PET geometries and protocols for veriﬁcation of proton therapy

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U NIVERSITY OF G RONINGEN

B

ACHELOR THESIS

PET geometries and protocols for verification of proton therapy

Monte Carlo simulations

Author:

Theun Sebastiaan VANDER ZEE

Supervisor:

Peter D^ENDOOVEN Daily Supervisor:

Karol BRZEZINSKI

Second Examiner:

Emiel VANDER GRAAF

This work was performed in the Medical Physics Group of KVI-Center for Advanced Radiation Technology, University of Groningen

This Bachelor Research Project was performed as part of the BSc Physics degree programme of the Faculty of Mathematics and Natural Sciences,

University of Groningen

July 14, 2016

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Abstract

Proton range verification is a crucial aspect of proton therapy and con- tributes to optimally taking advantage of the dosimetric benefit of protons.

Positron Emission Tomography (PET) is currently the only method clinically available for this purpose. Three concepts of range verification with PET have been brought forward: in-beam, in-room and off-line. In this study we compare three protocols and geometries with each other: one in-room protocol with a full ring scanner and two in-beam protocols with a dual head scanner. For this purpose, my work was to simulate a real head-and- neck case using the Monte Carlo framework, while a fellow student worked on the image comparisons. The Pearson Correlation Coëfficient (PCC), γ- index and Structural Simmilarity Index (SSIM-index) are used to quantitatively compare images. The in-room protocol scores the highest on all three metrics, with PCC: 0.9691, γ-pass: 98,49%, mean-γ: 0.2065 and mean-SSIM:

0.8448. Since washout was not simulated, it is likely that the results of in- beam PET might approach those of in-room, because washout impacts in- room protocols more than it does in-beam. Time Of Flight (TOF) removes most of the limited angle artefacts from the in-beam results, but not all. Be- tween our two in-beam protocols a tradeoff must be made. One in-beam protocol contains a scan in between fields, which provides information re- garding the correct dose deposition, before delivering the entire fraction.

This is at the expense of reduced sensitivity. The other in-beam protocol makes two scans at the end of the irradiation, losing the information of a scan in between fields, but improving sensitivity.

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Acknowledgements

For the past couple of months I’ve been cycling all the way to the KVI to perform my bachelor research. Besides myself, there were more individuals involved in all stages of this project. It are those individuals that I would like to dedicate some lines to in my acknowledgments.

First of all, I am particularly grateful for the excellent supervision provided by Karol. My gratitude goes to Ruben as well for our fruitful collaboration and a good time overall. I would like to thank Peter for reading an com- menting on my thesis. My appreciation goes to Sybrand, for his sublime company during lunchtime and cycling tours to the KVI. Last, my thanks goes to Anno for mentioning me in his acknowledgments as well.

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Introduction and Theory

1.1 Protons for cancer treatment

1.1.1 Introduction

With around 65 ion therapy centers worldwide and around 50 being build or planned ¹, we see that this form of therapy is becoming rapidly more available as a treatment of cancer. The two most commonly used ions are

12C and¹H (protons). Our study focuses on the latter. The shift in treatment from photons to protons, or ions in general, is of course not without a reason. In cancer treatment one would like to deliver the dose to the tumor, while sparing the surrounding healthy tissue. Protons can be more beneficial than photons, because of their underlying physics.

1.1.2 Proton physics

The characteristic dose-depth curve for protons comprises a shallow entry region followed by a sharp peak at the end, called the Bragg peak (see fig- ure1.1). Protons give a lower entry dose, while depositing more dose in the tumor region, relative to photons. While other ions like¹²C have a tail after the Bragg peak, protons do not, since only target fragmentation occurs in collisions between protons and other atoms. There will thus not be much dose after the position where the protons have stopped, just a slight varia- tion in where they stop due to range straggling. Their dose-depth character- istics are superior to photons as well, where the dose-depth curve increases to a maximum and then follows an exponential decrease.

The position of the Bragg peak can be shifted by using various proton beam energies. When superimposing these energies, a so called Spread- Out-Bragg-Peak (SOPB) is obtained, which can be shaped to fit a desired form. Thus a greater dose-to-tumor conformity and greater precision can be achieved when using protons as treatment modality over photons. In this way, more surrounding healthy tissue can be spared and side-effects and complications avoided.

As protons traverse matter they mainly lose energy via Coulomb interactions to electrons [1]. The energy loss per unit path length as presented in [2] and [3] is given by:

1http://ptcog.ch/

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FIGURE1.1: Image showing the dose-depth curves for photons and protons, including the SOPB. Adapted from [4].

−dE

ds = 4πe⁴z²

m0V² N B (1.1)

Here, B is the atomic stopping number, which in the case of the relativistic limit is:

B = Z[ln2m0V²

I − ln(1 − β²) − β²] (1.2) with ze the proton charge, velocity V = β · c, N the number of atoms per cm³, Z the atomic number of the material, m0 the proton rest mass and I the ionization potential.

Beside excitations, protons can undergo direct interactions with atomic nuclei and their electrons. Due to Coulomb interactions with electrons, the protons may follow askew paths. However, since protons are ± 1800 times heavier, this will not be a significant effect [1]. Repulsions due to Coulomb interactions with atomic nuclei cause greater deflections and go by the name of Multiple Coulomb Scattering (MCS). Unwanted beam broadening comes, among other sources, from MCS.

In addition to deflections, the probability exists that a proton will undergo a collision with an atomic nucleus. In elastic collisions, conservation of energy and momentum cause the proton to be deflected, resulting again in beam broadening. In inelastic collisions, a nuclear reaction will take place.

In inelastic collisions, a proton from the target nucleus gets converted to a neutron and the product of such a collision is unstable. Inelastic collisions thus produce radioactive isotopes, which decay via β⁺-decay [5, 1]. β⁺- decay can be depicted by the following reaction:

p → n + β⁺+ ν_e (1.3)

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1.2. Range verification 3

The positron place of creation is not the same as the place of annihilation, as mostly positrons which have no kinetic energy annihilate. The higher the energy of the produced positron, the longer its average range. As we shall see, these positron emitters are crucial for our method of range verification.

