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, jmfloberg@gmail.com

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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