A Dissertation entitled
Investigation of Radiation Protection Methodologies for Radiation Therapy Shielding Using Monte Carlo Simulation and Measurement
by Sean Tanny
Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Doctor of Philosophy De- gree in PhysicsWith a Concentration in Radiation Oncology Physics
Dr. E. Ishmael Parsai, Committee Chair
Dr. David Pearson, Committee Member
Dr. Diana Shvydka, Committee Member
Dr. Jon Bjorkman, Committee Member
Dr. Richard Irving, Committee Member
Dr. Patricia R. Komuniecki, Dean College of Graduate Studies
The University of Toledo December 2015 Copyright 2015, Sean Tanny
This document is copyrighted material. Under copyright law, no parts of this document may be reproduced without the expressed permission of the author. An Abstract of Investigation of Radiation Protection Methodologies for Radiation Therapy Shielding Using Monte Carlo Simulation and Measurement by Sean Tanny
Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Doctor of Philosophy De- gree in PhysicsWith a Concentration in Radiation Oncology Physics The University of Toledo December 2015
The advent of high-energy linear accelerators for dedicated medical use in the
1950’s by Henry Kaplan and the Stanford University physics department began a revolution in radiation oncology. Today, linear accelerators are the standard of care for modern radiation therapy and can generate high-energy beams that can produce tens of Gy per minute at isocenter. This creates a need for a large amount of shielding material to properly protect members of the public and hospital staff. Standardized vault designs and guidance on shielding properties of various materials are provided by the National Council on Radiation Protection (NCRP) Report 151. However, physicists are seeking ways to minimize the footprint and volume of shielding material needed which leads to the use of non-standard vault configurations and less-studied materials, such as high-density concrete.
The University of Toledo Dana Cancer Center has utilized both of these methods to minimize the cost and spatial footprint of the requisite radiation shielding. To ensure a safe work environment, computer simulations were performed to verify the attenuation properties and shielding workloads produced by a variety of situations where standard recommendations and guidance documents were insufficient. This project studies two areas of concern that are not addressed by NCRP 151, the ra-
iii diation shielding workload for the vault door with a non-standard design, and the attenuation properties of high-density concrete for both photon and neutron radia- tion. Simulations have been performed using a Monte-Carlo code produced by the Los
Alamos National Lab (LANL), Monte Carlo Neutrons, Photons 5 (MCNP5). Mea- surements have been performed using a shielding test port designed into the maze of the Varian Edge treatment vault.
iv Acknowledgments
I would like to acknowledge the Department of Radiation Oncology at the University of Toledo Medical Center for the phenomenal opportunities they have afforded me in my training and research. We always discuss the quality of the education that students receive within our program, and as I continue to discover other programs, the more I am convinced of the quality of the education I received at the hands of some of the most dedicated professionals I’ve met.
Thank you to Dr. Shvydka for tolerating the noise I can make when confused.
Thank you to Dr. Pearson for always offering sound advice, whether it be about car repair or complicated clinical measurements. Thank you Dr. Sperling for the camaraderie, sharing your scientific and technical expertise so freely, and all the great collaborative projects we’ve been able to produce. I owe so much to Dr. Parsai for the faith he’s shown in me. I certainly would not be the person I am today without his guidance and constant patience.
I want to thank Dan Harrell, Jim Noller, Brett Dietrich, and Manjit Chopra from Shielding Construction Solutions and Universal Minerals International for shar- ing their dedication, knowledge, and experience in material mixtures and radiation shielding design. Without their insight and contributions, the unique design of the
Dana Cancer Center and the shielding test port would never have come to fruition.
No graduate student is capable of navigating the complicated bureaucracy between two colleges on two separate campuses without the guidance and experience of the supporting staff. I want to acknowledge and thank Diane Adams, Lynda Obee, and
v Tiffany Akeman for their patience in explaining the necessary forms and pointing me in the right direction to make sure I can continue on in my research. Your help has been invaluable.
Finally, this dissertation would still be in disarray if it weren’t for the dedicated efforts of my wife, Kristen. Thank you so much for being there and tolerating all the late nights and weekends it has taken to finish this work.
vi Contents
Abstract iii
Acknowledgments v
Contents vii
List of Tables xi
List of Figures xiii
List of Abbreviations xv
Preface xvii
1 Introduction 1
2 Radiation Protection and Radiation Units 6
2.1 Radiation Units ...... 8
2.1.1 Exposure ...... 9
2.1.2 Dose ...... 9
2.1.3 Equivalent Dose ...... 10
2.1.4 Effective Dose ...... 11
2.1.5 Ambient Dose Equivalent ...... 12
2.2 Dose Limits for Radiation Protection ...... 13
2.2.1 Time-Average Dose Rate Limits ...... 15
vii 2.3 Radiation Interactions with Matter and Exponential Attenuation . . 16
2.3.1 Radiation Interactions with Matter ...... 16
2.3.1.1 Photoelectric Absorption ...... 16
2.3.1.2 Compton Scatter ...... 18
2.3.1.3 Pair/Triplet Production ...... 19
2.3.2 Attenuation Coefficients ...... 19
2.3.3 Exponential Attenuation ...... 20
3 NCRP Report 151 22
3.1 Primary and Secondary Barriers ...... 22
3.2 Occupancy Factors ...... 25
3.3 Use Factors ...... 27
3.4 Accelerator Workload ...... 28
3.4.1 Primary Workload ...... 28
3.4.2 Leakage Workload ...... 29
3.4.3 Patient-Scatter Workload ...... 30
3.5 Determining Barrier Thicknesses ...... 31
3.6 Door Shielding ...... 34
3.6.1 Photon Dose-Equivalent at the Door ...... 35
3.6.1.1 Photon Dose-Equivalent for Machines Producing ≤10
MV Photon Beams ...... 36
3.6.1.2 Photon Dose-Equivalent for Machines Producing >10
MV Photon Beams ...... 38
3.6.2 Neutron Dose-Equivalent at the Maze Door ...... 40
4 Monte Carlo Method 42
4.0.3 MCNP5 ...... 43
4.0.4 Tallies within MCNP ...... 44
viii 4.0.5 Variance Reduction Methods ...... 46
5 Specialized Treatment for Non-Standard Vault Geometry 50
5.1 Vault Layout ...... 51
5.2 Analytic Model ...... 53
5.2.1 Maze Barrier Scatter ...... 54
5.2.2 Photon Scatter from the Maze Wall ...... 56
5.2.3 Total Scattered Photon Dose at the Vault Door ...... 57
5.3 Scattering Fractions ...... 58
5.3.1 Side Scatter Radiation ...... 58
5.3.2 Patient Scatter Fractions ...... 60
5.4 Simulation Geometry ...... 62
5.4.1 Materials and Source Definitions ...... 63
5.4.2 Tally Selection and Placement ...... 66
5.5 Results ...... 67
5.5.1 NCRP Formalism for Door Workload ...... 68
5.6 Recommendations for Additional Scattered Radiation Calculations . . 70
6 Shielding Test Port Development 72
6.1 Shielding Test Port Development ...... 72
6.1.1 Risk Mitigation and Safety Interlocks ...... 73
6.1.2 Ease of Use and Block Design ...... 75
6.2 Parameters of Interest ...... 76
6.2.1 TVL Measurement ...... 76
6.2.2 Patient Scatter Fractions ...... 80
6.2.3 Differential Dose Albedo ...... 82
7 TVL Measurement and Simulation 84
ix 7.1 Experimental Setup ...... 84
7.1.1 TVL Measurement and Block Parameters ...... 84
7.1.1.1 Block Density Verification ...... 87
7.2 Monte Carlo Simulation ...... 88
7.2.1 Simulation Geometries ...... 88
7.2.2 Simulation Material and Source Specifications ...... 91
7.2.3 Variance Reduction and Tally Selection ...... 92
7.3 TVL Measurement and Simulation Results ...... 94
7.3.1 Measured TVL Thicknesses ...... 94
7.3.2 MCNP Simulation Results ...... 97
7.4 TVL Discussion ...... 100
8 Conclusions 110
References 112
A Fluence to Dose Conversion Factors from ICRP 116 126
x List of Tables
2.1 Dose Quality Factors for Different Types of Radiation ...... 10
2.2 Dose Weighting Factors for Different Body Tissues ...... 12
3.1 NCRP 151 Recommended TVLs ...... 26
3.2 NCRP 151 Recommended Occupancy Factors ...... 27
3.3 Patient-Scatter Fractions and TVLs ...... 31
3.4 NCRP 151 Concrete Differential Dose Albedos ...... 38
4.1 MCNP tallies ...... 44
5.1 Comparison of side scatter and patient scatter fractions ...... 60
5.2 Dimensions of the Truebeam vault ...... 62
5.3 Concrete compositions by weight ...... 65
5.4 Calculated maze scatter fractions compared to patient and side scatter
fractions ...... 69
5.5 Photon Dose at the Door per Gy at Isocenter ...... 69
5.6 Total Photon Workload at Door per 1000 Gy ...... 70
7.1 Test block densities ...... 88
7.2 Measured vs. Published TVL1 for concrete ...... 95
7.3 Measured vs. Published TVL2 for concrete ...... 95 7.4 Measured TVLs 1, 2, & 3 ...... 96
7.5 Simulated TVL2 for concrete at various field sizes ...... 98
7.6 Simulated vs. NCRP recommended TVL1 for flattened beams ...... 99
xi 7.7 Simulated vs. NCRP recommended TVL2 for flattened beams ...... 99
7.8 Comparison of simulated TVL1 for flattened vs unflattened beams . . . . 100
7.9 Comparison of simulated TVL2 for flattened vs unflattened beams . . . . 100
7.10 Simulated TVLs out to TVL4 ...... 101
A.1 ICRP 116 photon fluence to effective dose conversion factors ...... 127
A.2 ICRP 116 neutron fluence to effective dose conversion factors ...... 128
xii List of Figures
1-1 Example of a standard vault with a maze ...... 2
1-2 Example of a vault with a direct shielded door ...... 3
1-3 Example of a non-standard vault with a maze ...... 4
2-1 NCRP Background Exposure Breakdown ...... 7
2-2 Neutron weighting factors ...... 11
2-3 Radiation interaction importances as a function of Z and energy . . . . . 17
2-4 Comparison of narrow beam and broad beam geometries ...... 21
3-1 Primary and secondary barriers ...... 23
3-2 Primary barrier widths ...... 24
3-3 Two source rule for secondary barriers ...... 34
3-4 Vault geometry for scattered photon dose-equivalent calculation . . . . . 36
3-5 Vault geometry for capture gamma and neutron dose-equivalent calculation 39
4-1 Weight Windows Illustration ...... 48
5-1 Dana Cancer Center linear accelerator floorplan ...... 51
5-2 Standard and Non-standard Vault Layouts ...... 52
5-3 Geometries from Biggs and Facure investigations ...... 53
5-4 Truebeam Vault Geometry for Maze Scatter ...... 54
5-5 Side Scatter Geometry ...... 59
5-6 Patient Scatter Simulation Geometries ...... 61
5-7 Patient Scatter Measurement Geometry ...... 61
xiii 5-8 Truebeam vault geometry ...... 63
5-9 MCNP reproduction of the Truebeam vault ...... 64
5-10 Source verification for maze scatter simulation ...... 65
5-11 Comparison of simulated and calculated transmission ...... 67
5-12 Simulated maze scatter fractions ...... 68
6-1 Test Port Pre-Installation ...... 73
6-2 Test Port Location within Edge Vault ...... 74
6-3 Schematic of Test Port interlock ...... 75
6-4 Mass attenuation coefficients for different densities of concrete ...... 79
6-5 Potential geometry for patient scatter measurements ...... 81
6-6 Potential experimental setup to measure dose albedos ...... 82
7-1 Experimental setup of TVL measurements ...... 86
7-2 MCNP test port simulation geometry ...... 89
7-3 Uniform barrier thickness and density simulation geometry ...... 90
7-4 Measured Transmission Curves ...... 104
7-5 F4 vs. F5 vs. Measured Attenuation ...... 105
7-6 Measured vs. simulated transmission curves for unflattened beams . . . . 106
7-7 Test Port vs. Maze Barrier geometry comparison ...... 107
7-8 NCRP transmission vs. Maze Barrier transmission ...... 108
7-9 Measured vs. simulated transmission curves for unflattened beams . . . . 109
xiv List of Abbreviations
FFF ...... Flattening Filter Free (Hi-Dose Mode) SRS ...... Stereotactic Radiosurgery SBRT ...... Stereotactic Body Radiation Therapy RT ...... Radiation Therapy CT ...... Computed Tomography PET ...... Positron Emission Tomography OIS ...... Oncology Information System fx ...... Fraction, a single treatment of radiation CBCT ...... Cone-Beam Computed Tomography IMRT ...... Intensity-Modulated Radiation Therapy dmax ...... Depth of maximum dose PDD ...... Percent Depth Dose TMR ...... Tissue-Maximum Ratio HVL ...... Half-Value Layer TVL ...... Tenth-Value Layer RBE ...... Relative Biological Effectiveness AAPM ...... American Association of Physicists in Medicine NCRP ...... National Council on Radiation Protection ICRP ...... International Commission on Radiological Protection ICRU ...... International Commission on Radiation Units and Mea- surement LANL ...... Los Alamos National Laboratory MCNP/MCNP5 ...... Monte Carlo Neutrons, Photons, Monte Carlo code ca- pable of tracking neutron, photon, and electron trans- port NIST ...... National Institute of Standards and Technology OAR ...... Off-Axis Ratio RGE ...... Radiation Generating Equipment NARM ...... Naturally-occuring and Artificial Radioactive Material ALARA ...... As Low As Reasonably Achievable LD50 ...... Lethal Dose, 50%, the whole body dose at which 50% of those exposed would die
xv Gy ...... Gray, units of air kerma and dose, equal to 1 Joule per kilogram pcf ...... Pounds per cubic foot, a measure of density MV ...... Mega-volt, one million volts NAP ...... Nominal Accelerating Potential CPE ...... Charged Particle Equilibrium TCPE ...... Transient Charged Particle Equilibrium
xvi Preface
X-Radiation was discovered in 1895 by Wilhelm R¨ontgen when he accidentally left a radioactive sample near a piece of film [77,78]. Less than one year following, a physician in Chicago treated a superficial lesion with radiation, creating the field of radiation oncology [74]. Understanding of the risks and mechanisms associated with radiation interactions in tissue lagged far behind the use of radiation for science and medicine. The initial scientists working with radiation were oblivious to the risks and eventually developed a range of cancers because of their extreme radiation exposure.
The Radium Girls, a group of women who worked for a watch company painting glow- in-the-dark watch dials, are another famous example of the poor understanding of the risks of radiation [15]. Often encouraged to lick the brush-tips to achieve a fine point, the Radium Girls developed multiple bone cancers from the absorbed radioactive materials. Though radiation is a very effective carcinogen, its effects typically aren’t noticeable until a span of years has passed. The radiation doses and energies used in radiation therapy are so high that there is no real way to reduce radiation exposure with personal protective equipment. This means that protection to radiation exposure must be addressed on an institutional level for those organizations utilizing high doses of radiation. This paper will discuss the development of modern radiation shielding and protection and how this was applied to design the radiation oncology center at the University of Toledo Medical Center (UTMC).
Radiation is a double-edged sword: the mechanism that makes it harmful, DNA damage, is what makes it effective as a cancer therapy [28]. The energy imparted by
xvii ionizing radiation is called air kerma or dose depending on the situation and has the
units of Gray (J/kg). For reference, the lethal dose for 50% of a population (LD50)
for radiation lies between 2-4 Gy for a single whole body exposure. Whole body
exposures above 10 Gy have been uniformly fatal (LD100) [28]. Traditional methods
of radiation therapy involve focused doses between 1.8-2 Gy given in multiple fractions
over several weeks [43]. A high dose radiation treatment that is being used today to
great effect is Stereotactic Radiosurgery/Radiotherapy (SRS/SRT). The purpose of
this treatment is to ablate small tumors. This will involve delivering large doses (10-90
Gy) per fraction over a maximum of 5 fractions. The use of such large doses has led to
an escalation of an order of magnitude increase for the workload for modern radiation
therapy infrastructure, introducing further radiation protection concerns [84].
Radiation protection can be summarized in three principles: time, distance, and
shielding. The cumulative radiation dose to an individual is governed by the dose rate
in a particular area. This is inversely proportional to the square of the distance of the
areas from the source, and may be further limited by restricting the time that individ-
ual spends within the radiation area. Radiation shielding further attenuates the dose
rate below what distance and occupancy may achieve. Since radiation technologists
are required to always be within a distance that allows them to quickly respond to
any eventuality that may occur during treatment, the protection benefits from time
and distance are minimized. Space constraints place additional restrictions on the
ability to use distance as part of a radiation protection program. Thus, shielding is
essential in any radiation therapy department.
Radiation shielding for megavoltage (MV) therapy machines usually consists of
concrete barriers. Concrete is advantageous in that it is dense (ρ = 2.35 g cc−1, or
147 pcf), relatively cheap, and has the added benefit of having a high concentration of hydrogen, which is important to shield secondary neutrons that may be produced by higher-energy beams [68]. Concrete may be poured to meet a specified shape, or may
xviii be pre-cast in blocks at an aggregate yard and assembled on-site. A major disadvan- tage of concrete is that it is bulky. Standard concrete barriers for radiation therapy vaults can reach thicknesses in excess of 7 feet. However, different aggregates, such as steel and hematite, may be added to the concrete prior to casting to increase the density appreciably. The increased density allows for a reduction in barrier thickness, allowing heavily attenuating barriers to fit within smaller spaces. Standard radiation principles suggest that the reduction in barrier thickness should be proportional to the ratio of the increase in barrier density for beams in the MV range. Guidelines for reducing barrier thickness have not been studied in depth, particularly not since the increased prevalence of pre-cast blocks, which are able to achieve densities reaching into the 300 pcf range.
Radiation protection and shielding calculations need to ensure adequate protection every time. To help ensure that shielding calculations are performed correctly, the
National Council of Radiation Protection (NCRP) published Report 151 to guide physicists on shielding megavoltage photon sources [68]. In this document, two styles of example vaults are provided, along with worked out calculations demonstrating how to shield them. While the majority of vaults conform to these examples, some facilities can realize cost and space saving by using alternate designs. When deviating from the standard designs, the considerations for scattered radiation change, and there is little guidance present within NCRP 151 to help physicists ensure a safe radiation environment near treatment machines. There has been little detailed research into how to prospectively shield a radiotherapy vault beyond the traditional configuration presented in NCRP 151, an area of increased interest within the medical physics community [22,23,25,26,39,81].
This project is intended to better define the relevant parameters needed to ade- quately protect staff when using high density concretes and non-standard designs.
xix Chapter 1
Introduction
Radiation protection is an area of radiation physics that is simple to explain but is complicated in the details. The ultimate goal of any facility utilizing radiation is to maximize the efficiency of procedures and therapies, while maintaining a safe work environment for staff and members of the public. The use of radiation in medicine has become widespread, being used for diagnostic purposes in radiology, interventional procedures, and for therapeutic purposes in radiation therapy [69]. Maintaining a balance between medical benefit and public exposure is a necessary task for many departments in medicine, but few have such high radiation protection concerns as radiation therapy.
Radiation therapy utilizes large, targeted doses of radiation to kill cancer cells
[28]. The risks associated with these doses to members of the staff and public are a concern. This same cancer killing dose can cause complications in normal cells, turning them into potential secondary or primary malignancies [74]. If the member of the public is an embryo or a young person, certain developmental disabilities and genetic malformations may occur [28].
