The Microdosimetry of Boron Neutron Capture Therapy

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University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange

Doctoral Dissertations Graduate School

12-2008

Trent L. Nichols University of Tennessee - Knoxville

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Recommended Citation Nichols, Trent L., "The Microdosimetry of Boron Neutron Capture Therapy. " PhD diss., University of Tennessee, 2008. https://trace.tennessee.edu/utk_graddiss/581

This Dissertation is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council:

I am submitting herewith a dissertation written by Trent L. Nichols entitled "The Microdosimetry of Boron Neutron Capture Therapy." I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the requirements for the degree of Doctor of Philosophy, with a major in Physics.

Soren P. Sorensen, Major Professor

We have read this dissertation and recommend its acceptance:

Leo. L Riedinger, Carrol R. Bingham, George W. Kabalka, Laurence F. Miller

Accepted for the Council:

Carolyn R. Hodges

Vice Provost and Dean of the Graduate School

(Original signatures are on file with official studentecor r ds.) To the Graduate Council:

I am submitting herewith a dissertation written by Trent Lee Nichols entitled “The Microdosimetry of Boron Neutron Capture Therapy.” I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the requirements for the degree of Doctor of Philosophy, with a major in Physics.

Soren P. Sorensen, Major Professor We have read this dissertation and recommend its acceptance:

Leo. L Riedinger

Carrol R. Bingham

George W. Kabalka

Laurence F. Miller

Accepted for the Council:

Carolyn R Hodges

Vice Provost and Dean of the Graduate School

(Original signatures are on file with official student records.)

The Microdosimetry of Boron Neutron Capture Therapy

A Dissertation Presented for the Doctor of Philosophy Degree The University of Tennessee

Trent Lee Nichols, MD December 2008

ii Dedication This dissertation is dedicated to the memory of my father, Ted Nichols, whose love, support, and guidance has been so important to me. There is not a day that I do not think of him.

iii Acknowledgements Earning a Ph.D. is a reflection of all the professors who have influenced and shaped one’s career. It is not possible to thank everyone who has helped me to achieve this milestone. To all who have helped in one way or another, I wish to express my gratitude but there are several however who deserve special recognition. In undergraduate and graduate school, I was fortunate to have many excellent professors. Dr. P. G. Huray, my first physics professor and major professor for my masters degree, sparked my love for physics. Dr. W. E. Deeds taught me to question everything. Drs. R. D. Present, J.R. Thompson, T. A. Callcott, and E. G. Harris taught me how to think as a physicist. Dr. R. W. Lide provided imortant perspectives on life. A special thanks to Dr. M. W. Guidry who taught me how to integrate knowledge from one area of physics and apply it in another. Dr. Guidry’s belief in my abilities has much to do with me having the confidence to pursue this degree over such a long time. He gave me the opportunity of a lifetime by helping me to go to the Niels Bohr Institutet at the Københavns Universitet in København, Denmark. In working on the problem of Boron Neutron Capture Therapy, I have met, talked, and collaborated with colleagues throughout the world. To each I owe gratitude since each has contributed to my understanding of BNCT. In particular, I would like to recognize Drs. R. G. Zamenhof, P. M. Busse, J. Capala, J. C. Yanch, D. Nigg, A. Soloway, R. Barth, G. Smith, and T. Byrnes. In particular, I wish to thank my committee: Drs. S. P. Sorensen, C. R. Bingham, G. W. Kabalka, L. F. Miller, and L. L. Riedinger for being available to help me to obtain a life long goal. Dr. Bingham has been encouraging throughout my career. His quiet optimism has been an important role model. He is always willing to stop to answer questions or provide a new insight into nuclear physics. Early in my career, Dr. Bingham taught me much about experimental nuclear physics. Without the support and encouragement of Dr. Riedinger, I would not have been able to accomplish my goal of a Ph.D. in physics. He taught me electricity and magnetism, brought me into nuclear physics research, and has believed in me. Very

iv importantly, he convinced the graduate school to allow me to complete my interupted degree. Dr. Riedinger is a mentor and friend who exemplifies what it means to be a professor of physics. A special thanks to Dr. Miller whose help with the details of neutron beams and the details of the dose calculations was invaluable. He kept me focused on the tasks at hand rather than pursue interesting but unimportant avenues. His thoughts and views on the subject was an important part of this research. Without his cheerful and positive encouragement, this dissertation may have never come to fruition. An excellent mentor is essential to a graduate student. I was fortunate to have Dr. G. Kabalka as my mentor. He has taught me much about being a professional in research and in doing so he has become a close friend and confidant. We have shared research successes together as well as a few disappointments. His optimism, insights, and wisdom has been a positive influence in my life. I am a better person for having had the privilege to work with Dr. Kabalka. The culmination of a Ph.D. requires a major professor who can be critical, helpful, and encouraging all at the same time. Dr. Sorensen has provided me that guidance. He stepped in at a critical point in my research and has guided me to the completion of my degree. He has helped me to regain the critical thinking crucial to being a physicist that years of medical practice has dulled. Without his help and support, I would have likely never completed my degree. Obtaining my Ph.D. has required much sacrifice, understanding, and patience from my family. My parents, Ted and Audrey Nichols, have been supportive throughout my career. My wonderful children, Ted and Frances have long since learned that dad watches television only with a computer multi-tasking some sort of physics related project. I am so very proud of them both and I am enjoying watching their lives unfold. Most importantly of all, I wish to thank my wonderful wife Sally. Without her devotion, patience, support, and love my degree could never have been achieved. She has picked me up when I was down and has carried me through the hard times. She has helped me in every aspect of my dissertation but most importantly she encouraged me

v when I was ready to quit. We have shared many good times over the past 30 years and a few bad times. Sally is the love of my life and to her I owe the most.

vi Abstract Boron neutron capture therapy (BNCT) is a brachyradiotherapy that exploits the large thermal neutron (~0.025eV) cross-section of 10 B. After absorbing a neutron, a 11 B compound nucleus will spontaneously fission into an alpha particle and a lithium nucleus. An average energy of 2.31 MeV is deposited in a volume on the order of one cell diameter. The large masses and high energies of ion products constitute a high linear energy transfer (LET) reaction. High LET reactions cause double stranded deoxyribonucleic acid (ds-DNA) breaks that lead to cell death because the breaks cannot be accurately repaired. BNCT has been used in clinical trials to treat the aggressive infiltrative brain malignancy, glioblastoma multiforme, and the skin cancer, melanoma. The few studies on melanoma seem to be more promising than the trials on glioblastoma. The cellular level energy deposition pattern, the microdosimetry, reveals the reason for the observed differences. Programs were written modeling cells as ellipsoids arranged in a body centered cubic with nuclei that can be spheres or ellipsoids independent of the cell and non- concentric. The dose was calculated for various boron concentrations in the interstitium, the cell cytoplasm, and the cell nuclei for different geometries. The results demonstrate that cells closely packed receive a larger dose than widely separate cells. Also, the dose increases linearly with boron concentration so that better boron delivery agents will improve the efficacy. Infiltrative glioblastoma cells that are in small clumps or isolated receive a smaller dose than melanoma cells that are tightly packed. The microdosimetric model corresponds to clinically observed results. Also, the model predicts that improved boron delivery agents could make glioblastoma a disease that is curable by BNCT.

vii Preface Cancer causes much human suffering as well as economic losses due to lost wages and the cost of therapy. Despite monumental medical efforts, cancer remains difficult to cure for many cell types. Often, treatment regimens cause considerable morbidity and occasional mortality. The treatment regimen often has connected morbidities that are significant enough to cause the patient to miss work for some time after the completion of the therapy. The search continues to find a safe, focused, efficacious radiotherapy with minimal morbidity. Boron neutron capture therapy (BNCT) has shown promise in clinical trials for potentially achieving these goals for some cancers. The essential requirements for successful BNCT are the delivery of an adequate beam of thermal neutrons to the tumor and the preferential concentration of a boronated compound in the tumor cells. The requirement for an adequate fluence of thermal neutrons to the tumor volume is now met at all clinical treatment centers but the preferential concentration of a boronated compound in the tumor, as compared to the local normal tissues, has proven to be a more difficult goal to achieve. Current compounds used for BNCT tend to concentrate in the tumor compared to normal tissue in a ratio of 3-5:1. Increasing this ratio should improve the efficacy of BNCT so accurate determination of this ratio is imperative. Unfortunately, the determination of the boron concentration in various tissues, especially in vivo , has proved to be a difficult task. All current clinical techniques to determine this ratio have proven to be inadequate. The problem may be solved by fluorinating the BNCT compound, para -boronophenylalanine (BPA), with fluorine-18 (a positron emitting radionuclide) and performing positron emission tomography (PET). This allows direct identification of the tissue distribution of the 18 F-BPA. The resulting boron distribution map may then be used to modify the standard treatment plans. There are significant differences noted when the in vivo PET derived boron concentrations in dosimetry calculations are used; this could affect the clinical results. The actual cause of cellular demise immediately following radiation exposure is still not entirely known. Damage to the cell’s nucleus and deoxyribonucleic acid (DNA)

viii can lead to cellular death or premature apoptosis. This explains the cell death that occurs some hours, if not days or months, later, but does not explain the immediate cellular destruction that is seen after a substantial radiation exposure. Microdosimetry attempts to understand these phenomena and explain them in terms of fundamental physical processes on the cellular level. By examining the microdosimetry of BNCT, the use of this modality for cancer therapy may be enhanced and the possible causes of immediate cellular demise may be elucidated. BNCT has been used to treat the most common primary brain malignancy, glioblastoma multiforme. This is an aggressive infiltrative tumor that results in a life expectancy of six months without treatment. The optimal conventional therapy is debulking surgery, followed by photon beam radiation therapy, and then chemotherapy with carmustine (BCNU). This protocol increases the patient’s mean life expectancies to 12.5 months. Clinical trials using a single treatment of BNCT following debulking surgery have yielded median life expectancy of 14.5 months. Though impressive, these results do not seem to be consistent with the potential that the modality holds. Since infiltrative tumors have single cells that migrate away from the main tumor, there is not as high a boron concentration in surrounding cells as is found in a cell in the midst of the tumor. This is termed near neighbor effects. This study endeavors to explore the effects of near neighbors by modeling both densely and sparsely boronated systems in a more realistic model of the cellular system. This program has the possibility of being extended to evaluation of potential cellular damage and demise to structures other than the DNA in the nucleus. The microdosimetry of BNCT allows exploration of the likely efficacy of boron carrier absorbing tumors to be modeled. The results herein will demonstrate that some tumors will be more likely to be effectively treated than others. In the cases of glioblastoma multiforme and malignant melanoma, the microdosimetry explains the modest clinical results for glioblastoma and good results for malignant melanoma. Further work on both the macro- and micro-dosimetry BNCT will help to guide the advancement of this exciting modality for cancer treatment.

ix Table of Contents

I. Introduction...... 1 A. An introduction to and brief history of boron neutron capture therapy...... 1 B. A review of recent boron neutron capture therapy clinical trials...... 8 C. A brief review of problems encountered in boron neutron capture therapy...... 17 D. Treatment planning with 18 fluoro-boronophenylalanine positron emission tomography scans for boron neutron capture therapy...... 22 E. Statement of the Problem...... 27 II. Microdosimetric Models...... 30 A. Basics of microdosimetry ...... 30 1. Concepts of microdosimetry for BNCT...... 30 2. Stopping powers...... 35 3. Determination of the number of interactions...... 39 B. Review of prior models of BNCT microdosimetry...... 41 C. Simulation implementation...... 42 1. The Cells program...... 42 2. The Dose program...... 43 3. The Evaldose program...... 46 4. Mathematica and SigmaPlot programs...... 46 D. Program validation...... 47 1. Validations...... 47 2. Comparisons to the results of other authors...... 48 III. Results and Discussion...... 50 A. Characteristics of the neutron beams for BNCT...... 50 B. Contributions to the microscopic dose...... 56 1. The contribution from the 10 B(n, α)7Li and 10 B(n, α γ )7Li reactions to the dose57 2. The contribution of the 14 N(n,p) 14 C dose...... 59 3. Gamma ray dose from the 10 B(n,α γ )7Li reaction...... 62 4. Dose due to recoil protons ...... 66 5. Dose from the 1H(n, γ)2H reaction...... 69 6. Summary of the components to the radiation milieu...... 71 C. How the boron distribution affects the dose ...... 72 D. The effects of cell geometry on the dose ...... 75 IV. Summary and Conclusions ...... 91 V. Future Directions for Research into Boron Neutron Capture Therapy Microdosimetry...... 97

x List of Tables

Table I.1 Thermal neutron cross-sections for commonly occurring elements found in the body...... 2 Table II.1 Relative biological effectiveness for several different kinds of radiation...... 33 Table II.2 Range of BNCT associated ions in human tissue...... 38 Table II.3 Energy deposition as a percent of the total energy deposited, dose, and percent volume of three volumes to the total...... 49 Table II.4 The nuclear dose from the work of Charlton and from the program Dose..... 49 Table III.1 Measured maxima for thermal neutron flux as well as photon and fast- neutron absorbed dose rates at the seven different NCT facilities in the U.S. and Europe. 87 ...... 52 Table III.2 Typical tissue elemental abundance, number density, and elastic scattering cross section...... 53 Table III.3 Mean free path, λ, for different epithermal neutron energies...... 54 Table III.4 Elastic proton scattering as a function of incident neutron energy...... 69 Table III.5 Recoil proton range for various epithermal neutron energies with totally elastic scattering and average energy transfer...... 70 Table III.6 Dose contribution from different radiation components...... 72

xi List of Figures

Figure I.1 A typical SERA generated treatment plan for a glioblastoma multiforme based upon a MRI image...... 20 Figure I.2 Pre-operative 18 F-BPA-fructose PET scans of the same patient as in Fig. I.1 with a parietal glioblastoma multiforme...... 24 Figure I.3 Treatment plan generated by SERA using 18 F-BPA PET scan information... 25 Figure I.4 Two-dimensional activity plot showing inhomogenieties in the region of the glioblastoma multiforme...... 26 Figure I.5 18 F-BPA PET scan of a metastatic focus of malignant melanoma. The left hand frame shows a typical BNCT treatment plan with SERA ...... 28 Figure II.1 Ionizations and excitations along particle tracks in water, for a 5.4 MeV α- particle...... 32 Figure II.2 The stopping power for 5.49 MeV alpha particles in air demonstrating the Bragg peak near the end of the track...... 32 Figure II.3 The proton stopping power for the 14 N(n,p) 14 C reaction showing the energy deposition per unit length as a function of the remaining range...... 38 Figure II.4 The alpha particle stopping power for the 10 B(n, α)7Li reaction showing the energy deposition per unit length as a function of the remaining range...... 40 Figure II.5 An example of a few cells with a radius of 5 µm, an eccentricity of 0, and a separation of 1.0 µm. The cell was determined by the program Cells...... 44 Figure II.6 A few cells with a radius of 5 µm, an eccentricity of 1.5, and a separation of 1.0 µm whose positions were determined by Cells...... 44 Figure III.1 Thermal neutron (~0.025 eV corresponds to a neutron velocity of ~2200 m s−1 ) flux obtained from the analysis of gold foil activation at seven different clinical NCT facilities in Europe and the U.S...... 51 Figure III.2 The unfolded free beam neutron spectrum of the Washington State University reactor at 1 MW power in the source plane obtained by direct fitting.... 55

xii Figure III.3 Dose versus cell edge to edge separation for spherical cells of radius r c = 4.0

µm, nuclei of radius r n = 3.0 µm, and eccentricity of ε = 0 for boron concentraions of 10 ppm in the interstitium, 50 ppm in the cytoplasm, and 50 ppm in the nuclei...... 60

Figure III.4 Dose versus cell edge to edge separation for spherical cells of radius r c = 4.0

µm, nuclei of radius r n = 3.0 µm, and eccentricity of ε = 0 for boron concentrations of 10 ppm in the interstitium, 50 ppm in the cytoplasm, and 50 ppm in the nuclei...... 61 Figure III.5 Nuclear dose versus cell edge to edge separation for spherical cells of radius

rc = 4.0 µm with nuclei of r n = 3.0 µm and eccentricity of ε = 0 for boron concentraions of 10 ppm in the interstitium, 50 ppm in the cytoplasm, and 50 ppm in the nuclei...... 63 Figure III.6 Elastic scattering cross sections for protons as a function of incident neutron energy displaying a relatively flat distribution in for the incident neutron energies used in BNCT ...... 67

Figure III.7 The dose for the three regions of interest for typical cell sizes of radius rc =

5.0 µm with spherical concentric nuclei of radius rn = 4.0 µm and boron concentrations that have been experimentally determined...... 73

Figure III.8 The nuclear dose only for typical cell sizes of radius rc = 5.0 µm with

spherical concentric nuclei of radius rn = 4.0 µm and boron concentrations that have been experimentally determined...... 74

Figure III.9 The interstitial dose only for typical cell sizes of radius rc = 5.0 µm with

spherical concentric nuclei of radius rn = 4.0 µm and boron concentrations that have been experimentally determined...... 76

Figure III.10 The dose for the three regions of interest for typical cell sizes of radius rc =

5.0 µm with spherical concentric nuclei of radius rn = 4.0 µm and boron concentrations that are potentially achievable with new boron carrier molecules of 200 ppm in the cells and 100 ppm in the cells with 10 ppm in both cases...... 77 Figure III.11 Dose as a function of cell edge to edge separation for large spherical cells

of radius r c = 8 µm with nuclei of r n = 4 µm for boron concentration of 10 ppm in the interstitium, 50 ppm in the cytoplasm, and 50 ppm in the nuclei...... 80 xiii Figure III.12 Interstitial dose averaged over 50 cases with no separation at four cell radii.

Fitting is performed non-linearly with the function D = D 0 + a 0/r as derived from the ratio of the surface/volume for spheres...... 82 Figure III.13 The dose to the interstitium as a function of cell radius for a concentric nucleus of radius 3.0 µm and cell edge to edge separation for boron concentrations of 50 ppm in the cell (nucleus and cytoplasm) and 10 ppm in the interstitium...... 83 Figure III.14 The nuclear dose as a function of cell radius for a concentric nucleus of radius 3.0 µm and cell edge to edge separation for boron concentrations of 50 ppm in the cell (nucleus and cytoplasm) and 10 ppm in the interstitium...... 85 Figure III.15 The ratio of the dose to the cell to the dose to the interstitium as a function of cell radius and cell separation for boron concentrations of 50 ppm in the cell (nucleus and cytoplasm) and 10 ppm in the interstitium...... 86 Figure III.16 The relationship of the nuclear to cytoplasmic dose ratio for two different cellular boron concentrations and for varying cell radii...... 87 Figure III.17 A representative ellipsoid with radius 10 µm and an eccentricity of 1.5. .. 89 Figure III.18 Two cross sections through a cell with eccentricity of 2.5 and radius of... 89 Figure III.19 A comparison of the dose to an ellipsoidal cell and an equivolume sphere both with concentric nuclei of radius 4.0 µm...... 90 Figure IV.1 A typical cell survival curve for high and low LET radiation showing significant killing for doses predicted for BNCT...... 93

xiv List of Abbreviations α alpha particle AMU atomic mass unit B boron b barn (10 -24 cm 2) BBB blood brain barrier BMRR Brookhaven Medical Research Reactor BNCT Boron Neutron Capture Therapy BNL Brookhaven National Laboratory BPA para -boronophenylalanine BSH sodium borocaptate CSDA continuous slowing down approximation eV electron volts 18 F-BPA 18 fluorine- para -boronophenylalanine EU HFR European Union High Flux Reactor in Petten, Netherlands GBM glioblastoma multiforme GHz giga-hertz Gy Gray (1Gy = 1J/kg) Gy-eq Gray - equivalent He helium H/MIT The Harvard Medical School / Massachusetts Institute of Technology BNCT group INEEL Idaho National Engineering and Environmental Laboratory [now Idaho National Laboratory (INL)] ITC infiltrative tumor cells LET linear energy transfer Li lithium keV kilo-electron Volts kg kilogram MeV million electron volts

xv mg milligrams MGH Massachusetts General Hospital MIT Massachusetts Institute of Technology MITR Massachusetts Institute of Technology Reactor MM Malignant Melanoma mm millimeter mm 3 cubic millimeter RBE Relative Biological Effectiveness THOR Tsing Hua Open-pool Reactor in Taiwan µg micro-gram µm micrometer or micron µm3 cubic micrometers

xvi I. Introduction

A. An introduction to and brief history of boron neutron capture therapy

In January of 1932, Irene and Frederic Joliot used a strong polonium source to explore a new penetrating radiation that was able to eject protons from a hydrogen rich paraffin layer. Marie Curie and the Joliots attempted to explain the phenomena by using the recently described Compton scattering of the electron. Using Compton scattering as the theoretical basis for their calculations led to a cross-section about 3 million times larger than that of the electron scattering for other known situations. James Chadwick, who was working with Ernest Rutherford at the Cavendish Laboratory in Cambridge, realized that the interpretation of the data was incorrect and performed the same experiment using not only hydrogen as the target but also helium and nitrogen. The three different targets allowed him to compare recoils and determine that the particles were neutral with a mass approximately equal to that of the proton. Chadwick published his discovery of the neutron in the February issue of Nature. 1 Shortly thereafter, M. Goldhaber collaborating with Chadwick, 2 Taylor, 3 and Burcham 4 studied slow-neutron bombardment of the stable isotopes of boron, lithium, and nitrogen. They found that the tracks from the disintegration of boron-10 were two short straight segments consistent with two heavy charged particles. The average range of the particles was found to be ~8 µm in the photographic emulsion. These researchers would show that the actual reaction might be represented as two reaction channels:

110 11*93.7% 7 4 (I.A.1) 055n+B→ B → 32 Li+He+ γ(0.48 MeV)+2.31 MeV and

1106.3% 11* 7 4 (I.A.2) 05n+ B→ 5 B → 32 Li+He+2.79 MeV where 11 B* represents a metastable state that decays immediately by two reaction channels as shown in (I.A.1) and (I.A.2) where the percent probability of the reaction channel is in parentheses.

