design of a dual-mode tracking device for online dose ... mechanics. the type of processes permitted...

Sapienza Universita di Roma

Dipartimento di Ingegneria dell’Informazione, Elettronica e

Telecomunicazioni

Dottorato di ricerca in Elettromagnetismo XXVI ciclo

Design of a dual-mode tracking device for onlinedose monitoring in hadrontherapy

Luca Piersanti

Coordinatore:

Prof. Paolo Lampariello

Docente guida:

Prof. Luigi Palumbo

Tutor:

Prof. Adalberto Sciubba

Experience is what you get when you didn’t get what you wanted.

And experience is often the most valuable thing you have to offer.

– Randy Pausch, The Last Lecture

Contents

Introduction 5

1 Interaction of radiation with matter 91.1 Heavy charged particles . . . . . . . . . . . . . . . . . . . . . . . . 11

The Bethe-Bloch formula . . . . . . . . . . . . . . . . . . . . . . . 11

Energy dependence . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Nuclear fragmentation . . . . . . . . . . . . . . . . . . . . . . . . 16

1.2 Electrons and positrons . . . . . . . . . . . . . . . . . . . . . . . . 17

Collisional and radiative energy loss . . . . . . . . . . . . . . . . . 17

Multiple Coulomb scattering . . . . . . . . . . . . . . . . . . . . . 18

Backscattering of low energy electrons . . . . . . . . . . . . . . . . 20

Positron interactions . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.3 Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Photoelectric absorption . . . . . . . . . . . . . . . . . . . . . . . 22

Compton scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Pair production . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Attenuation coefficients . . . . . . . . . . . . . . . . . . . . . . . . 26

2 Radiotherapy and Hadrontherapy 272.1 Physical aspects of radiation therapy . . . . . . . . . . . . . . . . . 31

Absorbed dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Energy deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2

CONTENTS 3

Lateral beam spread . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.2 Biological aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Ionization density . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Relative Biological Effectiveness and cell survival curves . . . . . . 37

Oxygen Enhancement Ratio . . . . . . . . . . . . . . . . . . . . . 39

2.3 Protons or 12C . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.4 Beam delivery techniques . . . . . . . . . . . . . . . . . . . . . . . 42

Gantries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Treatment of moving targets . . . . . . . . . . . . . . . . . . . . . 46

2.5 Dose monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

PET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Prompt photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Charged particles . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3 Measurement of secondary radiation 533.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Start Counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Drift Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Angle of detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.2 Prompt photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Energy measurement . . . . . . . . . . . . . . . . . . . . . . . . . 61

Rate measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Preliminary data with GSI 220 MeV 12C beam . . . . . . . . . . . 64

3.3 Charged secondary particles . . . . . . . . . . . . . . . . . . . . . 66

Particle identification and fluxes measurement . . . . . . . . . . . . 66

Bragg peak position monitoring . . . . . . . . . . . . . . . . . . . 69

Charged particles production region . . . . . . . . . . . . . . . . . 71

4 Dose Profiler optimization 774.1 Detector overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

Neutral radiation operation mode . . . . . . . . . . . . . . . . . . . 79

Charged particles operation mode . . . . . . . . . . . . . . . . . . 81

4.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

Dose Profiler layout optimization . . . . . . . . . . . . . . . . . . . 83

4 CONTENTS

5 Event reconstruction and detector performance 935.1 Event reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 94

Prompt photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94


5.2 Detector performance evaluation . . . . . . . . . . . . . . . . . . . 104

Prompt photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104


Conclusions 109

Appendix A Kalman filter formalism 111

Bibliography 113

Introduction

Hadrontherapy, or ion therapy, is an emerging technique for cancer treatment

that exploits accelerated ions (mostly protons and carbons) instead of X-rays, as in

usual radiotherapy. This choice appears particularly advantageous when the pecu-

liar energy deposition in matter of charged particles is compared with the one of

photons. The former is characterized by an initial flat low deposition plateau, when

particle velocity is still high, and a very narrow peak (named after W. H. Bragg who

discovered it in 1903) that sharply rises at the end of particle’s range. The latter,

instead, shows a typical exponential trend that, after a broad peak centered in the first

2 ÷ 3 cm, depending on photon initial energy, decreases with increasing penetration

depth. Thus, the higher deposition selectivity of charged particles has made them

particularly appealing as projectile candidates for a new generation of therapy, since

a substantial sparing of the healthy tissues surrounding the tumor could be achieved

with respect to standard radiotherapy. Moreover, the possibility to dynamically shift

the Bragg peak depth, varying ions kinetic energy, opened the door to new and more

precise beam delivery techniques, named active scanning, that may allow to mini-

mize the number of passive devices on the beam line, reducing also patient clinical

complications induced by secondary radiation.

Unfortunately, radiotherapy’s standard monitoring techniques cannot be used in

this novel context. These rely exclusively on the fraction of primary beam transmit-

ted through the patient, that in a hadrontherapy treatment is negligible. For the afore-

mentioned reason, a great effort has been made in order to find the best approach to

monitor, possibly online, hadrontherapy treatment quality. Any novel approach must

rely solely on the secondary particles produced during the interaction of the beam

5

6 INTRODUCTION

with the patient.

The only technique that has been used in a clinical environment so far exploits the

collinear emission of photons due to positron annihilation. The e+ are due to the β+

decay of several radioactive isotopes (mostly 11C and 15O) produced by projectile

and target nuclear interaction. Back-to-back photons detection, usually performed

with detectors made of two “heads”, allows to estimate an activity map of the patient.

Then, an overall treatment quality assessment can be carried out once a correlation

between activity and deposited dose has been established (effectively and reliably

evaluated via Monte Carlo simulations). This approach, has been performed so far

only after the irradiation, placing the patient in a conventional PET scanner (this is

the reason why this technique is commonly referred to as PET). Such solution has

several drawbacks: (i) as time passes by, radioactive isotopes distribution is blurred

by patient metabolism (metabolic washout); (ii) the isotopes relatively short half-life

(11C ≈ 20 minutes and 15O ≈ 2 minutes) poses serious issues on the collectable

data sample, also considering the time needed to move the patient from the treatment

room to the PET ring; (iii) the isotopes low activity, if compared to standard PET,

requires longer acquisition times for data collection.

Other techniques have been recently proposed exploiting other secondary radia-

tion sources, such as prompt photons, emitted after nuclei de-excitation, or charged

particles, emitted after target or projectile fragmentation. Both approaches are un-

der study in order to assess their potential for online dose monitoring in a clinical

context. Prompt photons are emitted isotropically with an energy range that roughly

spans from 1 to 10 MeV. This makes their detection challenging, posing mechanical

issues (as collimators design and weight) in the detector development phase. Charged

particles, on the other hand, are easier to detect and to be tracked, but must exceed a

kinetic energy threshold needed to leave the patient body, that could actually limit the

available statistics and hence the spatial resolution on the dose release reconstruction.

The aim of this thesis is the description and the review of the preliminary mea-

surements on beam, the design, the subsequent optimization and the performance on

Monte Carlo data of a novel device able to detect both prompt photons and charged

particles for online dose monitoring in hadrontherapy applications. The reason of

such double functionality, never suggested so far, lies in the increased statistical sam-

ple that could be available with the detection of the two radiation sources. However,

this particular choice comes at a cost of a more complex design and mechanical re-

alization, as it will be pointed out in the following chapters. The design of this novel

detector has been included in the INSIDE project and it has been awarded a PRIN-

7

MIUR funding for the realization and the operation of such detector, together with

an online PET system, at CNAO treatment room.

In the first two sections a brief reminder of the main interaction mechanisms be-

tween radiation and matter (in the energy range of interest for medical applications)

and a state of the art of hadrontherapy and dose monitoring techniques will be pre-

sented. Then, the results of the feasibility measurements on beam (already published

on several peer reviewed journals) performed at LNS-INFN and GSI (Darmstadt)

laboratories, will be shown in the third chapter. The fourth and fifth will be devoted,

instead, to the project detailed description, and in particular to the layout optimiza-

tion, the reconstruction software development and the performance evaluation.

CHAPTER

1

Interaction of radiation withmatter

Content

1.1 Heavy charged particles . . . . . . . . . . . . . . . . . . . . . . . . 11

The Bethe-Bloch formula . . . . . . . . . . . . . . . . . . . . . . . 11

Energy dependence . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Nuclear fragmentation . . . . . . . . . . . . . . . . . . . . . . . . 16

1.2 Electrons and positrons . . . . . . . . . . . . . . . . . . . . . . . . 17

Collisional and radiative energy loss . . . . . . . . . . . . . . . . . 17

Multiple Coulomb scattering . . . . . . . . . . . . . . . . . . . . . 18

Backscattering of low energy electrons . . . . . . . . . . . . . . . . 20

Positron interactions . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.3 Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Photoelectric absorption . . . . . . . . . . . . . . . . . . . . . . . 22

Compton scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Pair production . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Attenuation coefficients . . . . . . . . . . . . . . . . . . . . . . . . 26

In this chapter the basic reactions, and their effects, which occur when radiation

encounters matter will be briefly reviewed. These processes are the basis for all cur-

rent particle detection devices and can characterize the sensitivity and the efficiency

of the detector itself. Moreover, these same reactions may also disturb and inter-

fere with a measurement: for instance, by causing energy information to be lost or

9

10 CHAPTER 1. INTERACTION OF RADIATION WITH MATTER

scattering a particle from its original trajectory. Finally these are also the processes

involved when living matter is exposed to radiation. Then, the knowledge of these

interactions is of enormous importance for experimental design of a new detector and

its optimization.

Radiation sees matter in terms of its basic constituents, depending on radiation

nature, energy and type of material, reactions may occur with the atoms, or the nu-

clei, or with their individual building blocks with a probability governed by quantum

mechanics. The type of processes permitted to each type of radiation define, among

other things, the penetrability through matter, the danger to biological organisms, the

difficulty or ease of detection and so on. The most common processes that character-

ize charged particles and photons passage trough matter are by far electromagnetic

interactions, in particular, inelastic collisions with the atomic electrons.

Because of their rather different nature is particularly useful to separate charged

particles in two classes: electrons and positrons and heavy particles (heavier than

electron, such as protons, α particles and other light ions). Because of additional

effects which arise, that are outside the aim of this thesis, heavy ions will be excluded

from this analysis.

Symbol Definition Units or value

T Kinetic energy MeVM Incident particle mass MeV/c2

mec2 Electron mass × c2 0.510998918(44) MeV

re Classical electron radius 2.817940325(28) × 10−15 mρ Density of absorbing material g/cm3

Z Atomic number of absorbing materialA Atomic weight of absorbing material g mol−1

e Elementary charge 1.602176565(35)×10−19 Cz Charge of incident particle in units of eNa Avogadro’s number 6.0221415(10)×1023 mol−1

h Planck’s constant 4.135667516(91)×10−15 eV sβ v/c of the incident particleγ Lorentz factor 1/

√1− β2

I Mean excitation potential eVν Average orbital frequencyδ Density correction to ionization energy lossC Shell correction to ionization energy loss

Wmax Maximum energy transfer in a single collision

Table 1.1: Summary of variables used in this chapter.

1.1. HEAVY CHARGED PARTICLES 11

1.1 Heavy charged particles

In general, there are two main features that identify the passage of charged parti-

cles through matter: energy loss and deflection from particle original direction. These

effects are primarily the result of two processes1: (i) inelastic collisions with the elec-

trons of the material; (ii) elastic scattering from nuclei. Of the two electromagnetic

processes, the inelastic collisions are almost entirely responsible for the energy loss

of heavy particles. Upon entering any absorber, the charged particle simultaneously

interacts with many electrons. For each interaction, the electron feels the attractive

impulse due to the Coulomb force as the particle passes nearby. Depending on the

closeness of such interaction, the impulse can be sufficient either to raise the electron

to a higher-lying shell within the atom (excitation) or to remove it completely from

the atom (ionization). Then the energy transfer comes at the expenses of charged

particle, and its velocity is therefore decreased. The maximum energy that can be

removed from a charged particle of mass M with kinetic energy T and given to an

electron of mass me in a single collision is 4Tme/M , hence very small. However,

the number of collisions per unit path length is so large, that a substantial cumulative

energy loss is observed even for thin layers of material. The net effect is a contin-

uous decrease of particle’s velocity until this is stopped or exits the medium where

it is traveling. Elastic scattering from nuclei also occurs frequently, not as often as

electron collisions though. Typically little energy is transferred in these collisions,

since the mass of the incident particle is usually very small compared to the nuclei

of most materials. Whether this is not the case, some energy is also lost trough this

mechanism. Even if inelastic collisions are statistical in nature, since their number

per unit path length is usually large, the fluctuations in the total energy loss are small

and it is then possible to work with the average energy loss per unit path length. This

quantity, often called the stopping power or commonly dE/dx, was first calculated

by Bohr using classical mechanics (a simplified version is due to Jackson [1]) and

later by Bethe et al. [2] using quantum mechanics.

The Bethe-Bloch formula

Bohr’s classical formula, as calculated by Jackson [1] is given by:

− dE

dx=

4πz2e4

mev2Ne ln

γ2mev3

ze2ν(1.1)

1emission of Cherenkov radiation, nuclear reactions (except nuclear fragmentation) andbremsstrahlung amongst others, will not be discussed in the following


whereNe is the electrons’ density. This formula gives a reasonable description of the

energy loss for heavy particles (from α to heavier nuclei). But for lighter particles,

e.g. protons, the equation (1.1) does not work properly because of quantum effects.

However, it contains all the fundamental characteristics of electronic collision loss

by charged particles. The complete quantum mechanical calculation, performed by

Bethe, Bloch and other authors, gives for the energy loss:

− dE

dx= 2πNar

2emec

2ρZ

A

z2

β2

[ln

(2meγ

2v2Wmax

I2

)− 2β2 − δ − 2

C

Z

](1.2)

The maximum energy transfer is possible with a head-on collision, given an incident

particle of mass M , kinematics indicates Wmax to be:

Wmax =2mec

2η2

1 + 2s√

1 + η2 + s2(1.3)

where s = me/M and η = βγ. If M me then

Wmax ' 2mec2η2

The mean excitation potential, I , is one of the most important terms of the Bethe-

Bloch formula and can be defined as the average orbital frequency from Bohr’s for-

mula times Planck’s constant, hν. Since this is a quantity very difficult to evaluate,

it is normally treated as an experimentally determined parameter for each element.

The quantities δ and C are density and shell corrections to the Bethe-Bloch formula

which become important at high and low energy respectively. In the first case, the

electric field of the traversing particle tends to polarize the atoms along its path.

Thus, electrons far from the particle trajectory will be shielded from the full electric

field intensity. Therefore, all the collisions with the outer electrons will contribute

less to the total energy loss than predicted by the equation (1.2). A comparison of

the Bethe-Bloch formula with and without density correction is shown in Figure 1.1.

The shell correction, instead, explains the effects which arise when the velocity of

the particle is comparable or even smaller than the orbital velocity of the atomic elec-

trons. In these cases, the hypothesis that the electron is stationary with respect to the

incident particle no longer holds and the equation (1.2) breaks down. The correction

is generally small, as it can be seen in Figure 1.1.

Energy dependence

An example of stopping power energy dependence is shown in Figure 1.2 which

reports the Bethe-Bloch formula as a function of kinetic energy for different particles.


Figure 1.1: Comparison of the Bethe-Bloch formula with (solid) and without (dashed) shelland density corrections for copper. As can be noticed in the low energy region, shell correc-tion contribution is very small, on the contrary, a clear effect can be seen for energies greaterthan 1 GeV. From Leo [3].

The term within square brackets of the equation (1.2) varies slowly with particle

energy. Thus, the general behavior of energy loss can be inferred from the behavior

of the multiplicative factor. For a non relativistic particle, dE/dx therefore varies as

1/β2, or inversely with particle energy, and decreases with increasing velocity2 until

a minimum is reached when v ' 0.96 c. At this point, particles are usually referred to

as minimum ionizing or MIP. As the energy increases beyond this point the term 1/β2

becomes almost constant and dE/dx rises again for the logarithmic dependence of

(1.2). However, this relativistic rise is compensated by the density correction.

When comparing different charged projectiles of the same velocity, the only fac-

tor that may change outside the logarithmic term in equation (1.2) is z2. Therefore

particles with greater charge will have larger specific energy loss. Analyzing differ-

ent materials as absorbers, instead, dE/dx depends mainly on the electron density

of the medium. High atomic number, high-density materials will, therefore, result in

the largest energy loss. Indeed, more energy per unit length will be deposited towards

the end of its path rather than at its beginning.

From Figure 1.2, it is clear that during the slowing down process also particle’s

kinetic energy changes. This effect is shown in Figure 1.3, which shows the amount

2this behavior can be heuristically justified observing that since the particle spends a longer timein the vicinity of any given electron whether its velocity is low, the impulse felt by the electron, and sothe energy transferred, will be larger.


Figure 1.2: The stopping power, dE/dx, as function of energy for different particles. FromLeo [3].

Figure 1.3: A typical Bragg curve showing the variation of dE/dx as a function of penetra-tion depth of 5.49 MeV α particles in air (from 241Am radioactive decay). It is clear how theparticles are more ionizing towards the end of their path.

of energy deposited by a heavy particle as a function of its penetration depth inside

the absorbing medium. This is known as a Bragg curve, and, as can be noted, most of

the energy is deposited near the end of the path. At the very end, however, the particle

begins to pick up electrons for part of the time, this lowers the effective charge of the

projectile and thus the dE/dx drops.


Range

The penetration depth of a particle traversing a medium before it loses all of its

energy is called range. Since the energy loss of charged particles can be safely as-

sumed to be continuous, this distance must be a well defined quantity, the same for

identical particles with the same energy traveling in the same material. Experimen-

tally, the range can be determined by passing a collimated source of particles at a

fixed energy through the medium under test varying its thickness and measuring the

ratio of transmitted to incident particles. A typical plot of this curve versus absorber

thickness is shown in Figure 1.4. As it can be seen, for small thicknesses, almost

all the particles survive. As the thickness approaches the range value, surprisingly,

this ratio does not drop immediately to zero, as expected of a well defined variable.

The curve slopes down, instead, over a certain range of thicknesses. This fact can be

Figure 1.4: Range (R) vs absorber thickness (t) plot for an alpha particle collimated source.I0 is the incident intensity, I is the transmitted intensity.

only explained assuming the energy loss mechanism not continuous, but statistical in

nature. Thus, in general, two identical particles with the same initial energy traveling

in the same material, will not undergo the same number of collisions and hence the

same energy loss. This phenomenon is known as range straggling. In a first ap-

proximation, the distribution of ranges for a set of identical particles has a gaussian

shape. Its mean value (R) is called the mean range and corresponds to the midpoint

on the descending slope of Figure 1.4. This is the thickness at which roughly half of

the particles pass through the material. In the practice, another quantity of interest is

the thickness at which all the particles are absorbed, this point is usually evaluated

by taking the tangent to the curve at the midpoint and extrapolating to the x axis

intercept (R0). This parameter is usually referred to as the extrapolated range.


Nuclear fragmentation

The possibility of accelerating heavy ions to energies of the order of several hun-

dreds of MeV per atomic mass unit, pointed out another process (the nature of which

is not electromagnetic) that needs to be taken into account when an accurate descrip-

tion of the radiation field produced after a collision of such particles with a target is

needed. This process is nuclear fragmentation. Two qualitatively different types of

collisions can be clearly distinguished by experimental observation:

1. the central (or near central) collisions, which comprise about 10% of all cases,

are characterized by an almost complete destruction of both the projectile and

target nuclei. These violent processes are high multiplicity events and a large

number of particles come out over a wide range of angles. In such a collision,

practically all nucleons in both colliding partners are participants;

2. the peripheral collisions, where, by contrast, the momentum and energy trans-

fers are relatively small. Only a few nucleons in the overlap zone effectively

interact during the collision and the number of participants nucleons is small.

