Physics and Astronomy Department
Physics and Astronomy Comps Papers
Carleton College Year
The physics of boron neutron capture
therapy: an emerging and innovative
treatment for glioblastoma and
melanoma
John FlobergCarleton College, [email protected]
This paper is posted at Digital Commons@Carleton College.
http://digitalcommons.carleton.edu/pacp/8
1
The physics of boron neutron capture therapy: an emerging and innovative treatment for glioblastoma and melanoma
John M. Floberg Senior Integrative Exercise
Department of Physics and Astronomy Carleton College
Advisor: Kris Wedding
Abstract: There is no one treatment for cancer, and the search for ways to combat cancer have led to many different treatments, including surgery, chemotherapy, and radiation therapy. However, these treatments are not always effective, and in such cases new treatments must be developed. Boron neutron capture therapy (BNCT) is a treatment that has been proposed to combat glioblastomas of the brain and malignant melanomas, two tumors that are resistant to traditional cancer therapies. BNCT is based on the 10B(n,α)7Li reaction, which can potentially deliver a very high and fatal radiation dose to cancerous cells by concentrating boron in them. It is a promising, though complicated treatment. Neutron beams must be generated with an adequate neutron flux, and moderated to therapeutically useful energy levels. The dose is difficult to calculate in BNCT because of all the types of radiation involved: photons, neutrons, and heavy charged particles. Dose is also highly dependent on boron distributions, which are not uniform and are difficult to measure. This makes accurate treatment plans difficult to develop. However, progress has been made on all these fronts and clinical trials have been conducted and shown that BNCT is a potentially safe and effective treatment for glioblastoma and melanoma. It provides an excellent example of the importance of innovation in the search for a cure to cancer.
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I. Introduction When considering the most sought after scientific achievements in the world, the
cure for cancer must rank toward the top. Cancer has touched nearly everyone in this
world in some way, but a definitive cure for cancer has proved to be elusive. Nor does it
seem that a definitive cure is even practical. There is great variety in the types of cancers
that affect humans, each affecting a specific organ or tissue and behaving in a specific
way, even if they are caused by the same basic mechanism: the rapid, unregulated, and
abnormal division of cells. Each case of cancer must therefore be treated individually.
An afflicted patient and his/her physician must carefully consider a number of factors
about the case: the type of cancer, the characteristics of the tumor, the stage of the
cancer, and if it has metastasized. One must also keep in mind that some cancers are not
curable given our current technology. Unfortunately, at times treatment must simply be
palliative, extending survival time and improving quality of life as much as possible.1
A variety of options are now available for cancer treatment. Perhaps the oldest
and most common treatment is surgery. The effective removal of a cancerous tumor is
the surest way to cure a patient. However, surgery is not always effective or possible,
and sometimes the risks involved and the potential side effects can be substantial
deterrents. For example, some tumors might be spread out within healthy tissues, making
it impossible to remove all of the cancerous cells, or they might be in or surrounding a
critical organ, such as the brain or a major blood vessel. As a result, other treatments for
cancer, such as chemotherapy, hormone therapy, and radiation therapy, have been
developed as alternatives or complements to surgery. A combination of treatments is
often used. For example, a patient might first undergo surgery to remove the bulk of a
3
tumor, and then undergo a series of radiation and chemotherapy treatments to remove or
control remaining cancerous cells.
Radiation therapy has proved to be one of the most effective ways to control or
cure certain types of cancer, often times in conjunction with another type of therapy. The
goal of radiation therapy is to deliver a high radiation dose to cancerous cells and a
minimal dose to healthy tissue, and there are a number of different treatment options.
Photon therapy, the treatment of tumors by bombarding them with x-rays, is the most
common and best studied, but therapies with electrons, protons, neutrons, heavy ions, and
even Π mesons have also been used or considered.2-4 Each particle offers potential
benefits for certain cancers, and though the physics differs depending on the type of
particle used, the general principles behind all treatments are the same. Since an entire
textbook could easily be produced on the physics of radiation therapy in general, this
report will present the general idea of the physics behind a radiation therapy treatment by
looking at a specific type of radiation therapy, boron neutron capture therapy.
Boron neutron capture therapy, or BNCT, is one type of radiation therapy that has
shown promise for treating tumors that have strongly resisted traditional treatments,
specifically glioblastoma and malignant melanoma.4-6 Glioblastoma is a malignant brain
tumor with a grim prognosis, survival times on the order of months, and melanoma is a
type of skin cancer that can spread to vital organs like the brain. These tumors are
usually spread out, making effective surgery difficult, and in the case of glioblastoma, the
blood brain barrier prevents chemotherapy drugs from being effective. Effective
radiation therapy is also difficult because of the diffuse nature of these tumors and
4
because they do not have a good supply of oxygen, which is necessary for creation of the
free radicals that do most of the damage in radiation therapy.
BNCT could be effective at treating these tumors because it provides a way to
deliver a very high radiation dose selectively to cancerous cells, even if they are spread
out. In BNCT, boron containing compounds, or boron delivery agents, are administered
to cancerous cells, which are then irradiated with neutrons, inducing the 10B (n, α) 7Li
nuclear reaction:
10B + nth(0.025 eV) 4He2+ + 7Li 3+ + 2.79 MeV (6%) (1a) 10B + nth(0.025 eV) 4He2+ + 7Li 3+ + 2.31 MeV + γ (0.48 MeV) (94%) (1b)
The energy of the neutrons used depends on the depth of the tumor. Thermal (<0.05 eV)
neutrons are used to irradiate superficial tumors, and epithermal neurons (1 eV- 10,000
eV) are used for deep seated tumors because they penetrate farther into the body before
being slowed down to thermal energies. This reaction delivers a very high, localized
dose of ionizing radiation that is much more effective at killing cancerous cells than
traditional x-ray ionizing radiation, assuming boron is selectively concentrated in them.
There are some drawbacks to BNCT. It is difficult to produce and control a beam
of neutrons adequate for BNCT, and even more difficult to selectively concentrate boron
in cancerous cells. The radiation dose in BNCT is also much more complicated than in
traditional forms of radiation therapy. Several types of radiation are involved in BNCT:
neutrons, photons, and heavy charged particles that can be produced in the 10B (n, α) 7Li
given in equation 1, as well as the 14N(n,p)14C and 1H(n,γ)2D reactions that can take place
as neutrons interact with healthy tissues.
5
14N + nth 14C + 1H+ + 0.626 MeV (2)
1H + nth 2D + γ(2.2 MeV) (3)
All of these factors make BNCT a complicated therapy to work with, and effective
treatments difficult to plan.
The study of BNCT provides a good way to examine and apply the general
principles behind radiation therapy. This paper will outline what is involved in a BNCT
treatment: the boron compounds used, the sources of neutrons and the filters used to
produce therapeutic neutron beams, the interactions of the types of radiation involved
with matter, the way treatments are planned, and actual clinical trials that have been
conducted or are under way. The development and study of BNCT also shows how the
cure for cancer progresses with the development of new and innovative tools.