1 Remarkably, boron neutron capture therapy (BNCT) was first proposed in 1936 by the German biophysicist, G.L. Locher, of the Franklin Institute at Pennsylvania 5 as a potential cancer therapy just four years after Chadwick’s discovery of the neutron and remarkably the same year that Taylor and Goldhaber described the 10 B(n, α)7Li reaction. Locher examined the theoretical biological effects of these particles and realized the therapeutic potential of this reaction for cancer therapy. Part of the attractiveness of this idea is that 10 B has a large cross-section for thermal neutrons (~0.025eV) compared to some other isotopes likely to be found in human tissues as is shown in Table I.1. Also, boron is non-toxic to humans even in large doses and 10 B is stable. It would be nearly two decades before this concept would actually be used in a cancer treatment for humans. There was much research done in the years after the discovery of neutrons and the first human trials on the effects on cells seen after exposure to the several different types of radiation. Researchers who saw BNCT as a potential cancer therapy were encouraged following the 1950 paper by Conger and Giles at Oak Ridge National Laboratory (ORNL). 6 They were able to demonstrate the deoxyribonucleic acid (DNA) damage from the particles generated in the (n, α) reaction when lily bulbs containing boron were exposed to a beam of slow (thermal) neutrons. This encouraged William Sweet and others at the Harvard University Medical School (HMS),

Table I.1 Thermal neutron cross-sections for commonly occurring elements found in the body. Element % Relative Abundance Cross Section (barns) B-10 19.9 3840.0 B-11 80.1 0.005 C-12 98.89 0.0035 N-14 99.634 1.8 Na-23 100.0 0.43 Cl-35 75.77 43.7 K-39 93.2581 2.1

2 Massachusetts General Hospital (MGH), the Massachusetts Institute of Technology (MIT), and the Brookhaven National Laboratory (BNL). 7 The Brookhaven Medical Research Reactor (BMRR) was constructed expressly for BNCT and contained a full clinical facility for onsite hospital care. An excellent review of the early work in BNCT at HMS/MIT and BNL may be found in an article written by Sweet. 7 As a neurosurgeon, Sweet wanted to treat the deadly, aggressive, and most common primary brain malignancy: glioblastoma multiforme (a carcinoma). Glioblastoma multiforme (GBM) is truly a horrific killer that recognizes no socio- economic factors, age group, race, or border. 8 It arises from the brain’s supportive astrocytoma cells and is known as a high grade or Grade III (or IV in some grading systems) astrocytoma. 9-11 The tumor is infiltrative in nature, which means that it extends by thin small streams of invasive cells analogous to the roots of a plant that infiltrate the soil. Remarkably, a glioblastoma multiforme is often quite large before symptoms occur that lead to the discovery of the tumor. The initial presentation is generally a fall, a seizure, or a subtle change in speech patterns. 8 Additionally, many of these tumors have cells that undergo an amoeboid-like transition where the cells ‘swim’ through the brain to distant locations. The cells that undergo an ‘amoeboid phase’ have been called infiltrative tumor cells (ITC) 12 and account for the failure of all attempts to date to achieve long term survival. This ‘amoeboid phase’ is the reason that the early neurosurgical attempts at a cure by performing a hemispherectomy were uniformly unsuccessful since the tumor spreads to the contralateral hemisphere. 12-16 There are no known risk factors or genetic links to the development of GBM. 10 The risk of developing a GBM is proportional to age until the latter years when the risk grows faster than age with the peak occurring in the 40 to 70 year age range. 8 In the 1950’s the median life expectancy after the diagnosis of GBM was about 21 weeks. The optimum therapy today consists of first performing debulking surgery to decrease the tumor burden with occasional placement of gliadel wafers, which contain an anti-tumor drug. 7, 8 After a few weeks, the patient will undergo traditional photon therapy that consists of approximately 36 treatments. The patient will occasionally then have chemotherapy with BCNU (carmustine) or a similar alkylating agent. Most recently, Ho, Lam, and Hui have used

3 gene therapy as well. 17 All of this additional treatment has extended the median life expectancy after diagnosis to ~11 months (~44 weeks). 16, 17 The course of the disease is one of progressive deterioration despite aggressive therapy so that the patient spends their most functional time going for treatments that often make them ill. The time following the patient’s therapy is then characterized by a low functional status prior to the inevitable death. Thus, there has been little improvement in the past 40 years in the quality of life for the glioblastoma multiforme patient despite a modest increase in life expectancy. In 1950, the first human BNCT trials were started at the 20 megawatt research reactor just commissioned at BNL. A thermal beam was created on the top of the reactor by removing some of the shielding. 7 The theoretical calculations indicated that a concentration of 50 µg/g boron in the tumor and 15 µg/g boron in normal brain tissue would be sufficient to deliver 3 times the dose to the tumor as compared to the normal brain. The first compound to be studied, borax (Na2B4O7⋅1OH 2O), met that requirement with 15-20 µg of boron/g of brain resulting in tumor: brain boron ratios of 3 to 28 being obtained. 7 The duration of the favorable ratios was short necessitating rapid treatment of patients. The external carotid arteries were ligated in the 10 patients to receive BNCT along with tight elastic bandages applied to the scalp all to prevent damage to the vascular scalp. The first five patients received a single fraction of radiation with the second five patients receiving 2 to 4 fractions. The patients had no significant complications from the therapy and lived 6 to 21 weeks after treatment, that was equivalent to the best treatments available at that time. 7 The autopsy results in six of the patients revealed little injury to the tumor but substantial damage to the scalp, which was often rather painful. These results were correctly interpreted to indicate that few thermal neutrons were delivered to the tumor. 7 Most thermal neutrons were deposited in the scalp and skull despite attempts to prevent this from happening. These results prompted the construction of an operating room underneath the MIT Reactor II that was being built at the time. The operating room would allow the scalp, skull, and dura to be surgically resected at the site of treatment and to be replaced after the treatment was completed. This would allow an improved thermal neutron flux to reach the tumor.

4 Parallel to the efforts to improve the delivery of thermal neutrons to the tumor was the development, beginning in 1958, of improved delivery systems for the boron-10 isotope by A. H. Soloway and his colleagues. Soloway’s team was able to develop models for the brain’s protective mechanism known as the blood brain barrier (BBB), the tight junctions between vascular endothelial cells that prevent the diffusion of most substances. 18 With their models, the researchers were able to prepare boron carriers that were of low toxicity and could cross the BBB at least to some extent. It was understood that the GBM would damage the BBB but that GBM cells far removed from the tumor body would depend on diffusion across the BBB in order to receive a sufficient boron concentration to provide a lethal radiation dose. They synthesized p- carboxyphenylboronic acid which was used in the next 16 patients; the last two patients 19, 20 were treated with sodium perhydrodecaborate (Na 2B10 H10 ). Sodium perhydrocarborate was the most soluble, biologically inert, and stable chemically that Soloway had developed to that date. The second BNCT trials, which took place at the MIT Reactor, involved a total of 18 patients who lived from 10 days to 11½ months post BNCT. Of those 18 patients, 14 underwent postmortem examinations of their brain. The findings included extensive radiation necrosis of the brain in nine of the cases, and in only two of the cases recurrent tumor was seen. 21 In a single patient, there was found to be extensive radiation necrosis and tumor. Of the 14 postmortem brains examined, only in one of the 11 glioblastoma patients were islands of glioblastoma no longer seen. This particular patient had a neutron fluence measure at the surface of the brain of 1.1 x 10 13 n/cm 2. This fluence was the third highest among the doses given in this series of patients. The patient had a radiation time of approximately 45 minutes which was less than half the longest treatment time, and the dose of 25 mg/kg of 10 B was slightly less than 30 mg/kg given to eight of the patients. At the time, the conclusion was that this tumor was less radiation resistant than most of the series. Unfortunately, as is often the case, data pertaining to the boron levels in the blood, normal brain, and tumor were not available. Finding patients who respond well to therapy despite being given less than maximal doses of BNCT is a theme echoed in later studies.

5 As had been true in the first studies, thickening of the blood vessel walls occurred due to endothelial cell proliferation and enlargement of their cells. This endothelial cell proliferation and enlargement resulted in vascular occlusion, which was termed ‘coagulation necrosis’. This coagulation necrosis had never been seen before and so was especially remarkable to the researchers. 22, 23 It was characterized by devitalized tissue rather than the usual liquefactive chain of events that took place with irradiation of blood vessels. The interpretation was that the fissioning of the boron in the blood stream induced vascular changes that resulted in coagulation necrosis. This result showed that any boron delivery agent would have to clear the vasculature somewhat prior to irradiation to avoid coagulation necrosis. Obviously, this can cause damage to normal tissue as well as the target malignancy. Work by Kitao 24 of the National Institute of Radiological Sciences in Japan, and by Rydin, Deutsch, and Murray 25 at MIT resulted in calculations that showed that, as a rule of thumb, the radiation dose to the vessel wall is comprised of one-third from the intra-luminal concentration of boron and two-thirds from the extra-vascular boron level. At this particular time in history, it was difficult to rapidly determine boron levels in the blood or tissues and many times researchers had to wait several days for the results to be obtained. Based on their best calculations the doses delivered were increased resulting in a patient who received a much higher dose than their initial calculations would have indicated. This was a consequence of measuring the boron at the time of treatment although the treatment plan had to be based on prior measurements. This unfortunate patient received a much higher dose than was prescribed resulting in the patient’s death of cerebral edema some 10 days after treatment. 7 At that time, the clinical trials were stopped due to lack of an agent that would allow rapid detection, delivery of adequate amount of boron to the target tissue, and a safe level of boron delivered to normal tissues. Identifying a compound that satisfied the above-noted requirements took much longer than had been anticipated. Twenty-four years later, Ralph Fairchild and his colleagues at Brookhaven National Laboratory, came up with a solution to this problem. 26 They were able to measure the concentration 10 B, which is only about 20% of the naturally occurring mixture of 10 B and 11 B. This technique is based upon the existence of

6 a 478 keV γ-ray that occurs 94% of the time in disintegrations of 10 B. This γ-ray is given off immediately at the decay of the metastable 11 B, which has a half-life on the order of nanoseconds. The thermal neutrons that are required to make the determinations were obtainable directly from the reactor where the therapies are done. The disappointing results of the MIT studies encouraged Soloway, who was now joined by H. Hatanaka, to continue looking for new and improved boron delivery compounds. By 1967, they had screened more than 150 compounds trying to find the 2- best one for BNCT. They developed a compound called BSH (B 12 H11 SH ), which was found to provide tumor:normal tissue boron ratios ranging from 1.4 to 20. 27 Unfortunately, BSH and its metabolic products were found to bind to serum albumin, which leads to coagulation necrosis problems. Additionally, BSH was shown to be somewhat toxic. Slow I.V. injection of 240 mg of boron/kg over five days at a rate of 40 mg/kg/day was, however, found to result in no toxic effects. After much work, a stable form of BSH for human use was developed by researchers at MGH. 28 At Shiongi, Hatanaka and colleagues purified and stabilized the BSH. 29 That permitted the use of this compound as a boron carrier for the series of 140 patients done by Hatanaka. Hatanaka had been working with Sweet and at others at Massachusetts General Hospital and MIT during some of the early years of BNCT. He later spent time at MIT working on the clinical trials concluding in 1967. Hatanaka took the idea of BNCT back to Japan with him. Being a neurosurgeon, he also had a great desire to try to cure malignant gliomas. In one series of experiments, he treated 40 patients with BNCT and the other 50 by multimodality combination of fractionated photon radiotherapy and chemotherapy. 29 The BNCT group had a five-year survival rate, four times that of his multimodality group despite being 10 years older on the average. This is a rather remarkable accomplishment considering that Hatanaka had only a 100 kW reactor in contrast with the multi-megawatt reactors available in the United States at the time. Hatanaka realized early that tumors greater than approximately 6 cm would probably receive an inadequate dose of thermal neutrons due to the inability of the beam to penetrate that deep. Therefore, Hatanaka was delighted to report a five-year survival rate of 58% for patients with glioblastoma multiforme, having relatively superficial tumors. 30,

7 31 This is very remarkable considering that the five-year survival rate reported by Charles Wilson in 1991 for his 449 patients with a diagnosis of glioblastoma at first operation was 4.7%. 32 Wilson’s patients were treated by radical surgery plus radiation and chemotherapy. Hatanaka, for this pioneering work, is in many ways the father of BNCT. It is his early success that has spurred interest in the field. Yutaka Mishima and his collaborators, beginning in 1972, started experimenting with boronated tyrosine analogs as boron carriers for neutron capture therapy. The idea was originally to attack the problem of malignant melanoma. 33, 34 However, it was found that the boronated phenylalanine also preferentially concentrated in glioblastoma, as well as in malignant melanoma. The 10 B-L-p-boronophenylalanine ( 10 B-BPA) is rather insoluble, making its delivery to human beings rather difficult. This was solved by creation of a fructose complex. It has been found that even very high doses of 10 B-BPA are innocuous to human beings. 35 The early days of BNCT were marked by difficulties in determining neutron fluence, penetration, and composition of the beam. The lack of an adequate boron carrier certainly plagued the early studies and continues to be a problem today. Unlike other early modalities such as radiation therapy, chemotherapy and, more recently, immunotherapy, BNCT has been used only for a very limited number of tumors. To date, the only clinical trials have been with glioblastoma multiforme, malignant melanoma, and a single patient with metastatic carcinoma of the colon. This situation is unlike other modalities of cancer therapy and, as will be seen, has caused problems for the field of BNCT.

B. A review of recent boron neutron capture therapy clinical trials

Hatanaka’s results were summarized and published in the 1980’s. 31, 36, 37 At that time, in the United States, BNCT had been languishing due to the poor results of the initial clinical trials. Lack of funding had prevented researchers in the field from developing new compounds and, though the work continued on developing better beams

8 and detection methods, no further clinical trials were performed. However, Hatanaka’s results received worldwide attention. Certainly, his claim to have a twenty-year survivor of glioblastoma multiforme was unheard of with other modalities. 38 However, there were some concerns about Hatanaka’s data raised by Larramore and Spence 39 which will be discussed below in some detail. Despite these concerns, interest in BNCT in the United States and Europe was revived. Clinical trials were resumed at Brookhaven National Laboratory as well as at Harvard and MIT in the early to mid 1990’s. Under J. A. Coderre, Brookhaven clinical trials were begun in September 1994 concluding in May 1999. 40 P. M. Busse at Harvard and MIT conducted clinical trials from mid 1996 until May 1999. 41 Prior work had found that BSH does not cross the blood-brain barrier and is typically renally excreted unchanged. 42-45 BSH is toxic in large doses with rapid infusions due to the ionic effect. It concentrates in GBM over normal brain tissue at about a ratio of 3.5-4.5:1. BPA, on the other hand, was found to be nontoxic in even very large doses and is also renally excreted unchanged. 35, 46, 47 BPA also concentrates in the glioblastoma in a ratio of about 3.5-4.5:1 but it does cross the blood-brain barrier which means that it has a greater opportunity to reach the infiltrative tumor cells. 48-50 Unlike the blood concentration in BSH that takes one to two hours to decrease, the blood concentration for BPA diminishes very rapidly. Thus, in the United States and in most places in the world, BPA has become the primary boron carrier for BNCT. Barth et. al. have experimented with compounds to disrupt the blood-brain barrier with mixed results. 50-53 The clinical trials at Brookhaven National Laboratory were designed to evaluate the tolerance of the central nervous system BNCT. A total of 53 patients in eight different phase I/phase II protocols were evaluated. 54 All of the patients received BNCT with BPA using 1, 2 or in some cases 3 radiation fields. A single patient was retreated (referred and managed by T. L. Nichols). The entry criteria for the Brookhaven trials required that the tumors be supra-tentorial, unilateral, unifocal, and surgically resected. There could be no evidence of congestive heart failure, the Karnofsky Performance Score had to be 70 or greater, and normal blood chemistries were required, in general that being a white count of around 2500/mm 3, a platelet count of 75,000/mm 3, and a creatinine of

9 1.6 mg/dL or better. All patients had to be 18 years of age or older. No separation was made on the basis of sex or race. There could be no history of phenylketonuria, prior radiation therapy to the brain, prior immunotherapy, and systemic or intrathecal chemotherapy prior to BNCT. Informed consent was obtained for all subjects. The results of this trial were reported for this group, at the Tenth International Symposium on Neutron Capture Therapy for Cancer in Essen, Germany in 2002. 40 All patients had died but the mean survival times were reported as 64.1 weeks for one field, with dose ranging from 8.9 to 14.8 Gy-eq; 52.4 weeks for two fields with a dose of 11.3 – 14.2 Gy-eq, and 51.6 weeks for three fields with a dose of 12.6 – 15.9 Gy-eq. It is important to note that, as the trials progressed and the dose progressed and the fields increased, the trials included patients with increasingly large tumors. 40, 55 Brookhaven also reported that the time to progression for the tumor was 34.5 weeks for one field, 21.1 weeks for two fields, and 18 weeks for three fields. This result is odd because the time to progression shows a negative dose response. This is unlike typical findings for radiotherapy, where increasing the dose gives an increased survivability, at least up until the time that radiation damage to normal tissue exceeds the benefits of the treatment. 55 This rather perplexing result as well as the example of some of the earlier data are not yet fully explained. The treatment planning for the Brookhaven National Laboratory trials was performed with a set of codes developed at Idaho National Engineering and Environmental Laboratory by Nigg and his colleagues. 56-60 The program solves the Boltzmann transport equation for neutrons and produces dose contours based upon the structures and composition of the brain. The results of the isodose curves are then scaled linearly for the presence of boron. This has been shown to hold true for boron concentrations in the realm that are currently being achieved in BNCT. Namely, boron concentrations up to ~100 ppm will allow linear scaling with only small errors. Simultaneously efforts were underway at MIT under the direction of Zamenhof to develop a treatment plan code entitled MAC-NCT Plan. 61-63 This treatment planning package was used to do all treatment planning and report doses for the patient’s treated at Harvard/MIT. Relatively recent work has shown that these two codes are compatible, yielding similar results if the input neutron beam specifications are the same. 64, 65

