# Feasibility of the J-PET to monitor range of therapeutic proton beams

Jakub Baran1,2,3∗, Damian Borys4,5,6, Karol Brzeziński6,7, Jan Gajewski6,
Michał Silarski1,2,3, Neha Chug1,2,3, Aurélien Coussat1,2,3, Eryk
Czerwiński1,2,3, Meysam Dadgar1,2,3, Kamil Dulski1,2,3, Kavya V.Eliyan1,2,3,
Aleksander Gajos1,2,3, Krzysztof Kacprzak1,2,3, Łukasz Kapłon1,2,3, Konrad
Klimaszewski8, Paweł Konieczka8, Renata Kopeć6, Grzegorz Korcyl1,2,3, Tomasz
Kozik1,2,3, Wojciech Krzemień9, Deepak Kumar1,2,3, Antony J.Lomax12,13, Keegan
McNamara12,13, Szymon Niedźwiecki1,2,3, Paweł Olko6, Dominik Panek1,2,3,
Szymon Parzych1,2,3, Elena Perez del Rio1,2,3, Lech Raczyński8, Moyo
Simbarashe1,2,3, Sushil Sharma1,2,3, Shivani1,2,3, Roman Y. Shopa8, Tomasz
Skóra14, Magdalena Skurzok1,2,3, Paulina Stasica6, Ewa Ł. Stępień1,2,3, Keyvan
Tayefi1,2,3, Faranak Tayefi1,2,3, Damien C.Weber10,11,12, Carla
Winterhalter12,13, Wojciech Wiślicki8, Pawel Moskal1,2,3, Antoni Rucinski6
1Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian
University, 30-348 Kraków, Poland  2Total-Body Jagiellonian-PET Laboratory,
Jagiellonian University, 30-348 Kraków, Poland  3Center for Theranostics,
Jagiellonian University, Kraków, Poland  4Silesian University of Technology,
Department of Systems Biology and Engineering, Gliwice, Poland  5Biotechnology
Centre, Silesian University of Technology, Gliwice, Poland  6Institute of
Nuclear Physics Polish Academy of Sciences, 31-342 Kraków, Poland  7Instituto
de Física Corpuscular (IFIC), CSIC-UV, Valencia, Spain  8Department of Complex
Systems, National Centre for Nuclear Research, Otwock-Świerk, Poland  9High
Energy Physics Division, National Centre for Nuclear Research, Otwock-Świerk,
Poland  10Department of Radiation Oncology, Inselspital, Bern University
Hospital, University of Bern, Bern, Switzerland  11Department of Radiation
Oncology, University Hospital of Zürich, Zürich, Switzerland  12Centre for
Proton Therapy, Paul Scherrer Institute, Villigen, Switzerland  13Physics
Department, ETH Zürich, Zürich, Switzerland  14National Oncology Institute,
National Research Institute, Krakow Branch, Krakow, Poland
<EMAIL_ADDRESS>
###### Abstract

Objective: The aim of this work is to investigate the feasibility of the
Jagiellonian Positron Emission Tomography (J-PET) scanner for intra-treatment
proton beam range monitoring.

Approach: The Monte Carlo simulation studies with GATE and PET image
reconstruction with CASToR were performed in order to compare six J-PET
scanner geometries (three dual-heads and three cylindrical). We simulated
proton irradiation of a PMMA phantom with a Single Pencil Beam (SPB) and
Spread-Out Bragg Peak (SOBP) of various ranges. The sensitivity and precision
of each scanner were calculated, and considering the setup’s cost-
effectiveness, we indicated potentially optimal geometries for the J-PET
scanner prototype dedicated to the proton beam range assessment.

Main results: The investigations indicate that the double-layer cylindrical
and triple-layer double-head configurations are the most promising for
clinical application. We found that the scanner sensitivity is of the order of
10-5 coincidences per primary proton, while the precision of the range
assessment for both SPB and SOBP irradiation plans was found below 1 mm. Among
the scanners with the same number of detector modules, the best results are
found for the triple-layer dual-head geometry.

Significance: We performed simulation studies demonstrating that the
feasibility of the J-PET detector for PET-based proton beam therapy range
monitoring is possible with reasonable sensitivity and precision enabling its
pre-clinical tests in the clinical proton therapy environment. Considering the
sensitivity, precision and cost-effectiveness, the double-layer cylindrical
and triple-layer dual-head J-PET geometry configurations seem promising for
the future clinical application. Experimental tests are needed to confirm
these findings.

Version date:

(corresponding author) *

Keywords— J-PET, PET, range monitoring, proton radiotherapy

##  1 Introduction

Radiation therapy is frequently applied as part of cancer treatment. Radiation
therapy using accelerated protons offers an excellent depth dose distribution,
characterized by maximum dose deposition at the end of the proton range
[Paganetti2012]. This enables increasing the dose to the target volume, while
reducing the dose to Organs-At-Risk (OAR), which, for selected indications,
results in a reduction of late side effects. These dosimetric properties make
proton radiation therapy the most popular choice of treatment
[nystrom2020treatment] for deeply seated brain and head and neck tumors
[durante2017charged].