II. History of BNCT
Different forms of radiation have a history of being put to use in medicine almost
immediately after they’ve been discovered. Only a few months after William Roentgen
discovered x-rays in 1895, he found they could be used to take pictures of bones. X-ray
cancer treatments came soon after.1,4 Radium was first used to treat cancer around 1901,
only three years after its discovery,2 and most important to this paper, neutrons were first
used in radiation therapy only six years after their discovery by Stone in 1938.3 BNCT
was first conceptualized in 1936, and the first trials began in 1952.7
The motivation for using different types of radiation stems from the increased
biological effectiveness of different types of particles (they kill cells more effectively
than photons). In the case of BNCT, it was known that boron was about 4000 times as
effective at capturing thermal neutrons (neutrons with a kinetic energy around 0.025 eV)
6
Figure 1: Illustration of intraoparative BNCT, like that done by Hatanaka in Japan. [Masaji Takayanagi, Boron Neutron Capture Therapy Irradiation Technology Forum, http://www.jaeri.go.jp, accessed February 28, 2005].
than atoms typically found in biological tissue.3 It was a quick step to consider how the
high energy ions released from the capture reaction in equation 1 could be used to kill
cancer cells and spare healthy cells if boron could be selectively concentrated in tumors.
When BNCT was first used to treat brain tumors in the 1950’s at Brookhaven
National Laboratory (BNL) and MIT, it met with little success. Patients were given
boron with the optimistic assumption that it would naturally be selectively taken up by
tumors, and that healthy tissues would be spared. They were then irradiated with a beam
of thermal neutrons from a research nuclear reactor. There was no evidence that these
trials prolonged survival times, and there was also typically excessive damage to the
scalp and normal brain blood vessels. The failure of these trials was attributed to poor
neutron penetration and poor specificity of the boron delivery agents for tumor cells.5,6
BNCT research continued in Japan from the late 1960’s through the 1990’s under
the guidance of Hatanaka.5,6 Hatanaka improved boron uptake by using a new boron
delivery agent, BSH (discussed in detail below), and improved neutron penetration by
performing BNCT intraoperatively, opening up
the scalp first (figure 1). Although there is a
bit of controversy surrounding how to interpret
the effectiveness of Hatanaka’s treatments, his
work renewed interest in BNCT.5
As with many types of radiation
therapy, the advent of faster computers and
new imaging modalities like MRI and PET
have greatly improved treatment planning for
7
BNCT and made new research and development possible. Current research areas for
BNCT include: improving the beam quality of incident neutrons, devising better
methods to accurately calculate dose, developing new boron delivery agents, finding
alternate sources of neutrons, and creating beams with epithermal neutrons, of energy 1
eV – 10 keV, that are capable of reaching deep seated tumors without the need for
operating.
BNCT has progressed to the point where significant tests have been done on
animals showing that it has great promise for the control and even cure of brain tumors
and melanoma.6 Clinical trials on humans have also been conducted, and are currently
being done all over the world. These trials are still principally aimed at establishing safe
and acceptable doses to healthy tissues, but they show great promise as a way to safely
deliver a high radiation dose to cancerous cells.5,6
III. Boron Compounds
Although there is not a lot of physics behind the boron compounds used in BNCT,
because the principal dose in BNCT comes from the boron-10 capture reaction, it is
important to have a good understanding of how these compounds are delivered and
selectively taken up by tumors. The two compounds currently most important to BNCT
are di-sodium undecahydro-mercapto-closo-dodecacarborate (BSH), mentioned above,
and p-boronphenylalanine (BPA) (see figure 2). These two compounds represent two
different approaches to delivering boron to tumors. BSH relies on passive diffusion from
the blood into brain tumors. Brain tumors disrupt the blood brain barrier (BBB), and as a
result BSH is able to diffuse into cancerous cells but not into healthy areas of the brain
where the blood brain barrier is still intact. Studies have shown that BSH can be taken up
8
Figure 2: The chemical structures of BPA and BSH, the two boron delivery agents currently in use for BNCT. Also shown are the chemical structures of CuTCPH and a liposome loaded with boron, two compounds that show promise as new boron delivery agents. [Rolf F. Barth et al., Neurosurgery 44 (3), 433 (1999)].
selectively by tumors, typically with a tumor/blood ratio between 1:1 and 2:1.6 BPA, on
the other hand, is actively taken up by cancerous cells. Because cancerous cells divide
more rapidly than healthy cells, they require more molecules needed for cell growth and
division. As an amino acid, phenylalanine is one such compound, and boron can be
attached to it relatively easily. Also, because it is incorporated into the cancerous cells,
BPA can potentially remain in cancerous cells long after it is administered. Studies have
shown that tumor BPA concentrations can reach 2-4 times higher than those in the blood
and other healthy tissues.6
Both of these compounds have been successfully put to clinical use as boron
delivery agents for BNCT, but they have their drawbacks. Cancerous cells do not take up
these compounds uniformly, so they deliver an uneven radiation dose, leaving some
9
cancerous cells alive and viable after a treatment. Also, concentrations in healthy tissues,
particularly in the blood, can be significant. Several remedies have been proposed for
these shortcomings. BPA and BSH could both be delivered at the same time. Since they
are supposedly taken up by different mechanisms, cancerous cells that do not take up one
might take up the other. Other boron delivery agents have also been proposed, the most
promising of which are boron-loaded liposomes and boronated porphyrins.6 Liposomes
are membrane enclosed vessels that can deliver large amounts of boron through the leaky
BBB around tumors, and porphyrins are basically molecular cages that have been shown
to selectively deliver boron to cancerous cells and to keep them there for extended
periods of time (see figure 2).
New methods for enhancing the uptake of boron delivery agents have also been
studied. These methods focus on increasing blood flow to the tumor and the permeability
of the BBB at the time of the boron delivery agent’s administration. This is typically
accomplished with different drugs. Direct injection of the boron delivery agent into the
tumor has also proved to be an effective way of increasing the boron concentration in
cancerous cells5. The concentration of boron in both healthy and tumor cells is extremely
important to BNCT, and the ways in which boron is delivered and taken up must always
be kept in mind when thinking of how dose will be delivered and how effective a BNCT
treatment will be.
IV. Sources of Radiation
An understanding of the sources of radiation is critical to understanding how a
radiation therapy modality works and the context in which it is used. One of the reasons
for the dominance of photon radiation therapy is the relative ease with which x-rays are
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produced and filtered. Conversely, one of the current obstacles for BNCT is the difficulty
of producing and controlling neutrons to create an adequate radiation beam.
Neutron beams for BNCT must have some very specific characteristics. They
must be thermal or epithermal, depending on the depth of the tumor, and they must be
uncontaminated by fast neutrons or gamma rays. They also must have an adequate
fluence rate, the total number of neutrons passing through a given area. This is
dependent on the concentration of boron in the target, but is typically around 109 cm-2 s-1,
so that the dose can be delivered in a short time, around 30 minutes. Finally, the beam
should be well collimated to avoid excessive dose to tissues outside the treatment area.6
Currently, the only sources of neutron beams that fit these criteria are research
nuclear reactors, which produce neutrons by the fission reactions that take place within
them, such as the uranium fission reaction.
