Ozan, Erik Engwall, Viktor Wase, Otte Marthin, Johan Sundström, Sophie Wuyckens, Karine Haustermans, Ana M. Barragán‐Montero, Kevin Souris, John A. Lee, and Edmond Sterpin.  Proton arc therapy for esophageal cancer: is the dosimetric benefit worth the effort?  Submitted to Physica Medica, 2023.
  * [26] Gezhi Zhang, Yong Long, Yuting Lin, Ronald C Chen, and Hao Gao.  A treatment plan optimization method with direct minimization of number of energy jumps for proton arc therapy.  Physics in Medicine & Biology, 68(8):085001, April 2023.  Number: 8.
  * [27] Gezhi Zhang, Haozheng Shen, Yuting Lin, Ronald C Chen, Yong Long, and Hao Gao.  Energy layer optimization via energy matrix regularization for proton spot‐scanning arc therapy.  Medical Physics, 49(9):5752–5762, September 2022.  Number: 9.
  * [28] Lewei Zhao, Gang Liu, Weili Zheng, Jiajian Shen, Andrew Lee, Di Yan, Rohan Deraniyagala, Craig Stevens, Xiaoqiang Li, Shikui Tang, and Xuanfeng Ding.  Building a precise machine-specific time structure of the spot and energy delivery model for a cyclotron-based proton therapy system.  Physics in Medicine & Biology, 67(1):01NT01, January 2022.  Number: 1.
  * [29] Lewei Zhao, Juntao You, Gang Liu, Sophie Wuyckens, Xiliang Lu, and Xuanfeng Ding.  The first direct method of spot sparsity optimization for proton arc therapy.  Acta Oncologica, 62(1):48–52, January 2023.


$\mu$ | VAIL(HalfCheetah): 0.5; others: 0.0 | VAIL: 1.0; GAIL: 1.0
$\delta$ | VAIL(HalfCheetah): 1.0; others: N/A | VAIL: 0.8; GAIL: 1.2
Table 1: Hyperparameters used in the training processes

Expert Demonstrations. Our expert demonstrations all achieve high rewards in
the task. The number of trajectories and the average trajectory total rewards
are listed in Table 2.

Task | Number of Trajectories | Average Tot.Rewards
---|---|---
Walker2d-v2 | 10 | 4133
HalfCheetah-v2 | 100 | 1798
Hopper-v2 | 100 | 3586
InvertedPendulum-v2 | 10 | 1000
Swimmer-v2 | 10 | 122
DoorKey-6x6-v0 | 10 | 0.92
SimpleCrossingS9N1-v0 | 10 | 0.93
Table 2: The number of demonstrated trajectories and the average trajectory
rewards

###  C.2 Additional Results

We append the results in three Mujoco benchmarks: Hopper-v2,
InvertedPendulum-v2 and Swimmer-v2 in Figure 7. Algorithm 1 performs similarly
to VAIL and GAIL in those two benchmarks. IQ-learn does not perform well in
Walker2d-v2 but performs better than ours and other baselines by a large
margin.

(a) Hopper-v2

(b) InvertedPendulum-v2

(c) Swimmer-v2

Figure 7: Comparing Algorithm 1 with baselines. The suffix after each ‘PAGAR-’
indicates which IRL algorithm is utilized in Algorithm 1. The $y$ axis is the
average return per step. The $x$ axis is the number of iterations in GAIL,
VAIL, and ours. The policy is executed between each iteration for $2048$
timesteps for sample collection. One exception is that IQ-learn updates the
policy at every timestep, making its actual number of iterations $2048$ times
larger than indicated in the figures.

###  C.3 Influence of Reward Hypothesis Space

In addition to the DoorKey-6x6-v0 environment, we also tested PAGAR-GAIL and
GAIL in SimpleCrossingS9N2-v0 environment. The results are shown in Figure 8.

(a) MiniGrid-DoorKey-6x6-v0

(b) MiniGrid-SimpleCrossingS9N2-v0

Figure 8: Comparing Algorithm 1 with baselines. The prefix ‘protagonist_GAIL’
indicates that the IRL algorithm utilized in Algorithm 1 is the same as in
GAIL. The ‘_Sigmoid’ and ‘_Categ’ suffixes indicate whether the output layer
of the discriminator is using the $Sigmoid$ function or Categorical
distribution. The $x$ axis is the number of sampled frames. The $y$ axis is
the average return per episode.