Apart from the advantages of proton radiotherapy, there are also some
limitations. One of the major ones is the uncertainty in the proton beam
range, which may lead to the underexposure of the target volume or
overexposure of the OAR to the therapeutic dose [Paganetti2012]. One approach
to overcoming this problem is the in-vivo verification of the radiation
delivery by monitoring beam range in real-time, providing information that may
motivate the interruption of the beam delivery once the proton range differs
from that in the prescribed treatment plan. Another option is to monitor the
beam range after the treatment and to compensate for any deviations from the
planned dose distribution by treatment adaptation [parodi2020latest,
parodi2022experience]. As the primary protons are fully stopped within the
patient’s body, measurement of the secondary particles is used in these
monitoring techniques. For these applications, prompt gamma imaging
[krimmer2018prompt, pennazio2022proton], secondary charged particles tracking
[traini2019review, Battistoni2015, marafini2017mondo, bashkirov2017inbeam] and
positron emission tomography (PET) techniques [Bauer2013, Bisogni2016,
Ferrero2018, lang2022towards] have been proposed and tested pre-clinically and
clinically.

The application of PET for proton range monitoring consists of imaging
$\beta^{\mathrm{+}}$-emitting isotopes, such as ${}^{11}C$
($T_{\frac{1}{2}}$=20.4 minutes), ${}^{10}C$ ($T_{\frac{1}{2}}$=19 seconds) or
${}^{15}O$ ($T_{\frac{1}{2}}$=2 minutes), produced during the nuclear
interactions of protons with the tissues in the patient. In general, four
different PET acquisition protocols for range monitoring are considered
[kraan2015range, shakirin2011implementation]. The in-room protocol enables the
acquisition of the PET signal just after the irradiation, in the treatment
room, where the patient is transported from the irradiation gantry to the
standalone PET scanner [zhu2011monitoring, min2013clinical]. The off-line
approach is similar, but differs in that the PET acquisition is performed in a
different room, freeing the treatment room for the irradiation of the next
patients [parodi2007patient, knopf2008quantitative, knopf2011accuracy,
hishikawa2002usefulness, handrack2017sensitivity]. Due to the fast decay of
short-lived $\beta^{\mathrm{+}}$-emitting radioisotopes and the effect of
biological washout, this approach suffers from the lowest count statistics.
The in-beam approach is performed during the patient irradiation and is
characterized by high noise levels, as all secondary particles introduce noise
to the registered coincidences [fiedler2010effectiveness, iseki2004range,
miyatake2010measurement]. Additionally, the inter-spill acquisition mode was
investigated for the synchrotron facilities, where the pauses between spills
are long enough to acquire PET signal [fiorina2021detection, Ferrero2018].

Considering the various PET acquisition protocols, different PET scanner
geometries have been introduced and tested, both experimentally or using Monte
Carlo simulations. The commercially available PET scanners are the first
choice option for the in-room and off-line approaches. It assures the best
image quality and the highest efficiency of the systems with no need for any
hardware or software development [handrack2017sensitivity]. However, next to
the radioactive decay and biological wash-out, the limitation (specifically
for the in-room application) is the room size and occupation time. It is
crucial to enable unrestricted rotation of both proton gantry and patient
couch between the irradiation of the subsequent treatment fields. For the
inter-spill and in-beam acquisition protocols, full-ring scanners are not an
option due to geometrical constraints. There are several geometrical
considerations for in-beam and inter-spill PET scanner: (i) the beam delivery
system (free nozzle rotation during the irradiation, PET system components out
of the way of the beam), (ii) patient couch (free movement between the
irradiation fields) and (iii) additional medical equipment (e.g. for the
anesthesia procedure) put additional requirements on the PET system
configuration. To overcome these constraints, unconventional PET scanners have
been designed and tested for in-beam/inter-spill proton beam range
verification. These included dual-head scanners [Ferrero2018,
fiorina2020detection, baran2019studies, rucinski2019investigations] or more
sophisticated configurations such as the axially shifted, single-ring OpenPET
[tashima2016development, yamaya2017openpet] or the axially slanted full-ring
and dual-ring [yoshida2017development, crespo2006detector] configurations.

To meet the requirements placed on PET-based range monitoring systems in
proton radiation therapy, the Jagiellonian Positron Emission Tomography
(J-PET) scanner [Moskal2021b, Moskal2021a, moskal2021simulating], a novel,
cost-effective, portable, modular PET scanner, based on plastic scintillator
technology, is being considered for this application.

Here, we present for the first time a feasibility study of the different J-PET
geometries for the application of proton beam range verification. We performed
Monte Carlo simulations in homogeneous media in order to compare between six
geometries (three dual-heads and three cylindrical), which could be
potentially considered for in-beam, inter-spill, in-room, and off-line beam
range monitoring. We report the relative efficiency of the scanners for Single
Pencil Beam (SPB) and Spread-Out Bragg Peak (SOBP) irradiation plans.
Quantitative analysis is conducted to assess the precision of range detection
in a uniform phantom of different scanner geometries and indicate the optimal
J-PET configuration for proton beam range monitoring.

