A MACROSCOPIC AND MICROSCOPIC STUDY OF RADON …

A MACROSCOPIC AND MICROSCOPIC STUDY

OF RADON EXPOSURE USING GEANT4 AND

MCNPX TO ESTIMATE DOSE RATES

AND DNA DAMAGE

by

Mary Evelyn van den Akker

A thesis submitted to the faculty of The University of Utah

in partial fulfillment of the requirements for the degree of

Master of Science

in

Nuclear Engineering

Department of Civil and Environmental Engineering

The University of Utah

December 2015

Copyright © Mary Evelyn van den Akker 2015

All Rights Reserved

The Un i vers i t y of Utah Graduate School

STATEMENT OF THESIS APPROVAL

The thesis o f _________________ Mary Evelyn van den Akker_______________

has been approved by the following supervisory committee members:

Tatjana Jevremovic , Chair 7/22/2015Date Approved

Terry Ring , M ember 7/22/2015Date Approved

Luther McDonald , M ember 7/22/2015Date Approved

and by ____________________Michael E. Barber____________________ , Chair/Dean of

the Department/College/School o f _______ Civil and Environmental Engineering_____

and by David B. Kieda, Dean o f The Graduate School.

ABSTRACT

Radon is considered the second-leading cause of lung cancer after smoking. Epidemiological

studies have been conducted in miner cohorts as well as general populations to estimate the risks

associated with high and low dose exposures. There are problems with extrapolating risk estimates

to low dose exposures, mainly that the dose-response curve at low doses is not well understood.

Calculated dosimetric quantities give average energy depositions in an organ or a whole body, but

morphological features of an individual can affect these values. As opposed to human phantom

models, Computed Tomography (CT) scans provide unique, patient-specific geometries that are

valuable in modeling the radiological effects of the short-lived radon progeny sources. Monte Carlo

particle transport code Geant4 was used with the CT scan data to model radon inhalation in the

main bronchial bifurcation. The equivalent dose rates are near the lower bounds of estimates found

in the literature, depending on source volume. To complement the macroscopic study, simulations

were run in a small tissue volume in Geant4-DNA toolkit. As an expansion of Geant4 meant to

simulate direct physical interactions at the cellular level, the particle track structure of the radon

progeny alphas can be analyzed to estimate the damage that can occur in sensitive cellular structures

like the DNA molecule. These estimates of DNA double strand breaks are lower than those found

in Geant4-DNA studies. Further refinements of the microscopic model are at the cutting edge of

nanodosimetry research.

CONTENTS

ABSTRACT iii

LIST OF TA B LE S vi

ACKNOWLEDGMENTS vii

CHAPTERS

1. INTRODUCTION ................................................................................................................ 11.1 Thesis Objectives ............................................................................................................ 31.2 Organization of Thesis...................................................................................................... 3

2. RADON EXPOSURE IN EPIDEMIOLOGICAL STUDIES, DOSIMETRIC MODELS, AND COMPUTATIONAL ANALYSIS 52.1 Epidemiological S tud ies................................................................................................. 52.2 Radon Dosimetry Studies ............................................................................................... 6

2.2.1 Dosimetric Models and Quantities......................................................................... 72.2.2 Units of Activity Concentration............................................................................. 9

2.3 Microdosimetry and Nanodosimetry S tud ies................................................................ 92.4 Computational Tools........................................................................................................ 10

3. LUNG CANCER INCIDENCE AND MORTALITY: RADON EXPOSURE IN UTAH 123.1 Introduction....................................................................................................................... 123.2 Levels of Radon in U ta h ................................................................................................. 123.3 Utah Lung Cancer Incidence ........................................................................................... 14

4. MACROSCOPIC ANALYSIS OF RADON EXPOSURE 184.1 Introduction....................................................................................................................... 184.2 MCNPX Lung M o d e l...................................................................................................... 18

4.2.1 Short-Lived Rd-222 Progeny ................................................................................ 184.2.2 Radon G a s ............................................................................................................... 24

4.3 Geant4 DICOM Lung M odel........................................................................................... 254.4 Estimating Risk from Radon Exposure........................................................................... 35

5. MICROSCOPIC ANALYSIS OF RADON EX PO SU RE 385.1 Introduction....................................................................................................................... 385.2 Geant4-DNA M o d e l........................................................................................................ 385.3 Particle Track Structure Analysis .................................................................................... 405.4 Merging the Geant4 Models............................................................................................. 45

6. CONCLUSION....................................................................................................................... 49

7. FUTURE W O R K .................................................................................................................. 51