There are three basic principles in radiation protection: time, distance, and shield- ing [56]. The dose received by an individual can be reduced by limiting the amount of time that person spends in a radiation area. Maintaining a safe distance from a
1 Figure 1-1: Example of a vault with a maze occluding the door. The primary beam is incident on the walls indicated by the arrows pointing away from isocenter.
radiation source will also reduce the dose received, as the dose rate decreases with increased distance. For most sources, the dose rate will fall off inversely proportional to the square of the distance from the source. If the reduction from both time and distance are not sufficient to reduce the dose rate to acceptably low levels, then atten- uating material must be used to absorb the radiant energy. This attenuating material is commonly referred to as shielding.
Radiation protection principles applied to radiation therapy are governed by reg- ulation [65]. Technologists are required be located nearby the machine while it is in operation. This limits the dose reduction we can achieve by decreasing time spent by a technologist near the source. It also puts a practical constraint on the distances they can be removed from the machine. Therefore, shielding becomes the mainstay
2 Figure 1-2: Example of a vault with a direct shielded door. The primary beam is incident on the walls indicated by the arrows pointing away from isocenter.
of a radiation protection plan within radiation oncology.
Radiation shielding works by attenuating and absorbing radiant energy. The types of shielding used will vary depending on the type of radiation being shielded.
For example, neutron radiation requires a combination of thermalizing material and photon absorbing material. To shield high energy photons, like those produced by a linear accelerator, high density material is used, such as lead, steel, and concrete.
Concrete is the most commonly used of these materials because of its versatility and low cost [68].
Many publications have studied how to utilize the three radiation protection prin- ciples of time, distance, and shielding in the context of radiation therapy. These have been reviewed and incorporated into official recommendations by the National
3 Figure 1-3: Example of a vault in a non-standard layout. The primary beam is incident on the walls indicated by the arrows pointing away from isocenter.
Council on Radiation Protection (NCRP). The most recent of these is NCRP Re- port 151, published in 2005 [68]. NCRP 151 updates recommendations from NCRP
49, published in 1977, to incorporate advancements in the techniques used in exter- nal beam radiation therapy (EBRT), such as intensity-modulated radiation therapy
(IMRT) [67]. The report also included recent information concerning photo-neutron production and shielding that results as a secondary product from photon beams with end-point energies >10 MV.
NCRP 151 presents information on the materials used for shielding. This in- cludes which types of radiation each material is useful for, the relative costs, typical densities, and tenth-value thicknesses (a characteristic of absorption). Materials dis-
4 cussed include concrete, lead, steel, dirt, and borated polyethylene. Heavy concrete, or high-density concrete, is mentioned, but it is not discussed in depth.
The details of shielding a radiotherapy vault depend heavily on how the machine is configured. The majority of vaults are arranged in one of two ways; there is a direct entrance into the vault or there is a maze occluding the door to the vault from directly scattered radiation. NCRP 151 thoroughly covers these two arrangements and the various methods that radiation may reach the vault entrance. Examples of these two layouts are demonstrated in Figures 1-1 & 1-2. They do not discuss the general principles for shielding a vault outside of these two configurations, such as a vault where the maze intercepts the primary beam. An example of such a layout is shown in Figure 1-3. While it is not difficult to predict that there are additional paths for scattered radiation to reach the entrance in this configuration, solving what the total dose at the door will be is not trivial. Unfortunately, there is not much guidance for physicists as to how to predict what workload the vault entrance should be shielded for.
The purpose of this project is to fill some of the gaps that remain in NCRP
151. In particular, we investigate calculation methods to accurately predict the ra- diation workload at the door of a non-standard vault and the attenuation properties of high-density concretes. Monte Carlo simulations of a non-standard vault design were performed to quantify the added workload burden at the door with the beam perpendicular to the maze. We have performed Monte Carlo simulations to quantify the attenuation properties of various forms of high density concrete, and compared these against measured results obtained from a unique, purpose-built test port.
5 Chapter 2
Radiation Protection and
Radiation Units
The use of ionizing radiation is fundamental to many aspects of medicine, but comes with a risk. However, man-made sources of radiation are not the only expo- sure that humans receive. Naturally occurring radiation contributes about half of the average annual exposure for an individual in the United States [69]. This natu- ral background radiation comes from radioactive materials within rocks, cosmic ray radiation, and by-products of radioactive decay, such as radon. The total exposure from naturally occurring sources when averaged over the whole population is referred to as background radiation.
The average annual exposure for a person within the United States is cited at 6.2 milliSievert by the NCRP for 2009 [69]. Approximately half of that total exposure that the average American will receive comes from medical uses [69]. The rapid rise of the use of computed tomography (CT) scans in medicine is the primary reason for such a large contribution, as shown in Fig 2-1. Note that radiation therapy does not contribute significantly enough to be included in medical exposure categories.
This is a surprising result because radiation therapy produces the greatest amount of dose of any other medical modality by far. In addition to patients, radiation
6 Figure 2-1: Chart from NCRP Report 160 demonstrating the relative con- tributions from different sources of radiation exposure for the United States population [69]. All sources have been rounded to the nearest 1% unless the quantity was negligible. The total exposure from all sources of radiation is 6.2 mSv.
therapy is a highly team-oriented discipline, requiring doctors, nurses, physicists, dosimetrists, therapists, and administrators that all work within close proximity to a highly energetic source of radiation.
There are many reasons the exposure from radiation therapy is so low. Radiation therapy facilities are extensively regulated because of the high risk involved with high- energy radiation. As a result, shielding protections need to be sufficient to reduce radiation exposure to the staff and to the public to an acceptable level. Regulations define several quantities and groups, such as who are considered radiation workers and who are members of the public, which areas are considered controlled and un- controlled, and what is an acceptable level of radiation for all of these respective 7 categories based on relative risks and personnel education. There are additional def- initions specific to external beam radiation, namely primary and secondary barriers, leakage, scattered and primary radiation, occupation and use factors, and the total machine workload. How these definitions evolved, and the role they play for modern radiotherapy shielding is explored in more detail in this section.
2.1 Radiation Units
No discussion of radiation protection and shielding is complete without a thorough discussion on the language and units used in discussing radiation protection. Both traditional units and SI units will be discussed and defined here, but the remainder of this dissertation will use only SI units. The essential quantities discussed in radia- tion protection are exposure, dose, equivalent dose, effective dose, and ambient dose equivalent.
In order to quantify these units accurately, we need to consider how radiation ionizes material. The interaction of radiation with matter creates ion pairs consisting of a positively charged ion and a free electron, typically with a great deal of residual energy [43]. Some or all of this residual energy is imparted to the electron from the ion pair, causing the electron to travel some distance from where it was generated. If enough electrons are able to move far enough away from their original positions, we have a difficult time measuring the amount of energy deposited or charge created. To accurately assess this, we impose the condition that for a given volume, the number of incoming electrons must be equal to the number of electrons departing the volume.
This condition is known as charged particle equilibrium (CPE) [37]. Oftentimes this strict theoretical definition cannot be met in practice. For a directed source of radiation, we can impose a weaker condition requiring that the number of upstream electrons entering a volume must be equal to the number of downstream electrons
8 exiting the volume. This is known as transient charged particle equilibrium (TCPE)
[37].
2.1.1 Exposure
Exposure is the original unit of radiation measurement [74]. Exposure is measured
in-air and is a measurement of the amount of a single polarization of charge produced
by ionization per unit mass. The traditional unit of exposure is the R¨ontgen (R). The
SI unit is Coulombs per kilogram [70]. The relation between the two units is given as
C 1R = 2.54 × 10−4 (2.1) kg
Because exposure is only defined in air, it becomes more difficult to quantify exposure as radiation energies increase. To suitably characterize a source of ionizing radiation, one must have a large enough column density in the detector to create conditions for transient charged particle equilibrium. To do this in air for energies
>3 MeV becomes inaccurate as the detector size becomes prohibitively large [37].
2.1.2 Dose
Radiation dose is the fundamental unit for therapeutic radiation physics. As the name suggests, this quantity was driven by the need to better quantify the medical application of radiation. Dose is defined as the energy delivered per unit mass. The traditional unit of dose was the rad, defined as 100 ergs delivered to 1 gram of matter.
The modern SI unit is the Gray (Gy), defined as 1 Joule delivered to 1 kilogram of matter [70]. One Gy is equal to 100 rads. The unit of dose is purely a physical quantity, meaning that one Gy from x-rays is equal to one Gy from proton radiation to one Gy from neutrons. However, these differing forms of radiation produce different biological effects for a given amount of energy deposited.
9 Radiation Type Weighting Factor Gamma & X-rays 1 Electrons, Positrons, Muons 1 Protons (E > 2 MeV) 2 α-particles 20 Neutrons 2 − [ln(En)] En < 1 MeV 2.5 + 18.0 exp 6 2 − [ln(2En)] 1 MeV < En < 50 MeV 5.0 + 17.0 exp 6 2 − [ln(0.04En)] En > 50 MeV 2.5 + 3.25 exp 6 Table 2.1: Weighting factors for different forms of radiation based on the most recent figures from the International Commission on Radio- logical Protection (ICRP) Publication 103 [72]. The major change between this and previous weighting factor estimates is the mod- ification to make neutron weighting factors a continuous function of energy.
2.1.3 Equivalent Dose
Equivalent dose is an attempt to account for the relative biological effectiveness
(RBE) of different types of radiation on tissue. This is accomplished by multiplying the delivered dose by a unit-less weighting factor based on the type of radiation. The amount of energy deposited per unit mass is unchanged from dose. The traditional unit of equivalent dose is the rem and the SI unit is the Sievert (Sv) [72]. One Sv is equal to 100 rem. Calculations for equivalent dose should follow the form,
X HT = QiDi (2.2) i where HT is the total equivalent dose, Qi represents the weighting factor, and Di is the dose contribution from that type of radiation. Table 2.1 lists accepted weighting factors for different types of radiation [72]. En in Table 2.1 refers to the energy of the neutrons depositing dose, as the linear energy transfer of neutrons is strongly energy dependent, as is shown in Figure 2-2.
10 Figure 2-2: Radiation weighting factor, Qi, for neutrons as a function of en- ergy. Reproduced from ICRP Publication 103 [72]
2.1.4 Effective Dose
Effective dose was introduced as a method for statistical interpretation of relative radiation exposure risks. It converts all forms of one-time radiation exposure to a comparable unit, such that the relative risk of a simple hand x-ray can be compared to a interventional CT procedure. To accomplish this, we again introduce a unit-less weighting factor, but this is weighted based on the relative risk of exposing different areas of the body. Unlike the radiation weighting factor for equivalent dose, which has a biologic basis, the weighting factor for effective dose is a statistical estimate of the relative risk from exposing different body parts. Different body parts are given higher or lower weights based on the relative impact of irradiating those organs. As before, the fundamental quantities are identical to dose, the traditional unit is the rem, and the SI unit is Sv [72]. Effective doses should be calculated using the equation,
11 Body Tissue Weighting Factor Bone Surface, Skin, Brain, Salivary 0.01 Glands Bladder, Liver, Esophagus, Thyroid 0.04 Gonads 0.08 Bone Marrow, Lung, Colon, Stomach, 0.12 Breast, Remainder
Table 2.2: Weighting factors for different body parts to be used in calcula- tions of effective dose. A whole-body uniform exposure requires no weighting factor as the sum of all weighting factors is 1. Weighting factors shown are from ICRP 103 [72]
X HT = wiQjDi (2.3) ij where wi is the weighting factor for the body part, Qj is the quality factor for the radiation type, and Di is the dose delivered to that body part. Table 2.2 lists the weighting factors for different body parts. Note that a whole body exposure would have an effective weighting factor of one.
2.1.5 Ambient Dose Equivalent
Ambient dose equivalent combines the concepts of dose and equivalent dose for common health physics and radiation protection applications. Conceptually, ambient dose equivalent is assuming the deep-dose equivalent of a spatially uniform radiation
field of various qualities. Rather than reporting that someone may be exposed to
X Gy of photon radiation and Y Gy of neutron radiation, we can report that they received an ambient dose equivalent of Z Sv. Ambient dose equivalent is defined in
ICRP Publication 74 as the dose equivalent at the center of a 10 cm sphere of water in a uniform field of parallel rays of radiation [71]. Despite this definition rarely existing in practice, ambient dose equivalent is a useful quantity for Monte Carlo calculations
12 of relative radiation exposures. Ambient dose equivalent is represented in Sv.
2.2 Dose Limits for Radiation Protection
Many people are familiar with the existence of acute radiation syndromes caused by large amounts of exposure over a short period of time [18, 28]. Obviously, efforts to eliminate these types of exposures are of critical importance in todays society.
Radiation is also a powerful carcinogen, causing damage to DNA that can result in cancer. This can be caused by low exposures to radiation over a prolonged period of time [?,28]. However, some exposure is a necessary risk. Medical use of radiation have greatly benefited our ability to diagnose and heal patients, such as fluoroscopically- guided stent placements or radiation therapy for local control of malignancy. The random nature of radiation mutations and carcinogenesis suggests that most people exposed to some small level of extra radiation will note no ill effects. We can estimate the likely risk increase for the development of cancer using data from population stud- ies, such as those exposed in nuclear accidents or from the atomic bombs. The current estimate from ICRP Publication 103 states that the relative chance of developing a malignancy from whole body radiation exposure is approximately 5.7% per Sv [72].
Regulatory and advisory bodies must attempt to balance the relative risk increases from increased exposure to the public with the benefit of exposure. There is also the additional concern of what is an acceptable dose limit for workers in a nuclear or radiation-based industry, who willingly participate and work in potentially high radiation environments. What constitutes an acceptable amount of radiation risk for individuals who are passersby and for those who purposefully devote themselves to earning a living dealing with radiation and radioactivity?
In the United States, these decisions are handled by the Nuclear Regulatory Com- mission (NRC) for exposures involving radionuclides, or on a state-by-state basis in
13 agreement states, such as Ohio. An agreement state is one in which the NRC has agreed with the state government to delegate the authority to regulate radionuclides to the state government [16]. Public exposure limits are set on a state-by-state ba- sis for radiation-generating equipment (RGE), such as x-ray tubes or medical linear accelerators. Most states have followed the NRC regulation and set the safe effec- tive dose limit to 50 mSv per year for occupational workers and 1 mSv per year to members of the public [65]. There are further stipulations on this for shallow and lens dose equivalent, ingested and inhaled amounts of radionuclides, etc. However in radiation therapy we are dealing with highly penetrating radiation dispersed over a relatively large area by scattering processes, so these further limits are usually not relevant. Although the occupational limit is set to 50 mSv per year, there is a sep- arate radiation dose limit to a fetus of 5 mSv per year, which effectively limits the acceptable dose for a pregnant radiation worker to the fetal dose limit. To allow for pregnant workers to continue their duties uninterrupted, medical facility design goals are typically an order of magnitude less than the occupational dose limit [68]. While this is a common practice, it is not a legal requirement.
Those qualifying for occupational dose limits have their radiation exposure mon- itored by the Radiation Safety Officer (RSO) of their institution and have received special training concerning the risk from exposure to radiation. These individuals can be radiation therapists, radiation oncologists, physicists, dosimetrists, nurses, ad- ministrative staff, housekeepers, etc. Members of the public include everyone else, individuals who do not have special training or monitoring of their exposure to radi- ation and have no expectation of receiving an unusually high dose because of their presence in a high-radiation environment. Medical staff from other areas of the same institution are also considered members of the public, so adjacent departments need to be adequately shielded for public exposure limits.
14 2.2.1 Time-Average Dose Rate Limits
While the standard dose limits are cited in terms of mSv per year, it is unreason- able to ignore the maximum amount of dose a bystander could be exposed to over the course of a week and the course of an hour. This has led to the concept of the
Time-Average Dose Rate (TADR). The main consideration is that someone should not receive their weekly or annual exposure limit if they were to spend an unusual amount of time in a thought-to-be low occupancy area. These considerations only ap- ply to uncontrolled areas, where access isn’t controlled, and can be used to determine the adequacy of a shielding barrier, as in the weekly TADR case, or to determine compliance with NRC requirements, as in the hourly TADR.
The dose equivalent in-any-one-hour is going to be proportional to the instan- taneous dose rate behind a barrier for a given workload and use factor while the machine is operating at its peak output. It will also be proportional to the maximum number of patients that can be treated in one hour. Considering set-up, imaging, and break-down to be included in a patient’s treatment, a very brisk pace of 10 patients in one hour is likely the maximum feasible for an experienced group of therapists [68].
Currently, our group of experienced therapists at the Dana Cancer Center (DCC) is operating at approximately 4 patients per hour. The maximum dose allowed in-any- one-hour is 0.02 mSv [65]. The maximum hourly dose rate for a machine, Rh, can be calculated by Eqn 2.4.
Nm Rh = Rw (2.4) Nh
Nm and Nh are the maximum number of patients in an hour and the average number of patients an hour, respectively, and Rw is the dose contribution per patient. This needs to be less than 0.02 mSv per hour for uncontrolled areas.
15 2.3 Radiation Interactions with Matter and Expo-
nential Attenuation
2.3.1 Radiation Interactions with Matter
Ionizing radiation interacts with matter primarily through three processes: the photoelectric effect, Compton scattering, and pair/triplet production [37, 43]. Other processes, such as Rayleigh (coherent) scattering, or photonuclear interactions, con- stitute a small fraction of the interactions relative to these three processes. The relative prominence of these three interactions is shown in Figure 2-3 as a function of atomic number (Z) and photon energy. For materials with a Zeff < 20, Compton scattering dominates the interactions of photons between 0.1 MeV to 10 MeV. This applies for both tissue and standard density concrete [3, 4, 8, 50, 53]. The amount of interaction from each process can be quantified through the use of a linear attenu- ation coefficient, which measures the relative decrease in intensity per unit length.
Linear attenuation coefficients are commonly divided by the density of the material to produce mass attenuation coefficients, as these demonstrate a much smaller variation between materials in the megavoltage range [37]. This also leads to thicknesses being quoted in density thickness, or mass area, which is the physical thickness multiplied by the density.
2.3.1.1 Photoelectric Absorption
The photoelectric absorption happens when a bound electron absorbs a photon with enough energy to liberate the electron from its potential well. The photon is absorbed, and the electron exits the orbital with an energy equal to the energy of the incident photon minus the energy required to liberate the electron from the atom. This interaction is more common in the diagnostic energy ranges (< 100 keV)
16 Figure 2-3: Relative importance between the photoelectric effect, Compton scattering, and pair/triplet production as a function of atomic number (Z) and incident photon energy.
and is primarily responsible for the increased contrast of diagnostic images relative
to megavoltage imaging [37]. Atomic number and photon energy dependence of the
photoelectric linear attenuation coefficient, σpe, for low energies is shown by Equation 2.5 [30].
Z4 σpe ∝ (2.5) (hν)3
The photoelectric mass attenuation coefficient, σpe/ρ, then must be proportional to Z3/ (hν)3. Therefore, high-Z material has a distinct advantage in blocking lower- energy radiation (< 100 keV) because of the Z3 dependence of the mass attenuation
coefficient. It is important to note that the energy dependence only applies once
the incident photon has exceeded the binding energy of the electron. If the incident
photon is of lower energy than the binding potential, or work function φ, of the
17 electron, then photon will not be absorbed at that energy level. This leads to a jagged appearance in the attenuation coefficients at energies below the K-shell binding energy [30].
