Introduction
1.1 Radiation Therapy
Cancer is one of the most prevalent diseases in the world. In 2011, 159,178 people died
from cancer in the United Kingdom [1] and the American Cancer Society estimates more
than 306,711 deaths from cancer in 2014 in the United States [2]. Radiation therapy
is one of the three main techniques employed to treat cancer, along with surgery and
chemotherapy [3].
Radiation therapy consists of using ionising radiation beams like photons, neutrons,
electrons, protons or other ionising particles to treat malignant diseases. Photon radiotherapy is the most common radiation technique used to treat cancer but it has some
major disadvantages like the dose delivered to healthy tissue due to the exit photon ( g.
1.1, a).
1.1.1 Proton Therapy
The potential of protons to treat malignant disease was rst recognized by Robert Wilson
in 1946 [4]. The physical characteristics of proton beams make them an ideal option for
radiation therapy.
There are two main processes for energy loss by protons: 1) multiple Coloumb scattering; 2) nuclear interactions. The rst point respects to de
ections through Coloumb
interaction with electrons (which can be ignored) and actual multiple Coloumb scattering through Coloumb interactions with atomic nuclei. The second point refers to direct
interaction with the atomic nuclei through elastic and in-elastic collisions. Elastic collisions leave the nucleus intact and cause de
ection of the incident proton, but in-elastic
collisions cause the loss of the incident proton and modify the nucleus, creating, among
others, short-lived radio-isotopes [5]. Unlike other particles, protons don't diverge much
from the beam axis, since their mass is much higher than that of the particles with which
they are interacting. This enables one to see a distinct range in tissue. The range of
protons depends on their kinetic energy and mass, which means that higher energies will
result in longer distances traversed in tissue.
This means that proton beams present superior dose selectivity, providing low energy
to healthy tissues { seen in the entrance plateau { and maximum energy in the target [5].
1
CHAPTER 1. INTRODUCTION
The rate of energy loss of charged particles due to Coloumb interactions in a certain
media of density is de ned through the stopping power, S(E):
S (E) =
@E
@z
(1.1)
For protons, the stopping power is described by the Bethe-Bloch equation [6][7] as follows:
S (E) = 0:307
Z
A
1
2
1
2
ln
2me
c
2 2 2
T
max
I
2
2
(1.2)
Protons' energy deposition per unit distance su
ers a steep increase when they lose
almost all of their kinetic energy, resulting in a high dose delivery when they reach that
depth. Thus, the dose deposition pro le presents a peak with a big fall-o
on the distal
edge ( g. 1.1, d), the so called Bragg peak. Their range occurs right after the maximum dose is delivered and, considering the continuous slowing down approximation, is
calculated through the following expression:
R =
Z
E
0
@E
@x
1
dE (1.3)
The range of two protons with the same energies can be di
erent, due to statistical
uctuations in the number of collisions and energy transfer that occurs in every interaction. Range is very often considered to be the depth where the dose decreased to 80% of
maximum dose [5][8].
Figure 1.1: Relative depth dose pro les in water for several particles with di
erent energies.
(a) Photons; (b) Neutrons; (c) Electrons; (d) Heavy charged particles [Adapted from [3]].
2
CHAPTER 1. INTRODUCTION
1.1.2 Range Uncertainties
As previously said, the Bragg peak presents a steep fall-o
on its distal edge. For this
reason, uncertainties in the range calculation are a major problem, since they can give
rise to big di
erences between the actual applied dose to the tumour and healthy tissues
and the planned dose, as seen in g. 1.2. In photon radiotherapy, this di
erence is only
of a few percent, but in the case of a Spread-Out Bragg peak proton therapy beam this
di
erence can be as high as 100% [5].
Figure 1.2: E
ect of range uncertainties in depth dose curves: (a)Photon
beam;(b)Monoenergetic proton beam (Bragg peak);(c)Proton beam (Spread-Out Bragg peak).
[Adapted from [5]].
In Proton Therapy, as in Photon Therapy, the planning and range calculations are
usually obtained using computed tomography (CT) data. As such, the values are a
ected
by the same problems of CT data acquisition, such as image noise and beam hardening
issues [5][8]. Since CT gives values of attenuation for photons, the Houns eld Units (HUs)
obtained are a relative measure of attenuation of x-rays in tissue, in comparison to water.
Thus, these values must be rstly converted to relative proton stopping powers and only
after that the ranges can be evaluated. Conversion of HUs to relative proton stopping
powers is dependent on the chemical composition, which means that two materials with
the same HUs can have di
erent proton stopping powers. It is estimated that a good
quality, well calibrated CT gives rise to range uncertainties of 3% [5].
Besides CT based uncertainties, there are also other sources of error for the range
calculation in proton therapy. One of which is
uctuation on the beam energy from one
session to another. Other source of uncertainties is the variation of the patient's positioning that can produce large errors, especially when treating areas with great density
heterogeneities [5][8]. One also has to consider that a regular radiation treatment occurs
over several weeks. During that period, patients' anatomy changes not only due to reduction of the mass of tumour but also because of weight changes or daily changes in the
lling of internal cavities (e.g. bladder, nasal cavities, bowel, etc.) [5].
