Conditions for installing a RF LINAC as a post accelerator for pre-clinical studies using proton minibeams

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Universit`

a di Pisa

Dipartimento di Fisica

Tesi di Laurea Magistrale

Anno Accademico 2018/2019

Conditions for installing a RF linac as a

post accelerator for preclinical studies

using proton minibeams

Candidate:

Advisors:

Raissa Berti

Prof. Franco Cervelli (Universit`

a di Pisa)

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Abstract

Proton minibeam radiotherapy, an innovative approach to reduce side effects in radiotherapy, has recently been developed at the ion microprobe SNAKE (Super-conducting Nanoprobe for Applied nuclear [Kern] physics Experiments) in Munich. It consists of a spatially fractionated radiotherapy method using sub-millimeter pro-ton beams. A homogeneous dose distribution can be achieved in the tumor, due to multiple Coulomb scatter, by applying multiple beams and adjusting beam size and inter beam distances. Moreover, the application of sub-millimeter proton beams spares a large number of healthy cells within the irradiation field.

Currently, the accelerator facility in Munich accelerates the proton beam up to 20 MeV using a Tandem Van de Graaff accelerator. Several experiments, both in vitro and in vivo, tested the absence of side effects at this energy ([1], [2]). A tandem post accelerator is planned to be built as a radio frequency linear accelerator, based on the TOP IMPLART project (ENEA institute, Rome), which allows the irradiation of small animals using a 70 MeV proton beam to further validate the potential of the proton minibeam therapy [3].

The aim of this thesis is to carry out a preliminary study of the conditions required to install a RF LINAC as post accelerator to ensure the efficiency of the proton minibeam therapy and the safety of the facility. For this purpose, three different experiments are performed.

The goal of the first experiment is to measure the beam spot size in function of the distance between the beam exit window and the target and of the thickness of attenuator material (aluminium). This experiment is performed using different irradiation setups to select which are suitable for proton minibeam technique. The beam spot size corresponds to the full width half maximum of the dose distribution and it has been proven that if F W HM ≤ 470 µm at the sample’s surface, the minibeams can spare healthy tissue and irradiate the tumor with a homogeneous dose [4]. The experiment is carried out using 20 MeV proton beam. The beamspots size at 70 MeV are estimated by finding the scale factor obtained comparing the simulation results of the beam spot size at 70 MeV and 20 MeV and by applying it to the experimental results at 20 MeV. The beam spots size at 20 MeV and 70 MeV are compared with the values obtained from simulations and theoretical cal-culations. The results show that choosing an air gap distance up to d = 80 mm the dose distribution has a F W HM < 470µm both considering a 7.5µm and 25µm kapton window. By inserting a foil between the nozzle and the detector to de-crease the beam energy, considering 0.2 mm, 0.4mm, 0.6mm aluminium thickness, F W HM = 470µm at d1 = (53 ± 1)mm, d2 = (38 ± 1)mm, d3 = (31 ± 1)mm

re-spectively. According to SRIM (Stopping and Range of Ions in Matter) simulation, the beam energy after crossing each aluminium thickness and the corresponding air

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CONTENTS 4

gap distance, is E1 = (69.5 ± 0.1) MeV, E2 = (69.1 ± 0.1) MeV, E3 = (68.7 ± 0.1)

MeV , respectively. This mean that using a 70 MeV proton beam, the energy lost crossing this attenuator is negligible.

The aim of the second experiment is to find how to match the TANDEM beam with the RF LINAC. The best configuration of the frequency of the chopper and of the aperture of the slits in the tandem beam lime is chosen in order to irradiate the target with a current of I=1 - 10 nA, necessary for preclinical studies. Opening completely the circular slits placed before the tandem and setting the aperture of the microslits as ∆Objx= 1mm, ∆Objy = 1.5mm, ∆DivX = 13mm, ∆DivY = 6mm, the current

measured after the microslits is I=8.5 nA. Considering a 20 MeV proton beam and these experimental values of the current and of the emittance ( = 35.5mm2_mrad2_),

the calculated beam brightness is B = 12 µAmm−2mrad−2MeV−1 and this value is much higher than the brightness previously measured , which corresponds to B = 2.3 µAmm−2mrad−2MeV−1 ([5]). Considering that the beam lost in the accel-eration process of the LINAC is about 85%, the predicted value of the current at the target is I = 1.3nA

The aim of the third experiment is to estimate the dose rate produced during the ac-celeration process, which should never exceed ˙D = 3 mSv_h to respect safety standards of the facility. In the LINAC, about 85% of the beam is lost up to E=18 MeV. The isotopes produced in this process (Copper 62, Zinc 63, Zinc 62, Copper 64 and Zinc 65) and their activity are measured using a HPGe detector and a mobile dosimeter by irradiating a piece of copper performing two different proton irradiations at this energy, which correspond to a single standard irradiation (I=10nA, t=1min) and an estimation of all the irradiations performed during an entire day of beam time (I=15nA, t=15min). Moreover, for every isotopes the maximum activity and dose rate achievable (at d=10 cm) and the time required to reach the dose rate safety cri-teria ( ˙D ≤ 0.1mSv_h ) are calculated. The same analytical calculations are performed considering the effects of all isotopes and using different beam time scenarios and the results show that the dose rate of ˙D = 3mSv_h is never reached.

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Chapter 1 Radiation therapy

The word cancer is a generic term for a large number of diseases in which a group of cells displays uncontrolled growth, invasion and metastases

Cancer is second most common disease and cause of death (after cardiovascular dis-eases) in Europe with more than 3.7 million new cases and 1.9 million deaths each year [6] .

The main approaches to treat cancer are surgical removal of the tumor tissue, chemotherapy and radiotherapy.

Not all tumors can be easily completely removed by a surgeon and the applicability and success of this method depends on many factors, as the size and the location of the tumor. Chemotherapy consists in using chemotherapeutic substances that affect mostly cell proliferation by interrupting the chemical processes involved in cell di-vision. To maximize the treatment efficiency and to prevent cancer recurrence, the surgical removal is often combined with a chemotherapy or radiation therapy. The most common approach is the radiation therapy, which is applied to about 50% of patients with cancer [7]. Radiation therapy exploits the effect of ionizing radiation to destroy tumor (curative or radical treatment) or to help by relieving symptoms if the tumor can not be eradicated (palliative treatment).

The main goal of the treatment is to inactivate all the tumor cells, which means that they are killed or at least not able to proliferate any more. To reach this goal a sufficiently high dose must be delivered to the tumor, which is the target of the radiation beam. High energetic particle beam used in radiotherapy mainly deposit energy in the matter by ionization events. The physical measure describing the mean energy deposition ∆E of ionizing radiation imparted in a matter of mass ∆m is the (absorbed) dose D.

D = ∆E

∆m (1.1)

which is expressed in Gray (Gy), 1Gy = 1_kgJ .

Dose deposition is not homogeneous within the target and different kinds of ioniz-ing radiation can have different biological and clinical effects. The Linear Energy Transfer (LET) is defined as the density of energy deposition along the track of a charged particle. According to the International Commission on Radiological Units (1962) LET is described as:

”LET of a charged particle in a medium is the quotient dE/dl, where dE is the average energy locally imparted to the medium by a charged particle of specified

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CHAPTER 1. RADIATION THERAPY 6

energy in traversing a distance of dl.”

LET = ∆E

∆L (1.2)

Particles which deposit a large amount of energy in small distances are defined ”High LET Radiation”, while particles that deposit less amount of energy along the track or that have infrequent ionizing events are defined ”low LET radiation” .