##  2 Materials and Methods

###  2.1 J-PET scanner and geometries for proton therapy range monitoring

The existing prototype of the J-PET scanner and the schematic illustration of
its operation principle is presented in Figure 1. The annihilation gamma-rays
leaving the imaged object to interact with the plastic scintillator strips.
They deposit energy in the plastic mostly via Compton scattering. The
scintillation light produced by these interactions propagates to the opposing
ends of the scintillator strip where the light is converted into an electronic
signal by silicon photomultipliers (SiPMs). The disadvantage of the plastic
scintillators with respect to the conventionally used crystal scintillations
is their efficiency [vandenberghe2020state] which in the case of the proton
range monitoring is enhanced as the expected statistics is far beyond the
level of clinical activities. Considering that the plastics scintillators are
relatively cheap and have photomultipliers at their ends, the improvement in
PET signal quality could be achieved by an increase of the thickness of the
plastic scintillator, adding subsequent layers of plastic modules or
increasing the length of the scintillators to enlarge the Field-Of-View (FOV)
[moskal2016time]. Application of any of these approaches will increase the
price of the system, however, the difference is not as substantial as for the
organic scintillators [vandenberghe2020state, moskal2020prospects]. Taking
into consideration, the relatively low price of the technology, its
portability and the possibility to build various geometries with the same
amount of modules, it makes J-PET scanner promising for proton range
monitoring. Additionally, the J-PET could be also applied with success in
Total-Body PET imaging [kowalski2018estimating, moskal2021simulating,
moskal2020prospects], multi-gamma tomography using e.g. positronium imaging
[Moskal2021b, moskal2019feasibility, moskal2021positronium], fundamental
physic studies on quantum entanglement [hiesmayr2019witnessing,
sharma2022decoherence], studies of discrete symmetries in nature [Moskal2021a]
or PET data reconstruction methods development [shopa2021optimisation,
raczynski20203d]. Moreover, plastic scintillators in J-PET are characterized
by short light signals with a decay constant of about 2 ns (factor of 20 to
150 less than these of crystal detectors) [moskal2021simulating]. Therefore
J-PET has by two orders of magnitudes lower chances for signal pile-ups with
respect to crystal PET systems, making it especially promising for the
application of monitoring flash radiotherapy with high power radiation dose
[vozenin2022towards].

Figure 1: The modular J-PET scanner (left panel) developed as a cost-
effective, diagnostic total-body PET prototype that was investigated in this
study for proton therapy range monitoring. The presented geometry corresponds
to the single layer cylindrical configuration (see Fig. 2A). The principle of
annihilation gamma-rays detection with the J-PET module is illustrated in the
right panel. Annihilation gamma-rays(black arrows) create in the plastic
scintillator photons (magenta arrows) which propagate to the ends of the strip
and are converted to the electronics signals by the silicon photomultipliers
(SiPM).

The modular J-PET technology (as presented in Fig. 1) was developed to allow
its reconfiguration for different applications. The J-PET module is built out
of 13 separate 50 cm long scintillator strips, each having a cross-section of
6$\times$24 mm2. Individual scintillators are covered with kapton and
reflective foils [niedzwiecki2017j, kaplon2020technical]. Each of the 13
scintillation strips is connected to 8 SiPMs, 4 at each side of the strip,
which convert the light into an electronic signal, further processed with the
FPGA electronics [korcyl2018evaluation].

For the purpose of proton therapy range monitoring, we propose and investigate
six PET scanner configurations, built from the J-PET modules (Figure 2). The
PET geometries can be classified as two general types: the cylindrical (Figure
2A-C) and the dual-head (Figure 2D-F) configurations, each of them in a
single-, dual-, and triple-layer geometry. The cylindrical setups could be
used for the off-beam/in-room applications, whereas dual-head setups could be
potentially also considered for the in-beam/inter-spill scenarios
[shakirin2011implementation, parodi2020latest]. Each layer of the multi-layer
cylindrical system consisted of 24 modules. The dual-head configurations
consisted of 12, 24 and 24 modules for single, double and triple layer setups,
respectively. The radius of the system, defined as the distance between the
isocenter and the surface of the innermost strip in the module, was equal to
369.9 mm and 300.0 mm for cylindrical and dual-head configurations,
respectively. The gap between adjacent layers was fixed to 44 mm for all
setups.

Figure 2: The J-PET based geometrical configurations proposed for application
in proton therapy range monitoring. In the Monte Carlo simulation study
presented here we investigated: single layer cylinder (A), double layer
cylinder (B), triple layer cylinder (C), single layer dual-head (D), double
layer dual-head (E), and triple layer dual-head (F) configurations. A
cylindrical water (blue) phantom was isocentrically positioned inside each of
the configurations. The number of modules per layer in each head for single,
double and triple layer dual-head setups is 6, 6 and 4, respectively. Purple
arrows show the direction of the proton beam.