235U + n 139Ba + 94Kr + 3n + 2γ (4)
Although there are several such reactors in the U.S., they must be specially modified to
produce neutron beams with the characteristics mentioned above. Elaborate filtering
system must also be attached to the reactor to properly shape the beam (figure 3). Such a
reactor would be too expensive and considered too dangerous to be put inside a hospital.
As a result, the only places at which BNCT experiments and treatments can be conducted
are at BNL and MIT in the U.S., and a few other reactors abroad.
To make BNCT more accessible and practical, the use of linear accelerators
(linacs) and cyclotrons as sources of neutron beams has been investigated. Linacs and
cyclotrons can produce neutrons by accelerating either protons or deuterons at lithium,
beryllium, or tritium targets. These protons and deuterons have enough energy to
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Figure 3: A schematic of how the BNCT treatment facility at the Japan Research Reactor No. 4 (JRR-4) is set up. Neutrons from the core are directed through a filtering apparatus to the patient’s head. [T. Yamamoto et al., Radiation Research 160, 70 (2003)].
overcome the repulsive coulomb forces of the target nucleus and get close enough to the
nucleus to feel the strong nuclear force. They are then captured by the target nucleus and
produce a new unstable nucleus that decays and gives off neutrons and other forms of
radiation, like γ rays. The physics behind linacs and accelerators is quite interesting and
is described in Appendix A. Linacs and cyclotrons are good candidates for BNCT
treatments because they can be made small enough to fit inside a hospital. 5,8-10
The main drawbacks with the current accelerator and cyclotron designs for BNCT
are that the neutron beams they produce do not have as good quality or as high a neutron
flux as the beams produced in reactors.6 The power of a proton beam needed to produce
an adequate fluence of neutrons from a lithium or beryllium target would be high enough
to melt and vaporize the target even with the most efficient cooling system.8 To try and
overcome this, different targets have been proposed. Li2O and Li3N, gas-to-metal tritium
targets, and W and Ta targets can all tolerate higher temperatures than standard targets.
12
The tritium and Ta targets also have a higher neutron yield, so they do not require proton
beams with as much power.8-10
V. Filtration
Whether neutron beams are produced by nuclear rectors, linacs, or cyclotrons,
they start with a broad energy range and are contaminated with other types of radiation,
and therefore require filtration. Although these neutron beams can be produced in
different ways, the same materials and techniques can be used to filter them. A good
neutron filter should posses some basic characteristics: it should maintain a high neutron
flux, significantly decrease the energy of fast neutrons without producing γ rays, filter out
unwanted γ rays, and filter out neutrons with an energy lower than desired.
The degree to which a filter does any of the above mentioned things to an incident
neutron beam depends on its cross-section for these various processes. The cross-section
is a way of describing the probability of an interaction taking place between two
particles, and is a very important concept in both the filtration of neutron beams, and the
way in which neutrons and other forms of radiation interact with matter and deliver a
dose to a patient, which will be discussed later. Cross-section is given as an area, so it
can be thought of as the area within which an incident particle must pass for it to interact
in a given way with the particle it is incident upon. Every type of interaction has a cross
section, and cross sections are dependent on the particles involved and their energies. It
should also be noted that two particles can often interact in a variety of ways, and each of
these interactions will have a cross section. A good analogy is to think of a skee ball
game. The ball is the incident particle, and each of the bins it can fall into represents
different interactions. There are several different interactions that can take place, just as
13
Figure 4: A neutron filter for an accelerator neutron source using D2O to slow down fast neutrons, 6Li neutrons to remove thermal neutrons, and lead to remove γ rays. The tally volume is the region in which the dose will be calculated. [D. A. Allen and T.D. Benyon, Physics in Medicine and Biology 40, 807 (1995)].
Figure 5: A neutron filter for an accelerator neutron source, using uranium, manganese, and fluental to moderate neutrons and create a therapeutically useful neutron beam. [Guido Martín and Arian Abrahantes, Medical Physics 31 (5), 1166 (2004)].
there are several bins, and each interaction has a different probability of occurring, just as
the ball is more likely to go in one of the larger bins than the smaller ones. Cross sections
are also dependent on energy, just as a slow ball will be more likely to go in some bins
than a fast ball.
There is no one magic material that has a sufficient cross section for all of the
interactions desired from a neutron filter; several materials are typically used in
succession, each filtering a specific component of the neutron beam. The most promising
materials to moderate fast neutrons while maintaining a high beam fluence and purity
seem to be heavy water (D2O) or a combination of heavy elements like uranium,
moderate elements like manganese and copper, and lighter fluorine compounds (figures 4
and 5). Heavy elements such as uranium slow down fast neutrons and increase neutron
14
Figure 6: Number of neutrons per original source neutron (N/N0) versus energy for an accelerator neutron source, using a filter of the type shown in figure 5. This filter was designed to produce an epithermal beam of neutrons, with neutron energy peaking around 10 keV. As can be seen, while this filter is very effective at eliminating higher energy neutrons, there is a very broad spectrum of neutrons at lower energies. [Guido Martín and Arian Abrahantes, (2004)].
flux by fission reactions, moderate elements like manganese further slow down the
neutron beam, and finally, the fluorides shape the neutron beam by brining all of the
neutrons to a desired energy level. Flourides shape the beam by preferentially scattering
neutrons. That is, neutrons with higher energies will continually be scattered until they
are at an energy where the scattering cross section with fluorine is much lower, and they
pass out of the filter at this energy. These filters are fairly good at eliminating high
energy neutrons, but they still give a fairly broad spectrum of lower energy neutrons (see
figure 6).5,8-10
In addition, a good filter for BNCT must remove unwanted forms of radiation,
such as neutrons with energies too low to be useful in treating deep seated tumors, and
γ rays. The best materials to remove low energy neutrons have a large capture cross-
section for neutrons, but do not produce unwanted forms of radiation after they capture
15
neutrons. 6Li seems to be the most promising material to remove thermal neutrons.8 To
remove γ rays contaminating the neutron beam lead is typically used because it has large
cross sections for various photon interactions (Figures 3 and 4).
Finally, some material must be used to reflect scattered neutrons back into the
beam to maintain a sufficient neutron flux to the patient. Lead and graphite are typically
used because they have high scattering cross sections for neutrons, but maintain a
sufficient flux of neutrons at the desired energy.8,9,11
16
Figure 7: An example of a dose depth distribution curve in a phantom for a neutron beam with a given energy. To generate this curve several assumptions were made, such as the radio biological effectiveness for the various radiation components, and the boron concentrations in the brain and the tumor. Displayed are the total dose to the tumor and healthy tissues, the dose to the tumor and healthy tissues due to boron, and the total dose from photons, thermal neutrons, and fast neutrons. If the energy of the neutron beam were to be adjusted, these curves would shift. [The Basics of Boron Neutron Capture Therapy, http://web.mit.edu/nrl/www/bnct/info/description/description.html, accessed April 2, 2005].
Once a neutron beam with the desired characteristics is generated with these
filters, it must be given the desired physical shape so that it is only incident on the
patient’s head. This can be done with any of the materials typically used as neutron
shields, which are compounds high in hydrogen such as wax, placed around the rest of
the filter (Figure 5).