1.2 Range verification

1.2.1 Principle of range verification

The main advantage of protons cannot be fully exploited as long as the proton range is not exactly known. An uncertainty can lead to overshooting of the proton beam, potentially damaging surrounding healthy tissue. Es- pecially in Intensity Modulated Proton Therapy (IMPT), where all the fields summed up produce the desired total dose, range uncertainties can cause noticeable inhomogeneities in the delivered dose [6]. To avoid collateral damage, more so when critical organs (e.g. an eye) are within short distance of the Planning Target volume (PTV), the safety margins are broadly set and prevent optimal use of the advantages of protons [7, 8, 9]. Accurate range verification in vivo is very desirable to allow reduction of these margins, although they do remain patient- and treatment-site-specific as well.

1.2.2 Uncertainties in range verification

There are different sources of uncertainty when it comes to predicting proton range. In treatment planning, it has been demonstrated that analytical pencil beam methods are inferior to Monte Carlo (MC) methods, especially in complex geometries [8]. Pencil beam methods can (among other factors) not model Multiple Coulomb Scattering (MCS) and range straggling as correctly as MC methods, although they do require less computation time [8].

Uncertainties associated with CT

Treatment plans are made based on Computed Tomography (CT) images of the patient, so inevitably uncertainties associated with CT are introduced.

These comprise image noise, spatial resolution of the CT and CT artifacts (e.g. the partial volume effect) [1,7]. The effect from noise can be reduced to below 1% when using dual energy CT [10]. Another important source of errors is using a calibration curve for the conversion of the CT’s Hounds- field Units (HU) to relative proton stopping powers, which are needed to calculate the proton range in the treatment plan. The error due to this is estimated to be 1-3 mm [11].

Movement errors

Outside treatment planning, movement errors of all sorts can potentially introduce significant discrepancies between the position of dose delivery and where it should be according to the treatment plan. Patient mispositioning or a changing patient anatomy over the course of the treatment fractions

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are common examples [7]. During treatment, organ motion, e.g. respira- tion and peristaltic motion, can cause local density variations, which a proton beam is very sensitive to. In the context of Image-guided Proton Therapy (IGPT), a complementary CT can avoid patient mispositioning errors, especially in regions with a high percentage of bone. This is at the expense of additional irradiation. The position of organs can, however, still differ, even after making a complementary CT and overlaying it. Multi-dimensional imaging, which is making real time CTs during scanning (Multi-dimensional

= 3 spatial dimensions + the dimension of time), can be of aid in these situ- ations [6].

1.3 Using Positron Emission Tomography for range ver- ification

1.3.1 Basic principles and nuclides

Proton beams stop inside the patient to deliver their dose, making direct range verification complicated, since imaging relies on radiation going through the patient. Several indirect methods have been proposed, like prompt gamma and MRI, however these are still not in clinical practice. Currently, the most feasible and only clinically implemented method to verify proton range is by using Positron Emission Tomography (PET). A handful of reviews and implementations on this topic can be found here: [12,13,7,9].

PET is a non-invasive technique that makes use of coincident detection of gamma rays, produced in the annihilation of a positron (β⁺) and an elec- tron (e⁻). The most important positron emitters that are created in the interaction of protons as they traverse a human body are summarized in the following table1.1adapted from [5,7].

From all the nuclides,¹⁵O and¹¹C are produced with the largest cross section/mb.¹⁵O is produced abundantly in soft tissue. It has a relatively short half-life and combined with its large cross section, it produces most of the signal in the beginning of the acquisition. Eventually¹¹C starts taking over as the dominant signal producing nuclide, due to its longer half-life [7].

Because protons only induce target fragmentation and the stopping power of protons is highly dependent on elemental composition, also the activity distributions will depend on the elemental composition of the irradiated tissue [14]. The relation between the deposited dose and the activity of the isotopes produced is in itself complicated, since dose deposition and nuclear reactions depend in a fundamentally different way on proton energy and material composition. The relation between dose and activity is further aggravated by problems like washout [5] (which will be explained here1.3.2).

As seen in table1.1 the production of β⁺-emitters has a threshold energy which also prevents comparison of dose and activation maps directly. When the protons decelerate they lose their energy and start depositing their dose in accordance with their characteristic dose-depth curve. The more protons

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1.3. Using Positron Emission Tomography for range verification 5

TABLE1.1: Nuclear reaction channels

Produced nuclide Half-life(s) Reaction channel Threshold energy(MeV)

15O 122.24 ¹⁶O(p,pn)¹⁵O 16.79

11C 1220.04 ¹²C(p,pn)¹¹C 20.61

14N(p,α)¹¹C 3.22

16O(p,α&pn)¹¹C 59.64

13N 597.9 ¹⁴N(p,pn)¹³N 11.44

16O(p,α)¹³N 5.66

14O 70.598

10C 19.290

30P 149.88 ³¹P(p,pn)³⁰P 19.7

38K 458.16 ⁴⁰Ca(p,α)³⁸K 21.2

FIGURE 1.2: A representation of the relation between the Bragg peak and β⁺emitters, adapted from: [9]

slow down, the more β⁺-activation takes place. This process goes in an almost linear fashion due to the weak energy dependence of the cross sections of the different β⁺-emitting nuclides at clinically used energies [9]. The weak energy dependence relation breaks down at lower energies, where higher cross sections are applicable. Therefore the number of activated β⁺- emitters build up and reach a maximum just before the Bragg peak, enabling indirect localization of where the maximum dose was deposited (see figure1.2).

Range verification in clinical practice must therefore be done by comparing measured activity distributions with simulated distributions using MC software [7]. This can be used to adjust the treatment plan if necessary only in hindsight.