The reminder of the paragraph is devoted to the description of this latter case. Ac-

cording to a proposition of Serber [4], inelastic nuclear reactions at relativistic en-

ergies can be described in two steps which occur in two different time scales. The

first interaction may modify the composition of the reaction partners and introduces

a certain amount of excitation energy. The characteristic time of this reaction step

is of the order of 10−23 s. In the second step the system reorganizes, that means it

thermalizes and de-excites by evaporation of neutrons, protons and light nuclei as

well as by fission and emission of gamma rays. According to the statistical model,

the characteristic time for particle emission varies between 10−16 s for an excitation

energy of 10 MeV and 10−21 s at 200 MeV. The abrasion-ablation model, introduced

by Bowman, Swiatecki and Tsang [5] and schematically shown in Figure 1.5, de-

scribes nuclear fragmentation in terms of the two aforementioned stages. Nucleons

in the overlapping zone of the interacting projectile and target nuclei are abraded and

form the hot reaction zone (fireball), whereas the outer nucleons (spectators) are only

slightly affected by the collision. In the second step (ablation), the remaining projec-

tile and target fragments as well as the fireball de-excite by evaporating nucleons and

light clusters. Those emitted from the projectile fragments appear forward peaked in

the laboratory frame, due to the high velocity of the projectile. The projectile-like

fragments continue to travel with nearly the same velocity and direction. Neutrons

1.2. ELECTRONS AND POSITRONS 17

Figure 1.5: A simplified sketch of the abrasion-ablation model of the nuclear fragmentationdue to peripheral collisions of projectile and target nucleus as described by Serber [4].

and clusters from target-like fragments are emitted isotropically and with much lower

velocities. The particles ablated from the fireball cover the range between the projec-

tile and target emission.

1.2 Electrons and positrons

Collisional and radiative energy loss

Similarly to heavy charged particles, also electrons and positrons suffer a colli-

sional energy loss when they traverse matter. But, while the basic mechanism of colli-

sion loss described for heavy charged particles holds true for electrons and positrons,

the Bethe-Bloch formula must be slightly modified for two reasons. Firstly for their

small mass: the assumption made for heavy charged particles that the incident par-

ticle remains undeflected, in fact, invalid. Large deviations in the electron path are

now possible, because its mass is equal to that of the orbital electrons with which it

is interacting. Secondly, since the collisions are between identical particles, a much

larger fraction of energy can be lost in a single encounter. Several terms must be then

changed in the equation (1.2), in particular, the maximum allowable energy transfer

becomes Wmax = Te/2, where Te is the kinetic energy of the incident electron (or

positron).

Furthermore, because of their small mass an additional loss mechanism has to

be considered: the emission of electromagnetic radiation caused by scattering in the

electric field of a nucleus (bremsstrahlung). From classical theory, any charge must

radiate energy when accelerated, and the deflection of the electron (or the positron)

in its interactions with the absorber’s nuclei corresponds to such acceleration. The


linear specific energy loss through this radiative process is given by:

−(dE

dx

)rad

=NTeZ (Z + 1) e4

137 (mec2)2

(4 ln

2E

mec2− 4

3

)(1.4)

where N is the atomic number density. This radiation component exists also for

heavy charged particles, but it is generally negligible (at least in the majority of the

practical cases) as suggested by the presence of the mass squared factor in the de-

nominator of the (1.4). The total energy loss of positrons and electrons, therefore,

can be expressed as the sum of two terms:

−(dE

dx

)tot

= −(dE

dx

)rad

−(dE

dx

)coll

(1.5)

The ratio of the two specific energy losses is given approximately by:

(dE/dx)rad(dE/dx)coll

∼=TeZ

700(1.6)

where Te is in units of MeV.

For example, secondary electrons produced from prompt photons interactions

during a hadrontherapy treatment (that are of interest in this work) have energies

lower than 10 MeV. Radiative losses are, therefore, always a small fraction of the

energy losses due to ionization and are significant only in materials with high atomic

number. However, as the energy is increased, the probability of bremsstrahlung

rapidly rises, so that at a few tens of MeV, radiation loss is comparable to or even

greater than the collision-ionization loss. Then, it is possible to define for each ma-

terial a critical energy Ec at which the two radiations equal each other. Above this

energy radiation component will dominate over collision loss and vice-versa below

Ec. An approximate formula due to Bethe and Heitler [2] to estimate Ec is:

Ec ∼=1600mec

2

Z(1.7)

Table 1.2 gives a short list of critical energies for various materials commonly used

in experimental physics applications.

Multiple Coulomb scattering

In addition to inelastic collisions with atomic electrons, charged particles travers-

ing matter also suffer repeated elastic Coulomb scatterings from nuclei even if with a


Material Critical energy (MeV) Material Critical energy (MeV)

Pb 9.51 Lucite 100

Al 51 Polystyrene 109

Fe 27.4 NaI 17.4

Cu 24.8 Anthracene 105

Air (STP) 102 H2O 92

Table 1.2: Critical energies of some commonly used materials.

rather smaller probability. The cross section of these collisions can be described (as

a first approximation) by the Rutherford formula:

dσ

dΩ= Z2r2

e

mc/βp

4 sin4(θ/2)(1.8)

where θ is deflection angle. Because of its sin4(θ/2) dependence, the majority of

these collisions result in a small angular deflection of the particle, assuming that the

nuclei are much more massive than the incident particle (the energy transfer to the

nucleus is thus negligible). Then the particle follows a random zigzag path as it

traverses the material. The cumulative effect is, however, a net deflection from orig-

inal particle direction. According to the number of interactions Ncoll, three different

situations can occur:

1. single scattering. If the absorber is very thin, such that the probability of more

than one Coulomb scattering is small, then the angular distribution is given by

the simple Rutherford formula in (1.8);

2. plural scattering. If the average number of scatteringsNcoll < 20 then we have

plural scattering. This is the most difficult case to treat since neither Rutherford

formula nor statistical methods can be simply applied;

3. multiple scattering. If the average number of collisions is Ncoll > 20 and

energy loss is small or negligible, the problem can be treated statistically to

obtain probability distribution for the net deflection angle as a function of the

thickness of the material traversed.

The third case is the most frequently encountered in common applications, and the

remainder of this subsection is devoted to this topic. In general, rigorous calcula-

tions of multiple scattering are extremely complicated and several formulations exist.


Among the most used are the small angle approximations by Moliere and by Sny-

der and Scott. Their formulations have been demonstrated to be generally valid for

all particles up to angles of θ ' 30. Ignoring the small probability of large-angle

single scattering, a good idea of the effect of multiple scattering in a given mate-

rial can be obtained by considering the distribution resulting from the small angle

(θ < 10) single scattering only. In such case the probability distribution is approxi-

mately Gaussian:

P (θ)dΩ ' 2θ

〈θ2〉exp

(−θ2

〈θ2〉

)dθ (1.9)

The parameter 〈θ2〉 represents the mean squared scattering angle, as can be obtained

integrating: ∫θ2P (θ)dΩ

from θ = 0 to ∞. The square root√〈θ2〉 is known as the RMS scattering angle

and should be equal to the RMS scattering angle of the full multiple scattering angle

distribution. However, since the Moliere distribution has a long tail, the true value is

slightly larger. A better estimate is obtained by using an empirical formula proposed

by Highland [6] which is valid to within 5% for Z > 20 and for target thicknesses

10−3Lrad < x < 10Lrad and gives the sigma of the Gaussian function:

σθ [rad] =14.1 [MeV ]

pβcZ

√x

Lrad

(1 +

1

9log10

x

Lrad

)(1.10)

with Lrad: radiation length of material; x: thickness of material; p momentum of

particle. For low velocities and heavy elements somewhat larger errors (10÷20)%

are obtained.

Backscattering of low energy electrons

Because of their small mass, electrons are particularly susceptible to large angle

deflections by scattering from nuclei. An electron entering one surface of an absorber

may undergo sufficient deflection so that it re-emerges from the surface through

which it entered. This phenomenon is called backscattering. These backscattered

electrons do not deposit all their energy in the absorbing medium and therefore can

have a significant effect on the response of detectors designed to measure the energy

of incident electrons. This phenomenon is more pronounced for electrons with low

energy and absorbers with high atomic number (for non-collimated electrons on high

Z material such as NaI, for example, as much as 80% may be reflected back). Figure

1.6 shows the measured fraction of monoenergetic electrons that are backscattered


(backscattering coefficient or albedo) when normally incident on the surface of var-

ious media, additional data for materials commonly used as electron detectors are

given in Table1.3.

Figure 1.6: Fraction η of normally incident electrons that are back scattered from thick slabsof various materials, as a function of incident energy E. From Tabata et al [7].

Electron energy (MeV)

Scintillator 0.25 0.50 0.75 1.0 1.25

Plastic 0.08 ± 0.02 0.053 ± 0.010 0.040 ± 0.007 0.032 ± 0.003 0.030 ± 0.005

Anthracene 0.09 ± 0.02 0.051 ± 0.010 0.038 ± 0.004 0.029 ± 0.003 0.026 ± 0.004

NaI (Ti) 0.450 ± 0.045 0.410 ± 0.010 0.391 ± 0.014 0.375 ± 0.008 0.364 ± 0.007

CsI (Ti) 0.49 ± 0.06 0.455 ± 0.023 0.430 ± 0.013 0.419 ± 0.018 0.404 ± 0.016

Table 1.3: Fraction of normally incident electrons backscattered from various detector sur-faces. From Titus [8].

Positron interactions

The Coulomb forces that constitute the major mechanism of energy loss for

both electrons and heavy charged particles are present for either positive or nega-

tive charge on the particle. Whether the interaction involves a repulsive or attractive

force between the incident particle and orbital electron, the impulse and energy trans-

fer for particles of equal mass are about the same. Therefore, the tracks of positrons

in an absorber are similar to those of electrons, and their specific energy loss and

range are about the same for equal initial energies. Positrons differ significantly in

the annihilation radiation (of two collinear 0.511 MeV photons) that is generated at


the end of positron track. Because these 0.511 MeV photons are very penetrating

compared with the range of the positron, they can lead to the deposition of energy far

from the original positron track. This unique feature of positrons must be seriously

taken into account in the project and the design of a gamma-ray detector, especially

if gamma-ray energies are in the order of tens of MeV where, as will appear in the

following section, the probability of pair production rapidly rises.

1.3 Photons

Although a large number of possible interaction mechanisms are known for gamma

rays in matter, only three major types play an important role in radiation measure-

ments: photoelectric absorption, Compton scattering and pair production. All these

processes lead to the partial or complete transfer of the photon energy to electron

energy. Then the photon either disappears completely or is scattered through a sig-

nificant angle. This behavior is in evident contrast to the one of charged particles

discussed earlier in this chapter, which slow down gradually through continuous si-

multaneous interactions with many absorber atoms.

Photoelectric absorption

The photoelectric effect involves the absorption of a photon by an atomic electron

with the subsequent ejection of the electron (usually referred to as photoelectron)

from one of the atom’s bound shells. The interaction is with the atom as a whole and

cannot take place with free electrons, since a free electron cannot absorb a photon

and also conserve momentum. For bounded electrons the nucleus absorbs the recoil

momentum instead. The energy of the photoelectron is then:

E = hν −B.E. (1.11)

where B.E. is the binding energy of the electron. For gamma-ray energies of more

than a few hundred keV, the photoelectron carries off the majority of the original

photon energy. Figure 1.7 shows a typical total cross section plot as a function of the

gamma-ray energy, where all the cross section contributes are emphasized. Consider-

ing the photoelectric component, the edge lying highest in energy corresponds to the

binding energy of the K-shell electron. For gamma-ray energies slightly above the

edge, the photon energy is sufficient to undergo a photoelectric interaction in which

a K-electron is ejected from the atom. Below the edge, the cross section drops dras-

tically since the K-electrons are no longer available. Theoretically, the photoelectric

1.3. PHOTONS 23

Figure 1.7: Gamma-ray total cross section for carbon, where: σp.e., σRayleigh, σCompton,κnuc, κe are the photoelectric effect, coherent scattering, incoherent scattering, pair produc-tion in nuclear field and pair production in electron field components respectively.

effect is difficult to treat rigorously, but it is interesting to note the dependence of the

cross section on the atomic number Z. This varies depending on the photon energy,

however, in the MeV range, it goes as Z to the 4th or 5th power. Hence, higher

Z materials are the most favored for photoelectric absorption and, as will be dis-

cussed in later chapters, are an important resource when choosing the best material

for gamma-ray detectors.

Compton scattering

The interaction process of Compton scattering arises when an incoming photon

is scattered on electrons. In matter, of course, the electrons are bound but, if the

photon energy is high, with respect to the binding energy, this latter component can

be neglected and the electrons can be considered as basically free. Hence, the pho-

ton is deflected through an angle θ with respect to its original direction (shown in

Figure 1.8). The photon transfers a portion of its energy to the electron (considered

initially at rest) which is then referred to as recoil electron. Since all angles are

possible, the energy transfer can vary from zero to a large fraction of the primary

energy. The expression of the scattered photon energy as a function of the scattering


angle, shown in equation (1.12), and the expression of the photon scattering angle,

as a function of the incoming photon energy, shown in equation (1.13), can simply

be derived by writing the equations for the conservation of energy and momentum.

Using the symbols defined in Figure 1.8:

Figure 1.8: Kinematics of Compton scattering.

hν ′ =hν

1 + γ(1− cos θ)(1.12)

cos θ = 1− 2

(1 + γ)2 tan2φ+ 1(1.13)

where γ = hν/mec2 is the relativistic factor, hν and hν ′ the photon energies before

and after the scattering respectively. The electron kinematics and its scattering angle

can be derived applying energy and momentum conservation as well:

T = hν − hν ′ = hνγ(1− cos θ)

1 + γ(1− cos θ)(1.14)

cotφ = (1 + γ) tanθ

2(1.15)

The probability of Compton scattering per atom of the absorber depends on the num-

ber of electrons available as scattering targets and therefore increases linearly with

Z. The dependance on gamma-ray energy is illustrated in Figure 1.7 for the case of

carbon and generally falls off gradually with increasing energy. The cross section

for Compton scattering was one of the first to be calculated using quantum elec-

trodynamics and is known as the Klein-Nishina formula, that predicts the angular

distribution of scattered photons:

1.3. PHOTONS 25

dσ

dΩ=Zr2

e

(1

1 + γ(1− cos θ)

)2(1 + cos2 θ

2

)·

·(

1 +γ2(1− cos θ)2)

(1 + cos2 θ)[1 + γ(1− cos θ)]

) (1.16)

The distribution is shown graphically in Figure 1.9 and underlines the tendency for

forward scattering at high values of the photon energy.

Figure 1.9: Polar plot of the number of photons scattered into a unit solid angle at thescattering angle θ for several photon initial energies.

Pair production

If the photon energy exceeds twice the electron rest-mass energy (1.022 MeV)

the process of pair production is energetically possible. This involves the transfor-

mation of a photon into an electron-positron pair. In order to conserve momentum,

this can only occur in the presence of a third body, usually a nucleus (sometimes

pair production can occur in the field of an electron, this process is called triplet pro-

duction and has an energy threshold of 4·(mec2) instead of 2·(mec

2) that directly

arises from energy and momentum conservation). As a practical matter, the prob-

ability of this interaction remains very low until the gamma-ray energy approaches

several MeV, therefore pair production is generally confined to high energy gamma-

rays. All the excess energy carried in by the photon above the threshold goes into

kinetic energy shared by the positron and the electron. Since the positron will most


likely subsequently annihilate after slowing down in the absorber (depending on the

medium within the process occurs), two annihilation photons are usually produced

as secondary products of the interaction. No simple expression exists for the pair

production cross section, but this varies approximately as the square of the absorber

atomic number Z and, as shown in Figure 1.7, rises sharply with energy.

Attenuation coefficients

The total probability for a photon interaction in matter can be expressed as the

sum of the individual cross sections outlined above. Expressing the cross section per

atom, following the notation introduced in Figure 1.7, this yields:

σtot = σp.e. + ZσCompton + κpair (1.17)

The Compton cross section has been multiplied by Z to take into account all the Z

electrons per atom of the absorber. This is shown (dots) in Figure 1.7 for carbon.

Thus the probability per unit length for an interaction can be obtained multiplying

σtot by atoms density N :

µ = Nσtot = σtot (Naρ/A) (1.18)

This is more commonly known as total absorption coefficient and it is simply the

inverse of the mean free path of the photon. Then the fraction of photons surviving a

depth x can be expressed as:

I/I0 = exp(−µx) (1.19)

where I0 is the incident photons intensity.

CHAPTER

2

Radiotherapy andHadrontherapy

Content

2.1 Physical aspects of radiation therapy . . . . . . . . . . . . . . . . . 31

Absorbed dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Energy deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Lateral beam spread . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.2 Biological aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Ionization density . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Relative Biological Effectiveness and cell survival curves . . . . . . 37

Oxygen Enhancement Ratio . . . . . . . . . . . . . . . . . . . . . 39

2.3 Protons or 12C . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.4 Beam delivery techniques . . . . . . . . . . . . . . . . . . . . . . . 42

Gantries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Treatment of moving targets . . . . . . . . . . . . . . . . . . . . . 46

2.5 Dose monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

PET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Prompt photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50


Radiotherapy is an essential instrument for cancer treatment, used both for cura-

tive and palliative management of patients. Currently more than 50% of all patients

with localized malignant tumors are treated with radiations as part of their initial

therapy, either alone or in combination with chemotherapy or surgery.

27

28 CHAPTER 2. RADIOTHERAPY AND HADRONTHERAPY

Ionizing radiation represents a very effective tool for human cells killing, suffi-

ciently high radiation doses, in fact, can control nearly 100% of the tumors. This

means that, in principle, any tumor can be sterilized providing that a sufficiently high

radiation dose is delivered. Unfortunately, also the healthy tissues surrounding the

target volume are unavoidably exposed to radiations and this limits the amount of

dose that can be actually delivered. Normal tissue complication is, in fact, one of

the crucial parameters that needs to be minimized in a typical treatment, maximizing

at the same time the Tumor Control Probability (TCP). Since human cells have the

capability to repair themselves when exposed to radiation, fractionation of the total

dose represents the strategy normally followed in clinical routine to reduce healthy

tissue complication. A typical radiation regime consists of 60-70 Gy delivered in

30-35 daily fractions of 2 Gy each. Technological improvements in radiotherapy de-

livery in the past years have been focused to widen the therapeutic window (that is

the difference between the TCP and the normal tissue complication probability as a

function of the dose), and in some cases, such as prostate cancer, it has been possible

to double the dose to the target.

In conventional radiotherapy high energy X-rays (up to 25 MeV) are employed

and these are normally produced by electron linacs. The first electron linac was built

for research purposes at Stanford University by W. Hansen and his collaborators in

the 1950s. Soon thereafter, this new tool took place of all other electron-photon

sources. Today about 10,000 linacs are installed and operate in hospitals all over

the world and radiotherapy is used every year to treat about 20,000 patients on a

population of 10 millions. Such enormous development has been possible thanks

to the advancements made in computer assisted treatment systems and in imaging

techniques, such as: Computed Tomography (CT), Magnetic Resonance Imaging

(MRI) and Positron Emission Tomography (PET) scans. Nowadays, the cutting edge

technology in conventional radiotherapy goes by the name of Image Guided Radi-

ation Therapy (IGRT) and it comprises the so called Intensity Modulated Radiation

Therapy (IMRT). This technique takes advantage of at least six (up to nine, in normal

practice) non coplanar and non uniform X-ray fields combined with multi-leaves col-

limator and CT imaging. IMRT allows to reach an extraordinary dose conformation

around the target volume, sparing at most the Organs At Risk (OAR) in its vicinity.