The modules in the cylindrical configurations were positioned parallel to the
beam direction. In contrast, the modules in dual-head configurations were
positioned perpendicular to the beam, motivated by the potential improvement
of the J-PET detector resolution in the direction perpendicular to the strips.
When the modules are positioned parallel to the beam direction (cylindrical
setups), the precision of the range measurement depends on the resolution of
the interaction position along the strip, which is determined by the
detector’s timing properties [moskal2016time]. On the other hand, for the
dual-head configurations, the range measurement depends on the resolution
determined by the width of the plastic strips (6 mm), which is superior to
that along the strip length.

###  2.2 Monte Carlo simulations

In this work, we exploited Monte Carlo methods for simulation and evaluation
of the feasibility of various J-PET geometries for proton therapy range
monitoring. We used the ProTheRaMon software framework, in which the delivery
of proton therapy treatment plans were simulated, scoring the $\beta^{+}$
activity produced by protons during the treatment, as well as the J-PET
scanner response to the annihilation gammas [borys2022protheramon]. The
ProTheRaMon framework utilizes the GATE platform for Monte Carlo simulations
[sarrut2022opengate], the CASToR package for PET image reconstruction
[merlin2018castor], and in-house developed Python and bash scripts. The
framework consists of five separate simulation and data processing steps.
ProTheRaMon offers complete processing of proton therapy treatment plans,
patient geometries based on Computed Tomography (CT), the simulation of
treatment delivery and intra-treatment PET imaging, taking into account
therapy and imaging coordinate systems, beam models specific to a given proton
therapy facility, as well as activity decay during the treatment and PET
imaging protocol [borys2022protheramon].

For simulations of the treatment plan irradiation, we used the Geant4
QGSP_BIC_HP_EMY physics list with the RadioactiveDecay model. The beam model
of the Cyclotron Centre Bronowice (CCB) Krakow proton therapy centre, along
with the CT calibration, were implemented as described in [Gajewski2021a]. For
the simulation of the two 511 keV photon propagation from the positron-
electron annihilation position to the PET scanner and their interaction with
the plastic scintillator, the emlivermore_polar physics list was used. We did
not simulate scintillation processes, but we considered the energetic
resolution of the scintillators [moskal2021simulating] calculated based on
experimental measurements, performed for the plastic scintillator strips
[moskal2014test]. A 200-380 keV energy window was set to extract a list of the
coincidences, along with a 3 ns time window [moskal2021simulating].

In this study, we simulated the irradiation of a PMMA phantom with proton SPB
and SOBP of various ranges, to investigate the feasibility of different J-PET
geometries for proton range monitoring. All treatment plans were optimized in
the Varian Eclipse 16.1 treatment planning system, used routinely in CCB for
patient treatment planning.

The SPB plans were prepared with nominal proton energies of 125.68 MeV, 127.15
MeV, 129.34 MeV, and 132.25 MeV, irradiating a $5\\!\times\\!20\\!\times\\!5$
cm3 PMMA phantom, achieving the corresponding Bragg peak range of 100 mm, 102
mm, 105 mm, and 109 mm, respectively. The plans were normalized to 8 Gy in the
Bragg peak maximum, which corresponds to about $3.3\cdot 10^{9}$ primary
protons.

Three sets of SOBP plans were prepared to obtain homogeneous dose
distributions in $3\\!\times\\!3\\!\times\\!3$ mm3,
$5\\!\times\\!5\\!\times\\!5$ mm3, and $7\\!\times\\!7\\!\times\\!7$ mm3
cubes, inside a $20\\!\times\\!15\\!\times\\!20$ cm3 PMMA phantom. Each of
these sets was optimized to obtain the SOBP range the same as for the SPB
plans, i.e. 100 mm, 102 mm, 105 mm, and 109 mm, leading to 12 SOBP plans of
varying volume and range. The plans were normalized to 4 Gy(RBE) in the SOBP
cube, leading the total number of primaries of about $4.0\cdot 10^{10}$,
$9.6\cdot 10^{10}$, and $2.1\cdot 10^{11}$, for the small, medium, and large
cubes, respectively. Both, the SPB and SOBP plans were irradiated along the y
direction of the corresponding phantom (see Figure 2).

For the simulation of 511 keV annihilation photons propagation, the phantoms
were positioned isocentrically inside the PET scanners. We assumed the in-room
PET acquisition scenario, with a 90-second time delay from the end of the
irradiation to the beginning of the PET acquisition, which lasted for 120
seconds. The available computing power enables performing simulations in a
relatively short time. In total, the mean simulation time of the proton
irradiation plans for SPB and consecutive SOBP plans from small to large cubes
was 12 minutes, 7.2 hours, 16.8 hours, and 14.3 hours, respectively.
Corresponding numbers for the PET acquisition simulation was 2.4, 31.5, 70.1,
and 135.0 minutes.

