A COMPUTATIONAL METHOD FOR VOXEL TO POLYGON MESH CONVERSION OF ANATOMIC COMPUTATIONAL HUMAN PHANTOMS AND AIRCREW DOSES FROM COSMIC RAY SOURCES
By JUSTIN L. BROWN
A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2017 © 2017 Justin L. Brown To Mom and Dad ACKNOWLEDGMENTS First, I would like to thank my adviser, Dr. Wesley Bolch for providing me with so many opportunities to better myself as a researcher and securing funding for my studies. Without his support and guidance, this work wouldn’t be possible. I also thank my committee member Dr. Lynn Rill for her efforts and guidance in serving on my committee. Next, I would liketo thank my fellow ALRADS members, for getting me started and keeping me going. I would like to thank Dr. Takuya Furuta for always being available to discuss my work. I would also like to thank Dr. Emily Marshall for keeping me diligent and inspiring me to be passionate about my work. Lastly and most importantly, I thank my family, girlfriend, and friends for their constant support throughout my life and academic career. With special thanks to my mother and father for always supporting my passions in no matter what area they may be.
4 TABLE OF CONTENTS page ACKNOWLEDGMENTS ...... 4 LIST OF TABLES ...... 7 LIST OF FIGURES ...... 8 ABSTRACT ...... 9
CHAPTER 1 INTRODUCTION ...... 11 1.1 Computational Phantoms ...... 11 1.2 Polygon Meshes ...... 12 1.3 Cosmic Radiation Sources ...... 13 1.4 Aircrew Dosimetry ...... 13 1.5 Research Purpose ...... 14 2 A COMPUTATIONAL METHOD FOR VOXEL TO MESH CONVERSION ..... 15 2.1 Introduction: Computational Phantoms ...... 15 2.2 Materials and Methods ...... 16 2.2.1 Data Preparation ...... 16 2.2.2 Surface Generation ...... 17 2.2.3 Surface Grouping ...... 18 2.2.4 Surface Simplification ...... 18 2.2.5 Line Grouping ...... 19 2.2.6 Line Simplification ...... 19 2.2.7 Polygon Detection ...... 19 2.2.8 Polygon Correction ...... 20 2.3 Results ...... 20 3 AIRCREW DOSIMETRY FROM COSMIC SOURCES ...... 24 3.1 Introduction: Aircrew Dosimetry ...... 24 3.2 Materials and Methods ...... 24 3.2.1 Source Modeling ...... 24 3.2.2 Airplane Computational Modeling ...... 25 3.2.3 Passenger Computational Modeling ...... 26 3.3 Results ...... 26 4 CONCLUSION AND FUTURE WORK ...... 34 4.1 A Computational Method for Voxel to Mesh Conversion ...... 34 4.2 Aircrew Dosimetry ...... 34
5 REFERENCES ...... 35 BIOGRAPHICAL SKETCH ...... 37
6 LIST OF TABLES Table page 2-1 Meshing time breakdown ...... 23 2-2 Mesh element reduction data ...... 23 3-1 Materials modeled in aircraft model ...... 28 3-2 Ratio of neutron rates at various positions ...... 29 3-3 Neutron rates at various positions within the aircraft ...... 30 3-4 Pilot dose due to neutrons ...... 33
7 LIST OF FIGURES Figure page 2-1 A graphical depiction of a voxel...... 21 2-2 Surface simplification process ...... 21 2-3 Line simplification process ...... 22 2-4 Hole detection process ...... 22 2-5 Ear clipping process ...... 22 2-6 Voxel and tetrahedral mesh comparison ...... 23 3-1 Lithium-6 versus Lithium-7 cross section ...... 27 3-2 Flight route ...... 27 3-3 Flight route particle spectra ...... 28 3-4 Flight route particle spectra summary ...... 28 3-5 Plane surface mesh ...... 29 3-6 Surface and tetrahedral mesh plane model ...... 29 3-7 Aircraft interior and tracking areas ...... 30 3-8 Seated UF adult reference phantoms ...... 30 3-9 Neutron fluence to all tracked areas in Aluminum model ...... 31 3-10 Neutron fluence to all tracked areas in Magnesium model ...... 31 3-11 Neutron fluence material comparison ...... 32 3-12 Neutron fluence probability density functions ...... 32 3-13 Neutron fluence cumulative probability density function ...... 33
8 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science A COMPUTATIONAL METHOD FOR VOXEL TO POLYGON MESH CONVERSION OF ANATOMIC COMPUTATIONAL HUMAN PHANTOMS AND AIRCREW DOSES FROM COSMIC RAY SOURCES By Justin L. Brown December 2017 Chair: Wesley E. Bolch Major: Medical Sciences Over the past 20 years, use of computational human phantoms within existing Monte Carlo radiation transport codes required those phantoms to be in a voxelized format. Recently, however, the current generation of codes such as MCNP, PHITS, and GEANT4 now allow the transport in human computational phantoms represented by polygon mesh structures for both the outer body contour and internal organ structures. While both phantoms provide a high degree of anatomic realism compared to first-generation stylized (or mathematical phantoms), mesh-type phantoms are now considered the state-of-the-art, and permit re-sculpting of individual organs, body circumferences, body size and shape, and extremity articulation – all features not readily available to voxel-based phantoms. However, over the past two decades, a tremendous number of voxel phantoms has been developed from either CT or MR data, and thus there is a need for conversion of existing voxel phantoms to mesh-type formats to allow these additional benefits of the new phantom formats. A major goal of this work isto develop an efficient and accurate methodology to convert voxel-based phantoms to mesh-based phantoms. For this conversion, a boundary detection algorithm is implemented in conjunction with polygon detection to form high-quality meshed data suitable for radiation transport simulations and finite element analyses. This conversion can result in a reduction of required simulation time as well as allowing current voxel data to be used in modern CAD software. An additional goal of this study was to use new mesh-type phantoms to assess the radiation