2.3.1.2 Compton Scatter
Compton scattering is the dominant interaction for photons in the range of ener- gies between 0.1 MeV to 10 MeV, the most common photon energies used in radiation therapy. Compton scattering is a process where an incident photon transfers some of its momentum and energy to a loosely-bound electron. The best description of this process is presented by Klein and Nishina [30, 37, 44]. One important feature of this theory is that the electron undergoing the interaction is assumed to be unbound, a condition rarely realized. Still, the theory of Klein and Nishina closely matches exper- imental results because of the very high energy of the photons undergoing this process relative to the binding energy of electrons. Because Compton scattering only involves loosely-bound electrons, the likelihood of Compton scattering within a material is de- pendent on the electron density (ρe). Electron density roughly scales proportionally with Z. Because of this, the linear attenuation coefficient, τComp is proportional to Z, as shown in Equation 2.6.
τComp ∝ Z (2.6)
The mass attenuation coefficient, τComp/ρ, is roughly independent of Z. Therefore, for a given density thickness, we should expect to see roughly the same attenuation regardless of what material the slab is composed of.
18 2.3.1.3 Pair/Triplet Production
Photons with energies above a threshold energy can interact with a strong elec- tric field to undergo pair production, turning a photon into an electron-positron pair [34, 37]. This threshold energy is equal to twice the rest mass of an electron, ,
2me. Any energy remaining from the initial photon is transferred into kinetic energy of the resulting particles. Pair production near an atomic nucleus introduces a Z2 de- pendence to the attenuation coefficient, κpair. Triplet production, which occurs near an orbital electron, is only proportionally dependent on Z, and is much less prominent an interaction than pair production because of the reduced electric fields [34].
The range of the positron is limited, as it will eventually combine with another electron and create two annihilation photons, each with energies of me. This process is utilized in medical imaging for positron emission tomography (PET). This process becomes important in radiation protection for high-energy bremsstrahlung beams, where appreciable fractions of the energy spectrum are above the threshold energy.
Also of note is that the energy of these annihilation photons is very similar to the end energy of high-angle Compton scattered photons, meaning that the needed thickness of material to attenuate these photons should not be significantly different from what is needed to attenuate Compton scattered photons [34,43].
2.3.2 Attenuation Coefficients
Photon interactions with matter will attenuate a source of radiation. How much attenuation is produced per unit length of a material is quantified by the linear attenuation coefficient. The total mass attenuation coefficient, µ/ρ, for a material can be calculated as the sum of the cross-sections for each of the interaction modalities, as shown in Equation 2.7.
19 µ σ τ κ = pe + Comp + pair (2.7) ρ ρ ρ ρ
Each component will have a small variation between the amount of attenuation and the amount of energy imparted to the material. This arises because the sec- ondary charged particles have a range and the fact that not all attenuated radiation is absorbed. The amount of energy imparted is the mass energy transfer coefficient,
µtr. For shielding measurements, we are mostly interested in the mass attenuation coefficient, but the mass energy transfer coefficient will determine the amount of dose we will measure beyond a barrier.
2.3.3 Exponential Attenuation
The mass attenuation coefficient determines how much of the intensity is attenu- ated, dI, per unit length, dl. This leads to the differential equation,
µ dI = I ρ · dl (2.8) ρ
The solution to this differential equation when integrated over a total thickness, t, is an exponential, as shown in Equation 2.9.
−( µ )ρ·t I (t) = I0e ρ (2.9)
This relationship holds for a well defined beam, where no scattered particles can reach the detector. This is often referred to as a narrow beam geometry. In reality, a narrow beam geometry is very hard to achieve. In radiotherapy applications, we rarely have a good geometry, particularly when considering shielding applications.
Instead, we operate in a broad beam geometry, where scattered particles contribute to our measured signal, increasing the necessary thickness needed to achieve equivalent attenuation. This has led to the implementation of build-up factors. Build-up factors
20 Figure 2-4: Illustration of particle paths and detector contributions for narrow-beam and survey-style measurements.
account for the deviation in attenuation of a real beam from perfect exponential behavior. These build-up factors are generally greater than 1, as radiation that is scattered within the primary beam is then re-scattered towards the detector. This is illustrated in Figure 2-4.
The use of build-up factors as a method to calculate dose beyond a shielded barrier becomes very complicated, as build-up factors are dependent on radiation energy, shield thickness, shield material, beam size, and detector distance [39]. Most shielding recommendations do not include the use of build-up factors because of these complications, and instead prefer to recommend half or tenth value layer thicknesses, which will be discussed in Section 3.1.
21 Chapter 3
NCRP Report 151
The main guiding document for radiation physicists on shielding megavoltage ra- diotherapy facilities is NCRP Report 151,“Structural Shielding Design and Evaluation for Megavoltage X- And Gamma-Ray Radiotherapy Facilities” [68]. This document is a comprehensive review of the basics of shielding principles and an update from the previous guidelines for radiotherapy facility shielding. The previous report, NCRP
Report 51, was published in 1977 before the advent of many widely employed modali- ties, such as IMRT and SRS, that create higher shielding requirements. The addition of higher accelerating potentials and the use of small-field radiation therapy requir- ing more use of the accelerator were two of the motivating factors for the updated report [68]. The majority of the information presented within this chapter is directly referenced from NCRP Report 151, as the methods presented are directly relevant to subsequent chapters.
3.1 Primary and Secondary Barriers
Radiotherapy vaults have two types of barriers: primary barriers, and secondary barriers. Primary barriers are those walls directly in the path of the beam when opened to its fullest extent. Secondary barriers need only be designed to shield the radiation workload produced by head leakage and patient-scattered radiation 22 and should cover the remainder of the room not shielded by primary barriers. The majority of modern linear accelerators are of the C-arm design, making primary barriers any wall that lies along the rotational plane. However, there are certain machines such as the Cyberknife, a 6-MV linear accelerator mounted on a robotic arm, where every wall is a potential primary barrier. The difference between primary and secondary barriers is illustrated in Figure 3-1.
Figure 3-1: Figure from NCRP 151 demonstrating the difference between primary and secondary barriers [68].
Primary barriers need to be wide enough such that any errors in the location of the machine isocenter during installation will still result in adequate primary shielding over the breadth of the useful beam. The primary barriers should also be wide enough to encompass any low angle scatter (< 20◦) from the patient. To accomplish this,
NCRP 151 recommends that primary barrier widths be the required width for the useful beam plus 30 cm on either side. This is shown in Figure 3-2. The barrier width should be calculated to the most distal side of the primary barrier.
These barriers can be made of many different materials, each offering their own 23 Figure 3-2: Figure from NCRP 151 demonstrating how to calculate the width of the primary barriers [68].
advantages. Concrete is typically chosen as it is the most cost-effective, but comes at
the cost of requiring a significant amount of space. The typical primary barrier made
of standard density concrete (2.35 g/cc, ∼ 147 lbs/ft3) is roughly 7 ft thick. Other materials can also be used, such as steel, lead, or landfill. Lead is a popular option for low-energy accelerators despite its price because of the space savings. Primary barriers can be shielded using 1-2 feet of lead instead of 7 ft of concrete. However, the space savings from using lead is countered by the need to add neutron shielding for beams with energies >6 MV. Lead is not only a poor neutron absorber but also an excellent material for photo-nuetron production ([γ, n] reaction). This means that shielding for high-energy beams cannot be lead alone, but requires extensive amounts of neutron absorbing material sandwiched between lead sheets. This is 24 typically borated polyethylene (BPE), which is chosen for its high hydrogen content and enhanced neutron cross-section with the addition of 5% by weight of boron.
Intermediate energy beams, such as 10 MV, can produce neutrons, as the threshold for production is ∼7 MeV in high-Z material, but the incidence is much lower as the majority of ionizing photons are well below this threshold [31]. Additionally, the cross-section for [γ, n] reactions in lead doesn’t become appreciable until beyond 10
MeV [29].
Shielding barrier thicknesses are typically calculated in terms of Tenth Value Lay- ers (TVL) and Half Value Layers (HVL). These are the necessary thicknesses to attenuate the radiation fluence to one tenth and one half, respectively, of its initial intensity. The relation between TVLs and HVLs is given in Equation 3.1.
# of HVLs = log2 (# of TVLs) (3.1)
TVLs and HVLs are energy and material dependent, making calculations more com- plicated for dual-energy accelerators [7]. Additionally, the beam characteristics may change after the first tenth value layer resulting in energy-degradation. Thus, TVLs can change based on the total thickness of the barrier (ie, there can be TVL1 &
TVL2, etc). NCRP 151 has recommended TVLs for standard density concrete, steel, and lead at different nominal accelerating potentials (NAP). These are reproduced for the energies relevant to the linear accelerators available at the University of Toledo in Table 3.1.
3.2 Occupancy Factors
The need to shield an area such as the control console, where someone will always be when the machine is in operation, is much higher than the need to shield a closet full of QA equipment. To account for these different shielding needs, we utilize an
25 NAP → 6 MV 10 MV 18 MV
Material TVL1 TVL2 TVL1 TVL2 TVL1 TVL2 (cm) (cm) (cm) (cm) (cm) (cm) Concrete 36 34 41 37 45 43 Steel 10 10 11 11 11 11 Lead 5.7 5.7 5.7 5.7 5.7 5.7
Table 3.1: NCRP 151 recommended TVLs in various materials for the nom- inal accelerating potentials available on the Varian Truebeam. TVL1 should be used for the first thickness of the barrier and subsequent thickness should use TVL2.
occupancy factor, T. This is intended to put more emphasis on occupied areas such as offices, exam rooms, and control areas and allow a moderately higher average dose in areas such as hallways, parking lots, and storage rooms. NCRP 151 has recommended occupancy factors for basic types of rooms, but these assessments need to be ratified by the qualified medical physicist before final shielding calculations can be submitted.
If an area doesn’t have a recommended occupancy factor, one can be estimated by taking the expected number of hours the space will be occupied during the week and dividing by the number of hours the machine will be treating, typically 40 hrs per week. Table 3.2 lists the recommended occupancy factors from NCRP 151.
Care must be taken to properly apply occupancy factors. For example, if there is a corridor directly adjacent to a treatment vault then it would be logical to apply the occupancy factor for a corridor. However, if there are clerical offices on the opposite side of the corridor and the added distance of the corridor is not sufficient to decrease the dose rate to within allowable levels for public exposure, then one must shield for the room with the higher occupancy factor.
26 Area Occupancy Factor Full occupancy areas, e.g. clerical offices, treatment planning 1 areas, treatment control rooms, nurse stations, attended waiting rooms, etc Adjacent treatment room, patient exam room 1/2 Corridors, lounges, staff restrooms 1/5 Treatment vault doors 1/8 Public restrooms, storage areas, unattended waiting rooms, at- 1/20 tics, etc Outdoor areas with transient occupancy, e.g. parking lots 1/40
Table 3.2: Occupancy factors suggested in Appendix B., Table B.1 of NCRP Report 151 [68].
3.3 Use Factors
Because linear accelerators are not isotropic sources, only a fraction of the total radiation workload is directed towards a specific primary barrier at a given time. To account for this, we apply a use factor, U. Use factors are only applicable for primary barriers and for some fraction of patient scatter, as any time the beam is on, secondary scatter and head leakage will always be incident on their respective barriers. Tradi- tional methods of radiation therapy utilized very simple field arrangements, such as direct anterior-to-posterior (AP) and posterior-to-anterior (PA) fields, or a four-field box, making use factors roughly equal on all primary barriers. While these tech- niques still are in use, the rise in use of IMRT and volumetric modulated arc therapy
(VMAT) can complicate the calculation of use factors. A simplifying approximation takes advantage of symmetry of these style treatments. IMRT plans are typically rotationally symmetric in their beam arrangement (although their dose weighting may not be) and VMAT plans are intrinsically so. Despite the beam weighting not necessarily being uniform, over the average of several patients we can expect that the relative weight from symmetric beam arrangements will be symmetric [79].
27 3.4 Accelerator Workload
The accelerator workload is a measure of the amount of radiation the accelerator produces in a given time period. This has two uses–it determines the dose delivered to the primary barriers by specifying the dose delivered to isocenter, and it determines the amount of head leakage and patient scatter produced. Since photon attenuation is dependent on the average energy, shielding calculations need to be designed to account for the multiple photon energies available on a modern accelerator. This starts with the workload. Workload calculations can be broken into three different categories: primary workload, leakage workload, and patient scattered workload.
NCRP 151 also recommends further categorization of workload to account for the dose produced by the physicists quality assurance (QA) measurements, but this dose does not follow the typical patterns of standard radiation therapy. The majority of QA is done with the gantry pointed at the floor and after-hours, so the majority of clinical staff are not exposed to the additional workload. The dominant head-up direction of QA measurements is taken into account by NCRP 151 by utilizing workload-use factor products, but the reduction in the occupancy factors of the adjacent areas is not.
3.4.1 Primary Workload
The primary workload is a straight-forward calculation. The simplest method is to take the maximum expected patients per day and multiply that by the average dose per fraction, assuming that all patients are receiving treatments at the highest and most penetrating energy. A more nuanced method is to weight the primary workload based on the fraction of patients receiving radiation at different energies [7]. The fraction of patients receiving IMRT does not impact the total primary workload as the same amount of dose is delivered to isocenter as with conventional radiotherapy.
28 The doses delivered for SRS and SBRT patients need to be properly evaluated to ensure an accurate workload estimate, as SRS and SBRT deliver doses 5 to 50 times greater than one fraction of conventional radiotherapy. The primary workload can be calculated in Equation 3.2.
X Wprimary = wX PdDp (3.2) W,Mod
Here, the summation is over energy and modality, wX is the fraction of patients treated using energy X, Pd is the maximum number of patients per day, and Dp is the dose per patient for each modality.
3.4.2 Leakage Workload
Head leakage is extraneous radiation produced by interactions inside the accelera- tor head as scatter from the primary collimator, off-kilt electrons striking accelerator components, and x-rays produced when bending the electron beam. This radiation is assumed to be of comparable quality to that of the primary beam and relatively isotropic. Manufacturers are required by law to keep this source of secondary radia- tion to <0.1% of the dose delivered to isocenter. Before the development of IMRT, it was a reasonable assumption to simply take the expected primary workload and multiply by 10−3.
With the advent of IMRT, the machine needs to produce a greater number of mon- itor units (MU), a measure of the radiation production for the machine, to produce a given dose at isocenter. Thus, the assumption that the leakage workload is simply
10−3 times the primary workload is no longer valid. This has led to the introduction of an IMRT modulation factor to be included in calculation of the secondary work- load. This modulation factor, MIMRT can be calculated as the average number of
MU needed to deliver an IMRT treatment, MUIMRT , divided by the average number
29 of MU needed to deliver a standard 3D treatment for a given dose, MU3D. This is shown in Equation 3.3.
MUIMRT MIMRT = (3.3) MU3D
This modulation factor only applies to the fraction of patients that are expected to receive IMRT, so the leakage workload calculation appears more complicated than the primary workload calculation. The formula to properly calculate the leakage workload, WL, for an IMRT machine is shown in Equation 3.4,
−3 X −3 X WL = 10 wX PdDp(1 − FIMRT ) + 10 wX PdDpFIMRT MIMRT (3.4) X,Mod X,Mod
where FIMRT is the fraction of patients at a given energy using IMRT.
3.4.3 Patient-Scatter Workload
Another effect shielding calculations need to account for is scattered radiation originating from the patient. The patient’s body acts both as an attenuator and a scattering medium. For secondary barriers, the contribution from patient-scatter, particularly at low-obliquity, is significant and can even dominate over head-leakage.
The quality of patient-scattered radiation is dependent on the angle of scattering as radiation scattered at 90◦ is significantly less penetrating than radiation scattered at 20◦. As the dominant interaction for radiation in the low megavoltage range (1-
10 MeV) is Compton scattering, predictive measures can be made to estimate the necessary thickness of concrete to constitute one TVL. Only a fraction of the incident radiation is scattered towards each angle. A scattering function, ax (θ), is presented in NCRP 151, along with corresponding TVLs of concrete for patient scattered radiation.
This is reproduced in Table 3.3.
30 NAP → 6 MV 10 MV 18 MV Scattering a(θ) TVL a(θ) TVL a(θ) TVL Angle (◦) (cm) (cm) (cm) 10 1.04 ×10−2 1.66 ×10−2 1.42 ×10−2 20 6.73 ×10−3 34 5.79 ×10−3 39 5.39 ×10−3 44 30 2.77 ×10−3 26 3.18 ×10−3 28 2.53 ×10−3 32 45 1.39 ×10−3 26 1.35 ×10−3 25 8.64 ×10−4 27 60 8.24 ×10−4 21 7.46 ×10−4 22 4.24 ×10−4 23 90 4.26 ×10−4 17 3.81 ×10−4 18 1.89 ×10−4 19 135 3.00 ×10−4 15 3.02 ×10−4 15 1.24 ×10−4 15 150 2.87 ×10−4 2.74 ×10−4 1.20 ×10−4
Table 3.3: Patient-Scatter Fractions, a(θ), and their respective TVLs in con- crete as recommended by NCRP 151. [68].
The patient-scatter workload can be calculated by Equation 3.5. F in Equation
3.5 is the maximum field size in cm2 for the machine. The majority of modern
accelerators can produce a maximum field size of 40 cm x 40 cm, meaning F is 1600 cm2.
X F W = w P D a (θ) (3.5) PS x d p x 400 x
3.5 Determining Barrier Thicknesses
Determining the necessary barrier thickness is the ultimate goal of any shielding
calculation. Again, the rigor of the calculation varies based on whether the barrier is
a primary or secondary barrier. The goal is to calculate the expected dose rate at the
point to be shielded, determine what the attenuation factor needs to be to reduce the
dose rate to safe levels, and then determine the number of TVLs necessary to achieve
that attenuation.
The calculation for the necessary attenuation factor for a primary barrier is given
in Equation 3.6, 31 W UT A = p (3.6) d2H where A is the attenuation factor, U is the use factor, T is the occupancy factor, d is the distance from the radiation source (not isocenter) to the shielded point, and H is the dose limit for that area. The number of TVLs needed to produce that attenuation is determined by taking the logarithm of the attenuation factor in base 10, as shown in Equation 3.7
# of TVLs = log10 (A) (3.7)
For primary barriers, we normally can assume that the contribution from sec- ondary radiations when the beam is not directed at the barrier is negligible. For example, if a barrier is shielded using 5 TVLs for primary radiation workload, when the beam is directed at 90◦ from the barrier, it is exposed to head leakage and patient scatter. The head leakage is of comparable quality to the primary radiation, but a factor of 1000 less. The patient scatter dose is also significantly lower (a (θ) ∼ 10−4 at 90◦) and the quality of radiation is much lower. Therefore, if the wall is able to properly attenuate a workload, Wp, it should be able to attenuate the secondary workload, Ws by,
W W ∗ 10−3 + W ∗ 10−4 s ∼ p p Wp Wp W s ∼10−3 Wp
This fraction should be small enough to safely be ignored.
To determine the shielding adequacy for secondary barriers, we need to consider that secondary radiations come from two sources, head leakage and patient scatter.
32 We need to determine if one source is dominant over the other, or if the barrier needs to be thicker than the contribution from either. The calculation for the needed attenuation for head leakage, AL, is given by Equation 3.8,
WLT AL = 2 (3.8) dLH where dL is now the distance from isocenter to the desired shielding point if the accelerator usage is symmetric about the isocenter. If it is not, then this distance should be the distance from the radiation source to the desired shielding location.
Note that there is also no use factor applied in this equation, as leakage radiation will be present whenever the machine is in operation.
The necessary attenuation for patient scattered radiation, APS, is given in Equa- tion 3.9,
WPST APS = 2 2 (3.9) dscadsecH where dsca is the distance from the radiation source to the patient and dsec is the distance from the patient to the shielding point. This equation also does not have a use factor, despite patient scattered radiation being strongly dependent on the direction of the radiation beam. The justification from NCRP 151 is that the assumption of
1 for the highest usage will make the barriers thicker, and thus more conservatively safe.