The LET is closely related to the stopping power, defined as the loss of particle energy caused by the retarding force acting on charged particles. The main difference between these quantities is that the energy loss due to the radiative energy loss (Bremsstrahlung) is not included in the LET. Considering ions, since the mass of ions is much larger to the one of electrons, stopping power and LET are nearly equivalent because energy loss via bremsstrahlung is negligible. The tumor control (TC) is the probability to eradicate or control a tumor using a given dose. Nevertheless, the dose deposition in the healthy tissue, that surround the tumor, is inevitable and this provokes side effects. The side effects depend on the radiation dose deposited and on the tissue sensitivity and this can be expressed as normal tissue complication (NTC). Side effects can be distinguished between acute (until 90 days after irradiation) and long-term side effects which can last until years after treatment.

The aim of radiotherapy is to get the largest TC to eradicate the tumor while keeping the NTC as low as possible. The ’therapeutic window’ is the difference between the dose required for tumor control and the normal tissue complication, shown in figure 1.1.

Figure 1.1: Probability for tumor control (TC) and normal tissue complication (NTC) versus dose. The complication free tumor control curve determines the ideal dose for maximum tumor control and acceptable side effects [2]

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1.1 Radiation effects on cells

Ionizing radiation can act directly on the cells structure, provoking chemical reac-tions leading to biological damage, or it can act indirectly, by interacting with water molecules (∼ 80% of a cell is composed of water) producing free radicals, which can damage the cells.

Particles with high linear energy transfer (LET > 10keV_µm) mainly interact directly with biological material, inducing DNA damage continuously along their tracks, while using low LET radiation, ∼ 60% of cellular damage is caused by the indirect effects.

The DNA molecule is composed of two chains which coil around each other to form a double helix carrying the genetic instructions used in the growth, development, functioning and reproduction of cells. Common damages of the DNA molecule are base damages and breaks of one strand (SSB:single strand break), with about 103 occurring per Gray in each cell for low-LET radiation. Single strand break is usually not a serious danger for the cell because the DNA can be repaired without losing information. The break of two opposite strands form a double-strand break (DSB). This is the most dangerous type of radiation-induced DNA damage and occurs about 35 times per Gray of low-LET radiation in each cell. Because such breaks are dif-ficult to repair, they can cause mutations, cell death (apoptosis) or permanent cell cycle arrest [8].

Indirect action occurs when ionizing radiation hits the water molecules and this leads to the production of free radicals, molecules that are highly reactive due to the presence of unpaired electrons. Free radicals can form compounds, such as hy-drogen peroxid H2O2, which are toxic for DNA and can provoke harmful chemical

reactions within the cells that can lead to the death of the cell [9].

The cells survival curve (figure 1.2) describes the relation between the delivered dose and the cells damage by testing their clonogenic ability after irradiation. The shape of the survival curves depends mainly on the kind of radiation and the type of the cells. Densely ionizing radiations leads to a cell survival curve that is almost an exponential function of the dose. For sparsely ionizing radiation the curve shows an initial slope followed by a shoulder ans then become really straight at higher doses. For a value of the dose D < 10Gy the curve can be approximated using the linear quadratic model [10]:

SF (D) = exp (−αD − βD2) (1.3) where SF (D) is the fraction of cells surviving a dose D, α is a parameter that de-scribes the initial slope of the cell survival curve, assuming that cell death is caused by a single lethal event, and β is a parameter that describes the shoulder of the survival curve, assuming that cell death is caused by an accumulation of harmful but non-lethal events.

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Figure 1.2: Example of linear quadratic model of cell survival curve expressed in semi logarithmic scale. The initial shoulder is caused by ionizing radiation, which means that many repairs occur in the cells after the irradiation for low dose level. The shoulder progressively reduces with increasing LET.

1.2 Radiotherapy treatment

Different kind of radiotherapy can be used to treat cancer. The choice of the treat-ment depends on several factors that depends on the features of the cancer and of the patient. Radiotherapy treatment can be divided in internal and external radiotherapy.

1.2.1 Internal Radiotherapy

Internal radiation therapy, also called brachytherapy, consists of placing radioactive containers directly in body, or in the tumor either close to it. The main advantage of brachytherapy is the ability to deliver a high dose radiation to a small area and at the same time reduce the side effects to the healthy tissue because ionizing particles do not have to cross the body to reach the tumor.

1.2.2 External Radiotherapy

The most common form of radiotherapy is external beam radiotherapy (EBRT) in which an external source of ionizing radiation is used to irradiate the tumor. The kind of the treatment can be defined by the beam delivery technique and the parti-cles used.

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Beam delivery technique

The most used delivery techniques are:

• Fractionated radiotherapy, which consists of dividing the total dose to be de-posited in a tumor into several, smaller doses over a period of several days to minimize the damage of healthy tissue.

• Intensity-modulated radiation therapy (IMRT), which is based on combina-tions of multiple intensity-modulated fields coming from different beam di-rections. This allows to deliver a radiation that maximizes tumor dose while minimizing the dose to close healthy tissue.

• Image-guided radiation therapy (IGRT), which consists of using imaging tech-nique to track the tumor during radiation therapy in order to improve the treatment precision. IGRT is widely used to treat tumors in areas of the body that move frequently, such as the lungs.

1.2.3 Particles used in radiotherapy

Photon Radiotherapy

Since photons are electrically neutral, crossing matter they can be absorbed in a single process in three different ways: photoelectric effect, Compton scattering or pair production. In the range of energy used for radiotherapy the dominant inter-action is due to Compton scattering [11]. These interinter-actions lead to partial or total transfer of the photon energy to electrons that ultimately deposit their energy in the matter. The LET has therefore no meaning when applied to photons, however it is possible to talk about ”gamma LET” referring to the LET of the secondary electrons.

The photon flux decreases following:

I(x) = I0 e−µx (1.4)

where I0 is the incident intensity,x is the target thickness and µ is the linear

atten-uation constant, which depends on beam energy and target composition. Because of the cross sections are usually small, but the energy transfer is very high the use of photon beam leads to an high dose deposition in the superficial tissue ( see figure 1.3,).

The dose region between the surface and the max dose is called the dose build-up region and results from the range of energetic secondary charged particles that first are released by photon interactions and then deposit their kinetic energy in the patient.

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Figure 1.3: Dose deposited in tissue for different particles energy as a functions of depth penetration. For 20 MeV photons (green line) most of the dose is deposited close to the surface and the build up region is evident. The 4 MeV electrons beam (purple line) lose all its energy after few mm depth. The 150 MeV proton beam (red line) deposit most of its dose in the Bragg peak region (described in the next section).

Proton Radiotherapy

Charged hadron particles, such as protons or carbons, lose kinetic energy mainly due to the Coulombic interactions with atomic electrons, but also due to Coulombic interactions with atomic nucleus and to nuclear reactions [12].

Protons passing close to the nucleus are elastically scattered or deflected by the repulsive force from the positive charge of the nucleus. Protons loses a negligible amount of energy in this kind of scattering. The number of single scattering events (Ns) that occurs in the body is high and it is called Multiple Coulomb scattering

for Ns > 20. The combined effects of all Ns scattering can be modeled to predict

the net angle of deflection (see section 3.3).

Protons can interact with the atomic nucleus via non elastic nuclear reaction in which the nucleus is transformed (e.g proton is absorbed by the nucleus and a neutron is ejected). These reactions lead to a small decrease in absorbed dose due to the removal of the primary protons and to a large extent due to the liberation of the secondary protons or other ions.