9 exposure due to passengers and aircrew resulting from secondary particle irradiation following to cosmic radiation exposures of the aircraft. At present, aircrew dosimetry is performed using radiation field models in conjunction with fluence-to-dose conversion coefficients. Thisstudy utilizes a mesh-based geometry and computational human phantoms to assess effective dose as well as organ absorbed doses explicitly during a simulated aircraft flight. A novel method of reduction in secondary neutron dose to the passengers and aircrew are further explored in this study.
10 CHAPTER 1 INTRODUCTION 1.1 Computational Phantoms
When assessing radiation dose to an individual whether, from a medical procedure or an occupational industrial exposure, various forms of radiation detectors are typically used to quantify the radiation dose and the energy spectra of radiation particles reaching the individual. These devices are typically placed on or near the patient (for medical exposures) or in the exposure environment (for occupational exposures). In all cases, these devices give rough estimates of radiation dose to the individual, but they do not accurately capture the true irradiation geometry of the situation. It would be impossible to determine doses to any arbitrary point in the human body with any modern dosimeter in a practical sense. A remedy for this dilemma is the application of computer simulations with detailed computational human phantoms. For radiation dosimetry, it is common to combine computational human phantoms with a general purpose Monte Carlo (MC) radiation transport code. A MC radiation transport code is able to transport particles with random sampling techniques so as to simulate a wide variety of radiation exposures and resulting organ doses. These MC simulations allow for accurate and realistic creation of scenarios in which an individual might be exposed to radiation where organ level doses can be computed. Computational phantoms have rapidly evolved over time progressing from stylized to voxel to hybrid models. Stylized phantoms were the earliest forms of human phantoms and are constructed using simple sets of 3D mathematical surface expressions such as spheres, ellipsoids, cylinders, and cones (Lee and Lee, 2006). These phantoms are limited because they cannot accurately represent the complex internal anatomical structures of the human body. The next generation of voxel-based phantoms provided a remedy to this problem. Voxel phantoms are simply sets of many small cuboids (voxels) assigned to material compositions and mass densities that collectively represent individual organs. Voxel phantoms are developed from segmented patient CT or MR data sets which allow them to much more accurately
11 represent internal and outer human anatomy. A limitation of voxel phantoms is that while they are anatomically accurate of the individual from whom the original CT or MR was taken, it is very difficult to alter in any non-uniform way organ structure, size, position, andbody shape and posture (Lee and Lee, 2006). Hybrid phantoms were thus developed to overcome the shortcomings of both stylized and voxel phantoms. Hybrid phantoms provide a flexible and scalable representation of the human anatomy which is capable to closely match a variety of different human morphometries (heights and weights and body shapes). They are based upon a variety of different surface models techniques such as NURBS surfaces, polygon meshes, or tetrahedral meshes. A study performed by at the University of Florida (UF) resulted in a comprehensive library of 351 hybrid phantoms representing both males and females, and both children and adults, or a wide array of height and weight combinations (Geyer et al., 2014). The UF hybrid phantom library was created from the Centers of Disease Control and Prevention (CDC) National Health and Nutrition Examination Surveys to allow for statistical averages of body contours of males and females at various height/weight combinations in the current U.S. population. 1.2 Polygon Meshes