These various filter components can be altered to create neutron beams of
different energies. Although dose has not yet been discussed, then energy of the neutron
beam is critical to determining how dose is distributed through a patient’s body. The
17
degree to which a neutron penetrates the body is dependent on its energy, so adjusting the
energy of a neutron beam changes where it deposits its energy. It is useful to display the
distribution of the energy deposited in tissue along a straight path, known as a dose depth
distribution curve (see figure 7).
Generating a neutron beam suitable for BNCT is certainly no easy task. An
adequate source of neutrons is much more difficult to find than a source of x-rays, and
filtering and moderating these neutrons so that they are adequate for BNCT is just as
difficult. However, as new sources of neutrons, such as accelerators, and more effective
ways of filtering and purifying them are developed, the potential for BNCT to effectively
treat certain types of cancer could be realized.
VI. Interactions of Radiation with Matter and Its Effects on Biological Systems
Radiation is damaging to biological tissues because it produces ions that disrupt
chemical processes important to the cell life cycle, damaging, altering, or killing cells.
Although this is true of all types of radiation, they interact with tissues in different ways,
and some forms of radiation are much more damaging to cells. BNCT involves several
different types of radiation: neutrons, heavy charged particles, and photons, and it is
important to understand how each of these interacts with biological tissues.
Low linear energy transfer (LET) radiation, principally electrons and photons, is
less damaging to cells. This radiation gives up its energy slower and primarily ionizes
water, creating free radicals (denoted below in equation 2 by dots) by the reactions:
H2O H2O+ + e-
H2O+ .OH + H+ (5)
H2O H2O* .H + .OH
18
These radicals then go on to react with chemicals in the cell, disrupting cellular
processes, some of which are essential to cell survival. The amount of damage done to a
cell from these radicals is dependent on the presence of oxygen, which helps create free
radicals. Radicals are far more damaging in the presence of oxygen than in anoxic cells.1
Heavy charged particles, or high LET radiation, gives up their energy much
faster, making them much more harmful to cells.1 A heavy charged particle will ionize
everything in its path. If such a particle passes through a cell’s DNA, it can cause serious
damage, resulting in cell death or destroying the cell’s ability to divide. This is one of the
principle reasons why BNCT has been proposed as a way to combat tumors that resist
traditional forms of radiation therapy. Traditional radiation therapy relies on low LET
radiation, which gives up its energy more gradually and is not as damaging to certain
types of cancerous cells, whereas only a few high energy heavy charged particles will
almost certainly kill any type of cell.5 The problem is that since these particles transfer
all of their energy so quickly, there is no real way to get them directly to cancerous cells.
The boron capture reaction in BNCT provides a way to create these high LET particles in
cancerous cells, in which they will deposit all of their energy and almost certainly kill.
To quantify the degree to which a type of radiation is damaging, quality factors
are used. These give the radiobiological effectiveness (RBE) of these various types of
radiation (see table 1). The higher the quality factor, the more damaging the radiation.
Table 1: Quality factors of ionizing radiation important to BNCT
Radiation Quality FactorPhotons and electrons 1 Thermal neutrons 5 Fast neutrons and heavy particles 20
19
The effects of radiation are also dependent on tissue. The rate at which the cells
in a tissue divide and the amount of oxygen they receive are two of the most important
factors determining how the tissue will be affected by radiation. Skin, central nervous
system (CNS) tissue, and the epithelia of blood vessels in the brain are the tissues most
important to BNCT because they receive the greatest dose. The skin absorbs a significant
dose from neutrons and γ rays, especially when BNCT is used to treat skin melanomas,
and a dose sufficient to warrant further medical attention or even skin grafts can be
delivered.12 When treating glioblastoma with BNCT, the epithelia of the blood vessels in
the brain receive a significant dose because of boron compounds in the circulatory
system. This can often be the dose limiting tissue for BNCT because of the high
radiation dose these stray boron compounds deliver.6 Healthy CNS tissue also receive a
significant radiation dose in BNCT, but because CNS cells divide so infrequently, the
problems caused by radiation in the cell cycles of more mitotic tissues are not manifest in
central nervous system cells.1
Before discussing how doses are determined and treatments are planned for
BNCT, and radiation therapy in general, one must have a good understanding of how the
different types of radiation involved in BNCT interact with matter and produce the free
radicals that are so damaging to biological tissue. Photons make up an important part of
the radiation dose received in BNCT. γ rays contaminating the neutron beam will deliver
a dose to the patient, as will γ rays produced as neutrons are captured by hydrogen and
nitrogen (see equations 2 and 3). This dose is significant and must be taken into account
in BNCT, especially when considering dose to healthy tissues with no boron since
photons can travel far from the tissues in which they are produced.5 The interactions of
20
photons with matter are well understood, and those most important to radiation therapy
are the photoelectric effect, Compton scattering, and pair production. All of these
processes act to liberate electrons, or positrons, which then go on to ionize other atoms.
This is why photons are called indirectly ionizing radiation. The physics describing how
these processes work is developed in Appendix B. Each of these interactions has its own
cross section that varies with photon energy, making certain interactions more important
at certain energies. For the energies involved in radiation therapy, Compton scattering is
most important.
Neutrons are another form of indirectly ionizing radiation. They can produce γ
rays by capture reactions with hydrogen, boron, and other nuclei (see equations 1 and 3),
which can then go on to produce electrons in the processes described in Appendix B.
Such capture reactions also typically produce heavy charged particles, such as the α
particle and lithium nucleus produced in the boron capture reaction central to BNCT
(equation 1). Neutrons can also impart energy to lighter nuclei, typically hydrogen, in
collisions, and these recoiling nuclei are also capable of ionizing atoms.
The heavy charged particles produced by neutron capture reactions are called
directly ionizing radiation. Because they are both massive and charged, these particles
are very interactive and will ionize a lot of atoms in a short range. As a high LET particle
passes an atom, its electric field interacts with the electric field from the atom’s electrons,
putting a force on these electrons. This force will be applied over a time, giving these
electrons momentum, which is related to the energy, given by:
(6) ΔE(b) =z 2ro
2moc4M
b2E
21
Figure 8: Diagram illustrating a heavy particle with mass M and charge +z interacting with an electron with point of closest approach b.
where b is the point of closest approach, z is the charge of the incident particle, M is its
mass, E its kinetic energy, ro is the classical electron radius, mo is the mass of the
electron, and c is the speed of light (see figure 8). This equation is derived in Appendix
B. If the electron is given sufficient energy, it will be knocked out of the atom. One of
the most important pieces of information given by this equation is that energy transfer is
inversely proportional to the kinetic energy of the heavy charged particle. Hence, more
energetic particles will travel a greater distance before depositing most of their energy.3
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Also the more massive an the more charged a particle, the more energy it will give up,
and the more damaging it will be.