To determine the necessary thickness of the secondary barrier, we need to compute the thickness needed to attenuate each source (head leakage and patient scatter) separately, using the same process as in Equation 3.7. We then must calculate if the dose transmission through the barrier will be similar for both sources. If one source requires a thickness more than one TVL greater than the other source, the larger thickness is used. If the two thicknesses are within one TVL of each other, we assume
33 Figure 3-3: Flowchart depiction of the method for determining secondary barrier thickness following the two source rule [68].
that the area in question is being irradiated by two sources and will need the dose rate from each to be reduced by half. Thus, we add one HVL to the larger of the two thicknesses to appropriately shield the barrier. This is known as the two-source rule.
A decision flowchart is provided in Figure 3-3 to demonstrate how to determine the needed thickness of the secondary barrier.
3.6 Door Shielding
Shielding the door of a radiotherapy vault is a very complicated calculation. It is of special importance as it protects the personnel who operate the machine and thus have the highest likelihood of exposure from the machine’s radiation. Door shielding must be adequate to stop photons, neutrons, and gamma-capture photons generated by thermalized neutrons being recaptured within the door shielding. To complicate this, not all of the parameters fundamental to door shielding are agreed upon. For example, there are two methods to calculate neutron fluence attenuation over the length of the maze, the Kersey method and the modified Kersey method, both presented in NCRP
151 [42, 68, 96]. NCRP 151 does not take a firm stand distinguishing between which method is appropriate for the true neutron dose equivalent at the maze door and
34 suggests taking an average of the two results as the safest conservative estimate.
The most common material used for photon shielding in vault door design is lead.
This quickly accumulates a significant mass in the door, amplifying the engineering challenge. Minimizing the amount of photon shielding necessary is an important as- pect of vault design to minimize the wear and tear on the door opening mechanisms over time. Neutron shielding, on the other hand, is usually made of high-density polyethylene (HDPE) or borated polyethylene (BPE) which is very light in compari- son. The large fraction of hydrogen and large neutron-capture cross-section of boron make these materials ideal for thermalizing fast neutrons and capturing them before penetrating the shielded barrier. BPE is very expensive and a poor attenuator of photons, therefore BPE should be placed to the inside of the vault or sandwiched between the lead shielding to ensure adequate shielding for capture gamma photons.
3.6.1 Photon Dose-Equivalent at the Door
For low-energy machines (≤10 MV maximum photon beam energy), the majority of the photon dose-equivalent comes from multiple scattering paths. While these con- tributions are present for all accelerators, multiply scattered photons are significantly less penetrating than capture gamma photons, making these contributions relatively insignificant for machines with photon energies capable of producing photo-neutrons.
Thus, the multiple scattered radiation dose-equivalents are only recommended as the shielding workload for machines where photo-neutron production is not possible or insignificant.
For high energy machines, we will need to calculate the dose-equivalent generated from capture gamma photons and the dose-equivalent incident from the remaining photo-neutrons. Because capture gamma photons are much more penetrating, and typically generate a higher dose-equivalent than the multiple scatter paths detailed for low-energy machines, NCRP 151 recommends only calculating the photon dose-
35 Figure 3-4: Illustration of the relevant geometry and quantities needed to calculate scattered photon radiation dose at the door of a vault with a maze. The maximum field size is included as dashed lines.
equivalent from capture gamma photons for machines capable of producing photon beams with energies >10 MV.
The generic vault with a maze given by NCRP 151, along with indications of the relevant quantities, is illustrated in Figure 3-4.
3.6.1.1 Photon Dose-Equivalent for Machines Producing ≤10 MV Photon
Beams
The photon dose-equivalent at the maze door comes from several components, namely primary beam scattered from room surfaces, patient-scattered primary again scattered from room surfaces, leakage scattered from room surfaces, and leakage trans- mission through the maze. These can be calculated according to Equations 3.10, 3.11,
36 3.12, and 3.13.
WpUGα0A0αzAz HWS = 2 2 2 (3.10) dhdt dz F Wpa (θ) UG 400 α1A1 HPS = 2 (3.11) (dscadsecdzz) WLUGα1A1 HLS = 2 (3.12) (dLSdzz) WLUGBmaze HLT = 2 (3.13) dL (3.14)
The subscripts WS, PS, LS, and LT refer to wall scatter, patient scatter, leakage
scatter, and leakage transmission respectively. Wp is the primary workload given by
Equation 3.2 and WL is the leakage workload as defined in Equation 3.4. UG is the use factor for Wall G as shown in Figure 3-4. α0, α1, and αz are the radiation dose albedos
for their respective walls and angles of incidence, while A0, A1, and Az are the areas of the respective scattering surfaces, as demonstrated in Figure 3-4. Radiation dose
albedo’s have been reproduced from NCRP 151 in Table 3.4. Bmaze is the attenuation factor of the maze. a (θ) is the patient scatter fractions given in Table 3.3. F is the
2 maximum field size in cm . dLS is the distance from the radiation source to Wall G
at a point along the door midline. dzz is the total length of the maze from the door
to the opposite wall. dsec is the distance from isocenter to the wall opposite the door
at the door midline. dL is the direct distance from the radiation source to the door
midline. dsca is the distance from the target to isocenter, typically 1 m. These all must take into consideration the distribution of workload per accelerating energy and
summed accordingly.
The inclusion of the use factor, UG, in the above equations implies we are only calculating the scattered dose reaching the door when the beam is pointed at Wall
37 θI 6 MV 10 MV 18 MV 0.5 MeV 0.25 MeV 0 5.3 ×10−3 4.3 ×10−3 3.4 ×10−3 1.9 ×10−2 3.2 ×10−2 30 5.2 ×10−3 4.1 ×10−3 3.4 ×10−3 1.7 ×10−2 2.8 ×10−2 45 4.7 ×10−3 3.8 ×10−3 3.0 ×10−3 1.5 ×10−2 2.5 ×10−2 60 4.0 ×10−3 3.1 ×10−3 2.5 ×10−3 1.3 ×10−2 2.2 ×10−2 75 2.7 ×10−3 2.1 ×10−3 1.6 ×10−3 8.0 ×10−3 1.3 ×10−2
Table 3.4: Differential dose albedos for bremstrahlung radiation at normal incidence presented in NCRP 151 [68].
G. We still need to account for the scattered dose reaching the door at all other beam angles. The approach recommended by NCRP 151 is to sum the total for the scattered doses with the radiation beam pointed at Wall G and multiply that by an empirically derived factor of 2.64. Thus the total photon dose at the door from these components over all beam angles should be,
HT otal,γ = 2.64 × (HLT + HPS + HLS + HWS) (3.15)
NCRP 151 recommends shielding thicknesses in accordance with an average pho- ton energy of 0.2 MeV provided that the dose-equivalent contributed from leakage transmission constitutes less than half of the total dose-equivalent at the door. If leakage transmission constitutes more than half of the total dose-equivalent, the av- erage energy of the incident radiation will be higher and will need to be shielded for the leakage energy.
3.6.1.2 Photon Dose-Equivalent for Machines Producing >10 MV Photon
Beams
The primary source of photon-dose equivalent for machines producing beams with energies >10 MV comes from photo-neutron capture. Photo-neutron capture happens when a neutron and an atomic nucleus interact. The nucleus absorbs the neutron,
38 Figure 3-5: Example vault to demonstrate the relevant geometry and quan- tities of interest to calculate capture gamma and neutron dose equivalent at the vault door. Reproduced from NCRP 151 [68]
and in the process emits a prompt gamma ray equal to the binding energy of the neutron [24, 90]. These capture gamma rays are very energetic, often between 3-11
MeV [24, 68, 90]. These require significant thicknesses of lead to attenuate. NCRP
151 recommends a 6.1 cm TVL of lead to attenuate capture gamma rays.
The relevant geometry and quantities necessary to calculate the capture gamma and neutron dose-equivalents incident on the door are presented in Figure 3-5.
We can calculate the neutron fluence, φA, inside the maze entrance, indicated by point A in Figure 3-5, as the sum of three components: direct neutrons, scattered neutrons, and thermalized neutrons. This is demonstrated in Equation 3.16
βQn 5.4βQn 1.3Qn φA = 2 + + (3.16) 4πd1 2πSr 2πSr 39 where β is the fraction of neutrons that are transmitted through the machine head
(β equals 1 for lead and 0.85 for tungsten). Qn is the neutron source strength, which is determined for each machine type and energy. d1 is the distance from isocenter to the closest visible point in the maze along the door midline. Sr is the total surface area of the room, excluding the maze.
The neutron fluence at point A can be converted into the capture gamma dose- equivalent at point A using the constant K, which has a value of 6.9 × 10−16 Sv m2
−1 MU . The capture gamma dose-equivalent at the maze door, Hcg, is then given by Equation 3.17,
− d2 Hcg = WLKφA10 TVD (3.17)
where d2 is the distance from point A to the door and TVD is the distance required to attenuated the photon dose-equivalent by a factor of 10.
3.6.2 Neutron Dose-Equivalent at the Maze Door
Calculating the neutron dose-equivalent is only important for high energy (>10
MV) machines, as energies below this threshold demonstrate negligible photo-neutron production. NCRP 151 recommends two different methods to calculate the neutron dose-equivalent at the door, the Kersey Method and the Modified Kersey Method.
Kersey originally proposed a method to calculate neutron dose equivalent in 1979 [42].
The neutron dose-equivalent, Hn,D, can be calculated as,
2 S0 d0 −( d2 ) Hn,D = H0 10 5 (3.18) S1 d1 where H0 is the neutron dose-equivalent produced at the reference point 1.41 m from the target per Gy of photon dose at isocenter. d0 is 1.41 m. S0 is the the area of the inner maze opening and S1 is the cross-sectional area of the maze itself. d2 is
40 the distance along the maze centerline to the door from the point where isocenter is just visible. These quantities are shown in Figure 3-5. This method assumes a Tenth
Value Distance (TVD) as the distance required to attenuate the neutron fluence by a factor of ten, of 5 m.
The Kersey method was reevaluated in the 1990s and found to have a wide range of accuracy [57]. This led to the development of the Modified Kersey Method in
2000 [60] and its subsequent modification in 2003 [96]. The Modified Kersey Method is given by,
r d d −15 S0 h −( 2 ) −( 2 )i Hn,D = 2.4 × 10 φA 1.64 × 10 1.9 + 10 TVD (3.19) S1 where φA is the same as defined in Equation 3.16. All other quantities are the same as described in the Kersey Method. One last difference is that the TVD is no longer √ a standard 5 m, but now should be calculated as TVD = 2.06 S1. NCRP 151 does not recommend one calculation over the other. In the worked out examples, NCRP 151 simply uses the larger value [68]. Many designers will average the two results, as it is expected that the Kersey method will overestimate the shielding workload [96].
41 Chapter 4
Monte Carlo Method
The Monte Carlo method for numeric solutions is a very powerful tool in radiation physics. Monte Carlo simulation is in essence a brute force solution, allowing physi- cists to simulate millions upon millions of stochastic interactions to arrive upon the likely result. Simulations require a knowledge of the relevant physics and probabil- ities involved. Without accurate assessment of these processes, Monte Carlo results can be incorrect without any indication. For these reasons, large codes developed by dedicated groups are the most widely used Monte Carlo programs within the med- ical physics community. These codes are Monte Carlo Neutron Photon (MCNP) from Los Alamos National Laboratory (LANL), Electron Gamma Shower (EGS) from the Canadian National Research Council (CNRC), Geometry And Tracking
(GEANT) maintained by an international consortium, and Penetration and Energy
Loss of Positrons and Electrons (PENELOPE), produced by the Nuclear Energy
Agency (NEA), part of the Organization for Economic Co-operation and Develop- ment (OECD) [1,41,61,80]. The physics capabilities, geometry flexibility, prevalence, and availability led us to utilize the MCNP code, version 5, for this project.
42 4.0.3 MCNP5
MCNP5 is maintained and benchmarked by the X-5 Monte Carlo Team at LANL
[61]. As indicated by the name, MCNP5 is capable of calculating neutron, photon, and electron transport, the latter being added in after the initial release. LANL provides a set of verified cross-section libraries in the ENDF-VI format for a variety of materials and interactions [91]. Coupled photon-neutron transport problems, such as those in high-energy radiation therapy vaults, are capable of being simulated with appropriate cross-section libraries being applied. Large numbers of histories allow these cross-sections and probabilities to be sampled repeatedly. Results from MCNP simulations are thus the statistical average of what would happen for a large number of interactions. This in turn requires MCNP results to be quoted with the appropriate statistical uncertainty, best understood as the precision of the simulation result. The statistical uncertainty will not reflect any potential sources of error induced by the mis-use of the modeling program, and thus MCNP results and simulations require careful benchmarking to verify their accuracy.
MCNP5 will take an input geometry consisting of a variety of surfaces and vol- umes that are assigned densities, cross-sections, and importances to create a virtual world to transport the given source and secondary particles. The program will then transport the specified source particles until they are either captured, fall below an energy or importance cut-off, escape, or are killed. Outputs from the program include summaries of the geometry, cell populations and collisions, mean-free paths within each cell, and any specified tallies. A tally is a way for the user to tabulate a pa- rameter of interest over a range of the simulation geometry. Tallies can be specified in areas of interest, modified with particular multipliers, or act as though they are tracking interactions through a specified material, which need not be entered into the geometry. MCNP has 6 built-in tally types: population, flux, fluence, path-length
43 Symbol Description Particle Types Std. Units Mod. Units F1 Surface Current N,P,E Counts MeV F2 Average Surface Flux N,P,E Counts cm−2 MeV cm−2 F4 Average Flux in a Cell N,P,E Counts cm−2 MeV cm−2 F5 Flux at a Point or Ring N,P Counts cm−2 MeV cm−2 F6 Energy Deposition per unit Mass N,P MeV g−1 jerks g−1 F7 Fission Energy Deposition N MeV g−1 jerks g−1 F8 Pulse Height Distribution P,E Pulses MeV
Table 4.1: Tally forms available in MCNP5 [61, 83]. There exists another modifier for the pulse height tally,“+F8”, which will report units of charge.
heating estimator, pulse-height, and a next-event estimation. Tallies are discussed in more depth in Section 4.0.4.
4.0.4 Tallies within MCNP
Tallies are the way that Monte Carlo results are tracked. MCNP represents tally cards with the leading character“f.” The available tallies within MCNP5 are presented in Table 4.1. Tallies can track multiple variables, including numbers of particles, energy deposition, flux, fluence, charge deposition, and heat transfer. Tally results are quoted as normalized per source particle. This means that each quoted tally result is the likely contribution to that location from each source particle. Often, the units for the output of each tally can be changed by the inclusion of a wildcard character preceding the“f” tag (e.g.,“*f6”). For most tallies, a particle is added when it passes through the surface or cell being tracked.
There is a special series of tallies that does not require the included particles to pass through the tally location. These are called next-event estimators or point detectors. A next-event estimator can be thought of as creating a virtual particle at every interaction. This virtual particle will include the potential contribution to the
44 tally, and is assigned an initial weight equal to the probability that the initial particle would be transported directly towards the point detector. The weight of this virtual particle is then adjusted by the likelihood of it successfully traversing the direct line of sight from the location of the interaction to the detector. This is similar to using an exponential transform to increase the number of counts at a certain location, but utilizing a lower weight per interaction. The effect of a next-event estimator is that it samples the likelihood of a result based on a total number of collisions rather than a total number of particles traversing the tally location [61]. In shielding problems, the total number of collisions tends to grossly outnumber the total number of particles that can pass through a barrier and be counted, making these a popular choice for shielding simulations.
To prevent unusually high variances introduced by high-weight interactions near the detector, an exclusion radius is applied around the detector. Interactions within this radius are not counted towards the final total for the detector. This exclusion radius should extend at least one half of a MFP and should not overlap multiple materials. Because of this, the detector should not be located within a strongly scattering medium. Instead, it should be placed within a void or a lightly scattering medium, such as air [27].
Tallies within MCNP5 can be multiplied by and manipulated by the user in several ways. One of the more useful methods for this project is the ability to only score histories or collisions that occur in particular cells within the geometry. This allows the user to track which regions within the simulation are contributing to the final tally results, as well as the relative importances of those regions to the total. While extremely useful to determine the extent that different cells contribute to the tally, the user needs to be careful to verify that they are not unwittingly excluding a region of importance to the final result.
Another useful feature with MCNP5 is the ability to multiply tally results by vari-
45 ous conversion factors. In medical physics, conversion factors from fluence-to-effective dose have been studied by the ICRP in Report 116 [73]. These conversion factors are energy and particle dependent. Factors exist for photons, electrons, neutrons, protons, pions, and heavy ions. Multiplier functions used to convert tallies to dose are indicated with the leading character“d”. These can be applied across all tallies or specified on a per tally basis.
Tally choice is an important decision to obtain accurate results from a Monte
Carlo simulation. There are three main methods for physicists to determine dose from computational simulations: use of a fluence tally and applying appropriate con- version factors, tracking energy deposition through a medium by primary particles (ie, photons), or direct tracking of secondary electron and photon energy deposition [27].
The choice of method depends highly on the details of the simulation in the area of the tally. The use of fluence-to-effective dose conversion factors is only valid when the scenario is equivalent to the setup for determination of the conversion factors.
A track length energy deposition estimate, used by F6 or F4 with multipliers, is only valid under CPE or TCPE [27]. This is frequently referred to as the air kerma approximation, where energy deposition in the medium is easily related to the dose deposited. For situations where CPE or TCPE does not exist, use of the *F8 tally to directly track secondary charged particles is necessary for an accurate assessment of dose. This method is necessary to obtain accurate megavoltage depth dose curves, as the range of secondary charged particles is great enough that TCPE does not ex- ist near the surface of a phantom. The drawback to this approach is that explicitly simulating electrons dramatically increases simulation runtime [83].
4.0.5 Variance Reduction Methods
Variance reduction refers to any methodology that is used to improve statistics for a given condition. With Monte Carlo techniques, this typically takes the form of
46 increasing the number of particles with a particular property (i.e. direction, energy, location, etc) while reducing the relative weight of the particle. This is referred to as splitting. When a tally is performed, instead of counting the raw tally number, it instead will count the raw tally multiplied by the particle weight. Other variations include killing particles that are likely insignificant to the final result so as to increase the speed of the computation. This is referred to as Russian roulette.
Weight windows and cell importances are two methods of particle splitting for given regions. Cell importances are exactly what they sound like - they rank the importance of a particle based on its location within the geometry. Cell importances can be individualized by particle type, but they cannot be based on particle energy.
When a particle moves from a lower importance region to a higher importance region, the particle has a probability of being split given by the ratio of the two importances.
When the particle moves back from a high importance region into a low importance region, it undergoes Russian roulette with a probability again given by the ratio of the importances. The sequence of importances that a particle sees is called an importance function. Cell importances should be varied gradually so that particles making the transition from a low to high importance region are not unreasonably split. This will help to ensure the accuracy of the final result. For problems with very high importance regions, this will mean complicating the geometry to achieve this gradual importance increase.
Weight windows function similarly to cell importances in that they focus on the importance of a particle passing through a region of the geometry. Rather than specify that Cell 1 has importance 1 and Cell 2 has importance 2, weight windows would prescribe the minimum and maximum particle weight passing through the window.