10 The Harvard/MIT phase I trial was designed to determine the maximum tolerable dose to normal tissue for cranial BNCT irradiations. Although this trial did incorporate dose escalations to be given to the patients, there was no phase II portion planned. The patient eligibility was similar to that at BNL in that the patient had to have a biopsy- proven and resected glioblastoma multiforme. They would also treat patients with multiple brain metastases of biopsy-proven malignant melanoma as well as treating malignant melanoma confined to the arms or legs. 66, 67 As in the case of the BNL trials, the patient had to have a Karnofsky Performance Score of 70 or greater, no history of prior intracranial irradiation, no previous chemotherapy, no history of phenylketonuria, be 18 years or older, and all patients had to provide informed consent. The patients were given BPA through an I.V. infusion through a central venous line at doses of 250 mg/kg over 60 minutes, up to 300 mg/kg over 60 minutes, or 350 mg/kg over 90 minutes. The initial dose was 8.8 Sv and was increased by 10% after every three subjects were treated. Twenty-four patients were entered in the trial, 22 were irradiated, and two subjects were excluded due to decline in performance status by the time of arrival at Harvard. Of the irradiated subjects, two had metastatic melanoma. The remainder had glioblastoma multiforme. The median age was 56 with an age range of 24 to 75. Six dose cohorts were completed at doses of 8.8, 9.7, 10.6, 11.7, and 12.8, and 14.2 RBE-gray. Depending on the location of the tumor for the particular dose cohort, one to three radiation fields were used. According to Busse, “of those patients surviving beyond six months, no MRI white matter changes were observed and no long-term complications attributable to BNCT were evidenced”.41 No survival data have been reported on these phase I trials, but via personal communication, they are comparable with the experience from BNL with median life expectancies on the order of 14 months. 68 In the mid 80’s, Hatanaka died and his collaborators continued the trials with BNCT being the current treatment of choice for glioblastoma multiforme in Japan. The Japanese also employ BNCT for the treatment of malignant melanoma involving the extremities. The Japanese continue to report long-term survival rates higher than the trials seen at Brookhaven and at Harvard, 69 which may be partially accounted for by their continued use of a thermal beam rather than the epithermal neutron (1 eV-10 keV) beam

11 employed at BNL and MIT. 70, 71 Epithermal beams of neutrons with their slightly higher energies allow neutrons to penetrate further, thermalizing by the time they reach the depth of the tumor. The Japanese solved this problem a different way by continuing to use a thermal column and, reflecting the scalp and the skull prior to irradiation. Also, after debulking neurosurgery for the glioblastoma, they filled the void created with essentially a ping-pong ball. It is believed that this may provide better uniformity of dose and cause less attenuation of the thermal neutron beam. There has been much interest in the Japanese data. The neuropathologists George E. Laramore and A. M. Spence at Washington State University have re-analyzed some of the Japanese data. Laramore took the Japanese results and tried to identify patients who were from the United States. On that cohort of patients, he was able to obtain original pathology reports. He reevaluated those cohorts and felt that some were misdiagnosed. They claimed that many of the pathologic diagnoses were not accurate and that the patients also had lymphomas and other malignancies. When re-evaluated, he stated, “The only long-term survivors in the BNCT group had anaplastic astrocytomas and favorable prognostic criteria” (classes I and II of Curran et. al.). 39 The patients that Laramore felt did not meet the criteria for glioblastoma multiforme, had a three-year survivability rate of 22% versus 13% for ‘correctly’ diagnosed patients whom they agreed had a GBM. Two-year survivability for the non-GBM patients was 20% versus 10% for the GBM patients. Thus when the disputed patients were removed, the cohorts with GBM had results like patients in other trials. These findings therefore cast some doubt upon the Japanese results. He was unable to obtain any other data from the Japanese; therefore, the Japanese results present something of a conundrum. It is prudent to remember that in grading (and therefore determining the classifications) of high-grade astrocytomas, the actual grade is rather subjective in nature. The relative disorganization of the tumor tissue and the relative abnormality of the nuclei determine the grade awarded it by the pathologist. Also, it should be noted that the patients would have had to have an initial pathological diagnosis of a GBM by a pathologist in the USA prior to being sent to Japan in the first place. Furthermore, a Japanese pathologist would have reviewed the pathology slides prior to any treatment. Therefore, with the subjective nature of the

12 process, a definitive answer may have to await other studies to determine the actual results of the Japanese experience. The more recent Japanese results are, though still better than most other centers comparable to other results. 69 The Brookhaven National Laboratory experience with BNCT yielded a life expectancy of 14.2 months in their cohort of 53 patients. 40 One patient of interest was the only patient in the world to be treated twice with BNCT and she was a referral from The University of Tennessee (UT) research program to BNL. She was one of six glioblastoma multiforme patients referred from UT to either Brookhaven National Laboratory or Harvard/MIT. (A seventh patient was sent to Harvard/MIT with multiple brain metastases from malignant melanoma.) This GBM patient was an active retiree who swam on a regular basis. She had had her GBM resected at a local hospital and did not want conventional radiation or chemotherapy. She was referred to Brookhaven where she received a single dose treatment of BNCT. Thereafter, she immediately resumed her active lifestyle having only minor alopecia in the region of the irradiation, and some mild problems with mucus gland swelling on the left side of her face where her left parieto-occipital GBM was irradiated. She remained active post BNCT with very little interruption into her normal schedule. In fact, it was rather difficult to get her to the office for scheduled appointments for the clinical trials due to her busy schedule. Approximately 10 months following her initial debulking surgery, she developed some depression, lethargy, and according to family members, a mild change in her affect. She was then referred a neurosurgeon at the University of Tennessee Medical Center who noted regrowth of the tumor adjacent to the initial tumor site. This tumor was once again resected and she was sent back to Brookhaven for a second irradiation. Once again the treatment was accomplished with no obvious ill effects except for mucositis, mild alopecia, and reddening of the scalp. She required steroid treatment with dexamethasone following the resection and following both treatments with BNCT. She died about four months after her second BNCT treatment, surviving a total of about 14 ½ months from the time of diagnosis. Of great interest, however, are her pathology reports. The initial pathology report was read as 95% of the specimen consistent with glioblastoma multiforme and approximately 5% consistent with a gliosarcoma. Gliosarcomas are

13 much more rare than glioblastomas and have no known effective therapy and are extremely aggressive. The biopsy from her second resection showed quite the opposite situation. There were almost no elements of glioblastoma multiforme seen and those that were seen appeared to be necrotic. The remainder of the tumor was consistent with gliosarcoma. As with all of the patients who received BNCT through UT Medical Center’s referrals to the two clinical trial centers, the patients had virtually no ill effects except for some mild alopecia and mucositis. In all cases, the patient and the family were pleased with the treatment. This case does illustrate some of the problems in interpreting the biopsy data for this complicated disease and understanding the disease process. The renewed interest in the United States in BNCT also sparked increased interest worldwide. Since the time that the US trials restarted, programs have begun in Sweden, Finland, the Netherlands, Romania, Italy, and Argentina. Most of these trials utilize BPA as the boron delivery agent. Most of the trials are treating glioblastoma multiforme but Harvard also treated malignant melanoma, as are the Japanese. The Japanese are using BNCT as the treatment of choice for GBM and have started exploring the possibility of treating hepatocellular carcinoma 72 and pancreatic carcinoma. 73 Undifferentiated thyroid carcinoma as well as other head and neck tumors has been explored by a group in Argentine. 74 The Italians are treating carcinoma of the colon 75, 76 and head and neck tumors at their TAPIRO BNCT facility. 77 The Italian effort deserves some discussion. They have recently explanted a liver after loading the patient with BPA. 76, 78, 79 The liver was then taken to a nearby reactor, which has only a thermal neutron beam available. The liver contained at least 22 distinct metastases of carcinoma of the colon. As is well known, this large a tumor load of the liver is virtually an untreatable situation. The liver was then irradiated by the thermal neutrons and reimplanted. The patient lived ~4 years post BNCT with signs of regression of all liver lesions but dying of disease elsewhere as related personally. There were no known ill effects other than the typical surgery morbidity with the explantation, irradiation and reimplantation. Thus, BNCT is being applied to many different malignancies where it may become a valuable, if not, lifesaving treatment. It is well recognized that two great advantages BNCT has compared to conventional radiation therapy are that a much larger dose is delivered to the tumor and

14 that doses are delivered in a single or small number of fractions. So that the patient spends less time meeting in a health care setting since for terminal conditions, the patient will have more time for themselves and their family. Another case may help illuminate some of these points. The patient was an active 53-year-old white male elementary school principal from middle Tennessee. He had been found to have a primary malignant melanoma on his back. For reasons that are not clear, there was a delay after the initial biopsy in undertaking definitive therapy of several months. By this time, he had developed a massive melanoma tumor load in his chest and had four distinct intracranial metastases as indicated by positron emission tomography (PET). The patient, when apprised of his grim diagnosis, looked for alternative therapies and was referred to the program at Harvard. From Harvard, he was referred to UT Medical Center for positron emission tomography imaging and subsequent management of his thoracic tumor load following intracranial BNCT. Of interest, the four lesions were not clearly seen on CT or MRI but were readily seen with PET. The patient underwent BNCT in late October, receiving his intracranial irradiations in three fractions on Wednesday and Thursday of that week. He returned home to play golf on Sunday and was back to work on Monday morning. The patient did very well following the irradiation, being placed only on dexamethasone. His only ill effects from the BNCT were local alopecia and some very mild mucositis. Approximately one month following BNCT, the patient entered UT Medical Center for chemotherapy and immunotherapy for his large thoracic tumor load of melanoma. It should be emphasized that there is no known effective treatment for metastatic malignant melanoma of the brain with more than a single focus. Therefore, the immuno- and chemotherapy that were begun would not be expected to significantly affect the course of the brain metastases but only that of the tumor load elsewhere in his body. Unfortunately, following his initial dose of chemotherapy and immunotherapy, the patient developed sepsis from his immuno- suppression. He quickly developed adult respiratory distress syndrome (ARDS) resulting in intubation and mechanical ventilation. He had a long and complex stay in the intensive care unit during which time he also developed acute renal failure requiring hemodialysis. His renal function did improve after several weeks of dialysis and his

15 kidney function gradually returned. However, his mental status did not improve as much. He was never fully cognizant of his surroundings or others following his extubation. After an MRI was read as having multiple micrometastases of malignant melanoma, the family decided not to pursue further treatment and he was discharged to a nursing home where he died a short time later. Upon his death, approximately five months post BNCT, a limited postmortem was done upon his brain alone. His death was due to the thoracic tumor load. The postmortem examination of the brain revealed that what was thought to be micrometastases of melanoma was actually a saponification related to the ARDS. All four of the malignant melanoma metastases were found to be necrotic and were involuting. There was no evidence of other intracranial melanoma and the melanoma present was in the process of dying. 67 This patient had a similar course as the first patient treated at Harvard for melanoma of the brain who survived a year after BNCT. This patient had evidence of complete resolution of melanoma in his brain but died due to tumor load elsewhere in his body. 66 The results from the worldwide clinical trials for BNCT to date are difficult to interpret. The American experience would only show a modest increase in life expectancy for glioblastoma multiforme patients. In the case of malignant melanoma, there is reason to believe that brain metastases could be cured, although the tumor load and the rest of the body may still overwhelm the patient. The Japanese experience is more positive than that of the American but there are detractors who represent competing therapies (fast neutron therapy). The European experience is still in its infancy but the Finns now have a commercially viable BNCT program. The Italians, Japanese, and Finns are opening exciting new vistas by applying BNCT to different tumors. When examined from the perspective of a GBM patient or a patient with multiple melanoma brain metastases, BNCT is already a success. This is not due to BNCT adding time to the life expectancy, but is rather because it provides a short and serious complication-free treatment that allows the patient to enjoy the best quality of life that can be provided from these horrific diseases.

16 C. A brief review of problems encountered in boron neutron capture therapy

As may be inferred from the above discussion, there are four factors that will ultimately determine the effectiveness of BNCT. The first two deal with the beam quality. It is estimated that the fluence of thermal neutrons in the tumor region needs to be on the order of 10 12 which corresponds to a flux of about 10 9 neutrons per second. 80 Less flux will result in unreasonably long irradiation times and more flux will likely increase the toxicity without increasing the tumor dose. The other issue is the beam quality. It is well known that fast neutrons are harmful and other beam contaminants such as γ-rays and other ionizing particles can change the delivered dose, sometimes dramatically. In order to achieve the best efficacy, a flux of neutrons which is thermal at the depth of the tumor, a pure beam of epithermal neutrons is requisite. 80 Due to difficulties in neutron beam measurement in the 50s and early 60s, this was difficult to achieve. However, it is now felt that available beam quality is more than adequate. The neutron beams have few other types of ionizing radiation and are typically epithermal in nature so that the neutrons will be thermalized by the time they reach the depth of the tumor. 81-86 Fluences are now commonly achieved in the 5 x 10 12 range. 87-89 At this point in time, no significant advances are required in beam quality or fluence. The other two issues that relate to the efficacy of BNCT have to do with the delivery of boron-10. The delivery method must first of all be relatively nontoxic in nature. For some boron containing molecules (i.e. BPA), in order to achieve sufficient tumor to normal tissue ratios, large amounts of infusate over a long periods of time are required. A compound and all its active metabolites must have low toxicity. Lastly, the boron containing molecule must concentrate preferentially in tumor cells over normal tissue in a ratio of at least 3:1. 90 That will ensure that approximately three times the dose will be deposited in tumor cells rather than normal tissue. In order to prevent coagulation necrosis, the vascular washout needs to be complete or nearly complete at the time of irradiation. In a tumor such as glioblastoma multiforme that has infiltrative tumor cells (ITC) 12 that may be far away from the main body of the tumor, a 3:1 ratio of boron in all tumor cells to

17 compared normal tissue must be attained. Obtaining a favorable boron ratio in these ITCs is a much more difficult criterion to meet. In traditional radiation therapy, treatment plans are produced showing isodose curves. These treatment plans provide the macrodosimetry for that particular radiation modality. In BNCT, the major irradiation dose is variable throughout the tissues partially due to the variation in nitrogen concentration through the (n,p) reaction and primarily due to significant concentration differences for in 10 B through the (n, α) reaction. If there is a sufficient boron concentration (approximately 15 µg normal tissue and 50 µg or more in the tumor), the (n,p) and (n, α) reactions account for more than two-thirds of the total radiation dose. 91 Other significant reactions are from the proton recoil from hydrogen, carbon recoil, and the γ-rays given off from the 10 B reaction. The proton recoil from the 1H(n, γ)2H reaction has a small thermal neutron cross-section of only 0.332 b and will produce a somewhat homogeneous dose due to the ubiquitous hydrogen distribution. The range of the carbon ion recoil from the 14 N(n,p) 14 C reaction is only ~0.26 µm. The γ- rays are produced isotropically from the 1H(n, γ)2H and 10 B(n, α γ )7Li reactions and have long ranges with much of the energy deposition occurring outside of the brain. The most significant variability in dose will be delivered by the protons, alpha particles, and lithium nuclei from the 14 N(n,p) 14 C and 10 B(n, α γ )7Li reactions. The essential treatment failure in BNCT at this time is due to an inadequate concentration of boron in the tumor cells as compared to normal tissue. This manifests itself as either a lack of sufficient therapeutic ratio (3:1 or better) in tumor cells to normal cells or due to a lack of total 10 B concentration. Analysis of studies in the literature and discussions with the researchers in this area would seem to indicate that the problem is in both of these areas. 41, 60, 63, 69, 92-102 Previously, treatment planning was performed either by extrapolation from animal models such as dogs and mice or by utilizing data taken at the time of initial neurosurgical debulking surgery. These two sources have provided all of the data about the 10 B distribution and also present problems. For animal models, it is unclear how the results should be scaled to the humans especially in regards to the active and passive diffusion rates of the boron containing compound. 44, 103-108 The problem is different for the neurosurgical debulking data. Since this is human data, the concerns with diffusion 18 rates and scaling are not a factor. 109-116 A description of the data acquisition follows. After obtaining informed consent and just prior to the patient’s surgery, the patient is loaded with 250 mg BPA/kg of IV BPA. 117 At the time of debulking surgery, the pathological specimens are divided between the pathologist and the BNCT researcher from BNL. The pathological specimens provided to BNL were analyzed for absolute boron content. 111, 114, 115, 118 While this provides information about boron distribution within the tumor itself, no information is gained about the boron concentrations at other locations in the brain – even near the tumor. 54 Because the neurosurgeon will not inflict more harm than is necessary, little normal tissue from around the tumor has ever been sampled. This means that inadequate information was obtained to model the 10 B concentration in the surrounding tissues. Adding to the problem was the logistics. Patients were often far from BNL or were referred for BNCT after debulking surgery had been performed. Thus, few patients had data regarding the boron concentration. However, for most of the trials, data obtained by Coderre indicated a tumor to normal brain concentration of 4.5 to 1 has been used in treatment plans. 94, 111, 114, 117-126 Another problem with data obtained at the time of debulking surgery is that the tumor physiology is altered by the disruption caused by the surgery itself. The tumor size, blood supply, and relationship to surrounding tissues are different at the time of BNCT several weeks after the debulking surgery. Therefore, whatever the concentrations of boron found at the time of debulking surgery, they will likely not reflect the actual concentrations at the time of BNCT. 54 Also, the vascularity may increase or decrease depending on multiple local factors that cannot be determined as well as the integrity of the blood brain barrier. Therefore, the boron concentration ratio of 4.5:1 for the residual tumor to the surrounding normal brain is not likely to be obtained for most patients. Thus, the treatment planning (macrodosimetry) problem in BNCT presents many challenges. Inadequacies in this area could lead to inadequate dosing to certain areas of the tumor and tumor containing regions as well as over dosing of normal surrounding tissue. A typical treatment plan for BNCT generated by the code SERA developed at INEEL 127 using the 4.5:1 tumor to normal tissue boron ratio is shown in Figure I.1.

Figure I.1 A typical SERA generated treatment plan for a glioblastoma multiforme based upon a MRI image. The tumor is the white area inside the ellipsoid like curves. The curves are isodose lines indicating predicted tumor killing. The innermost line is the 95% isodose curve indicating that 95% of tumor cells within the curve will be killed. The remaining curves represent 5% intervals.

20 The goal of treatment planning is to take into account the clearly demarcated tumor, and to develop a treatment plan in which the isodose lines of 90% kill lie approximately of 2 cm outside the tumor margins. 102, 127 In later trials, investigators included the edematous region around the tumor, which is known to have many tumor cells. In Figure I.1 one can see oval isodose curves with the 55% curve encompassing most of the brain. Unfortunately, the clinical trials found that most recurrences occurred in tissues immediately adjacent to the visible tumor. 40, 41, 54 With the current macrodosimetry model, this is a puzzling result since the central areas within the 90% kill range are often receiving in excess of 60 gray equivalents of radiation. 40, 41, 69, 128 That is a large radiation dose that should be lethal to any cells within that range that are loaded with boron. These results indicate that the region of interest (the targeted tumor region and surrounding edematous region) is not actually receiving the dose that the treatment plan predicts. Therefore, a better way of determining in vivo boron concentration is needed. In addition to solving the macrodosimetry problems, more efficacious boron delivery compounds must be found. There has been much work in compound development over the world in the last 30 years. Many promising delivery agents (including monoclonal antibodies) have been created as well as mechanisms to improve delivery of currently employed agents (BPA and BSH). 129-166 Unfortunately, either there is toxicity from the compounds and their metabolites or there was inadequate discrimination between tumor and normal tissue. BPA is still the boron delivery system of choice for most BNCT (especially for melanoma since phenylalanine is a precursor to melanin), which means that, at least for glioblastoma multiforme, it appears to be inadequate for tumor eradication.