While the capability of X-rays for cancer treatment was perceived shortly after

their discovery in 1895, it was only in 1946 that the potential of hadrontherapy1 was

1Hadrontherapy is a collective word commonly used to indicate all forms of radiation therapy thatmake use of beams of particles made of quarks: protons, neutrons, pions and also heavier nuclei such

29

foreseen by Robert R. Wilson. In fact, he had measured at the Berkeley cyclotron

charged particles depth profiles recognizing a significant increase in dose at the end

of particle range, the so called Bragg peak (see Figure 2.1), which was observed fifty

years before in the tracks of alpha particles by W. Bragg. It is very interesting to

note that in his original paper, that mainly refers to protons, Wilson cites also alpha

particles and carbon ions:

“The intense specific ionization of alpha particles [...] will probably make them

the most desirable therapeutically when such large alpha particle energies are at-

tained. For a given range, the straggling and the angular spread of alpha particles

will be one half as much as for protons. Heavier nuclei, such as very energetic carbon

atoms, may eventually become therapeutically practical”, from Wilson [10].

Figure 2.1: Dose deposition curves for different radiations: typical radiography X-rays(cyan), gamma rays from 60Co radioactive decay (blue), standard 18 MeV radiotherapy pho-tons (green), 135 MeV protons (black) and 250 MeV/u carbon ions (red).

In the following years, researchers at Lawrence Berkeley Laboratory (LBL) con-

ducted extensive tests on protons, pursuing the intuitions of Wilson and in 1954 the

first patient was treated with hydrogen, followed by helium in 1957 and neon ions

in 1975. The first treatments on humans were focused on breast cancer metastatic

patients. In particular, they were aimed at pituitary gland inhibition from producing

hormones that would stimulate the cancer cells to grow. Moreover, this choice was

as helium ions (alpha particles), lithium, boron, carbon, oxygen ions etc. Amaldi [9]


particularly favorable since the gland exact position was easily localized on standard

X-ray films. At LBL between 1954 and 1975 about 1,000 patients were treated with

protons. Three years after Berkeley, in 1957, the first tumor was irradiated with pro-

tons in Europe at Uppsala cyclotron by B. Larsson. As mentioned before, cancer

Country Facilities in operation Facilities planned Patients treated(or under construction) (operative facilities)

Protons Heavy ions Protons Heavy ions Protons Heavy ions

USA 11 0 9 1 38429Europe 10 2 8 4 19768 983Japan 5 3 1 2 10607 9139Russia 3 0 1 1 6608China 1 1 1 2 1078 194South Korea 1 0 1 1 1041South Africa 1 0 0 0 521Canada 1 0 0 0 170Taiwan 0 0 2 0Saudi Arabia 0 0 1 0South America 0 0 1 0Australia 0 0 1 0

Table 2.1: Geographical distribution of particle therapy facilities. Data from Particle Ther-apy Co-Operative Group 2012 survey [11] and Loeffler et al.[12].

therapy with heavy ions started in the 1970s at LBL, where Cornelius A. Tobias sug-

gested, following Wilson’s intuition, that particles heavier than protons could give

additional advantages (Tobias et al. [13]) and since then is constantly increasing.

The Particle Therapy Co-Operative Group (PTCOG) is an international institution

that regularly monitors the hadrontherapy centers all around the world. Its last sur-

vey, published on March 2013, reports that 93,895 patients have been treated with

protons, more than 10,000 with carbon ions and about 3,500 with other ions. As

can be seen from Table 2.1, the number of hadrontherapy facilities, planned or un-

der construction, is rapidly increasing insomuch as the total could double in the next

decade.

In Europe the development of cancer therapy with protons took place at the Paul

Scherrer Institute (PSI) in Villigen (Switzerland) Pedroni et al. [14], while carbon

ion therapy was pioneered at the GSI Helmholtz Centre for Heavy Ion Research in

Darmstadt Haberer et al. [15], from which the HIT (Heidelberg Ion Therapy center)

Haberer et al. [16] was born. Italy’s first hadrontherapy center, CATANA [17] was

2.1. PHYSICAL ASPECTS OF RADIATION THERAPY 31

built at Laboratori Nazionali del Sud (INFN) in Catania and is aimed to choroidal

and iris melanoma therapy. The first patient was treated in 2002 and, according to

PTCOG statistics [11], 293 patients have been irradiated so far with protons accel-

erated by a super-conducting cyclotron. At the end of 2011 the first patient course

of treatment with protons was completed at Centro Nazionale di Adroterapia Onco-

logica (CNAO) [18] in Pavia. A year later the first carbon ion treatment started, and

nowadays the center normally operates with both particles on a daily basis. Together

with Ion Beam Therapy center (HIT) in Heidelberg, CNAO is the only facility in

Europe that allows both protons and carbon ions therapy.

2.1 Physical aspects of radiation therapy

Absorbed dose

In radiation therapy absorbed dose is one of the fundamental quantities to which

the radiobiological and clinical effects are directly related, regardless of the type of

radiation and the nature of the biological effect. It is defined (ICRU report [19])

as the mean energy deposited (E) by ionizing radiation per unit mass (m) and it is

expressed in gray (1 Gy = 1 J/kg):

D =dE

dm(2.1)

Considering a parallel particle beam with fluence F (dN particles traversing a surface

dS), the dose deposited in a thin slice of absorber material with mass density ρ can

be calculated as follows:

D [Gy] = 1.6× 10−9 × dE

dx

[keV

µm

]× F

[cm−2

]× 1

ρ

[cm3

g

](2.2)

where dE/dx is the additive inverse of the energy loss per unit path length (also re-

ferred to as stopping power) defined in equation (1.2). A quantity closely related to

the stopping power is the Linear Energy Transfer (LET) which refers to the energy

deposited in the target medium by the slowing-down particle and it is measured in

keV/µm. When a charged particle traverses matter several secondary electrons are

produced as a consequence of the process of ionization (usually called delta rays if

their energy is, in turn, high enough to ionize). In some practical cases, one might be

focused only on the energy deposited in the track vicinity, and exclude interactions

that produce delta rays with an energy larger than a certain threshold. This limit is

meant to exclude secondary electrons that carry energy far away from the original


track. This usually refers to restricted linear energy transfer. If the threshold tends

to infinity, the quantity is called unrestricted linear energy transfer and it equals the

electronic component of the stopping power. Even though LET depends on particle

energy and species, normally photons and protons are referred to as low-LET radia-

tion for their typical sparse ionization density, while carbon ions are called high-LET

particles due to their larger ionization density as shown in Figure 2.2.

Figure 2.2: Comparison of the microscopic structure of proton and carbon tracks at differentenergies with a simplified depiction of a DNA molecule. Ionization and consequently thedamage to the DNA is low at high energies but, for carbons, increases significantly decreasingthe energy. This yields to a clustered damage that is more difficult to repair. For protons,even at low energies, the ionization density is rather sparse, resulting in a lower LET andRBE values. From Fokas [20]

Energy deposition

As already mentioned in the previous chapter and shown in Figure 2.1, the energy

released by photons decreases exponentially with the penetration depth, showing a

peak between 1 and 2÷3 cm depending on the photon initial energy. This shift is

mostly due to buildup processes that arise when the gamma energy grows. On the

contrary, heavy charged particles exhibit a peculiar dose deposition curve, that fol-

lows the Bethe-Bloch equation (1.2). This is characterized by a small amount of

2.1. PHYSICAL ASPECTS OF RADIATION THERAPY 33

energy lost when the particle velocity is high (entry channel), while most of it is re-

leased in a very narrow portion of the path, close to the end of particle range (the so

called Bragg peak). Moreover, being the range a function of the energy, the depth of

the Bragg peak inside the patient can be varied and adjusted by changing the energy

of the beam (as shown in Figure 2.3). Thus, in a radiotherapeutic context, this sharp

Figure 2.3: Measured depth-dose curves in water for carbon ions with different beam ener-gies. From Schardt et al. [21].

and very precise deposition could lead to a better conformation to the target volume

and it could be extremely useful for treatment of deep seated tumors (where photon

irradiation becomes very uneffective), or tumors near OAR. Furthermore, given the

relatively low energy lost along the entry channel, the overall dose delivered to the

healthy tissues surrounding the tumor is lower, as shown in Figure 2.4 and Figure 2.5,

being constant the dose deposited on the tumor.

Lateral beam spread

As described in the previous chapter, the passage of a particle or, in our case

of interest, a particle beam through matter will lead to a generalized diffusion of

the beam itself with respect to its original direction. The beam spread is mainly

caused by elastic Coulomb interactions with the target nuclei (multiple scattering),

while scattering due to electronic interactions can be neglected. For small angles the

angular distribution can be approximated by a Gaussian function whose sigma can


Figure 2.4: Comparison between desired dose profile (a), photon therapy with a singlefield (b), proton therapy (c) and carbon ion therapy (d) for a given tumor volume (pink) inproximity to an OAR (yellow). A higher conformity to target volume can be achieved withprotons or carbon ions and, at the same time, the OAR receives a much lower dose withrespect to photon therapy.

be obtained from equation (1.10). Hence, targets with heavy elements will cause a

larger angular spread than light elements with the same thickness. In general the

angular spread of heavy charged particles is small for thin targets, but as the energy

decreases it becomes more significant due to the βpc term in the denominator of

(1.10). Considering two different beams with the same range (e.g. 150 MeV protons

and 285 MeV/u carbon ions with R = 15.6 cm) a lateral spread three times larger

can be observed for protons. In general, two different contributions to the overall de-

flection can be distinguished: the scattering from the materials in front of the patient

(beam pipe exit window, external beam monitors, collimators, compensators and air),

and the scattering inside patient tissues, between the entry channel and the stopping

depth. While the former is dominant at low energies, where even a small angular

spread translates in a significant deflection (considering the typical traveling distance

of 0.5÷1.0 m), the latter dominates at high energies, where the penetration depth in

the patient increases. For all the aforementioned reasons, and especially for protons,

the material in the beam path in front of the patient should be minimized. Examples

of Monte Carlo calculations of lateral beam spread for protons and carbon ions are

reported in Figure 2.6 and Figure 2.7.

2.2. BIOLOGICAL ASPECTS 35

Figure 2.5: Comparison of treatment plans for a target volume sited in the skull base: twofields with carbon ions (left) and nine fields with IMRT (photons). Even though a comparabledose conformation can be achieved with both techniques, the use of carbon ions will lead toa dramatic reduction in the integral dose to the surrounding healthy tissues and the sparing ofOAR. From Durante et al. [22].

2.2 Biological aspects

Ionization density

The main difference between photon and heavy ion irradiation is in their micro-

scopic spatial energy distribution. The probability of a ionization event by a photon

within the volume of a single cell is, in fact, very small. This means that a large

number of photons is needed in order to deposit a relevant dose but, since photons

interaction points are randomly distributed, the net effect is that the ionization den-

sity can be assumed to be homogeneous. On the contrary, heavy ions energy spatial

distribution is completely different. It is, in fact, localized and can be divided in

two stages: (a) the emission of secondary electrons (often referred to as δ rays), as

a consequence of Coulomb interaction between projectile and target, (b) δ electrons

scattering inside the medium and their consequent energy loss. The mean free path

for δ rays results of the order of few nanometers, this implies a higher probability

(with respect to photons) for a double ionization to occur on each of the two opposite

DNA strands (whose separation is 2 nm), therefore inducing a more severe damage

to the cell. Moreover, since cells repair capability is reduced if the DNA damage is


Figure 2.6: Calculated beam spread for carbon ions (red) and protons (blue) in a typicaltreatment beam line. A parallel particle beam (5 mm FWHM) that passes through a nozzle(including a thin vacuum window and beam monitors) and enters a water target placed at1 m distance from nozzle exit has been simulated. At low energies the beam width is mainlydetermined by scattering in the nozzle, while at higher energies the scattering in the targetdominates. Carbon ions show a much smaller spread than protons for the same penetrationdepth. From Schardt [23].

Figure 2.7: Monte Carlo simulation of a 230 MeV proton pencil beam traversing a waterphantom. Picture courtesy of K. Zink.

2.2. BIOLOGICAL ASPECTS 37

complex, radiation damage from heavy ions is larger than photons’. An example of

microscopic dose deposition distributions for X-rays and 15 MeV/u carbon ions is

shown in Figure 2.8.

Figure 2.8: Illustration of the different microscopic dose distribution by X-rays and15 MeV/u carbon ions. In both cases the macroscopic dose is 2 Gy. From Scholz [24]

Relative Biological Effectiveness and cell survival curves

In order to estimate correctly the effectiveness of heavy ions as projectiles, the

definition of Relative Biological Effectiveness (RBE) must be introduced. The RBE

is a very powerful and versatile concept that takes into account and, to some extent

summarizes, several treatment specific parameters, such as: radiation quality, tissue

specific response, biological endpoint (e.g. TCP and normal tissue complication) and

the dose. RBE is defined as the ratio of the dose of a reference radiation (typically60Co γ-rays) and the dose of the radiation under test needed to produce the same

biological effect (this is usually referred to as iso-effect condition).

RBEiso =Dref

Dtest(2.3)

It is of fundamental importance to note that not only is the RBE different in each

biological tissue, but it can be different for every location of the treatment, even

within the same tumor volume. This feature must therefore be taken into account

whenever the treatment is being planned, e.g. developing more sophisticated models

for the determination of RBE values.

A very powerful tool commonly used in radiobiology to compare the different

effects of different radiation types are cell survival curves. These curves illustrate the

relationship between the fraction of cells that maintain their reproductive integrity

and the absorbed dose. Conventionally the surviving fraction (S, defined as the ratio


of survivor cells and seed cells) is depicted on a logarithmic scale on the ordinate

against dose on a linear scale on the abscissa. The radiation type is characterized by

a different contour shape. Densely ionizing radiations show an almost exponential

relationship between survival and dose, represented as a straight line on the semi-

log plot. On the contrary, sparsely ionizing radiation curves show an initial slope

followed by a shoulder region and then an almost straight line for high values of the

dose. The most common way to parametrize the survival is by means of the Linear

Quadratic (LQ) model developed by Hall [25]:

S(D) =Nsurv

Nseed= e−(αD+βD2) (2.4)

where D is the absorbed dose and α [Gy−1] and β [Gy−2] are two experimental

parameters (that depend on tissue and tumor type) that characterize the initial slope

of the curve and its bending respectively; the ratio α/β defines the shoulder of the

curve and represents the amount of dose for which linear term contribution equals

the quadratic term. Moreover, from these plots it is possible to graphically determine

RBE values of a certain radiation, fixing a determined survival level. An example is

shown in Figure 2.9.

Figure 2.9: Cell survival curves and RBE determination for 10% and 1% survival level fora typical heavy ion (red, dashed) and photon (black, solid) irradiation. Confronting the twocurves for a certain survival rate, it can be noted that RBE is not constant with D even for thesame radiation.

Summarizing, RBE is a very powerful benchmark to describe radiation efficacy

in tumor cells killing. But it must be reminded that it is not a constant value for a

given radiation2: fast moving heavy ions have low LET and hence RBE is approx-

imately one (i.e. close to that of X-rays), slow heavy ions have high LET and then2this holds true for heavy ions. For treatment planning calculations with protons a constant value

of RBE = 1.1 is typically used.

2.3. PROTONS OR 12C 39

are more effective than photons in killing human cells. This can represent an advan-

tage for tumor therapy, since in the entrance channel (where ion velocity is high) the

killing efficiency must be as low as possible, while in the Bragg peak region (where

the ion is about to stop) it will be enhanced.

Oxygen Enhancement Ratio

When tumors are growing in size new vessels need to be generated to supply oxy-

gen to the cells in the tumor core. For various reasons, e.g. vessels are not generated

fast enough or their quality is not good, this can result in hypoxic regions (regions

with lower oxygen level than normal cells) and this poses a demanding challenge in

tumor therapy. Hypoxic regions, in fact, occur frequently in the center of the cancer

mass and are characterized by a larger radio-resistance. This effect is still not well

understood but can be quantified defining the Oxygen Enhancement Ratio (OER):

OER =Dhypoxic

Daerobic(2.5)

where Dhypoxic and Daerobic are the doses with reduced and normal oxygen supply

respectively resulting in the same clinical effect. Typically is around 3 for conven-

tional radiation, while is somewhat lower for heavy ions. In Figure 2.10 are reported

the cell survival studies carried out at LBL laboratories as a preparation for heavy

ion treatments. As can be observed, the difference between hypoxic and normal cells

is reduced for high-LET radiation as their curves tend to converge. Moreover, the

OER decreases as particle energy decreases, as one could expect from highly ioniz-

ing radiation. A consistent behavior has been observed for a wide variety of ions and

cell lineages Barendsen et al. [26], Bewley [27], Furusawa et al. [28] and Staab et

al. [29], where minimum OER values have been found for heavier ions, such as neon

or carbon with respect to light ions (e.g. helium). These lower values are probably

due to the higher radiation damage caused by ion direct hits, that is less sensitive to

the presence of oxygen, compared to the indirect hits induced by free-radicals (typ-

ical of X-rays). In hypoxic regions, in fact, the amount of free-radicals that can be

produced is lower than in normoxic cells, keeping dose constant.

2.3 Protons or 12C

As far as it has been discussed, hadrontherapy seems a promising alternative to

conventional radiotherapy for those applications where the use of photons or surgery


Figure 2.10: Influence of oxygen level on cell survival of human kidney cells for carbonions at different energies and hence different LET: 33 keV/µm (blue) and 118 keV/µm (red)compared to X-rays (black). Curves based on experimental data by Blakely et al. [30]. FromSchardt et al. [23].

is particularly discouraged (e.g. treatment deep seated tumors or malignancies near

organs at risk). In order to give a wider overview and a deeper insight on the two main

“competing technologies” in hadrontherapy, in this section the main advantages and

disadvantages of protons and carbon ions will be briefly discussed.

As introduced in Chapter 1, heavy ions undergo nuclear fragmentation as a con-

sequence of their interaction with the target (fragmentation in air has a much smaller

impact). This produces a certain amount of low Z fragments that lead, from a treat-

ment point of view, to several drawbacks: fragments have longer range, different

directions and different RBE with respect to primary particles. An overall mitigation

of the beam occurs and this is the reason why there is a visible tail in the Bragg peak

curve of carbon ions in Figure 2.1. On the contrary, protons nuclear fragmentation is

a negligible effect and the relative depth-dose curves show a sharp falloff.

A second physical aspect that must be considered involves multiple scattering.

From equation (1.10) is clear that the deflection is inversely proportional to particle

mass. This is the reason why carbon ions suffer much less lateral beam spread than

protons, as it is shown in Figure 2.11 and Figure 2.12. Therapeutically speaking, a

lower beam spread translates in a more definite dose deposition and hence in a more

precise tumor conformation.

Another key feature of carbon beam is a higher value of RBE with respect to

2.3. PROTONS OR 12C 41

Figure 2.11: X-ray film images of a collimated carbon ion (top) and proton (bottom) beamin water as a function of depth. The blurring effect visible from 7.5 cm bottom film is a clearindication of the higher multiple scattering undergone by protons.

(a) (b)

Figure 2.12: Treatment planning comparison for carbon ions (a) and protons (b). A bet-ter tumor conformation and normal tissue sparing due to lower multiple scattering can behighlighted for carbon ions. Pictures courtesy of GSI (a) and iThemba labs, Cape Town (b).

protons (especially in the Bragg peak region), that makes heavy ions even more ef-

fective in tumor killing and can be easily understood from Figure 2.2, where proton

and carbon ionization tracks are reported for different particle energy. The ionization

of carbon ions is, in fact, so dense that the probability of a double ionization on both

DNA strands is much higher when compared to sparsely ionizing proton tracks. This

leads to a more complex cell damage that is harder to be repaired. Furthermore, the

effects produced with carbon ion irradiation are less sensitive to cells oxygenation,


being the OER in the Bragg peak region close to 1.