So, for this example, the weight window for Cell 1 could specify a minimum weight of
0.5 and a maximum weight of 1, while cell 2 could have a minimum weight of 0.3 and a maximum of 0.6. When a particle with a weight higher than the maximum allowable
47 Figure 4-1: Illustration from the MCNP Manual, Vol. II showing the basic operation of weight windows in MCNP [61].
weight of the window enters that region, it will undergo splitting until the weight is within the window. When a particle with a weight lower than the minimum enters the region, it goes through Russian roulette, with a probability of being killed set by the ratio of its current weight to a predefined weight set by the user. This predefined weight must be within the window. If the particle survives Russian roulette, its weight will be set to the predefined weight. This process is illustrated in Figure 4-1.
Weight windows offer several advantages over cell importances. Weight windows can be defined based on the cell geometry, or can exist as a user-defined mesh. This mesh does not need to correspond with surfaces within the geometry, and in fact should not overlap to avoid interface issues. Mesh based weighting windows allow for problems with highly spatially variant importances to maintain a simple geometry while simultaneously achieving the desired variance reduction. These windows can also be energy dependent, allowing for rarer, high-energy events to undergo more splitting than common low-energy events. Weight windows are also dependent on
48 the absolute weight of the particles, not the relative importances, so particles that are generated with other variance reduction techniques interact more appropriately.
In certain cases, the weight window game is turned off in a region of the geometry, such as when a cell has forced collisions. Weight windows can also be generated by MCNP5 using the weight window generator. This has the possibility to create windows that are more compatible with the geometry of the problem than if the user were to forward plan them.
49 Chapter 5
Specialized Treatment for
Non-Standard Vault Geometry
The radiation therapy vaults at the Dana Cancer Center at UTMC were designed and installed in 2012 and 2014. There are two machines, both from Varian Medical
Systems (Palo Alto, CA, USA). The first machine installed was a Truebeam, pur- chased with 4 photon modes, the highest of which is an 18 MV beam. The second machine, installed in 2014, is an Edge with 3 photon modes, the highest of which is an unflattened 10 MV beam. The layout of the Dana Cancer Center is demonstrated from an architect’s schematic in Figure 5-1.
In an attempt to keep the entrances and control spaces for both vaults very close while still allowing some shielding to be shared, the decision was made to use a non- standard vault orientation. Specifically, the rotation plane of the machines makes it such that the primary beam points directly at the maze. While the primary beam does not directly intersect the door, it does come close and the maze barrier thickness is not enough to fully attenuate the beam to bring the dose into allowable levels.
Therefore, we needed a more innovative approach to fully handle the door shielding.
The purpose of this investigation was to quantify the additional shielding burden produced by the non-standard layout of the Truebeam vault, and to determine the
50 Figure 5-1: Architect’s floorplan showing the two vaults in the Dana Cancer Center at UTMC. The vault on the left contains the Varian Edge and the one on the right contains the Varian Truebeam.
best way to calculate the dose contribution for future vaults.
5.1 Vault Layout
There are two basic vault designs that are employed at the majority of radiother- apy centers: a direct-shielded door, and a maze layout. These two configurations are directly addressed in NCRP 151. An example of the maze layout discussed by
NCRP 151 is shown in panel A of Figure 5-2. The Dana Cancer Center vault layout is neither of these configurations, and requires special consideration. At UTMC, the
Truebeam’s rotation axis is pointed towards the wall opposite the door with a maze located between the accelerator and the door. The schematic is shown in panel B of Figure 5-2. While this does not impact the secondary shielding in any way, this does change the paths available to scattered radiation from the isocenter to the door.
Additionally, because the maze does not adequately shield the entire primary fluence, then it becomes a scattering foil that will contribute additional scattered radiation to the door not accounted for in the NCRP 151 methods.
51 Figure 5-2: Figures of the NCRP example vault layout (A), and the Dana Cancer Center Vault Layout (B). The primary difference is the orientation of the radiation beams, which is represented by the arrows.
The selected orientation allows the two machines to share a primary wall, which is a significant savings in shielding cost. Putting the gantry rotation axis in the left- right direction of Figure 5-2 means that no special consideration needs to be given for the hallways and patient restrooms south of the vault for primary shielding concerns.
There are only limited studies of non-standard vault geometries. Biggs studied a similar design to the Truebeam vault using a barrier that did not intercept the primary beam, but instead only shielded against leakage transmission [12]. This is shown in
Figure 5-3. They utilized a Monte Carlo model to evaluate the dose distribution across the door. They concluded that accounting for wall scatter near the door was the most important effect to include in the calculation. The simulated results were confirmed with measurements using an ionization chamber. They demonstrated agreement to within a few percent between the measured and simulated results.
Facure et al. evaluated the change in scattered photon workload for a room where the beam axis was pointed at the maze opening as well as when it was pointed directly at the maze [22]. This is shown in Figure 5-3. They found a reduction in scattered
52 Figure 5-3: Simulation geometries used by Biggs (left), and Facure (right) [12,22].
dose when the beam was directed at the maze, but an increase in scattered dose by a factor of 2 for when the beam axis was aimed at the maze opening.They used
Monte Carlo simulation to compute the scattered dose at the door, but were unable to confirm these results with measurements. Facure et al. only studied the relative increase in scattered dose, and did not attempt to determine how to calculate the resulting shielding workload [22].
5.2 Analytic Model
A more detailed illustration of the Truebeam vault geometry and relevant quan- tities for the following derivation is presented in Figure 5-4. Dimensions labeled in
Figure 5-4 are presented in Table 5.2.
The paths for patient scatter, head leakage scatter, and head leakage transmission to reach the door are all the same as discussed in Section 3.6.1.1. However, the wall scattered radiation discussed in Section 3.6.1.1 is not present. Instead, there are two new sources of scattered radiation incident on the door: radiation scattered from the maze barrier and radiation reflected off of the maze wall. This section develops the
53 Figure 5-4: Detailed view of the Truebeam vault with the relevant scattering paths to calculate the photon workload at the vault door. The path for leakage transmission has been excluded for clarity.
equations necessary to calculate the additional scattered workload at the door.
5.2.1 Maze Barrier Scatter
To calculate maze barrier scattered radiation, we need to define our source. Pri- mary radiation incident on the maze barrier is attenuated, but attenuation comes from two processes, absorption and scattering. Radiation scattered within the maze may still be absorbed, but that becomes less and less likely as the remaining thickness of the barrier decreases. Thus, the maze barrier acts as an attenuating medium until some point, where it transitions into a scattering medium. This transition should occur when the remaining thickness of the maze becomes equal to one mean free path for the scattered photons. The mean free path (MFP) for radiation of a given quality can be calculated by Equation 5.1.
54 HVL MFP = (5.1) ln (2)
Using Equations 3.1, 5.1, and the NCRP 151 recommended TVL values of 34 cm
and 43 cm of concrete for 6 MV and 18 MV respectively, the MFP is 15 cm for 6 MV
and 19 cm for 18 MV. Radiation scattered within the final MFP of the maze barrier
then becomes our source for maze scattered radiation. The source strength from the
final MFP of the maze barrier can be calculated as the initial primary workload at
isocenter attenuated from transmission through the barrier and corrected for inverse
square. The attenuation for a given energy, i, of the maze barrier to the final MFP,
Bmi , can be calculated using Equation 5.2,
L−TVL −MFP 1i i − 1+ TVL 2i Bmi = 10 (5.2)
where L is the thickness of the maze barrier, and TVL1i , TVL2i , and MFPi are all given by NCRP 151 for the energy being calculated. Besides the attenuation from
the maze barrier, the intensity of radiation will decrease with the inverse square of
the distance from the scattering surface to the door centerline, dk, as well as with the
inverse square of the distance from the target to the scattering surface, dtar. Only a certain fraction of the radiation scattered from the maze is directed towards
the door. We must determine the angular scattering distribution for each energy,
similar to the patient scatter fractions, a (θ), defined in Section 3.4.3, a(θ). This angular scattering distribution for concrete is an unknown, and the key focus for this project. Determining the angular scattering distribution is discussed more in Sections
5.3, 4, and 5.4.
For patient scatter incident on secondary barriers, calculations often use only a single angle. This is an appropriate approximation as the distance dsec in Equation 3.9 is much larger than the scattering source (∼32 cm diameter cylinder). For maze
55 scatter, the scattering source is the full width of the primary beam (Atot in Figure 5-4) and much closer to the door. This means the size of the scattering source is comparable to the distance the scattered radiation travels to the door. This extended source size very near the door means that the maze scattered radiation is incident on the door from a wide range of angles. This suggests that it may be more appropriate to integrate over the extended source rather than use a more simplified single angle approach.
We can compare the variation between the use of a single angle or a summation over the barrier. Calculating the maze scatter dose-equivalent, HMS, with the single angle approach is done using Equation 5.3. To sum over the various scattering angles and area of the maze exposed to the primary beam, we use Equation 5.4.
X WiUmBiai (θ) HMS = 2 (5.3) i (dtardk)
X ai (θk) Ak HMS = WiUmBmi 2 (5.4) ik (dtardk) Atot
Um is the use factor for the maze barrier. Ak is the area of the maze scattering radiation at angle θk, and Atot is the total area of the maze exposed to the primary beam. For the single angle approach, we should use the shallowest angle from the primary beam to the door centerline because the scattering fractions are the most intense for shallow angles.
5.2.2 Photon Scatter from the Maze Wall
The other added scattered photon source in the Truebeam layout comes from the primary beam incident on the maze wall that is then reflected in the direction of the door. This can be calculated in a similar manner to the wall scattered radiation discussed in Section 3.6.1.1. Using the same definitions from Chapter 3, the maze
56 wall scattered component of the photon dose-equivalent, HMWS, is calculated using Equation 5.5,
X WpUmBmi αiAwall HMWS = 2 (5.5) i (dtwdwd) where Awall is the area of the maze wall exposed to the primary beam, dtw is the distance from the radiation source to the maze wall, and dwd is the distance from the maze wall to the door. The other aspect of this investigation is to evaluate if the dose albedos for the primary energy are suitable for a situation where the beam has been attenuated by a thick barrier, or if a degraded energy fits the scatter distribution better.
5.2.3 Total Scattered Photon Dose at the Vault Door
The total scattered photon dose-equivalent at the door in the non-standard con-
figuration needs to be calculated differently than the total dose-equivalent in the standard configuration. In contrast to the NCRP 151 example vault, two scattered dose-equivalent components are not present when the beam is not directed towards the maze barrier. For a the case where the beam is directed towards the maze barrier, we can calculate the photon dose-equivalent, HMaze, as
HMaze = HMS + HMWS + HPS + HLS + HLT (5.6)
Instead of summing all of the photon dose-equivalent for a single beam angle and then multiplying by an empirical factor, we can exclude the maze scatter and maze wall scatter photon components from the total. Therefore, the total scattered photon dose-equivalent over all gantry angles, Htot, can be calculated as shown in Equation 5.7,
57 Htot = HMS + HMWS + 2.64 (HPS + HLS + HLT ) (5.7)
5.3 Scattering Fractions
NCRP 151 dedicates a lot of effort to accurately evaluating the scattered radiation present in radiation protection situations. There are two main scatter distributions discussed; side scatter produced within a barrier and patient scatter from primary radiation. This section discusses how these scatter distributions arise, how they were determined, and if they are appropriate to use for the maze scatter component discussed in Section 5.2.1.
5.3.1 Side Scatter Radiation
Side scatter radiation as discussed in NCRP 151 was based primarily on the work of Zavgorodni [68,99]. Zavgorodni evaluated the dose-equivalent in high-rise buildings nearby radiotherapy centers that did not fully shield the ceiling to account for public occupancy. The setup evaluated by Zavgorodni is illustrated in Figure 5-5.
Side scatter fractions were modeled using the Monte Carlo code EGSnrc, and compared with measurements obtained using survey meters. They demonstrated agreement to within 20% between simulated and measured dose rates and found that a fourth order polynomial fit matched the simulated scatter distribution for all energies simulated [99]. They also presented a method to prospectively calculate the dose-equivalent from side scatter radiation, HSS. This is presented in Equation 5.8,
WpUC AC BC f (θ) HSS = 2 (5.8) (dC dB) where UC is the use factor of the ceiling, AC is the area of the ceiling irradiated by the primary beam, f (θ) is the scatter fraction for angle θ, dC is the distance from
58 Figure 5-5: Geometry presented in Zavgorodni’s 2001 paper on side scatter radiation [99].
the radiation source to the top of the ceiling of the vault, dB is the distance from the
top of the vault ceiling to the location in the nearby building. BC is the attenuation factor of the ceiling of thickness t, which is calculated according to Equation 5.9
t−TVL1 − 1+ TVL BC = 10 2 (5.9)
As a result of this work, NCRP included these scatter fractions as one of the special considerations for shielding a vault [68].
On first look, side scatter fractions appear to be a good fit for the situation presented with maze scatter. The two situations are similar in that the primary beam has traversed a thick barrier. The scattering geometry is a slab in both cases, in comparison to patient scatter which is assumed to come from a spherical phantom.
The scattering material is concrete in both situations. Even the method for dose-
59 Angle (deg) f (θ) 6 MV a (θ) 18 MV a (θ) 20 0.36 6.73 ×10−3 5.39 ×10−3 30 0.26 2.77 ×10−3 2.53 ×10−3 40 (45) 0.16 1.39 ×10−3 8.64 ×10−4 50 (45) 0.10 60 0.065 8.24 ×10−4 4.24 ×10−4 70 (90) 0.035 80 (90) 0.014 4.26 ×10−4 1.89 ×10−4 85 (90) 0.005
Table 5.1: Comparison of side scatter fractions (f (θ)) versus patient scatter fractions (a (θ)) for 6 and 18 MV beams. Angles for patient scatter fractions that do not align with the angles of the side scatter fractions are listed in parentheses.
equivalent calculations are similar between Equations 5.3 and 5.8. However, the scatter fractions calculated by Zavgorodni are significantly different from the patient scatter fractions. A comparison of patient scatter fractions and side scatter fractions is presented in Table 5.1. As shown, side scatter fractions are almost a factor of 1000 greater than the patient scatter fractions.
5.3.2 Patient Scatter Fractions
Patient scatter fractions were recently studied by Taylor and Shobe in 1999 [82,87].
Taylor utilized ITS, a predecessor to MCNP, to simulate 6 to 24 MV bremsstrahlung beams incident on a 30 cm sphere of water. They surround the sphere with water rings and evaluated what fraction of the dose was scattered through each angle, which was presented in Table 3.3. The geometry for the multiple different scattering angles used by Taylor are presented in Figure 5-6 [82,87].
Shobe performed measurements corresponding with the simulations from Taylor
[82, 87]. Using TLDs and an ion chamber, they found agreement between simulated and measured scatter fractions within 50%. Their measurement geometry is presented
60 Figure 5-6: Simulation geometries to calculate patient scatter fractions from Taylor et al. 1999 [87].
Figure 5-7: Measurement geometry for patient scatter fractions from Shobe et al. 1999 [82].
in Figure 5-7.
Patient scatter fractions are not an ideal match for the situation with maze scat- tered radiation for many reasons. First, the beam does not pass through a thick barrier, only 30 cm of water. Second, the simulation and measurement geometries both assume symmetry about the scattering object, either spherical or cylindrical, where the scattering geometry from the maze is a slab which will present variable length escape paths for the scattered radiation. Third, the scattering material for the patient scatter simulation and measurements is water or nearly water-equivalent
61 Label on Fig 5-8 Dimension Distance (m) 1 Isocenter to Wall G 4.42 2 Outer Boundary of Door to Far Edge of Maze 3.97 3 Outer Boundary of Door to Field Central Axis 2.60 4 Isocenter to Maze Barrier 3.28 5 Maze Barrier Thickness 1.22 6 Maze Width 198 Surface Area Not Numbered 200 m2
Table 5.2: Relevant dimensions of the vault design for the Dana Cancer Cen- ter reproduced in MCNP5.
material. Despite these differences, the variation between the patient scatter fractions and the side scatter fractions are too great to ignore the possibility that this patient scatter distribution more closely represents the scattered radiation distribution from the maze barrier.
Ultimately, determining the scatter distribution from the maze barrier is a complex problem that does not appear to have an accurate published result. This type of problem is best determined using Monte Carlo simulation.
5.4 Simulation Geometry
The majority of this work was done using the geometry from the Truebeam vault in the Dana Cancer Center. This vault is shown in Figure 5-8. Table 5.2 shows the labeled dimensions identified in Figure 5-8. The edges of the beam are shown as dashed lines. A screenshot of the MCNP5 simulation geometry is presented in Figure
5-9.
Point I shows a 40x40x40 cm3 water phantom centered about isocenter. This was used to create appropriate scatter, as well as to track the dose delivered to isocenter.
This was used to normalize the dose tallied in the door per dose delivered to isocenter. 62 Figure 5-8: Geometry of the vault design with the relevant distances for the simulation and calculation labeled by numbers 1-6. These num- bers correspond to distances presented in Table 5.2
Point M in Figure 5-9 shows a 10x10 cm2 section of the maze barrier centered
along the CAX. This 10x10 cm2 section is broken into 11 cm thick cells. The layer of the maze barrier closest to the maze is further subdivided into cells that correspond to 10 degrees of divergence from the target. These are located at Point D in Figure
5-9. Point T in Figure 5-9 shows the location of 10x10 cm2 cells centered vertically
about the CAX in the layer just beyond the door.
5.4.1 Materials and Source Definitions
The Pacific Northwest National Laboratory (PNNL) has compiled a list of material
cards for various styles of concrete, ranging from standard Portland concrete to barite
concrete [95]. Their listing for ordinary concrete was used to simulate standard density
63 Figure 5-9: Reproduction of the Truebeam vault produced in MCNP5, also depicting the multiple cells used for variance reduction and tally collection.
concrete. The material composition by weight is presented in Table 5.3.
Photon spectra from the Pinnacle3 Treatment Planning System for 6 MV and 18
MV beams were simulated in MCNP5. The source was a plane source with uniform spatial sampling located at 72 cm from the isocenter. This location corresponds to the end of the jaw collimators on the Truebeam accelerator. The plane source was given an opening angle equal to a 40x40 cm2 field. An image of the source particles being propagated through the geometry is presented in Figure 5-10. The dots overlaid on the geometry are locations of collisions from source particles, and their color represents
64 H O Na Mg Al Si K Ca Fe 2.2 57.5 1.5 0.12 2.0 30.5 1.0 4.3 0.6
Table 5.3: Simulated concrete material composition by percent weight [95].
Figure 5-10: Image depicting the collisions of primary particles overlaid on the vault geometry. The figure on the left shows an overhead view, while the figure on the right is a side view.
the energy of the particle. Red indicates high energy particles and blue indicates low energy particles.
These simulations included the three interaction processes described in Section
2.3: photo-electric absorption, Compton scattering, and pair/triplet production. We did not simulate coherent scattering, as this effect is unimportant in the megavoltage range, nor did we model photonuclear interactions. Although photonuclear inter- actions play a role in neutron activation and producing capture gamma photons, the cross-sections for these reactions within concrete is negligible relative to the cross-sections of Compton scatter and pair/triplet production for high-energy pho- tons [24,90].
65 5.4.2 Tally Selection and Placement
Tallies are located throughout the maze barrier. The 10x10 cm2 section of the maze barrier centered along the CAX broken into 11 cm thick cells were tracked using
F6 tallies. This is an appropriate choice within a uniform material exposed to the primary portion of the beam, where TCPE exists. The layer of the maze barrier closest to the maze was used to evaluate the relative contribution to dose at the door from scattered radiation from the maze barrier. The F6 tally was used to track the dose deposited within these cells.
Tracking dose outside the door was more complicated. Four sets of simulations were run to test each type of tally, one using F6, another using *F8, another using an
F4 tally using fluence-to-effective dose conversion factors, and a final set using the F5 point detector tallies with the fluence-to-effective dose conversion factors from ICRP
116 [73]. An exclusion radius of 30 cm was applied to the point detector tallies to prevent scatter events near the detector from overly influencing the tally results. To track the dose along the width of the door, three tallies were placed: one nearest the maze barrier, one at the door centerline, and another nearest the maze wall. These tallies were located along the door at Point T in Figure 5-9.