21 D. Treatment planning with 18 fluoro-boronophenylalanine positron emission tomography scans for boron neutron capture therapy

In the 1970s, Phelps and Ter-Pogossian developed the technique of positron emission tomography as a possible imaging technique. 167-170 The technique uses a positron emitting nuclide attached to a carrier molecule. Although ammonia and water have been used for PET, the most commonly used molecule is fluorodeoxyglucose (FDG) which is a sugar that distributes like glucose. The emitted positron annihilates when it encounters an electron producing two 511 keV γ-rays at 180 degrees to each other. The common positron emitting nuclides employed in PET are the four short half

isotopes: carbon-11 (t 1/2 ~20min), nitrogen-13 (t 1/2 ~10min), oxygen-15 (t 1/2 ~2min), and fluorine-18 (t 1/2 ~110min). After the positron emitter is produced in a cyclotron, it is chemically attached to a carrier compound. For example, fluorine-18 produced in a cyclotron, is chemically combined with glucose to form fluorodeoxyglucose. As with glucose utilization, the fluorodeoxyglucose is preferentially transported into the most metabolically active tissues. Therefore, the most metabolically active tissues have high glucose utilization, which means that the FDG collects in the same tissue. The images were obtained by filtered back projection of the coincidence counts in the PET scanner. The resulting images provide a metabolic distribution map of the structures imaged. For example, a positron emission tomography scan of the brain would show the most intense activities in areas that are active at the time of the scan. So, when the eyes are open, increased activity is seen in the occipital region. Unlike MRI, CT, ultrasonography, and plain x-rays, PET scanning allows the determination of dynamic information about a tissue. The first clinical PET center in the country was established at the University of Tennessee Medical Center in the late 1980s. Kabalka at UT and Ishiwata in Japan realized that the 18 F could be successfully added to BPA to form 18 F-BPA (2-fluoro-4- boronophenylalanine). 116, 171-174 Pharmacokinetic studies show that fluorine stays attached to the BPA until the complex is renally excreted 175, 176 so that PET scans identify the 10 B distribution. 116 Thus, the in vivo boron distribution can be determined for BNCT 22 patients. The patient can be imaged after healing from debulking surgery and prior to the BNCT. Figure I.2 is a PET scan of the same patient shown in Figure I.1 that was generated using 18 F-BPA. The GBM is the oval in the lower left portion of the scan. The information contained in the PET scan may be directly correlated with the boron content in the brain. The patients were infused with only 10 mCi of activity, which contributes to the graininess of the images. The other source of graininess in PET images is due to the fact that a positron moves up to 10 mm prior to annihilation. Since the positron emission tomography scan is a boron distribution map, this information can be used to scale the results of a treatment plan generated by one of the standard BNCT treatment planning programs. The treatment plan in Figure I.1 was redone with the PET data input into SERA to provide the boron concentration throughout the brain. Since the total boron concentration never gets as high as 100 ppm anywhere in the brain, it is possible to use these data in post-process scaling. When this is done, dramatic differences in the isodose contour lines are seen as shown in Figure I.3. The contours are much more closely packed and irregular which may be explained by inhomogenieties in the uptake of the 18 F-BPA. This is not an unexpected finding in the postsurgical tumor bed in the peritumor regions with small clusters of cells and ITCs. Figure I.4 depicts the 18 F-BPA distribution in the same plane through the brain (slightly rotated). The distribution is clearly inhomogeneous in the remaining tumor bed and the peritumor region. It is clear that there is a high probability that the center of the tumor will be totally obliterated by BNCT but cells only small distances away from the center of the tumor will receive a significantly less dose. These findings explain the observed lack of local control and local recurrence of the glioblastoma multiforme. 177, 178 Evaluation PET scans on patients from UT Medical Center treated with BNCT often indicate the area of recurrence. 178 In all cases, PET based dosimetry demonstrated a superior predictive value over the conventional treatment planning. 177, 178 Though, PET based dosimetry is becoming widely used in BNCT treatment planning 94, 107, 178-182 there are still some issues that have yet to be resolved. The

Figure I.2 Pre-operative 18 F-BPA-fructose PET scans of the same patient as in Fig. I.1 with a parietal glioblastoma multiforme.

Figure I.3 Treatment plan generated by SERA using 18 F-BPA PET scan information.

18 F-BPA 3-D Activity Plot

Figure I.4 Two-dimensional activity plot showing inhomogenieties in the region of the glioblastoma multiforme.

26 pharmacokinetics of 18 F-BPA PET scans have been reported 183, 184 but the issue of scaling the dose has not been verified. The patient receives approximately 10 mCi of activity (~10 ml) for an 18 F-BPA PET scan. This is in contrast to 1-2 liters of infusate (containing 2-3 g of BPA) that is given to the patient prior to BNCT. 54 The problem is currently solved mathematically using a convolution integral technique to scale the results to that which would be seen with the larger amount. However, at this time, the approach has not been verified with clinical studies to show that these are equivalent, i.e., that the convolution interval in a PET scan recreates what happens in the patient given several grams in 1-2 liters of infusate of 18 F-BPA. 185-187 Most remarkable are the results from a patient with metastatic malignant melanoma a seen in Figure I.5. Unlike glioblastoma, the distribution of BPA inside the tumor is much more homogeneous. The 90% isodose curve is along the edge of the tumor with close spacing so that most of the dose is near and in the tumor. In this case, only the tumor and neighboring cells would be expected to be killed by BNCT, which is unlike the case for glioblastoma. Since malignant melanomas tend to expand in a more or less spherical manner, what appears on the scans to be tumor is most likely the extent of the tumor. That is in contrast to the glioblastoma where its infiltrative nature means that there are small clumps and single cells far removed from the tumor itself. Therefore, one would expect that malignant melanoma would be entirely destroyed by BNCT whereas glioblastoma multiforme would not. These findings correlate well with results from the clinical trials to date. 18 F-BPA PET scanning provides an important addition to the treatment planning for BNCT. Unfortunately, it is difficult to make 18 F-BPA so that not all BNCT treatment planning is being performed with 18 F-BPA PET scan data. However, as PET centers proliferate, the use of a 18 F-BPA PET scan to provide the boron-10 distributions is becoming the standard for treatment planning for BNCT.

E. Statement of the Problem

One of the important clinical issues facing BNCT is to better understand the reasons for the modest success in treating glioblastoma multiforme as compared to the 27

Figure I.5 18 F-BPA PET scan of a metastatic focus of malignant melanoma. The left hand frame shows a typical BNCT treatment plan with SERA while the right hand frame uses the PET data.

28 early impressive results with solid malignancies such as metastases from adenocarcinoma of the colon and malignant melanoma. The treatment plans based upon 18 F-BPA PET scans when compared to traditional treatment plans provide a macroscopic explanation but the basic idea of BNCT is that boron-10 laden tumor cells will be preferentially destroyed as long as those cells are in the neutron beam. The ITCs in the periphery of glioblastomae are the apparent source of the local failure for this tumor. The radiation milieu for these cells as compared to cells on the edge of a solid tumor such as melanoma should provide the explanation. The local radiation milieu for ITCs will be determined by the neutron beam characteristics that then determine the nuclear reactions and scattering reactions. The boron-10 reactions provide the largest component of the dose as will be shown. The microscopic boron-10 distribution will determine most of the effects upon cells along the tumor periphery. The geometrical arrangement of boron-10 laden cells should affect the dose to ITCs. The near neighbor cells are postulated to increase the dose to non-boron-10 laden cells. The effects of boron-10 concentration and cell geometries will be examined to explain the clinical observations in BNCT clinical trials.

29 II. Microdosimetric Models

A. Basics of microdosimetry

1. Concepts of microdosimetry for BNCT “Microdosimetry is the area of study that deals with the microscopic distribution of energy in small volumes of matter by ionizing radiation”. 188 In the ‘60s, ‘70s, and ‘80s, Rossi and Zaider pioneered microdosimetry 189-198 culminating in a textbook published in 1996. 198 In their studies, Zaider and Rossi began to understand concepts of energy deposition in cells and the mechanisms of cellular damage. 198 For human cancer therapy, there are three important aspects of micro-dosimetry: the physical distribution of absorbed energy (dose) into a small volume (on the order of microns) of tissue, the relative biological effectiveness (RBE) of the delivered dose, and the process that ionizing radiation leads to cellular demise. Turning first to the physical energy distribution of energy deposited in a tissue, it is important to examine the spatial energy distribution for a given ionizing radiation. The energy deposited in a tissue depends upon the kinetic energy, charge state, and mass of the ion. The majority of interactions for an ion are electromagnetic scattering from electrons in the outer orbitals of molecules in the target. The cross section for nuclear scattering of ions with appropriate radiotherapy energies and masses is low. 188, 198 Ions possessing larger charge states will have stronger interactions with the orbital electrons, which results in a greater deceleration than lesser charge states. Ions that are energetic and heavier (i.e. possess more linear momentum) tend to penetrate more and undergo less deflection from the orbital electrons. The differences in ion tracks are demonstrated in Figure II.1 where an alpha particle, electrons generated by a photon, and 125 I which has two-step nuclear decay: 125 I (Electron Capture) → 125m Te (Isomeric Transition) → 125 Te where the first step involves emission of K x-rays and Auger electrons. The 5.4MeV alpha particle is seen to have a linear path and to produce electrons by scattering from the outer orbitals. This is contrasted to the electrons produced by Compton scattering by 1.5 keV X-ray photons where the electrons have complicated tracks from scattering from

30 other electrons. The higher energy Auger electrons produced in the decay of 125 I initially have straighter tracks but soon slow down and display many more scattering interactions. Thus, heavy, energetic, highly charged ions tend to travel in a more linear manner producing scattered electrons along the path of the ion. As particles slow down along the track, the ion will have a peak in energy deposition near the end of the track and will travel a short distances seen in Figure II.2. In three dimensions, the energy deposition will resemble a teardrop and will generate free radicals in the same teardrop distribution. As the ion slows, the track will become less linear because the interaction time with a given electron orbital increases, allowing a greater time for the electromagnetic interaction to alter the path. Despite the alterations in the track and the distinctly non-linear energy deposition along the track as depicted in Figure II.2, most microdosimetry utilizes a linear stopping power approximation. The stopping power is approximated by a straight line beginning at the initial ion energy at a displacement of zero and ending at an energy of zero at the maximum range. Obviously, the range is a statistical value rather than a definite value but in microdosimetry it is usually taken as a definite value. In this work, a linear stopping power is not employed but the range is taken as a fixed value. Instead of a linear stopping power approximation, the stopping power curves are integrated along the required portion of the track. The dose is defined by the amount of energy deposited in a region per unit mass with units of Gray (1 Gray = 1 J/kg). The dose to a tissue does not fully describe the effect on a given tissue. The kind of ionizing particle depositing the energy affects the damage to a tissue. It is important to note that all radiation therapies rely on charged particle formation to damage cellular apparatus. As an example, traditional photon therapy creates charged particles by Compton scattering of electrons in outer electron orbitals. These electrons produce free radicals along their tracks, which damage nearby molecules. However, some ionizing particles cause more biological damage than do other kinds. In particular, high LET radiation causes greater biological damage than do photons. To adjust for these differences the concept of relative biological effectiveness (RBE) was developed. The RBE for a given radiation that has a dose, D, is: D (II.A.1) RBE = X D 31

Figure II.1 Ionizations and excitations along particle tracks in water, for a 5.4 MeV α- particle (top left), for electrons generated following the absorption of a 1.5 keV X-ray photon (top right) and electrons generated during the decay of iodine-125. 199

Figure II.2 The stopping power for 5.49 MeV alpha particles in air demonstrating the Bragg peak near the end of the track where much of the energy is deposited. The image is courtesy of Helmut Paul.

32 where D X is the dose produced by a standard X-ray (often a 250 keV x-ray). A typical set of RBE values is provided in Table II.1. The neutrons in Table II.1 are fission spectrum neutrons, which are different from the epithermal beams used in BNCT. The BNCT doses are often expressed as gray-equivalent (Gy-Eq), which is the sum of the various physical dose components multiplied to appropriate biologic effectiveness factors. The BNCT literature contains a great deal of debate as to what values should be assigned to RBEs. In this dissertation, the boron (n, α) and nitrogen (n,p) reactions are the only ones considered for reasons to be presented later. For clarity, the results are presented in Gray rather than Gray-Equivalent. Lastly, the radiation dose in radiotherapy is designed to destroy the malignant cell and to spare normal cells. In general, it is felt that destroying the cell’s DNA is the way to destroy a cell. The dosing is designed to deliver a smaller dose to normal cells and concentrate the dose into tumors. The methods of doing this usually have to do with using multiple directions of a photon beam or placing a radiation source directly into a tumor (which in a sense is what occurs in BNCT). The charged particles from radiation therapy directly deposit energy through electromagnetic interactions as the cellular constituents slow down the charged particle forming free radicals. The charged particles can hit large molecules, such as DNA, directly which will cleave chemical bonds. However, more damage is probably done to the cell and its constituents by the effects of the free radicals. 200-202 Free radicals can cleave bonds damaging nearby proteins, RNA, and DNA. Since the number of free radicals formed is much greater than the single charged particle, more damage is done. Heavy ions (in a biological sense an alpha or

Table II.1 Relative biological effectiveness for several different kinds of radiation. Radiation RBE X-rays 1 γ-rays 1 β particles 1 α particles 10 to 20 protons 1.1 Neutrons: Immediate radiation injury 1 Neutrons: Cataracts, Leukemia, and Genetic changes 4 to 10 33 heavier) can do significant damage. As a high LET radiation, heavy ions will cause single and double strand breaks in DNA. Double strand breaks are more difficult for the cell to repair than single strand breaks or single base deletions. The DNA damage from heavy ion generated free radicals is usually less than the damage from heavy ions hitting DNA molecules. Since free radicals diffuse away from the original sites, free radicals increase the likelihood for DNA damage. Therefore, a heavy charged particle moving energetically past DNA may cause significant damage to the DNA without ever striking it due to free radical generation. It is important to understand that the accepted method for cellular demise is from DNA damage. The DNA damage can result in either apoptosis or relatively more rapid cellular demise. 203 The apoptosis, i.e. programmed cell death, means that the natural life expectancy of the cell has been ‘reprogrammed’ to an earlier time. When examined microscopically, these cells have no noticeable DNA damage. Other cells are seen to have microscopically evident DNA malformations. 203 The DNA malformations can result in two lethal outcomes. First, the cell may not be able to perform mitosis successfully leading to cell death at that time. The other result may be the loss of the ability to make a particular protein or proteins. If those protein(s) are essential in the maintenance of homeostasis, the cell will die when the protein(s) are degraded through normal processes. This mode of death can occur in a few days. Finally, radiation therapy can cause immediate cell death that does not involve the above processes as is seen from blood samples immediately after a radiation treatment. 204 The source of this immediate cell death is being studied with ion microbeams. In some circumstances, neighboring cells (termed bystanders) provide protection to irradiated cells. The opposite effect is seen as well where a cell damaged by radiation causes damage to bystander cells through a non-humoral mechanism. 205-218 Knowledge gained in the study of microdosimetry has helped to explain the oxygen effect that was already known to radiation oncologists. Increased oxygen concentration intensifies the damage from radiation. Intuitively, this is not expected since oxygen deprivation may be expected to cause more damage than an oxygen-rich

34 environment. However, free radical formation is enhanced in high oxygen concentration and diminished in situations when the oxygen concentration is low. The understanding of the microdosimetry of BNCT will be shown to be necessary to understand the clinical implications of BNCT.

2. Stopping powers Interest in the theory of energetic ions interacting with matter and slowing down dates back to Marie Curie’s work in 1898-1899 on radioactivity. 219 Niels Bohr was the first to provide a theory of stopping powers 220, 221 after the experimental work of Geiger and Marsden 222 and the theoretical explanation of their work by Rutherford. 223 Bohr’s treatment did not take into account quantum effects. The first to include quantum effects was Bethe. 224, 225 Bethe’s work was later refined by Bloch. 226, 227 Stopping powers are expressed now by the Bethe-Bloch equation as refined by Fano. 228 The history of determination of stopping powers is well reviewed by Ziegler. 229 The major contribution to the stopping power for ions is due to the electromagnetic interaction between the target electrons and the positively charged ion. The stopping power, S, may be written as: dE κZ (II.A.2) S=−=2 ZL2[()β + ZL ( β )+ ZL 2 (...] β ) dx β 2 10 11 22 where

2 2 (II.A.3) κ= 4 π r0 me c ,

(II.A.4) Z1 = ion charge ,

(II.A.5) Z2 = target atom charge ,

(II.A.6) β = v , c e2 (II.A.7) r0 ≡ 2 , me c

(II.A.8) me = electron mass , (II.A.9) c = speed of light , (II.A.10) v = ion velocity , and

35 2 (II.A.11) L(β)= [() L0 β + ZL 11 ( β )+ ZL 22 (...] β )

where L0 is the stopping number that contains corrections to the stopping power. The 228 primary stopping number, L0, contains the largest correction and Fano expressed it theoretically by: 2 2  1 2me cβ ∆ E max 2 C δ (II.A.12) L0 =ln2  −−−β ln I 2 1− β  Z2 2

where C/Z 2 is the shell correction for the target atom, is the mean ionization energy of the target atom, and δ/2 is the density correction. The largest possible energy loss in a single collision with a free electron is given by:

−1 2  2 2    2mceβ  2 m e m e  (II.A.13) ∆=Emax   1 +1 2 +   1− β 2  2 M   M1 ()1− β 1  where M1 is the mass of the ion. The shell correction term takes into account the assumption that the ion velocity is much larger than the target electron velocity. The calculation requires careful accounting of the ion with the electrons in the various electron shells in the target. The mean ionization corrects for the quantum mechanical energy levels that target electrons have available for transfer. Finally, the density term corrects for polarization effects in the target.

The L1 term in equation (II.A.11) is called the Barkas correction after the work by 230 Barkas et. al. and the L2 term is the Bloch term. These terms deal primarily with two experimental observations. The first is that two ions of the same mass and velocity in the same target have different ranges where the only difference is for different sign of the ion charge. The other effect is the corrections required for the magnitude of the charge. For example, according to the basic Bethe-Bloch equation, an ion with charge +2 should have four times the stopping of a similar particle of charge +1 but experimentally the stopping exceeds a factor of four. The greatest interest in the calculation of stopping powers has traditionally been focused on high energy ions rather then the low energy ions used in BNCT. The standard for the BNCT field, as well as many other fields for calculating stopping powers is a program that was developed by Ziegler 231, 232 (originally in FORTRAN) several decades

36 ago that has been refined and improved over the years. The program is now called SRIM2008 (Stopping Range In Matter), which is available, online at www.srim.org . The program uses the basic Bethe theorem of charged particles stopping with Bloch shell, and Barkas corrections to generate a theoretical curve that is then compared to and matched with experimental data. The results provide accurate (1 to 2%) results for high energy ions, > 5 MeV/amu, but can be off as much as 20% for low energy ions, < 1 MeV/amu, because at low energies the ions will travel distances on the order of Ångstroms (see details at www.srim.org ). The calculation of stopping powers also requires the use of an approximation termed the continuous slowing down approximation (CSDA). The actual path of an ion involves quantum mechanical interactions with molecular electron orbitals. The ion slow down is not smooth and continuous but has discrete interactions (though the range is large since they are electromagnetic in nature). The details for this calculation are difficult to obtain so the CSDA is used where there is little data. The program also allows for the selection of a number of compound targets including tissues based upon the additivity of stopping powers. Type II breast tissue was used in these calculations since it best emulated brain tissue and there are no brain tissue options in the targets. The calculations of the stopping powers for the proton from the 14 N(n,p) 14 C reaction as well as the alpha particle and the lithium nucleus from the 10 B(n, α)7Li reaction for this work were performed with SRIM2008. The range for the five ions is shown in Table II.2 where it is noted that the lithium ions have very short ranges. The maximum range for these ions is that of the proton which is still only 10.52 µm. The proton range is on the order of one cell diameter so none of the ions will affect cells more than one or two cells removed from the site of the reaction. This emphasizes that the radiation is very focused wherever the reactions occur. Figure II.3 contains the stopping power plot for the proton from the 14 N(n,p) 14 C reaction showing the Bragg peak that occurs near the end of a particle track. The starting energy of 590 keV is obtained by integrating: dE  (II.A.14) E= −  dx deposited ∫ dx  where dx is along the particle track. The stopping power for the other ions are similar but start closer to their Bragg peak as is seen for the 1,780 keV alpha particle from the

37 Table II.2 Range of BNCT associated ions in human tissue. Ion Atomic Number Atomic Mass Initial Energy (keV) Range ( µm) H 1 1.008 590 10.52 He γ 2 4.003 1470 7.39 He 2 4.003 1780 9.06 Li γ 3 7.016 840 3.93 Li 3 7.016 1010 4.38

Proton stopping power for the 14 N(n,p) 14 C reaction

120

100

80 m) µ

-dE/dx (keV/ 40

0 0.01 0.1 1 10 Range ( µm)

Figure II.3 The proton stopping power for the 14 N(n,p) 14 C reaction showing the energy deposition per unit length as a function of the remaining range. The peak is known as the Bragg peak and is near the terminus of stopping powers for all energetic ions where there is a peak in energy deposition prior to stopping.

38 10 B(n, α)7Li reaction in Figure II.4. It should be noted that most authors in BNCT employ a linear slowing approximation where the ion is considered to slow down from the initial energy to zero linearly over the range of the ion not taking into account the actual stopping power utilizing SRIM2008 only to find the ion range. The present work uses the actual stopping power rather than a linear stopping.