1.3.2 Methods of proton range verification with PET

There are currently three approaches to proton range verification with PET:

in-beam, in-room and off-line. These three concepts are discussed in detail below. While each method makes a compromise between several factors, a general rule to keep in mind is that the scan should be as long as

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possible and as quickly as possible after irradiation to achieve an optimal image [15]. One problem all methods have to deal with is that biological processes transport the positron-emitting nuclides away from their place of creation. This process is called washout. Washout degrades the signal and adequate modeling of this effect in relation to protons has not yet been achieved. Models based on data from the irradiation of small animals with carbon ions are used in some other studies. These models may serve as a first approximation, but their implementation in realistic studies remains questionable. Some discrepancies are that a distinction between different radionuclide species is not made when assigning washout parameters and local variations are not incorporated [7]. Biological washout was therefore not taken into account in our study.

In-beam

With ’in-beam PET’, the scanner is mounted on the proton gantry or situated in the irradiation position, enabling acquisition with practically no delay after irradiation or in the pauses of pulsed irradiation, when using a synchrotron to produce the proton beam. [15, 16]. The signal from short- lived isotopes, like¹⁵O, is stronger and less affected by biological processes (washout), enabling shorter acquisition times [7,1].

Conventional full-ring PET scanners cannot be used as an in-beam system, because they would hinder the proton beam delivery. Other geometries like a flat-panel dual head geometry [17] have already been implemented in the verification of heavy charged particle therapy. A part-of-a-ring design [18]

or OpenPET [19] have also been investigated, but no clinical implementation of these geometries yet exists [20].

Because the in-beam PET scanner is situated in the irradiation position, this negatively affects patient throughput for irradiation. The integration of the scanner in the gantry head is more expensive and technically more challenging than the other options as well, but makes imaging after single fields feasible [15,1]. Furthermore, the secondary radiation that is produced in treatment with protons might damage the detector, especially if they are close to the patient, which is typically the case when using in-beam to get better counting statistics and a better angular coverage. [21] demonstrated that the hardness of detector equipment and readout electronics are sufficient to withstand about 13 years of damage free usage. Direct exposure of the detectors to the proton beam, should still be avoided whenever possible.

Since the patient can remain on the treatment table, repositioning errors can be reduced. A complementary CT is not yet possible with in-beam protocols, a feature that is standard with in-room and off-line protocols.

No direct CT availability makes the PET image harder to overlay with the planning CT [7].

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1.3. Using Positron Emission Tomography for range verification 7

Off-line

The ’Off-line’ method comprises imaging at a remote site using a standard PET/CT scanner. Off-line imaging is the cheapest option, as it does not require installation of new equipment [15]. If a new scanner has to be acquired for proton range verification purposes, the statement above does not hold. Moving the patient from the treatment room to a remote site takes about 10 minutes. In these 10 minutes, the signal is heavily degraded by decay and washout [20, 22], making it necessary to employ long acquisition times to get reasonable statistics. Naturally this method also suffers from patient motion the most. Patient motion can be alleviated by simulta- neously making a CT scan as well, enabling co-registration.

The feasability of this method has been demonstrated in vivo [13], conclud- ing that range verification within 1-2 mm should be possible, but this is only for bony structures and a head-and-neck case (same as in our study) [22,23]. Bones do not suffer from biological washout as much as soft tissue, thus giving a better signal and their co-registration with the planning CT is easier. Although its potential for range verification has been shown, we will not consider this method in our study, as it falls behind in feasibility compared to in-room and in-beam verification.

In-room

’In-room PET’ refers to the method of making a scan with a short delay (1- 2 minutes) after the irradiation in a standalone full-ring PET scanner. An in-room protocol is a compromise between in-beam and off-line imaging.

Most counts can be registered with an in-beam concepts, but integration costs were estimated to be very high and full-ring scanners cannot be used.

Off-line PET will have extremely low counting statistics and if a new scanner has to be acquired, the argument that off-line PET is a cheaper solution, does not hold any longer. Employing the full-ring scanner that is used in off-line PET as well, while introducing a short delay after irradiation, in- room PET is said to be an optimal compromise between ’quality of measured data and integration efforts’ according to [15].

Despite the short delay between irradiation and imaging, counts from the most abundant isotope, ¹⁵O (half-life of ± 122s), still contribute consider- ably to the signal. Since ¹⁵O is still highly abundant, the distal fall-off is sharper, as the total signal consists for a substantial part out of the contribution of only one nuclide. In off-line PET/CT, different reaction channels contribute to the signal, all with different threshold energies, blurring the distal edge and allowing for less accurate range verification [12].The most important advantage is that this stronger signal greatly reduces the acquisition time, compared to off-line PET, from approximately 30 to 3 minutes.

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1.4 This study

Reliable proton range verification is an important aspect in proton therapy.

This study aims at determining the optimal factors in a geometry and protocol for proton range verification with PET scanners. Reconstructed PET images, obtained from simulations of various protocols and geometries, were quantitatively compared to emission maps. We have an in-room protocol, which is considered the gold standard today. It will be interesting to see if our in-beam protocols can match the performance of our in-room protocol.

Determining optimal factors in both geometries and protocols will be an objective of this study.

This bachelor project was a collaboration between two students. My part focuses on the simulations, while Ruben focuses on the quantitative visual image comparison.

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Chapter 2

Method and Materials

2.1 Simulating using GATE

GATE (GEANT4 Application for Emission Tomography) is an open source software package, designed to perform simulations for medical imaging and radiotherapy purposes using the well validated GEANT4 Monte Carlo code [24]. As a particle simulating software, GATE needs some way to track the particles. The typical particle tracking is as follows. After a particle is generated with initial values of position, energy, particle type, time and momentum, a ’step’ is applied. During a step a particle gets update position, momentum etc. All the steps of a particle together form its ’track’.