Finally, an undeniable advantage of proton therapy lies in the lower cost of a

proton facility with respect to a carbon ions accelerator. Protons, in fact, can be

accelerated to hadrontherapy’s typical energies by means of cyclotrons (normal or

super conducting) that can easily fit into a hospital environment. Carbon ions, on

the other hand, need a much bigger facility, being their mass twelve times the one

of protons and their magnetic rigidity (defined as R = Bρ = p/q) two times larger

for the same particle velocity. This is the reason why all the existing centers use

a synchrotron (with a diameter of tens of meters) to accelerate ions heavier than

protons. This implies that bigger, more complex and more expensive facilities must

be operated.

2.4 Beam delivery techniques

In order to cover the entire tumor region, the Bragg peak must be spread out

overlapping several beams with different energies. The resulting Spread Out Bragg

Peak (SOBP) aims to provide a constant biological effect within the target volume.

Thus, the Treatment Planning System (TPS) must take into account the variation of

the RBE as a function of the penetration depth and of the beam type. For instance,

the distal part of the volume, that is irradiated only with highly effective ions, will

receive a higher dose with respect to the more proximal regions, for which the to-

tal dose deposited is the sum of the contribution of all the low-RBE traversing ions.

This leads to the flat profile shown in Figure 2.13. In order to homogeneously dis-

tribute the dose on the target area, as planned in the TPS, two main strategies have

been followed in the various ion therapy facilities all over the world: passive beam

modulation and active beam scanning. As the name suggests, passive systems adapt

in three dimensions the beam to the target volume only using passive field shaping

elements (schematically shown in Figure 2.14). The initially narrow beam delivered

by the accelerator is broadened by a scatterer, then the monoenergetic particles are

spread out with a range modulator, in order to cover the whole volume depth. At

this point an additional range shifting can be performed and then a collimator and

a compensator (tailored specifically for each patient) adapt the beam shape to the

target. One of the major limitations of this technique is SOBP fixed width. This, in

fact, can lead to a significant dose deposition outside the target volume (especially in

the proximal part, since the particle range is adjusted to match the distal contours),

as shown in Figure 2.14. Even though this problem could be partially overcome (di-

2.4. BEAM DELIVERY TECHNIQUES 43

Figure 2.13: Spread out Bragg peaks with carbon ions (red) and protons (green) comparedto the dose deposited by photons (blue). From Durante et al. [22]

Figure 2.14: Scheme of a fully passive modulation delivery system. All the principal ele-ments are outlined: the scattering system that broadens the beam, the range modulator forenergy modulation and the range shifter to spread out the Bragg peak. Healthy tissues areshielded by a collimator, while the adaptation to the distal contour of the tumor is performedwith a compensator. The net result is a non negligible dose to the normal tissues in theproximal part of the tumor (double hatched area). From Schardt et al. [23]

viding the tumor volume in more sub-volumes which are irradiated consecutively),

another limitation arise from the presence of several centimeters of material directly

on the beam path: the dose from secondary particles (especially neutrons).

In the second approach, instead, the volume is divided in several iso-energetic

slices and each slice is sub-divided in a grid of elementary volumes (voxels). Each


voxel is then sequentially irradiated by the scanning beam by means of two pairs of

deflecting magnets. The scan path follows a zigzag line connecting all the voxels

in the grid. When an entire slice has been irradiated, the beam extraction is inter-

rupted, extraction energy is then changed and the irradiation of the next slice can

begin. A sketch of this second technique is shown in Figure 2.15. The active scan-

Figure 2.15: Left: GSI active scanning system working principle. The target volume isirradiated by moving a pencil beam with fast scanning magnets, beam parameters are sup-plied synchronously to each pulse by control system. Right: the entire tumor is divided inseveral iso-energetic slices, (the slice being irradiated is magnified). During the irradiationeach voxel (white dot) receives the planned dose, the green dots represent pencil beam arrivalpoint. From Schardt et al. [23]

ning has several advantages: no patient specific hardware is needed for treatment

(except for immobilization); any irregular volume can, theoretically, be homoge-

neously irradiated; dose can be varied for each voxel (this allows to compensate for

pre-irradiation of proximal regions); the material in the beam line can be minimized,

reducing beam attenuation and fragmentation. On the other hand, more demanding

control and safety systems are required together with remarkable accelerator perfor-

mances on stability and reproducibility of beam position. However, active scanning

allows a much more flexible capability to tailor the dose distribution than passive de-

livery systems. For this reason the term Intensity Modulated Particle Therapy (IMPT)

has been introduced, in analogy to the IMRT techniques in photon therapy, to address

such delivery system.

For a long time the only two facilities that pioneered this latter approach were

PSI (Switzerland) and GSI (Germany) for protons and carbon ions irradiation respec-

tively. Their research on the active scanning technique, albeit with some variations,

proceeded in parallel and the acquired experience represents the basis for comparison

for all the other treatment facilities worldwide and also for industrial solutions.


Recently, the National Centre of Oncology (CNAO) was created in Pavia (through

the collaboration of the Istituto Nazionale di Fisica Nucleare (INFN), CERN (Switzer-

land), GSI (Germany), LPSC (France) and of the University of Pavia (Italy)) with

the goal of treating tumors by using both protons and carbon ions. It operates a

synchrotron capable of accelerating protons up to 250 MeV and carbon ions up to

480 MeV/u with an active scanning technology. At the end of 2011 the first patient

course of treatment with protons was completed and a year later the first carbon ion

treatment started. Nowadays the center normally operates with both particles on a

daily basis.

Gantries

In conventional radiotherapy, as well as for other imaging techniques like MRI,

CT or PET, the patient is treated in supine position, in order to minimize unwanted

organ movements. The electron linac is mounted, in fact, on a rotational support

(gantry) that, in combination with the routable patient couch, allows to choose the

most favorable angles for the treatment. Every commercial radiotherapy system in-

cludes a 360 rotating gantry and there is not any limitation on the angles that can be

used for therapy.

During particle therapy’s early stages, i.e. when treatments were performed in-

side research laboratories with large accelerators designed for nuclear physics re-

search, the beam was typically transported horizontally. The scenery changed when

the first proton therapy facilities were planned. In order to demonstrate the superi-

ority of particle therapy, a full exploitation of the more favorable depth-dose profile

was required. The main technical issue is the high magnetic rigidity of the beam that

implies a bending radius of the order of 1 m. For heavy ions the situation is much

worse, because an even higher bending power is required (this is the reason why

carbon ion facilities need larger accelerators). The magnetic rigidity of 380 MeV/u

carbon ions with a range of 25 cm in water is, in fact, about three times the one of

protons with the same range. Furthermore, a high precision on the rotating move-

ment is required. For all the aforementioned reasons, a gantry system for ion therapy

represents an expensive and a very challenging work of engineering. The first ro-

tating isocentric gantry system for heavy ions was built at HIT center (Heidelberg,

sketched in Figure 2.16) and is in operation for both protons and carbon ions since

late 2012.


(a) (b)

Figure 2.16: (a) HIT gantry treatment room 3D drawing. (b) Gantry view from the accel-erator room. With its 13 m diameter, 25 m length and 670 tons of weight (compared to theusual 100÷120 tons of proton gantries) this is the largest gantry ever built. Figure (a) FromHIT website [31], Figure (b) courtesy of University Hospital Heidelberg.

Treatment of moving targets

So far organ irradiation with scanned beams has been carried out only in areas

that could be immobilized by external aids. In these cases the target can be assumed

to be still and the uncertainties due to patient motion (e.g. by breathing) are negli-

gible. The patient needs, however, to be immobilized with masks, belts or special

frames, in order to take advantage of the highly conformal dose deposition. This

procedure can be problematic if the target organ is in the abdomen or in the thorax,

where breathing motion or pressure related problems (e.g. bladder) are unavoidable.

Moreover motion patterns are in general complex even though in the upper abdom-

inal region are mostly translational. This can lead to variation in the radiological

path length of the target voxels, that for hadrontherapy result in a high impact on

the quality of the treatment, since Bragg peak is shifted accordingly to such varia-

tion, as shown in Figure 2.17 and Figure 2.18. Conventional radiotherapy does not

suffer from this complication, being the depth-dose variations negligible. Irradiation

of moving targets is a very active field of research and several options to take into

account patient motion have been suggested so far:

1. Planned target volume expansion. In this way the moving target results com-

pletely covered at any time. This has the clear disadvantage that the dose on


(a) (b)

(c) (d)

Figure 2.17: Calculated dose deposition for a lung tumor without (a) and with motion (b).As it is clearly visible, the presence of motion leads to severe overdosage or underdosage inthe target volume. Carbon ions range modification during the two breathing phases: inhale(c) and exhale (d). Iso-range curves are shown in blue (2 cm), green (4 cm), yellow (6 cm),orange (8 cm) and red (10 cm). Figures courtesy of C. Bert, private communication.

normal tissues limits the overall dose that can be given to the target volume.

2. Rescanning. This strategy is based on a statistical assumption: if the scanning

is repeated N times, the variance of the average dose decreases with a factor

of 1/√N , if target motion and beam motion are considered uncorrelated. This

technique has the disadvantage of prolonging the irradiation time and, since the

dose per scan has to be lowered, it can cause problems to the beam monitoring

ionization chambers, that are not sensitive to low currents.

3. Gating. In contrast to the previous options this one requires the monitoring

of breathing cycle. Observing the time evolution of the target motion a flat

minimum region can be found at the end of the exhale phase. If the irradia-

tion is restricted to this time frame, uncertainties due to target motion can be

reduced to less than 10% of the free breathing case. The only drawback is the


Figure 2.18: As a consequence of breathing induced motion, the same beam could traveltrough different beam paths causing a shift of Bragg peak position. While this effect is almostnegligible for photons, it has a higher impact on carbon ions where a large amount of energycould be deposited outside the tumor volume (red vertical lines).

prolonged treatment time needed to keep constant the delivered dose.

4. Tracking. This strategy requires a synchronous three dimensional online mo-

tion compensation. The beam, in fact, must follow target movements at any

time and ideally this approach should lead to the same result of the static case.

Motion tracking technique is still under evaluation, but detailed simulations

have already demonstrated the potential of 3D motion compensation. How-

ever, some critical technology issues arise such as: the availability of a dy-

namic treatment planning and a beam delivery system permitting lateral tracing

and fast range adaptation (in order to properly shift the Bragg peak depth).

Recently, the combination of two amongst the aforementioned movement mitigation

strategies has been proposed, for instance gating and rescanning are planned to be

used together at the gantry2 at PSI Gottschalk et al. [32].

2.5 Dose monitoring

Hadrontherapy’s higher precision in tumor irradiation urgently demands the de-

velopment of brand new dose release monitoring techniques. This potential clinical

benefit requires, in fact, the conformal dose delivery to be monitored in-situ and non

invasively. A reliable treatment feedback is, in fact, extremely needed since heavy

ions dose release is much more sensitive to morphological variations or patient mis-

placements Karger et al. [33]. Monitoring in-vivo (or online) the energy deposition

2.5. DOSE MONITORING 49

during tumor treatment will surely boost therapy effectiveness, allowing for a fast

quality control within and around target volume. Then, a system capable of mea-

suring the delivered dose and able to verify the conformity of the actually irradiated

volume with the treatment planning is highly needed Pedroni et al. [34].

Unfortunately, X-rays standard methodologies for patient positioning cannot be

used, since these require that a non-negligible fraction of the treatment beam would

be transmitted through the patient. A simple reconstruction of patient position is in

fact performed on body anatomy or fiducial markers. Such techniques are clearly not

applicable in hadrontherapy, where the deposited energy sharply decreases behind

the target and almost no exit dose (for protons) or only a small fraction of it (for

carbon ions) is available after the Bragg peak. In the following, a brief state of the art

of the existing techniques, as well as the one still under evaluation from the scientific

community, for dose monitoring in hadrontherapy will be presented.

PET

Historically, the first method that has been proposed is the Positron Emission To-

mography (PET), which exploits the back to back photon production of β+ emitters

(mostly from 11C and 15O radioactive decay) generated as a consequence of the ir-

radiation after nuclear fragmentation of the target and the projectile Paans et al. [35]

and Parodi et al. [36]. Considering the geometrical constraints of a treatment room,

it is not possible to install a standard PET scanner to monitor the patient during the

irradiation. Only limited geometries are, in fact, allowed (so-called double head),

but these are limited by a low angular acceptance and by the presence of artifacts

that limit the quality of the reconstructed image Pawelke et al.[37] and Enghardt et

al. [38]. The availability of Time of Flight (ToF hereafter) techniques, that exploit

also the time information carried by the two collinear photons, has reduced the back-

ground noise and the artifacts of standard PET, leaving untouched the acceptance

issues though. Another limitation of this approach is its intrinsic off-line nature,

given the rather long 11C half-life (≈ 20 minutes). This does not allow to collect

sufficient data within treatment duration, causing a spatial resolution worsening. The

aforementioned limitations can be avoided performing an off-line PET, i.e. placing

the patient inside a conventional PET scanner just after the treatment. On the other

hand, with this latter solution, metabolic processes (e.g. blood circulation) interact

with the radioactive nuclides. The overall image quality and the spatial relation be-

tween dose deposited and activity will then appear deteriorated. Fortunately, this

latter effect is well taken into account by Monte Carlo simulations, it is then possible


to reconstruct the dose deposition pattern from β+ activity even though this do not

show a clear correlation with the expected dose profile, as shown in Figure 2.19

Figure 2.19: Top: Treatment plan (left) and Monte Carlo calculation (right) of the dose re-ceived by a patient with pituitary adenoma treated with two orthogonal fields (lateral followedby posterior-anterior) at 0.9 GyE/field. Bottom: Measured (left) and Monte Carlo calculatedβ+ activity. Range of color wash display is from blue (minimum) to red (maximum). FromParodi et al. [39]

However, this opportunity has been tested at Massachusetts General Hospital

and at Heidelberg Ion-Beam Therapy Center (HIT) for several clinical cases Parodi

et al. [40] [39].

Prompt photons

All the issues of the PET approach have called the scientific community upon

the development of a novel monitoring technique that uses the proved correlation be-

tween Bragg peak position and prompt photons emission region Min et al. [41] [42]

Testa et al. [43] and Agodi et al. [44]. Since prompt radiation occurs within few ns as

a result of target and projectile nuclear de-excitation, this method is metabolism in-

2.5. DOSE MONITORING 51

dependent. In order to detect prompt radiation, a Single Photon Emission Computed

Tomography (SPECT) approach can be followed. Moreover, the geometrical con-

straints are less stringent with respect to PET, since the detectors are not requested

to be placed one in front of the other. Unfortunately a standard SPECT solution

cannot be used in practice, given prompt photons rather wide energy spectrum (that

it has been measured by Agodi et al. [44] and is comprised between 1÷10 MeV),

that would require too thick collimators leading to an insufficient statistics. An in-

novative approach, with respect to SPECT, would be to realize a Compton camera

(as proposed by Kabuki et al. [45]) in order to track the prompt radiation. In its

simplest version only two position detectors with a good energy resolution can be

employed (a scatterer and an absorber, that must detect and contain Compton elec-

tron and scattered gamma respectively). The information about the photon direction

is then obtained via software.

More refined solutions can be found in astrophysics applications that could be

tailored to this specific context: e.g. detectors able to reconstruct both electron and

gamma ray trajectories after Compton scattering inside the detector itself (Kormoll

et al. [46]). These latter systems are currently under evaluation by the scientific com-

munity, but they may suffer from low statistics issues, since the amount of secondary

photons produced during a standard treatment is limited. In order to enhance the

available statistics, the angular acceptance could be increased, for instance widening

the dimensions of the detector or reducing its distance from the patient. Unfortu-

nately, this solution is not always compatible with the available space in treatment

rooms. Moreover, the neutron background, always present in treatment rooms, could

represent an unwanted and unavoidable source of additional noise for such a detector.

The use of prompt photons as instruments to evaluate the dose deposition during a

hadrontherapy treatment is still in its prototyping phase, this means that it has never

been used in a clinical environment so far.

Charged particles

A recent proposal, based on novel measurements of secondary charged parti-

cles (mostly composed by hydrogen and its isotopes) produced after the interaction

between target and projectile Braunn et al. [47], Agodi et al. [48], suggests to ex-

ploit such radiation for Bragg peak monitoring. The kinetic energy of such particles

is comprised between 10÷150 MeV, while their production region spans the whole

beam path inside the patient. The energy spectrum varies with the emission angle,

being high energetic protons production more favored by forward emission (with re-


spect to the beam direction). Since secondary protons production follows the beam

path, its location can be correlated with Bragg peak position. Additional measure-

ments of secondary charged particles produced as a consequence of phantom irradia-

tion have been recently performed at GSI laboratories Piersanti et al. [49] and at HIT

Gwosch et al. [50]. In both cases the results seem to encourage the exploitation of

secondary protons to monitor the dose release. Additional data from phantom irradi-

ation with a therapeutical proton beam have been collected at CNAO clinical facility

and are about to be published.

What has been observed so far is a clear correlation between charged particle

emission point and Bragg peak position (as it will be shown in the next chapter).

Then, it has been proposed that the shape of the emission profile could be used to

identify the Bragg peak position during each irradiation. Moreover, this profile has a

very steep rise (in correspondence to the patient entry channel) and hence could be

also potentially used to verify patient correct positioning online.

A future detector, capable of exploiting secondary charged radiation, has to be

made of a tracker and a calorimeter in order to point back each trajectory and ap-

propriately weight it according to its energy. Given the actual know-how, charged

particles tracking and energy measurement (in the MeV range) does not represent a

technology issue. However, especially for proton beams where the target is the only

actor in the fragmentation process, some statistics issues could arise for high angle

measurement (90 or 60 with respect to the beam direction). This could be a possi-

ble limitation of this novel approach that, in order to represent a valid alternative to

PET, will need nevertheless extensive testing and solid results.

Summarizing, at the state of the art there is not any monitoring system for hadron-

therapy currently used in medical routine, while systems that exploits PET or SPECT

technologies are now under evaluation by the international community and have been

already tested for some clinical cases. These latter systems, however, don’t seem to

guarantee a concrete feasibility for online monitoring given prompt photons wide

energy spectrum. The opportunity to use Compton cameras or secondary charged

particles, instead, is a very recent discovery that could pave the way for new interest-

ing possibilities.

CHAPTER

3

Measurement of secondaryradiation

Content

3.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Start Counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Drift Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Angle of detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.2 Prompt photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Energy measurement . . . . . . . . . . . . . . . . . . . . . . . . . 61

Rate measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Preliminary data with GSI 220 MeV 12C beam . . . . . . . . . . . 64

3.3 Charged secondary particles . . . . . . . . . . . . . . . . . . . . . 66

Particle identification and fluxes measurement . . . . . . . . . . . . 66

Bragg peak position monitoring . . . . . . . . . . . . . . . . . . . 69

Charged particles production region . . . . . . . . . . . . . . . . . 71

In order to meet hadrontherapy’s improved capability in matching the dose re-

lease with cancer position, new dose monitoring techniques need to be developed

and introduced into clinical use. A careful study of charged and neutral particles,

produced as a consequence of nuclear fragmentation and de-excitation processes,

53

54 CHAPTER 3. MEASUREMENT OF SECONDARY RADIATION

plays a crucial role in the design of any dose monitoring device and it would be

extremely useful to tune Monte Carlo simulations.

During patient irradiation, in fact, several interaction mechanisms take place and

both neutral and charged secondary radiation is produced. The former is composed

mostly of prompt photons (emitted as a consequence of nuclear de-excitation of

the target) and back-to-back photons (produced after positron emission, and subse-

quent annihilation, by β+ emitters, like 15O and 11C, created during the irradiation).

Charged particles, on the other hand, are produced as a consequence of nuclear frag-

mentation of the projectile (mostly in forward direction) and of the target (almost

isotropic but with lower energies).

The uncertainty on energy release position can be due to several factors: cal-

ibration of the CT images, possible patient morphological changes or patient mis-

positioning on the treatment couch. Hence, the design of a novel imaging detector,

that can exploit the secondary radiation produced during patient irradiation, is eagerly

needed.