3. Determination of the number of interactions It is important to consider the number of 10 B(n, α)7Li interactions that occur in a given volume of tissue. The number of interactions, n i, can be determined by:

3840 barns 10-24 cm 2 4x10 13 neutron 50 µg 10 -6 g I = * * *** B atom barn cm2 g µg (II.A.15) 6.023x1023 atoms 1 mole 1g 10 -12 ml interactions * * * = 0.46 1 mole 10 g ml µm3µm 3 where the commonly accepted neutron fluence is 4 x 10 13 n/cm 2, the boron thermal neutron cross section is 3840 b/atom, the density of tissue is ~1 g/ml, and the boron concentration is taken to be 50 µg/g (= 50 ppm). Thus, there is actually few 10 B(n, α)7Li interactions in any given volume of boron concentration 50 ppm. The value of 50 ppm is an accepted value for the cellular boron concentration with the interstitial space and normal tissue having a concentration of 10 ppm. 114, 115, 117 The model herein uses ellipsoids arranged in a body centered cubic. So for example, consider a cell of radius 5.0 µm with a concentric nucleus of 4.0 µm in a body centered cubic structure (as are all geometries herein) so that the cells are touching (i.e. a separation of 0 µm). The sides of the region of interest are taken so that the entire cells lie within the boundaries of the region of interest. In that case, the sides for 5 x 5 x 5 cells in a body centered cubic are 55 µm x 55 µm x 38.28 µm for a total volume of 115,797 µm3 with a cellular volume of 4  (II.A.16) V=125π r 3  = 65,449.85 µm 3 . Total Cells 3  So that the total number of boron interactions will be: 0.46 (II.A.17) I =0.46() 65,450 +() 115,797 −= 65,450 34,738 interactio ns 5 39 Alpha particle stopping power for the 10 B(n, α)7Li reaction 300

250

200 m) µ

150

-dE/dx (keV/ 100

0 0.0001 0.001 0.01 0.1 1 10 100 Range ( µm)

Figure II.4 The alpha particle stopping power for the 10 B(n, α)7Li reaction showing the energy deposition per unit length as a function of the remaining range. The alpha track is seen to start near to the Bragg peak.

40 for the entire volume. Newer boron carriers 121 promise better tumor concentration of the order of 20:1 which would give for the same example a total of 125,060 interactions with the increase of 90,322 interactions all occurring in the tumor cells. The linear nature of number of interactions in tumor cells emphasizes the importance of developing more tumor specific boron carrier molecules.

B. Review of prior models of BNCT microdosimetry.

The microdosimetry of BNCT has been approached by two techniques. One approach is to construct a very structured regular three dimensional array of cells and the corresponding nuclei and distribute boron within that system. This approach can be best seen in the work of Hartman 233, 234 and Carlsson 235 who developed a cubic structure to model the cells with a spherical centered nucleus. The other approach to the problem has been to model a single cell with a very large interstitial volume. The best illustrations of this technique are by Charlton, 236-238 a group at Petten, 239-242 and a group at Harvard/MIT. 243-245 The reason for the two approaches noted above is the difficulty of following particle tracks in complex geometries. The single cell code allows for ellipsoidal cells and ellipsoidal nuclei. Therefore, if the cells (i.e. cytoplasm and nuclei) contain most of the boron, their arrangement in proximity to one another can influence the dose on each. Actual cells are stacked very close to one another with about 15% of the volume of a cube of brain tissue being interstitial fluid, the rest being intracellular. The nuclei tend to be eccentric and are spheroidal. The cells are not spheres or ellipsoids though for some cell types these are reasonable approximations. Tumors are often pallisading. Even in highly organized tissues such as those found in the kidney and the liver, the computer models are more organized than the tissues. These two approaches use Monte Carlo techniques to generate the tracks and interactions. The dose components that are calculated determine only the doses due to the boron (n, α) reaction and the nitrogen (n,p) reactions. These reactions account for ~70% of the total dose delivered to the tissues if the boron concentration in the tumor is 50 ppm. 91 Hartman and Carlsson noted that membrane-bound boron could add a non-negligible dose component to each cell. 235 They 41 also determined that boron needs to be present in the cytoplasm and nucleus of most every cell in order to have sufficient dose to kill the cells. Charlton 238 and Santa Cruz et. al. verified these findings. 7 They demonstrated that boron attached to the surface of the cells, as with boronated antibodies, would not likely deliver sufficient nuclear dose to kill the cell. Also, they showed that large interstitial boron concentrations would not provide nuclear dose sufficient to destroy the cell. These authors have independently shown that most of the boron has to be concentrated in the cell cytoplasm and/or nucleus.

C. Simulation implementation

1. The Cells program Cells is a program designed to arrange the ellipsoids that represent cells in a body centered cubic. The simulation programs (Cells, Dose, and Evaldose) were written in FORTRAN using the Fortran 95 Pro v5.7 compiler by Lahey Computer Systems, Inc. The program design is essentially linear where after the user inputs control parameters for the program, the code first uses well known relationships to determine the cell centers for the ellipsoids. The nuclei are then determined based upon the user input parameters. The results are then output for viewing and for input into Dose. The program can loop over cell radii by setting an initial radius, an increment, and the number of loops. The same thing can be done for the nuclear radius, the eccentricity, and the cell separation. The eccentricity is taken by the common usage in nuclear physics that keeps a constant volume as the eccentricity varies. 246 For an ellipsoid defined by the parametric equations:

(II.A.18) x= acosθ sin φ + x 0

(II.A.19) y= bsinθ sin φ + y 0

(II.A.20) z= ccos φ + z 0 where

2 2 2 2 2 2 2 (II.A.21) r=−()()() xx0 +− yy 0 +− zz 0 =++ abc . So that the eccentricity is related to the axes by

(II.A.22) a= b = r 1+ ε

42 and (II.A.23) c= r (1 + ε ) . Thus, the volume of the ellipsoid is given by

4π 4  2 4 π (II.A.24) V== abcπr  r()1 += ε r 3 ellipsoid 3 31+ ε  3 which clearly is independent of ε so that the volume of the ellipsoid remains constant for variable eccentricity. The nuclei can have the same ellipsoid shape as the cell or to remain a sphere that is closer to the in vivo situation. The nuclei can be constrained to be concentric with the cell center or it can be non-concentric. The non-concentric nucleus can be randomly determined for every cell for each loop or can be randomly determined for the first loop and same nuclear centers will be used for the remaining loops. The randomness can be in the displacement from the center and two angles defining a unique direction defined by the user. Alternatively, the displacement can be user defined and the displacement randomly determined. Finally, the user can define a direction and displacement for the nuclei. The program will not pick a nuclear center that will produce a nucleus that lies partly outside of the ellipsoidal cell but user defined nuclei are not checked. Dose cannot correctly handle cells with nuclei that lie partly outside of the cell and will produce error messages. A few spherical cells are shown in Figure II.5 showing the body centered cubic configuration for spheres showing the cell placement. This can be contrasted with cells of the same radius but with an eccentricity of 1.5 as defined in equations (II.A.22) and (II.A.23). The cells lie side by side as the eccentricity increases which is seen in muscle and neural tissues among others as seen in Figure II.6.

2. The Dose program The Dose program calculates the energy deposited into the interstitium, cytoplasm, and the nuclei. It should be pointed out that Dose outputs energy deposition rather than actual dose. The next program, Evaldose, converts from energy deposited to actual dose by a multiplicative constant and the tissue density. Dose requires the

Figure II.5 An example of a few cells with a radius of 5 µm, an eccentricity of 0, and a separation of 1.0 µm. The cell was determined by the program Cells.

Figure II.6 A few cells with a radius of 5 µm, an eccentricity of 1.5, and a separation of 1.0 µm whose positions were determined by Cells contrasting with spheres of the same radius.

44 ellipsoidal geometry output from Cells and certain user determined inputs. The user determines whether the particular case is a validation run which only increases the amount of information that is output. Other user input has to do with the method for maintaining charge, particle, energy, and momentum conservation. One method involves a particle that departs the region of interest is replaced by another particle of equal charge, momentum, energy, etc entering on the opposite side at the same position on that side. The other method involves picking a random side. Both give good validations but the first method was used exclusively in this work. The random position inside the region of interest can be designated as uniform throughout the volume or it can have a three dimensional Gaussian distribution with the peak centered in the geometric center of the region of interest. The second method roughly emulates a capillary as a source of BPA. The source in even a small space should be cylindrical so that this option was not used in the present work. The program then asks whether the dose due to the 14 N(n,p) 14 C is to be calculated. Next the user inputs the boron-10 concentration in parts per million for each of the three regions considered. The last user input determines how the number of interactions is to be determined. One option is to input the number of interactions in the total region of interest for each case. The alternate option is to use equation (II.A.15) to determine automatically the number of interactions in the region of interest. The first option is used for validation and statistical evaluations whereas all other cases allowed the program to determine the number of interactions. The program then loops through the number of interactions that has been set. The first part of each loop is to generate an (n, p) or (n, α) reaction based on the relative likelihood. Then three random numbers are generated to determine a point in the region of interest. After determining whether the point lies in the interstitium, cytoplasm, or a nucleus, a random number is generated to determine whether the point is to be accepted based on volume percent and boron concentration at the point. If the point is rejected, another point is generated and the process repeated until there is a valid interaction. By generating numbers in a unit cube rejecting all that lie outside of a unit sphere, random directions can be obtained to determine the direction of the first ion: a proton from the

45 (n,p) reaction and two pairs of ions from the (n, α) reaction with differing energies (if there is a γ-ray or not). The alpha and lithium ion pairs are separated by π radians. Thus, a track or tracks are determined. The track is then examined to see what boundary it crosses: the region of interest, the cell, or the nucleus. The track is then broken into a first piece. The same process is repeated until the entire ion track has been broken up. Once the track has been broken into pieces, each piece is integrated with a Gauss quadrature code using the actual stopping power curve for that portion. The actual stopping power curves are used rather than a linear stopping power in order to improve the accuracy of the results. The energy deposited into the interstitium, a particular cell cytoplasm, or a particular cell nucleus is summed with previous contributions. The process is repeated until all interactions have been calculated. As with all codes, the program was written in double precision to achieve the best results.

3. The Evaldose program The program Evaldose is a post-processing program that takes the output data from Dose summing and arranging it into a tabular form rather than as separate data sets. It also converts from energy deposition to the dose using the average density of tissue taken as 0.99 g/ml 3. It requires no user supplied input and performs no calculation except for summing. The first sums are to sum the doses for all cells, cytoplasm and nuclei independently, for a given geometry and boron distribution. Then the total dose to all of the cells is determined as well as the total dose to the region of interest, i.e. the total of all of the cells and the interstitium for the region of interest. The data set is then output to a file in a tabular form suitable for graphing.

4. Mathematica and SigmaPlot programs SigmaPlot 2000 for Windows version 6.00 is a program available from Systat Software, Inc., 1735 Technology Drive, Suite 430, San Jose, CA 95110. It is designed for plotting data and fitting that data to various functions (both linear and non-linear) as well as performs basic statistical evaluations. All of the data plots in chapter III were generated with SigmaPlot 2000 except for the plots of ellipsoidal cells. The ellipsoidal cells were drawn with Mathematica 6.0.3.0, Wolfram Research, Inc., 100 Trade Center 46 Drive, Champaign, IL 61820-7237. Mathematica is a powerful code designed for interactive mathematical programming to arbitrary accuracy. It also possesses advanced graphics capabilities that were used to produce the plots of the ellipsoidal cells. Neither of the codes was used for data generation or analysis with the exception of some statistical analysis of the dose results and some graphically displayed fitting to different functions.

D. Program validation

1. Validations Examining the centers, radii, and eccentricity of the cells and nuclei easily validates the output from the Cells program. Evaldose essentially sums the data from Dose so that it is validated by comparing the sums for small data sets to manually calculated sums for the same data sets. Cells and Evaldose are essentially validated by inspection. Validating a complex code such as Dose is much more involved. As the code was developed, portions of the code were tested independently to assure proper functioning. When the code was completed, several tests were devised to assure that the program functioned correctly. Dose tracks starting and ending track locations by two different particles that are output and are identical. The whole region of interest (ROI) is a rectangular parallelepiped that encompasses the ellipsoidal cells in their entirety. The requirements for validation are particle, energy, and momentum equilibrium. These requirements have been met to statistical accuracy as is demonstrated for the case: cells of radius 6.0 µm having concentric nuclei of radius 4.0 µm both with eccentricity of 0 and with the boron concentration of 50 ppm everywhere with both 10 B(n, α)7Li and 14 N(n,p) 14 C calculated. For this example, there are 13,077 boron interactions (6,539 originating in the interstitium, 4,601 in the cytoplasm, and 1,937 in the nuclei) and 3,082 nitrogen interactions for a total of 16,159 interactions in the volume. The number of particles leaving the ROI is 4,642 which is the same as the number entering so that:

(II.A.25) Ionsleaving= Ions entering .

47 The ions have a charge of 2 + for alphas and 3+ for lithium so that for charges, q, and from the result of (II.A.25) charge equilibrium is preserved when

(II.A.26) ∑qα+ ∑ qLi = ∑ q α + ∑ q Li in in out out which is always satisfied. The net momentum in the x, y, and z directions sum exactly to 0 for each of the components so that the momentum vector has the value of

(II.A.27) P= Pin + P out = 0 . The total energy entering the rectangular parallelepiped is 8.289 x 10 5 J and the total energy leaving the region is 8.289 x 10 5 J so that:

(II.A.28) E= Ein + E out = 0 . For this case, the energy deposited in each of the three volumes (the nulcei, cytoplsm, and interstitium) should have the same proportion to the total energy deposited as that volume represents of the entire volume. This is because the boron and nitrogen concentrations are the same everywhere. Likewise, the dose should be the same everywhere so that it provides another validation to the code. The data for this case are shown in Table II.3. The agreement is quite good. The program has met tests on components and has been validated. Most of the above information is compiled on every run so that there are checks on every run for the dose program. The programs written for the determination of the microdosimetry of BNCT have been validated.

2. Comparisons to the results of other authors Currently, the standard of comparison in the field of BNCT microdosimetry is the work of D. E. Charlton in 1991. 238 In this work, the dose to a single spherical cell is calculated for two cases. In both cases, the nitrogen dose was calculated for a concentration of 3.5 g/100g and the boron dose was calculated for a boron-10 concentration 5 µg/g. In the first case, the cell radius was 5 µm with a concentric nucleus of 2.5 µm while in the second case the cell radius was held constant and the concentric nucleus had a radius of 3.5 µm. The results are summarized in Table II.4 showing good agreement.

48 Table II.3 Energy deposition as a percent of the total energy deposited, dose, and percent volume of three volumes to the total. Energy Deposition Volume Dose (Gy) (% of total) (% of total) Interstitium 50.31 50.00 22.81 Cytoplasm 34.93 35.18 22.51 Nuclei 14.76 14.82 22.58

Table II.4 The nuclear dose from the work of Charlton and from the program Dose. Nuclear Size ( µµµm) Charlton dose (Gy) Dose (Gy) 2.5 3.51 3.46 3.5 3.55 3.56

49 III. Results and Discussion

A. Characteristics of the neutron beams for BNCT

Despite considerable effort to achieve an accelerator based neutron beam source, 247-256 accelerator derived epithermal neutron beams have yet to be able to deliver a sufficient flux of neutrons to perform BNCT in a reasonable time for a patient to be relatively motionless without sedation (on the order of a few tens of minutes). So to date all human and most animal studies have been performed with reactor based neutron sources. Since BNCT is dependent on the large absorption cross section of 10 B for thermal neutrons, i.e. neutrons with energies < 1 eV but with most being ~0.025 eV which is a mode of the Maxwell–Boltzmann distribution, it is necessary for the neutron energies to be in the thermal range at the depth of the tumor. Most tumors of interest do not occur on the surface of the body so that techniques have been developed during the early years of BNCT to deal with deep-seated tumors such as GBM. In Japan, Hatanaka 38 approached the problem by using a thermal beam from a power reactor and reflected (removed a piece of the skull and placed it back in place after the surgery) the skull for the irradiation. However, the Japanese have largely abandoned this approach in favor of using an epithermal neutron beam. 181, 257 In the United States, epithermal neutron beams were developed at the MIT reactor (MITR) and the Brookhaven Medical Research Reactor (BMRR) so that the neutrons would be sufficiently energetic to penetrate a few centimeters of tissues before slowing to thermal energies. Binns, Riley, and Harling 87 compared the characteristics of seven different neutron beans for BNCT reporting air epithermal neutron flux ranges 0.2 to 4.3 x 10 9 n cm -2 s-2. Figure III.1 contains a summary of the thermal neutron flux as a function of depth in an ellipsoidal water phantom using gold foil activation analysis. The peak occurs around 2-4 cm in depth for the beams studied with a fall off of 50% at approximately 6 cm. The thermal neutron flux maxima used in producing Figure III.1 are given in Table III.1 for the seven beams that were studied. 87 The distance traveled in matter by an epithermal neutron may be estimated if it is assumed that each

Figure III.1 Thermal neutron (~0.025 eV corresponds to a neutron velocity of ~2200 m s−1 ) flux obtained from the analysis of gold foil activation at seven different clinical NCT facilities in Europe and the U.S. Measurements were performed in an ellipsoidal water phantom under conditions pertinent to clinical irradiations. The results for each beam are normalized to the measured maximum shown in Table III.1 and have an estimated uncertainty of 4.4% at shallow depths increasing to 6.0% at 10 cm. 87

51 Table III.1 Measured maxima for thermal neutron flux as well as photon and fast- neutron absorbed dose rates at the seven different NCT facilities in the U.S. and Europe. 87 In-phantom Maxima MIT FCB a Studsvik b FiR-1 BMRR c ReZ HFR MIT M67 c 9 -2 -1 f2200 (10 n cm s ) 5.70 2.68 1.95 1.48 1.18 0.72 0.20 Photon dose rate 31.0 18.1 9.8 6.3 9.5 5.0 2.6 (cGy min -1) Fast-neutron dose rate 3.2 4.3 2.3 1.6 6.7 1.6 1.7 (cGy min -1) Note. These values are used to normalize the flux depth profile and depth-dose curves illustrated in Figs. 1-3. aFision converter operating at 83 kW. bBeam line configured with 9-mm-thick 6Li flter installed. cDecommissioned. interaction is an elastic scattering. For low energy n-p reactions, the scattering is largely elastic which allows evaluation by a classically derived relation: 1 (III.A.1) E= E ()1 − cos φ p2 n where φ is the center of mass scattering angle, E n is the energy of the incident neutron, E p is the energy of the recoil proton, and the mass of the proton and neutron are taken to be equal which is sufficient for the estimation here. This means that, on average for elastic scattering, the neutron losses ½ of its kinetic energy in each collision with the proton in a hydrogen atom so that: 1 (III.A.2) E= E . p2 n

So, for an initial neutron energy of E i that undergoes n collisions, the final average

energy, E f, is approximated by:

n (III.A.3) E1 = E i( 2) f or solving for n: E  (III.A.4) n= Ln−1 ( 1 ) Ln f  2 Ei 

So for a maximal epithermal neutron of initial energy E i = 10 keV being thermalized to a final energy of E f = 0.025 eV, n 10 keV = 18.6 or ~19 collisions. Compared to n 1 eV ∼5 52 collisions for neutrons with an initial energy of 1 eV. The mean free path of a neutron may be approximated from the elastic cross section, σi, and the number densities, N i, of the target constituents by:

  −1 (III.A.5) λ= ∑ Ni σ i  . i  Table III.2 contains a typical elemental abundance of light elements along with the corresponding number densities, elastic scattering cross sections, number density-elastic cross section products. Using equation (III.A.5), the thermal neutron mean free path is:

(III.A.6) λthermal = 0.46 cm Using the same calculations, Table III.3 contains the mean free path as a function of epithermal neutron energy. Using a typical value for the mean free path of 0.67 cm and 19 collisions, an epithermal neutron with an initial energy of 10 keV will travel 12.7 cm prior to reaching a thermal energy, while a neutron with an energy of 1 eV will travel ~3.4 cm until the neutrons are thermalized. The neutrons scatter in random directions; the total distance traveled is not a straight line. So most of the epithermal neutron flux has thermalized by a depth in a phantom of ~10 cm as inferred from Figure III.1. At typical tumor depths of a few centimeters, much of the neutron beam will be thermalized. Also, the multiple scattering reactions result in neutrons having momenta vectors with random directions especially on the scale of microdosimetry calculations (<~150 µm). The important implication for the microdosimetry of BNCT is that, except for superficial

Table III.2 Typical tissue elemental abundance, number density, and elastic scattering cross section. Element Percent Atomic Number σ (b) Nσ( cm -1) Abundance Weight Density (cm -3) H 0.11 1.008 6.51E+22 30.39 1.977084 C 0.51 12.010 2.53E+22 4.746 0.120158 N 0.02 14.010 8.51E+20 12.19 0.010372 O 0.36 16.000 1.34E+22 3.97 0.053320 Na 0.001 22.990 2.59E+19 3.92 0.000102 P 0.001 30.970 1.92E+19 4.37 0.000084 S 0.001 32.070 1.86E+19 1.52 0.000028 Cl 0.001 35.450 1.68E+19 65.32 0.001099