The predominant type of interaction of protons in matter consists in the continuously kinetic energy loss via inelastic Couluombic interactions with atomic electrons. The dose deposition is mainly due to this interaction. The electrons are either excited in their atom or removed from their orbital resulting in an ionization of the atom. The energy which is transferred to a single electron within a recoil is low because of the huge mass differences of protons and electrons (mp ' 1836me) and for this reason

protons usually travel along a nearly straight path. For a particle with electric charge z and velocity β = v_c (Lorentz factor γ = (p1 − β2₎−1_{, the mean specific}

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energy loss rate D_ρdxdEE is well described by the Bethe-Bloch formula for energies > 100keV − dE ρdx = 4πNAremec 2_z2_Z Aβ2 [log 2mec2β2γ2 I − β 2₋ δ 2− C Z] (1.5) where NAis Avogadros number, re is the classical electron radius, me is the electron

mass, Z is the atomic number of the absorbing material, A is the atomic weight of the absorbing material, I is the mean excitation potential of the absorbing material, δ the density effect correction to the ionization energy loss and C is the shell correction term, which is important only for low energies where the particle velocity is near the velocity of the atomic electrons. The range of a proton beam is defined as the depth at which half of the protons are stopped on matter. Since the the mass of the protons is much greater than the mass of electrons, most protons travel along a nearly straight line and the range can be written as:

R = Z 0 E0 dE dx −1 dE (1.6)

where E0 is the initial energy of the beam. Crossing tissue, protons lose energy

because of the huge amount of interactions of the particles in matter. The dose peak in the depth range where most of protons have a very high LET and deposit a lot of energy before they are stopped is called Bragg peak. The depth of the Bragg peaks depends on initial energy and the relation between the energy of the particle beam and the range in water is expressed as :

R = R0 A Z2 E0 mc2 1.82 (1.7)

where R0 = 425cm is the value of range in water and E0 is the initial kinetic energy

of the beam, respectively [13].

Figure 1.4 shows the Bragg Peak depth for mono energetic carbon ions of different initial energies. The unit M eV_u is introduced to compare ion beams with proton beams. Considering ions with mass number A and atomic number Z, the maximum range scales as:

Rion(β) = Rproton(β)

A

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Figure 1.4: Depth dose profiles for12C beams with different initial energies

To irradiate the tumor volume with a lethal dose it is desired to reach a homogeneous dose distribution within the target volume. To reach a homogeneous dose different single Bragg peak are overlapped, both by modulating beam energy and using beam coming from different directions. In this way it is possible to achieve a homogeneous dose called Spread Out Bragg Peak (SOBP).

Tha main advantage of hadron therapy is that, compared to photons, the dose released in the tissue before the tumor is much smaller, reducing side effects. From equation 1.5 it could be noticed that, since the energy lost by charged particles is inversely proportional to the square of their velocity, the peak occurring just before the particle are completely stopped. For this reason barely any dose is deposited behind the tumor.

Figure 1.5: Dose of protons and carbon over depth. Concerning the proton beam it is showed both the single Bragg peaks and the sum of the single Bragg peaks that is called spread out Bragg peak.

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Electron Radiotherapy

An electron traveling in matter loses energy as a result of collision interactions and radiative process (Bremsstrahlung) [14].

Collisions are due both to inelastic collisions with atomic electrons in the material and elastic scattering with nuclei. The stopping power of this process is described by the Bethe-Bloch formula (equation 1.5) with some modifications which consider that incident particle and target electron have same mass. The Bremsstrahlung is electromagnetic radiation due to deceleration of electrons in Coulomb field of nucleus. The energy loss per unit thickness due to this process can be described as:

−dE dx rad = E X0 (1.9)

where X0 describes the so-called radiation length, which characterizes the target

thickness for which the particle energy is reduced to the e-th part of the initial energy and can be written as:

1 X0 = 4αr_e2N0Z2log 183 Z13 (1.10)

where α is the fine-structure constant, re is the classical electron radius and N0 is

the atomic density of a medium with atomic number Z. Due to the large Multiple Coulomb scattering of electrons, equation 1.6 gives the mean length of the path in matter, measured along the trajectory which has a high number of large defections caused by the high mass difference with nuclei Electron beams are commonly used to treat tumor close to a body surface because the maximum of the dose deposition occurs near the surface and dose decreases rapidly with depth (as shown in figure 1.3). Electron beams usually have nominal energies in the range 4-20 MeV and they penetrate the body in a range of 1-5 cm .

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Chapter 2 Proton Minibeam Radiotherapy

The proton minibeam is a novel concept of spatially fractionated proton beam based on the use of focused or collimated submillimeter beams. The application of minibeam spares a large number of cells in the irradiation field, reducing the side effects in healthy tissue, while a homogeneous dose distribution can be deposited in the tumor, because the beam spreads itself when penetrating tissue and the beam spot size in-creases with depth due to multiple Coulomb scatter. Proton microchannel radiation therapy, developed at the ion microprobe SNAKE (Superconducting Nanoprobe for Applied nuclear [Kern] physics Experiments) in Munich, has provided implementa-tions of minibeam technique. In this chapter the technique of minibeam irradiation is described and the benefits of minibeam, carried out with simulations and experi-ments, are shown.

2.1 Proton minibeam spatial fractionation

The “spatial fractionation technique ”consists in dividing the treatment area into several smaller regions of not necessarily equal size and shape and of which not all receive the same high dose required for tumor control. This means that some area can receive much higher doses than by a homogeneous irradiation (“peak”), while other can receive barely any dose (“valley”) [15].

The first implementations of this idea consists in performing irradiations through a metal grid or sieve, which divided the large irradiation field in several small beams that were interrupted by shielded areas. While in grid therapy applications the irradiation fields are up to 2 cm, minibeam radiation therapy use focused beams up to sub-millimeter size (σ0 = 20 − 200µm). The dose profile of the irradiation

field is characterized by the peak-to-valley dose ratio (PVDR), which is the ratio of the dose in the center of the minibeams and the dose between the beams. To optimize radiotherapy efficiency large PVDR values are required, which means high peak doses and low valley dose.

On a cellular level, peaks-and-valleys irradiation leads to serious damage and hence an high chance of cell death in the peak area, while it provokes barely no effect in the valley zone. This leads to higher tolerance of healthy tissue for spatially fractionated proton beam than for continuous radiation beams. The higher tolerance for a spatially fractionated proton beam than for continuous radiation beams is attributed to the ”dose volume effect”. This means that in some tissue as skin,

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CHAPTER 2. PROTON MINIBEAM RADIOTHERAPY 15

that is always irradiated by external radiotherapy beam, the maximum tolerable dose (which means the dose before complications of radiotherapy appear) increase as irradiated tissue volumes are made smaller. This is attributed to the migration of uninjured cells adjacent to the areas damaged by irradiation where no critical value of dose are deposited, while in the volume control area the migration phenomenon occurs barely due to the less amount of undamaged cells. Using proton minibeams an homogeneous dose distribution can be achieved in the tumor, due to multiple Coulomb scattering, by applying multiple submillimeter beams ( figure 2.1). The depth of the homogeneous dose can be adjusted by changing the beam distance, usually measured in center-to-center distance, and the initial size of the minibeams. To optimize center-to-center distances, the irradiated area of healthy tissue should be minimized to allow cells between mininibeam to repair injured tissue. Typical values of inter beam distances are few millimeters so that usually hundred minibeams are applied for a macroscopic tumor to be covered.

Figure 2.1: Comparison between profile of homogeneous (top) and minibeam irradiation (bottom) of a target volume with a homogeneous tumor dose. It is evident that minibeam irradiation deposit less dose than homogeneous irradiation in the superficial tissue. ( [1]).

Figure 2.2: 3D representation of the minibeam concept. Non-overlapping minibeams are applied on the patients skin on a square grid. Crossing tissue the beam spreads, forming a homogeneous dose in the target volume ([1]).

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2.2 The ion microprobe SNAKE

The experiments performed at SNAKE take place at the 0o _{beam line of the}

ac-cellerator tandem laboratory in Garching, Munich (see section 5.3). The facility can focus protons up to 30 MeV as well as heavy ions up to 200 q_A2 MeV. The SNAKE irradiation setup used for biological experiments is showed in figure 2.3.

Figure 2.3: Schematic drawn of tandem accelerator and SNAKE setup [2].

After the tandem, the beam is focused and cut to a diameter up to 10 µm by a two stage microslit system, which also limit the beam divergence. The beam lateral position is defined by the deflection unit composed by a magnetic scanning unit in X-direction and a fast electric scanning unit in Y-direction, which allows the generation of various mm-wide irradiation patterns.