However, the key features of such secondary radiation (energy spectrum, fluxes,

cross sections and so on) for this kind of interactions in this energy range are still

rather unexplored and must be better understood.

Two main products of the target-projectile interaction will be described in the fol-

lowing: prompt photons and secondary charged particles production from 12C beam

impinging on a poly-methyl-metacrylate (PMMA) target. Three different on beam

measurements will be briefly reviewed in this chapter: prompt photons (Agodi et

al. [44]) and charged particles production (Agodi et al. [48]) from 80 MeV/u fully

stripped 12C on PMMA performed at LNS-INFN Laboratories (Catania, Italy) and

charged particles production from 220 MeV/u fully stripped 12C on PMMA (Pier-

santi et al. [49]) performed at GSI Laboratories (Darmstadt, Germany).

3.1 Experimental setup

All the aforementioned measurements shared the same experimental setup, with

some minor changes due to the different beam energies and data taking conditions

though. A fast plastic start scintillator (Start Counter), a PMMA target, a charged

particle tracker (Drift Chamber) and a calorimeter (LYSO), used to detect both neu-

tral and charged radiation, represent the common detectors used. For GSI data taking

an additional Start Counter and a Veto plastic scintillator (2 mm thick), placed in

front of the Drift Chamber in order to stop low energy electrons (E < 0.6 MeV),

3.1. EXPERIMENTAL SETUP 55

have been employed. A sketch of the experimental setup of both measurements is

schematically shown in Figure 3.1.

Figure 3.1: Schematic view of the experimental setup for the two experiments; in both casesthe DAQ is triggered with the coincidence of the Start Counter and LYSO. The Veto plasticscintillator has been included to stop low energy electrons before entering the Drift Chamber.

A PMMA cube (4×4×4 cm3) has been chosen as target for LNS measurement

(since the range of 80 MeV/u 12C is of the order of 2 cm), while the ≈ 10 cm range

of GSI 220 MeV/u ions demanded a longer target (5×5×20 cm3).

Start Counter

The Start Counter is made of a 1.1 mm thick plastic scintillator (BC-404) read out

by two photomultiplier tubes (Hamamatsu H10580) and it is placed directly on the

beam line. This detector has been designed for timing and triggering purposes and

holds a role of fundamental importance. It aims, in fact, at secondary particles Time

of Flight (ToF hereafter) measurement as well as incident carbon ions measurement.

In order to reduce the background noise and to increase the time resolution, the time

coincidence of the two PMTs has been taken as trigger reference signal and in the

following the term Start Counter will refer to this quantity.


Drift Chamber

A Drift Chamber, made of twelve planes (each one composed of three cells) dis-

tributed on two views, has been used as charged particle tracker and is shown in

Figure 3.2. Some dedicated studies on Drift Chamber efficiency and spatial resolu-

tion have been performed in order to find its best working point. Efficiency plot as

a function of high voltage and spatial resolution as a function of the distance from

sense wires have been carried out and are shown in Figure 3.3 and Figure 3.4

(a)

(b)

Figure 3.2: (a) Drift Chamber mechanical drawing. (b) Drift Chamber lateral layout, all thesense wires of the lateral view are shown (red dots).

It has been operated with an Ar/CO2 80%-20% gas mixture and its performances

(single cell spatial resolution σDCH ≤ 200 µm, single cell efficiency εDCH = (93± 3)%

have been reviewed by Abou Haidar et al. [51], since this detector has been used as

beam monitor in the FIRST experiment at GSI (Pleskac et al [52]). Apart from


Figure 3.3: Drift Chamber efficiency study performed at LNS with different gas mixturesand ionizing particles. 80 MeV/u carbon ions with P10 (blue) and ArCO2 80%-20% (black).80 MeV protons with ArCO2 80%-20% (red).

Figure 3.4: Drift Chamber single cell spatial resolution as a function of the track distancefrom sense wire. Data from LNS 80 MeV protons dataset.

charged particles tracking, the Drift Chamber plays also the role of charged particles

veto, neutral events, in fact, are selected when no signal comes out of it.

Calorimeter

Finally, the calorimeter is made of a 2×2 matrix of 1.5×1.5×12 cm3 cerium-

doped Lutetium Yttrium ortho-Silicate (LYSO) crystals, whose scintillation light is

read out by one EMI 9814B photomultiplier. The reason of this choice lies in LYSO’s

very fast response (that is of crucial importance when measuring ToF), high density

and high light output. This particular type of crystals find a wide application in

medical imaging although in smaller sizes (e.g. PET imaging) and an exhaustive set


of LYSO features is reported in Table 3.1.

LYSO characteristics

Effective atomic number 66Density (g/cm3) 7.4Decay constant (ns) 40÷44Peak emission (nm) 428Light yield (% NaI) 75Refractive index 1.82

Table 3.1: LYSO optical characteristics.

Data acquisition

The Data acquisition system (DAQ hereafter) was triggered by Start Counter

and LYSO coincidence and both charge and arrival time of the secondary particles

have been recorded (by an ADC and a TDC module respectively). All the required

analogue signals need to be delayed in order to properly take into account signal

transit time in the various logic modules. For the Drift Chamber analysis, instead,

only the arrival time of the ionization electrons on the sense wires has been used. A

sketch of the DAQ signal flow chart that has been developed for the two experiments1

is shown in Figure 3.5 and a series of pictures of the experimental setup at GSI is

shown in Figure 3.6

Figure 3.5: Data acquisition flow chart. The trigger is defined as the time coincidencebetween Start Counter and LYSO detectors. Once the trigger signal has been created it goesto the dead time logic (DT) and the data acquisition can begin.

1A similar logic scheme has been developed together with a custom VME DAQ system for theradiation physics group at GSI, as reported by Piersanti et al. [53]


Figure 3.6: Top: Experimental setup mounting phase at GSI Laboratories. Bottom: DAQelectronics and drift chamber detail.

Angle of detection

As it can be noted from Figure 3.1, a detection angle of θ = 90 has been adopted

(this angle has been varied in Piersanti et al. [49] to measure charged particles pro-

duction also at θ = 60 and θ = 120). This choice has been made for two distinct

reasons: avoid DAQ dead time saturation and reconstruction issues due to beam-spot

size. In fact, if the emission spectrum of prompt photons is isotropic, charged parti-

cles’ is not. Secondary fragments are produced preferably with forward angles with

respect to the beam direction (θ < 90 in Figure 3.1). Hence, choosing a smaller

measurement angle will result in a higher number of charged fragments within de-

tector’s acceptance. This will lead to a higher DAQ rate and hence more likely to

dead time saturation. The second problem arise for every angle θ 6= 90. When any

charged particle track is pointed backwards to the PMMA, the emission shape spatial

resolution worsens as (sin θ)−1, due to the projection along the beam line, and this

effect could become dominant for small detection angles. Furthermore, if θ 6= 90,

the emission shape is convoluted with the size of the primary beam spot projected

on the beam line (see Figure 3.7), adding a term ∝ σbeam · cotg(θ) to the emission

profile. Thus, as the two aforementioned factors increases for smaller angles, the

tracking accuracy, from a geometrical point of view, improves with larger detection

angles.


Figure 3.7: Sketch of the beam spot size (grey cylinder) and its contribution to the recon-struction of the fragments emission region. The experimental setup is supposed to be at anangle θ with respect to the primary beam direction.

3.2 Prompt photons

In this section the main results obtained from the interaction of a 80 MeV/u12C beam on PMMA will be reviewed. Moreover, some preliminary data (yet un-

published) regarding prompt photon production from 220 MeV/u 12C GSI beam on

PMMA will be presented as well.

Calibration

Together with the standard 22Na (0.511 MeV) and 60Co (1.17 and 1.33 MeV)

radioactive sources, the LYSO energy calibration has been carried out exploiting a

source which produces photons of energy well above 1 MeV. Unfortunately it was

not possible to use one amongst the standard isotopes, given their usual low lifetime,

and an indirect production mechanism has been exploited instead. Thus, an AmBe

neutron source (2.5×106 neutrons/s) hosted inside a 5 cm thick paraffin (Cn H2n+2)

container has been used, as reported in Bellini et al. [54]. The container allowed both

to moderate the neutron flux (that otherwise would have saturated the detector) and

to produce two gamma lines: the first at 2.22 MeV from deuteron formation and the

second at 4.44 MeV from 12C∗ de-excitation. The measured spectrum is shown in

Figure 3.8. The two photon lines are clearly visible, together with the so-called single

escape lines (that is a phenomenon that occurs when one of the two collinear photons

produced by the annihilation of a positron escapes the detector without interacting).

Interposing a 2 mm thick nichel rod between the source and the detector it is possible

to generate a set of high energy lines centered around a mean value of 8.8 MeV. The

calibration curve is hence derived and is shown in Figure 3.9.

3.2. PROMPT PHOTONS 61

Figure 3.8: LYSO energy spectrum with AmBe source moderated with paraffin.

Figure 3.9: Linear calibration curve (black dashed) for LYSO detector obtained combining22Na, 60Co with AmBe data (red circles).

Energy measurement

In order to select a prompt photon event, the time difference (∆T ) between the

energy deposition in the LYSO (TLYSO) and carbon ion arrival time on the Start

Counter (TSC) is considered. The correlation between reconstructed photon energy

E and measured ∆T is shown in Figure 3.10a. Here four distinct regions can be

highlighted: prompt photons main population (green); a faster component (red) due

to prompt production inside the Start Counter; LYSO flat background noise (blue -

E < 2 MeV) and a diffuse cloud mostly due to neutrons whose arrival time is not

correlated with prompt radiation (magenta). From Figure 3.1 is evident how prompt

photons produced inside the Start Counter traverse a shorter path and hence are faster

than photons coming from the target. The shape of prompt photons population is


not vertical, as one would expect. This is due to a time slewing effect induced by

front-end electronics fixed voltage threshold. This artifact can be adjusted fitting the

distribution of ∆T in bins of energy and extracting the correction function C(E)

shown in Figure 3.10b. The energy spectrum as a function of the corrected time

∆Tcorr = ∆T − C(E) is reported in Figure 3.10c together with the time resolution

(σ∆Tcorr) of the detector as a function of the energy, Figure 3.10d. For E > 3 MeV

σ∆Tcorr ≈ 300 ps has been obtained.

(a) (b)

(c) (d)

Figure 3.10: (a) Calibrated LYSO energy as a function of ∆T , four major components areunderlined: (i) prompt photons produced inside the target (green - slower population, theirpath towards the detector is longer), (ii) prompt photons produced inside the start counter(red - faster component), (iii) a flat background with E < 2 MeV due to LYSO intrinsicnoise (blue), (iv) a diffused cloud mainly due to neutrons (magenta). (b) Estimated timeslewing correction. (c) Energy versus ∆T corrected spectrum. (d) Time resolution σ∆Tcorr asa function of the measured energy, for E >3 MeV a resolution of the order of 300 ps hasbeen achieved.

In order to estimate prompt radiation energy spectrum, the number of photons for

each energy bin has been calculated fitting the ∆Tcorr distribution with a superimpo-

sition of a Gaussian function (signal), centered in zero with a sigma fixed at σ∆Tcorr ,


and a polynomial function (background) and evaluating the area under the Gaussian.

This value has been corrected for the dead time fraction (εDT) of the DAQ and nor-

malized to the number of incident ions (for further details see Agodi et al. [44]). The

measured energy spectrum is shown in Figure 3.11 and it has been compared to the

one predicted by Monte Carlo code FLUKA (Ferrari et al. [55] and Battistoni et

al. [56]), obtained within the detector acceptance and folded with detectors response

(LYSO and Start Counter efficiency, resolution and acceptance). Data-Monte Carlo

agreement on the shape and on the normalization is not perfect, this is due to the

lack of experimental cross sections for these interactions in this energy range. For

this reason, yield and energy measurements, for both neutral and charged secondary

radiation, are eagerly needed by Monte Carlo community to improve the analytical

models currently employed to describe such reactions.

0

0.05

0.1

0.15

0.2

0.25

0.3

2 3 4 5 6 7 8 9 10

Cou

nts/

prim

ary

(x10

-6)

Energy [MeV]

Exp. DataSimulation

Figure 3.11: Data (black dots) - Monte Carlo (FLUKA, red solid line) comparison of promptphotons energy spectrum from a 80 MeV/u 12C beam impinging on PMMA target. Bothspectra are normalized to the number of incident ions.

Rate measurement

In order to design a detector that exploits prompt radiation to monitor the dose

deposition, the measurement of photons differential rate is of crucial importance to

assess the available statistics in a typical treatment. As first step, the fraction of

observed photons with E > 2 MeV (this energy threshold is needed to reject LYSO

intrinsic noise) has been evaluated as the ratio of measured prompt rate and carbon

ions rate. This fraction has been calculated and it averages to:

Fprompt =Rprompt

RC= (3.04± 0.01stat ± 0.20sys)× 10−6 (3.1)


as shown in Figure 3.12. An uncertainty contribution from systematics is required to

justify the data dispersion that is well above statistical fluctuations.

Figure 3.12: Fraction of prompt photons as a function of carbon ions beam rate. The redline is the linear fit to the data and the red band accounts for both systematic and statisticalerrors.

The double differential rate for prompt photons has been evaluated to be:

d2Nγ

dNC dΩ(θ) =

1

NmeasC /εSC

[Nmeasγ

εDT εSC εLYSO ΩLYSO

]90

(3.2)

where NmeasC is the number of carbon ions measured with the Start Counter, Nmeas

γ

is the number of prompt photons detected by LYSO, εDT is the dead time fraction of

the DAQ, εSC is the Start Counter detection efficiency εSC = (96 ± 1)% (as reviewed

in Agodi et al. [44]), ΩLYSO and εLYSO are the angular acceptance and scintillation

efficiency of LYSO detector. These last two quantities have been evaluated by using

FLUKA for all the isotopes and detection angles to be: ΩLYSO ' 1.6 × 10−4 sr and

εLYSO = (81.3 ± 2.5)%. For the aforementioned setup a flux of:

dN2γ

dNCdΩ(θ = 90) = (2.323± 0.007stat ± 0.151sys)× 10−3 sr−1 (3.3)

has been obtained.

Preliminary data with GSI 220 MeV 12C beam

Additionally, some preliminary data (yet unpublished) from 220 MeV 12C beam

impinging on a 5 × 5 × 20 cm3 PMMA target collected at GSI will be briefly re-

viewed in the following. The experimental setup is conceptually equivalent to the


one at LNS, as it can be noted comparing the upper sketch with the bottom one in

Figure 3.1. However, the main difference at GSI is due to the “therapeutic-like”

energy of the primary particles, if compared to the 80 MeV/u of LNS data taking.

Thus, the experiment outcome will be characterized by a more realistic (closer to the

clinical reality) energy spectrum and flux of prompt photons. The same data analysis

technique, that has been described in the previous paragraphs, has been used also

with this dataset, and prompt photons energy spectrum for different detection angles

is shown in Figure 3.13.

Figure 3.13: Energy spectra of prompt photons detected by LYSO scintillator at θ = 60,θ = 90 and θ = 120. These spectra have been normalized to the number of incident car-bon ions and have been corrected for dead time efficiency, detector efficiency and detectorgeometrical acceptance.

The fluxes for all the three detection angles have been estimated as well:

dN2γ


dN2γ


dN2γ


In the systematic error, the only contribution comes from the systematic error on the

dead time efficiency εDT. The rate at (θ = 90) can be compared to the one measured


by Agodi et al. [44] reported in equation (3.3). Since the path of the carbon ion

in the target is related with the number of prompt photons emitted, a different rate

for different energy beams is thus expected (since the depth is proportional to the

incident beam energy). As confirmation of this assumption, the beam with higher

energy produces a higher prompt photon flux than the lower one.

3.3 Charged secondary particles

Charged fragments can represent an innovative tool to monitor Bragg peak po-

sition during a hadrontherapy treatment. Their eventual use has been proposed only

recently and extensive data taking campaigns must be foreseen in order to assess

their real potential. In the following the main results of 80 MeV/u 12C on PMMA

(referred to as LNS) and 220 MeV/u 12C on PMMA (referred to as GSI) experiments

will be reviewed.

LNS measurement was aimed at protons flux evaluation and Bragg peak position

monitoring. Even though the beam energy is not in hadrontherapy typical range, the

capability to follow the Bragg peak shift, when changing the penetration depth of the

beam, and the estimation of protons flux are fundamental questions that need to be

addressed before this new technique could be even proposed. Then, with GSI mea-

surement some more refined aspects have been evaluated: the possibility to recon-

struct the emission shape of charged particles and a quantitative method to link some

geometrical parameters of this shape with the actual Bragg peak position. Moreover,

during this latter experiment different detection angles have been studied (θ = 60,

90 and 120).

Particle identification and fluxes measurement

As discussed in section 3.1 the Drift Chamber is used also as veto detector, to dis-

criminate between neutral and charged events. In fact, considering the experimental

setup geometry, an ion traveling from the target towards LYSO calorimeter will most

likely hit all the twelve tracking planes of the Drift Chamber. Hence, an event selec-

tion based on the number of wires fired by the ion can be performed. The distribution

of hit cells (Nhits) measured at GSI is shown in Figure 3.14, where data is compared

to Monte Carlo predictions for each hydrogen isotope. A clear peak at Nhits = 12

is observable, this indicates that charged particles tend to cross all the planes hitting

only one cell per plane. Then, each event with Nhits > 8 has been flagged as charged

particle. Isotopes discrimination can be performed exploiting ToF information car-

3.3. CHARGED SECONDARY PARTICLES 67

ried by charged particles together with the energy deposited inside LYSO crystal.

The ToF, as it has been recorded by front end electronics, is the sum of two con-

Figure 3.14: Comparison data (circles) and Monte Carlo (solid line) of the number of hitcells (Nhits) in the Drift Chamber when an event is recorded in the LYSO with E > 1 MeVat 90. In the simulation each isotope contribution has been underlined: protons (upwardtriangles), deuterons (squares) and tritons (downward triangles). The clear underestimationin the simulated data for Nhits < 7 could be due to several contributions: Monte Carlo lowerbackground (with respect to GSI experimental hall) and absence of electronic cross talk.

tributions: the time needed by a carbon ion to travel from the Start Counter to its

fragmentation point (x) in the target (Tch(x) − T12C) and the time needed to travel

from the fragmentation point to LYSO detector (TLY − Tch(x)). An estimate of the

time needed by the carbons to reach their interaction point has been evaluated with

FLUKA. Using this information the ToF associated to each fragment can be finally

calculated. An example of particle identification performed on GSI data (θ = 90) is

reported in Figure 3.15a, a Monte Carlo comparison is shown in Figure 3.15b, where

a very good agreement between data and simulation can be noticed. Three popu-

lations are clearly visible in the plots, which correspond to protons, deuterons and

tritons. For θ = 120, see Figure 3.15d, there is a significant drop in statistics, for

this reason all the measurements and the results that will be reviewed in the following

will only refer to the more abundant data samples at 60 and 90.

The double differential production rate of each secondary particle isotope nor-

malized to the number of incoming carbon ions (NC) has been estimated exploiting

the same definition reported in equation (3.2) with an additional term due to Drift


(a) (b)

(c) (d)

Figure 3.15: Energy versus ToF distributions. (a) Data θ = 90. (b) Monte Carlo θ = 90,single isotope contributions have been separated: protons (black), deuterons (red), tritons(green), electrons (blue). (c) Data θ = 60. (d) Data θ = 120. The lines used to separateprotons, deuterons and tritons in (a) are superimposed.

Chamber tracking efficiency (εtrack):

d2Np,d,t

dNCdΩ(θ) =

1

NC/ εSC

[Np,d,t

εDT εSC εtrack εLYSO ΩLYSO

]60,90

(3.7)

The Monte Carlo simulation of the experiment produced: εtrack = (93 ± 3)% and

96%<εLYSO<97% for all the isotopes and the angle configurations. The main source

of uncertainty on particles flux measurement is due to particle identification and dead

time estimation. The former has been evaluated by moving the boundary lines shown

in Figure 3.15a, obtaining a maximum relative error up to 20%, depending on the data

sample.