###  2.3 PET image reconstruction

The CASToR software [merlin2018castor] v. 3.1 was used for the PET data
reconstruction. Since CASToR does not allow TOF modelling of the scintillation
quanta propagation along the plastic scintillator strips, these were
discretized to 100 artificial scintillators ($6\\!\times\\!24\\!\times\\!5$
mm3) along the longest dimension of the plastic strip. This discretization
corresponds to the TOF resolution ($FWHM=5~{}mm$) along the the J-PET strips
[smyrski2017measurement, moskal2021simulating]. The list-mode TOF MLEM
reconstruction algorithm was used with TOF resolution equal to 500 ps (FWHM)
and with Siddon projector. Reconstructed images were corrected for sensitivity
and attenuation. The PMMA linear attenuation coefficient was set to 0.104
cm-1. Reconstruction voxel was 2.5 mm3, isotropic. The reconstructed images
were smoothed with the 3D Gaussian filter with $\sigma$=1 voxel
[baran2019studies]. The images were reconstructed with 3 iterations.

###  2.4 Analysis

The comparison of J-PET setup configurations was conducted considering (i) the
sensitivity, and (ii) the precision of range shift detection.

We defined the sensitivity, denoted $\eta$, as the ratio of the number of
detected coincidence events per primary proton. It was calculated for each
geometry and SPB/SOBP of different range. The $\eta$ factor is given as:

$\eta=\frac{c}{p},$ (1)

where $c$ is the number of registered coincidences and $p$ is the number of
simulated primary protons. In order to compare the six J-PET configurations,
we defined and calculated the geometry-dependent normalized sensitivity factor
$H$ given as:

$H=\frac{\eta_{geom}}{\eta_{ref}}\quad,$ (2)

where the $\eta_{geom}$ is calculated for the investigated simulation setup
(considering both SPB and SOBP simulations) and $\eta_{ref}$ is calculated for
the single layer cylindrical geometry.

The mean value $\overline{H}$ was calculated separately for the SPB and SOBP
studies for each geometry. For the SPB $\overline{H}$ was averaged over 4 beam
ranges and for the SOBP over 4 beam ranges and 3 different dose cube sizes.

We also performed a quantitative analysis of the precision which can be
expected for detecting proton beam range with different J-PET geometry
configurations. The dose range, $R_{D}$, was calculated as the depth of 80% of
the distal fall-off of the integral depth dose (IDD) profile of SPB or central
axis profile of SOBP. Combinations of four dose ranges of SPB or SOBP, i.e.
$R_{D}$ were equal to 100 mm, 102 mm, 104 mm, and 109 mm, allowed to analyze
six dose range differences, $\delta R_{D}$, i.e. 2 mm, 3 mm, 4 mm, 5 mm, 7 mm,
and 9 mm. The differences in dose range, $\delta R_{D}$, of SPB or SOBP
irradiations were assumed to be the reference for the activity range analysis.

The activity range, $R_{A}$ [camarlinghi2014beam], was calculated by fitting a
sigmoid function to the distal fall-off of the 3D activity distribution
reconstructed with a given J-PET geometry. Based on the fit, the $R_{A}$ was
determined at 50% of the distal fall-off maximum [kraan2015first,
kraan2015range, min2013clinical]. The difference of six activity ranges,
$\delta R_{A}$, associated with the six reference differences in dose range,
$\delta R_{D}$, was calculated by subtracting the range of fitted activity
profiles. The deviation between activity and dose range difference, $\Delta
R$, was individually calculated for each geometry setup and for SPB and SOBP,
as:

$\Delta R=\delta R_{D}-\delta R_{A}\quad.$ (3)

Note that for a PET scanner that flawlessly reconstructs the emission activity
distribution, the $\Delta R$ is expected to be equal to zero.

We calculated the uncertainty of the deviation between activity and dose range
difference ($\Delta R$) for each investigated scanner geometry and for SPBs
and SOBPs of different field size. For this purpose, the mean
$\overline{\Delta R}$ and standard deviation $\sigma{\Delta R}$ of $\Delta R$
was calculated, $\sigma{\Delta R}$ being proposed as a metric of the precision
of the activity range detection.

##  3 Results

###  3.1 Sensitivity

The ratio of detected coincidence events per primary proton ($\eta$), and the
normalized sensitivity factor ($\overline{H}$), all computed for SPB and SOBP
irradiations in six J-PET geometries are given in Tab. 1. The $\eta$ factor
for the SPB ranges from $0.4\cdot 10^{-5}$ to $4.8\cdot 10^{-5}$ for single
layer dual-head and triple layer cylindrical setups, respectively. For the
SOBP the numbers are smaller due to the bigger phantom (greater attenuation)
and range from $0.25\cdot 10^{-5}$ to $2.0\cdot 10^{-5}$ for single layer
dual-head and triple layer cylindrical setups, respectively. The greatest
value of $\overline{H}$ is observed for the triple and double layer
cylindrical setups and the lowest for the single layer dual-head. For the SBP
irradiation, the sensitivity of the J-PET geometries consisting of the same
number of modules, i.e., single layer cylindrical, double layer dual-head and
triple layer dual-head is comparable within about 10%. However, for the SOBP
scenario, the geometry-specific sensitivity factor $\overline{H}$ varies
significantly (about 2-2.4 times) for double and triple layer dual-head setups
with respect to the single layer cylindrical geometry. It shows the advantage
of adding the subsequent detector layers over the greater coverage of the FOV
when the same number of modules is available. For the cylindrical setups, the
addition of the new layer of modules increases the sensitivity of the system.