The beam is focused up to a factor of 200 in both x - y direction by superconducting lenses operating as a quadrupole triplet with two lenses that are 90◦ rotated to each other and a third lens that has the same configuration of the second lens to introduce multipole corrections [16]. The main part of the lens is the central ceramic tube (Al2O3), in which are sited the poles, by CoFe. The superconducting coil wire

are composed by NbTi filaments wirh a diameter of d=2 mm.

The superconducting multipole lenses are situated in a helium bath cryostat together with the scanning unit, surrounded by liquid nitrogen tank. The liquid nitrogen enables to keep the lens at T = 77 K between beam times, while the helium bath cryostat cool the lens until T = 4 K during irradiation time. The focused beam exit from a window in the nozzle covered with some polyimide material as kapton or mylar and it reaches the sample.

Behind the sample, a detector composed by a plastic scintillator and photomultiplier tube is installed. The PMT signal triggers a high voltage chopper which deflects the beam from the sample after the selected number of ions have reached the scintillator, allowing for the delivery of a defined dose to the sample. The detector signal is also used to control the deflection unit. To apply several microbeams in a certain area, the beams are delivered next to each other by moving mechanically the irradiation set-up.

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2.2.1 Proton minibeam simulation

Both the reducing side effects in the healthy tissue and the homogeneous dose depo-sition in the tumor have been tested by simulations (Sammer at al, [17]) to prove the benefits of minibeams. The simulations were performed considering a tumor placed 10 cm underneath the skin and with a thickness of t = 5 cm and a E = 117 − 148 MeV proton beam. The spatial dose distributions of minibeam scenarios depend on the ratio σ_d, where σ is the beam size and d is the center-to-center distance (figure 2.4).

Figure 2.4: Quadratic (a), hexagonal (b) and line (b) arrangement with Gaussian

minibeams. The white lines indicate the corresponding lattice constant d and the black lines show the display cell.(Taken from [4])

The minibeam width is given by σ =pσ2

0+ σsc2 where σ0 is the initial beam size,

chosen as 0.2 mm, and σsc is the beam spread due to multiple scattering . Since the

small angle scattering of protons dominates the beam size, beam divergences are neglected.

A homogeneous dose can be deposited in the tumor if 0.975 ≤ _DD

0 ≤ 1.035 in the

planning target volume (PTV) where D is the dose at the PVT and D0 is the

mean dose. By approximating a single minibeam by a Gaussian distribution, the parameter σ_d for a quadratic (16 x 16 beams ), hexagonal (16 X 16 beams) and line arrangement (17 beams) to irradiate the tumor with a homogeneous dose were found. The normalized dose _DD

0 obtained using minibeam arrangements is used to

estimate the coverage area, which is defined as the fraction of area receiving a dose larger than a certain limit dose required to eradicate the tumor:

Acoverage =

A(D > Dlimit)

Atotal

(2.1)

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Figure 2.5: Area coverage versus limit dose for different beam sizes ( in units of d). Each beam size is plotted for the hexagonal (solid line), quadratic (dotted line) and line (dashed) arrangement. For better comparison, all arrangements are set to deliver a homogeneous dose distribution for a beam size σ = 0.508. The hatched area marks the 0.975 < D < 1.035 homogeneity constraint, an example is given for the reader for easier understanding as following: considering a beam size σ of 0.15 for hexagonal arrangement (red solid line) and a limit dose 0.5 (normalized dose in the plot, therefore dimensionless). The area coverage is then at 0.35, hence 35% of the irradiated area receives more than 50% of the

mean dose D0 [17].

3D dose distributions are simulated for every minibeam arrangement and they are used to calculate the mean cell survival for 2 Gy and 10 Gy tumor dose with linear quadratic model using different irradiation setups. According to the particle irradiation data ensemble (PIDE, [18]), the parameters for the survival model (1.2) are chosen as α = 0.425 Gy−1, β = 0.048 Gy−1 to take into account the mean value of all listed human cells.

This result shows that both broad beam and minibeam deposit a homogeneous dose in the tumor. The benefits of the use of minibeam is evident because up to d ' 7cm depth a large number of cells are spared in the healthy tissue compared to broad beam irradiation.

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Figure 2.6: Mean cell survival for 2Gy (solid lines) and 10Gy (dashed lines) tumor dose vs depth. The different colors mark the different applied irradiation modes. [17]

2.2.2 Experiment using proton minibeams

Several experiments are carried out at SNAKE to prove the reduced negative irra-diation effects of microchannel irrairra-diation compared to a homogeneous broad beam irradiation. One of the first experiment performed at SNAKE is carried out using an in vitro 3-dimensional human skin model [1]. In this experiment, skin models are irradiated with a 20 MeV proton beam applying an average dose of 2Gy using 10 µm or 50 µm wide irradiation channels on a quadratic raster with distances of 500 µm between each channel (center to center). For comparison, other samples are irradiated homogeneously at the same average dose. Levels of inflammatory pa-rameters are significantly lower in the human skin tissue sample after microchannel irradiation than after homogeneous irradiation. The genetic damage, determined by the measurement of micronuclei which are chromosome or a fragment of a chromo-some not incorporated into one of the daughter nuclei during cell division, is lower using proton minibeam compared to homogeneous irradiation

In preclinical experiments [19], side effects caused by proton broadbeam and proton minibeam are compared using an in vivo animal model. To study the acute radiation response, 20 MeV proton beam is administered to the central part (7.2x7.2mm2_{) of}

the ear of BALB/c mice, using either a homogeneous field with a dose of 60 Gy or 16 minibeams with a nominal 6000 Gy (4 x 4 minibeams, size 0.18 × 0.18 mm2, with a distance of 1.8 mm). By using this different irradiation techniques the same average dose is deposited over the irradiated area and the results are compared with ear mice that are not irradiated. In this experiment it is proven that homogeneous irra-diation increases mice ear thickness and provokes a high degree of edema, erythema, desquamation and hair loss in the irradiated area. In contrast, mice irradiated using minibeam show no effects (figure 2.8). Moreover, the number of micronuclei

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mea-CHAPTER 2. PROTON MINIBEAM RADIOTHERAPY 20

sured in the blood of mice irradiated by using homogeneous fields is much higher compared by using minibeams.

Figure 2.7: Right: Mean ear thickness of the right ears of mouse model by applying proton minibeam (MB), homogeneous (HF) and sham-irradiation (CO) (Taken from [2]).

Left: Complete skin response following proton irradiations, i.e. erythema and desquama-tion ([2]).

Figure 2.8: Time course of the skin response after minibeam (MB) and homogeneous (HF) irradiation. Severe erythema, desquamation and hair loss appears after 3 weeks using homogeneous beam, while barely no effects are showed using submillimiters beam ([2] )

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Chapter 3 Study of the beam spot size at 20

MeV

The beam spot size is defined as the full width half maximum of the dose distri-bution. Considering the beam distributed as a gaussian with radially symmetrical shape, it has been proven both with calculation and experiments, that the full width half maximum of the dose distribution at the surface of the sample should be less than 470µm to maximize the benefits of minibeam. The aim of this experiment is to measure the beam spot size in fuction of the distance between the beam exit window and the detector using 20 MeV proton beam. The measures are performed consider-ing different irradiation setups and rhe experimental results are compared with the theoretical calculations and simulations.

3.1 Experimental Setup

This experiment is performed at the ion micropobe SNAKE, described in section 2.2. The setup used to measure the beam spot size is displayed in figure 3.1. The beam exits the vacuum chamber by passing through a window covered with a kapton foil and it is detected by a scintillator or by a film that is placed in a holder on a microscope slide. The microscope is used to acquire images from the scintillator and to move the detector. The beam spot size depends on the distance between the nozzle and the detector (air-gap distance) and on the thickness of aluminium foil that can be placed after the nozzle. The values of the air gap distance are 0 ≤ d ≤ 80 and 0 ≤ d ≤ 40 respectively for the setups with and without the aluminium foil, because these values representing reasonable distance to place the sample for preclinical studies in order to keep the beam spot size small.