When considering the above mentioned facts, one concludes that the optimal solution
for range uncertainty control would be a method that enables 3D dose monitoring online
in a non-invasive way.
3
Chapter 2
State of the art
2.1 Proton radiography and proton tomography
Proton radiography is a technique that has been studied since the second half of the 20
th
century as an imaging tool [5]. It consists of irradiating the patient with higher energy
protons, thus shifting the Bragg peak to depths outside his body. The protons are then
detected (outside the patient) and a residual range can be measured.
Unlike similar one dimensional techniques (e.g. range probe concept used for point
measurements), proton radiography uses a 2D
uence and the position of entrance and
exit of each proton is detected with the range measurement in order to improve spatial
resolution [5].
Knopf [5] considers that the most interesting justi cation to the usage of proton
radiography is the fact that it provides directly measured stopping powers of the irradiated
tissue, which are crucial for planning the treatment. As mentioned in 1.1.2, when X-Rays
are used for this purpose, the attenuation values of the tissue have to be converted to
proton stopping powers, providing a source of uncertainties. Thus, one of the advantages
of proton radiography for range veri cation is that it provides on line in vivo information
that can be directly used during the course of the treatment without adding any sources
of uncertainties. Moreover, the quantitative behaviour of protons is easier to understand
and allows the use of inexpensive detectors with 100% quantum e ciency [9].
However, proton radiography presents the disadvantage of low spatial resolution, due
to multiple Coulomb scattering. Protons su
er numerous de
ections due to the Coulomb
eld of the nuclei of the traversed material, giving rise to uncertainties when reconstructing their paths within the patient [5]. Nonetheless, Schneider et al [10] reported space
resolutions as good as 1 mm, through of the entrance and exit coordinates positions along
with measurements of the entrance and exit angles.
Proton radiography can be achieved through three physical phenomena: 1) marginal
range radiography, which takes advantage of the steep fall in proton intensity near the
mean range; 2) density pro le and porosity measurements, that use the energy lost by
individual protons during the path; 3) multiple scattering radiography, where the information is extracted from the angular spread of the proton beams as they traverse the
tissue [5].
Proton radiography can also be used for 3D measurements by means of tomography.
4
CHAPTER 2. STATE OF THE ART
Thus, it allows 3D range veri cation. However, ths technique is used mostly to calculate
protons stopping powers for treatment planning with higher accuracy [5].
This technique is the one which provides the most direct way of range monitoring
during proton therapy. Knopf [5] considers it as a 'true proton-beam's-eye-view projections', since these proton transmission images can be obtained with the same geometrical
setup of the actual treatment. The fact that it delivers low doses to the patient makes
(since only the entrance plateau deposits energy in the body) it possible to apply proton
radiography for range veri cation in every fraction of the treatment, allowing a better
overview of the patients anatomy and position changes, thus reducing sources of range
uncertainties [5].
Although proton radiography has proven to be capable of performing online in vivo
range veri cation, to the moment, no literature refers its usage in clinical environment.
2.2 Prompt gamma imaging
Prompt gamma imaging relies on the detection of the gammas emitted due to nuclear
interactions. Prompt gammas are produced from the excitation of the nuclei by the
incident protons. Unlike coincident gammas that result from positron annihilation (used
for Positron Emission Tomography), only one gamma is emitted when the nuclei come
back to their ground state. This technique was rst proposed by Min et al [11] and has
been, since then, vastly studied in several research centres around the globe [5].
During therapy, protons interact with the atomic nuclei during almost all their path
until they lose large amounts of energy in the pre-Bragg peak depth (until 2-3 mm before).
This means that prompt gammas are correlated with the penetrated path of the beam
in tissue, enabling the usage of prompt gammas for range veri cation. Since there is an
o
set between the gamma fallo
and dose fallo
, one has to consider that di
erence before
drawing conclusions. Thus, only when working with well known and consistent di
erences
this method can be applied.
According to Knopf [5], the main advantage of this technique is its ability to be used
online, since the gammas can be detected almost immediately after production. The fact
that no additional dose is delivered to the patient also supports the usage of prompt
gamma imaging. Min et al reported a spatial resolution of 1-2 mm for the position of
the Bragg peak of a 100 MeV proton beam traversing a phantom. Furthermore, several
groups con rmed this resulted and presented results from Monte Carlo simulations that
demonstrate the feasibility of the technique for pencil monoenergetic beams through all
the range energies clinically used [5]. This illustrates the aplicability of prompt gamma
imaging in clinical practice.
Knopf [5] also points out that the feasibility of using this technique for scattered
SOBP is theoretically proven, but measurements performed with a collimated detector
failed to detect the gamma fallo
at the position of the Bragg peak. The possible reason
he points for this problem are the background neutrons and stray gammas that blur the
position of the Bragg peak. Thus, there's still a need for future studies of other detector
systems that may overcome this problem. However, given the huge development of this
technique since it was rst proposed, there's a good chance of clinical applicability with
good accuracy results when a suitable detector is built [5].