Scattering fractions were calculated from the tallies within the door. The method for calculating the scattering fraction from simulation is shown in Equation 5.10,
2 2 DCellj dk 400cm aj (θk) = (5.10) DCellk 1m F where aj (θk) is the scatter fraction to cell j in the door from cell k in the maze, θk is
the angle between the beam line and the ray between cell k to cell j, DCellj is the dose
registered in cell j in the door from cell k in the maze, DCellk is the dose registered in cell k, and dk is the distance from cell k to cell j.
66 Figure 5-11: MCNP simulated transmission for 6 and 18 MV beams com- pared with calculated transmission curves using NCRP 151 TVL values.
5.5 Results
Figure 5-11 demonstrates the agreement between the predicted HVLs and the
MCNP simulated HVLs. Calculations demonstrate a maximum difference between
simulated and expected HVLs of 2 mm. The mean difference between intensity curves
for 6 MV and 18 MV was 0.97% and 0.23%, respectively. All statistical uncertainties
were below 0.05%. Of the additional photon dose in the door, 90.8 ± 2.8% was contributed by the final 11 cm of the maze barrier for both 6 and 18 MV.
The maximum dose in the door from maze-scattered radiation relative to the dose at isocenter was 6.81x10−9± 17.6% for 6 MV. The maximum dose in the door per
Gy at isocenter was 5.20 x 10−7± 0.3% and 5.84 x 10−7± 0.2% for 6 and 18 MV, respectively. The location of maximum dose in the door was at the corner furthest from the maze barrier. The tallies nearest the maze barrier recorded on 80 ± 0.4% of the maximum dose within the door for 6 MV. Scatter fractions from concrete are
67 Figure 5-12: MCNP simulated scatter fractions from the Truebeam vault simulations for 6 and 18 MV beams.
presented in Figure 5-12 and numerically in Table 5.4. The range of angles covered extends from 16 to 78 degrees.
5.5.1 NCRP Formalism for Door Workload
Photon workload from each component (patient scatter, leakage scatter, leakage transmission, maze scatter, wall scatter) at the door per Gy at isocenter for 6 and 18
MV accelerators are presented in Table 5.5. There is no capture gamma component to the 6 MV photon workload at the door as there should be negligible photo-neutron production for that energy. The maze scatter is calculated using scatter fractions pre- sented in Table 5.4 derived from our Monte-Carlo simulation. Table 5.6 demonstrates what this shielding burden would be for all gantry angles and a workload of 1000 Gy wk−1 at isocenter. Simulations were not run at all cardinal beam angles, so no value is presented for the simulated dose at the door over all beam angles. capture gamma photons were not simulated and are not counted in simulated results for 18 MV.
However, 90% of the dose that is transmitted to the door from the maze barrier comes from the final 11 cm. This suggests that the escape distance for scattered
68 6 MV 18 MV Angle (deg) Maze Scatter Patient Scatter Maze Scatter Patient Scatter Side Scatter 20 1.42 ×10−3 6.73 ×10−3 1.44 ×10−3 5.39 ×10−3 0.36 30 6.74 ×10−4 2.77 ×10−3 4.95 ×10−4 2.53 ×10−3 0.26 40 (45) 0.16 2.99 ×10−4 1.39 ×10−3 1.98 ×10−4 8.64 ×10−4 50 (45) 0.10 60 2.74 ×10−4 8.24 ×10−4 1.10 ×10−4 4.24 ×10−4 0.065 70 (90) 0.035 80 (90)4.26 ×10−4 1.89 ×10−4 0.014
Table 5.4: Calculated maze scatter fractions compared to patient and side scatter fractions.
Scattered Photon Component 6 MV (Sv per Gy @ iso) 18 MV (Sv per Gy @ iso) Patient Scatter 1.68 ×10−8 1.17 ×10−8 Leakage Scatter 1.21 ×10−8 1.21 ×10−8 Leakage Transmission 2.23 ×10−10 8.31 ×10−10 Maze Scatter 3.99 ×10−10 1.95 ×10−10 Wall Scatter 2.27 ×10−8 1.25 ×10−7 Gamma Capture — 6.49 ×10−7 Total (Excluding Gamma Capture) 5.23 ×10−8 1.49 ×10−7
Table 5.5: Relative intensities of scattered photon dose-equivalent at the vault door per Gy of photons delivered to isocenter. Calcula- tions are done only for the beam being directed towards the maze barrier.
photons is less than the calculated MFP from the concrete HVL of 14.4 cm and 18.8 cm for 6 and 18 MV, respectively. This should correspond to a reduction in the effective source strength and may indicate that the beam spectrum has been softened by the maze barrier.
Equation 5.7 calculates that the additional shielding workload at the door accounts for 20% of the photon dose equivalent at 6 MV for a single gantry angle and is approximately 9% of the overall photon dose for all gantry angles. MCNP simulation results demonstrate a significantly smaller effect. The components of wall scatter and
69 6 MV Calculated 6 MV Simulated 18 MV Calculated 18 MV Simulated −5 −4 −4 −4 HMaze 5.23 ×10 1.3 ×10 1.57 ×10 1.46 ×10 −4 −4 HT ot 1.01 ×10 – 8.41 ×10 –
Table 5.6: Total photon workload at the vault door for a machine that pro- duces 1000 Gy wk−1 at isocenter.
maze scatter only contribute to 3% of the total photon dose at the door, while all components besides capture gamma contribute 7%. This supports that scatter doses to the door can still be disregarded for high-energy accelerators in this configuration.
While the relative contribution of photon dose-equivalent for 18 MV is lower, the absolute contribution is still larger than the contribution from 6 MV. This supports the previous findings of Biggs [12]. Similarly to what Biggs found, we also determine that the dose distribution at the door is no longer uniform in this configuration, but varies across the door by 20% for 6 MV. The location of dose maximum is at the corner of the door furthest from the maze barrier, which should be expected as it will have the shallowest scattering angles from maze scatter.
5.6 Recommendations for Additional Scattered Ra-
diation Calculations
We have developed an equation to account for additional photon dose-equivalent at the maze door for a high-energy therapy accelerator that has been verified by
MCNP simulation. This equation utilizes scatter fractions and TVLs of concrete available to the medical physicist from NCRP 151. Close agreement between analytic calculations using patient-scatter fractions and simulated results demonstrated that the additional dose-equivalent at the vault door was roughly 10% of the total photon dose-equivalent for the layout presented here, discounting capture gamma photons.
70 For low-energy machines (<10 MV), additional photon workload at the door needs to be calculated, from both maze-scattered radiation and additional reflected radi- ation from patient scatter and maze transmission. For high-energy machines (> 10
MV), capture gamma photons are the dominant contributor by an order of magnitude.
Additionally, they have a higher average energy than multiply scattered radiations
(several MeV relative to hundreds of keV). In these situations, the standard method of NCRP calculation are adequate to safely shield the door.
71 Chapter 6
Shielding Test Port Development
Radiotherapy shielding parameters are most often obtained through Monte Carlo simulation owing to the great flexibility of the Monte Carlo method and the reduced radiation risk to staff and personnel. There are still many works that perform mea- surements to allow for benchmarking Monte Carlo simulations, or comparison with previously obtained simulation results. Shielding measurements are difficult to per- form as they require the use of heavy shielding materials, rare detectors that have a high sensitivity, and experimental design that minimizes the multiple sources of secondary scattered radiations that can contaminate readings in low-dose areas. The unique design of the radiotherapy vaults at the Dana Cancer Center provided an opportunity to create a dedicated testing facility using a clinically commissioned ma- chine to perform measurements of shielding parameters, while intrinsically allowing for the reduction in secondary scattered radiation. This chapter describes the devel- opment and use of the shielding test port installed at the Dana Cancer Center.
6.1 Shielding Test Port Development
The shielding test port is, in essence, a hole in a wall, as shown in Figure 6-
1. This hole penetrates through the whole of the maze barrier in the Varian Edge vault, as shown in Figure 6-2. The opening is centered along the beam central axis 72 Figure 6-1: Photographs of the two blocks containing the test port pre- installation. The red blocks encasing the port at 3’ × 3’ × 3’ of 200 pcf concrete.
(CAX) when the gantry is oriented at 90◦. The main opening of the port is 30 cm by 30 cm, and can fit up to 91.5 cm of shielding material. There is a specific set of shielding blocks that are kept in the port during operation as part of the state approved shielding design.
A dedicated test port requires three main components: appropriate safeguards to mitigate any concern of inadvertent personnel exposure, flexibility and ease of use, and minimization of contaminating background and scattered radiations. This section will describe how each of these concerns is addressed by the test port in the
Dana Cancer Center.
6.1.1 Risk Mitigation and Safety Interlocks
The maze in the Edge vault utilizes the same compound primary barrier design as the Varian Truebeam vault described in Chapter 5. This allows for the radiation exiting the test port to still be contained within a shielded area to remove any risk of inadvertent exposure. The beam path through the test port points directly into
73 Figure 6-2: Top-down schematic illustrating the test port location relative to the door, isocenter, and the radiation field.
the Truebeam vault, as shown in Figure 6-2, meaning that any radiation exiting the
Edge vault will be contained within the Truebeam vault. The test port has several design features intended to minimize radiation transmission through the barrier while in routine clinical use. As shown in Figure 6-2, the test port has two sections: a 20 cm
× 20 cm section that is 30.5 cm long, and the main 30 cm × 30 cm opening comprises the remaining 91.5 cm. The test blocks are only inserted into this remaining 30 cm ×
30 cm section. The initial 20 cm × 20 cm section is left completely unoccupied at all times. This two step opening was utilized to eliminate direct paths along the edges of the shielding blocks for primary radiation to stream through. The port is encased in a high-density concrete block (3.2 g cc−1, 200 pcf) to reduce internally scattered radiation. The standard set of shielding blocks, composed of 3.35 g cc−1 (215 pcf) concrete, fills the 30 cm × 30 cm section and provides the equivalent attenuation of
122 cm of 2.35 g cc−1 (147 pcf) concrete.
Safe operation of the machine requires that all of the standard shielding blocks must be in place to allow the beam to be enabled. Varian machines have an extra set of inputs into the beam-enable loop, called the Customer Minor Interlock (CMNR).
We utilized this set of inputs to create an interlock for the testing port. The first and last sections of the standard set of blocks have a special bar magnet embedded within
74 Figure 6-3: Circuit diagram demonstrating how the interlock for the shield- ing test port ties into the treatment machine.
them. These correspond to a pair of magnetic reed switches wired in series that tie into the CMNR interlock. The reed switches were chosen because of their mechanical simplicity, ensuring reliable operation. When the blocks are in place, the circuit is closed and the beam may be turned on. If either the first or last block is absent, then the machine will not allow for the beam to be turned on while in treatment mode. This interlock may be overridden in service mode, allowing for operation of the beam for the purpose of testing. A key-based override switch is wired in parallel with the magnetic reed switches to allow the beam to be turned on in case of failure of the interlock circuit. Activating the override switch illuminates an LED bulb to indicate that the interlock is overridden. A schematic of the interlock circuit is shown in Figure 6-3.
6.1.2 Ease of Use and Block Design
Two design features were required to allow for samples frequently >15 kg to be repeatedly inserted and removed. To reduce friction and wear on the blocks as they dragged along the port, a thin metal sheet was placed along the bottom and right
75 lateral wall of the port. This metal sheet provides a smooth, non-interacting surface for the blocks to slide along. To allow for easy extraction and lifting, two threaded inserts were cast into each block. These interlock with corresponding custom lifting and positioning bars of 1’ and 3’ length, respectively. The inserts are composed of stainless steel, which is denser than the concrete itself. However, these inserts also displace ∼1.5 cm of the intended shielding. Therefore, care is taken during placement to ensure that these inserts are offset relative to the inserts in all of the other blocks.
These threaded inserts are also useful for suspending the blocks, if needed.
6.2 Parameters of Interest
This section describes the scientific goals of the test port. Parameters necessary for radiation protection calculations are often simulated, or measured in situations that are not designed for such measurements [6,22,23,38,51,63,82,87]. The novelty of the test port is that this geometry is designed to allow for dedicated radiation protection measurements. The main areas of interest for this project are measuring TVLs for high density concrete, measuring patient scatter fractions and their associated TVLs, and measuring differential dose albedos. To date, only TVL measurements have been possible given the present set up of the test port and the equipment available at the
University of Toledo. However, we outline the methods and equipment necessary to obtain direct measurements of patient scatter fractions and differential dose albedos, and leave those experiments as areas for future work.
6.2.1 TVL Measurement
The test port allows for measurement of several quantities of interest in radiation protection and shielding. The most obvious application is the measurement of TVL thickness for various concretes and shielding materials. These should be composed
76 of multiple layers of a consistent thickness. NCRP 151 includes a discussion on the various materials commonly used for radiation shielding [68]. They do not address high density concretes for photon beams, probably due to commercial availability of many different formulations and densities. There is also limited simulation data on the various high density concretes, leaving little guidance for clinical physicists when using these concretes. Given that Compton scattering is the dominant interaction mechanism in the 1-10 MeV range for photon radiation and that the interaction cross-section is linearly proportional to electron density, we would expect that the attenuation properties of concrete should scale according to the mass-thickness of a given section of concrete. Therefore, we should be able to calculate the TVL for a given density of concrete from the TVL of a different density of concrete, using
Equation 6.1,
ρstd TVLHD = TVLstd (6.1) ρHD where ρstd and ρHD are the densities of the standard and high density concretes, respectively.
Evaluating the total photon interaction cross sections for standard concrete (2.40 g cc−1; 150 pcf), 3.43 g cc−1 (215 pcf) concrete, and 4.0 g cc−1 (250 pcf) concrete, as shown in Figure 6-4, demonstrates that the assumption supporting Equation 6.1 does not hold beyond the 1-10 MeV energy range [10]. The typical spectrum for 6 and 18 MV photon beams are overlaid in Figure 6-4 to demonstrate the range of energies present in a clinical beam. Below 0.5 MeV, the photoelectric cross section becomes dominant, which has a Z3 dependence. Above 10 MeV, pair production begins to dominate Compton scattering, which includes a Z2 dependence. When heavy concrete is used, the increased presence of iron (Z=26) relative to standard concrete could lead to a reduction in the TVL for photon irradiation beyond what
77 Equation 6.1 would predict.
Groups such as the NCRP have always assumed the most conservative value for
TVL thicknesses of a material to prevent the costly situation of needing to renovate a fully built vault. However, the use of high-density concretes is much more expensive than standard concrete, so even small savings on barrier thicknesses can translate into very tangible cost differences [23, 68]. Therefore, having accurate evaluations of the TVL for high density concretes is a high priority for shielding contractors. There has been some work on simulating these concretes, but it has not been comprehensive
[3,6,23,38–40,54]. This may stem from the fact that there are a wide variety of heavy concretes, each with unique compositions for a given density [38,40]. Such variations make it difficult to accurately predict what the TVL should be for a given beam energy and concrete density.
Facure and Silva used MCNP to evaluate TVLs for multiple high-density concretes and compared them with TVL values from NCRP 151 scaled to the TVL for high density using Equation 6.1 [23, 68]. Karoui and Kharrati used MCNP to evaluate build-up factors for mono-energetic beams throughout the clinical range of energies and utilized these to calculate TVL values for poly-energetic beams [39]. This in- cluded one density of heavy concrete. Neither of these works compare their simulated results to any measurement of TVLs for either standard or high-density concretes.
Measurements of leakage TVLs for high density concrete were performed by Kase et al., but these did not involve primary TVLs [40]. Jones et al. measured primary and scattered TVLs for a single density of high-density concrete, but only evaluated these using 40 cm of prefabricated blocks [38]. Experiments of this type can evaluate
TVL1 and TVL2, but cannot determine if TVL2 stays constant to be conservatively safe for barriers as thick as 7 TVLs. The test port, on the other hand, is designed to measure across significant variations in barrier thickness. It also can handle multiple densities of pre-cast concrete blocks.
78 Figure 6-4: Comparison of the mass attenuation cross-sections, µ/ρ, for 2.4 (150), 3.43 (215), and 4.0 (250) g cc−1 (pcf) concretes. Dashed lines illustrate normalized energy spectra for 6 and 18 MV bremsstrahlung beams.
Comparison between TVLs for flattening filter free beams (FFF) and traditional
flattened beams is also possible using the test port. Some simulation and limited measurement work has been done on this. Kry et al. used MCNP to simulate TVLs for both flattened and unflattened beams [47] . They concluded that unflattened beams demonstrated a TVL 11% lower than flattened beams, mostly attributed to the lower mean energy. They also noted that because of the higher output per pulse, unflattened beams produce less leakage radiation, and thus can contribute another reduction to the secondary shielding workload. Other works have not investigated the impact of removing the flattening filter from the machine head on shielding requirements, specifically on whether a reduced TVL should be incorporated or not.
79 6.2.2 Patient Scatter Fractions
Patient scatter fractions play an important role in shielding calculations, as demon- strated in Chapter 3. Significant effort was put into modeling and measuring patient scatter fractions for multiple energies by several authors [64,82,87]. Extreme care was taken by Shobe et al. to measure these accurately with a well-shielded large volume detector [82]. While these measurements are very precise, they do not include con- siderations for FFF beams. Unflattened beams should be expected to have a higher relative scattering fraction because of the lower mean energy.
The setup of the test port allows for a very precise determination of the scattered dose at a particular angle by using the port as an external collimator for a scatter detector. The angular opening of the port viewed from isocenter is 3.5◦. A large scattering phantom can be placed at isocenter. Dose at isocenter can be measured using a calibrated Farmer-type ionization chamber, with a sensitive volume of 0.6 cc, while scattered dose will be measured using a large-volume chamber, with a sensitive volume of 30 - 100 cc. The gantry angle will determine the scattering angle to be measured. Multiple field sizes can be measured to evaluate whether the scattering fractions scale linearly with irradiated area, the current assertion from NCRP 151 [68].
Backscattered radiation from the wall between the treatment vaults will be min- imized by placing the detector directly in the port itself. We will be able to more accurately measure low-angle scattered radiation, as our detector can be placed an additional meter further away from the scattering source than was possible in Shobe’s measurements [82]. Contaminating primary radiation will be further attenuated by the maze barrier itself, allowing for a dedicated measurement of the scattered pho- tons. A potential experimental setup to measure patient scatter fractions, similar to what is described above, is shown in Figure 6-5.
The test port has the additional benefit of being well-suited to measuring TVLs for
80 Figure 6-5: Illustration depicting a potential set up to perform patient scatter measurements using the test port at the Dana Cancer Center.
scattered radiations. Nogueira and Biggs measured TVLs for patient scatter fractions at a 30◦ angle, but work in evaluating patient scatter TVLs is lacking beyond that [63].
The test port setup can produce TVL measurements for scattering angles below 20◦ and up to 150◦ degrees, allowing for a comparison with the primary beam TVL and recommended patient scatter TVLs. Patient scatter TVLs can also be evaluated for high-density concretes, as an extension of the primary TVL measurements. TVL measurements of this type will likely require the detector to be placed outside of the testing port to allow for the detector to remain stationary during variation of the attenuator thickness.
Accurate measurement of scattering fractions requires any obstruction to be re- moved from the port entrance. Presently, there is a laser mounted in front of the port to allow for visual identification of isocenter during clinical operation. This will need to be moved prior to any measurement involving scatter fractions. Additonally, the sensitive volume needed for accurate TVL1 and TVLe measurements on scatter frac- tions require a significantly larger chamber than is necessary to measure the scatter
81 Figure 6-6: A top-down view of a way to utilize the test port to measure dose albedos for normal incidence on high density concretes.
fractions themselves. A chamber of this size has yet to be acquired by the university.