53 Table III.3 Mean free path, λλλ, for different epithermal neutron energies.

-1 Ei (eV) Nσ( cm ) λ( cm) 1 1.5131 0.66091 10 1.4939 0.66937 100 1.4919 0.67031 1000 1.4846 0.67356 10000 1.4277 0.70043 tumors, there is no preferred direction for the thermal neutrons making the probability of a 10 B(n,p) 7Li reaction dependent only upon the distribution of 10 B in the region of interest. The beams from the reactors are collimated and provide a relatively flat distribution of neutron energies. For example, the Washington State University reactor has a flat distribution curve within a factor of about 2 for the epithermal neutron energies from ~0.414 eV to ~10 keV and produces a measured epithermal neutron flux of 4.94 x 10 8 n/cm 2-sec while operating at 1 MW as shown in Figure III.2. This distribution allows for the most flexibility in treatment planning so that the lower energy neutrons are thermalized in the first 1-2 cm while the higher energy neutrons are not completely thermalized until ~10 cm into the phantom as shown in Figure III.1. The peak number of thermal neutrons, as shown in Figure III.1, occurs in the 2-4 cm range and slowly tails off which dictates that most of the tumor region should be within ~6 cm of the body surface. Large or deep tumors are not going to be as amenable to treatment due to a lack of thermal neutron flux without prolonged irradiation times and increased damage to surrounding normal tissues. Fast neutron contamination of the epithermal beam is a potential source of dose in the microscopic region of interest. One of the common components of the beam filters for BNCT is Al 2O3 that decreases the fast neutron flux while allowing epithermal neutrons. Using Equation (III.A.5) and cross sections for a reactor produced fast neutron of 1 MeV, the fast neutron mean free path is λfn = ~2.4 cm. Following the same reasoning as above, the fast neutron will travel ~60 cm before being thermalized

Figure III.2 The unfolded free beam neutron spectrum of the Washington State University reactor at 1 MW power in the source plane obtained by direct fitting. The spectrum demonstrates a relatively flat distribution of epithermal neutron energies within a factor of ~2. 263

55 after undergoing some 25 collisions and depositing the 1 MeV of energy. The reactor neutron beam filters are carefully designed to minimize the fast neutron flux that actually reaches the patient. For example, the reactors that were used in the US clinical trials had dose rates of 1.7 and 1.6 cGy sec -1 for the Brookhaven and MIT reactors respectively. 87 For typical treatment times of 45 minutes, the patient receives a total fast neutron dose of ~0.75 Gy. The new fission converter beam at MIT has a larger dose rate of 3.6 cGy sec -1 but the treatment time is only ~10 minutes so that the total neutron dose is 0.36 Gy which is about half of the above dose. Another way to examine the problem is from the fast neutron flux. The fast neutron flux from the Taiwan THOR reactor is 7.66 x 10 6 n/(cm 2 sec) while the fast neutron flux from the EU HFR reactor is 2.61 x 10 6 n/(cm 2 sec). As was done before, the dose may be approximated for this case by:

(III.A.7) Dfn= EI fn = EN fnφσ fn . So for a 1 MeV fast neutron, the dose may be written as:

−13 22H atoms  − 242 Dfn = φ ()1.062210 x J 6.51x103  () 4.24610 x cm (III.A.8) cm  = φ () 4.42910x−14 J / cm where the fluence, φ, is determined by multiplying the flux by the treatment time. Using a typical treatment time of 45 minutes and remembering that the density of the brain is ~0.99 mg/cm 3 = 0.99 kg/m 3, the fast neutron dose at THOR is 0.092 cGy and HFR is 0.031 cGy. Thus, fast neutrons are capable of contributing a significant dose via recoil protons but the small fluxes prevent them from playing an important role.

B. Contributions to the microscopic dose

The radiation milieu in BNCT is complicated by neutron interactions in tissue and from radiation from the reactor ‘contaminating’ the neutron beam. 80, 239, 258-262 The beams have different filters to produce a neutron beam with a relatively flat energy distribution in the epithermal range as discussed above in section A. The characteristics of the radiation is dependent upon the particular beam which is a function of the reactor and filters. 87 Most beams have some γ-ray contamination but the intensity and energy 56 spectrum is dependent on the details of the particular reactor and beam. These contaminants to the epithermal beam will not be considered because it is installation dependent. The major sources of the radiation dose from the neutron interactions with tissue do need to be considered. The most important are the reaction products from the 10 B reaction, i.e. the alpha particles, the lithium nuclei, and the γ-ray. Additional components in the radiation milieu are the proton produced in the nitrogen (n,p) reaction. Recoil protons produced when neutrons elastically scatter from hydrogen atoms attached to organic molecules will also be considered. Also, hydrogen has a non-negligible cross section for neutron capture that results in deuterium and a γ-ray. Since hydrogen is in all organic molecules, this contribution to the dose will also be considered. The cross sections for other reactions or the number density are so small that other reactions will not be considered. 58, 262, 264, 265

1. The contribution from the 10 B(n, ααα)7Li and 10 B(n, α γα γ )7Li reactions to the dose The major dose components in BNCT derive from the 10 B reaction itself so a discussion of the radiation components making up the total dose will begin with the BNCT reaction. As discussed in chapter II, the characteristics of energy deposition in the region of interest determine the microscopic dose. BNCT has many potential sources of energy deposition and so the dose calculation for the macroscopic dose is complex. Barth, Soloway, et. al. report that if the tumor boron concentration is 20-40 micrograms per gram (10 9 10 B atoms/cell) then 75-80% of the radiation dose arises from the 10 B(n, α)7Li and 10 B(n, α γ )7Li reactions. 90 Along with the proton dose are other reactions such as the recoil reaction of the proton in hydrogen from the incident neutrons and the γ- ray from the 10 B reaction, which provide the remainder of the dose from reactions other than the 10 B reaction. The dose from the γ-ray produced in the 10 B(n, α γ )7Li reaction will be considered in section III.B.3. Some of the components, which are important in calculating the macroscopic dose, are of a lesser significance to the understanding of the microscopic dose due to magnitude and lack of significant spatial variation on a

57 microscopic basis. To understand the microdosimetry of BNCT, it is instructive to begin with the ions produced in the BNCT reactions:

110 11*93.7% 7 4 (III.A.9) 055n+ B→ B → 32 Li+ He+ γ(0.48 MeV)+2.31 MeV and

110 11*6.3% 7 4 (III.A.10) 05n+ B→ 5 B → 32 Li+ He+2.79 MeV . The heavy ions produced are charged to the 2+ state for the alpha particle and 3+ state for the lithium nucleus. These highly charged ions have relatively short ranges in matter. The high charge states interact with the electron clouds and the nuclei by Coulomb interactions quickly slowing down and depositing all the energy from the disintegration 11 -12 266 of the metastable B that decays immediately (t 1/2 ~10 s). The short ranges of the ions from BNCT are shown in Table II.2 that was generated by the SRIM2008 code discussed in chapter II. The short ranges are beneficial because the ions travel on the order of a cell diameter (which varies depending on the cell type but generally is about 10 µm) depositing their entire energy. Thus, a cell may have the entire energy from the 10 B(n, α)7Li reaction (an average of 2.34 MeV) deposited within the cell. The Coulomb interactions with the molecules along the path of the ions results in the production of short lived free radicals which then significantly damage nearby molecules as discussed chapter II.A.1. Any ion paths through the cell’s nucleus can result in major damage to the DNA from two mechanisms. The first is from direct damage by the heavy charged ions resulting in double strand DNA breaks which the cell is less able to repair than single strand breaks. The second mechanism is from free radical formation, which also damages the DNA. Traditional photon beam radiation damages cells by free radical formation so that the combination of the two is often lethal to the cell. Thus, the effectiveness of BNCT is dependent upon the local boron concentration 91 as will be shown. Nearby normal cells or tumor cells in the G0 (resting) phase will not accumulate the boronated carrier molecule as avidly as tumor cells and will receive a smaller radiation dose than the active tumor cells where the boronated carrier molecule concentrates. The 10 B(n, α)7Li and 10 B(n, α γ )7Li reactions are generally considered to responsible for about 80% of the total macroscopic dose with most of the variability due to the variation in boron concentration. 91 58

2. The contribution of the 14 N(n,p) 14 C dose Nitrogen is a common element in all human tissues and the 14 N(n,p) 14 C reaction can produce a significant dose in BNCT. The nitrogen capture reaction may be summarized by:

1 14 14 1 (III.A.11) 0n + 7 N→ 6 C + 1 H + 0.59 MeV , which occurs in all tissues. The proton deposits 0.59 MeV in a range of ~10.5 µm in human tissue as determined by SRIM2008. The distribution of nitrogen is not entirely homogeneous for different cell types with the concentration being higher in protein rich as opposed to lipid laden tissues but the heterogeneity is small except for adipose tissue. Even adipose cells have typical cellular architecture with proteins, RNA, DNA and other nitrogen rich molecules. The in vivo heterogeneity is not significant for most tissues and in particular for tumors that rarely have lipid laden cells (except for the rare liposarcoma). There are no studies describing the nitrogen distribution on a cellular or sub-cellular level and nitrogen is ubiquitous in all tissues so that it is not unreasonable to model the nitrogen distribution as homogeneous. If the nitrogen distribution is homogeneous, the contribution to the total dose would be expected to be small and additive. This may be

shown by plotting the dose for spherical cells of radii r c = 4.0 µm with nuclei of radii r n = 3.0 µm that are plotted as a function of the edge to edge separation of the cells in a body centered cubic. The 10 B concentrations being 10 ppm, 50 ppm, and 50 ppm in the interstitium, cytoplasm, and nuclei respectively, which is consistent with experimentally determined values. 114, 115, 126 Figure III.3 contains the doses from the 14 N(n,p) 14 C contribution whereas Figure III.4 depicts doses without the proton dose. The three curves represent the dose to the nuclei, cytoplasm, and interstitium. As the separation between the cells increases, the dose to the nuclei and cytoplasm decreases since there is less dose from neighboring cells due to the short range. Likewise, the volume of the interstitium receiving a dose from a cellular source remains nearly constant (when cells are close together, some of the ion tracks will go from one cell to another but

59 Dose versus separation with the 14 N(n,p) 14 C dose incuded 20

10 Dose(Gy)

5 Interstitium Cytoplasm Nuclei

0 0 5 10 15 20

Cell edge to edge separation ( µm)

Figure III.3 Dose versus cell edge to edge separation for spherical cells of radius r c = 4.0 µm, nuclei of radius r n = 3.0 µm, and eccentricity of ε = 0 for boron concentraions of 10 ppm in the interstitium, 50 ppm in the cytoplasm, and 50 ppm in the nuclei. Dose includes contributions from the boron (n, α) and nitrogen (n,p) reactions.

60 Dose versus separation with 14 N(n,p) 14 C dose not included 20

10 Dose (Gy) Dose

Interstitium Cytoplasm Nuclei 0 0 5 10 15 20

Cell edge to edge separation ( µm)

Figure III.4 Dose versus cell edge to edge separation for spherical cells of radius r c = 4.0 µm, nuclei of radius r n = 3.0 µm, and eccentricity of ε = 0 for boron concentrations of 10 ppm in the interstitium, 50 ppm in the cytoplasm, and 50 ppm in the nuclei. The dose includes contributions only from the boron (n, α) reaction.

61 the effect falls off rapidly as seen by the nuclear dose). As the cellular separation increases, the percentage of the interstitial volume receiving a dose originating inside of a cell decreases. These effects and the implications for the efficacy of treatment will be discussed further in subsequent sections. Since the destruction of the nucleus is generally considered the goal of radiation therapy, Figure III.5 contains the nuclear dose as a function of cell edge to edge separation for both cases, i.e. with and without the dose from the 14 N(n,p) 14 C reaction. The nuclear dose curves are seen to be the same shape with a mean difference of 1.68 Gy with good correlation between the two curves. The proton dose is seen to be ~12% 10 7 higher in the asymptotic tail ( ≥ 10 µm separation) than the dose from the B(n, α) Li reaction alone. Since, in the current models, the nitrogen distribution is homogeneous, the 14 N(n,p) 14 C reaction will produce a constant additive dose of ~2 Gy. Other authors in the field of BNCT microdosimetry either omit the dose from the 14 N(n,p) 14 C reaction or model it as a homogeneous distribution. In order to understand spatial variability, the dose from the 14 N(n,p) 14 C reaction will generally be omitted unless otherwise stated.

3. Gamma ray dose from the 10 B(n, α γα γ )7Li reaction In 93.7% of the 10 B interactions, a γ-ray is produced as is shown in equation (III.A.9). This 480 keV γ-ray is penetrating which means that only a portion of the γ-ray energy will be deposited into the tissue with much of the energy being deposited outside of the body. Nonetheless, it is an important dose component to be considered. For the 10 B(n, α)7Li and 10 B(n, α γ )7Li reactions in equations (III.A.9) and (III.A.10), the thermal neutron cross section is: (III.A.12) σ = 3837 b . The accepted 10 B concentration in the cytoplasm and the nuclei is ~50 ppm while the interstitial concentration is ~10 ppm. 114, 115, 126 The interstitium occupies ~15% of the volume for the brain with cells and cytoplasm occupying the remaining volume 56, 267 so the number density may be determined starting with the relative tissue composition:

(III.A.13) N = 0.85 50 ppm + 0.15 10 ppm = 44 ppm = 44 mg ()() kg

Nuclear dose versus separation 20

10 Dose (Gy) Dose

5 (n,p) dose not calculated (n,p) dose calculated

0 0 5 10 15 20 Cell edge to edge separation ( µm)

Figure III.5 Nuclear dose versus cell edge to edge separation for spherical cells of radius r c = 4.0 µm with nuclei of r n = 3.0 µm and eccentricity of ε = 0 for boron concentraions of 10 ppm in the interstitium, 50 ppm in the cytoplasm, and 50 ppm in the nuclei. The dose includes contributions from the boron (n, α) and nitrogen (n,p) reactions for the upper curve and only from the boron (n, α) reaction for the lower curve.

63 or 44 mg10 B 1 g  1 mole   6.0221367x1023 atoms  N =      1 kg 1000 mg  10.0129 g10 B   1 mole  (III.A.14) . atoms = 2.65x10 21 kg The γ-ray energy from the 11 B metastable nuclear decay is:

-14 (III.A.15) Eγ = 0.48 MeV/interactions =7.69x10 J/inter actions . The total number of interactions is given by: (III.A.16) IN= φσ where the fluence, φ, for BNCT is a typically: 87, 97 neutrons (III.A.17) φ = 4 x10 12 cm 2 so that that the total number of interactions given by Equation (III.A.16) is (III.A.18)

12 21 atoms 410neutronsx  −242 13 interactions I= 2.6510x2  () 383710 x cm= 4.09310 x . kg cm  kg

Now consider an infinite medium, so that all of the γ-ray energy will be deposited in the medium. Then the total dose will be given by J (III.A.19) D= E I = 2.89 = 3.15 Gy . γ γ kg The mass energy-absorption coefficient 0.48 MeV γ-ray in human brain tissue may be determined from the Tables of X-Ray Mass Attenuation Coefficients and Mass Energy- Absorption Coefficients at the National Institute of Standards and Technology (NIST) online site and it is:

2 µ −2 cm (III.A.20) en = 3.276x 10 . ρ g This may be applied to human brain tissue that is largely water and has a density, ρ: g (III.A.21) ρ = 0.99 . cm 3

By combining (III.A.20) and (III.A.21) energy-absorption coefficient, µen , is:

64 -1 (III.A.22) µen = 0.032 cm . Considering the mean chord length in a convex volume can approximate a mean distance likely to be traversed by the γ-ray. The Cauchy relation for the mean chord length in a convex volume provides such an approximtion: 268, 269 V (III.A.23) l =4 ∗ A where V is the volume of the object and A is the area. So for a sphere of radius r, the mean chord length is: 4r (III.A.24) l = . 3 In the present case of microdosimetry, the region of interest is small cubes of side approximately 150 µm corresponding to a volume of 3.375 x 10 6 µm3 = 3.375 x 10 -6 cm 3. The cube can be approximated by a sphere of the same volume which would then have a radius, r = 9.3 x 10 -3 cm. The mean chord length is then 4*9.3x 10−3 cm (III.A.25) l = = 0.0124 cm . 3 The dose to the sphere may then be given by:

µ l  −en   2  −4 (III.A.26) DDe=γ 1 −  = 6.2410Gy x .   Extrapolation to the whole brain is difficult because less is known about the distribution of boron for the entire brain. A typical glioblastoma may easily be 2-4 cm in diameter (some may be quite large but would not be a candidate for any present clinical trials) so consider a 4 cm diameter tumor that would have a volume of 33.51 cm 3 with a boron concentration of 44 ppm [see equation (III.A.13) above]. The remainder of a typical 1400 cc brain 270 would have a concentration of ~10 ppm. Let us first consider an infinite medium of uniform distribution defined by:

33.51  1400-33.51  mg (III.A.27) N = 44 ppm + 10 ppm   = 10.81 ppm = 10.81 . 1400  1400  kg So for an infinite medium:

(III.A.28) I= Nφσ = 9.2410x 12 interactions kg 65 using the construction of equation (III.A.19) the total γ ray dose is:

(III.A.29) D =0.768J = 0.768 Gy . γ kg The volume of a typical human brain is on the order of 1400 cc 270 so approximating the brain by a sphere of volume V = 1400 cc, then the radius is r = 6.94 cm. So that the mean chord length is: (III.A.30) l = 9.253 cm giving a tumor dose of

µ l  −en   2  (III.A.31) D= Dγ 1 − e  = 0.106 Gy .   Equations (III.A.26) and (III.A.31) show that, on the microdosimetric or macrodosimetric scale, the γ-ray from the 10 B(n, α γ )7Li reaction adds a small dose as compared to the doses on the order of 10-15 Gy for the microdosmetric region and will be ignored in the present work.

4. Dose due to recoil protons As was discussed in III.B.1, most of the neutrons are thermalized at the depth of the tumor that is usually a few centimeters into the brain. Protons are bound as hydrogen atoms in organic molecules, most commonly to carbon and oxygen. The bond energies may be found in many standard chemistry texts and have values of:

(III.A.32) E =413J = 4.28 eV H− C mole and

(III.A.33) E =498J = 5.16 eV . H− O mole Low energy n-p reactions will largely demonstrate elastic scattering which has a rather flat cross section of ~20 b versus incident neutron energy over the entire range under consideration as shown in Figure III.6. As previously shown for elastic scattering reactions in a low energy range in

equation (III.A.2), for energy ranges from 0 ≤Ep ≤ E n , the average energy of the free

66 Elastic Proton Scattering Cross Sections 10000

1000

100

10 Cross Section (barns)

0.1 1e-9 1e-8 1e-7 1e-6 1e-5 1e-4 1e-3 1e-2 1e-1 1e+0 1e+1 1e+2 1e+3 1e+4 1e+5 Incident Neutron Energy (MeV)

Figure III.6 Elastic scattering cross sections for protons as a function of incident neutron energy displaying a relatively flat distribution in for the incident neutron energies used in BNCT obtained from ENDF data set at the National Nuclear Data Center.

67 recoil proton is half that of the incident neutron. The binding energy of the hydrogen to its parent organic molecule decreases the recoil proton kinetic energy in the following manner: 1 (III.A.34) E' = EE − = EE − p pB2 nB

where E′p is the net recoil proton energy and EB is the binding energy which for this discussion is either equation (III.A.32) or (III.A.33). Equation (III.A.34) defines a minimum average energy that the neutron must possess in order to break the bond and leave the proton with energy E′p = 0 so that the neutron must possess:

(III.A.35) En≥ 2 E B in order to break free from the molecule. Thus, the neutrons must have more than ~10 eV of energy to generate recoil protons. Thermal neutrons with energies on the order of 0.025 eV will not have sufficient kinetic energy to break the common hydrogen bonds. Neutrons that have not yet been thermalized can potentially break the chemical bonds as long as equation (III.A.35) is satisfied. So, for the H-C bond, the neutron will have more than 8.56 eV of kinetic energy while the energy required to break a H-O bond with elastic scattering would have to be greater than 10.32 eV. If the neutron kinetic energy is equal to the bond energy, the bond will be broken but the particle will have no kinetic energy to dissipate and so provides no dose. Also, it is important to remember that especially low energy neutrons, i.e. those with a few eV of kinetic energy, may excite vibrational modes in the molecule to which the hydrogen is bound so that not every interaction of sufficient energy will produce a recoil proton. The exceedingly large number of different molecular species found in humans with complex vibrational excitation patterns makes the estimation of this mode of energy dissipation beyond the scope of this work. The dose, D, may be determined similarly as was shown in equations (III.A.16), (III.A.17), and (III.A.19) above. For the H-C bonds, the results are summarized in Table III.4 where the fluence has been taken as 4 x 10 12 n/cm 2. The neutron energy distribution as a function of depth can only be measured in phantoms or in animals so that the actual fluence is not well known so that these doses can be viewed as the upper limits of the potential dose. Thus, the recoil protons constitute a small 68 Table III.4 Elastic proton scattering as a function of incident neutron energy.