Table 1: The sensitivity $\eta$ and normalized sensitivity factor $\overline{H}$ for SPB and SOBP irradiations computed for the investigated J-PET geometries. The reference geometry is the single layer cylindrical setup. | SPB | SOBP
---|---|---
Setup | $\eta[10^{-6}]$ | $\sigma(\eta)[10^{-6}]$ | $\overline{H}$ | $\eta[10^{-6}]$ | $\sigma(\eta)[10^{-6}]$ | $\overline{H}$
Single layer cylindrical | 9.45 | 0.29 | 1.0 | 3.64 | 0.22 | 1.0
Double layer cylindrical | 27.41 | 0.80 | 2.9 | 10.76 | 0.65 | 2.9
Triple layer cylindrical | 45.72 | 1.26 | 4.8 | 18.00 | 1.11 | 5.0
Single layer dual-head | 3.79 | 0.13 | 0.4 | 2.45 | 0.19 | 0.7
Double layer dual-head | 10.55 | 0.35 | 1.1 | 7.21 | 0.56 | 2.0
Triple layer dual-head | 10.22 | 0.26 | 1.1 | 8.92 | 0.78 | 2.4

###  3.2 Examples of reconstructed activity distributions and profiles

We selected exemplary images for cylindrical and dual-head configurations
considering the sensitivity ($\overline{H}$ factor) and cost-effectiveness of
the setup. For the cylindrical setup, the $\overline{H}$ factor increases by
about 300% between single (24 modules) and double layer (48 modules)
configuration, while increasing only by about 70% from the double (48 modules)
and triple layer (72 modules) configuration. We, therefore, consider the
double layer geometry as the more cost-effective solution for the cylindrical
configuration [borys2022protheramon, moskal2021simulating]. The triple layer
dual-head is characterized by the highest $\overline{H}$ factor and is
constructed of only 24 modules.

Reconstructed PET images from the double layer cylindrical and triple layer
dual-head geometry, for SBP and SOBP irradiations, are shown in Fig. 3 and
Fig. 4, respectively. For both geometries, the relation between reconstructed
images and the corresponding dose, production, and emission distributions, was
previously shown in Borys et al. 2022 [borys2022protheramon]. Furthermore, in
Fig. 5 we show an example of profiles taken through images reconstructed
following the SPB and SOBP irradiations, together with the fitted sigmoid
functions, as well as the corresponding emission profiles for comparison. As
in Fig. 3 and Fig. 4, only the double layer cylindrical and triple layer dual-
head configurations are shown.

Note that the fall-off reconstructed image profiles for the SBP irradiations
are qualitatively more similar to the emission fall-offs than the fall-offs
obtained from the SOBP irradiations.

Figure 3: Example of the reconstructed PET images resulting from the SPB
irradiation at 125.68 MeV and range of 100 mm. The activity distributions
reconstructed with 3 iterations are shown for the double layer cylindrical
(top row) and triple layer dual-head (bottom row) geometries. Post-
reconstruction 3D Gaussian smoothing of the activity distribution with
$\sigma$ equal to 1 voxel was applied. The PMMA phantom size is
5$\times$20$\times$5 mm3. The voxel size is 2.5$\times$2.5$\times$2.5 mm3.

Figure 4: Example of the reconstructed PET images resulting from irradiation
of the SOBP of 5$\times$5$\times$5 cm3 and 100 mm range. The activity
distributions reconstructed with 3 iterations are shown for the double layer
cylindrical (top row) and triple layer dual-head (bottom row) geometries.
Post-reconstruction 3D Gaussian smoothing of the activity distribution with
$\sigma$ equal to 1 voxel was applied. The PMMA phantom size is
20$\times$15$\times$20 mm3. The voxel size is 2.5$\times$2.5$\times$2.5 mm3.

###  3.3 Precision of range shift detection with various J-PET geometries

Figure 5: Examples of emission profiles, reconstructed activity profiles and
sigmoid function fitted to the reconstructed profiles for SPB (left column)
and SOBP irradiations (right column) for double layer cylindrical (top row)
and triple layer dual-head (bottom row) geometry configurations.

Fig. 6 and Fig. 7 show $\Delta R$, the difference between the range shift in
the dose and the range shift as measured from the reconstructed activity
distributions after fitting the sigmoid function, for simulations of SPB and
SOBP field irradiations, respectively. The figures have six panels, each of
them showing the results for one of the investigated geometrical
configurations of the J-PET scanner. For the SOBP irradiations, the results
for three irradiation fields of different sizes are given. Additionally, in
Table 2 calculated mean and standard deviation values are given separately for
the SPB and SOBP irradiation.