7.1 Respiratory Dynamics and Attached/UnattachedFractions............................................................................................................................ 51

7.2 Chemical Reactions in the C e l l ...................................................................................... 52

APPENDICES

A. MCNPX INPUT FILE ......................................................................................................... 53

B. PYTHON S C R IP T ................................................................................................................245

C. GEANT4 DICOM MACRO ............................................................................................... 248

D. GEANT4-DNA M ACRO .......................................................................................................249

E. DBSCAN SCRIPT ................................................................................................................250

REFERENCES ..............................................................................................................................251

v

LIST OF TABLES

1.1 238U decay chain with short-lived radon progeny in bold................................................. 2

3.1 Average radon concentrations in Utah counties of interest (30) 14

4.1 MCNPX equivalent dose rates from homogeneous distribution of radon progeny de­cay products in the lung 23

4.2 Radon gas inhalation dose equivalent in MCNPX 25

4.3 Equivalent dose rates (mrem/yr) obtained from Geant4 absorbed dose (C=cylindrical source and E=ellipsoidal source and all source volumes in mm3) 31

4.4 Dose conversion factors per Geant4 source volume 34

5.1 Ionization events and clusters of size 3.2 nm for alpha particle energies 42

5.2 Probability of DNA hits per cell from ionization clusters found using DBSCAN and Geant4-DNA and (5.2) 45

5.3 Number of DSBs per cell cycle using number of deposited alpha emitters from Geant4 DICOM source volume 47

ACKNOWLEDGMENTS

Many thanks to Dr. Jevremovic and the entire group at UNEP for support, encouragement,

and learning opportunities. I was fortunate to benefit from the computational expertise of Seth

Streitmatter, Greg Moffitt, and Matt Lund; thanks to each of them for their guidance and help with

MCNP and Geant4. I was supported by a fellowship from the Nuclear Regulatory Commission

and I am grateful for the the opportunities made possible by them. I am grateful for the love and

encouragement from my father and my family. Love to Wylie for helping me find grit.

CHAPTER 1

INTRODUCTION

The study of low-dose radiation exposure is complicated because the dose-response curve in the

low-dose region is not well understood. It is not known if the risks of exposure to ionizing radiation

are beneficial at low levels (hormesis), if the risk is linear with exposure (Linear No-Threshold), if

there is some threshold at which radiation exposure is safe, or if the risk is greater at lower levels

(supralinear). At present the model most relied upon is the Linear No-Threshold (LNT) model,

which posits that any exposure to ionizing radiation, no matter how small, carries an excess relative

risk (ERR) of cancer mortality (1) and this risk increases linearly with exposure.

222Rn is a source of low-dose ionizing radiation that contributes significantly to a person’s annual

background dose. It is present in the decay chain of 238U and, as a noble gas with a half-life of 3.82

days, it has the opportunity to escape from the soil and rocks and become airborne. The complete

238U decay chain is presented in Table 1.1 (2).

Once airborne the heavy, inert gas can collect in poorly ventilated, low-lying enclosures. Evi­

dence for this occurrence manifests in homes and other dwellings containing measurable concentra­

tions of alpha-emitting radon. Being chemically inert, radon gas poses little threat in relatively small

activity concentrations because it does not collect or deposit in the body. It is the short-lived radon

progeny, two of them alpha-emitters, which can deposit, collect, and decay in the airways. When

the radon decays, the solid decay products (in descending order: 218Po, 214Pb, 214Bi, and 214Po) can

attach to aerosol materials as the “attached fraction.” The decay products can also remain somewhat

free, or bound to water molecules. These are referred to as the unattached fraction and are the most

likely to deposit firmly in the respiratory system, mostly the main bronchial airway (3)(4)(5). The

alpha radiation from the 218Po and 214Po delivers the majority of the dose due to its short range in

tissue. The beta and gamma emissions contribute significantly less dose and are often neglected

when estimating radon effects.

There are two other radon isotopes: 220Rn (thoron) and 219Rn (actinon). Their gaseous form

might give them the chance to collect in homes but their half-lives are so short (56 s and 4 s,

respectively) compared to the 222Rn that their chance of decaying before escaping their matrix

2

Table 1.1: 238U decay chain with short-lived radon progeny in bold.

238U Decay Chain Half-Life Main Decay Path238u 4.5 x 10 6y a234Th 24.1 d P234Pa 1.159m P234U 2.4 x 105y a230Th 7.5 x 104y a226Ra 1600 y a222Rn 3.8 d a218Po 3.1 m a214Pb 26.8 m P214Bi 19.9 m P214Po 164 ̂ s a210Pb 22.2 y P210Bi 5.0 d P210Po 138.4 d a206Pb stable -

formation and becoming airborne is much greater (4). Thus, contributions of thoron and actinon

progenies to lung dose are usually neglected (4).