The yield of all isotopes normalized to the number of incoming carbon ions and

to the solid angle covered by the LYSO detector were calculated for the data sets at


60 and 90:

dN2p

dNCdΩ(θ = 60) = (11.03± 0.09stat ± 0.80sys)× 10−2 sr−1

dN2d


dN2t


dN2p


dN2d


dN2t


Bragg peak position monitoring

In order to change the penetration depth of the beam, the target has been placed on

a single axis movement stage, that allows to perform a position scan (along x axis, i.e.

beam direction) with an accuracy of 0.2 mm. Hence, shifting the target (to simulate

a Bragg peak displacement with respect to the experimental setup) would allow to

evaluate wether a correlation between the positions of Bragg peak and fragments

production peak does exist. The configuration with the centers of PMMA, Drift

Chamber and LYSO aligned along z has been taken as reference and the position of

the target in the stage reference frame has been named as “0”. From this point the

target has been moved up to 19 mm backward and 13 mm forward with respect to

x axis positive direction, as schematically shown in Figure 3.16.

From the Monte Carlo simulation of the experiment, Bragg peak expected po-

sition has been estimated to be xBragg = (11.0 ± 0.5) mm from the front face of the

PMMA, this has been also visually confirmed by direct observation of the target dete-

rioration after data taking, visible as a yellow band shown in Agodi et al. [57]. In the

current frame of reference (the front face of PMMA is at x = 2 cm), that corresponds

to xBragg = (9.0± 0.5) mm. Then, for each run with different target position, the pro-

duction point of the protons has been monitored using the mean of the Gaussian fit

to the distributions of the fragment emission coordinates xPMMA and yPMMA. Since

yPMMA is the coordinate of proton production in the vertical plane, it should not be

affected by the position scan. Thus, its behavior has been used to estimate the tech-

nique’s systematic uncertainty. The relationship between xPMMA, yPMMA and xBragg


Figure 3.16: Schematic view of Bragg peak position scanning performed during LNS ex-periment. The Bragg peak position relative to the “0” configuration has been determined withFLUKA to be: xBragg = (9.0 ± 0.5) mm. The picture is not to scale.

for proton energy Ekin > 60 MeV is shown in Figure 3.17. A linear behavior can

be clearly observed, meaning that charged secondary particle emission point follows

accurately Bragg peak movement. As expected, no dependency on yPMMA can be

noted, since the shift has been performed along x axis only.

Figure 3.17: Correlation between charged particles production coordinates mean values(xPMMA black dots, yPMMA white dots) and Bragg peak coordinate expected position (xBragg).Bragg peak position has been shifted moving the target along the beam direction (x coordi-nate in the current frame of reference). A clear linear dependency between xPMMA and xBraggcan be observed, while yPMMA shows no dependency at all.


Charged particles production region

As previously mentioned, once the tracks have been reconstructed in the Drift

Chamber, these are then extrapolated backwards to the PMMA position, in order to

identify charged fragment production point (xPMMA, yPMMA) along the beam path.

xPMMA distributions for the two experiments are shown in Figure 3.18 together with

the simulated dose deposition. A bi-dimensional reconstruction of the interaction

point has been carried out with GSI data, leading to the impressive shape reported

in Figure 3.19, where the front part of the target (up to Bragg peak position) can be

clearly identified from the extrapolation of Drift Chamber tracks.

(a) (b)

Figure 3.18: Simulated depth-dose distribution (hatched) superimposed on the longitudinalprofile (solid line) of secondary charged particles emission point as a function of the targetthickness (x) at 90. (a) LNS experiment: the beam enters the target in x = 2 cm and movestowards left. (b) GSI experiment: the beam travels from left to right and PMMA front face isin x = -(6.45 ± 0.02) cm.

Given the rather different beam energies a comparison between Figure 3.18a and

Figure 3.18b is not possible, however starting from GSI data (that have been obtained

on a therapeutical beam) a strategy to link the shape of the xPMMA distribution in

Figure 3.18b to the Bragg peak position has been developed. First of all, there is

a clear correlation between the beam entrance position and the sharp rising edge of

the emission profile. Moreover, since xPMMA distribution is well described by the

empirical function:

f(x) = p01

1 + exp(x−p1p2

) 1

1 + exp(−x−p3

p4

) + p5 (3.10)

it has been possible to link Bragg peak position to two specific parameters ∆40 and

δ40 of such function. These represent the width of f(x) at 40% of its maximum


Figure 3.19: GSI charged fragments emission point (xPMMA, yPMMA) spatial distribution at90. The vertical dashed line on the left indicates the coordinate of the beam entrance in thePMMA at xBE = -(6.45 ± 0.02) cm. The dashed line on the right indicates the theoreticalcalculation of the Bragg peak position xBragg = (1.80 ± 0.02) cm, in the current frame ofreference.

(∆40 = Xright - Xleft, being Xleft and Xright the x coordinates corresponding to the

rising and the falling edges respectively), and the distance between Xleft and the

x intercept of the tangent to f(x) at x =Xright, as shown in Figure 3.20. It is important

to note that the emission profiles of all isotopes relative to both datasets at 60 and

90 are well described by f(x).

The accuracy of this method strongly depends on several factors: the statistics

of collected data, multiple scattering suffered by the particle along the path inside

the patient and intrinsic fluctuation of nuclear fragmentation process, due to its sta-

tistical nature. While statistics of collected data strongly depends on the dose that

is being delivered and the geometrical acceptance of the detector, in the reminder of

this section the other two sources of uncertainty will be analyzed.

The contribution of multiple scattering to the global resolution can be evaluated

from the distribution of yPMMA. This, in fact, represents the vertical component of

the beam profile and should be, theoretically, comparable with the beam spot size

of the accelerator. This is nominally a Gaussian centered in y = 0 with a standard

deviation of σbeam ≈ 1 cm. Then, the multiple scattering worsening can be obtained

from:

σ2yPMMA

= σ2beam + σ2

MS + σ2DCH (3.11)


Figure 3.20: Longitudinal profile of charged particles emission point as a function of thetarget thickness described with the function proposed in equation 3.10. All the interestingquantities are represented as well as a graphical definition of Xleft and Xright.

where σ2yPMMA

can be derived from data (see Figure 3.21), while the quadrature con-

tribution of Drift Chamber tracking resolution (σDCH ≈ 200 µm) has to be swum

over 40 cm from the Drift Chamber to the beam line. In a worst case scenario this

will lead to:

σPMMADCH ≈ l · σDCH/d√

Nhits≈ 400 mm · 2 · 0.2 mm/80 mm√

4≈ 1 mm (3.12)

where l is the distance from the chamber to the target, d is the distance between

the first and the last plane of the chamber (80 mm) and a safe value of hit cells per

view Nhits = 4 has been chosen. Hence, for this particular setup, the uncertainty

due to multiple scattering has been inferred to be σMS ≈ 6 mm. This contribution

could increase of a factor 2÷3 during a real treatment, where the amount of material

traversed by the ions is somewhat larger. Multiple scattering can pollute the spatial

information carried by the particle and its minimization is of vital importance in

order to properly reconstruct the emission profile. However, considering the energy

spectra measured at GSI reported in Figure 3.22, selecting a particular subset of data

(e.g. protons with kinetic energy larger than 100 MeV), the deflection of particle

trajectories due to multiple scattering would be of minor importance.

In order to estimate the fluctuation of the emission mechanism, the available data

have been subdivided in reference samples of 103 events. These roughly correspond

to 2.3 × 108 impinging carbons at 90 and 4.7 × 107 at 60, according to the fluxes

reported in equation (3.8) and (3.9), given the reduced acceptance of the LYSO de-

tector. As a reference, in a standard treatment a single pencil beam aimed at the


Figure 3.21: Comparison between GSI data (left) and Monte Carlo simulation (right) ofyPMMA distribution at 90.

Figure 3.22: GSI measured kinetic energy at 90 for protons (blue), deuterons (red) andtritons (magenta).

distal contour of the tumor (for which the detector monitoring capability is of crucial

importance) receives an ion density of the order of 108 particles per cm3. Then, for

every subset of 103 events ∆40 and δ40 have been evaluated. All data sets acquired

at 60 need a further pre-processing step. The measured shape results, in fact, in a

convolution of the beam spot size σbeam and the detection angle: σ = σbeam · cotgθ


(as shown in Figure 3.7). The results on a population of 13 subsets at 90 and 100

at 60 are listed in Table 3.2 where the precision of the measurement of ∆40, δ40 and

Xleft and their mean values are reported.

Angle (deg) σ∆40 (cm) σδ40 (cm) σXleft (cm) ∆40 (cm) δ40 (cm)

90 0.34 0.37 0.08 6.60 ± 0.09 9.40 ± 0.1060 0.31 0.28 0.09 6.83 ± 0.03 9.44 ± 0.03

Table 3.2: Mean values and dispersion of ∆40 and δ40 parameters.

An extensive calibration campaign with several beam energies (and hence sev-

eral penetration depths) is eagerly needed and will be crucial for this method to be

validated. Furthermore, the precision obtained onXleft could represent an interesting

added value, since it is strongly related to the beam entrance position in the patient

and it potentially could be used to spot eventual patient mis-positioning during the

treatment.

CHAPTER

4

Dose Profiler optimization

Content

4.1 Detector overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

Neutral radiation operation mode . . . . . . . . . . . . . . . . . . . 79

Charged particles operation mode . . . . . . . . . . . . . . . . . . 81

4.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

Dose Profiler layout optimization . . . . . . . . . . . . . . . . . . . 83

In order to monitor the dose release during a hadrontherapy treatment, an innova-

tive detector able to exploit both prompt photons and charged fragments to identify

the Bragg peak position has been designed, and its project will be carefully described

from this chapter on. This twofold nature in a single detector is a unique feature,

never suggested so far, that will allow to maximize the information on dose depo-

sition that can be collected during a conventional treatment, considering its highly

restrictive time constraints. Lack of statistics, together with detector encumbrance

and clinical workflow necessities, is, in fact, one of the most challenging issues to

overcome when treatment-like conditions come into play. Detector spatial resolu-

tion and, therefore, reconstruction precision of secondary radiation emission, only

to mention a few, are strongly affected by the number of events actually available.

This is also one of the reasons why only small angles (with respect to beam direction)

have been considered for charged particles monitoring so far. The optimization of the

detection angle θ, as mentioned in the previous chapter, is a crucial task. At narrow

angles the measurement has the clear advantage that the emission flux is enhanced

77

78 CHAPTER 4. DOSE PROFILER OPTIMIZATION

and that charged particles energy spectrum is harder. Thus, the multiple scattering of

protons, deuterons and tritons (charged fragments or simply charged in the follow-

ing) inside the patient is minimized. On the other hand, due to the projection on the

beam line, the spatial resolution on the emission shape should worsen as sin(θ)−1

and this geometrical contribution could become dominant for small detection an-

gles. Furthermore, for measurement at θ 6= 90, the emission is convoluted with the

transverse beam spot size projected on the beam line. Both quoted effects get worse

as the detection angle shrinks. On the other hand, the spatial distribution of neu-

tral radiation is isotropic. This in principle does not pose any constraint for prompt

gamma detection, but in order to avoid DAQ saturation due to charged fragments for-

ward peaked emission distribution, and considering the limited space available for an

external monitoring device in a treatment room, detection angles larger than 30 are

strongly encouraged. Taking into account all the aforementioned issues, this proposal

has been included in the “INSIDE” project, that has been awarded a MIUR PRIN-

2010 funding. INSIDE foresees the development of a dual mode device that will be

installed and operated at CNAO treatment room, together with an online PET sys-

tem, at a detection angle θ ≥ 60 with respect to the beam direction. In Figure 4.1

is shown the 3D rendering of CNAO treatment room with the integration of the two

detectors.

4.1 Detector overview

The Dose Profiler has been designed to work as a charged particle detector and

a Compton camera simultaneously. It is composed of two main sub-detectors: a

tracker (made of six active planes) and a calorimeter (respectively TRK and CAL in

the following). Additionally, an electron absorber (ABS hereafter) has been placed

after the tracker, in order to prevent any recoil electron from reaching the calorimeter.

The reason of such choice will be discussed in the following paragraphs.

Such twofold nature, especially considering prompt gammas measured energy

spectrum (shown in Figure 3.11), implies a careful study and optimization of the ma-

terials that constitute the detector itself. Compactness, reliability, large geometrical

acceptance and high tracking efficiency represent, in fact, the minimum requirements

of such detector, considering its foreseen use into clinical workflow. A sketch of the

longitudinal section of the Dose Profiler and its 3D reconstruction taken during the

simulation phase is shown in Figure 4.2, where all the active elements, as well as the

building structures, are depicted.

4.1. DETECTOR OVERVIEW 79

Figure 4.1: 3D rendering of Dose Profiler integration (green) inside CNAO treatment room.(Top-left) parking position; (top-right) operation during treatment at +90; (bottom-left) op-eration during treatment at -90; (bottom-right) particular of Dose Profiler mechanical struc-ture.

Neutral radiation operation mode

As previously stated, prompt photons detection will be performed exploiting a

working principle similar to that of a Compton camera. Such device, in its classi-

cal realization, is made of two distinct detectors: a scatterer and an absorber. The

incoming photon, while traversing the scatterer medium, has a certain probability

to undergo Compton scattering, depending on thickness and atomic number of the

medium itself. This will produce a deflected photon (γ′), that is detected by the ab-

sorber (Eγ′ , ~rγ′) and a recoil electron (e′), whose energy and position are recorded

by the scatterer itself (Ee′ , xe′ , ye′ , ze′). From Compton equation (1.12) a cone of

acceptable directions is then derived. The original gamma ray source is determined

integrating different events (i.e. by the intersection of various cones).

A slightly different approach has been chosen for the Dose Profiler, that is com-

posed, in fact, by six scattering planes. These will provide additional information on

the electron, allowing to track also its direction. In order to close Compton kinemat-

ics, scattered photon direction must be detected as well. This can be done exploiting


(a) (b)

Figure 4.2: Dose Profiler simulated layout. (a) Dose Profiler longitudinal section. All theactive elements of the detector are present as well as the main support structures: trackingplanes (black - plastic scintillator), front-end electronics printed circuit boards (green - fiber-glass), electron absorber (cyan - plastic scintillator), calorimeter (red - LYSO) and detectorcase (gray - aluminum). (b) 3D view of the detector.

the high density scintillating crystal placed behind the ABS with a position sensitive

readout (e.g. using Multi-Anode-PhotoMultiplier Tubes). The choice of such a scin-

tillator is justified considering the final application of the detector, that must be as

compact as possible for its operation in a clinical environment. However, given the

compactness of the calorimeter and LYSO absorption length for the expected energy

range (≈ 16 ÷ 18 mm), the energy information of the Compton gamma would be

surely deteriorated because of poor photon containment or low interaction probabil-

ity. For this reason, a statistical approach for Compton kinematics reconstruction has

been proposed and it will be reviewed in the following chapter.

Additional issues arise wether both scattered photon and electron are detected

inside the CAL. In this situation at least two clusters of photoelectrons will reach

the photocathode, as shown in Figure 4.3. The localization of scattered photon is

thus more complicated (especially if clusters are close one to another) and generally

less precise. Moreover, the presence of a high Z material (such as LYSO, Zeff = 66)

results, for the electrons, in a higher probability of being back-scattered (Tabata et

al. [7] and Table 1.3). This will produce a backward traveling track inside the TRK,

that acts as background. For this reason a slab of plastic scintillator has been placed

in front of the calorimeter. Not only should the backscattering probability drastically

4.1. DETECTOR OVERVIEW 81

Figure 4.3: Simulation of a double cluster event in the calorimeter. In this particular casethe two populations are well separated and their boundaries are easily defined.

decrease (according to Tabata et al. [7] a reduction of a factor ten could be obtained)

but, if the thickness is properly adjusted, it should also absorb completely the electron

flux, reducing calorimeter clustering multiplicity and providing a very useful electron

energy measurement.

In the end, an additional help could come from the detection of e+ e− pairs,

produced after photon interaction with the TRK. This contribution is, of course, lim-

ited (its impact strongly depends on TRK building material) even though it could

complement Compton statistics only in the high energy range (i.e. Eγ ≥ 5 MeV).

Charged particles operation mode

As far as detector design is concerned, charged particles tracking in an energy

range of 10 ÷ 150 MeV does not represent a crucial issue from a technological

point of view. Dose Profiler spatial resolution, in fact, will be anyhow limited by

multiple scattering inside several centimeters of patient tissues. Since detector overall

resolution is given by the quadrature sum of the single uncertainty contributions, the

use of cutting-edge tracking devices with sub-millimetric precision would result in

an avoidable overshoot, when the uncertainty due to multiple scattering should be

comprised in the range of 8 ÷ 10 mm. For this reason, the tracker spatial resolution

has been designed to be of the order of few millimeters. In this way the overall


resolution should not remarkably worsen and, at the same time, the realization of

such detector will be not too critical in terms of costs and technology efforts.

Charged particles tracking will be performed by the six active layers that will pro-

vide a set of hit-points (xi, yi) and the same tracking algorithm of Compton electrons,

thoroughly described in the following chapter, will be used to reconstruct particle’s

trajectory. Moreover, the possibility to measure the energy of such radiation, even

with a poor resolution, would offer a valuable information on track quality. Charged

particles could be weighted, in fact, according to their kinetic energy, penalizing low

energy tracks that are more likely to have suffered larger deflection due to multiple

scattering inside the patient. For this reason also, a compact high density calorimeter

has been placed behind the TRK.

4.2 Simulation

The simulation of the detector has been focused on two main topics, resulting in

different levels of accuracy for the geometrical description of the simulated model. A

simplified geometry has been employed to define project foundations, eagerly needed

for detector dimensioning, such as: materials definition and size optimization, total

readout channels estimation and reconstruction software training. Then a more de-

tailed and refined simulation has been developed, in order to study, with the required

precision, the Dose Profiler behavior in different working conditions and to bench-

mark its performances. The reminder of this chapter will be devoted to describe

the optimization work while the following is devoted to present the reconstruction

software and the on beam simulated performances.

The Monte Carlo software used for the Dose Profiler simulation is FLUKA (re-

lease 2011.2). FLUKA is a general purpose tool for calculations of particle transport

and interactions with matter, covering a wide range of applications spanning from

proton and electron accelerator shielding to target design, calorimetry, activation,

dosimetry, detector design, cosmic rays, radiotherapy and so on. It can simulate the

interaction and propagation in matter of about 60 different particles including pho-

tons and electrons from 1 keV up to thousands of TeV. FLUKA can handle even very

complex geometries, using a combinatorial geometry package that allows to track

charged particles in presence of electric or magnetic fields. The software is fully

customizable via a set of user interface routines (written in Fortran 77), that allow to

control each step of the simulation, helping the user to meet any particular require-

ment. The simulation of the Dose Profiler demanded the development of several

4.2. SIMULATION 83

custom routines to better reproduce a realistic environment and to tailor the output

data to the foreseen DAQ data format. To this extent, the structure of the data for

each simulated event has been organized according to different abstraction levels. A

general track database has been created to store the information regarding all the

particles created for each event, such as: initial and final position (x, y, z)i,f , mo-

mentum (px, py, pz)i,f , particle type, particle parent, time of generation and so on.

Then, to each sub-detector has been associated another database containing all the

energy releases of the particles interacting with them. Quenching effect inside scin-

tillators has been taken into account according to Koba et al. [58]. Finally, a library

that interfaces FLUKA to ROOT (Brun et al. [59]), a commonly used data analysis

framework for high energy physics, has been built from scratch, in order to share the

same code both for the simulation analysis and the data analysis.