A polygon mesh is loosely defined as a list of vertices and rules as to how theyare inter-connected. A vertex is simply an arbitrary point in three-dimensional space. A polygon is a collection of lines forming a closed loop. A facet is a collection of coplanar polygons forming a surface with or without the presence of holes. A polygon mesh is thus a collection of facets. Polygon meshes are commonly implemented in modern CAD software to represent a variety of complex shapes. Meshes can be broken down into two categories: surface and volumetric. A surface mesh is a mesh which encloses a volume and can contain an arbitrary number of facets; additionally, there may be other meshes contained within this volume. A volumetric mesh is a collection of mesh elements where all elements have the same number of facets. The most common and flexible of a volume mesh would be a tetrahedral mesh. In thiscase, every mesh element is a tetrahedron where no tetrahedron contains another tetrahedron. These
12 tetrahedral meshes are used in finite mesh analyses as well as radiation transport simulations (Furuta et al., 2017) as it is simple to determine if you are within a specific tetrahedron. By construction, the volume enclosed within each tetrahedron is homogeneous in its elemental and mass composition. 1.3 Cosmic Radiation Sources
Cosmic radiation is ionizing radiation composed of high-energy particles, primarily atomic nuclei originating from space and the sun (ICRP, 2016). These particles interact with the atmosphere and other matter generating additional particles. Particles of importance with respect to dosimetry are: neutrons, protons, photons, electrons, positrons, muons, and although not large in quantity, pions, and nuclear ions. Cosmic radiation can generally be broken up into two components. Galactic comic radiation (GCR) which is radiation originating outside the solar system and solar cosmic radiation(SCR), which is radiation from the sun. Although infrequent the earth can also be exposed to large bursts of highly energetic particles from the sun, known as Solar Particle Events (SPEs). The GCR spectrum is largely composed of protons (85%) with a broad energy range extending to over 1020eV which contribute greatly to dose (ICRP, 2016). The SCR is typically composed of protons with energy below 106eV (99%). The GCR and SCR interact with the earth’s atmosphere to produce a cascade of secondary reactions; all of which can contribute dose. Being primarily charged these particles are also affected by the magnetic field of the sun as well as the earth. Due to theearth’s magnetic field, cosmic radiation is largely directed toward earth’s poles. 1.4 Aircrew Dosimetry
Currently, the U.S. Federal Aviation Agency (FAA) has no regulations regarding radiation exposure to aircrew. In the U.S. presently, only man-made radiation sources are subject to federal regulations on annual radiation dose. Nevertheless, the International Commission on Radiological Protection recommends a consistent approach to all radiation exposure situations so as to optimize radiation exposures and maintain them as low as reasonably achievable (ALARA). At high altitude flights, especially on polar flight routes where the magnetic fieldis
13 weak, aircrew are subjected to increased levels of degraded cosmic radiation. On a transatlantic flight, dose rates have been observed up to9.7 µSv h-1 (Bottollier-Depois et al., 2000). Many other studies have reported similar values on the order of a few µSv h-1. There have been epidemiological studies of aircrew that report the sampled individuals showed reduced cancer mortality (Zeeb et al., 2012). This reduction is likely due to the healthy worker effect. However, certain types of cancer were found to occur at an elevated rate including melanoma and brain cancer (Zeeb et al., 2012). In evaluating dose to aircrew, there are currently several implementations in place. The software package EXPACS (Sato, 2015) uses PHITS (a Monte Carlo radiation transport code) to transport galactic cosmic ray particles through earth’s atmosphere. The resulting particle energy spectra at various atmospheric depths and latitude/longitude locations is used in conjunction with dose conversion coefficients to estimate the flight averaged effective dose. Another study performed by Ferrari etal.(Ferrari et al., 2001) aimed to calculate the effects of aircraft shielding through a detailed mathematical model of the aircraft. The resulting radiation doses to aircrew were assessed using the MC radiation transport code FLUKA. Passengers and crew members were approximated in this study as water cylinders and only whole-body dose was reported. The purpose of this aim of the study is to employ state-of-the-art computational human phantoms to the study of aircrew dosimetry from cosmic ray exposures and to explore the ability of a reduction in secondary neutron dose through the introduction of thermal neutron absorbers within the aircraft passenger seats. 1.5 Research Purpose
The purpose of this research is to develop an efficient methodology to convert voxelized data into a mesh-type surface that is as simplified as possible and suitable for MC radiation transport simulation. Additionally, this thesis aims to evaluate the effect of different metal alloys on neutron dose to aircrew and to validate current techniques for aircrew dosimetry through a detailed model of the aircraft structure and the internal organ anatomy of the passengers and aircrew.