Currently, the lung cancer risk estimates for occupational and residential radon exposures are

based on epidemiological studies of miners. Lung cancer mortality is correlated with exposure

to radon progeny in the miners, typically working in conditions that do not qualify as low-dose

exposure. The results of these studies are extrapolated to those whose exposure is residential and

low-dose. Uncertainty accompanies every measurement or calculation but is often absent when these

epidemiological data are used for residential radon exposure risk assessment. The BEIR VI report

addressed these issues and found that data on individual exposures were not well defined in terms of

spatial variation of radon concentrations, time spent in different zones, and various other parameters

having to do with individual work load, respirator use, and different types of work (6). Ruzer also

reported on the problem of accurate reporting in mines where data were suppressed if they were

outside the established safety limits. Ruzer found that for these studies the uncertainties amounted

to “hundreds of percent” and consequently put into question all of the risk estimates based on these

studies.

Computed Tomography (CT) data comprising patient-specific geometries are a promising way

to model the radon progeny deposits and simulate the resulting doses to the lungs. These files can be

converted to geometries in Monte Carlo particle tracking codes like MCNP and Geant4 (7)(8). The

study must go further to estimate not just a dose rate associated with radon concentrations but also

the damage caused by interactions of the radon progeny alphas on a cellular level. The Geant4-DNA

3

application, dnaphysics, is used to gather information on the radon progeny alpha track structure.

Ionization events are collected and clustered using a DBSCAN algorithm to determine which events

would interact in a close enough distance to form a possible double strand break (DSB) in the DNA

molecule of a cell (9)(10).

Determining the expected number of alpha-emitters from an indoor radon concentration that

could deposit in the bronchial bifurcation during a given time and using the probabilities of DSB for

each alpha energy, the macroscopic models and the microscopic models are linked through source

volume to DNA damage. The patient-specific models and DNA damage models can predict dose

rates and illuminate the effects of low-dose radiation exposure.

1.1 Thesis ObjectivesThere are currently no studies using CT scan geometries that attempt to predict the dose from

radon progeny in human lungs. The dose rates are historically estimated using dosimetric models

put forth by ICRP using human phantoms (11). However, these phantoms do not account for unique

patient geometries that can influence the deposition of the radon progeny, such as main bronchial

bifurcation diameter. The challenges with all dosimetric models are associated with respiratory

dynamics, the most important of which include: lung clearance mechanisms, respiration rate, and

lung organ capacity. Furthermore, the dose rates averaged over a whole body or a lung are not readily

correlated with biological effects at the low-dose level. This is why much of the ongoing research is

being done on the cellular level to determine the direct and indirect effects of ionizing radiation that

lead to damage of the DNA molecule. The nanodosimetry is a relatively new field that attempts to

link the physical interactions of the ionizing particle in the cell with biological endpoints, like cell

mutagenesis. The objectives of this research are as follows:

1. Analyze the risks associated with radon concentrations commonly found in Utah.

2. Use Monte Carlo codes MCNPX and Geant4 to estimate dose rates from short-lived radon

progeny using CT scan geometry.

3. Obtain nanodosimetric quantities from radon progeny alphas in a small cell volume and relate

these quantities to DNA damage due to ionization events.

4. Relate indoor concentrations of radon and respiratory dynamics to damage incurred at a cel­

lular level from radon progeny deposits.

1.2 Organization of ThesisA literature review is presented in Chapter 2. Chapter 3 includes information on the radon

concentrations, lung cancer incidence rate, and smoking statistics in Utah counties. Chapter 4

describes the Monte Carlo codes and methods used to model the large-scale radon exposure in the

4

lungs. Chapter 5 describes the nanodosimetric simulations and the ionization event clustering. The

results are discussed in Chapter 6. The work is concluded with recommendations for future work in

Chapter 7.