In GATE all particles are tracked in time and space through ’hits’, which store information about a particle’s interaction in matter. In GEANT4 a hit stores¹:

• Position and time of a step

• Momentum and energy along the track

• Energy deposition of a step

• Interaction type of the hit

• Volume name containing the hit

2.1.1 Architecture of the simulation

Simulating in GATE requires learning the input commands that the software can handle. A convenient way to pass the input to GATE is by writ- ing macros. A macro is a small program that automates a series of commands. These commands are put in following a ’tree structure’, meaning several commands relating to the same feature are structured under the same part of an input command. For example all digitizer commands are under /gate/digitizer/ . . .. In each simulation, the minimal set of parameters one has to give as input are²:

1http://www.opengatecollaboration.org/sites/default/files/GATE_

v6.2_Complete_Users_Guide.pdf

2http://www.opengatecollaboration.org/sites/default/files/GATE_

v6.2_Complete_Users_Guide.pdf

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1. scanner geometry with /gate/geometry/ . . .

2. phantom geometry with /gate/”nameof phantom”/ . . . 3. physics with /gate/physics/ . . .

4. initializing simulation with /gate/run/initialize 5. detector model with /gate/digitizer/ . . .

6. source with /gate/source/ . . .

7. data output format with /gate/output/ . . .

8. start acquisition with /gate/application/startDAQ

Instead of giving GATE the input line by line, one usually writes separate macros for all the eight items above. By making one macro that loads all

these macros (the ’supra-macro’) with the command /control/execute”macroname”, a tree structure is created. In the case of a bug, one can easily adjust that

macro and reload it.

The dimensions of the geometries we consider in this study, are explained in sections2.3.1and2.3.2. All our geometries were made following a tree structure. When defining any geometry, first, the virtual simulation space where GATE will keep track of the particles has to be defined. This simulation space is called the world. Inside the world, you make the actual PET scanner. One notable feature to the tree structure is that when defining your geometry, the dimensions of an underlying component of the geometry (called the ’daughter volume’) cannot exceed the dimensions of the volume in which it is contained (called the ’parent volume’). For example, a PET crystal cannot exceed the dimensions of the detector block it is contained in. It is advised to make the dimensions of the parent volume somewhat larger than the daughter volume, to avoid the edges from over- lapping.

The phantom and source were loaded by using parameterized voxels, so that different parameters (e.g. shape and size) can be assigned to each voxel.

The phantom is a virtual representation of the CT of our patient. For a voxelized phantom the so called ’InterFile-Reader’ converts the greyscale of an image, which is in Houndsfield Units (HU), to a material, using a range translator. The range translator assigns a predefined interval of values to a specific material. A voxel falling in that range of values gets those particular material properties assigned to it. These properties are the atomic weight fractions of several atoms, its thermodynamic state and density.

The source was obtained from proton simulations performed earlier. These proton simulations gave production maps as output. We obtained these production maps per nuclide and per treatment field. The 7 nuclides we simulate are presented in table1.1. Production maps are in number of nuclides per voxel, which first need to be converted to activities, to serve as a correct input for GATE. The details of various modifications that were performed on the source files, are explained in more detail later in this chapter,

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2.1. Simulating using GATE 11

in subsection 2.4.3. The InterFile-reader was used to load in the 7 different activity maps. Subsequently, a range translator converts the grayscale values of the source image to an activity.

After some steps in the simulation, a positron, emitted from a β⁺-emitting isotope, will annihilate and form two photons which will reach the modeled detector. GATE uses the digitizers to convert a hit into digital values. A photon will likely interact multiple times within a crystal volume, thus will produce multiple hits. These are summed by a so called ’adder’ module, in order to specify that only one photon was detected. After readout, the digitizer stores the individual photons as ’singles’, which are equivalent to the observable signal seen from a detector. Since a time-stamp was added to the singles, the digitizer can later store coincidences by sorting them out of the singles. It is also on digitizer level that a more realistic detector response is modeled. This is done by blurring the energy spectrum, to mimic the energy resolution of the detector. We also implemented both a thresholder and upholder, to discard low and high energetic photons. In our study we used an energy blurring of 0.13, a thresholder of 400 keV and an upholder of 650 keV.

The information from these singles and coincidences can be stored in different output formats. In this study we used the .root format, so the output can be analyzed using the software ’root’ and used for further processing.

In this study vGATE6.2 was used to model the different PET scanner geometries and to set up the simulations. vGATE stands for Virtual GATE and it is a virtual machine that runs on the Ubuntu operating system. The Ubuntu operating system can be run inside VirtualBox³, which in turn can be ran on any host operating system. vGATE6.2 includes GATE6.2, its software dependencies and analysis programs (e.g. root). All dependencies are already set up, making vGATE a convenient simulation environment to use. More information about GATE and Geant4 can be found here^{4 5}.

3https://www.virtualbox.org/

4http://www.opengatecollaboration.org/

5http://geant4.web.cern.ch/geant4/

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2.2 Patient case

FIGURE2.1: Figure showing the positioning of the full-ring scanner and the dual-head scanner in the position of

field 5.

FIGURE2.2: Figure showing the positioning of the full-ring scanner and the dual-head scanner in the position of

field 1.

FIGURE2.3: Sagittal view of the tumor location. The red square is one

dual-head panel.

FIGURE2.4: Coronal view of the tumor location and both panels of the

dual-head scanner in red.

The patient case studied in this thesis has a tumor in the head and neck region, as illustrated in figures2.3 and2.4. Proton therapy can be beneficial to head-and-neck cases as the more accurately defined range of protons can help spare the sensitive tissue around the tumor. Since there are a high number of sensitive tissues close to the tumor in a head-and-neck case, proton range verification is of the utmost importance.

The treatment plan was made at the UMCG. It consists of five fields en- tering the patient from different directions to optimize dose-to-tumor conformity. The fields are given in their ascending order from 1 to 5. Figure 2.5 shows the directions of the five fields and table 2.1 the gantry angles corresponding to these fields. The gantry angles are measured from the ˆy axis.

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2.3. Geometries and protocols 13

FIGURE 2.5: Field directions of the treatment plan, dis- played together with a transverse slice from the CT of our patient. The positive ˆz-direction is pointing into the page.

TABLE2.1: Gantry angles

Field Angle(°)

1 310

2 50

3 225

4 145

5 180

2.3 Geometries and protocols

Scanner geometry and acquisition protocol are not two separate factors, but should be combined to determine what optimally fits a certain patient case.