14 CHAPTER 2 A COMPUTATIONAL METHOD FOR VOXEL TO MESH CONVERSION 2.1 Introduction: Computational Phantoms
Most general-purpose Monte Carlo (MC) transport codes utilize a primitive geometry representation, where geometries are defined by basic geometric surfaces such as planes, spheres, ellipsoids, cylinders, and other basic geometric structures. These structures were used in the 1960s and 1970s to represent the human body in radiation transport simulation, owing to the limitations in computer technology at that time, and the need for efficiencies in particle tracking. These so-called stylized phantoms, while fit for purpose at the time of their development, did not provide for very anatomically realistic representations of either the outer body contour or internal organ structure. These limitations of geometric representation led to the development of voxel-based phantoms, defined by a collection of rectangular parallelepipeds of a given size enclosing a given tissue material. Voxel phantoms originate from the image segmentation of CT and/or MR data sets. The voxel size is given either by the resolution of the image data used in the construction of the voxel phantom or the resolution defined when converting a mesh-based phantom to a voxel-based phantom format via a process termed voxelization. This unit voxel size results in much redundancy in large volumes where many voxels are surrounded by voxels of the same material. Recently, advancements have been made enabling the use of meshed geometries in MC radiation transport simulations. These include add-on software to existing MC codes such as DAGMC (Tautges et al., 2009) and explicit incorporation of mesh-capabilities such as in the MC code PHITS (Furuta et al., 2017). In MC radiation transport, voxel representations of human anatomy cause an unnecessary increase computation time due to unneeded estimates of boundary crossing identification. Although mesh-based phantoms are increasingly developed for computational radiation dosimetry, they must be voxelized first to become compatible with the transport code if ameshed geometry is not supported. Even if the transport code supports meshed geometry, utilizing a meshed phantom may not be possible due to surface intersections within the phantom
15 caused either by construction, scaling, or deformation of the phantom. The voxelization process is thus necessary as by construction it eliminates intersections between regions. It also allows for accurate organ volume and mass calculations. A computational method to convert a voxel phantom to a polygon mesh phantom suitable for MC transport and importable to modern CAD software was developed in this study. This method eliminates geometric redundancies allowing for a minimal geometric representation for simulation. This is beneficial for computational human phantoms due to the voxel size being governed by the smallest anatomy to be represented. A mesh phantom is not limited in this respect. This algorithm additionally allows users to utilize the significant number of existing voxel phantoms that have been developed over the past 20 years without making any labor-intensive modifications. 2.2 Materials and Methods
The conversion algorithm developed in this study can be divided into 5 steps. These include (1) data preparation, (2) surface generation, (3) surface simplification, (4) polygon detection, and (5) polygon correction. The resulting mesh has unique vertices and facets with no intersections. 2.2.1 Data Preparation
Several arrays of data are created in the Data Preparation step. First, the phantom data are read into a three-dimensional array of specified size:
16 • The vertex array – an array of three-dimensional points;
• The line array – an array containing two integers representing two connected vertices within the vertex array;
• The facet array – an array containing arbitrary numbers of integers representing the integer position of connected lines within the line array; and
• The facet tag array – an array containing the ordered materials which separate the facets. 2.2.2 Surface Generation
Next, the voxel data is iteratively scanned. Each voxel is checked to determine if neighboring voxels are of a different material composition. If all neighboring voxels areof the same material as the current voxel, no operations will be performed on the current voxel. If a neighbor voxel is found to be of different material, the next step is to determine the needed facets to be produced. At this step, a facet is simply given as a rectangle between the two voxels of different materials. For each facet, there is a possibility of 6 facets, 8 vertices, and12 lines that could be produced as shown in Figure 2-1. Facets, vertices, and lines are produced depending on which adjacent voxels are of different materials. Given which neighbors areof different materials, the required lines and vertices are determined. Once the required lines and vertices are determined, a sliding window of vertices and lines is checked to determine if this information already exists. If the data has already been generated, it is added to the current voxel position in the sliding window. If the data have not already been generated, the data are generated and added to the appropriate arrays. The position of the vertices in three-dimensional space is simply given by the current position within the three-dimensional voxel array. The required lines are given by the required facets. At this point, a facet is composed of only 4 lines forming a square. This process is repeated throughout the phantom array and the window is shifted along the longest axis through which it is iterated. At this step, a surface mesh phantom has been generated whose boundaries only different between different materials (e.g., organs and tissue structures). These boundaries are represented by gridded surfaces which will have to be further simplified and optimized.
17 2.2.3 Surface Grouping
After all necessary facets, lines, and vertices have been generated, the surface grouping process can begin. Surfaces are grouped by three values: separated material, whether x, y, or z is constant, and the value of this constant. The array is sorted as this is the quickest way to determine which facets have these four values equal to other facets. After sorting the facet array, co-planar facets separating the same materials are adjacent in the array. The facets are then put into groups which all separate the same material and are co-planar to one another. The purpose of this grouping is two-fold. First, this grouping reduces the required computation time for the surface simplification step because comparisons only need to be made between grouped facets rather than across the entire list. Secondly, this grouping allows for the surface simplification to be performed in parallel. 2.2.4 Surface Simplification
After facets are grouped together, the facets are then merged. For every facet within each group, a Boolean Union process is performed. To determine if coplanar facets can be combined, the facets are checked to see if they share a line. If the two facets indeed share a line, they can be combined. The Boolean Union process involves three sub-steps:
1. The common line is determined and removed from both facet 1 and facet 2.
2. The remaining lines of facet 2 is added to facet 1.
3. Facet 2 is marked for removal. This process is repeated until no more facets can be incorporated within each group of facets. The facets marked for removal are then removed from the array. After this process is completed, unused lines and vertices are removed and facets and lines are updated to reflect new vertex positions and line positions within their respective arrays. At this point,the phantom surface mesh has been reduced to a minimal number of polygons as demonstrated in Figure 2-2.