CHAPTER 2

RADON EXPOSURE IN EPIDEMIOLOGICAL

STUDIES, DOSIMETRIC MODELS, AND

COMPUTATIONAL ANALYSIS

2.1 Epidemiological StudiesRadon is considered a lung carcinogen and the second leading cause o f lung cancer. Many

studies have been done around the world to identify the risk associated with radon exposure and

epidemiological evidence is the way the risk is characterized (12). The four elements of risk as­

sessment as defined by the United States National Research Council in a 1983 report titled Risk

Assessment in the Federal Government: Managing the Process include hazard identification, dose

response assessment, exposure assessment, and risk characterization. In the case o f radon, these

elements identify whether radon is a hazard, how the risk of being exposed to it varies with dose, what

patterns ofexposure the public may have, and the magnitude ofthe hazard as well as the associated

uncertainties (12). These help identify weaknesses in current knowledge, opportunities for research,

and serve as a tool to approaching risk management associated with exposure to naturally occurring

radioactive material. There is a need to minimize the risk of cancer mortality and identify levels at

which the radon concentration indoors poses less than or equal to an acceptable risk.

The largest challenge facing researchers is to define the dose-response relationship at low doses.

A comprehensive review of available biological and biophysical data supports an LNT risk model

that predicts that the risk of cancer proceeds in a linear fashion at lower doses without a threshold

and that the smallest dose has the potential to cause a small increase in risk to humans (1). Cohort

studies ofminers working in high to moderate dose environments provide a framework from which

to extrapolate the excess relative risk (ERR) at low-dose residential concentrations.

The association between radon and lung cancer risk have been examined in large-scale studies

and pooled studies to determine how increasing radon concentrations are related to lung cancer mor­

tality. The bulk ofthe work agrees that radon exposure correlates to lung cancer and that there exists

an ERR of 15% for each 100 Bq/m3 increase in radon concentration (13). These studies support the

Linear No-Threshold dose response model that posits that the exposure to infinitesimal amounts o f

6

radon progeny carries a risk of cell mutation and neoplastic transformation (14). Furthermore, the

Committee on the Biological Effects of Ionizing Radiation BEIR VII report has also supported these

findings citing the availability of new and more extensive data which have strengthened confidence

in these estimates (1). Since the shape of the dose response curve at low doses is not well understood,

the risks estimated by the epidemiological studies are also not well known (15). Further research on

the mechanisms of cancer formation at the cellular and DNA level may help to elucidate the shape

of the dose response curve in the low-dose regime and improve the precision of the epidemiological

studies (15).

The 2013 Multidisciplinary European Low Dose Initiative (15) report found the precision in

the epidemiological results wanting and called for more information on the mechanisms of cancer

formation to more clearly understand the shape of the dose response curve at low doses. Their

definition of low dose is <10mGy and moderate dose <100mGy (15). With respect to excess lung

cancer risk, the report states: “The precision with which these risks can be estimated is limited as epi­

demiological studies can only produce a reliable risk estimate when the excess cancer incidence can

be statistically differentiated from the sporadic cancer occurrence. This restricts the risk estimates

to those irradiated individuals receiving a high to moderate dose. Consequently, a risk extrapolation

must be made from high to low doses, and this is the key problem.” The report acknowledges the

validity of findings that indicate that the dose response curve is nonlinear at low doses (15).

2.2 Radon Dosimetry StudiesRadon is found in nature as a part of the Uranium-238 decay scheme. As an inert gas the radon

is mobile and can seep into houses and collect in low-lying areas like basements. If inhaled the

gas is not likely to irradiate sensitive tissues in the lungs. It is the solid radon progeny, specifically

Po-218 and Po-214, that plate out on particles in the air and easily deposit in the lungs and irradiate

the tissues with alpha particles of energy 6.0 MeV and 7.69 MeV (Table 1.1). The main bronchial

bifurcation is the main deposition location with some deposition occurring in the smaller bifurcation

generations (3). In much of the literature the contribution of beta emitters is omitted due to the small

contribution to the overall dose (16). The beta emissions of the radon progeny are released with

much less energy than the alpha particles. More importantly, the beta radiation has a longer range

in the tissue and imparts its energy over a longer track.

Almost always, the quantity of interest in many studies is radon concentration even though

it is the radon progeny that are the main source of tissue irradiation. A dwelling with a given

concentration of radon will then have an associated concentration of radon progeny. The equilibrium

fraction of radon to its decay products is dependent on factors including ventilation, etc., usually

7

taken to be 0.4 for a residence (17).