Dose Profiler layout optimization

All the simulations needed for the optimization of the layout used a customized

point-like source of 106 primary photons with an energy spectrum extracted from

the one measured by Agodi et al. [44] and reported in Figure 3.11. Prompt photons

expected statistics for a distal tumor slice of 2÷ 3 mm of thickness is about one order

of magnitude lower. Thus, simulating 106 primaries should reduce the statistical

fluctuations of the optimization study.

The photon emission has been chosen perpendicular to the TRK and aligned

with planes’ axis and a simplified detector geometry (planes, electron absorber and

calorimeter with a transverse section of 10 × 10 cm2) has been employed.

Tracker

Tracking planes design has been focused on two main aspects: the optimization

of the material constituting the TRK and its thickness. Given standard Compton

camera features, in fact, the choice of high Z materials (such as CMOS detectors) as

planes building blocks is rather appealing, because of their favorable Compton cross

section with respect to lighter materials. However, this option has to be seriously

pondered considering prompt photons measured energy spectrum (that is roughly

comprised between 1 ÷ 10 MeV, as shown in Figure 3.11). Scattered electrons ki-

netic energy, in fact, is expected to have a mean value of 2 ÷ 3 MeV and, since

multiple scattering is the main limiting factor of detector resolution, the higher the Z

of the planes the larger the electron’s angular straggling. Hence, planes dimension,


spacing, thickness and material have been severely tested and optimized, in order

to maximize the geometric acceptance and Compton cross section but, at the same

time, to control multiple scattering deflection of charged particles and electron tracks.

As already mentioned in the previous sections, the quest for TRK best material is a

crucial task, that can affect Dose Profiler global capability to work with the limited

amount of statistics foreseen in a typical hadrontherapy treatment. Hence, a compro-

mise between larger interaction probability and maximum deflection allowed must

be found. The two parameters that need to be optimized are clearly: (i) the number

of Compton events, and (ii) particle’s deflection angle due to multiple scattering (and

hence its contribution on the overall detector resolution).

The number of Compton events can be increased either enlarging the thickness

of the TRK planes or choosing a material with high atomic number (i.e. whose

Compton scattering cross section is enhanced). Unfortunately both these choices

have the undesirable effect of boosting the multiple scattering deflection. As rule of

thumb, recalling the equation 1.10, it would be preferable to increase the thickness of

the tracking planes, instead of using a high Z material, since in the former case the

standard deviation of multiple scattering angle increases as the square root of layer

thickness, while in the latter it grows linearly with the atomic number. A careful

analysis of the possible materials and thicknesses suitable for TRK has been made

considering multiple scattering contribution only on the first plane traversed (since

the electron track will be reconstructed relying mostly on the first two hits).

The choice has been restricted only to two options commonly used for charged

particle tracking: scintillating fibers (polystyrene) and CMOS sensors (silicon). While

the former solution needs two orthogonal planes to collect both the transverse inter-

action coordinates (xhit, yhit), with the latter a simultaneous readout can be performed

resulting in thinner planes. Squared scintillating fibers (0.25 ÷ 1 mm thick) and sili-

con strips (0.2÷ 0.3 mm thick) have been tested in order to find the best compromise

for TRK geometry.

The angular straggling suffered by the electrons inside the tracker has been esti-

mated as the angle between their production direction (pprode′ ) and the entry direction

in the following plane (i.e. the exit direction from the first plane pexite′ , being the

deflection in air negligible), as it is sketched in Figure 4.4.

In order to limit the data analysis only to interesting events, a realistic experimen-

tal “trigger condition” has been defined. This considers events with recoil electron

passing through at least 3 tracking planes and the scattered gamma ray interacting

inside the calorimeter. All the results presented in the following refer to this experi-

4.2. SIMULATION 85

Figure 4.4: Multiple scattering evaluation scheme. The angle between pprode′ and pexit

e′ hasbeen chosen as parameter to estimate the deflection suffered by Compton electron in the firstlayer.

mentally driven condition, unless differently stated.

Multiple scattering contribution to detector spatial resolution worsening has been

evaluated as follows:

1. once a Compton scattering matching the trigger condition occurs, the deflec-

tion angle of the electron track is calculated between the first two tracking

planes, as shown in Figure 4.4;

2. scattered photon direction and energy have been assumed to be known (ex-

tracted directly from Monte Carlo data);

3. the original photon direction is reconstructed and pointed backwards to its pro-

duction point, being the sources of uncertainty the deflection angle and the

Doppler correction of Compton scattering kinematics.

The photon source has been placed at a distance of 30 cm from the detector to

reproduce a realistic operating condition inside a treatment room. In Figure 4.5 the

distributions of the reconstructed source coordinates (xproj, yproj) for 2 × 1000 µm

scintillating fibers have been reported. The photon source was centered in (0,0,-30).

As it can be noted, these show a peculiar shape that results from the convolution of the

two aforementioned physical effects with the experimental cut introduced after the

trigger condition request. In order to find the best estimate for the multiple scattering

deflection two methods have been used: (i) a two Gaussians fit to the xproj, yproj

distributions, and (ii) the RMS extracted from the same dataset. In order to take

into account also the particles that undergo a severe scattering, this latter approach

has been used to estimate the single event resolution. The complete set of results,


relative to all the materials and the thickness under test is reported in Table 4.1 and

graphically summarized in Figure 4.6.

Figure 4.5: Distribution of the reconstructed source coordinates xproj (left) and yproj (right)obtained with planes of 2 × 1000 µm squared scintillating fibers. The global fit (red - solid)has been performed summing two Gaussian functions (black and blue - dotted) with the sameexpected value.

Material Thickness Compton evt. N. layers hit xproj yproj xproj/√N yproj/

√N

(µm) (trigger) (avg) (cm) (cm) (cm) (cm)

Polystyrene 2× 250 728 3.07 2.088 1.882 0.077 0.070Polystyrene 2× 500 1024 2.73 2.528 2.146 0.079 0.067Polystyrene 2× 750 1154 2.48 2.610 2.516 0.077 0.074Polystyrene 2× 1000 1033 2.29 2.622 2.592 0.082 0.081Silicon 200 612 3.04 2.859 2.394 0.116 0.097Silicon 300 789 2.87 3.154 3.282 0.112 0.117

Table 4.1: Multiple scattering study for tracker materials. Several scintillating fibers havebeen tested, as well as the two thinnest options on the market for silicon strips. The reso-lution has been evaluated projecting the reconstructed photon towards its production point(xproj, yproj). The RMS of xproj and yproj distributions has been used as evaluation parameterfor multiple scattering deflection. The total number of simulated primary particles is 106.

The aforementioned resolution, evaluated as the residual distance of the recon-

structed track from the photon source considering multiple scattering as the sole

source of uncertainty, gives an idea about the interplay of the two parameters that

have been optimized. For this reason it cannot be considered as a resolution in all

4.2. SIMULATION 87

Figure 4.6: (left) Single event resolution on xproj and yproj coordinates. (right) Overallresolution due to multiple scattering deflection. The single event resolution has been dividedby the square root of the number of events.

respects, since tracker efficiency, spatial resolution and tracking algorithm efficiency

have been neglected.

In order to better understand the dramatic impact of multiple scattering effect on

tracking accuracy, in Figure 4.7 have been reported the 2D plot of yproj versus xproj

when the effect is switched off (a) and on (b) directly in the simulation.

(a) (b)

Figure 4.7: Photon source reconstruction when (a) multiple scattering has been switched offfrom the simulation and only Doppler correction is present; (b) both effects are enabled inthe simulation. The source has been placed in (0,0,-30).

The evident tradeoff between the number of Compton events and the maximum

acceptable angular straggling of both the electron and, even if with minor conse-

quences, of the charged track has suggested to discard the silicon option (also con-

sidering its higher costs and technological issues for large geometries). Moreover,

from the results in Table 4.1 is clear that increasing the thickness of the planes, and

thus accepting to deal with a higher multiple scattering, can somewhat lead to a better


overall resolution (since the√N factor is enhanced).

Considering the results reported in Table 4.1 either 500 µm or 750 µm fibers

could be considered as the best compromise between number of Compton events,

angular straggling, detector’s efficiency and assembling simplicity. However, in or-

der to minimize the amount of material traversed by charged particles, 500×500 µm2

scintillating fibers have been chosen as tracking planes building blocks.

Electron absorber

The role of the ABS is to stop any recoil electron right after the TRK, in order

to minimize clustering effects inside the calorimeter. In fact, when a Compton scat-

tering occurs two secondary particles are produced. These, with a certain probability

distribution, could both reach the calorimeter interface producing two signals. Thus,

the CAL readout will show two clusters (one relative to the recoil electron and the

other to the scattered photon) that can worsen the detection accuracy and hence the

reconstruction of photon interaction point in the calorimeter. Moreover, interposing

a plastic scintillator before the CAL will also drastically reduce the number of back-

scattered electrons, thanks to its low effective atomic number (Zeff = 3.5) compared

to the one of LYSO (Zeff = 66). Then, the parameter that has been minimized is the

number of recoil electrons at the CAL boundary matching a trigger condition. ABS

thickness has been varied from 0.5 cm to 2.5 cm and the results of the optimization

are reported in Table 4.2 and in Figure 4.8.

Thickness e− on CAL e− on CAL e− stopped(cm) w/o ABS with ABS (%)

0 5785 5785 00.5 5686 1082 80.971 5578 506 90,93

1.5 5645 120 97.872 5579 26 99.53

2.5 5680 8 99.86

Table 4.2: Optimization of the electron absorber.

A thickness of 1.5 cm with over 97% of electrons absorption has been chosen as

final value.

4.2. SIMULATION 89

Figure 4.8: Stopping efficiency of the electron absorber as a function of its thickness.

Calorimeter

An array of LYSO scintillating crystals (widely used for PET imaging) has been

chosen as high density calorimeter and its role is, like the whole detector itself,

twofold. It is needed, in fact, for charged tracks weighting according to their own

kinetic energy (assigning a higher weight to harder particles, i.e. are more likely

to suffer less multiple scattering straggling) and for Compton photon direction re-

construction. Its readout will be performed via position sensitive photomultipliers

(Multi-Anode PhotoMultiplier Tubes, or MAPMT) made of an array of 8 × 8 sen-

sitive anodes. In light of what has been discussed thus far, it follows that a thicker

crystal would enhance scattered photon interaction probability and charged particles

energy measurement accuracy. It would also increase, however, the angular error

induced by the so-called Depth Of Interaction (DOI in the following) uncertainty. In

fact, the longitudinal interaction coordinate of Compton photon inside the CAL (zint)

cannot be directly determined with such detector, at least on first approximation. This

implies that the depth used for event reconstruction (zreco) has to be always set equal

to the calorimeter midpoint. Thus, the thicker the crystal the larger the uncertainty

on photon real direction (∆θ). Assuming ∆θ as the only source of uncertainty of

the detector, then the impact of such parameter on the overall tracking performance

has been evaluated. A simplified sketch of reconstruction uncertainty due to DOI is

shown in Figure 4.9, while the complete results of the optimization procedure are

reported in Table 4.3 and in Figure 4.10.

Since the contribution of DOI to the overall uncertainty is rather small, espe-


Figure 4.9: Sketch of DOI uncertainty on reconstructed photon direction. The prompt pho-ton undergoes a Compton scattering inside the tracker (black dot), scattered photon γ′ inter-acts inside the calorimeter at z = zint, while z = zreco (i.e. CAL half depth) is the coordinateused for event reconstruction. The uncertainty due to DOI can be estimated by means of theangle ∆θ. The sketch of the electron absorber has been omitted for clarity.

Thickness N. γ′ on CAL ∆θ Resolution uncertainty(cm) (trigger) (deg) (cm)

1 491 0.862 0.0271.5 648 1.140 0.0313 867 2.097 0.050

4.5 1044 2.605 0.0566 1157 3.031 0.062

Table 4.3: Calorimeter thickness optimization results considering only events matching thetrigger condition.

cially when it is compared to multiple scattering deflection, as it can be seen from

Table 4.3, only the interaction probability has been considered as optimization pa-

rameter. However, given the linearly growing costs and overall weight of thicker

crystals (that has to be somewhat contained for mechanical reasons), a thickness of

2 cm has been chosen as reference for the calorimeter.

In the following chapter the detailed simulation, the event reconstruction code,

that has been developed for the Dose Profiler, together with the global performances

on Monte Carlo data will be widely reviewed.

4.2. SIMULATION 91

Figure 4.10: Cyan - Number of Compton photons interacting inside the calorimeter. Red -Resolution worsening due to DOI uncertainty (arbitrary units).

CHAPTER

5

Event reconstruction anddetector performance

Content

5.1 Event reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 94

Prompt photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94


5.2 Detector performance evaluation . . . . . . . . . . . . . . . . . . . 104

Prompt photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104


In this chapter the event reconstruction working principle, its software implemen-

tation and the results on Monte Carlo data will be reviewed. As stated in the previous

chapter, a fully comprehensive simulation (scintillating fibers, front-end electronics

printed circuit boards and aluminum case included) has been developed in order to

have a more realistic and reliable dataset, with respect to the one used for layout

optimization. All the geometrical parameters and materials used for this simulation

have been reported in Table 5.1.

The event reconstruction will be focused mostly on neutral events, since charged

particle tracking does not represent a challenging issue for the development of a ded-

icated algorithm. In fact, as it will be clearer in the following, the direction of a

proton can be traced in the same way of a recoil electron produced as a consequence

of Compton scattering. Hence, a higher emphasis will be placed on Compton kine-

matics reconstruction.

93

94CHAPTER 5. EVENT RECONSTRUCTION AND DETECTOR

PERFORMANCE

Component Active area (cm) Material Density (g/cm3) ZeffDetector case 24.2 x 24.2 x 17.1 Aluminum 2.70 13Front-end frames 23.2 x 23.2 x 0.3 Fiberglass 1.85 –Tracker planes 19.2 x 19.2 x 0.05 Polystyrene 1.05 3.5Electron shield 20.0 x 20.0 x 1.5 Polystyrene 1.05 3.5Calorimeter 20.0 x 20.0 x 2.0 LYSO 7.40 66

Table 5.1: Dose Profiler simulated components.

5.1 Event reconstruction

The data analysis software that has been developed for the Dose Profiler has

been written in C/C++ and has been directly interfaced with ROOT, a commonly

used framework for particle physics data analysis.

Prompt photons

Event topology

For each event a pre-processing of Monte Carlo data has been performed in or-

der to classify the event itself according to photon interaction modality (Compton

scattering or pair production) and to the region where the first interaction took place.

Thus, five different possibilities are allowed: (i) air event, (ii) TRK event, (iii) ABS

event, (iv) CAL event and (v) no interaction. For each one of the aforementioned

possibilities either Compton or pair flag can be associated to the event (given the

photon energy range, photoelectric effect has been neglected). In order to have a

first glance on the event typology, a point-like source of isotropic prompt photons

has been simulated. Their energy has been extrapolated from LNS measured spec-

trum (see Figure 3.11). In order to reduce the statistical fluctuations, a sample of 106

primary photons has been employed. To estimate the average number of photons pro-

duced during the irradiation of a tumor slice with n Gy of carbon ions, the following

formula has been used:

Nexpγ = n [Gy] · dNC

slice · Gy·dN2

γ

dNCdΩ· dΩDP (5.1)

the second multiplicative factor, as suggested by Kramer et al. [60] for a 120 mm3

tumor divided in 39 slices with 3 mm pitch, can be assumed to be 1.8 × 107 carbon

ions per slice per Gray. The third factor is obtained from GSI measured flux, reported

in equation (3.5), while the solid angle covered by the Dose Profiler (dΩDP) can be

5.1. EVENT RECONSTRUCTION 95

evaluated supposing to place the detector at a distance of 30 cm from the patient:

dΩDP ≈SLYSO

d2=

20.8× 20.8 cm2

[(30 + 14.6) cm]2= 0.22 sr (5.2)

Thus, the simulated sample roughly corresponds to a flux ten times bigger than the

one expected for a single tumor slice irradiated with 4 Gy:

Nexpγ = 4 [Gy] · 1.8× 107

[12C/slice · Gy

]× 5.6 · 10−3

[Nγ/

12C · sr]× 0.22 [sr]

that leads to Nexpγ ≈ 90,000 photons/slice.

The results of the event typology scan have been reported in Table 5.2. As ex-

Event type Isotropic source

No interaction 60.69 %CAL event 32.22 %ABS event 4.65 %TRK event 2.25 %AIR event 0.19 %

Table 5.2: Event typology scan, the uncertainty on the reported values is of the order of0.1 %.

pected, the probability of a Compton event inside 500 µm of scintillating fiber is

rather low (of the order of 2 %). If the experimental trigger condition defined in the

previous chapter is requested (at least 3 planes traversed by the recoil electron and the

scattered photon detected in the CAL), this probability drops down to 0.1 %, hence

representing the main limitation to this technique. Its main advantage, on the other

hand, lies in prompt photons capability to exit the patient regardless of their energy,

as opposed to protons that, instead, clearly show an energy threshold behavior that

will be reviewed in the following.

Direction reconstruction: a Monte Carlo driven approach

In a standard Compton camera, to reconstruct the direction of the incoming pho-

ton, both the energy and the position of the scattered photon and the recoil electron

are needed. Considering the poor energy resolution of 500 µm scintillating fibers, a

statistical approach, driven by Monte Carlo simulation, has been proposed instead.

The kinematics of Compton scattering (assuming the atomic electron to be at rest) is

given by:

~pγ = ~pγ′ + ~pe− (5.3)


PERFORMANCE

that can be reformulated as follows:

|pγ | pγ = |pγ′ | pγ′ + |pe− | pe− (5.4)

pγ = c1 pγ′ + c2 pe− (5.5)

where c1 and c2 are two positive coefficients defined by:

c1 =|pγ′ ||pγ |

; c2 =|pe− ||pγ |

(5.6)

that must satisfy the normalization condition:

c21 + c2

2 + 2c1c2 cos θ = 1 (5.7)

being θ the angle between scattered photon and recoil electron direction. In this way,

once the direction of the scattered particles is known, it is possible to reconstruct the

direction of the original gamma ray using, for instance, the mean values of c1 and

c2 distributions extracted from Monte Carlo simulation (cMC1 , cMC

2 ), that are shown

in Figure 5.1. Moreover, an important information could be derived if the electron

energy would be recorded by ABS. This, in fact, would represent a valuable weight

for cMC2 (and consequently for cMC

1 ) choice. However, an extensive calibration of this

method, for different beam energies and primary ions, is required in order to optimize

the coefficient selection technique.

Then, the reconstructed momentum unit vector (p recoγ ) has to be extrapolated

backwards to its generation point (~p recoγ ). An error vector ∆~r can be hence defined,

whose projections along x and y axes (∆y and ∆y respectively) have been considered

as transverse resolution estimators, as sketched in Figure 5.2.

Compton event reconstruction

Once a Compton event has been recognized, the reconstruction will proceed in

two steps: (i) recoil electron tracking and (ii) photon interaction point detection inside

the CAL. The two steps will be thoroughly described in the following paragraphs and

the flow chart of the reconstruction algorithm has been sketched in Figure 5.3.

Electron direction The reconstruction of the electron direction represents the most

challenging part of the tracking process. In the energy range of interest for hadron-

therapy applications, the electron trajectory inside the detector is far from being

straight, due to the multiple scattering contribution. To this extent, a simple linear

chi square fit would not achieve satisfactory results and a more complex algorithm


c1 coef.Entries 2050Mean 0.3647RMS 0.2131

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50


(a)


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50


(b)

Figure 5.1: Monte Carlo values of cMC1 (a) and cMC

2 (b) parameters obtained simulating anisotropic point-like source of photons with LNS energy spectrum.

has been developed. The tracking process is then divided in two separate subsequent

tasks: (i) track finding and (ii) track fitting.