18 2.2.5 Line Grouping
After a minimum number of polygon surface representations has been generated, these polygons contain more lines than necessary to enclose the area required. Prior to simplifying the lines, they are grouped in a similar manner. First, lines are scanned iteratively to determine for every vertex how many lines use that vertex. Next, lines are subdivided into co-linear groups. This subdivision allows for the line simplification process to be performed in parallel and thus minimize the time needed as fewer comparisons will need to be made. 2.2.6 Line Simplification
To simplify lines, each group of co-linear lines is scanned iteratively. Line pairs are flagged if both lines share a common vertex. If the lines share a vertex, a Boolean Union can be performed if the vertex that is shared is only used by two lines globally. If this is the case, then by definition only these two lines share this vertex and they are both not necessary to properly represent a surface. The Boolean Union process is then performed for these two lines in a similar manner as used for facets:
1. The common vertex shared by only line 1 and line 2 is determined
2. The shared vertex in line 1 is replaced by the unshared vertex in line 2.
3. Line 2 is marked for removal. This process is repeated until no additional lines can be incorporated within each group of lines. The lines marked for removal are thus removed. The unused vertices are then also removed. The line and facet arrays are then updated to reflect the new position of the vertices and lines in their respective arrays. At this stage, the surface phantom is represented by the minimum possible surfaces and these surfaces are represented by the minimum possible number of lines as demonstrated in Figure 2-3. 2.2.7 Polygon Detection
After these two simplification processes, the facets are now composed of an unordered set of lines and polygons. By construction, the lines contained within each facet must form at least one closed loop (i.e., a polygon). Within each facet, polygons are formed by simply end
19 matching lines until no more lines remain. If within one facet multiple polygons are formed by construction, one of these polygons must be interior to the other, thus forming a hole within the outer polygon. This is determined easily by a bounding box as demonstrated in Figure 2-4. This process is repeated for each facet. 2.2.8 Polygon Correction
Even though the technique is computationally fast, using an end matching method to construct polygons can possibly create self-intersections within each polygon. Self-intersections occur because as each line is added to the polygon vertex repetition is not checked as it would result in a significant decrease in efficiency. Instead, after polygons have been created, they are checked to see if any vertices other than the start/end vertex have been used multiple times. If this is the case, an ”ear-clipping” method is employed. To ear-clip a polygon, one creates a new polygon from the lines between the vertex that is used multiple times. These lines are then removed from the larger polygon and a new polygon is added to the facet as demonstrated in Figure 2-5. At this point, the mesh is now a quality mesh that is represented by the list number of surfaces. If the surface-mesh phantom is to be converted to a tetrahedral-mesh phantom, as required by the PHITS radiation transport code, the open-source conversion code Tetgen (Si, 2015) may be applied. The mesh can also be triangulated and exported in a file format acceptable to most modern CAD software codes. 2.3 Results
The conversion algorithm developed in this study produces a topologically equivalent mesh phantom from the source voxel data as a minimum representation of surfaces enclosing homogeneous volumes (Figure 2-6). Since this is a conversion of voxel data the surfaces will be stair-stepped in nature, to correct a smoothing process will need to be developed. The entire process takes less than 5 minutes on a single processor (Intel E5-2698 v3,2.3Gz) with the longest portion being the surface simplification stage as shown in Table 2-1. The code presently used was compiled using Intel’s C++ compiler with the ”-O3” option. The reduction greatly decreases the mesh elements by factors ranging from 2 to 3 as shown in Table 2-2.
20 Figure 2-1. A graphical depiction of a voxel depicting the material(green), lines(red), facets(blue) and vertices(black).