Neutron E´ p (eV) Elastic Cross D (Gy) Energy (eV) Section (b) 10 0.72 20.16 5.56 x 10 -4 100 45.72 20.15 0.035 1,000 495.72 20.05 0.38 10,000 4995.72 19.20 3.67

additive dose to the total dose with the dose distribution being homogeneous due to the ubiquitous presence of hydrogen in organic molecules. Finally, it is important to determine the range of the recoil protons so that the implications for microdosimetry may be better understood. Using the program SRIM that is commonly used for targetry, ion deposition, and in the BNCT community to calculate the range, the proton ranges are listed in Table III.5. The dose from recoil protons is deposited in the immediate region of the hydrogen, i.e. in the cell in which the interaction occurs. Thus, the dose from recoil protons is a small contribution to the microdosimetry in BNCT that has no understood spatial variability. For the present study, the dose due to the recoil protons will not be included.

5. Dose from the 1H(n, γγγ)2H reaction The cross section for thermal neutron capture by hydrogen is not small and hydrogen is found in abundance in all organic molecules. The treatment of the γ-ray produced will be handled in a similar manner, as was the γ-ray from the BNCT reaction. In addition to elastic and inelastic scattering events, some of the thermal neutrons will be captured by the hydrogen nucleus which will emit a 2.22 MeV γ-ray in the following reaction:

1 2 (III.A.36) n+1 H → 1 H + γ (2.22 MeV) . The cross section for thermal neutron capture by a hydrogen nucleus may be found online at the National Nuclear Data Center and is: (III.A.37) σ = 0.33 2 b . where the γ-ray energy from the capture of the neutron by the proton is:

69 Table III.5 Recoil proton range for various epithermal neutron energies with totally elastic scattering and average energy transfer. Incident Proton Proton Proton Neutron Energy Range Range Energy (eV) (eV) (Å) (µm) 10000 5000 1314 0.1314 1000 500 166 0.0166 100 50 22 0.0022 10 5 4 0.0004

−13 (III.A.38) Eγ = 2.2 MeV/interactions = 3.56 x 10 J/interac tions . The concentration of 1H in human tissue is ~10% by weight so using the same calculations as in prior subsections the number density is:

1 (III.A.39) N= 5.97x 10 25 H atoms . kg tissue The total number of interactions is given by Equation (III.A.16) and for this case becomes:

(III.A.40) I= 7.93x 10 13 interactions . kg As was done previously, consider an infinite medium so that all of the γ-ray energy will be deposited in the medium so by using the form of (III.A.19) the γ− ray dose is:

(III.A.41) D =28.22J = 28.22 Gy γ kg The mass energy-absorption coefficient for a 2.0 MeV γ-ray in human brain tissue may be determined from the Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients at the (NIST) online site:

µ −2 2 (III.A.42) en = 2.595x 10 cm ρ g where the density for human brain tissue is given in Equation (III.A.21) so that

-1 (III.A.43) µen = 0.026 cm . As before, for a typical human brain volume of 1400 cc the brain can be approximated by a sphere of volume of radius r = 6.94 cm. so that the mean chord length is: (III.A.44) l = 9.25 cm .

70 The dose to the whole brain is then

µ l  −en   2  (III.A.45) DDe=−γ1  = 0.11 D γ = 3.16 Gy   In the case of microdosimetry, the region of interest is much smaller. In the present case the larger regions of interest are approximately cubes of side ~150 µm corresponding to a volume of 3.375 x 10 6 µm3 which could be approximated by a sphere of the same volume with a radius of r = 9.3 x 10 -3 cm. Then the mean chord length becomes (III.A.46) l = 0.0124 cm which results in a dose to the region of interest of (III.A.47) D= 4.94 x 10−3 Gy . On the macrodosimetric scale, with doses to the normal brain dose of 2-3 Gy and tumor dose of 30-61 Gy, 95 or on the microscopic scale of 10-15 Gy, presented herein, the dose from the 1H(n, γ)2H reaction adds a small component to the total dose. The dose from the radiative capture reaction will thus not be included in the present study.

6. Summary of the components to the radiation milieu Several authors have reported that the 10 B(n, α)7Li reactions account for approximately 86% of the total dose. 7, 271 The present work can then be compared to these earlier works providing further evaluation of the code. In order to compare the results, a case was run with cells of radius 5.0 µm, nuclear radius 4.0 µm, eccentricity of ε = 0, and a separation of 0.0 µm. The dose from recoil protons is dependent upon the details of the neutron beam. Figure III.2 showed that a typical neutron beam has a rather flat neutron energy distribution in the requisite energy range. Furthermore, the elastic cross sections as a function of incident neutron energy is also flat in the epithermal energy range as was shown in Figure III.6. So the elastic proton doses can be averaged as an approximation of the actual dose. The results are presented in Table III.6. The agreement is quite good especially since there are no contributions from neutron beam contaminants as discussed above.

71 Table III.6 Dose contribution from different radiation components. Radiation Component Dose (Gy) Percent of Total (%) 10 B(n, α)7Li 43.12 89.8 14 N(n,p) 14 C 3.79 7.9 γ from 10 B(n, α)7Li 0.099 0.21 1H(n, γ) 2Η 0.0049 0.01 Elastic recoil protons 1.02 2.12 Totals 48.04 100.0

C. How the boron distribution affects the dose

As the boron concentration increases in a region, the number of boron interactions will increase proportionately. Since the dose is localized, the result should be scaled in a linear manner. Figure III.7 shows a typical case for spherical cells of radius rc = 5.0 µm

with spherical concentric nuclei of radius rn = 4.0 µm where the dose in seen to be higher when the cells are closer which will be dealt with in more detail later. In the asymptotic region where the cells are too far apart to affect each other, the nuclei and cytoplasm receive a larger dose than dose the interstitium where the concentration is a fifth that of the cells. In order to better understand the role of the boron concentration, the dose may be broken into components. The components may be calculated by setting the boron concentration to zero in two of the three regions with the remaining region having the concentration as depicted in Figure III.7. Examining the nuclear dose only in Figure III.8 it is seen that the sum of the three component curves produces the independently calculated upper curve from Figure III.7 demonstrating the linearity of the dose in a given region as a function of the boron concentration. Of note is the small increase noted in the first portion of the nuclear dose when all of the boron is in the interstitium. The increase is due to the empty (of boron) cells being next to each other being replaced by boron

Dose as a function of separation 20

Dose (Gy) 8

4 Interstitium Cytoplasm 2 Nuclei 0 0 5 10 15 20 Cell Edge to Edge Separation ( µm)

Figure III.7 The dose for the three regions of interest for typical cell sizes of radius rc = 5.0 µm with spherical concentric nuclei of radius rn = 4.0 µm and boron concentrations that have been experimentally determined as 50 ppm in the cells and 10 ppm in the interstitium.

73 Nuclear dose for different boron concentrations

20 N: 50, C: 50, I: 10 N: 50, C: 0, I: 0 N: 0, C: 50, I: 0 N: 0, C: 0, I: 10

10 Dose(Gy)

0 0 5 10 15 20 Cell Edge to Edge Separation ( µm)

Figure III.8 The nuclear dose only for typical cell sizes of radius rc = 5.0 µm with spherical concentric nuclei of radius rn = 4.0 µm and boron concentrations that have been experimentally determined. The three lower curves are the produced by allowing only one of the three regions of interest to have boron with the remaining two regions to have a boron concentration of zero. The sum of the lower three curves is seen to produce the independently calculated upper curve.

74 containing interstitial space as the cells separate. A similar effect is seen in Figure III.9 where only the dose to the interstitium is shown. The three lower curves are once again seen to sum to the independently calculated upper curve. The interstitial dose when all the boron is concentrated in the interstitial space is of interest since it is seen to increase with separation. This is because when the cells are close together a larger proportion of the ions will deposit energy into a cell than into the interstitium. As the cells separate, a larger proportion of the ions will have their entire track in the interstitium. Also of interest are cases where the ratio of cellular boron to interstitial fluid and normal cells is higher than has been currently seen with BPA as the boron carrier molecule. Early animal experiments have produced ratios of 10-20:1 which would mean 100-200 ppm in the cells with 10 ppm in the interstitial fluid and normal cells. 121 The effect of these ratios is seen in Figure III.10 where the corresponding nuclear and interstitial curves are seen to be twice the dose at 200 ppm in the cells compared to 100 ppm. The cellular doses are seen to be enormous and the scaling is again seen to be linear. These potentially obtainable doses are truly remarkable when it is remembered that the lethal free air whole body dose required for a 95% lethality is ~7 Gy. The most important aspect of Figure III.10 is that the nuclear dose is >50 Gy even for widely separated cells for the 200:1 cell to interstitium boron concentrations. So that active (in the sense of avidly accumulating the boron carrier molecule) tumor cells will be destroyed with doses as high as 65 Gy for nuclei in the body of the tumor. At the same time, the surrounding tissue will receive < 5 Gy which is a reasonable dose. The normal tissue will be preserved with much more effective killing of tumor cells even if widely separated. Thus, as new boron carrier molecules are produced that increase the tumor to normal tissue ratio, the effectiveness of the modality will likewise increase.

D. The effects of cell geometry on the dose

The hypothesis of this dissertation is that cells closely packed together will provide a significant dose to neighboring cells as well as to the interstitial space which in the present model contains normal cells and cells in the G 0 (resting) phase. The model

Interstitial dose for different boron concentrations 12

10 N: 50, C: 50, I: 10 N: 50, C: 0, I: 0 N: 0, C: 50, I: 0 N: 0, C: 0, I: 10 8

6 Dose (Gy)

0 0 5 10 15 20 Cell edge to edge separation ( µm)

Figure III.9 The interstitial dose only for typical cell sizes of radius rc = 5.0 µm with spherical concentric nuclei of radius rn = 4.0 µm and boron concentrations that have been experimentally determined. The three lower curves were produced by allowing only one of the three regions of interest to have boron with the remaining two regions to have a boron concentration of zero. The sum of the lower three curves is seen to produce the independently calculated upper curve.

76 Nuclear and interstitial doses for different boron concentrations 70

50 Interstitial dose for 100 ppm boron 40 Nuclear dose for 100 ppm boron Interstitial dose for 200 ppm boron Nuclear dose for 200 ppm boron 30 Dose (Gy)

0 0 5 10 15 20 Cell Edge to Edge Separation ( µm)

Figure III.10 The dose for the three regions of interest for typical cell sizes of radius rc = 5.0 µm with spherical concentric nuclei of radius rn = 4.0 µm and boron concentrations that are potentially achievable with new boron carrier molecules of 200 ppm in the cells and 100 ppm in the cells with 10 ppm in the interstitium in both cases.

77 permits dose variance estimations to both the cells and the interstitium as the cells are separated. Observing the separation of the tumor cells corresponds to examining the edge of tumors. The cells will gradually thin out until they are more widely separated. This situation is especially true for infiltrative tumors such as GBM but less so for other tumors such as melanoma which tends to be more circumscribed with few cells separated from the main tumor body. In order to understand the actual in vivo microdosimetry, boron concentrations will be set as 10 ppm in the interstitium, 50 ppm in the cytoplasm, and 50 ppm in the nuclei, which is similar to the determinations of boron concentrations in actual patients as determined by Coderre, et. al., 115, 272 unless otherwise specified. The size and shape of normal cells is quite variable with cells varying from small (on the order of 3-4 µm in radius) to those up to radii of over 10 µm. Likewise, nuclei can vary from a radius of 1-2 µm up to 8-10 µm for some types of tumor cells. Cell shapes are also quite variable. Some are small, almost cuboidal, as in the Kupffer cells in the liver, others are spherical (especially in white blood cells such as lymphocytes and monocytes), and some are elongated such as myocytes (muscle cells) and neurons. 273-275 Spinal neurons may be more than a meter in length extending from the cell body in the upper lumbar spine to the foot. Tumor cells typically display more variability in size and shape than the tissues from which they arise especially in regards to the nuclei which are often larger and more eccentric in shapes. 10, 276, 277 Furthermore, new studies are demonstrating that living cells are constantly changing shape responding to the local biochemical and physical milieu. The programs written for this dissertation are designed for ellipsoidal tumor cells. But by simply changing the underlying geometry, the microdosimetry of different tumors may be modeled. For example, closely packed spherical cells simulate melanoma whereas a very eccentric geometry with spherical nuclei far from the cell center better approximates neurons. Glioblastoma multiforme cells are somewhere in between these two geometries. So to understand the microdosimetry of BNCT, several cases will be considered. Figure III.7 shows the effect of separating cells that initially are just touching and gradually move apart. The figure shows a 16% increase from the asymptotic ‘tail’ to the peak when the cells are just touching. This means that the nucleus of each cell receives an

78 additional dose from neighboring cells which could be viewed as a near neighbor effect. Also, significant is the ratio of 2.46 of the maximum of the interstitial dose when the cells are just touching to the dose in the asymptotic tail of the interstitial dose. The then interstitium receives a significantly larger dose from neighboring cells. As the cell radius increases, the effect on the nuclei diminishes if the nuclear radius does not increase in a like manner. This decrease in effect can be seen in Figure III.11 for spherical cells of radius 8.0 µm and a nuclear radius of 4.0 µm. The dose to the nuclei is essentially flat whereas the dose to the interstitium shows the earlier noted effect. The explanation has to with the short range of the ions. The maximum range of the alpha particle from the 10 B(n, α)7Li and 10 B(n, α γ )7Li reactions (refer back to Table II.2) is 9.06 µm (6.3% of the time) and 7.39 µm (93.7% of the time) for a mean range of ~7.5 µm. Similarly, the mean range of the lithium nucleus is ~4 µm. When the cell radius is 8.0 µm and the nuclear radius is 4.0 µm, a boron disintegration must be near to the cell edge along a line of centers for the ions to reach the nearest neighbor nucleus. When the cell edges are 1 µm apart, essentially no lithium ions reach the nearest neighbor nucleus and when the edges are 5 µm apart there is no contribution from the alpha particles. Also, the particles are losing energy along the track as defined by the stopping powers defined in chapter III so that the tail of the particle tracks deposits little energy into the neighboring nucleus. Figure III.11 contains a summary of the dose as a function of separation for cells when the cell radius is 8.0 µm and the nuclear radius is 4.0 µm. The decrease in the nuclear dose is clearly demonstrated in Figure III.11 where there is a small decrease in the dose over the first 2-3 µm. Thus, the geometry of the cells has an impact upon the nuclear doses. The interstitial dose is affected in a similar manner, with the magnitude of the effect (peak dose/asymptotic dose) is lower than that presented in Figure III.7. The ratio of peak dose/asymptotic dose for the smaller cells (Figure III.7) is ~2.3 versus the larger cells where it is ~1.9 (Figure III.11). This effect can be understood by first examining the packing fraction of a region defined for this case as the total volume inside the cells (ellipsoids) divided by the total volume of the region of interest. So consider a cube that encloses eight spheres of radius r so that the cube has side l = 2*(2r) = 4r and the volume of the cube is: 79 Effects of separation on large spherical cells

Interstitum

Dose (Gy) 10 Cytoplasm Nuclei

0 0 5 10 15 20 Cell edge to edge separation ( µm)

Figure III.11 Dose as a function of cell edge to edge separation for large spherical cells of radius r c = 8 µm with nuclei of r n = 4 µm for boron concentration of 10 ppm in the interstitium, 50 ppm in the cytoplasm, and 50 ppm in the nuclei demonstrating the increase in dose to neighboring cells and interstitium (at small separations). The effect is less than that observed with smaller cells.

80 (III.A.48) Vl=3 =(4) r 3 = 64 r 3 . c The total volume enclosed by the spheres is eight times the volume of one of the spheres or: 4  (III.A.49) V= 8π r 3  . s 3 

The packing fraction, P f, is then given by: 4  8π r3  Vs 3  π (III.A.50) Pf ==3 == 0.524 Vc 64 r 6 which is a constant so that the variation seen is not due to the packing fraction for a given separation. Now consider the surface to volume ratio of a sphere that is: (4π r 2 ) 3 (III.A.51) RSV = = . 4 3  r π r  3  Figure III.12 contains a summary of the average dose to the interstitium over 50 cases at 4 cell radii (5 µm, 8 µm, 11 µm, and 14 µm) for a separation of 0.0 µm fit by non-linear regression to: a (III.A.52) D= D + 0 . 0 r The fit is seen to be rather good, meaning that part of the explanation for the smaller dose has to do with the fact that the surface area is increasing less rapidly than the boron containing cell volume. However, the fit does not satisfy Equation (III.A.51), which suggests that there are other factors that must be considered such as ions that pass from one cell to another. The basic observations are that near neighbors contribute to the dose of a cell and that, when cells are widely separated, the dose to the interstitium decreases. These findings have significant implications for the types of tumors that can be treated with BNCT as will be discussed in the chapter IV. The effects of the cell radius and cell separation are shown in Figure III.13 for the interstitial dose. The dose in the interstitium is highest when the cells are small and

81 Intersitital dose versus cell radius at a separation of zero 14

Fit with D = D + a /r 12 0 0 Generated points

10 Interstitialdose (Gy) 8

6 4 6 8 10 12 14 16 Cell radius ( µm)

Figure III.12 Interstitial dose averaged over 50 cases with no separation at four cell radii. Fitting is performed non-linearly with the function D = D 0 + a 0/r as derived from the ratio of the surface/volume for spheres. Nonlinear regression was used to fit the data with D 0 = 5.97 Gy and a 0 = 24.52 Gy· µm.

82 Interstitial dose for spheres

4 )

y 10 6

G (

8 e

s 10 o

D 8 12 14

6 4 6 ) m ( µ 4 s 8 iu d a 2 r 10 ll 4 e Ce C ll edg 6 e to e 12 dge s 8 epara tion µ ( m)

Figure III.13 The dose to the interstitium as a function of cell radius for a concentric nucleus of radius 3.0 µm and cell edge to edge separation for boron concentrations of 50 ppm in the cell (nucleus and cytoplasm) and 10 ppm in the interstitium.

83 densely packed. As the cells increase in radius or the cells are farther apart, the dose decreases and, if both occur, the dose can decrease by a factor of 2. Thus, normal tissue will receive lower doses when the tumor cells are far apart and large. The corresponding nuclear dose for the same geometries is shown in Figure III.14. The data in this figure reveal that the nuclear dose decreases as the cells become more separated but increases as the cells increase in size. For large cells, there is little change as the cells separate for the concentric nuclei. Thus, large tumor cells display less near neighbor effects because of the distance to the nucleus. Since the idea of BNCT is to deliver a significantly larger dose to the tumor than is delivered to normal tissue, it is useful to plot the ratio of the total cellular dose to the interstitial dose, which, represents normal tissue, as a function of separation and cell radius. The results are plotted in Figure III.15 where it is clear that normal cells far from the tumor will have a greater therapeutic benefit than those near or in the tumor. This once again demonstrates the effects of neighboring cells on the dose. In Figure III.16, the relative dose to the nucleus, as compared to the cytoplasm is plotted as a function of the cell radius for cellular boron concentrations of 50 ppm and 200 ppm while the interstitial boron concentration is 10 ppm for each case. The slight proportional decrease in dose to the nuclei is geometric for the increasing cytoplasmic volume in which an ion can travel without encountering the nucleus. As the nuclear volume goes from 51.2% of the cell volume for a nuclear radius of 4.0 µm and a cell radius of 5.0 µm to 4.8% when the cell radius increases to 11 µm, any given ion is more likely to deposit all of its’ energy in the cytoplasm rather than in the nucleus. The implications of these results combined with an improved boron carrier are obvious. Consider cells of radius 10 µm with concentric nuclei of radius 4 µm separated from one another by 20 µm and boron concentrations of 200 ppm in the cell and 10 ppm in the interstitium. In this situation, the boron reaction dose would be 5.82 Gy to the interstitium, 62.71 Gy to the cytoplasm, and 82.28 Gy to the nuclei. The interstitial dose is still reasonable while the nuclear dose is quite high with a nuclear to interstitial dose ratio >15. This would kill all cells that concentrated the boron carrier molecule with little damage to normal tissue in a single treatment. The patient could receive subsequent

treatments to hopefully destroy any tumor cells far from the main tumor that were in a G 0

84 Nuclear dose for spherical cells with varying radii and separations

22 10 20 12

14 )

y 16

G 18 (

18 e

s 20 o 16

D 22 24 14 12 12 10 ) m 10 ( µ 8 s iu d 5 ra l 6 el 10 C Cel l sep 15 4 arati on (µ 20 m)

Figure III.14 The nuclear dose as a function of cell radius for a concentric nucleus of radius 3.0 µm and cell edge to edge separation for boron concentrations of 50 ppm in the cell (nucleus and cytoplasm) and 10 ppm in the interstitium.