The track finding algorithm has the role to find and gather together all the hits

of a single track. Its simplified working principle is shown in Figure 5.4 and can be

summarized as follows:

1. the track segments (or seeds) are built considering all the combinations of the

hits (black stars) in the first two adjacent planes (s1, s2, s3 in Figure 5.4);

2. each seed is linearly extrapolated to the next plane;

3. the hit that minimizes the distance from the projected seed is clustered to the

segment (currently each hit can be associated to only one segment);


PERFORMANCE

Figure 5.2: Reconstructed prompt photon direction (p recoγ ) is extrapolated backwards to itsproduction point (~p recoγ ). An error vector (∆~r) and its projections along x and y axes havebeen considered as spatial resolution estimators.

Figure 5.3: Compton event decoding flowchart: the raw data collected by the DAQ electron-ics are pre-processed in order to cluster adjacent fiber signals to form the so-called hits. Thenthe event can be decoded (Compton or charged particle) according to the hits distribution inthe tracker: if a Compton event has been recognized the process splits in two sub-routinesto reconstruct both electron and photon direction. Once the track parameters of the twosecondary particles have been obtained, the statistical reconstruction approach described inthe previous section can be applied. The boxes are colored differently depending on whichsub-detector is involved: green - tracker, gray - calorimeter and blue - absorber.

4. once the last plane is reached, a list of candidate tracks can be built.


Figure 5.4: Track finding algorithm working principle. All the possible combinations of theexperimental hits (black stars) on the first two planes are used as seeds (s1, s2 and s3). Theseare then linearly extrapolated to the following planes and the hit that minimizes its distancefrom the projection is clustered to the track candidate.

Once all the hits have been clustered, the track fitting algorithm takes place in

order to give a quantitative description of the track parameters. As first step, a simple

chi square linear fit is performed separately for each view:

χ2 =∑N

(mi − fi,j)2

σ2i

(5.8)

wheremi is the i-th particle position measurement, fi,j = ai,jz+bi,j is the measure-

ment expectation value (function of the j-th track) and σi is the uncertainty of the i-th

measurement. The track parameters obtained with the linear fit (ax,zi,j , bx,zi,j , ay,zi,j and

by,zi,j ) are then passed to a Kalman filter [61], [62], that represents the second step of

the fitting algorithm.

What goes under the name of “Kalman filtering” is really a two step process,

consisting of a “filter” and a “smoother”. The former begins at the first hit of the track

making a prediction for the location of the next hit. The prediction is then refined,

according to the actual measurement, updating the error matrices. This procedure

goes on until the end of the track is reached. When the filtering process is finished,

the estimation of the track at any given plane does not have any information in it

about the hits further down the track. For this reason a smoothing is required in

order to incorporate such information. It steps back up the track from the bottom,

refining the track parameters at each step using the information from the “last” hits.

As it will be explained in the Appendix A, where a wider description of the Kalman


PERFORMANCE

formalism used in this thesis is available, the use of a Kalman filter has the advantage

of balancing the multiple scattering effect and the measurement error.

Photon direction The calorimeter readout will be performed by 4× 4 Multi Anode

PhotoMultiplier Tubes (MAPMT) matrix, each of them made of 8 × 8 active anodes

directly coupled to LYSO crystals. In order to investigate the possibility of improving

the resolution along z coordinate (dominated by DOI effect), a continuous crystal

has been simulated as well. The optical photons distribution at the photocathode has

been hence used to carry out a detailed analysis focused on the optimization of the

longitudinal resolution.

In order to find the best evaluation method of photon interaction position inside

CAL, two strategies have been tested: (i) center of gravity and (ii) 2D Gaussian

fit. With the former, the center of gravity of the optical photon distribution in the

transverse plane has been calculated according to:

CG =

∑n1 Ni,j · ri,j∑n

1 Ni,j(5.9)

where Ni,j is the number of optical photons on a single pixel, ri,j is the pixel position

vector.

The second approach, instead, performs for each event a bi-dimensional Gaussian

fit to the optical photons distribution with a function defined by:

f(x, y) = A · exp

[−(x− µx)2

σ2x

− (y − µy)2

σ2y

](5.10)

where A is a positive constant, µx and µy are the mean values of the Gaussian func-

tion (they also represent the x and y coordinates of the measured interaction point)

and σx and σy its standard deviations (that give the spatial resolutions for the two co-

ordinates). In order to benchmark the two aforementioned methods, the same Monte

Carlo dataset has been used to test the two techniques. The result of such test, in

terms of spatial resolution on the transverse coordinates, has been shown in Fig-

ure 5.5, where the advantage of using the 2D fit in spite of center of gravity is clearly

evident. The 2D Gaussian resolutions for x and y coordinates have been reported in

Figure 5.6.

Depth of interaction As already mentioned in the previous chapter, since the

calorimeter readout will be performed in the transverse plane, there is no direct way

to measure scattered photon Depth of Interaction (DOI) inside the scintillating crys-

tal. However, this could be estimated from the shape of the transverse optical photon


Figure 5.5: Resolution on reconstructed photon interaction point with center of gravity (red)and 2D Gaussian fit (black) methods for x (left) and y (right) coordinate.

Figure 5.6: Resolution on photon interaction point x coordinate (left) and y coordinate(right) with 2D Gaussian fit. In both cases a resolution of the order of 400 µm has beenobtained.

distribution. In fact, a deeper interaction will result in a narrower photon distribution

and viceversa. For this reason a deterministic method has been proposed to guess the

DOI. The relationship between σx (and similarly σy) and the Monte Carlo true value

of zMCint has been evaluated from the calibration curve shown in Figure 5.7. Then, the

DOI (zestint) can be deduced from:

σx = AzMCint +B

zestint =

σxA−B (5.11)

The resolution on the depth of interaction has been computed and it is shown in


PERFORMANCE

Figure 5.7: Calibration curve used for depth of interaction evaluation. On the y-axis the σx(a similar behavior has been obtained also with σy) of the 2D Gaussian fit has been plottedversus the true interaction depth (from Monte Carlo simulation).

Figure 5.8. In order to fully appreciate the benefits of this approach, it is interesting

to compare the σDOIz < 1 mm obtained with DOI calibration to the one that would

be obtained from a uniformly distributed variable along CAL thickness (20 mm)

σunifz = 20/

√12 ≈ 5.8 mm.

Figure 5.8: Resolution on z coordinate obtained with DOI calibration. In order to fullyappreciate the outcome of this approach, the final value of σz ≈ 800 µm must be comparedto the one that would be obtained from a uniformly distributed variable along calorimeterthickness (20 mm) σunif

z = 20/√

12 ≈ 5.8 mm.


Charged particles

As already mentioned in the previous sections, the reconstruction of charged par-

ticles does not pose any further complication as far as the software development is

concerned. In fact, the same logic scheme of recoil electrons can be applied also to

protons (since they do undergo multiple scattering as well, even though with minor

impact given their greater mass). The flow chart of proton tracks decoding algorithm

is shown in Figure 5.9 and, as it can be clearly noted, it is fully inherited from the

one of the Compton case. In this case the only difference is given by CAL and ABS

Figure 5.9: Charged event decoding flowchart. The logical flux is the same of the oneof recoil electrons shown in Figure 5.3. The only difference lays in CAL and ABS trackweighting according to proton’s kinetic energy. This step is of fundament importance, sinceit balances and limits the multiple scattering worsening effect on detector resolution. Theboxes are colored differently depending on which sub-detector is involved: green - tracker,gray - calorimeter and blue - absorber.

weighting of the track according to its kinetic energy. In the decoding phase it is

useful, in fact, to assign a higher importance to those particles which are more likely

to have suffered less multiple scattering (i.e. high energy protons) and hence whose

spatial information is more accurate.


PERFORMANCE

5.2 Detector performance evaluation

Prompt photons

Two different sets of simulations have been produced in order to evaluate de-

tector performance and to test reconstruction algorithm capabilities against prompt

photons. In a preliminary phase, in order to maximize the geometrical acceptance of

the detector, a mono-directional gamma source emitting photons towards the center

of the Dose Profiler front plane has been simulated. Then, to represent a more real-

istic situation, an isotropic gamma source has been chosen. Both sources have been

placed at 30 cm from detector front plane and have been aligned along detector lon-

gitudinal axis. The energy spectrum of the source has always been extracted from the

experimental one measured at LNS (see Figure 3.11). A sketch of the two simulated

geometries has been shown in Figure 5.10. For each photon source another fiber

Figure 5.10: Simulated setup for prompt photons performance evaluation. Left: mono-directional source emitting towards the detector center. Right: isotropic photon source.

thickness scan has been performed, in order to validate the results obtained with the

layout optimization taking into account also photon and electron tracking efficiency,

event selection efficiency and the different spatial resolution of the interaction point

coordinates. The complete results have been reported in Table 5.3, while an exam-

ple of resolution distribution for 2×500 µm scintillating fibers and isotropic photon

source has been shown in Figure 5.11. It is interesting to observe that while the

single event resolution does not show a significant change for the two configurations,

the number of triggering events is drastically reduced, as expected, with an isotropic

source. This affects the overall resolution, since it is obtained dividing single event

resolution by the square root of the event number.

However, given the originality and the prototypical nature of such detector, that

still needs a severe optimization and calibration of the reconstruction algorithm, an

overall resolution of (6.42 ± 0.16) mm represents certainly a very promising result.

5.2. DETECTOR PERFORMANCE EVALUATION 105

Source Fiber thickness N. trigger Single evt. resolution Overall resolution(µm) (mm) (mm)

mono-directional2 × 250 245 57.9 ± 0.7 3.70 ± 0.042 × 500 440 65.8 ± 0.6 3.14 ± 0.032 × 1000 736 76.5 ± 0.6 2.82 ± 0.02

isotropic2 × 250 66 61.3 ± 1.9 7.55 ± 0.232 × 500 120 70.3 ± 1.7 6.42 ± 0.16

2 × 1000 159 81.0 ± 1.2 6.42 ± 0.11

Table 5.3: Prompt photon performance with two different source typologies: mono-directional and isotropic gammas emitted on-axis at 30 cm from the Dose Profiler. Thenumber of trigger events has been evaluated for a realistic primary sample of 90,000 pho-tons/slice. The overall resolution has been obtained dividing single event resolution for thesquare root of N. trigger.

Figure 5.11: Single event resolution for an isotropic on-axis prompt photon source. Witha fiber thickness of 500 µm a single event spatial resolution of (70.3 ± 1.7) mm has beenobtained, dividing this number by the square root of the expected statistic sample an overallresolution of (6.42 ± 0.16) mm can be achieved.

Charged particles

In order to test the behavior of Dose Profiler against charged particles a some-

what different simulation has been implemented. A patient head, schematized by

two concentric spheres made of cortical bone (outer: rbo = 10 cm) and brain (inner:

rbr = 9 cm) ICRU certified materials, has been modeled and two proton sources have


PERFORMANCE

been placed in the center of the sphere and at 5 cm from the center, as shown in Fig-

ure 5.12. In this way two different clinical scenarios can be reproduced: a worst case

where the tumor is located exactly in the center of patient head, and an intermediate

case where the tumor is closer to patient bone. This variation of the simulated setup

has been imposed by proton’s different interaction with matter, with respect to pho-

tons. Charged particles, in fact, lose energy in a continuous way and the presence of

10 cm or 5 cm of patient head will change dramatically the performance of the detec-

tor. Proton’s initial kinetic energy has been varied between 75 MeV and 250 MeV for

Figure 5.12: Simulated setup for protons performance evaluation. Two concentric sphereshave been used to model a human head, choosing ICRU certified materials for cortical boneand brain. A proton source placed at the center of the head (blue) and one placed at 5 cmfrom the skull (red) have been employed to schematize two different clinical scenarios.

the centered source and between 70 MeV and 140 MeV for the displaced source. The

results of the efficiency scan (number of tracked protons divided by the number of

incoming protons) have been reported in Figure 5.13, while the spatial resolution as a

function of the initial kinetic energy has been shown in Figure 5.14. A clear thresh-

old effect is present, as expected, for charged particles detection. Once the energy

threshold is exceeded, protons can escape from the patient head and can be detected

with a rapidly increasing efficiency. This holds true also for Dose Profiler spatial

resolution, that converges around 2 ÷ 3 mm. As mentioned above, such resolution

represents a very promising milestone for charged particle monitoring, considering

the fact that this technique has been proposed only in the last couple of years and it

needs extensive calibration and verification campaigns in order to validate its results.

Additionally, the observed threshold effect makes the possibility to use also prompt

radiation even more appealing, since it could complement and increase the statistic

data sample acquired during a therapeutic treatment.

5.2. DETECTOR PERFORMANCE EVALUATION 107

Figure 5.13: Dose Profiler efficiency versus proton’s initial kinetic energy. As expected,a threshold effect (Ekin ≈ 120 MeV for the centered source, and Ekin ≈ 80 MeV for thedisplaced source) is present. However, it is interesting to note that once the charged particlecomes out from the patient, this is detected by the Dose Profiler with a rapidly increasingefficiency.

Figure 5.14: Dose Profiler spatial resolution versus proton’s initial kinetic energy for thecentered (blue) and the displaced (red) sources. For both cases the effect of the energy thresh-old is clearly visible. When the kinetic energy is slightly larger than the threshold value themultiple scattering effect pollutes the spatial information of the track. However, increasingthe energy the resolution rapidly converges to 2 ÷ 3 mm.

Conclusions

Hadrontherapy is a fast growing reality in cancer treatment, which is rapidly

proving to be a valid alternative to radiotherapy for an increasing number of tumors.

More than ten facilities are currently operating in Europe (two of them in Italy alone)

and this number will duplicate in the next few years. One of the major hindering

factors that is actually limiting its diffusion is, without any doubts, the lack of mon-

itoring devices that could allow a reliable and precise treatment-quality evaluation.

The higher spatial selectivity of ions in their energy deposition poses, in fact, serious

issues and constraints both on the beam delivery and on the required precision of

dose monitoring for a fast and effective treatment-quality feedback.

As of today, a single technique (referred to as PET) has been used in a clinical

environment, although for research purposes only. It exploits the collinear emission

of photons due to positron annihilation induced by β+ emitters produced as a conse-

quence of nuclear fragmentation of the projectile and the target. Unfortunately, this

method has shown several drawbacks the most limiting of which are its offline nature

and β+ emitters low activity.

However, other secondary particles have been proposed as means to estimate the

dose deposited inside a patient such as: prompt photons and charged particles emitted

after nuclei de-excitation and nuclear fragmentation respectively. The possibility to

use such sources to monitor the treatment quality is still a matter of research currently

under evaluation of the scientific community. It has been shown by several authors,

however, that a clear correlation between prompt photons, charged particles emission

region and Bragg peak position does indeed exist and it could be usefully exploited

for dose monitoring purposes.

109

110 CONCLUSIONS

The work presented in this thesis was firstly aimed at the preliminary measure-

ments on beam needed to demonstrate such correlation and then at the design of a

novel device capable of monitoring the Bragg peak position exploiting both prompt

photons and charged particles detection. This dual-mode functionality is a unique

feature, never suggested so far, that will allow to increase the data sample collectable

during a typical treatment considering its highly restrictive time constraints. Lack of

statistics, together with detector encumbrance and clinical workflow necessities, is,

in fact, one of the most challenging issues to overcome when treatment-like condi-

tions come into play. However, this dual working modality comes at the expenses

of a more complex layout, that needs to be carefully optimized for several, often

conflicting, effects.

The device, called Dose Profiler, will work as a charged particles tracker and a

Compton camera and is made of three sub-detectors: (i) a scintillating fibers tracker,

(ii) a plastic scintillator absorber and (iii) a LYSO calorimeter. The first has the

twofold role of tracking protons and scatter photons, the absorber stops all the recoil

electrons measuring also their energy, while the calorimeter weights proton tracks

(according to their kinetic energy) and provides scattered photon direction by means

of a position sensitive readout. In order to close Compton kinematics avoiding scin-

tillating fibers poor energy measurement, a statistical approach, driven by Monte

Carlo simulations, has been proposed instead.

The Dose Profiler layout has been optimized limiting the multiple scattering ef-

fect in the tracker layers, increasing the absorber stopping efficiency and minimizing

the contribution due to depth of interaction uncertainty on photon position detec-

tion inside the calorimeter. Then, a dedicated software for the event reconstruction

and the performance evaluation has been developed and tested against two sets of

simulations. A point-like isotropic photon source and a simplified model of human

head with a proton source inside it have been used to assess the capabilities and

the criticality of such detector. The preliminary results, although obtained only on

Monte Carlo data, seem very promising showing a spatial resolution on the recon-

structed dose release position of the order of 5 ÷ 6 mm for photons and 2 ÷ 3 mm

for protons. Considering the originality of the proposed approach and the fact that

the detector is still in its early prototyping phase, this novel device showed great po-

tential for its application in a treatment room foreseen in 2016. It needs, however,

to be severely tested on beam, in order to confirm such encouraging performance,

as its reconstruction software still has to be optimized, thus leaving room for further

improvements.

APPENDIX

A

Kalman filter formalism

The Kalman filter formalism, that has been used for the electron reconstruction

algorithm, focuses on a p × 1 state vector (xk) that contains the state parameters to

be estimated, and on a model that propagates the state vector from layer to layer. The

state vector extrapolation model is given by:

xk = Fk−1 xk−1 + wk−1 (A.1)

where Fk−1 is the Jacobian matrix of xk, that propagates the state vector from point

k − 1 to point k, and wk−1 represents the noise that corrupts the information con-

tained in the state vector, that in our case of interest is due to multiple scattering.

The process noise is assumed to be unbiased and to have finite variance, its covari-

ance matrix is represented by Qk. However, the components of xk are not measured

directly. The m measurements mk at point k are linear functions of xk such that:

mk = Hk xk + εk (A.2)

where mk is a m × 1 vector, Hk is the observation model which maps the true state

space into the observed space (m× p matrix), and εk represents measurement noise

(in analogy to the process noise also εk is assumed unbiased and with finite variance,

its covariance matrix is Vk).

The working principle of the filter can be divided in two distinct phases: predic-

tion and update. In the prediction phase the estimate of x at time k given observations

up to and including at time k−1 (xk−1k ) is called “a priori” state estimate. The a priori

prediction is then updated with the actual observation to refine the state estimate, thus

obtaining the so called “a posteriori” state estimate (xkk). The two phases typically

111

112 APPENDIX A. KALMAN FILTER FORMALISM

alternate. In the prediction phase the predicted state estimate and estimate covariance

are given by:

xk−1k = Fk xk−1

k−1 (A.3)

Ck−1k = Fk C

k−1k−1 F

Tk +Qk (A.4)

After observation and actual measurement the information about the predicted state

can be complemented. Let rk andRk be the measurement residual and its covariance

matrix respectively, these are defined as:

rk = mk −Hk xk−1k (A.5)

Rk = Hk Ck−1k HT

k + Vk (A.6)

The Kalman optimal gain Kk is:

Kk = Ck−1k HT

k R−1k (A.7)

and finally the updated state estimate and the state covariance can be derived as:

xkk = xk−1k +Kk rk (A.8)

Ckk = (I −KkHk)Ck−1k (A.9)

In our case of interest a 4 × 1 state vector x0 has been defined:

x0 =

P1

P2

P3

P4

=

x0 − z0 · ax,0y0 − z0 · ay,0

ax,0

ay,0

(A.10)

where (P1,P2,0) is the intercept of the unscattered track with the reference x-y plane

at z = 0, P3 and P4 are the angular coefficients in the reference system (ax,0 and

ay,0). In this particular case, the multiple scattering covariance matrix Qk has been

evaluated by Wolin et al. [63] to be:

Qk =

z2

0 〈P3, P3〉 z20 〈P3, P4〉 −z0 〈P3, P3〉 −z0 〈P3, P4〉

z20 〈P3, P4〉 z2

0 〈P4, P4〉 −z0 〈P3, P4〉 −z0 〈P4, P4〉−z0 〈P3, P3〉 −z0 〈P3, P4〉〈P3, P3〉〈P3, P4〉−z0 〈P3, P4〉 −z0 〈P4, P4〉〈P3, P4〉〈P4, P4〉

(A.11)

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