Figure 2-2. A graphical depiction of the surface simplification process
21 Figure 2-3. A graphical depiction of the line simplification process
Figure 2-4. A graphical depiction of the hole detection process
Figure 2-5. A graphical depiction of the ear clipping process
22 Table 2-1. Time breakdown of the voxel to mesh conversion process. Step Time(seconds) Read in Data 1 Generate Surfaces 15 Surface Grouping 15 Surface Simplification 100 Line Grouping 5 Line Simplification 5 Polygon Detection & Correction 5
Table 2-2. Number of mesh elements in the UF adult male voxelized reference phantom following conversion to a gridded mesh both before and after the surface and line simplification steps. Mesh Object Before Reduction After Reduction Vertices 3,795,904 1,636,236 Lines 8,112,530 2,869,443 Facets 4,318,451 1,236,156
Figure 2-6. Comparison of a voxel representation (left) and a tetrahedral mesh (right) representation of a head
23 CHAPTER 3 AIRCREW DOSIMETRY FROM COSMIC SOURCES 3.1 Introduction: Aircrew Dosimetry
This study aims to assess the effects of replacing industry standard aluminum seats within an aircraft with a magnesium alloy doped with a thermal neutron absorber. Materials for this study were selected with goals of both weight reduction and neutron fluence reduction as design goals. For the current study, only the passenger seat of the airline was replaced with a magnesium alloy. All other aircraft components were left unchanged from the current design. In most aircraft, the seats account for an appreciable percentage of total aircraft mass. The material selected, which has been produced in the laboratories of Dr. Michele Manuel at the University of Florida, is a magnesium alloy consisting of magnesium, lithium, and aluminum with an overall mass density 1.42 g/cm(3). This alloy consists of 89% magnesium, 8% lithium-6, and 3% aluminum by mass. For a comparative material, 7075 aluminum was selected with an overall mass density of 2.81 g/cm(3). This alloy consists of 91.1% aluminum, 5.6% zinc, 2.1% magnesium and 1.2% copper by mass. The lithium in the magnesium alloy was assumed to be fully enriched in the isotope 6Li. This isotopic enrichment was selected as a best-case scenario for its high neutron cross-section with a goal of fluence reduction of cosmic-ray generated secondary neutron (Figure 3-1). 3.2 Materials and Methods
3.2.1 Source Modeling
The atmospheric source considered for this study was taken from Excel-based Program for Calculating Atmospheric Cosmic-ray Spectrum (Sato, 2015). EXPACS, developed by Dr. Sato from the Japan Atomic Energy Agency (JAEA), allows the user to select altitude, latitude, longitude, and date from which the user may output the local cosmic ray particle energy spectrum at that flight location. For this study, a flight route from Los Angeles International Airport (LAX) to London Gatwick Airport (LGW) was considered with a cruising altitude of 30,000 feet (Figure 3-2) . The flight route was computed using a geodesic route, acommon
24 method of determining flight routes. A geodesic route is simply defined as the shortest route between two points on a spherical surface. Using 100 sampled points along this route, the resulting flight cumulative particle spectra were generated by averaging the EXPACS spectrum output data across these sampled flight positions. The particle energy spectra and a summary of the distribution of particle types are given Figure 3-9 and Figure 3-4. Almost 80% of the particles incident upon the aircraft are photons, which neutrons accounting for an additional 16% of all incident particles. 3.2.2 Airplane Computational Modeling
For this study, a Boeing 747 airplane polygon mesh model was used matching the specifications in a published Boeing technical reportBoeing ( , 2011). For the hull and floor, a thickness 2 cm of aluminum was assumed although, in the literature, this value can be highly variable (Ferrari et al., 2004). Airplane fuel and cargo mass were modeled to match the mass specified in the Boeing report. For radiation transport, the mesh model was converted from a triangulated surface mesh to a tetrahedral mesh. An in-house Python script was written to convert the surface mesh (Figure 3-5 ) into a format acceptable by TetgenTM. This script assumes that the triangulated surfaces used to represent the aircraft have surface normals directed outward of the volume and projects a point inside the volume. With interior points defined, the mesh was then converted to a tetrahedral mesh using Tetgen (Figure 3-6) for Monte Carlo radiation transport. To minimize computation time, volumes defining the air, passengers, and seats (magnesium alloy or aluminum) were homogenized. Table 3-1 gives further details for the modeled materials. PHITS, a general-purpose Monte Carlo radiation transport code was used to perform radiation transport. For transport, the tetrahedral airplane model was imported into PHITS surrounded by air of density and composition appropriate for the altitude. The atmospheric source was modeled as an isotropic source around the plane. All generated particles were transported and tracked to various positions about the cabin(Figure 3-7). This transport was performed twice, one for each alloy to assess the difference in selected chair alloys.
25 All simulations were performed on the University of Florida HiPerGator2.0 cloud computing platform which alloys researchers access for over 35,000 discrete computing units. This large amount of resources is necessary as for present study over 1 billion particles were necessary to be transported for reliable data. On a traditional computer, this would require months to years of computational time. 3.2.3 Passenger Computational Modeling
To model the radiation environment to the passengers, the UF adult reference male and female phantoms were used. First, the phantoms were altered with an in-house script to be positioned in a seated position (Figure 3-8). The particle fluence spectrum obtained at the passenger location was then transported as an isotropic source around the seated phantom. To model the effects of neighboring passengers, the volume around the phantom was modeled asa homogenized material in the same way it was in the full airplane simulation. The Monte Carlo radiation transport code PHITS was used to compute both organ doses and particle fluences at the passenger and crew locations. 3.3 Results
From the PHITS simulation results, it can be seen that replacing the aluminum with the 6Li-doped magnesium alloy within the seats causes a dramatic reduction of the neutron fluence at the pilot position (see Table 3-3). The use of the magnesium alloy significantly reduces the low-energy secondary neutrons due to the presence of Lithium-6 (Figure 3-11). This results in an overall harder neutron energy spectrum (Figures 3-12 and 3-13 ) due to the reduction of low-energy neutrons while high-energy secondary neutrons are not altered significantly. Throughout the aircraft for both alloys, there is a down shifting in neutron fluence(see Table 3-2) depending on the amount of surrounding material (fuel, luggage, or passengers) but no change in energy distribution (Figure 3-9 and Figure 3-10). After continuing particle transport on both the male and female phantoms, it can be seen that the seat material does not have much impact on the effective dose of a passenger (see Table 3-4) as the values are nearly equivalent.