5
CHAPTER 2. STATE OF THE ART
2.3 Positron Emission Tomography imaging
As mentioned in 2.2, PET imaging makes use of coincident gammas generated by positron
annihilationby by electrons. These are generated by the interaction of protons with atomic
nuclei of the tissue, producing unstable isotopes that decay to more stable states. One
of the advantages of this method is that no additional dose delivery in the patient is
necessary.
The usage of PET imaging in radiotherapy was rst proposed in the late 1980's for
pion, neutron, and heavy-ion radiotherapy [5]. It was later studied the possibility of
applying the same technique for in vivo dose monitoring during proton therapy.
The production of the isotopes, unlike conventional PET imaging, is done solely by
the interaction with protons. Thus, it depends greatly on the elemental composition of
the tissue [5]. The relation between the distribution of the activity within the patient
and the energy deposition is not direct, which means that di
erent activity distributions
can be achieved resulting from the same dose deposition delivered in di
erent tissue
inhomogeneities. So far, attempts to determine the total dose distribution have failed due
to this problem [5]. Furthermore, the relation between dose and activity is also a
ected
by the minimum energies necessary to produce beta
+
-isotopes, resulting in a drop of
coincident gamma production before the dose fallo
, since protons lose most of their
energy in the Bragg peak, which causes the dose and activity distributions to be shifted
against each other [5].
There is also another impediment regarding the activity distribution: it changes depending on the timing of acquisition due to di
erent half-lives of the isotopes produced
and due to wash-out e
ects (in perfused tissues) [12][13]. The combinations of this problems prevents a direct range monitoring by the comparison between activity and dose.
Thus, a comparison of the measured activity with a modelled activity is needed in order
to take conclusions regarding dose deposition. This, however, isn't straightforward, since
complex Monte Carlo calculations are necessary for the prediction of the activity in patients [5]. Moreover, Monte Carlo calculations have to be complemented with functional
information about the patient. That information only exists for animal studies, so far [5].
To overcome this problems, an alternative to Monte Carlo calculations was presented
by Parodi et al [14] and consists of convolving the planned dose distribution with a lter
function, which can be achieved analytically. This method only evaluates the distal fallo
region of the PET measurements, but this isn't an issue, since it provides information
about the depth of interest, i.e. the Bragg peak depth [5]. One advantage of this method
is that it can be inverted, providing dose information from a PET signal by inverting the
lter functions [5].
Either one of the two approaches mentioned above have limitations regarding the
knowledge of the elemental composition and wash-out processes. There are some institutes
already applying this technique for in vivo range veri cation, but it's clinical bene ts still
raise doubts, since quantitative data is hard to produce [5].
6
Chapter 3
Purpose, objectives and project outline
The purpose of this work is to develop a novel computational model for protoacoustic
in vivo range veri cation during proton therapy using the Monte Carlo particle physics
toolkit Geant4 and "k-Wave" toolbox for the time domain simulation of acoustic elds.
As stated in 1.1.2, range uncertainties are the main restraining factor when applying
proton therapy. This means that studies to overcome this problem are necessary, so
that this technique may be used at its full potential. Considering the state of the art,
protoacoustics may become one of the main techniques employed for range veri cation,
since it is theoretically able to provide submillimetric spatial resolution with no additional
dose for the patients. It also may have the advantage of low-cost implementation, but this
kind of consideration still needs further studies regarding the whole setup of equipments
in a real clinical environment.
The model constructed in this project will be used to test the feasibility of this technique during treatment by providing acoustic data generated by the interaction of proton
beams with a water phantom. It is expected that the data obtained will provide information about the position of the Bragg peak within the phantom, enabling optimization of
the planned dose during treatment.
Moreover, the data will be used to assess the geometry of the optimal setup for
the technique, by comparing di
erent placements of acoustic transducers. The obtained
acoustic data will also be used to solve the inverse problem of the distribution of the
dose delivered by the proton beam, by means of the inverse time domain simulation tool
available in "k-Wave".
Figure 3.1 presents a
owchart of the outline of the project. Stage 0 is currently being
performed to assess di
erent ways of implementing the initial model. Although literature
still doesn't present much information about this topic, photoacoustic studies may be a
useful resource, since the same mechanism is responsible for the production of acoustic
waves.
Stage 1 will be initiated on during the second half of February, 2015. It will consist
of thorough computational simulations to stress out the optimal setups for protoacoustic
studies. This will include beam positioning, phantom size, beam energy and dose at
the Bragg peak. Moreover, it will also include the position and number of the acoustic
transducers used to acquire the signal.
7
CHAPTER 3. PURPOSE, OBJECTIVES AND PROJECT OUTLINE
Stage 2 will be performed after an optimal setup is obtained. It will consist of taking advantage the available tool of "k-Wave" for the time inverse simulation of acoustic
dynamics. This feature will be used in order to solve the inverse problem of the dose
distribution that generated the measured super cial acoustic waves.
Stage 3 will only be implemented if the previous stages show promising results and if
there are enough available resources to perform the experimental studies.