We consider two geometries: the full ring and dual-head scanner, and three protocols. The two in-beam protocols use a dual-head scanner and one in-room protocol uses a full-ring scanner. The scanner specifications are presented in table 2.2 and worked out in more detail in subsections 2.3.1 and2.3.2.

Crystal

LSO crystals were used despite their intrinsic radioactivity of about 240 Bq cm⁻³ [25], coming from the element ¹⁷⁶LU [9]. Proton range verification exhibits lower counting statistics than in the conventional use in nuclear

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TABLE2.2: PET scanner specifications

full ring Dual head

diameter (mm) 842 *

Axial FOV (mm) 221.4 221.4

Number of Blocks 192 32

Number of Crystals per block 169 169

Dimensions Block (ˆx, ˆy, ˆz) (mm) 20, 54.6, 54.6 20, 54.6, 54.6 Dimensions Crystal (ˆx, ˆy, ˆz) (mm) 20, 4, 4 20, 4, 4 Translation (ˆx, ˆy, ˆz) (mm) 0, 15, -10 0, 0, 25

Scintillation Material LSO LSO

*depends on panel positions, see "dual head" section (2.3.2)

FIGURE2.6: TOF principle as explained in this paragraph, figure adapted from [29]

medicine, an issue which intrinsic radioactivity only aggravates. It was investigated that in the case of an off-line PET/CT system, which has to deal with low count rates more than in-beam and in-room do, LSO’s intrinsic radioactivity does not contribute to image degradation, rather other factors [26]. Using an energy window will further separate the false coincidences coming from the LSO crystal [27]. The widespread use of LSO in state-of- the-art PET scanners makes it the reason we implement it in our simulations as well.

Time Of Flight

In our simulations we used Time of Flight-PET (TOF-PET). This will especially improve the quality of the in-beam protocols, as the TOF implementation mitigates limited angle artifacts. An important indication of limited angle artifacts is object elongation towards the edges of the FOV [25, 28].

Another advantage is the improved suppression of random coincidences and Compton scattered events [25].

The principle of TOF-PET is quite straightforward. The two annihilation photons reach the detectors along their Line of Response (LOR). By mea- suring the time at which the photon arrives at a detector, the position of positron annihilation on the LOR can be calculated with x = v ·^∆t₂ where x

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(A) (B)

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FIGURE2.7: The figures above show how the three geometries are loaded into GATE. Figure 2.7a is the dual-head scanner in the position of field 5. Figure 2.7bis the dual- head scanner in the position of field 1. Figure 2.7c is the

full-ring scanner

is measured from the center of the LOR and ∆t = tb− t_a, the time difference between the arrival of the photons at detector a and b. Because the timing resolution is not perfect, a Gaussian distribution with a certain FWHM will appear, see figure 2.6. The Coincidence Resolving Time (CRT) is the maximum time that can elapse between two pulses, which is still processed as a coincidence. We implemented a CRT of 350 ps in our study.

2.3.1 Full ring geometry

The specifications of the components of the full ring PET scanner are presented in table 2.2. Full-ring scanners have been successfully tested and proven feasible in combination with in-room protocols before [12]. The full-ring scanner we use in the simulations was modeled after an existing state-of-the-art PET scanner: the Siemens Biograph 64.

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The translations (see table2.2) are to position the scanner such that the tumor is in the center of the Field Of View (FOV). The translations were obtained by overlaying the CT with the production maps. Figure2.7ashows how the full-ring geometry looks in GATE.

2.3.2 Dual head geometry

The scanner specifications for the dual-head scanner are presented in table 2.2. The dual-head geometry we consider is called a flat-panel design. The feasibility of a dual-head scanner with TOF-PET has been demonstrated before [25]. Here we use a scanner that consists of fewer blocks, 16, but the same number of crystals per block as compared to the full-ring scanner. We devised this sort of geometry to get to know more about the feasibility of such a design in combination with our in-beam protocols.

A flat-panel design allows for flexible positioning. The two detector heads should rotate, such that they are perpendicular to the proton gantry, when imaging, to avoid direct exposure. The Planning CT images overlayed with irradiation fields were used to determine how close the panels can be positioned to the tumor. An advantage of the flat-panel design, compared to full-ring scanners, is that the panels can be positioned closer to the tumor (i.e. reduce the scanner diameter). This will improve sensitivity and the limited angular coverage can to a certain extent already be compensated for.

When imaging isotopes from field 1, the panels are placed such that the system has a diameter of 350 mm and a rotation of -50° in the xy-plane.

Imaging after field 5 allows the panels to be placed such that the diameter of the system is 320 mm with a rotation of 0°, see figures: 2.1,2.2,2.7band 2.7c. To avoid direct exposure, the panels were placed such that they were perpendicular to the proton beam.

PET detectors have their highest sensitivity in the center of the FOV. The detectors can however not always be placed such that the tumor is located in the center of the FOV, because body parts, mostly the shoulders, physically obstruct the panels, as can be seen in figure2.4. This is a limitation when positioning the panels close to the patient. Full-ring or partial-ring systems, which have a larger diameter, do not get in the way of the shoulders. It was previously reported that a partial-ring dual head scanner with an opening of 46° performs almost as well as a full-ring scanner in the case of a small target volume, like our head and neck case [18]. In this study we consider a flat panel design instead, because its detector arrangement is less expensive and offers more flexible positioning.

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(A)

(B)

(C)

FIGURE 2.8: The figures above represent the different acquisition protocols. Figure2.8arepresents protocol 1, figure 2.8bprotocol 2 and2.8cprotocol 3. ’F’ stands for ’field’, ’R’

for gantry rotation and the numbers for which field or rotation. A solid vertical line in between two fields represents a rotation A dashed line means no rotation. F and R are associated with a time duration. Specifying for ’F’ how long the irradiation takes, i.e. how long it takes to give one field and for ’R’ how long the rotation of the gantry from one position

to the other takes.