26 Figure 3-1. Lithium-6 versus Lithium-7 energy-dependent neutron cross section. Data from OECD JANIS database.
Figure 3-2. LAX to LGW Google Earth flight route
27 Figure 3-3. LAX to LGW many particle spectra outputted from EXPACS.
Figure 3-4. LAX to LGW many particle spectra distribution from EXPACS
Table 3-1. Materials modeled in aircraft model Object Material Hull 7075 Aluminum Cargo Cellulose Fuel Aviation Turbine fuel Floor 7075 Aluminum Passenger Area Water ,Alloy, and Air (homogenized by mass)
28 Figure 3-5. The surface mesh Boeing 747 aircraft showing the fuel(red), cargo(purple), floor(blue), and aluminum hull(green)
Figure 3-6. The surface mesh before (left) and after (right) conversion to a tetrahedral mesh
Table 3-2. Neutron rates at various positions within the aircraft ratios normalized to the pilot position (1) n0 n0 n0 n0 Position Aluminum (( s )i /( s )1) Magnesium (( s )i /( s )1) 1 1 1 2 0.45 0.52 3 0.36 0.42 4 0.49 0.55 5 0.76 0.76 6 0.67 0.67
29 Figure 3-7. Interior of Boeing 747 aircraft showing areas where particle fluence is tallied
Figure 3-8. The UF adult reference male and female reference phantoms in seated positions.
Table 3-3. Neutron rates at various positions within the aircraft Position Neutrons per Second Atmospheric Source 2.844529E+09 Aluminum Pilot Position 1.763854E+07 Magnesium Alloy Pilot Position 8.981620E+06
30 Figure 3-9. The resulting neutron fluence to all areas of the airplane for the Aluminum alloy.
Figure 3-10. The resulting neutron fluence to all areas of the airplane for the Magnesium alloy.
31 Figure 3-11. The resulting neutron fluence to the pilot area of the airplane for both Aluminum and Magnesium alloys.
Figure 3-12. The resulting neutron fluence probability density function (PDF) to the pilot area of the airplane for both Aluminum and Magnesium alloys. The atmospheric neutron source is also shown.
32 Figure 3-13. The resulting neutron fluence cumulative probability density function (CDF) to the pilot area of the airplane for both Aluminum and Magnesium alloys. The atmospheric neutron source is also shown.
Table 3-4. Pilot dose due to neutrons Alloy Male Effective Dose Female Effective Average Effective per Second (Sv/s) Dose per Second Dose per Second (Sv/s) (Sv/s) Aluminum Pilot 2.381E-08 2.385E-08 2.383E-08 Position Magnesium Pilot 2.371E-08 2.381E-08 2.376E-08 Position
33 CHAPTER 4 CONCLUSION AND FUTURE WORK 4.1 A Computational Method for Voxel to Mesh Conversion
The proposed algorithm is both efficient and accurate and converts a voxelized dataset into a surface mesh. The resulting mesh can be used in MC radiation transport codes capable of utilizing surface or tetrahedral mesh geometries. This algorithm can be applied to any voxelized data including segmented DICOM data. The proposed algorithm is easy to parallelize and can run in OpenMP implementations. The voxel-to-surface mesh conversion algorithm should offer near linear speedups as no sections require a process safe lock (mutex). Future work entails the development of an in-house triangulation software so the resulting mesh can be more easily used in CAD software. Additionally, a mesh smoothing algorithm will need to be developed for applications requiring smoother surfaces. 4.2 Aircrew Dosimetry
The current study demonstrated that the replacement of standard aluminum-based airline seats with a new Mg-based alloy doped with Li-6 provided a significant decrease in low-energy neutron fluence at various passenger locations in the aircraft. However, higher-energy neutrons produced via atmospheric cosmic-ray interactions are still present in both aircraft composed of both materials, and thus no decrease in passenger effective dose was seen with this seat composition change. Although the proposed material performed extremely well in reducing lower-energy neutron fluence, the fluence reduction was not within the energy regionthat contributes the most organ and effective dose. Even though the dose reduction wasnot apparent, the weight reduction is still very significant for aircraft construction and fuel efficiency. Future work will be focused on further validation of EXPACS dosimetry for airline crew exposures to cosmic rays and their secondary particles.