The mean of the differences in range shift, between the reference and the
measurements made on reconstructed images, ranges from -0.37 mm to 0.85 mm.
These values are smaller than the voxel size of the reconstructed PET image
(isotropic 2.5 mm). The standard deviation of $\Delta R$, which we associate
with the precision of the range detection, is below 1 mm for both, SPB and
SOBP irradiations. For all the investigated geometries, higher precision is
observed for the SPB than SOBP. The best precision for the SPB is found for
the triple layer dual-head and the worst for the single layer dual-head. All
cylindrical configurations show similar precision for the SPB investigation.
Among the dual-head setups, the single layer geometry has the worst results
for both SOBP and SPB studies.

Comparing the geometries with the same number of modules, for the SPB the best
range detection precision was found for the triple layer dual-head, whereas
for the SOBP the double layer dual-head configurations was found to be
superior.

Figure 6: $\Delta R$ for all six geometries of the J-PET scanner investigated
for SPB irradiations. Top row shows the results for cylindrical geometries and
the bottom for the dual-head setups. The columns from left to right present
the results for the single, double and triple layer scanner geometries.

Figure 7: $\Delta R$ for all six geometries of the J-PET scanner investigated for SOBP irradiations with different fields size. Top row shows the results for cylindrical geometries and the bottom for the dual-head setups. The columns from left to right present the results for the single, double and triple layer scanner geometries. Table 2: Calculated distances between measured and reference difference (SOBP study). | SPB study | SOBP study
---|---|---
Setup |  $\overline{\Delta R}$ [mm] |  $\sigma_{\Delta R}$ [mm] |  $\overline{\Delta R}$ [mm] |  $\sigma_{\Delta R}$ [mm]
Single layer cylindrical | 0.22 | 0.26 | 0.10 | 0.50
Double layer cylindrical | 0.45 | 0.27 | 0.17 | 0.36
Triple layer cylindrical | 0.40 | 0.27 | 0.31 | 0.64
Single layer dual-head | 0.79 | 0.58 | 0.07 | 0.83
Double layer dual-head | 0.33 | 0.42 | -0.37 | 0.43
Triple layer dual-head | -0.06 | 0.04 | -0.05 | 0.56

##  4 Discussion

We proposed and compared six geometries of the modular J-PET scanner (three
dual-head and three cylindrical) in terms of sensitivity and precision for
proton beam range measurements. We used the ProTheRaMon software framework to
conduct Monte Carlo simulations of SPB and SOBP irradiations in a uniform PMMA
phantom. We reconstructed the resulting $\beta^{\mathrm{+}}$activity
distributions using the CASTOR software. The number of detected coincidences
per primary proton ($\eta$) varies between the investigated J-PET scanners
from $0.4\cdot 10^{-5}$ to $4.7\cdot 10^{-5}$ for a SPB and from $0.2\cdot
10^{-5}$ to $2.0\cdot 10^{-5}$ for a SOBP. The sensitivity of the scanners
relative to single-layer cylindrical geometry, $H_{geom}$, for the SPB and
SOBP irradiation plans approaches 5 for triple-layer cylindrical geometry.
Quantitative analysis was conducted to assess the precision of range detection
with different scanner geometries, which for the investigated SPB and SOBP
irradiations and using uniform PMMA phantoms was found to be below 1 mm.

The $\Delta R$ values, the difference between the range shift in the dose and
the range shift as estimated from the reconstructed activity distributions,
are mostly smaller than the expected J-PET resolution, which is at the level
of a few millimeter [moskal2021simulating]. Therefore, it can be concluded
that following experimental verification, in principle, all investigated
configurations could be considered for practical application in proton range
monitoring. However, it should be stressed, that the investigations presented
here were performed in a uniform phantom. Further studies that are currently
under review [Brzezinski2023_PMBsubmitted] are required to assess the
feasibility of range detection for heterogeneous Intensity-Modulated Proton
Therapy treatment plans in non-uniform patient tissue. Therefore, small
differences between the investigated geometries observed here for simplified
quality assurance settings may result in much more significant differences in
a clinical setting. In this context, both precision and sensitivity should be
considered essential factors for geometry optimization, taking into account
that the general rule for PET imaging is that greater statistics will improve
the reconstructed image quality.

The presented results, considering both sensitivity and precision, as well as
the cost-effectiveness of J-PET based configurations, indicate that the
double-layer cylindrical and triple-layer dual-head configurations are the
most promising for in-room/off-beam and inter-spill/in-beam applications,
respectively. The triple layer dual-head geometry has the greatest efficiency
factor $\overline{H}$ (as it is shown in Table 1) among the scanners with 24
modules. This is the number of modules currently available and undergoing
commissioning with the modular prototype of the system. The double-layer
cylindrical geometry is the envisioned final Total-Body J-PET geometry
[moskal2021simulating] and would potentially benefit from the experience of
the J-PET group in scanner construction and future operation. Note that the
double-layer setup has a sensitivity increase of 300% with respect to the
single-layer setup, while the triple-layer setup has a sensitivity increase of
about 70% with respect to the double-layer configuration, pointing to the
double-layer scanner as the most cost-effective configuration.