Because of this, measurement of patient scatter fractions and their respective TVLs will be a focus for future work.
6.2.3 Differential Dose Albedo
Differential dose albedo is the term given to radiation reflected from a barrier.
This becomes one of the dominant forms of radiation dose at the door for low-energy machines [51,86]. Lo initially measured these factors using primarily the ITS Monte
Carlo code, a predecessor to MCNP [51] . Their simulations demonstrated reasonable agreement with measurements, with a maximum difference between measured and modeled values of 35%. The intensity of reflected radiation increased with increasing atomic number, suggesting that vaults utilizing high density concretes may need to use different dose albedos to accurately predict the scattered photon dose to the door.
Lo noted difficulty in these measurements, citing primarily a difficulty in obtaining a good geometry that minimizes background and other secondary radiations. This type of measurement is precisely what our test port is designed to investigate.
Measurement of differential dose albedo can be accomplished by directing a beam
82 through the empty test port directly incident on the wall separating the treatment vaults. A potential experimental setup is presented in Figure 6-6. Two parameters are needed for this measurement: the incident radiation intensity and the reflected radi- ation intensity. A Farmer-type ionization chamber with sufficient build-up placed far away (>1 m) from the scattering wall can be used to measure the incident intensity, but this may perturb the primary radiation field if the chamber is placed too promi- nently in the field. The scattered radiation may be measured using a larger ionization chamber, such as the 30 cc chamber acquired for TVL measurements, placed at least
1 m from the shield wall. As dose albedo is dominated by backscattered radiation, the quality of the reflected radiation may be dramatically different from the quality of the incident primary beam. Thus, varying thicknesses of build-up should be used to accurately measure the dose reflected from the shielding wall. This chamber can be placed at varying angles relative to the scattering wall.
To vary the scattering material, the current sets of test blocks may be used to construct a barrier of sufficient thickness and width to adequately reflect the primary radiation. This wall will need to be constructed from multiple blocks to make the scattering structure wide enough to encompass the entire beam. The wall will also need to provide the equivalent attenuation of 30 cm of standard density concrete, as this thickness was identified by Lo as the point where backscattering intensity plateaued [51].
83 Chapter 7
TVL Measurement and Simulation
We have evaluated through measurement and Monte Carlo simulation the neces- sary TVL thicknesses required to adequately shield a radiotherapy vault using multi- ple high density concretes. This chapter describes the experimental setup, simulation geometry, results, and a discussion of our findings and how they fit with previously published work.
7.1 Experimental Setup
7.1.1 TVL Measurement and Block Parameters
Shielding Construction Solutions, Inc. (SCS) supplied the University of Toledo with multiple densities of custom made concrete test samples. These densities are all used in radiotherapy vault shielding according to SCS. Concrete blocks 5 cm thick were used to allow for sufficiently fine sampling of the TVL, and also to allow for ease of handling. TVL measurements are done by removing all of the shielding blocks from the test port and then measuring the transmission value as each layer of concrete is added back into the path of the beam. The distance between the final block and the measurement chamber must be kept constant. Temperature and pressure corrections should be applied for each layer measured, as the total time of these measurements
84 can allow for large (1-2%) temperature and pressure fluctuations. Beam energies available on the Varian Edge are 6 MV, 6 FFF, and 10 FFF. All were measured.
Preliminary measurements were obtained using a 0.6 cc Farmer-type ionization chamber with a 10 MV buildup cap. A restricted set of densities were tested to determine the suitability of this setup. Field sizes at isocenter of 4 cm × 4 cm, 9 cm × 9 cm, and 30 cm × 30 cm were measured. These preliminary measurements demonstrated that a larger chamber was necessary to obtain suitable signals through multiple TVLs, notably for the higher densities being tested. We observed very little field size variation, likely because the test port acted as a tertiary collimator, effectively limiting the field size being measured to a 4 cm × 4 cm field. Therefore, all further measurements only utilized a 4 cm × 4 cm field.
Based on the results of our preliminary investigations, a 30 cc cylindrical stem ionization chamber designed for use in health physics applications was used. This was inserted into a Co-60 buildup cap of 5 mm water-equivalent thickness, with an additional 2 cm plastic slab placed in front of the detector to provide appropriate buildup for 10 MV beams. The collected signal is ∼50 times greater for the 30 cc chamber compared to a typical Farmer-type ionization chamber (0.6 cc sensitive volume) purely owing to the added sensitive volume. The 30 cc chamber is capable of measuring until the fourth or fifth TVL in some cases. The measurement geometry, including the relevant distances, is illustrated in Figure 7-1.
The TVL can be calculated in many ways. Two common methods report TVLs for the total thickness of concrete, and for each individual slab. Because the beam from a linear accelerator has a polyenergetic spectrum, the TVL for the total thickness of concrete will be different from the TVL for each individual layer. Whichever method is used, the general formula to calculate TVLs is shown in Equation 7.1.
85 Figure 7-1: Experimental setup used for TVL measurements. Not pictured are the build-up slab and the test blocks.
tn TVL = (7.1) log In−1 10 In
th where tn is the thickness of the n layer, In−1 is the measured signal through the previous layer, In is the measured signal after addition of the next layer of shielding.
For total thickness TVLs, tn is the total thickness of concrete to layer n, In−1 repre- sents the initial measured intensity with no blocks and In is the measured intensity through thickness tn of concrete.
NCRP 151 defines two TVLs per energy per shielding material: a TVL1 and a
TVLe (refer to Table 3.1 for examples of TVL thickness) [68]. The initial shielding layer is thicker than the subsequent layers as the scatter within the shield builds up and eventually achieves an equilibrium. This equilibrium value is maintained through the remainder of the shield. To evaluate whether the shielding layers ever achieve a meaningful equilibrium, we track the TVL thickness from one TVL to the next. For
th this case, tn in Equation 7.1 is the thickness to the n layer starting from the nearest previous complete TVL, and In−1 is the measured signal from the nearest previous
86 complete TVL. To illustrate this, assume that 5 layers of concrete, t5, produce 2 TVLs worth of attenuation, I5. The third TVL, TVL3, is produced with an additional 3 layers of concrete, t8. Then the calculation for TVL3 would go as follows,
t8 − t5 TVL3 = I5 log10 I8 To maintain consistency with the framework of NCRP 151, we report TVLs ac- cording to this method.
7.1.1.1 Block Density Verification
The densities of each block were estimated by measuring the block weight with a scale and using a tape measure to determine the volume of a perfect rectangular prism. However, the blocks produced for the test port required hand production, leading to non-uniformity across their surface and sides. Variations of 1-2 mm were common. These variations can cause differences of as much as 10 pcf in the final calculated densities. Therefore, a more accurate measure of the blocks final density was required.
Densities of each block were verified using the Archimedes method. The weight of each block was measured in air, and then again in water. Each block was suspended using a pair of connected hooks that thread into the inserts within each block. For a sealed block, the density of the block, ρblock can the be determined as,
wair ρblock = (7.2) wair − wsubmerged where wair is the weight of the block in air, wsubmerged is the weight of the block submerged in water. It is important that the blocks be sealed to prevent water from filling any air pockets within the concrete, as these air pockets will be present during irradiation and detract from the total attenuation. A single set of blocks
87 Desired ρ (g cc−1) Measured ρ (g cc−1) 2.40 (150 pcf) 2.37 2.90 (180 pcf) 2.96 3.43 (215 pcf) 3.28 3.68 (230 pcf) 3.68 4.00 (250 pcf) 3.84 4.48 (280 pcf) 4.48
Table 7.1: Table of desired test densities and the measured densities of each set of test blocks.
was not properly sealed, resulting in an erroneous estimation of a density of 360 pcf.
For this set of blocks, the true density likely lies somewhere nearer 280 pcf based on transmission measurements. A list of desired and measured densities of the test blocks is presented in Table 7.1. Measurement densities will continue to be referenced by their desired densities, as this will allow for a better comparison of their compositions by weight with simulated results. This excludes the 280 pcf blocks, as they have no simulated counterpart.
7.2 Monte Carlo Simulation
7.2.1 Simulation Geometries
The geometry of the test port was reproduced in MCNP5 from architect and designer drawings. There is a laser casing and mounting plate directly in front of the test port opening when viewed from within the room. The laser geometry is too complex to model in MCNP, but the steel mounting plate was included in our simulation geometry. This was visualized using the Visual Editor provided with
MCNP5. Screenshots of the reproduced MCNP5 simulation geometry, including the testing layers, are presented in Figure 7-2. A separate simulation geometry was produced for each testing density, as well as an individual simulation for each thickness
88 Figure 7-2: Simulation geometry using the full thickness of the test port. The Farmer chamber and build up cap are visible on the right of the image, while the steel laser mounting plate is visible on the left.
of attenuating material. Test port blocks were assumed to have a perfect size of 30 cm × 30 cm × 5 cm, with densities exactly equal to the desired testing density. The actual port only allows for blocks with widths and lengths of 29.5 cm × 29.5 cm.
Blocks larger than this often got stuck and were unable to be used. The difference between 29.5 cm × 29.5 cm blocks and 30 cm × 30 cm blocks was not evaluated as part of this project, but the effect is predicted to be minimal.
One confounding factor of the test port is that it can only fit a 4 cm × 4 cm square field within it. Larger fields become collimated within the port and act as a much smaller field, distorting the measured result for larger fields. The ultimate goal of this shielding project is to evaluate the TVLs for a 40 cm × 40 cm field for these high density concretes. Therefore, two additional geometries were used to achieve this goal. The first simulations described above test that the simulated test port corresponds with the measurements from the test port.
89 Figure 7-3: Demonstration of the second geometry simulated, replacing the more complicated structure of the test port (top row) with a uniform barrier thickness with density equal to the density of the testing sample (bottom row).
The second geometry used removed the test port geometry and replaced it with a uniform barrier with a thickness equal to the thickness of the layers measured and a density equal to the density of the test sample. For example, if the simulation called for 4 layers of 3.52 g cc−1 concrete, then the entire maze barrier would be uniformly
20 cm thick and 3.52 g cc−1. An example of this is shown in Figure 7-3. This allows us to confirm that the test port geometry accurately represents the attenuation that would happen in a uniform barrier equal to the parameters of the test setup. This geometry is referred to as “Maze Barrier” in the following figures.
The third geometry used simulates the full 40 cm × 40 cm field incident on a uniform barrier of varying thickness. These simulated values should allow for the best comparison to the TVL data reported in NCRP 151 when scaled by Equation
90 6.1. The maze barrier geometry remains the same as shown in Figure 7-3, but to reduce the influence of the secondary scatter the surrounding walls and floors were removed.
7.2.2 Simulation Material and Source Specifications
Material specification is an important aspect to this project, particularly for high- density concretes. Concrete is a mixture, and there are many ways to assemble all of the components to achieve specific densities. Standard poured concrete, for example, must have a higher water content to aid in pumping compared to cast-block concrete, which does not require the extra fluidity. In addition, cast-block concrete may have been kiln dried following casting. This relates to radiation shielding in two ways; the more dense the concrete, the less is needed to attenuate a photon beam, and the higher the water content, the more hydrogenous material for neutron attenuation around high energy accelerators. Both depend on the composition of the concrete.
The Pacific Northwest National Laboratory (PNNL) has compiled a list of mate- rial cards for various styles of concrete, ranging from standard Portland concrete to barite concrete [95]. Their listing for ordinary concrete was used to simulate standard density concrete. High density concrete compositions were obtained from Shielding
Construction Solutions, Inc. and Universal Minerals International, Inc. These are proprietary, and the vendors have asked that the exact materials not be published.
Simulated densities include 2.40, 3.20, 3.43, 3.59, 3.84, and 4.00 g cc−1, corresponding to 150, 200, 215, 220, 240, and 250 pcf.
The source was simulated as a point source, surrounded by an 8 cm tungsten shell with a divergent, square field opening corresponding to a 4 cm × 4 cm field at isocenter for the first two geometries, or a 40 cm × 40 cm field for the third simulation geometry.
Source spectra were reproduced from Sheikh-Bagheri and Rogers for flattened beams
[81]. Unflattened beam spectra were determined differently.
91 Varian Medical Systems has decided not to provide exact technical details on the acceleration column, or beam production components of the Truebeam linear accelerator [17]. Instead, detailed Monte Carlo modeling in GEANT4 was performed by the Varian physics and engineering teams to determine the typical particle fluences directly following the flattening filters. These are distributed via myvarian.com under the Varian research agreement. These phase-space files are extremely large (∼50 GB per energy), containing hundreds of million source particles over a large opening angle. All direction, energy, and type information of each particle is stored on a curved plane in a IAEA format. While analyzing the whole 50 GB of particles for each energy was too computationally expensive, multiple smaller files were able to be evaluated for photon energy information. These provided the spectral distribution of several million particles. This energy distribution was used as the source energy distribution for unflattened beams.
7.2.3 Variance Reduction and Tally Selection
Variance reduction in these simulations was minimal. Despite several TVLs of attenuation, the primary point of interest is still within the direct beam. This re- duces the necessary variance reduction measures compared with the maze-scattered situation. Therefore, all regions of the simulation were set to an equal importance of 1. The small opening angle of the active field required the use of source biasing.
The angular distribution of the point source was set such that 0.1% of the source particles were sent into the head shielding. The remaining 99.9% were generated to pass through to the active beam. The relative weight of the particles was scaled by the ratio of the solid angle which they were sent towards divided by the relative frac- tion that were allowed to pass through that opening angle. Thus, for particles sent through the small opening in the head shielding, their weight was reduced as there are many more particles generated in that direction than there normally would be, and
92 the weight of the particles sent towards the head shielding was increased to account for the lesser number of particles that enter that region than normally would be.
This results in a uniform weight per solid angle distribution about the point source while reducing the number of particles that are absorbed within the head shielding and therefore reducing simulation run time. The point source was biased towards the opening in the tungsten head only for simulations using the F4 tally. Source biasing was not used for simulations using the F5 tally, as it caused too much statistical un- certainty. Thus, the point source was only directed through a conical opening angle that circumscribed the square opening in the head shielding.
There is also some uncertainty as to whether or not a detector tally (F5) is an appropriate choice for situations with no shield or only a thin shield. The direct contributions to the tally may cause some issues, such as those demonstrated in the
MCNP Primer by Shultis and Faw [83]. Therefore, comparisons between using a cell flux tally (F4) and a point detector (F5) were performed. The point detector was placed along the beam central axis at a distance of 5.5 m from isocenter (6.5 m from the source). An exclusion radius of 30 cm was applied to prevent air-scattering events from near the detector point from influencing the tally results. For comparison, a Farmer ionization chamber was reproduced in MCNP5 with a buildup cap. An F4 tally was applied to the sensitive volume of the chamber. The volume was centered about the beam central axis, also at a distance of 5.5 m from isocenter. Both tallies had the photon fluence-to-dose conversion factors applied from ICRP 116 [73].
An F4 tally was applied to each test block of concrete. These were binned ac- cording to energy to track spectral changes introduced through increasing thickness of concrete. These bins were also then used to recompute the relative intensity within each layer as a verification of the determined TVL from the detector or ion chamber measurement.
93 7.3 TVL Measurement and Simulation Results
7.3.1 Measured TVL Thicknesses
All measured attenuation curves are shown as a function of mass-thickness in
Figure 7-4. Measured attenuation curves presented in Figure 7-4 suggest that there is some deviation from the scaling law presented in Equation 6.1 for the expected
TVLs. If Equation 6.1 were to hold perfectly, all of the measured attenuation curves would overlap when plotted as a function of mass thickness. Instead, the measured attenuation curves demonstrate a spread.
Measured TVL1 thicknesses are presented in Table 7.2. Recommended TVLs from NCRP 151 are included for comparison [68]. Comparison TVLs for high density concretes come from NCRP 151 recommended TVLs for flattened beams or the sim- ulated TVLs reported by Kry et al. for unflattened beam, scaled using Equation 6.1, and Facure’s simulation work for on high density concrete [23,47,68]. The measured
TVL1 is consistently lower than those proposed by NCRP 151 or found from simula- tion work. This may tie to the reduced field size that is able to be used with the test port. Measured TVL2 values are presented in Table 7.3, again with comparisons to recommended and simulated TVLs. These values demonstrate better agreement with the simulated TVLs from Facure, often to within 1 cm [23]. The measured TVL2 for a 6 FFF beam also demonstrates agreement to within 1 cm for most densities with those reported by Kry et al. In contrast, the measured TVL2 for a 10 FFF beam is typically thinner than those presented by Kry et al., by as much as 3 cm [47].
Variations between TVLs for flattened versus unflattened beams appear to be minimal beyond the first TVL. The average variation in TVL2 thickness is only 6 mm. This does not support the assertion that unflattened beams can produce a
10% reduction in the amount of shielding necessary, as asserted by Kry et al. [47]. To produce 7 TVLs of attenuation for a 6 MV beam, our measurements predict a required
94 Figure 7-4: All measured transmission curves for multiple photon energies through multiple densities of high density concrete.
104 6 MV 6 FFF 10 FFF Density (g cc−1) Measured NCRP Facure Measured Facure Kry Measured Facure Kry 2.40 26.1 36.3 23.4 30.0 29.7 35.3 2.88 21.5 30.2 26.0 18.8 26.0 29.4 23.5 28.0 29.4 3.44 18.5 25.3 21.0 17.5 21.0 20.5 21.4 25.5 24.6 3.68 16.8 23.6 20.5 15.9 20.5 19.2 19.0 22.1 23.0 3.84 15.4 22.7 19.3 14.0 19.3 18.4 17.6 20.7 22.1 4.48 13.4 19.4 16.9 12.5 16.9 15.8 14.8 17.8 18.9
Table 7.2: Measured TVL1 values compared with accepted and published TVL1 values. All TVLs are in cm [23,47,68].
6 MV 6 FFF 10 FFF Density (g cc−1) Measured NCRP Facure Measured Facure Kry Measured Facure Kry 2.40 27.8 32.3 27.6 26.5 34.2 35.3 2.88 22.8 27.0 24.3 21.6 24.3 22.1 26.1 27.5 29.4 3.44 20.2 22.6 20.9 19.7 20.9 18.5 23.3 21.8 24.6 3.68 18.4 21.1 19.3 18.0 19.3 17.3 20.6 21.0 23.0 3.84 17.5 20.2 18.4 16.9 18.4 16.5 19.6 19.7 22.1 4.48 14.7 17.3 16.2 14.1 16.2 14.2 16.2 16.9 18.9
Table 7.3: Measured TVL2 values compared with accepted and published TVL2 values. All TVLs are in cm [23,47,68].
192.9 cm thickness of 2.40 g cc−1 concrete. If that beam were a 6 FFF beam, the barrier would instead need to only be 189 cm thick, a reduction of 3.9 cm. This is a reduction of 2% in the total barrier thickness. The majority of that difference, 2.7 cm, comes from the variation in TVL1 between the flattened and unflattened beam. This calculation does not attempt to evaluate the variation in necessary barrier thickness with off-axis distance.
Our measurements demonstrate that the second TVL is not necessarily the equilib- rium TVL. Many measurement sets went to 3 full TVLs thick, with each successive
TVL increasing in thickness. The full measurement set is presented in Table 7.4.