34 REFERENCES Boeing. “Airplane characteristics for airport planning - 747.” Boeing Commerical Airplanes (2011).November: 126. URL http://www.boeing.com/assets/pdf/commercial/airports/acaps/747{_}8.pdf Bottollier-Depois, J F, Chau, Quang, Bouisset, Patrick, Kerlau, Gilles, Plawinski, Luc, and Lebaron-Jacobs, Laurence. “Assessing exposure to cosmic radiation during long-haul flights.” Radiation research 153 (2000).5 Pt 1: 526–532. URL http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.511.3179{&}rep= rep1{&}type=pdf Ferrari, A, Pelliccioni, M, and Rancati, T. “A method applicable to effective dose rate estimates for aircrew dosimetry.” Radiation protection dosimetry 96 (2001).1-3: 219–22. URL https://watermark.silverchair.com/api/watermark?token= AQECAHi208BE49Ooan9kkhW{_}Ercy7Dm3ZL{_}9Cf3qfKAc485ysgAAAfEwggHtBgkqhkiG9w0BBwagggHeMIIB2gIBADCCAdMGCSqGSIb3DQEHATAeBglghkgBZQMEAS4wEQQM-gcz6W5cvHyk8wFwAgEQgIIBpG5XCunWjpPN6bqXq9Of0jQrcv3u2Px-tueCy9ljpC9B0 Ferrari, A., Pelliccioni, M., and Villari, R. “Evaluation of the influence of aircraft shielding on the aircrew exposure through an aircraft mathematical model.” Radiation Protection Dosimetry 108 (2004).2: 91–105. Furuta, Takuya, Sato, Tatsuhiko, Han, Min Cheol, Yeom, Yeon Soo, Kim, Chan Hyeong, Brown, Justin L, and Bolch, Wesley E. “Implementation of tetrahedral-mesh geometry in Monte Carlo radiation transport code PHITS.” Physics in Medicine and Biology 62 (2017).12: 4798–4810. URL http://stacks.iop.org/0031-9155/62/i=12/a=4798?key=crossref. 533a7d928e2b2023c605e89e594185ce Geyer, Amy M, O’Reilly, Shannon, Lee, Choonsik, Long, Daniel J, and Bolch, Wesley E. “The UF/NCI family of hybrid computational phantoms representing the current US population of male and female children, adolescents, and adults—application to CT dosimetry.” Physics in Medicine and Biology 59 (2014).18: 5225–5242. URL http://stacks.iop.org/0031-9155/59/i=18/a=5225?key=crossref. 8836e5770fdf382ee635ca96b3e5553a ICRP. “Annals of the ICRP 132.” Radiological Protection from Cosmic Radiation in Aviation 45 (2016).1: 5–48. Lee, Choonsik and Lee, Jai-Ki. “Computational anthropomorphic phantoms for radiation protection dosimetry: evolution and prospects.” Nuclear Engineering and Technology 38 (2006).3: 239–250. URL https://www.kns.org/jknsfile/v38/JK0380239.pdf
35 Sato, Tatsuhiko. “Analytical model for estimating terrestrial cosmic ray fluxes nearly anytime and anywhere in the world: Extension of PARMA/EXPACS.” PLoS ONE 10 (2015).12. URL http://journals.plos.org/plosone/article/file?id=10.1371/journal.pone. 0144679{&}type=printable Si, Hang. “TetGen, a Quality Tetrahedral Mesh Generator.” AMC Transactions on Mathemati- cal Software 41 (2015).2: 11. URL http://dx.doi.org/10.1145/2629697 Tautges, Timothy J, Wilson, Paul P H, Kraftcheck, Jason A, Smith, Brandon M, and Henderson, Douglass L. “Acceleration Techniques for Direct Use of Cad-Based Geometries in Monte Carlo Radiation Transport.” Computational Methods & Reactor Physics (2009): 1–11. URL http://mathematicsandcomputation.cowhosting.net/MC09/pdfs/202864.pdf Zeeb, Hajo, Hammer, Gaël P, and Blettner, Maria. “Epidemiological investigations of aircrew: an occupational group with low-level cosmic radiation exposure.” Journal of Radiological Protection 32 (2012).1: N15–N19. URL http://iopscience.iop.org/article/10.1088/0952-4746/32/1/N15/pdfhttp://stacks.iop. org/0952-4746/32/i=1/a=N15?key=crossref.931f6f9ce07ea3dae7d4ac0b4e3c97e5
36 BIOGRAPHICAL SKETCH Justin L. Brown was born in 1994 in Boise, Idaho to Mark and Eladia Brown. He attended Timberline High School and graduated in 2012. He chose the University of Idaho to further his education graduating with a Bachelor of Science in applied mathematics with an emphasis in computational modeling and general physics and a Bachelor of Science in applied physics in May 2015. He plans to continue his research under the direction of Dr. Wesley E. Bolch in pursuit of a PhD.
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