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CHAPTER 3. STUDY OF THE BEAM SPOT SIZE AT 20 MEV 22

Figure 3.1: CAD drawing of the SNAKE irradiation setup [2]

3.1.1 Kapton foil window

A nozzle with a kapton window is placed at the end of the vacuum chamber. Kapton is a tough, aromatic polyimide film developed by DuPont. Kapton is widely used in IMRT radiotherapy because it remains stable across a large range of temperatures, has a low effective nuclear charge (Zef f) so to minimize multiple scattering events

in the foil and it can withstand the high pressure due to the vacuum chamber [20]. The optimal kapton thickness for the nozzle’s window used for 20 MeV proton beam experiment is 7.5µm, because this value does not increase the angular straggling considerably. Therefore this value is used for all the experiments but one, where a 25µm is chosen because it is suitable to cover the bigger nozzle’s window that could be used for preclinical experiment at higher beam energy.

3.1.2 Aluminium foil

Aluminium foils of different thickness are used as attenuator material to reduce the energy of the beam. In order to achieve a homogeneous dose at a certain depth and to create a Spread Out Bragg Peak reproducing the tumor shape, it is necessary to overlap several beams with different energy (see section 1.2). In general an attenua-tor is considered optimal if it can significantly decrease the energy of the beam but, at the same time, the beam spot size does not increase significantly.

Aluminium foils can be placed in the holder between the exit nozzle and the mi-croscope. The foils used in this setup have an area of 5x5cm2 _{and thickness of}

0.2 mm, 0.4 mm, 0.6 mm. Since atomic number and density of aluminium are z = 13 and ρ = 2.7_cmg3, when crossing this material many multiple coulomb scattering

in-teractions occur between protons and aluminium nuclei. For this reason the beam spot size highly increases with the thickness.

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3.1.3 Detection of the beam

The detectors used in this experiment are the YAG scintillator and the Gaf chromicT M

film EBT3. The resolution of Gafchromic film is 21µm so it is not suited for small beam size measurements. Using the scintillator it is possible to acquire a magnified digital image of the detected beam spot size by using the microscope (see section 3.1.4). For this reason the scintillator is used to measure small beam spots, so concerning the configuration without aluminium foil and for small air gap distance.

YAG(Ce) Scintillator

YAG (Yttrium Aluminum Garnet activated by Ce3+) is a synthetic crystalline ma-terial of the garnet group doped with Cerium impurities. These impurities, called activators, modified the gap structure, creating energy states within the band gap. When protons hit the scintillator, the electrons from the filled valence band are ex-cited to the empty conduction band and at the same time holes are created in the valance band. Both electrons and holes seek to find the lowest energy levels available close to them, which are respectively the state levels of the activation centers near the conduction band and near the valence band. Free electrons and holes recombine via an excited state of the impurity causing photons emission.

Gafchromic film

Gaf chromicT M _{film ETB3 is a particular type of radiochromic film. In general}

radiochromic film consists of a single or double layer of radiation-sensitive organic microcrystal monomers on a thin polyester base with a transparent coating. Upon irradiation the color of the radiochromic films turns to a shade of blue. The mate-rials in the radiochromic film that are responsible for the coloration are crystalline polyacetylenes, called diacetylene, that due to the radiation exposure start a poly-merization reaction.

The film is composed by an active layer, nominally 28µm thickness, sandwiched be-tween two 125µm matte-polyester substrates. The active layer contains the active component, a marker dye and stabilizers [21]. Gaf chromicT M _{EBT3 is one of the}

most suitable detector for many applications in IMRT because it offers a dose-rate independent response and a good spatial resolution. Besides due its composition (43.3 % C, 39.7% H, 16.2 % O, 1.1 % N, 0.3 % Li, 0.3 % Cl ) has a Zef f = 6.98 that

makes it near tissue equivalent.

3.1.4 Microscope

The fluorescence microscope (Zeiss Axiovert 200M), installed behind the beam exit nozzle, is used for positioning and moving the detector and to acquire digital imagine of the detector using a magnification factor up to 40X [22].

The microscope can be moved along the beam axis from a remote control. Using the microscope software it is also possible to configure the irradiation matrix with defined distances by moving the sample with the microscope stage.

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3.2 Experimental procedure

The minibeam used in this experiment is obtained by varying the current of the superconducting lens until the beam is focused to sub-millimeters dimensions (de-magnifiation 88X in x direction and 24X in y direction). The irradiation of the detector is made using a 20 MeV proton beam with a current of I=8nA and a fre-quency of f= 500 kHz. The minibeam is generated with a rectangular shape but, as displayed in figure 3.2, due to the interaction with the crossed materials the shape of the beam can be considered nearly gaussian.

Figure 3.2: Generation of Gaussian shaped minibeam [23]

While the particles are crossing the target, the beam spreads itself due the in-teraction between the protons and atomic nuclei and for this reason the beam spot size increases. In particular the size of the beam spot increases with the distance from the target (air-gap distance) and with the thickness of the Aluminium foil. The FWHM of the beam spot size is measured using 5 different setups in function of the air-gap distance d.

The FWHM of the dose distribution can be written as:

F W HM = q

(F W HM )2

0+ (F W HM )2sc+ (F W HM )2div (3.1)

where (F W HM )0 is the initial beam size and (F W HM )sc is the beam spread due

to multiple scattering and (F W HM )div is the contribution of the divergence.

In this experiment the apertures of the object and the divergence microslit, which are distant L=5.7 m, are fixed for every irradiation and they are given by ∆ObjX =

40µm, ∆ObjY = 20µm, ∆DivX = 50µm, ∆DivY = 100µm. Hence the beam angle

at the divergence microslits can be calculated using:

Divergencex,y '

∆DivX,Y

L (3.2)

and the final beam divergence is estimated by taking into account the demagnifica-tion factor due to the quadrupole lenses (f=88 in x direcdemagnifica-tion, f=24 in y direcdemagnifica-tion),

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the distance between the divergence microslits and the quadrupole lenses (l=24m) and the air-gap distance. The initial beam spotsize (in the vacuum chamber) can not be measured, but since the spread due to the kapton foil is small, (F W HM )0

is estimated considering the value of the beam spotsize after crossing 7.5µm kapton foil and corresponds to (F W HM )0 = 0.9µm

Figure 3.3: Right: Example of beam spot matrix irradiation taken with GafchromicTM

film.

Right: Example of beam spot taken with the scintillator and processed with ImageJ to better display the image.

3.2.1 Measures taken using the scintillator

The YAG scintillator, which is positioned at the microscope stage, is put in con-tact and centered with the nozzle to determine the desired area of irradiation. For every configuration, the scintillator is irradiated a single time using a number of protons to reach a dose of D = 4 Gy (see section 3.2.2). The spot size detected by the scintillator is saved as digital image using the ZEISS camera of the microscope AXIOCAM with a magnification factor of 40X. The images are analysed with the software IMAGEJ to estimate the spot size (figure 3.3). The procedure to estimate the beam spot size consists of finding the center of the spot by selecting the max-imum grey value pixel, tracking a line which passes trough this pixel and plotting its grey value profile.

The full width half maximum (FWHM) of the grey values distribution is evaluated using the software MATLAB. In particular, since the distribution is not a proper gaussian, the FWHM is obtained using a linear interpolation among the point closer to the value of the half maximum.

To have a good statistic, exploiting the radial symmetry, for every measure the pro-jected profile plot is extracted 50 times in different direction. The beam spot size measure is given by the mean of the FWHM values and the error related is given by

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the standard deviation. The systematic error due to interpolation method is signif-icantly much smaller than stochastic error calculated with the standard deviation, so it can be neglected. Concerning the use of the scintillator, it can be assumed that there is a direct correspondence between the proton distribution and the dose distribution.