One of the major drawbacks with BNCT is that all the types of radiation discussed
here are present and can affect all types of tissues, not only cancerous cells. Since the
damage to a cell is dependent on the radiation type, it is hard to compare the effects of
different types of radiation. It is generally accepted that there are four separate dose
components in BNCT: the dose from the 10B(n,α)7Li capture reaction; the proton dose
due to 14N(n,p)14C reactions; the neutron dose from fast neutrons; and the γ ray dose from
θ
cos θ = br
dxdt
= v
tanθ =xb
sec2 θ =dxdt
=vb
dt
22
γ ray contamination in the neutron beam and the 1H(n,γ)2D capture reaction.13 Although
these doses can all be weighted based on the quality factors given in table 1, Rassow et
al. have questioned the usefulness of such a combined dose as each of these types of
radiation affects cells in different ways. They stress the need to consider each dose
separately.13 The next two sections will describe ways in which dose to tissue can be
estimated based on the interactions described above.
VII. Dosimetry
The accurate determination of the radiation dose delivered to each part of the
body is central to any type of radiation therapy. It insures that healthy tissues are not
excessively damaged and cancer cells are actually killed. This is no easy task in a
complicated therapy like BNCT, which includes the doses from many types of radiation.
In general, dose is a measure of the energy deposited in a tissue, weighted by the quality
factors given in table 1. This is determined by different methods for each type of
radiation. Several of these methods are important to BNCT because of all the types of
radiation it involves.
For photons, the first step in determining dose is measuring the ionizing power of
a radiation beam, which is called the exposure. While this can be done in many different
ways, the most standard way is to place an ionization chamber in the path of the beam.
An ionization chamber is typically a cylindrical chamber filled with a noble gas, with a
metal wire charged to a high positive voltage running through the middle of it. When
photons ionize the gas, liberated electrons are accelerated towards the metal wire.
Electrons hitting the wire induce a current, which can be measured and related to the
amount of ionization the radiation caused (figure 9). Ionization chambers can also be
23
Figure 9: Diagram illustrating the basic ideas behind an ionization chamber to measure radiation exposure.
used to measure the overall exposure from all the types of radiation involved in
BNCT.14,15
Once the exposure has been found, it can be related to absorbed dose through a
quantity called kerma, which is the kinetic energy of all the ionizing particles liberated by
incident radiation in a given volume. The kerma is directly proportional to the energy
fluence, ψ, of the incident radiation, as well as the exposure. It takes a certain amount of
energy to produce an ion in air, and this idea can be used to find the dose from the
exposure:
AXfD medmed **= (7)
where fmed if a factor relating the degree to which the medium absorbs energy relative to
air, X is the exposure, and A is a factor relating the energy fluence at a point in the
medium relative to air. This equation is derived in Appendix C. It’s important to note
24
Figure 10: A solid phantom anatomically shaped and sectioned transversely for dosimetric studies. [Faiz M. Khan, The Physics of Radiation Therapy, Second ed. (Lippincott Willams & Wilkins, Philadelphia, 1994)].
that fmed and X are quantities that can be measured and A is just a factor that can be looked
up, so this provides a simple and effective way of calculating the dose a beam of
radiation will deliver to a patient.
Calculation of the neutron dose starts by measuring the neutron fluence. This is
typically done using metal detectors that are activated by neutrons. The activated metals
then decay and emit other forms of radiation like γ rays and β particles (electrons) that
can be detected using ionization chambers, plastic scintillators, or other standard
detectors. Gold and nickel foils are typically used.12,16 Plastic scintillators can also be
used by themselves to determine neutron fluence.
It is a bit more complicated to relate the neutron fluence to the dose because of all
the neutron interactions involved: the boron capture reaction, the nitrogen capture
reaction in healthy tissues, and protons recoiling from collisions with fast neutrons. The
two are typically related by some factor that is dependent on the neutron beam’s
characteristics: its energy spectrum, angular distributions, and spatial intensity
distributions.17 These characteristics can either be measured with the detection methods
mentioned, or predicted using computer simulations.
Since it is impractical to insert ionization chambers
and metal foils into a patient, these detectors are put into
phantoms that simulate tissues. A good phantom must have
approximately the same electron density as the body, or the
part of the body to be irradiated, since electron density is the
primary determining factor as to how radiation will interact
with a material. Water is often used, as it is a good
25
approximation for muscle and soft tissues, but is sometimes impractical. As a result,
many solid phantoms have also been developed (see figure 10). One of the most useful is
an epoxy resin-based solid called solid water. The dimensions of a phantom must be
sufficient so that the entire dose from the radiation beam is accounted for. Finding the
appropriate sized phantom for BNCT can be difficult because the required phantom
dimensions depend on the individual neutron beam’s characteristics: its energy, the
number of fast neutrons and γ rays contaminating it, and its diameter among other
parameters.15
Since the absorbed dose can often be complicated, especially in the case of
BNCT, there are other methods that can be used to try and measure it directly.
Calorimeters find the energy absorbed by water by measuring change in temperature, and
hence can provide an absolute measurement of absorbed dose, at least in the absence of
boron.14 This would be very practical way of determining the dose to healthy tissues
containing no boron. The problem with calorimeters is that they must be very precisely
constructed to measure the minute changes in temperature due to absorbed radiation.
However, studies have shown that calorimeters can accurately measure dose with an error
as small as 3%.14 Gel dosimeters have also been suggested as a way to accurately
measure the total dose delivered by neutron beams, without regard to the different
components of the beam.18 These are attractive methods for BNCT because they provide
ways to measure total dose, without regard to the different types of radiation involved.
VIII. Treatment Planning
With an understanding of how ionizing radiation delivers a dose to cells and
tissues, treatments for radiation therapy can be put together. Each treatment plan is
26
unique, taking into account the specific geometry of the patient in order to find a way to
deliver the dose necessary to kill the tumor, without delivering an excessive radiation
dose to healthy tissues. In order to do this, the radiation dose delivered to every point in
the body for a given irradiation must be estimated and then optimized. Once calculated,
these estimates can be displayed as isodose curves (curves along which the radiation dose
is the same, superimposed on medical images). Calculating these estimates is not an easy
task, especially in the case of BNCT with all the different dose components described
above. To develop an accurate an effective treatment plan for BNCT, one must know the
anatomy of the patient, the dimensions of the tumor, the concentration of boron in all the
parts of the body to be irradiated, the components of the neutron beam, and how they will
interact with the tissues present. Thanks to new imaging modalities and high-powered
computers and software, creating effective plans is possible.
The precise prediction of how a beam of radiation will interact with any target,
especially a complex biological one, is all but impossible. Any number of interactions is
possible, each with its own probability. For example, a thermal neutron may enter the
body, scatter off a hydrogen nucleus, imparting some of its energy, and then be captured
by a boron nucleus, causing 10B(n,α)7Li reaction described in equation 1. The α particle
and 7Li nucleus will then go on to ionize different particles, stripping electrons away
from atoms, which may then emit x-rays that will go on to Compton scatter off other
nuclei, and so on. Calculating the effects of even just one particle is quite an arduous
task. Fortunately, Fortunately, computer programs, particularly Monte Carlo simulations,
have made it possible to do many such calculations in a reasonable amount of time.
27
Figure 11: A schematic of how a Monte Carlo simulation works. Information about the neutron source, the geometry of the target, and the cross sections of the target are input into a computer program. The program then estimates how the particles involved travel through the target, and calculates dose on both a macroscopic and microscopic level, which it then displays, usually overlaid on medical images. [David W. Nigg, International Journal of Radiation Oncology, Biology, Physics 28 (5), 1121 (1994)].