2.3.3 Acquisition protocols

For our study we consider three acquisition protocols presented in figures:

2.8a, 2.8b and 2.8c. In these figures. The time structure for the different fields, rotations and scans, is presented in table2.3, while table2.4gives the time between a certain field and a scan.

Protocol 1 - in-room

Protocol 1 is an in-room protocol. In-room protocols are considered to be the gold standard in PET range verification. After five fields of irradiation and a 60 seconds delay, to mimic moving the patient to the scanner, a full- ring PET scanner performs a scan with 120 seconds of acquisition time, see figure 2.8a. The scan time should be optimized to give sufficient counts, while on the other hand, it should not greatly affect patient throughput.

After three minutes (the time from finishing the irradiation to the end of the scan), most of the signal from short lived isotopes like ¹⁵O, will have decayed, making longer scan times less favorable.

A scan in-between fields is left out, as every time the patient has to travel between the irradiation table and the scanner, you introduce a 60 seconds delay. Hence, more decay without imaging and more washout takes place.

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TABLE2.3: Time structure of the protocols F and R Time(s)

F1 75.60

R1 21.66

F2 75.00

R2 34.16

F3 84.00

R3 18.33

F4 72.80

R4 10.84

F5 82.50

R5 13.30

scan 60.00 scan* 120.0

TABLE2.4: Time between irradiation and scan Protocol/scan t1(s) t2(s) t3(s) t4(s) t5(s)

1 459.3 362.2 244.5 153.3 60.0

2a 0 - - - -

2b 459.3 302.6 184.5 93.3 0

3a 399.3 302.6 184.5 93.3 0

3b 472.6 375.9 257.8 166.6 73.3 This table gives the time from the end a certain field to the scan, for each protocol. t1 to t5 correspond to the time from that field until the scan. A ’-’ means a certain time is not

present for that specific scan.

Protocol 2 - in-beam

Protocol 2 consists of a scan after the first field and a scan at the end. Both scans are with a 60 seconds acquisition time, making the total acquisition time 120 seconds, see figure2.8b. The scan after field 1 is more viable with an in-beam concepts, as it does not require patient re-positioning. A scan in-between fields can be used as a direct check, before delivering the entire fraction.

The scan in-between fields can best be done after field 1. When imaging after field 5, field 1’s isotopes contribute the least to the total number of counts as compared to the other fields, due to radioactive decay. Introduc- ing a 60 seconds acquisition time here will not have as great of an impact on the image after field 5 as introducing it after field 4 for example. Both scans are made with the dual-head-flat-panel geometry.

Because of the two scans, this simulation had to be subdivided into two parts and later combined. In our formalism, the simulation of the first scan is named ’2a’ and ’2b’ is the term for the simulation of the final scan.

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2.4. Methods 19

Protocol 3 - in-beam

Protocol 3 comprises a scan in the position after field 5 and subsequently the detector heads are rotated to scan in the position of field 1, as can be seen in figure2.8c. Making a scan in two different positions improves the angular coverage. These scans are both made with a dual-head scanner.

Again, because of the two scans, the simulation of this protocol was subdivided into two parts, which were later combined. The simulation of the first scan in the position of field 5 is referred to as ’3a’, while the simulation of the last scan is called ’3b’.

2.4 Methods

2.4.1 Simulations

For our simulations, we first made the required geometries in GATE. These were based on existing macros, but modified to fit our study.

First we checked our geometries with a simple back-to-back 511 keV emitting point source, to see if they gave the predicted response. Next, test simulations with a source file of one of the β⁺-emitting nuclides at a time was used. Due to memory issues, not all sources could be loaded into GATE when one uses a virtual box. Voxelized sources and phantoms cannot be visualized directly by any visualizer GATE supports. To check if both are correctly aligned, one can look at the root-output in hindsight.

All test simulations were done on regular computers. The actual simulations were run on the Peregrine high performance computer cluster of the Center for Information Technology of the University of Groningen. On the cluster, we used 500 nodes per simulation with 16GB of memory dedicated to each node. Using this many nodes speeds up the simulation process, because the simulations are able to run in parallel. The maximum walltime was about three hours, while the actual run time was on average 15 minutes for one node. All 5 simulations could be done within 24 hours. After the simulations were completed we used the gate job merger (gjm) to merge all the 500 simulations into one complete file.

2.4.2 Image reconstruction

Image reconstruction was performed using the iterative Maximum Likelyhood- Expectation Maximization (ML-EM) algorithm. The reconstruction was done on 4x4x4 mm³voxels.

The optimal iteration was determined using the Pearson Correlation Coëffi- cient (PCC) and the iteration with the highest PCC was used for further analysis. The PCC compares a simulated image to an emission image pixel for pixel and assigns a number between 0 and 1 based on how much the images match (with 0 = nothing matches and 1 = perfect match). After a certain number of iterations the PCC will reach a maximum and then start

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to decrease again, which is due to the statistical noise that gets amplified with increasing iteration number. The PCC can be expressed as:

P CC = Pn i=1

((x_i− ¯x)(y_i− ¯y)) s n

P

i=1

(x_i− ¯x)² ^Pⁿ

i=1

(y_i− ¯y)²

(2.1)

Where xi& ¯xare the individual and average activities in the reconstructed images and yi & ¯y the individual and average activities in the emission maps.

In the reconstruction sensitivity and attenuation corrections were performed.

Scatter was removed from the data. The sensitivity correction corrects for the non-uniform sensitivity in a PET scanner, in which the sensitivity is the highest in the center of the FOV and gets progressively lower towards the edges. Attenuation correction corrects every Line Of Response (LOR) for the attenuation of photons in the patient. There were little random events, since our source activity was low. Randoms correction was therefore not performed.

The corrected images were quantitatively compared with the emission maps using two measures of image fidelity: the γ-index and Structural Similarity index (SSIM-index).For more theoretical background on these quantitative visual comparison methods, one should have a look at the bachelorthesis of Ruben Hijlkema.