NCRP 151 assumes the second TVL remains constant for the remainder of the bar- rier. This may be a good approximation, or at least a conservatively safe guess, but it
95 6 MV 6 FFF 10 FFF Density (g cc−1) 2.40 2.88 3.44 3.68 3.84 4.48 2.40 2.88 3.44 3.68 3.84 4.48 2.40 2.88 3.44 3.68 3.84 4.48 TVL1 26.1 21.5 18.5 16.8 15.4 13.4 23.4 18.8 17.5 15.9 14.0 12.5 29.7 23.5 21.4 19.0 17.6 14.8 TVL2 27.8 22.8 20.2 18.4 17.5 14.7 27.6 21.6 19.7 18.0 16.9 14.1 34.2 26.1 23.3 20.6 19.6 16.2 TVL3 29.5 24.2 21.8 19.8 18.0 15.3 29.5 23.2 21.4 19.4 17.8 14.7 36.1 27.6 24.8 22.3 20.3 16.7
Table 7.4: Measured TVLs beyond the first and second TVL. All values are in cm.
is not intuitive. The energy spectrum of polyenergetic beams, such as those produced by bremstrahlung radiation, is constantly changing while being attenuated, as each energy gets attenuated at varying rates. Lower energy photons will be scattered and absorbed in a smaller thickness than high energy photons, leading to beam hardening.
The beam also has a greater scatter component as it traverses through a thick barrier, which will convert higher energy photons into lower energy photons, leading to beam softening. Which process is dominant is unknown as this variation in the energy spectrum is very difficult, if not impossible, to measure. These TVL measurements suggest that the beam hardening process has a slight edge for the measured field size.
Each successive TVL was larger than the previous one, in some cases by as much as
5 mm.
More evidence for beam hardening comes from the transition from TVL1 to TVL2. The TVLs presented in NCRP 151 show a drop of anywhere between 5-8 cm in the needed thickness from TVL1 and TVL2. Our measurements demonstrate an opposite trend, with TVL2 being several centimeters thicker than TVL1. This inversion sug- gests that much of the lower energy component of the beam gets absorbed rapidly, with the remaining high energy components able to penetrate further through the barrier.
96 7.3.2 MCNP Simulation Results
A comparison of simulated attenuation curves determined using the F4 tally and
the F5 tally versus measured data is presented in Figure 7-5.
The attenuation simulated with either F4 or F5 tallies match extremely well
through multiple TVLs. At very high levels of attenuation, the associated uncertainty
with the F4 tallies becomes high enough to cause some differences in the calculated
TVL. These differences are within the statistical uncertainty of the F4 simulation.
The uncertainty for those same measurements using an F5 tally was much better and
still statistically significant. Simulated TVLs reported during the remainder of this
chapter are from simulations using the F5 tally.
Measured attenuation for 6 MV matches the simulated attenuation very well for
150 pcf and 240 pcf, but not as well for 215 pcf. Based on measured density data, this
set is likely closer to 205 pcf, which is supported by the simulation data. Rescaling the
mass thickness to account for this difference in density brings the measured dataset
into very good agreement with the simulated data. Agreement between measured
and simulated transmission curves is presented in Figure 7-6. Simulated TVLs for 6
FFF match measured TVL data to within 2 cm, with a maximum percent difference
of 5.8%. This is demonstrated in Table 7.5.
Figure 7-7 demonstrates the agreement between the full test port and the uniform
slab geometry for a 4 cm × 4 cm field. The excellent agreement between the two
simulated transmission curves with each other and the measured data demonstrate
the suitability of the test port to represent an idealized measurement. This also
allows us to generalize our model to simulate a larger field size with a high degree of
confidence.
TVL2 data for 4 cm × 4 cm and 40 cm × 40 cm fields simulated using the uniform barrier are compared with the measured 4 cm × 4 cm fields in Table 7.5. Simulated
97 Figure 7-5: 6 MV attenuation curves from simulations (F4 and F5 lines) compared with measured data.
105 Figure 7-6: Measured vs. simulated transmission curves for unflattened beams.
106 Figure 7-7: Transmission curves for 6 MV (top row), 10 MV (middle row), and 18 MV (bottom row) beams incident on the test port and a uniform maze barrier for 3 densities. Measured 6 MV transmis- sion curves are also presented for comparison.
107 Figure 7-8: Transmission curves for 6 MV (top row), 10 MV (middle row), and 18 MV (bottom row) beams incident on a uniform maze bar- rier for 3 densities compared with calculated transmission curves using NCRP 151 recommended TVLs, as well as simulated TVLs from Facure [23,68].
108 6 MV 6 FFF 10 FFF Density (g cc−1) Measured 4x4 40x40 Measured 4x4 40x40 Measured 4x4 40x40 2.40 27.8 26.7 31.1 27.6 26.0 29.8 34.2 31.6 36 3.20 19.9 23.3 19.5 22.3 22.8 26.2 3.44 20.2 18.7 21.7 19.7 18.1 20.9 23.3 21.3 24.3 3.52 18.1 21.2 17.8 20.4 20.7 23.7 3.84 17.5 16.5 19.4 16.9 16.2 18.7 19.6 19.1 21.8 4.00 15.9 18.6 15.3 17.9 18.1 20.8
Table 7.5: Simulated TVL2 values for 4 cm x 4 cm and 40 cm x 40 cm fields compared with measured TVL2 values for a 4 cm x 4 cm field. All TVLs are in cm.
TVLs for a 4 cm × 4 cm field are ∼ 1 cm thinner than measured values. Over a primary barrier of 7 TVLs, this will result in a change of barrier thickness of less than
3”. Increasing the field size from 4 cm × 4 cm to 40 cm × 40 cm results in a more dramatic increase in TVL. The trend of TVL1 being thinner than TVL2 is reproduced by simulations of a 4 cm × 4 cm beam, as shown in Table 7.5, but reverts to TVL1 being thicker than TVL2 for a simulated 40 cm × 40 cm field. This confirms that the variation between TVL1 and TVL2 is dependent on the field size of the radiation beam.
Tables 7.6 & 7.7 show simulated TVLs for multiple high density concretes com- pared with recommended TVLs from NCRP 151 scaled using Equation 6.1.
Comparison between the calculated attenuation curves from the scaled NCRP
TVLs against the simulated TVLs demonstrates two effects [68]. 10 MV and 6
MV TVLs scale very well with density. The agreement between NCRP and simu- lated transmission is extremely close for 10 MV, as demonstrated by the transmission curves, as well as the calculated TVLs presented in Table 7.6. The agreement be- tween the scaled NCRP TVLs and the simulated transmissions for 6 MV is worse, with average differences between TVL2 of about 1 cm. TVL1 demonstrates a greater disagreement, with simulated values between 2-4 cm thinner. However, the difference
98 6 MV 10 MV 18 MV Density (g cc−1) Simulated NCRP Simulated NCRP Simulated NCRP 2.40 32.1 36.3 39.3 40.2 43.4 44.1 3.20 24.4 27.2 29.1 30.1 31.5 33.1 3.44 22.7 25.3 26.9 28.0 29.4 30.8 3.52 22.1 24.7 26.2 27.4 28.6 30.1 3.84 20.2 22.7 24.1 25.1 25.8 27.6 4.00 19.7 21.8 23.0 24.1 25.0 26.5
Table 7.6: Simulated vs. NCRP recommended TVL1 in high density concrete for flattened beams.
6 MV 10 MV 18 MV Density (g cc−1) Simulated NCRP Simulated NCRP Simulated NCRP 2.40 31.1 32.3 37.8 36.3 41.8 42.1 3.20 23.3 24.3 27.5 27.2 29.7 31.6 3.44 21.7 22.6 25.5 25.3 27.3 29.4 3.52 21.2 22.1 24.8 24.7 26.6 28.7 3.84 19.4 20.2 22.7 22.7 24.2 26.3 4.00 18.6 19.4 21.8 21.8 23.1 25.3
Table 7.7: Simulated vs. NCRP recommended TVL2 in high density concrete for flattened beams.
in TVLs approximately scales with increasing density. While our simulated TVL val- ues do not agree with those presented by NCRP 151, the average difference remains constant across the densities simulated [68].
Our simulations do not demonstrate the same reduction in shielding thickness that Facure observed [23]. All instances where data from Facure was available demon- strated that using their TVL thicknesses resulted in over-predicting the transmitted intensity. Facure only evaluated 4, 6, and 10 MV beams, not 18 MV beams which is where we observe the largest difference between recommended and simulated shielding thicknesses.
99 Endpoint Energy → 6 MV 10 MV 4x4 40x40 4x4 40x40 Density (g cc−1) MV FFF MV FFF MV FFF MV FFF 2.40 22.9 20.7 32.1 29.2 30.1 26.2 39.3 35.0 3.20 17.3 14.9 24.4 22.0 22.1 19.0 29.1 26.1 3.44 16.3 14.1 22.7 20.6 20.6 17.9 26.9 24.3 3.52 15.9 13.8 22.1 20.1 20.1 17.5 26.2 23.7 3.84 14.3 12.8 20.2 18.5 18.2 16.2 24.1 21.7 4.00 13.8 12.3 19.7 17.7 17.5 15.5 23.0 20.8
Table 7.8: Comparison of simulated TVL1 for flattened vs unflattened beams
Endpoint Energy → 6 MV 10 MV 4x4 40x40 4x4 40x40 Density (g cc−1) MV FFF MV FFF MV FFF MV FFF 2.40 26.7 25.6 31.1 29.8 33.1 31.6 37.8 36.0 3.20 19.9 19.2 23.3 22.9 24.4 22.8 27.5 26.2 3.44 18.7 17.4 21.7 20.9 22.6 21.2 25.5 24.3 3.52 18.1 17.1 21.2 20.4 22.0 20.7 24.8 23.7 3.84 16.5 15.6 19.4 18.4 19.9 19.1 22.7 21.8 4.00 15.9 15.1 18.6 17.9 19.1 18.1 21.8 20.8
Table 7.9: Comparison of simulated TVL2 for flattened vs unflattened beams
Simulated TVLs for 40 cm × 40 cm fields appear to stabilize after TVL2. TVLs out to TVL4 are presented in Table 7.10.
7.4 TVL Discussion
We have presented measured and simulated TVLs for multiple densities of high density concrete. The lowest density tested, 2.40 g cc−1, is very close to the density of standard concrete, 2.35 g cc−1. This allows us to directly compare our simulated results with recommended TVLs from NCRP 151 [68]. For 10 and 18 MV beams, the simulated TVLs match the recommended TVLs extremely well (within 1 cm) for
100 6 MV 10 MV 18 MV Density (g cc−1) 2.40 3.20 3.44 3.52 3.84 4.00 2.40 3.20 3.44 3.52 3.84 4.00 2.40 3.20 3.44 3.52 3.84 4.00 TVL1 32.1 24.4 22.7 22.1 20.2 19.7 39.3 29.1 26.9 26.2 24.1 23.0 43.4 31.5 29.4 28.6 25.8 25.0 TVL2 31.1 23.3 21.7 21.2 19.4 18.6 37.8 27.5 25.5 24.8 22.7 21.8 41.8 29.7 27.3 26.6 24.2 23.1 TVL3 31.8 23.8 22.2 21.5 19.7 18.9 27.3 25.4 24.7 23.1 21.8 29.4 26.7 26.2 23.7 22.6 TVL4 23.9 22 21.5 19.9 19 23.3 22.7 23.3 22.7
Table 7.10: Simulated TVLs for a 40 cm × 40 cm beam incident on a uniform barrier through TVL4.
2.40 g cc−1 concrete. The agreement between simulated and recommended TVLs for
10 MV holds for all densities simulated.
For 6 MV, the simulated TVLs are thinner when compared to the recommended
−1 TVL for 2.40 g cc concrete. The greatest difference is 4.2 cm for TVL1, with TVL2 only demonstrating a 1.2 cm difference. For a 7 TVL primary barrier, this would produce an 11.4 cm difference in barrier thickness. For high density concretes, the differences between simulated and recommended TVLs appear to scale according to
−1 density. For 4.00 g cc concrete, the simulated TVL1 and TVL2 are 2.1 cm and 0.8 cm thinner, respectively. Using Equation 6.1, these correspond to attenuation by
3.5 cm and 1.3 cm of 2.40 g cc−1 concrete, very similar to the simulated differences.
Therefore, we must conclude that the TVLs for high density concrete in a 6 MV beam are accurately represented by the recommended TVLs for standard density concrete scaled according to Equation 6.1.
For 18 MV, our simulated values agree very well for 2.40 g cc−1 concrete. How- ever, as the density increases, TVL2 values begin to differ from the recommended TVLs by as much as 2 cm for the 4.00 g cc−1 [68]. This variation becomes notable for concrete densities >2.40 g cc−1. The increase in density from 2.40 g cc−1 over the standard density of 2.35 g cc−1 is minor, and accomplished without using a significant amount of steel aggregate. Increasing the concrete density beyond 3.0 g cc−1 requires an increase in the amount of steel necessary, resulting in an increased likelihood of
101 pair production. Our simulations demonstrate that the increased amount of pair pro-
duction decreases the expected TVL for high density concrete beyond what Equation
6.1 would predict.
Measured TVLs and transmission curves obtained using the test port demonstrate
strong agreement with simulated values for the test port geometry. Measured TVLs
also demonstrate agreement within 1 cm for simulations removing the more compli-
cated test port geometry, but utilizing an identical field size. However, the measured
TVLs appear to suffer from a field size effect, as demonstrated in Table 7.5. As the
field size increases, TVL1 increases. When larger field sizes are measured using the test port, the attenuation caused by the surrounding block effectively collimates the
beam to a field very nearly equivalent to a 4 cm × 4 cm field until at least 2 TVLs
have been traversed. This limits the potential usefulness of the test port as a method
to directly verify TVLs for high density concretes, but it strongly supports the use of
the test port for traditionally difficult measurements in radiation protection, where
secondary contaminating radiations confound measurement [51, 82]. The use of the
test port also has verified the high degree of accuracy of our simulations.
Comparison between measured TVLs for unflattened to flattened beam primary
TVLs demonstrate negligible differences (within 1 cm). We do observe a variation in
TVL1 between unflattened and flattened beams, but differences in TVL2 are small enough to be ignored when designing a barrier. Simulated broad beam TVLs do show
some difference in TVL2 that is not present in the smaller measured fields. Figure 7-9 demonstrates that there is a slight decrease in the transmission of unflattened
beams compared to flattened beams. The maximum percent difference in the calcu-
lated TVL2 is <5%. This is less than the percent difference between the measured and simulated TVLs for a 4 cm × 4 cm field. This does not support decreasing the necessary TVL thickness for unflattened beams as has been suggested [47]. In con- trast, this supports that the penetration of unflattened beams is very comparable to
102 Figure 7-9: Measured vs. simulated transmission curves for unflattened beams.
109 that of flattened beams, to within the sensitivity of our measurements.
There is other evidence that the penetrating ability of unflattened beams should not be very different than flattened beams. Variations in dmax depth for unflattened beams are on the order of millimeters and PDD(10) values are equivalent to within
3% when compared to flattened beams [32, 45, 89]. It is also important to note that unflattened beams are produced differently by different manufacturers [97]. Varian machines are the only ones that do not compensate for the loss of beam hardness.
In contrast, Elekta machines increase the NAP so that the resulting PDD curves are nearly identical between flattened and unflattened beams of the same nominal energy. This would suggest that the recommended TVL should be increased for
Elekta machines using FFF beams, as the NAP is higher than it is for traditional
flattened beams.
103 Chapter 8
Conclusions
We have presented extensive simulation work and measurement investigating areas not covered by the current shielding recommendations for radiation therapy vaults.
Many of these results have been applied with great success at the Dana Cancer Center at UTMC. We will continue to investigate the multiple areas that our unique facility allows us, such as differential dose albedos and patient scatter fractions.
For nonstandard vault designs, our simulations demonstrated that the most sig- nificant contribution of scattered photon dose at the vault door was from maze wall scatter. This was a factor of 20 greater than maze scattered radiation. We conclude that maze wall scatter needs to be included in these calculations, and the dose albedo factor for 0.5 MeV should be used. For machines generating >10 MV beams, the capture gamma photon dose overshadows the additional scattered photon dose and requires shielding for more penetrating radiation. Therefore, the additional scattered photon component for a nonstandard vault design can be ignored for high energy accelerators.
Our measurement and Monte Carlo investigation of TVLs for high density con- cretes has demonstrated good agreement between measured and simulated results.
While the inability of the test port to measure full broad-beam TVLs is a limitation of feasibility, the simulation results have been directly compared and verified against
110 measured transmission curves. For 6 and 10 MV beams, scaling recommended TVLs from NCRP 151 represents the most conservative estimate of the required shielding thickness for high density concretes. Unflattened beams did not demonstrate a sig- nificant difference in the simulated transmission relative to flattened beams, contrary to what has been claimed in the literature [47]. For 18 MV beams, there is a notable difference (∼2 cm) between our simulated TVLs and the recommended scaled TVLs from NCRP 151 for concrete densities requiring an appreciable fraction of steel [68].
We attribute this to the increased prevalence of pair production when steel and iron constitute a large fraction of the aggregate by mass. This reduction in TVL thickness corresponds to a 15 cm reduction in the needed barrier thickness for 7 TVLs of high density concrete.
Monte Carlo simulation has demonstrated the suitability of the shielding test port to present a “good geometry” that allows for us to perform accurate measurements of scattering fractions and dose albedos, a geometry that has not been produced in other measurements to the authors knowledge. This allows UTMC a unique advantage in performing radiation protection measurements, as well as direct comparisons to simulation.
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125 Appendix A
Fluence to Dose Conversion
Factors from ICRP 116
126 Energy Conversion Factor Energy Conversion Factor 0.01 0.0685 0.511 2.52 0.015 0.156 0.6 2.91 0.02 0.225 0.8 3.73 0.03 0.313 1.0 4.49 0.04 0.351 1.33 5.59 0.05 0.370 1.5 6.12 0.06 0.390 2.0 7.48 0.07 0.413 3.0 9.75 0.08 0.444 4.0 11.7 0.1 0.519 5.0 13.4 0.15 0.748 6.0 15.0 0.2 1.00 8.0 17.8 0.3 1.51 10 20.5 0.4 2.00 15 26.1 0.5 2.47 20 30.8
Table A.1: Fluence to effective dose conversion factors for photons as a func- tion of energy from an Anterior-Posterior (AP) direction repro- duced from ICRP 116 [73]. Energies are presented in MeV, flu- ence to dose factors are in units of pSv cm2.
127 Energy Conversion Factor Energy Conversion Factor 1.0 ×10−9 3.09 0.15 60.6 1.0 ×10−8 3.55 0.2 78.8 2.5 ×10−8 4.00 0.3 114 1.0 ×10−7 5.20 0.5 177 2.0 ×10−7 5.87 0.7 232 5.0 ×10−7 6.59 0.9 279 1.0 ×10−6 7.03 1.0 301 2.0 ×10−6 7.39 1.2 330 5.0 ×10−6 7.71 1.5 365 1.0 ×10−5 7.82 2.0 407 2.0 ×10−5 7.84 3.0 458 5.0 ×10−5 7.82 4.0 483 1.0 ×10−4 7.79 5.0 494 2.0 ×10−4 7.73 6.0 498 5.0 ×10−4 7.54 7.0 499 0.001 7.54 8.0 499 0.002 7.61 9.0 500 0.005 7.97 10.0 500 0.01 9.11 12.0 499 0.02 12.2 14.0 495 0.03 15.7 15.0 493 0.05 23.0 16.0 490 0.07 30.6 18.0 484 0.1 41.9 20.0 477
Table A.2: Fluence to effective dose conversion factors for neutrons as a func- tion of energy from an Anterior-Posterior (AP) direction repro- duced from ICRP 116 [73]. Energies are presented in MeV, flu- ence to dose factors are in units of pSv cm2.
128