3.2.2 Measure taken using the Gafchromic

TM

film

Since the Gafchromic EBT3 has a dynamic dose range between 0.2Gy to 10Gy, it is necessary to calculate the number of protons used during the irradiation of the detector to not exceed the maximum dose [24].

If the protons are distributed homogeneously over the target volume, then the dose D depends only on the applied fluence F :

D = E m = F × LETH2O ρH2O = 0.16 Gy µm 3 _LET H2O F KeV (3.3)

where F is the protons flux, ρH2O is the water density and LETH2O is the value of

prtons in water since the the cells are mainly composed by water. Considering a 20 MeV proton beam, the value of the LETH2O can be written as:

LETH2O = 2.648

keV

µm (3.4)

Fixing the value of D = 4 Gy in order to stay in the dynamic range of Gafchromic EBT3 the value of the flux obtained is:

F = 9.44 1 µm2

(3.5)

Considering in first approximation the dose distribution as a gaussian, the number of protons is given by:

N = F Z ∞ −∞ e− x−µ 2σ2x 2 dx Z ∞ −∞ e− y−µ 2σ2y 2 dy (3.6) N = 2πσxσyF (3.7)

Assuming that the gaussian has a radially symmetrical shape, to calculate σx = σy,

every configuration of the experiment is simulated using the software SRIM (see section 3.5).

GafchromicTM _{film is irradiated using the number of protons calculated in equation}

3.6 with a rectangular matrix of irradiation created using the software Zeiss AxioVi-sion (see figure 3.3 ). In particular for every configuration the detector is irradiated 4 times and the irradiations are spaced by 1 mm in order to avoid the overlap of the beam spotsize. The detector is read with a flatbed color scanner (Epson Perfection V700 Photo) two days after irradiation. The red color channel pixel values (PVR) of the EBT3 film are analyzed with ImageJ (figure 3.3). The PVR are converted

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into a net optical density (netOD) using

netOD = − log₁₀ R0 Rexp

(3.8)

where the ”exp” refers respectively to exposed and ”0” to unexposed films. Calibra-tion of EBT3 film is required to calculate the dose from the optical density (figure 3.4). Using an irradiation field of A = 5x5mm2 _{and placing the EBT3 film in}

con-tact with the nozzle, the detector is irradiated using a number of protons given by :

N = D A

2.424 Gy µm2 (3.9)

Calibration of EBT3 films is realized creating a dose response curve of the film using

D = a netOD + b netODc (3.10)

where D is the dose, netOD the optical density and a, b, c are unknown parameters.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 netOD [#] 0 2 4 6 8 10 Dose [Gy] Experimental Data

Figure 3.4: Relationship between the dose and the net optical density (netOD) for a Gafchromic EBT3 film. The data are fitted using the equation 3.10’ and the value of the

parameters correspond to a = 11.1±0.6 [Gy] b = 76.3±0.9 [Gy] c = 2.9±0.2 (χ2_dof = 0.98)

The method to estimate the beam spot size is similar to the method used with scintillator, but the pixel which determine the center of the spot is the minimun intensity value.

3.3 Multiple Coulomb Scattering

Considering small-angle scattering crossing thin thickness matter and an initially well-collimated proton beam, the beam angular spread and the lateral spread can

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be calculated considering the theory of multiple scattering [25]. Crossing matter, the particle beam spread itself due the interaction with atomic nuclei and for this reason the beam spot size increases. The deflection of ions due to the interaction with atomic electrons is negligible compared to that caused by the Coulomb interaction with atomic nuclei. The dominant process that lead to the beam spread is the ”Multiple Coulomb Scattering”, that means that each particle of a beam undergoes many small-angle scattering events on its track through matter and it is statistically adding up to a net angular and lateral deviation from the original beam direction. Considering small-angle scattering and initially well-collimated ion beam, the full width half maximun (FWHM) of the angle scattering function ∆Φ can be calculated using :

∆Φ = ∆Φred

µ (3.11)

where ∆Φredis the reduced small angle scattering function and µ the transformation

parameter that can be calculated using:

µ = E0a 2ZbZt e2 0 4πε0 (3.12)

where Zb is the atomic number of the particle beam, Zt the atomic number of the

target, E0 the beam energy, e the electron charge, ε0 the dielectric permittivity of

vacuum and a is the Thomas Fermi screening length:

a = 0.886aB Z 2 3 b + Z 2 3 t (3.13)

where ab = 0.529 × 1010m describes the Bohr radius. The parameter that

char-acterized the small scattering function ∆Φred is the reduced path length τ given

by:

τ = πa2NTd (3.14)

where NT is the atomic density in _cmat3 and d is the matter thickness. The reduced

small angle scattering function ∆Φred is parametrized using:

ln(∆Φred) = a1ln(τ ) + a2 (3.15) for τ > 2000 and ln(∆Φred) = − b1 b2 ln(cosh(b2ln(τ ) + b3)) + b4ln(τ ) + b5 (3.16) for τ 6 2000

with bi and ai are the fit parameters with b1 = 0.62920, b2 = 0.27958, b3 = 0.55575,

b4 = 1.20229 and b5 = 0.03047 and a1 = 0.573 , a2 = 0.329, respectively. The

projected angular distribution function due to small angle scattering of a particle with no initial angular spread can be described using:

px,y(θx,y, d, E) = 2Γ(mΓ+1 2 ) ∆Φ(d, E)Γ(mΓ 2 ) √ π q 2mΓ+12 _{− 1(1 +} 4θ 2 x,y(2 2 mΓ+1 − 1) ∆Φ(d, E)2 ) (3.17)

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where Γ is the Γ-function and mΓ a parameter that can be calculated using:

mΓ = 0.05754 log2(τ ) + 0.62037 log(τ ) + 2.0887 (3.18)

According to [26], the lateral spread ∆ρ due to small angle scattering can be calcu-lated using: ∆ρ = ∆Φred µ d Γm = ∆Φ d Γm (3.19)

where Γm is the transformation function that can be calculated using:

Γm = (1 + 2m)

1

2m (3.20)

with m the parametrization function:

m = 1

2(−b1tanh(b2ln(τ ) + b3) + b4)

(3.21)

3.4 Beam spread in thick material

If the material crossed by the particle can not be considered thin, which it means that the particle energy lost is not negligible compared to the beam energy E0, the

multiple scattering distribution is better described by an iterative algorithm [25]. The algorithm, developed using MATLAB, consists in dividing the material into layers of thickness in which τ = 1, and applying the average energy approximation to each layer to obtain the individual p(θ, d, E) distribution. At the end of the target the total multiple scattering is determined by successive convolution of the distributions calculated from each layer. This approximation is valid because the to-tal multiple coulomb scattering contributions of the different layers are independent from one another.

3.5 SRIM Simulations

The software used to simulate the spread of the beam is based on a Montecarlo algorithm and it is called SRIM (Stopping and Range of Ions in Matter). SRIM is based on following large number of individual ion particle trajectories in a target [27]. The input required are the kind, number and energy of the particles, the composition and thickness of the targets and the angle of incidence of ions.

It is assumed that while the particles cross materials, they change direction as a result of nuclear collisions and moves in straight free-flight-paths between collisions. The energy is reduced as a result of nuclear and electronic energy losses and the trajectory is terminated either when the energy drops below a pre-specified value or when the particle’s position is outside the target. The nuclear and electronic energy loss are assumed to be independent. Thus, particles lose energy in discrete amounts in nuclear collisions and lose energy continuously from electronic interactions. To have a good statistic, a 20 MeV beam composed by 105 _{protons is used for every}

simulated configuration. The FWHM of the distribution is calculated using the same interpolation method used for the experimental beam spot size.

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The systematic error related do FWHM due to interpolation method is significantly much smaller than the error due to the simulation, which is 3.9% of the value of full width half maximum itself.

3.6 Results

For every setup configuration used at 20 MeV the beam spot sizes are measured as a function of the air-gap distance d and they are compared with the value of SRIM simulations and the theoretical results.