2.4.3 Modifications

Format

For the voxelized sources and phantom the InterFile-Reader of GATE ac- cepts the ’LITTLEENDIAN’ and ’BIGENDIAN’ byte order, we used Lit- tleendian. As number format, only ’Unsigned Integer’ can be loaded into GATE, not ’Float’. Special consideration should go to the fact that only sources and phantoms saved in 16 bit (2 bytes per pixel), give the correct output.

Conversion factors

Besides the correct format, several conversion factors were added to the source files, to ensure that the activity maps are correct when loaded into GATE. For this purpose a Matlab code was developed. The source files we obtained were production maps of the different β⁺-emitting isotopes, generated per field and per isotope. This means different conversion factors apply to each field and isotope. Figure 2.9 shows the order in which the different modifications were added.

How the activity maps, which we load into GATE, are generated from the production maps can be expressed as the following mathematical formula:

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2.4. Methods 21

FIGURE 2.9: Overview of the different modifications that were done on the source files. These modifications are done

per isotope and per field.

A = 286 · 10¯ ⁴^X

j

Pjλe^−λt^j (2.2)

In the formula ¯A is the activity map for one isotope, Pj is the production map for a field j, tj is the time from the end of field j till the beginning of the scan. These times are presented in table2.4and enable us to adjust the activity of the sources in coherence with the time structure of the different protocols.

Constants

The production maps were generated with proton simulations, which used

1

286 protons per Monitor Unit (MU). We add a factor of 286 to get the correct number of protons in our simulation.

The factor of 10⁴ up-scales the values of the source image to fit the desired bit range, in order to retain maximum precision. The activity values should, for a 16 bit image, be between 0 and 2¹⁶. This factor also makes sure the input is in Unsigned Integer instead of Float. Because this second factor of 10⁴ has no further physical justification or meaning, a factor of 0.0001 has to be added in GATE to get the actual activity values again.

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The details of the different steps, which are visualized in figure 2.9, are explained in more detail below.

Step 1

In the original production maps we obtained from the previous proton simulations the ’number of radionuclides per voxel’ were given, rather than

’activity per voxel’, which is what GATE has as input. The factor of λ ac- counts for this, as A = λ · N , where A is activity in Becquerel (Bq), λ the decay constant and N the number of β⁺-nuclides.

Step 2

The activity at a later time for a certain isotope can be calculated using the following formula:

A_t= A₀· e^−λt (2.3)

A_tand A0are the activity after some time t and initial activity in Bq respectively, λ is the decay constant in s⁻¹and t the time in seconds.

The factor e^−λtwas added to simulate the loss of activity during treatment, which is again isotope and protocol specific. This factor takes into account, for example, that when imaging after field 5, most isotopes produced in field 1 have already decayed.

These modified activity maps are the source files we load into GATE.

Step 3

The third step is making emission maps. The factors 1 − e^−λ˜^t, where λ is the decay constant in s⁻¹ and ˜t the acquisition time, will take the decay during the acquisition time into account. This is to generate a map of what the scanner actually is meant to measure. GATE will simulate this decay, but the ’modified activity maps’ do not take this into account. How the emission maps are generated from the production maps can be expressed through the following mathematical formula:

E = 286 · 10¯ ⁴^X

i

X

j

Pi,jλie^−λⁱ^t^j(1 − e^−λⁱ^˜^t) (2.4)

Where ¯E is the emission map and Pi,j the production map. The formula sums over the 7 different nuclides i and the 5 different fields j.

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23

Chapter 3

Results

3.1 Counting statistics

The number of coincidences for all protocols are listed in table3.1. Protocol 1 has the highest number of counts, followed by protocol 3 and 2. Protocol 2 and 3 have less counting statistics due to their geometry. The dual head geometries have limited angular coverage and even though a 60 second delay was introduced, the full angular coverage provided in protocol 1 gives improved sensitivity.

The gap in number of coincidences between protocol 2 and the remaining protocols is due to protocol 2 having a scan after field 1, so it only receives the contribution from that field, instead of all the fields.

TABLE3.1: Number of Coincidences per Protocol Protocol Coincidences

Protocol 1 4930183 Protocol 2 2926505 scan 2a 662273 scan 2b 2264232 Protocol 3 3513713 scan 3a 2287894 scan 3b 1225819

3.2 Image reconstruction

Image reconstruction was performed with an iterative algorithm. We used the Pearson Correlation Coefficient (PCC) to determine the optimal iteration by comparing emission maps to reconstructed images. A mathematical expression for the PCC can be found in equation 2.1. From figure 3.1 the optimal iteration, that is: the iteration with the highest PCC, of the ML- EM algorithm were determined. This gave for protocol 1, that iteration 3 was the best; for protocol 2 and 3 that iteration 1 was the best. The values are in table 3.2 In can be observed that the PCC curves for protocol 2 and 3 have a steeper negative slope than protocol 1 after the maximum PCC was reached. The reason why the PCC curves have a maximum is that after a certain number of iterations the noise gets amplified, deteriorating

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FIGURE3.1: The PCC curves for protocol 1, 2 and 3

the image quality and causing the PCC score to decrease again. The lower number of coincidences in protocol 2 and 3 cause the noise to be amplified faster. This causes the steeper negative slope for protocol 2 and 3 in figure 3.1.

3.3 Image comparison

TABLE 3.2: Image comparison values for transverse and sagittal images

Protocol 1 Protocol 2 Protocol 3

γ-pass (%) 98.49 96.23 96.90

mean-γ 0.2065 0.2497 0.2480

mean-SSIM 0.8448 0.7627 0.7864

PCC 0.9691 0.9650 0.9662

γ-pass (tr) (%) 96.92 93.33 93.62

mean-γ (tr) 0.2623 0.3408 0.3282

mean-SSIM (tr) 0.8033 0.6820 0.7075 γ-pass (sag) (%) 96.28 96.77 94.47

mean-γ (sag) 0.2988 0.3510 0.3407

mean-SSIM (sag) 0.8030 0.7740 0.7921 Here the parameters without the suffix (im) correspond to the entire volume, (tr) to the transverse images and (sag) to

the sagittal images, note that these are slice dependent.