Monte Carlo simulations essentially look at the behavior of large systems of
particles and have a variety of uses. For radiation therapy, Monte Carlo simulations take
into account the characteristics of an incident radiation beam, such as the number of
neutrons and photons, their energy spectra, and angular distributions, and the geometry of
the target, given by data from MRI (magnetic resonance imaging), CT (computed
tomography), and PET (positron emission tomography) images, and simulate the many
possible trajectories of each incident particle, arriving at an average result. Medical
images are used to create a set of regions, either by breaking down an image into small
voxels (three dimensional pixels), or by separating different tissues with generalized
surface equations. Each region is assigned certain material characteristics, such as
electron density, and especially important to BNCT, boron concentration. The path of
each particle is then simulated and tracked through each of the small regions it
encounters. Based on probabilities determined by the characteristics of the particle and
28
the region it is traveling through, such as the cross sections of various interactions, the
program decides whether or not the incident particle interacts within the given region. If
it does, then the energy imparted in the reaction is calculated and assigned as the dose to
that region. If the interaction generates other particles, such as α particles and 7Li nuclei,
these particles are given a trajectory, again based on probabilities, and their history is
tracked. If the particle does not interact, the process is repeated in the next region.17
Figure 11 provides a good schematic of all the processes involved in a Monte Carlo
simulation. These dose delivered to each region calculated by this method is integrated,
and isodose curves can then be generated, connecting regions that receive the same dose
(see figure 12).
The biggest challenge in accurately calculating dose for BNCT is the boron
distribution in tissues. In the simplest treatment planning programs, the boron
concentration in tumor cells is given a certain value and assumed to be uniform
throughout the tumor, and boron concentration in healthy tissues is assumed to be zero.17
These concentrations are based off in vivo or in vitro measurements of boron
29
Figure 12: Three dimensional isodose contours generated from a Monte Carlo treatment plan overlaid on a MRI image for a glioblastoma patient. A 3D isodose surface lies in the middle of the image. The neutron beam travels perpendicular to the MRI slice. [A. B. Andrews et al., http://www.ccd.bnl.gov/visualization/ gallery/bnct/bnct.html, accessed April 2, 2005].
concentrations in cancerous cells in
animals or in tissues removed from
humans during surgery.19,20 This is
however a gross misrepresentation
of the actual boron distribution. As
mentioned above, boron
concentration within the tumor is
highly variable, between patients
and within single patients between
different boron administrations, and
not all tumor cells take up the same
amount of boron.5,17
Various methods have been
developed to try to account for this. In one method, blood and tissue samples are taken
after the patient has been administered boron, and changes in boron concentration are
measured over time.12 These data can then be input into treatment programs to create a
more accurate dose distribution and to optimize the neutron beam. More promising is the
use of PET to track radio labeled boron compounds in the body. By attaching a
radioactive nucleus, typically fluorine-18, to the boron delivery agent administered, the
distribution of boron in both cancerous and healthy cells can be determined much more
accurately and much better dose distributions can be calculated (figure 13).20 The use of
PET not only improves treatment plans, but it has also proven to be a good prognostic
30Figure 13: Isodose contours generated from a treatment plan that uses PET to measure boron distributions on the left, and by assuming a uniform boron distribution on the right. The dose contours are much more irregular and significantly different when boron distribution is accounted for. [T. L. Nichols et al., Medical Physics 29 (10), 2351 (2002)].
tool. PET scans of boron distributions give information about how a tumor will react to
BNCT and if the treatment will be effective.21
Because the products of the boron capture reaction, which deliver the primary
dose in BNCT, give up their energy in such a short distance, dose distributions on a
microscopic scale are important to treatment planning.6,17 One must know where in the
cell the energy from the 10B(n,α)7Li reaction is deposited. If it is delivered to the nucleus,
it is much more damaging than it is deposited elsewhere in the cell. Monte Carlo
programs are also typically used to predict the track lengths of the particles produced in
the 10B(n,α)7Li reaction, but in order for these programs to make accurate calculations,
they must be given accurate measurements of microscopic boron distributions.17 The
most promising techniques to provide these measurements seem to be the PET scans
mentioned above, and gamma spectroscopy. In vivo microdosimetric measurements
would significantly improve treatment planning by providing much better data on how
radiation dose is actually distributed.
A number of treatment variables can be adjusted to determine the best possible
31
BNCT treatment for the given tumor. The optimal energy of the neutron beam can be
calculated so that the maximum dose is deposited at the site of the tumor; the beam can
be shaped so that the tumor receives a uniform dose from the neutron beam and healthy
tissue is spared; and the position of the patient can be varied so that as little healthy tissue
is put in harm’s way as possible. Other experimental variables include the use of
multiple beams to help escalate the dose to cancerous cells,11 and delivering the dose in
multiple treatments.6 Treatment planning for BNCT is a continually evolving process,
and as it continues to evolve, it makes BNCT an ever more attractive and effective
treatment for tumors that have resisted traditional radiotherapy.
IX. Current Clinical Trials
Although BNCT is still a fairly new and developing form of radiation therapy,
significant clinical trials have been done on humans and are advancing. Most clinical
trials are still moving out of the initial stages testing the safety and feasibility of BNCT,
but they have shown that BNCT can work as an effective treatment for both glioblastoma
and melanoma with tolerable side effects. Trials at Brookhaven and MIT have shown
that a significantly higher dose can be delivered to glioblastomas than healthy brain tissue
with a very low incidence of somnolence syndrome,5,6 a neurological disorder common
following brain irradiations, particularly when the whole brain dose remained below 5 Gy
(see figure 14). Trials have also shown that BNCT can be used to successfully cure skin
melanoma with tolerable damage to healthy skin cells.12
Clinical trials have been about as successful at treating glioblastoma as traditional
photon radiation therapy. As can be seen in figure 15, BNCT kills a significant number
of cancerous cells. However, as is the case in this figure, some cancerous cells remain
32
Figure 14: Peak dose versus the whole-brain average dose for the fifty patients treated at BNL and twenty patients treated at MIT between 1994 and 1999. Shaded boxes and squares represent patients who eventually developed somnolence. As can be seen, patients who received a whole brain dose of 5 Gy or more had a significantly greater chance of developing somnolence. [J. A. Coderre et al., Technology in Cancer Research & Treatment 2 (5), 355 (2003)].
after BNCT, particularly around the periphery of the tumor, and these typically cause the
death of the patient anywhere from a few months to a couple years after BNCT.
New trials are evaluating several different approaches to escalating the radiation
dose to tumors. One method is to modify the radiation beam or the way in which it is
delivered. The simplest modification is to increase the amount of neutrons the patient is
exposed to. Other methods, such as irradiating the tumor from multiple angles, or
delivering the radiation in multiple exposures, seem more promising. A lot of work is
also being done on finding better ways to deliver boron to tumors. As mentioned earlier,
boron compounds other than BSH and BPA are being tested, as well as new ways to
deliver them, such as in combination with drugs that disrupt the blood brain barrier.