Concerning the set up without aluminium foil, for smaller gap-air distance the trend of the beam spot size is linear

F W HM = a × d + b (3.22)

while for bigger gap-air the FWHM of dose distribution can be written as

F W HM = c × dk (3.23)

Concerning the experimental data of the setup without aluminium, for d ≤ 20mm the measures are acquired using scintillator, while for bigger air gap distance the detector used is the EBT3 film.

0 10 20 30 40 50 60 70 80 90 Distance [mm] 0 50 100 150 200 250 300 350 400 450 FWHM dose distribution [ m]

Experimental measure 7 m Kapton using scintillator Experimental measure 7 m Kapton using EBT3film Simulation result 7 m Kapton

Theoretical calculation 7 m Kapton

Figure 3.5: Beam spots size vs air-gap distance using 20 MeV proton beam with 7.5µm kapton window. The data are fitted using equation 3.22 up to d=13 mm (solid line) and using equation 3.23 for d > 13 mm (dashed line). The parameters (a,b,c,k) from the experimental data (red curve), simulation results (green curve), and analytical calculations (blue curve) correspond to a1 = (4.73 ± 0.08) × 103, b1= (2.47 ± 0.06)[µm] (χ2_dof = 0.76)

c1 = (3.95 ± 0.06) × 103 k1 = (1.15 ± 0.02) (χ2_dof = 0.79), a2 = (4.73 ± 0.07) × 103, b2 =

(0.19 ± 0.01)[µm] (χ2

dof = 0.77) c2 = (3.81 ± 0.07) × 103 k2 = (1.11 ± 0.05) (χ2dof = 1.16),

a3 = (4.88 ± 0.09) × 103, b3 = (0.78 ± 0.05)[µm] (χ2_dof = 1.11) c3 = (3.24 ± 0.08) × 103

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CHAPTER 3. STUDY OF THE BEAM SPOT SIZE AT 20 MEV 31 0 10 20 30 40 50 60 70 80 90 Distance [mm] 0 100 200 300 400 500 600 FWHM dose distribution [ m]

Figure 3.6: Beam spots size vs air-gap distance using 20 MeV proton beam with 25µm kapton window. The data are fitted using equation 3.22 up to d = 15 mm (solid line) and using equation 3.23 for d > 15 mm (dashed line). The parameters (a,b, c,k) from the experiment data (red curve), simulation results (green curve), and analytical calculations (blue curve) correspond to a1 = (5.68 ± 0.08) × 103_{, b}

1= (4.22 ± 0.08)[µm] (χ2_dof = 0.67) c1 = (3.95 ± 0.07) × 103 k1 = (1.11 ± 0.08) (χ2_dof = 0.77), a2 = (3.45 ± 0.06) × 103, b2 = (0.81 ± 0.05)[µm] (χ2_dof = 0.72) c2 = (3.79 ± 0.05) × 103 k2 = (1.11 ± 0.02) (χ2dof = 1.08), a3 = (4.91 ± 0.07) × 103, b3 = (0.78 ± 0.06)[µm] (χ2_dof = 0.71) c3 = (3.24 ± 0.04) × 103 k3 = (1.15 ± 0.06) (χ2dof = 0.89), respectively.. 0 5 10 15 20 25 30 35 40 Distance [mm] 0 200 400 600 800 1000 1200 FWHM dose distribution [ m] Experimental measure 0.2 mm Al Simulation result 0.2 mm Al Theoretical calculation 0.2 mm Al

Figure 3.7: FWHM of the beam dose distribution vs air-gap distance using 20 MeV proton beam with 7.5µm kapton window and 200µm aluminium sheet. The data are fitted using equation 3.22The parameters (a,b) from the experiment data (red curve), simulation results (green curve), and analytical calculations (blue curve) are a1 = (24.3 ± 0.6) × 103

b1 = (45.6 ± 0.9)[µm] (χ2_dof = 0.76), a2 = (22.3 ± 0.7) × 10−3 b2 = (45.5 ± 0.9)[µm]

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CHAPTER 3. STUDY OF THE BEAM SPOT SIZE AT 20 MEV 32 0 5 10 15 20 25 30 35 40 Distance [mm] 0 500 1000 1500 FWHM dose distribution [ m] Experimental measure 0.4 mm Al Theoretical calculation 0.4 mm Al Simulation result 0.4 mm Al

Figure 3.8: FWHM of beam dose distribution vs air-gap distance using 20 MeV proton beam with 7.5µm kapton window and 400µm aluminium sheet. The data are fitted using equation 3.22. The parameters (a,b) from the experiment data (red curve), simulation

results (green curve) and analytical calculations (blue curve) correspond to a1 = (34.3 ±

0.7) × 103_b

1 = (81.8 ± 0.9)[µm] (χ2_dof = 0.38), a2 = (33.4 ± 0.7) × 103b2 = (68.2 ± 0.2)[µm]

(χ2_dof = 0.38), a3 = (32.4 ± 0.5) × 103, b3 = (66.1 ± 0.9)[µm] (χ2_dof = 0.56), respectively.

0 5 10 15 20 25 30 35 40 Distance [mm] 0 500 1000 1500 2000 FWHM dose distribution [ m] Experimental measure 0.6 mm Al Theoretical calculation 0.6 mm Al Simulation result 0.6 mm Al

Figure 3.9: FWHM of the beam dose distribution vs air-gap distance using 20 MeV proton beam with 7.5µm kapton window and 600µm aluminium sheet. The data are fitted using equation 3.22. The parameters (a,b) from the experiment data (red curve), simulation results (green curve), and analytical calculations (blue curve) correspond to a1 = (42.6 ± 0.7) × 103 b1 = (78.9 ± 0.8)[µm] (χ2_dof = 0.86), a2 = (41.8 ± 0.7) × 103

b2 = (58.7 ± 0.7)[µm] (χ2dof = 0.49), a3 = (40.7 ± 0.5) × 103 b3 = (71.7 ± 0.6)[µm]

(χ2

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3.7 Conclusions

As shown in figures 3.5, 3.6,3.7, 3.8, 3.9, for every experimental setup the calculated FWHM beam dose distribution are in good agreement with the experimental mea-sures and with simulation results. This means that the experimental procedure are accurate.

Using a 7.5µm kapton foil the requirement to obtain the beam spot size F W HM < 470µm is fulfilled for every air-gap considered (figure 3.5), while considering the setup with 25µm kapton the F W HM < 470µm up to d = 38mm (figure 3.6). Moreover, from figures 3.7,3.8,3.9 it could be noticed that using the setup with alu-minium foil the beam spot size increase considerably with the air gap. Considering t1 = (200 ± 10)µm, t2 = (400 ± 10)µm and t3 = (600 ± 10)µm aluminium

thick-ness, F W HM = 470µm at d1 = (17 ± 1)mm, d2 = (12 ± 1)mm, d3 = (9 ± 1)mm

respectively. According to SRIM simulation, the final energy of a proton beam with an initial energy E0 = 20M eV after crossing each aluminium thickness and the

corresponding air gap distance, is E1 = (18.7 ± 0.1) MeV, E2 = (17.7 ± 0.1) MeV,

E3 = (16.4 ± 0.1) MeV , respectively.

This mean that at this energy aluminium cannot be considered a good degrading material since the spotsize increase significantly with the thickness.

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Chapter 4 Scale of the beam spotsize at

70MeV

Experiments at SNAKE can be carried out with a proton minibeam of energy up to 20MeV. Considering in first approximation the tissue composed by water, the range of protons at this energy in tissue is d ' 4mm. To increase the energy of the proton beam in order to test the benefits of minibeam, a RF LINAC based on TOP IMPLART project (ENEA institute, Rome) is planned to be built after the tandem accelerator (described in section 5.4). The installation of the RF LINAC allows to accelerate particles up to 70 MeV. Since the LINAC is not built yet, the beam spot size at this energy is estimated, using the setup considered in section 3.1, by finding the scale factor obtained comparing the simulation results of the beam spot size at 70 MeV and 20 MeV and by applying it to the experimental results at 20 MeV.