Direct comparison with other PET range monitoring systems in not
straightforward due to the differences in the experimental setup, e.g. phantom
size or irradiation plans. Recently, the mobile PET system DoPET, developed at
the University of Pisa, Italy [kraan2019analysis, topi2019monitoring], has
been investigated for the application of range monitoring in proton therapy.
Various phantoms were irradiated and PET signal was acquired immediately after
the irradiation for five minutes, mimicking the in-room range monitoring
approach. Their experiments and Monte Carlo simulations with FLUKA
[battistoni2015overview, augusto2018overview] revealed that the efficiency
factor (number of coincidences per primary protons) is at the level of
$\eta$=2.85⋅10-5. The double- and triple-layer J-PET scanners investigated in
this study have the sensitivity of the same order of magnitude as the DoPET
system. However, a comparison of the precision in range measurement is
challenging, considering the different irradiation and PET acquisition
scenarios (phantoms, treatment plan, acquisition protocol), and is beyond the
scope of this manuscript. In comparison to DoPET, the J-PET systems show
similar sensitivity, while its advantages are the cost-effectiveness and
modular design, which enable construction systems capable of various PET
acquisition scenarios and facilitate installation in treatment rooms of
different designs.

The uncertainties of the presented simulations study are related to the
assumptions made. We applied an artificial discretization of the plastic strip
into a hundred 5-mm long pseudo-crystals, which in the first approximation is
in agreement with the expected resolution of the currently produced 3rd
generation J-PET scanner that uses Wave Length Shifters (WLS) that offer
improved time resolution [smyrski2017measurement, moskal2021simulating]. Minor
uncertainties may relate to the physics modelling used for the simulation of
the activity production and propagation of the 511 keV annihilation photons
[borys2022protheramon]. Based on the clinical protocols used in CCB Krakow
proton therapy centre, we have also assumed 2 minutes PET acquisition time
[Brzezinski2023_PMBsubmitted], while the detected PET signal may substantially
vary when modifying acquisition time. The uncertainties related to the PET
image reconstruction are related to e.g. sensitivity correction,
normalization, attenuation correction, number of iterations used in the
reconstruction, post-reconstruction image filtering. To simplify the presented
preliminary analysis, we have omitted the propagation of the uncertainty
related to the fitting of the activity profile fall-off to the $\delta R$ and
$\sigma R_{D}$ values. The simulated phantom irradiations were performed with
relatively high doses of 4 Gy (SBP) and 8 Gy (SOBP), characteristic of the
hypofractioned treatments, where range monitoring is of particular importance.
Range monitoring of patients with 2 Gy fraction doses will result in lower
coincidence statistics and is being further investigated in
[Brzezinski2023_PMBsubmitted].

For the assessment and characterization of diagnostic PET scanners, NEMA norms
[NEMA:2018] are used. We propose that the sensitivity and precision analysis
presented here be the first step towards introducing similar norms for the
evaluation of PET scanners for proton beam range monitoring. This evaluation
should, furthermore, consider such aspects as cost-effectiveness and the
suitability of the technology for intra-treatment PET imaging. We believe that
the ProTheRaMon framework, offering a standardized simulation and image
reconstruction environment, may be helpful for reliable comparison of
different setups. A consensus and guidelines for the evaluation of PET-based
range monitoring techniques would be of great benefit in fostering future
developments in proton beam range monitoring and in its translation into the
clinic.

##  5 Conclusions

In this paper, the feasibility of the J-PET detector for PET-based proton beam
therapy range monitoring was investigated. Six different scanner geometries
were tested by means of Monte Carlo simulations. Relative efficiency and range
assessment precision were computed in order to find the optimal geometrical
configuration.

The study reveals that considering the sensitivity, precision and cost-
effectiveness of different approaches, the most promising for the clinical
application are the double-layer cylindrical and triple-layer dual-head
configurations, dedicated for in-room/off-beam and inter-spill/in-beam
applications, respectively. Among the scanners with 24 modules of the J-PET
detector, the best results were obtained with the triple-layer dual-head
system. All the systems show the feasibility of range assessment with
precision at the level of 1 mm for both SPB and SOBP irradiations.
Experimental validation of the presented results is needed and ongoing.

## Acknowledgments

This work was supported by the National Centre for Research and Development
(NCBiR), grant no. LIDER/26/0157/L-8/16/NCBR/2017. Calculations were performed
on the Ziemowit computer cluster in the Laboratory of Bioinformatics and
Computational Biology at the Biotechnology Centre, the Silesian University of
Technology, created in the EU Innovative Economy Programme
POIG.02.01.00–00-166/08 and expanded in the POIG.02.03.01–00-040/13 project.
Development of ProTheRaMon was supported by the National Centre for Research
and Development (NCBiR), grant no. LIDER/43/0222/L-12/20/NCBR/2021. We
acknowledge also support by the Foundation for Polish Science through the TEAM
POIR.04.04.00-00-4204/17 program, the National Science Centre of Poland
through grant 2021/42/A/ST2/00423, and the SciMat and qLife Priority Research
Areas budget under the program Excellence Initative - Research University at
the Jagiellonian University, and Jagiellonian University project no.
CRP/0641.221.2020.

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