33
Figure 15: MRI images from a glioblastoma patient. (A) Shows the patient immediately after surgery, (B) the patient prior to BNCT, (C) 2 weeks after BNCT, and (D) 6 weeks after BNCT. The bright white region in these images is the tumor, and the black region is necrotic tissue. The images show a dramatic increase of necrotic tissue within the tumor following BNCT. The residual tumor remaining around the edge eventually caused the patient’s death. [T. L. Nichols et al., (2003)].
Finally, work is being done to integrate the new treatment planning methods taking into
account the microdistribution of boron in tumors. Although these methods have shown
promise as a way to more accurately calculate dose, they have not yet been put to clinical
use6.
Based on the success of these initial trials, clinical BNCT is moving forward.
Trials are being conducted all over the world and the BNCT community is expanding.
Other uses for BNCT, such as treating liver tumors, have also been proposed.19 Although
it is a difficult treatment to perform, clinical BNCT has shown promise, and it will
hopefully become increasingly effective and feasible as research moves forward.
34
X. Conclusions
More than anything else, BNCT seems to be a very complicated and difficult
therapy. Neutrons beams are not easy to create, and it is even harder to shape them so
that they are therapeutically useful. On top of this, the radiation dose from BNCT is very
complex, consisting of four components that cannot be easily related to each other.
Treatment planning is further complicated by the fact that the dose in BNCT is highly
dependent on boron distributions. These distributions are very difficult to measure and
are highly variable. Calculated doses therefore have great errors associated with them,
and as a result it is easy to give cancerous cells an insufficient radiation dose to kill them.
One might be tempted to ask why even use BNCT. The answer lies within the
point stressed above that there is no one cure all treatment for cancer. Different tumors
require different treatments, so it is perhaps not even useful to consider certain treatments
standard or conventional. The battle against cancer demands innovation and depends on
the development of more effective methods to treat different types of tumors.
BNCT does just this. It has proven itself to be a viable alternative to standard
forms of radiation therapy for the control of glioblastoma and melanoma, and studies
have indicated that with continued development, it may significantly improve control
over these tumors and even cure them. Despite its current drawbacks and complications,
clinical trials have proceeded and proved that BNCT can be safe and that it is indeed
capable of combating very virulent and deadly tumors. It provides an excellent example
of the importance of innovation to the much sought after cure for cancer.
35
Figure A.1: A traveling wave linac. Charged particles travel down the accelerator tube with the electromagnetic radiation as the electric fields oscillate.
Figure A.2: A standing wave linac. At time T=0, there is constructive interference at A,E, and I to the right, and at C and G to the left. At T/4, there is destructive interference everywhere, and at T/2, there constructive interference has reversed directions. Bunches of ions are thus continually accelerated by electric fields.
Appendix A: The physics of linear accelerators and cyclotrons
Cyclotrons and linacs both accelerate charged particles using electric fields, and
in the case of cyclotrons magnetic fields as well. There are two types of linacs: traveling
wave and standing wave linacs, and the general principle behind both is to use high
frequency electromagnetic waves, in the microwave range, to accelerate charged
particles. Pulses of microwaves are generated by either a magnetron or a klystron and
injected into an accelerator tube made of copper with a series of evenly spaced copper
discs. The microwaves are produced so that their wavelength is equal to four times the
distance between these metal discs, making the discs spaced at intervals of ¼ of a
wavelength. Charged particles are simultaneously injected into the accelerator tube at
high energies. In traveling wave linacs, the microwaves are allowed to propagate down
the accelerator tube, creating electric fields between the copper discs. At a given initial
time, the electric field will be to the right between the first two discs, zero between the
second and third, to the left between the third and fourth, and zero again between the final λ
36
Figure A.3: A diagram illustrating the operation of a cyclotron. Ions are produced at the center and accelerated in a spiral by electric and magnetic fields until they strike a target, causing nuclear reactions.
two in a repeating pattern that propagates down the accelerator tube with time (figure
A.1). The charged particles and the microwaves travel together so that the particles are
continuously accelerated by electric field pointing to the right, much like a surfer is
carried by a wave. Microwaves can also be reflected to generate a standing wave linear
accelerator, in which the electric field between two discs alternates from right to zero to
left to zero. The standing wave case is illustrated in figure A.2. Here, charged particles
will alternate between discs with an electric field to the right and an electric field of zero
so that they are also accelerated down the tube.2,3
Cyclotrons are the other potential source of neutrons for BNCT. The basic design
of a cyclotron is two hollow conducting semicircles, called D’s, placed side by side, as
shown in figure A.3. These D’s are placed between a strong magnet, producing a
magnetic filed coming either up out of the D’s,
or down into them, and are charged to a high
voltage. Charged particles are liberated
between the D’s and accelerated by the electric
field between them. Once inside one of the
D’s, the particle makes a semicircle loop due to
the magnetic field back between the D’s where
it is accelerated again. Because it has a larger
velocity, it then traces a larger semicircle in the
next D. This process is repeated as ions are
given more and more energy. Both linacs and
cyclotrons are capable of producing ions with
several MeV’s of energy.3
37
Figure B.1: Diagram illustrating the photoelectric effect.
Appendix B: Interactions of Ionizing Radiation with Matter Photons make an important contribution to the dose in BNCT, and can interact
with matter to produce ions in a number of different ways: the photoelectric effect,
Compton scattering, and pair production. Each of these interactions is important at
different energies. The photoelectric effect is most important at photon energies below
about 10 keV.22 In this process the energy of an incident photon is completely absorbed
by an atomic electron, which is then ejected with a kinetic energy
K = hv-EB (B.1)
where K is the kinetic energy, hv is the energy of the photon, and EB is the binding
energy of the electron (figure A.1). As mentioned above, the cross-section for the
photoelectric effect varies with energy, and therefore so does the probability that an
electron at a given energy level will be ejected. It should be noted that after an electron is
ejected, electrons from higher energy levels will fall to take its place, emitting x-rays in
the process.
Compton, or incoherent
scattering, involves the collision of a
photon and an electron (figure B.2).
Compton scattering has a large cross
section between about 10 keV and 10
MeV, making it the most important
interaction in radiation therapy.22
The Compton effect provides proof
for the particle nature of light, as a
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
38
Figure B.2: Diagram illustrating Compton scattering. θ is the angle the ejected electron makes with the path of the origional photon, and φ is the angle at which the photon is scattered.
photon imparts some of its energy and momentum to the electron, given by:
(B.2)
(B.3)
Where E, hv’, and hvo are the energies of the electron, the scattered photon, and the
incident photon respectively, and α = hvo/mec2, where mec2 is the rest mass energy of the
electron.
Finally, with higher energy photons, there is a greater probability of pair
production. In pair production, a photon interacts with the electromagnetic field of the
nucleus and gives up all its energy to produce a positron/electron pair. This is an
example of the energy mass equivalency given by Einstein’s famous equation E = mc2.
When positrons interact with electrons, they will annihilate, creating two 511 keV
photons, equivalent to the rest mass energy of an electron or positron.