4.1 Scaling to 70 MeV

For each setup used in the section 3.2, the scale factor is obtained by calculating the average of the ratio between the beam spots size at 20 MeV and at 70 MeV for every air-gap distance, and the related error is the standard deviation. Since the FWHM of the particle distribution depends on the inverse of the energy, it is reasonable that the value of the scale factor is f ' 0.29. However, since the angle due to the multiple scattering decrease by increasing the energy, considering higher energy the beam cross a smaller thickness of the material to reach the detector. Moreover, the relation ∆ρ ∝ E−1 (see section 3.3) is valid considering a single proton. The collective effects such as the repulsive force due to the high number of particle beams ( N ' 3 × 103− 3 × 107_{) should be take into account. For this}

reason the scale factor obtained by comparing simulation at 20 MeV and 70 MeV is higher than the ratio of the energy. To predict the value of the beam spot size at 70 MeV, the scaling factor is applied to the experimental measures at 20 MeV. The theoretical calculations and the simulations are performed as explained in section 3.3 and section 3.5, respectively. To select the setup suitable to maximize the efficiency of the minibeam technique ( F W HM ≤ 470µm), the value of the FWHM of the dose distribution is plotted in fuction of the air-gap distance.

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CHAPTER 4. SCALE OF THE BEAM SPOTSIZE AT 70MEV 35

Figure 4.1: Schemtic beam spreads crossing the target. The beam with lower energy pass through a thicker target.

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CHAPTER 4. SCALE OF THE BEAM SPOTSIZE AT 70MEV 36

4.2 Results

0 10 20 30 40 50 60 70 80 90 Distance [mm] 0 50 100 150 FWHM dose distribution [ m]

Figure 4.2: Beam spots size vs air-gap distance using 70 MeV proton beam with 7.5µm kapton window. The scale factor used to estimate the 70 MeV spotsize is f = 0.34 ± 0.02. The data are fitted using equation 3.22 up to d=13 mm (solid line) and using equa-tion 3.23 for d > 13 mm (dashed line). The parameters (a,b,c,k) from the experimen-tal data (red curve), simulation results (green curve), and analytical calculations (blue

curve) correspond to a1 = (1.33 ± 0.09) × 103, b1 = (1.17 ± 0.06)[µm] (χ2dof = 0.71)

c1 = (1.31 ± 0.06) × 103 k1 = (1.16 ± 0.06) (χ2_dof = 0.86), a2 = (1.17 ± 0.05) × 103,

b2 = (0.19 ± 0.02)[µm] (χ2_dof = 1.37) c2 = (0.71 ± 0.04) × 103 k2 = (1.11 ± 0.07)

(χ2

dof = 1.11), a3 = (1.27 ± 0.06) × 103, b3 = (0.19 ± 0.04)[µm] (χ2dof = 0.81)

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CHAPTER 4. SCALE OF THE BEAM SPOTSIZE AT 70MEV 37 0 10 20 30 40 50 60 70 80 90 Distance [mm] 0 50 100 150 200 FWHM dose distribution [ m]

Figure 4.3: FWHM of the beam dose distribution vs air-gap distance using 70 MeV proton beam with 25µm kapton window. The scale factor used to estimate the 70 MeV spotsize is f = 0.33 ± 0.01. The data are fitted using equation 3.22 up to d=15 mm (solid line) and using equation 3.23 for d > 15 mm (dashed line). The parameters (a,b,c,k) from the experiment data (red curve), simulation results (green curve), and analytical calculations (blue curve) correspond to a1 = (1.88 ± 0.08) × 103, b1= (0.81 ± 0.06)[µm] (χ2dof = 0.67)

c1 = (1.31 ± 0.07) × 103 k1 = (1.11 ± 0.08) (χ2_dof = 0.78), a2 = (1.56 ± 0.05) × 103, b2 =

(0.21 ± 0.02)[µm] (χ2_dof = 1.21) c2 = (1.28 ± 0.04) × 103 k2 = (1.12 ± 0.02) (χ2_dof = 1.19),

a3 = (1.61 ± 0.05) × 103, b3 = (0.26 ± 0.04)[µm] (χ2dof = 1.78) c3 = (1.07 ± 0.03) × 103

(39)

CHAPTER 4. SCALE OF THE BEAM SPOTSIZE AT 70MEV 38 0 5 10 15 20 25 30 35 40 Distance [mm] 0 50 100 150 200 250 300 350 400 FWHM dose distribution [ m] Experimental measure 0.2 mm Al Simulation result 0.2 mm Al Theoretical calculation 0.2 mm Al

Figure 4.4: FWHM of the beam dose distribution vs air-gap distance using 70 MeV proton beam with 7.5µm kapton window and 200µm aluminium sheet. The scale factor used to estimate the 70MeV spotsize is f = 0.35 ± 0.02. The data are fitted using equation 3.22. The parameters (a,b) from the scaled data (red curve), simulation results (green

curve), and analytical calculations (blue curve) corresponds to a1 = (8.5 ± 0.7) × 103

b1= 15.9 ± 0.6[µm] (χ2_dof = 0.86), a2 = (7.8 ± 0.5) × 103 b2 = 15.7 ± 0.8[µm] (χ2_dof = 0.38), a3 = (8.2 ± 0.5) × 103 b3 = 15.3 ± 0.9[µm] (χ2dof = 0.62), respectively. 0 5 10 15 20 25 30 35 40 Distance [mm] 0 100 200 300 400 500 600 FWHM dose distribution [ m] Experimental measure 0.4 mm Al Theoretical calculation 0.4 mm Al Simulation result 0.4 mm Al

Figure 4.5: FWHM of the beam dose distribution vs air-gap distance using 70 MeV proton beam with 7.5µm kapton window and 400µm aluminium sheet. The scaling factor used to estimate the 70 MeV spotsize is f = 0.34 ± 0.02. The data are fitted using equation 3.22. The parameters (a,b) from the scaled data (red curve), simulation results (green curve), and analytical calculations (blue curve) corresponds to a1= (11.6 ± 0.7) × 103b1 =

(27.8 ± 0.6)[µm] (χ2_dof = 0.38), a2 = (11.4 ± 0.7) × 103 b2 = 22.4 ± 0.7[µm] (χ2dof = 0.28),

Conditions for installing a RF LINAC as a post accelerator for pre-clinical studies using proton minibeams

Universit`

a di Pisa

Dipartimento di Fisica

Tesi di Laurea Magistrale

Anno Accademico 2018/2019

Conditions for installing a RF linac as a

post accelerator for preclinical studies

using proton minibeams

Candidate:

Advisors:

Raissa Berti

Prof. Franco Cervelli (Universit`

a di Pisa)

Contents

Abstract

Chapter 1

Radiation therapy

1.1

Radiation effects on cells

1.2

Radiotherapy treatment

1.2.1

Internal Radiotherapy

1.2.2

External Radiotherapy

1.2.3

Particles used in radiotherapy

Chapter 2

Proton Minibeam Radiotherapy

2.1

Proton minibeam spatial fractionation

2.2

The ion microprobe SNAKE

2.2.1

Proton minibeam simulation

2.2.2

Experiment using proton minibeams

Chapter 3

Study of the beam spot size at 20

MeV

3.1

Experimental Setup

3.1.1

Kapton foil window

3.1.2

Aluminium foil

3.1.3

Detection of the beam

3.1.4

Microscope

3.2

Experimental procedure

3.2.1

Measures taken using the scintillator

3.2.2

Measure taken using the Gafchromic

film

3.3

Multiple Coulomb Scattering

3.4

Beam spread in thick material

3.5

SRIM Simulations

3.6

Results

3.7

Conclusions

Chapter 4

Scale of the beam spotsize at

70MeV

4.1

Scaling to 70 MeV

4.2

Results