The reconstructed PET images were compared with the emission maps. The γ-index and the SSIM images are used for quantitative visual inspection.

The γ-map is an image showing the gamma index values per pixel in one slice. The values corresponding to the different transverse and sagittal images and the values averaged over the entire volume are given in table3.2.

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3.3. Image comparison 25

(A) (B) (C)

(D) (E) (F)

(G) (H) (I)

(J) (K) (L)

FIGURE 3.2: The transverse images of each column correspond to an image from the same protocol. From left to right, this gives: protocol 1, 2 and 3.3.2a-3.2care the emission maps. 3.2d - 3.2fare the reconstructed PET images.

3.2g -3.2i correspond to the γ-maps and in 3.2j -3.2l the SSIM-maps are presented

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(A) (B) (C)

(D) (E) (F)

(G) (H) (I)

(J) (K) (L)

FIGURE3.3: The sagittal images of each column correspond to an image from the same protocol. From left to right, this gives: protocol 1, 2 and 3.3.3a-3.3care the emission maps.

3.3d-3.3fare the reconstructed PET images.3.3g-3.3icor- respond to the γ-maps and in3.3j-3.3lthe SSIM-maps are

presented

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27

Chapter 4

Discussion

4.1 Visual comparison

Visually comparing the transverse PET images with their emission maps we see that the general shape of the head is reproduced in all three images.

The cold spot that is clearly visible in the transverse emission maps, is reproduced with less contrast in the reconstructed images. This is also clearly visible on the transverse γ-maps, where the cold spot is marked white in all three protocols, with a value of around 4. The cold spot corresponds to a region where no PET-nuclides are produced, as seen from the emission maps, while the surrounding area receives a high dose. This cold spot is due to an air cavity in the head. Because 1000 · ρair ≈ ρ_tissue, the PET nuclide production in the cavity will also be 1000x smaller and since it is air, the nuclides and the positron that is emitted (and seen by PET) will probably not stop in air, but move to the side of the cavity. The steep dose gradient that is formed in this way is problematic when comparing using a γ-index.

Since a certain spatial distance to agreement is set, a small shift will already cause a bright spot in the γ-map. In the sagittal images, the same effects are visible.

The outline of the transverse reconstructed PET images of protocol 2 and 3 (figures3.2eand3.2f) exhibits a subtle elongation to the sides. These are limited angle artifacts, coming from the dual head scanners. Protocol 1, which uses a full ring scanner, does not present such blurring. This shows up in the SSIM images as the yellow outline along the head of the patient (see figures 3.2j - 3.2k) and provides an explanation for the significantly lower values of the mean-SSIM for protocol 2 and 3 (table3.2). Other geometries, like OpenPET and a partial-ring system, might synergize better with the in-beam protocols than the flat panel design considered in this study, because the shoulders do not block the detector in that case. In this way the tumor can be placed in the center of the FOV. It was however previously reported that OpenPET has reduced sensitivity when compared to a partial-ring scanner with an opening of 46°[28] and both are more expensive to manufacture and implement than the flat panel configuration considered in this study.

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4.2 Protocol comparison

From table3.2is can be seen that protocol 1 produces an image that corresponds the most to the actual emmision maps, as its γ-pass (98.49%), mean- SSIM (0.8448) and PCC (0.9691) are the highest, while the mean-γ (0.2065) is lowest. Taking into account that washout was not simulated in this study, it is probable that the scores of the visual comparison methods of protocol 2 and 3 will approach protocol 1, since washout will impact protocol 1 the most.

One should keep in mind that the results presented and analyzed here are for a head and neck case. Its small PTV is ideal for our dual-head scanner design, where the panels can be placed close to the tumor, but not even enclose all activity. Therefore our results cannot be extended to larger PTVs directly, where there is a higher chance that the patient will obstruct the scanner and activity will fall outside the FOV. This has to be considered per patient case. For a full ring scanner on the other hand, the image is not expected to get worse when the treatment planning contains a larger PTV.

4.3 In-beam comparison

Comparing our two in-beam protocols, we see that a tradeoff is made. Pro- tocol 2 has about 6 · 10⁵ counts less than protocol 3. That is about ¹₅ of protocol 2’s total number of counts, which is quite a substantial part. De- spite reduced sensitivity, the mean γ pass of protocol 2 is slightly lower than protocol 3, with 96.23% to 96.90% respectively. The mean-γ is only 1.7 · 10⁻³ lower, and the mean-SSIM 2.37·10⁻²higher. Dose deposition can be quickly checked by scanning in-between fields and this might be a decisive factor when choosing between these two protocols. However, when low counting statistics is a problem, protocol 3 should be considered instead, since more coincidences are collected in that protocol.

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29

Chapter 5

Conclusion

Proton range verification will continue to help improve the quality of proton therapy. Positron Emission Tomography (PET) scanners can be successfully used for this purpose. We have presented three protocols, one in-room and two in-beam, for proton range verification and simulated them using the Monte Carlo package GATE. On the one hand, our in-room protocol has a more sensitive scanner which is possibly cheaper to implement as well. These factors are balanced by more decay, washout and possibly positioning errors. On the other hand, in-beam protocols have a less sensitive geometry which is more expensive and technically more challenging to in- tegrate, but a stronger signal, less washout and no positioning errors are inherent.

In the case of a small Planning Target Volume (PTV), the performance of in- beam protocols will possibly approach in-room when washout is taken into account. When using in-beam protocols, a scan in the middle of two fields, is a useful feature, perhaps more valuable than two scans at the end of all fields. When there is a low number of coincidences, however, the scan in- between fields should be omitted, since two scans at the end give improved counting statistics.

The dual head flat panel geometry we use in this study is a viable option for head-and-neck patients, especially if the tumor can be placed in the center of the Field Of Fiew (FOV). When imaging in other regions and/or the patient makes panel placement more difficult, different in-beam geometries or even a full ring scanner with an in-room protocol should be considered.

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