Heavy charged particles also make an important contribution to the dose in
BNCT. The way in which these particles interact with matter can be understood fairly
well using classical mechanics. As a heavy charged particle approaches an electron at
some vertical distance b, the electron feels a force from the electric field between the two
particles. It will continually
feel this force as the heavy
charged particle passes by, and
hence some momentum will be
imparted to it in the vertical
direction. Because the charged
particle is so much more
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
E = hvoα (1−cosφ )
1+α (1−cosφ )
hv'= 11+α (1−cosφ )
θ φ
39
massive than the electron, the changes in its velocity can be neglected, and hence the net
force in the horizontal direction will be zero.
The change in the electron’s momentum however can be calculated by taking the
integral
Δp = Fydt−∞
∞
∫ (B.4)
=zke2
bvcosθdt
−∞
∞
∫ (B.5)
Using the classical electron radius, r0 =ke2
m0c2 , and changing variables, this becomes:
zke2
bvcosθdθ
−π / 2
π / 2
∫ =2zr0m0c
2
bv (B.6)
where z is the charge of the incident particle, v is its velocity, r0 is the classical electron
radius, m0 is the mass of the electron, and b is the point of closest approach (see figure 6).
Now, energy is related to momentum by:
E =(Δp2)2m0
(B.7)
Substituting in Δp, you finally get
E(b) =2z2r0
2m0c4
(bv)2 =z2r0
2m0c4
b2ME
(B.8)
the energy that will be given to the electron as the heavy charged particle passes by. If
this energy is great enough, the electron will break away from the atom it is bound to.
40
Appendix C: Relating Exposure to Dose
Absorbed dose, the amount of energy deposited per unit mass, can be related to
exposure, the number of ions produced per unit mass, through kerma. Kerma is the sum
of the kinetic energies of the charged particles produced by ionizing radiation in some
given mass, and it can be given by:
K =ψ(μρ
) (C.1)
where ψ is the energy flunece of the incident radiation, and μ/ρ is the mass energy
coefficient, a factor describing how incident radiation imparts its energy to a given
medium. The kerma in air, or the noble gas in an ionization chamber, can be related to
exposure because it takes a certain amount of energy to produce an ion, given by We
,
where W is the average energy required to produce a unit charge, e. So the kerma in air
can also be given by
Kair = X (We
) (C.2)
Under conditions of electronic equilibrium, that is all the ions produced in an ionization
chamber are detected by the chamber, kerma can be taken as the dose, since under these
conditions all the particles produced by incident radiation deposit all of their energy in
the unit mass in which they are produced.
However, this just gives the dose in air, not in biological tissue. The dose to
medium such as an organ can be found by looking at the ratio of the dose in that medium
to the dose in air
Dmed
Dair
=Kmed
Kair
(C.3)
41
Substituting in equations C.1 and C.2 into this,
Dmed =ψmed (μ /ρ)med
ψair (μ /ρ)air
⋅ X ⋅Wair
e= fmed ⋅ X ⋅ A (C.4)
where
fmed =Wair
e(μ /ρ)med
(μ /ρ)air
(C.5)
and
A =ψmed
ψair
(C.6)
Note that fmed is just an intrinsic property of the medium being used and can be looked
up in a table, and A and X can be measured. Therefore, this provides a way to calculate
dose by measuring exposure and energy fluence.
42
Selected Annotated Bibliography
Faiz M. Khan, The Physics of Radiation Therapy, 2nd ed., (Lippincott Williams & Wilkins, Philadelphia, 1994).
Khan provided me with the basic physics of radiation therapy in general.
Although it focused primarily on photon therapy, it had a lot of good information, and the concepts on dosimetry and treatment planning could easily be applied to BNCT.
Harold E. Johns and John R. Cunningham, The Physics of Radiology, 4th ed., (Charles C.
Thomas, Springfield, 1983) This book provided a good compliment to Khan. It was a little older, but it
covered some topics that Khan did not touch on, particularly the physics behind linear accelerators and cyclotrons. It also covered the interactions of neutrons and charged particles with matter in more depth.
Sidney Lowry, Fundamentals of Radiation Therapy. (Arco Publishing Company, Inc.,
New York, 1975). Although this source was older, it had some information on the biological effects
of radiation that the more physics intensive texts did not have. It also had some nice outlines of how some specific tumors are identified and treated.
Rolf F. Barth, Albert H. Soloway, Joseph H. Goodman et al., Neurosurgery 44 (3), 433
(1999). This article provided a good overview of the concepts behind BNCT. It had
substantial information on the types of boron compounds and the neutron beams used for BNCT, and the way in which dose is calculated. It also had information about current clinical trials.
J. A. Coderre, J. C. Turcotte, K. J. Riley et al., Technology in Cancer Research &
Treatment 2 (5), 355 (2003). This was another article that gave a good outline of the current state of BNCT. It
had some information that Barth’s article did not have, such as information on side effects, and had information on more current clinical trials.
Guido Martín and Arian Abrahantes, Medical Physics 31 (5), 1116 (2004). This article had an overview about the necessary characteristics of neutron filters
used for BNCT. Although it provided only one technique for filtering neutrons, it had a good discussion of the general properties neutron filters must have.
43
David W. Nigg, International Journal of Radiation Oncology, Biology, Physics 28 (5), 1121 (1994).
This was an excellent source on the various treatment planning methods used for
BNCT. It had a very good discussion on how Monte Carlo simulations are used for radiation therapy in general, and BNCT in particular. Most of my other sources referred to this article when discussing how treatments were planned and doses were calculated.
T. L. Nichols, G. W. Kabalka, L. F. Miller et al., Medical Physics 29 (10), 2351 (2002). This was my primary source for information on the importance of microscopic
distributions of boron. It focused on the ways in which PET is being used to find microscopic distributions of boron in the brain and plan more accurate BNCT treatments.
44
Sources Cited:
1 Sidney Lowry, Fundamentals of Radiation Therapy. (Arco Publishing Company, Inc., New York, 1975).
2 Faiz M. Khan, The Physics of Radiation Therapy, Second ed. (Lippincott Williams & Wilkins, Philadelphia, 1994).
3 John R. Cunningham and Harold E. Johns, Physics of Radiology, Fourth ed. (Charles C. Thomas, Springfield, Illinois, 1983).
4 Joseph Selman, The Basic Physics of Radiation Therapy. (Charles C. Thomas, Springfield, Illinois, 1960).
5 Rolf F. Barth, Albert H. Soloway, Joseph H. Goodman et al., Neurosurgery 44 (3), 433 (1999).
6 J. A. Coderre, J. C. Turcotte, K. J. Riley et al., Technology in Cancer Research & Treatment 2 (5), 355 (2003).
7 H. Paganetti, Technology in Cancer Research & Treatment 2 (5), 353 (2003). 8 D. A. Allen and T. D. Beynon, Physics in Medicine and Biology 40, 807 (1995). 9 Guido Martín and Arian Abrahantes, Medical Physics 31 (5), 1116 (2004). 10 S. Yonai, T. Aoki, T. Nakamura et al., Medical Physics 30 (8), 2021 (2003). 11 H. R. Blaumann, S. J. González, J. Longhino et al., Medical Physics 31 (1), 70
(2004). 12 H. Fukuda, J. Hiratsuka, T. Kobayashi et al., Australasian Physical & Engineering
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