85 Ratio of cell dose to interstitial dose

8 2

e 3

os 4

D 7

l 5 a

i t

i 6 t 6

rs 7 e

Int /

e 5 9

l 4 20 e

C ) m 3 15 µ ( n o 10 ti 2 ra a 12 p e 10 s 5 ll 8 e C C 6 ell ra 0 dius (µ 4 m)

Figure III.15 The ratio of the dose to the cell to the dose to the interstitium as a function of cell radius and cell separation for boron concentrations of 50 ppm in the cell (nucleus and cytoplasm) and 10 ppm in the interstitium.

Nuclear to cytoplasmic dose ratio as a function of cell radius 1.5

1.4

1.3

1.2

Cellular boron of 50 ppm Nuclear dose / cytoplasm dose 1.1 Cellular boron of 200 ppm Linear regressions

1.0 4 6 8 10 12 Cell radius ( µm)

Figure III.16 The relationship of the nuclear to cytoplasmic dose ratio for two different cellular boron concentrations and for varying cell radii. The noisiness in the 50 ppm boron concentration data is due to the smaller number of boron reactions in total as well as the smaller proportion of the total number of reactions for the region of interest, i.e. 20:1 versus 5:1.

87 or resting state. The combination of boron distribution and tumor cell architecture has an enormous impact upon the dose to the tumor cells. The eccentricity of an ellipsoid is a measure of how far the ellipsoid is from spherical. One method of defining the three axes of an ellipsoid (commonly used in nuclear physics because the volume remains constant as the eccentricity or deformation changes) was previously described in equations (II.A.22) and (II.A.23).246 As shown in equation (II.A.24), the volume, defined by a sphere of radius r, remains constant as the eccentricity varies. This definition of an ellipsoid also possesses rotational symmetry about the a axis. When ε equals zero, the ellipsoid is a sphere. As ε gets larger, the ellipsoid becomes more elongated, which is referred to as prolate as shown in Figure III.17. Eccentricities in the range –1 < ε < 0 lead to a flattened (pancake) shape referred to as oblate. Another view of the ellipsoidal cells is seen in the two cross sections of an ellipsoidal cell shown in Figure III.18 with a radius of 10 µm and eccentricity of 2.5 encompassing a nucleus of radius 4 µm. To determine the effect of the eccentricity on dose, the ratio of the nuclear dose for an ellipsoid with a radius of 10 µm to the dose of an equivolume sphere both with concentric nuclei is shown as a function of eccentricity and cell separation in Figure III.19. The plot is essentially flat indicating that the response is like that just described for large spherical cells. Ellipsoidal cells can be approximated by spherical cells especially for understanding effects rather than numerical values. Finally, the nucleus can be allowed to be eccentrically centered. It can be randomly eccentrically centered in every cell, randomly eccentric in the first cell that is then applied to all subsequent cells, or a fixed direction or a fixed distance from the center specified with the other parameter randomly determined. The results from this are of interest because there is essentially no difference between the spherically concentric or randomly placed nuclei. The results are surprisingly similar. For example, the su m of the squares difference between spherical cells of radius 10 µm with concentric spherical nuclei of radius 4 µm and spherical cells of radius 10 µm with randomly placed spherical nuclei of radius 4 µm is 0.06. The data are very similar to those for concentric spherical nuclei and spherical cells and the same observations hold true.

Figure III.17 A representative ellipsoid with radius 10 µm and an eccentricity of 1.5.

Figure III.18 Two cross sections through a cell with eccentricity of 2.5 and radius of 10 µm and concentric spherical nucleus of radius 4 µm.

89 Comparison of the dose to an ellipsoidal cell and an equivolume spherical cell

p s

e 1 1 s

o 2

o s

p 0

l l

E 5 ) 0 m ( µ n 1 10 io at ar ep 15 l s el Ec C cen 2 tric ity 20 Figure III.19 A comparison of the dose to an ellipsoidal cell and an equivolume sphere both with concentric nuclei of radius 4.0 µm. The spherical cell and ellipsoidal cell have the same radius of 10 µm. For an eccentricity of ε, the three axes (a, b, and c) of the ellipsoid are defined as: c= r (1 + ε ) and a= b = r 1 + ε .

90 IV. Summary and Conclusions

The information presented in chapter III leads to the conclusion that boron distribution, cell geometry, and the cell’s relationship to other cells are important factors in determining the total dose delivered to a given nucleus. The dose to the nucleus is considered by experts in the field as the important radiation dose, destroying the cell’s ability to make essential proteins to maintain homeostasis. Damage to the DNA can also lead to the inability to undergo successful mitosis leading to death or a halt to further replication (either case is a success in cancer control). Lastly, damage to the DNA can lead to advanced apoptosis, i.e. the programmed cell death is temporally advanced. So the results in chapter III are viewed from the standpoint of the nuclear dose. The interpretation of the results must take into account the region termed as interstitium in this work. Technically, the interstitium is the fluid filled space between cells in a tissue. In this work, the interstitium refers to the space between tumor cells or more specifically between cells loaded with boron. So in this model, the interstitium can also contain normal cells or tumor cells that do not avidly uptake the boron carrier by either active or passive means. The dose to the interstitium in tumors such as malignant melanoma and adenocarcinoma of the colon represents the dose to the normal tissue so that low doses are important. In infiltrative tumors such as glioblastoma multiforme and angiosarcoma, the interstitium will contain both normal cells and tumor cells that did not avidly uptake the boron agent. This has significant clinical significance as will be discussed. Considering the above observations, there are several ways to summarize the results from chapter III. First, returning to Figure III.7, it was shown that there is a 16% increase in the nuclear dose when the cells are touching each other versus being widely separated. Whereas the dose to the interstitium is ~2.4 greater when the cells are touching than when widely separated. Thus, closely packing cells increases the nuclear dose, which will improve the efficacy. The much greater increase in dose to the interstitium means that cells without boron loading will receive a significantly larger dose when cells are close together but a small dose when they are apart. Furthermore, the ratio of the nuclear dose to interstitial dose ratio is greater when the cells are widely separated, 91 with the tumor cells still receiving a dose greater than 15.5 Gy. Cell death is a statistical phenomena and is expressed by a cell survival curve as shown in Figure IV.1. This figure demonstrates that the doses delivered by BNCT are adequate for cell killing. This is especially true when the dose to the cytoplasm is combined with the nuclear dose to determine the cellular dose used in the Figure IV.1. For example, referring again to Figure III.7, the cellular dose for no separation is ~32 Gy and for the asymptotic range is ~27 Gy. Both doses should clearly be lethal. The distribution of boron in the cell is also seen to be important with the greatest dose occurring when the boron is concentrated in the nuclei rather than the interstitium by a factor of ~2 as seen in Figure III.8. The boron in the interstitium provides a small nuclear dose and is the most important constituent of the dose to the interstitium itself. The greater the concentration of boron in the cell holding the interstitial boron concentration constant, the greater the nuclear dose, in a basically linear nature. The effect on the interstitial dose is minimal. This highlights the dependence of BNCT upon boron carrier molecules. If a carrier molecule can increase the absolute tumor cell boron concentration and increase the ratio of cell to interstitium boron, the efficacy of BNCT will greatly increase. As cells increase in radius while keeping a constant nuclear radius, the nuclear dose will increase and the influence of nearby cells decreases. Also, the greatest ratio of cell to interstitial dose occurs for large separated cells. The influence of a non-concentric nucleus is relatively small for the geometries studied. In summary, the nuclear dose for small cells is increased by nearby cells but shows little near neighbor effect for large or greatly separated cells. The greater the boron concentration, the greater the nuclear dose. If the cell to interstitial boron concentration increases as the cellular boron increases, the interstitial dose changes little but, if the cellular concentration of boron is linearly increased, this should translate into much greater efficacy. BNCT has been used to treat several malignancies including glioblastoma multiforme, malignant melanoma, head and neck tumors, undifferentiated thyroid carcinoma, and adenocarcinoma of the colon. 79, 181, 278-294 Of these, the most clinically

Low LET

Figure IV.1 A typical cell survival curve for high and low LET radiation showing significant killing for doses predicted for BNCT. 295

93 studied tumor is GBM. As discussed in chapter I, the standard therapy for glioblastoma multiforme is neuro-surgical resection followed by 36 standard photon beam radiation treatments and in some cases chemotherapy. This standard protocol provides a life expectancy of approximately 12 months from the time of diagnosis. 8 The BNCT trials substitute BNCT for conventional photon therapy and demonstrate a survivability of approximately 14 months. 41, 55, 66, 296, 297 The clinical trials have all observed that the glioblastoma recurs at the edge of the tumor bed. Since the tumor is infiltrative, the edge of the tumor will be ragged with cells extending into the surrounding tissue. The microdosimetry of BNCT provides an answer. Consider cells in this periphery that did

not accumulate a significant boron concentration (in G 0 phase or poor local availability of the boron carrier). This would correspond to a cell in the interstitium that is in the widely separated region. These cells will receive only a few Gray of dose (~5 Gy) unlike a cell in the interstitium in the tightly packed case with the dose being more than twice that of the periphery. These doses can go from possible to likely lethality. This model would indicate that infiltrative tumors cannot be successfully treated with BNCT with current boron carrier molecules. The reason for the failure of local control has not been clearly elucidated before. The only way that an infiltrative tumor can be successfully treated with BNCT is to find an agent that concentrates in tumor cells avidly, even if the cell is in the G 0 phase, or to administer therapy given over several days. Though giving dose fractions might be successful, fractionating the treatment decreases the attractiveness of the therapy when compared to a single session treatment (allowing for multiple beam angles in some cases). Turning to melanoma and adenocarcinoma of the colon, the results are much more favorable. Brain metastases in malignant melanoma and liver metastases in adenocarcinoma of the colon have been successfully treated using BNCT, though the patients died of massive tumor load elsewhere. Microdosimetry provides insight into the effectiveness of the treatment for these tumors. First, initial inferences have demonstrated modestly improved boron concentrations in the tumors. 79, 100, 150, 271, 294, 298- 303 The more important issue is the geometry of tumors. They are more solid (closely packed), grow by direct extension, and do not typically have individual tumor cells.

94 Examining the cells on the periphery, once again they are more analogous to a solid sphere with the cells on the edge in close contact with the main tumor body. The microdosimetry model predicts that all of the cells would be close together so that even tumor cells not loaded with boron on the edge of the tumor will receive a reasonable dose (~10 Gy). This would correspond with the clinical results that have demonstrated good tumor control. 67, 97, 294, 301 The microdosimetry of BNCT is dependent upon cellular geometry and boron concentration. Clinical results correlate with microdosimetric predictions. As this exciting cancer treatment modality progresses, 18 F-BPA will become the standard for treatment planning since it can identify the distribution of boron laden cells which, if used in concert with the microdosimetric results, will provide a methodology to determine the likely efficacy of treatment. In conclusion, this dissertation has advanced the understanding of the microdosimetry of BNCT in several ways. The program uses the actual stopping power curves to determine the energy deposition for a given ion instead of a linear approximation that improves the accuracy. The effect of neighboring cells on tumor cell dose is explored showing a benefit from densely packed cells for the dose to tumor cells. The dose to tumor cells that accumulate boron in the same concentration as normal cells (the interstitium in this model) receive a significantly larger dose when the boron laden tumor cells are closely packed around the non-boron laden cells. The effects of the location of the nucleus within the cell on the dose is described and found to be a small effect. This work agrees with other calculations showing that the nuclear boron concentration is the most important component of the nuclear dose. 238, 241, 244 Cell size and boron concentration correlate with a larger nuclear dose as well as a larger dose to surrounding normal cells if the separation of the boron laden tumor cells is small. The data also demonstrate that for widely separated tumor cells, i.e. ITCs, there will be a relatively small dose of only ~4-5 Gy for tumor cells accumulating boron in the same manner as normal cells and the interstitium. These results have been compared to actual clinical results in order to explain the clinical observations. The microdosimetric model presented is shown to explain the clinical results. This serves to validate the usefulness

95 of the study of the microdosimetry of BNCT. Thus, this dissertation advances the field and clinical understanding of boron neutron capture therapy.

96 V. Future Directions for Research into Boron Neutron Capture Therapy Microdosimetry

As discussed, a primary problem for microdosimetric modeling is geometry, i.e. how to best represent the cells and their sub-structures. Another problem is the paucity of data relating to the stopping powers for the ions in BNCT in the low energy portions of their tracks (< 1 MeV/amu). The continuous slowing down approximation (CSDA) could be replaced by a more realistic step function approach since some of the energy loss is quantum mechanical and thus not continuous. A better theoretical treatment seems unlikely at this time due to the great complexity of the interactions with the partially charged ions due to less than maximal ionization as the heavy ions slow down to much less than relativistic speeds. In the low energy spectrum for the stopping power calculations, the quantum mechanical effects of the target electrons (especially electrons in the outer shells) play a significant role in two ways. The first is by the direct interaction of the electron cloud with the ions, which changes the velocity of the ions. Also, the nearly free outer shell electrons partially shield the ion, effectively changing the charge state, z, to z * such that 1 < z */z. The diminution of the ion charge obviously also alters the electromagnetic interaction between the ion and the electron clouds. The partial shielding represented by z * is obviously an idealization of the quantum mechanical interactions that are occurring where an electron binds to the ion for a short time and is averaged to a partial charge. The second effect is the creation of large numbers of delta waves (secondary electrons from an ionization process), which alters the local charge milieu, creates many free radicals, and adds to the microdosimetric dose. The production of delta waves may in fact be the most significant portion of any dose of ionizing radiation. The number of these interactions increases per unit track length traversed because, as the charged particles start to slow down, there is more contact time for the interactions to occur which increases the production of delta waves. It cannot be over emphasized that the experimental data in the low energy region (< 1 MeV/amu) often varies as much as 20% and that binding energies for organic bonds are on the order of a few eV. Thus, the effects of better stopping power data is of great importance to the understanding of microdosimetric processes. The complexity of the theoretical problem 97 is too great at this time to allow a model capable of accurate predictions. Therefore, it is likely that improvements will have to be made in measurements of the stopping powers in actual tissue. Unfortunately, there is little interest from national funding agencies at this time to extend this research. The data obtained from SRIM2008 are probably reasonable at this point in time with the current understanding of all of the other aspects of microdosimetry. SRIM2008 has become the accepted standard in microdosimetry. As the field moves forward, the need for better stopping power data will become a more significant problem. A more complete array of the radiation components that contribute to the total dose could be added to the Dose program. This would aid in determining likely peak doses. This would be a straightforward addition to the dose. Allowing for γ-rays and fast neutrons from beam would be reasonable. Addition of the dose from beam derived γ-rays would be straightforward but the contributions from fast neutrons will be more challenging. Fast neutrons have more varied nuclear reactions that will need to be included. The other area in which this model could be improved is related to the geometry of the cells. Attempting to construct a more representative cell, without creating complex shapes out of simple geometric figures, is a rather daunting project. It would appear that the relatively new field of chaos presents the possibility of constructing more realistic cells. The constructs for the chaos theory may not increase computational time although it is always difficult to know where the ion track lies within a cell, etc. The application of chaos theory to microdosimetry seems imminent especially after the positive results shown here. Finally, the new field of microbeam technology could be used to study the effects of radiation on the cell and its’ organelles. There is much research being done to better understand what damage is done to the nucleus when the radiation deposition is not in the nucleus, when it is in the nucleus, and when it is in a neighboring cell. It is known that ionizing radiation causes free radical formation. The free radicals diffuse away from the ionization event causing damage at some distance (on the order of 1 or 2 microns). These free radicals can cause significant DNA damage even though the ionization track lies

98 outside of the nucleus. These free radicals may induce other chemical species yet to be characterized that can damage DNA. Also, it is known that cells can communicate with one another so that the damage or protection inferred upon one cell might be communicated to other cells around it. This exciting area of research will have large implications for microdosimetric codes. The results of such calculations may be incorporated rather straightforwardly, into the current code by assuming that a particular cell that has a given dose will provide a protective factor and/or, depending on the author, a destructive factor to near-neighbor cells. The effect could be allowed to diffuse through the volume of interest. Adding or subtracting some percentage of the dose around cells that receive a given dose is a straightforward way to model this effect. So that the model can be updated rather quickly whenever microbeam research produces pertinent results. The microdosimetric model presented here provides a powerful technique to evaluate BNCT results. The model appears to be sufficiently accurate to provide predictive information, though ideally more testing should be done before too much emphasis is given to any prediction. Incorporating improved stopping powers or results from microbeam technology can also be done in a straightforward manner. Changes involving chaos theory are likely to prove somewhat more difficult. The level of difficulty is based upon how difficult it is to know where any given point lies – in the interstitium, the cytoplasm of a particular cell, or the nucleus of a particular cell. The model presented in this dissertation thus makes a significant and unique contribution to the microdosimetry of boron neutron capture therapy.

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113 Vita

Trent Lee Nichols was born in Knoxville, Tennessee on 4 April 1954 to Ted and Audrey Nichols. He was raised in Knoxville attending Holston High School where he graduated 18 th of 269 and was elected to the National Honor Society and was Honorable Mention for the National Merit Scholarship. He played in the high school band earning the first trumpet part for all four years and was selected for the All State East band as a junior. He competed on the high school golf team as a sophomore, junior, and senior. He earned the rank of Eagle Scout in 1968 after previously earning his God and Country Award. After graduation, he entered the University of Tennessee, Knoxville where he earned a B.S. with Honors in Engineering Physics in 1976. The Sigma Pi Sigma National Honor Society for physics elected him to membership in 1975 and he served as president for his junior and senior years. After joining the Society of Physics Students, he was elected vice-president as a sophomore and president. In 1978, he was earned a M.S. in Physics at the University of Tennessee for research in condensed matter physics with a thesis entitled “Partial Wave Analysis of the Charge Density Distributions for Impurities on Gold.” under the guidance of Paul G. Huray, Ph.D. He then began work on a Ph.D. in theoretical nuclear physics. After passing his preliminary examination for the Ph.D. degree in 1979 on the first attempt, he was awarded a grant by the Danish Government to study at the Niels Bohr Institutet in Copenhagen, Denmark. While at the Niels Bohr Institutet for several months in 1979 and 1980, he worked with M. W. Guidry, Ph.D. on computer codes to calculate the formfactors for one- nucleon and two-nucleon transfer reactions in a system in which one of the two nuclei is permanently deformed. In 1980 and 1981, he worked part time as a computer analyst with a Q clearance at Oak Ridge National Laboratory while pursuing his Ph.D. In 1982, Trent temporarily left graduate school to earn a Doctor of Medicine from the University of Tennessee Center for the Health Sciences in Memphis, Tennessee. During the two option quarters, he was awarded grants from the National Institutes of Health to perform Fourier analysis of body surface mapping data under the guidance of David M. Mirvis, M.D. leading to a publication for each of the grants. Following graduation, he completed a residency in Internal Medicine at the University of Tennessee Memorial

114 Research Center and Hospital in Knoxville, Tennessee. Dr. Nichols spent three years in private practice with Internal Medicine Associates at St. Mary’s Medical Center in Knoxville, Tennessee. He left private practice to rejoin academia and resume his graduate studies in 1992. He was asked by the University of Tennessee to help organize the medical staff at the University of Tennessee Memorial Research Center and Hospital for managed care contracting. He helped to form and was the first president of the University Physicians Association, being elected twice to that office. The University Physicians Association is now a multi-million dollar corporation. While continuing to practice half time with University Internal Medicine and teaching internal medicine residents, Dr. Nichols restarted his doctoral research though now in boron neutron capture therapy with Professor George W. Kabalka. He has participated in the boron neutron capture therapy trials at Brookhaven National Laboratory and Harvard Medical/MIT by managing patients imaged with 18 F-lableled para -boronophenylalanine by Positron Emission Tomography and managed patients following boron neutron capture therapy for glioblastoma multiforme and malignant melanoma. After completing his doctoral degree, Dr. Nichols plans to continue his current research and develop related research.

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