The US Environmental Protection Agency (EPA) ranks radon as the second leading cause of

lung cancer. The EPA estimates that out of a total of 157,400 lung cancer deaths nationally in 1995,

21,100 (13.4%) were radon related. When taking into account smoking prevalence data they found

that 1 in 4 lung cancer incidences in never smokers was due to radon and 1 in 8 lung cancer incidences

in ever smokers was due to radon exposure. Even though the relative risk is higher for nonsmokers,

the risk baseline for ever smokers is higher and the larger share of cancer incidence is likely due to

smoking. Based on an assumed average equilibrium fraction of 40% between radon and its decay

products and an indoor occupancy of 70%, the estimated risks from lifetime exposure at the 4 pCi/L

action level are: 2.3% (all), 4.1% (Ever Smokers), and 0.73% (Never Smokers) (17). The estimates

for current smokers were more difficult to obtain due to limitations of the data from the miner cohorts

but the EPA estimates the ERR for smokers to be over 6% for a lifetime exposure at 4 pCi/L. The

effects of radon exposure and smoking are synergistic: smokers who are also exposed to radon will

be at higher risk of lung cancer mortality (17).

2.2.1 Dosimetric Models and Quantities

Dosimetric models can be of use in estimating the absorbed dose received by radiation exposure

in a whole body, an organ, or tissue. Absorbed dose is a measure of the average amount of energy

deposited in a unit mass and is described dimensionally in J/kg and is named gray (Gy). The energy

deposited by the radionuclide decay can be calculated for the target tissue or material. There are

mathematical descriptions of the human geometry, or phantoms, that describe the organs and tissues

as a reference for typical absorbed doses in different scenarios. External irradiations would be

treated differently than internal irradiations, for example. An internal radionuclide can be deposited,

absorbed into the bloodstream, or excreted. Once the absorbed dose is calculated, quantities like

equivalent dose and effective dose can be calculated.

Equivalent dose is a quantity defined by the International Commission on Radiological Protec­

tion (ICRP) that takes into account how an ionizing particle deposits energy in a medium by assigning

quality factors for radiation relative to a gamma ray dose of the same energy (4). This allows for the

summation or comparison of doses from different radioisotopes. Alpha particles have a high linear

energy transfer (LET) and also have a high weighting factor (quality factor); for an alpha particle wR

is usually given a value of 20 (4). An alpha particle of energy 1 MeV will have a higher equivalent

dose than a gamma ray of the same energy. Using equivalent dose, exposure to sources of different

types of radiation can be compared on a radiological protection basis. The equivalent dose in tissue

T due to radiation R is given by the product of absorbed dose, Dt ,r , and radiation weighting factor,

8

w r :

H t ,r = w r D t ,r (2.1)

The effective dose, also an ICRP-defined quantity, is calculated by applying tissue-weighting

factors to the organ/tissue equivalent dose to estimate the dose received by the whole body. In the

case of radon exposure, the whole-body dose received by the short-lived radon progeny would be

the organ equivalent dose multiplied by the factor 0.12 (18). The contribution of the equivalent dose

in the lungs to the total body effective dose could be expressed with tissue-weighting factor, wt , as:

H eff = w t H t ,r (2.2)

Dosimetric models are constructed using human phantoms that describe the typical human ge­

ometry as well as the tissue and organ materials with values for tissue composition and density

provided by ICRP reports (19). In Kendall and Smith, a mathematical phantom was used along with

two different biokinetic models that described the rates of absorption of the radon progeny and the

resulting doses to the lungs and other organs and tissues (20). In one model, the radon progeny were

considered to decay entirely in the bronchial airway and in the other, there was some absorption and

dose in other organs and tissues in the body. This study provides interesting dose comparisons for

the macroscopic model.

In the study by El-Hussein (5) the chosen dosimetric model calculated the doses in all epithelial

cells in the tracheo-bronchial region. This study gathered physical parameters like attached and

unattached fractions, breathing habits, indoor equilibrium fraction, and aerosol sizes and integrated

them into the chosen dosimetric model to obtain dose rates that will also be used for comparison in

the macroscopic model.

Phantoms can also be constructed from images from tomographic data like CT scans or MRI

scans. The assessment of the accuracy of available dosimetric models by Harrison and Day un­

derscores the importance of patient-specific geometries in calculating absorbed doses (21). Any

dosimetric model must assess the intake of a radionuclide; in the case of radon exposure this would

involve some analysis of the inhalation. The radon progeny are inhaled and deposit in the airways and

decay very rapidly. Some radionuclides are longer-lived and, after intake, can be absorbed into the

blood or other tissues in the body depending on their chemical properties. Careful consideration must

be taken to make sure the dosimetric model is an appropriate tool for the given application. The next

step is to calculate the absorbed dose averaged over an organ or tissue. Appropriate weighting factors

are applied to the radiation for the equivalent dose, which provides a benchmark for any biological

9

effects compared to a gamma ray exposure of the same energy. Then, if needed, tissue-weighting

factors are applied to irradiated organs and tissues to estimate the dose recieved by the whole body.

2.2.2 Units of Activity Concentration

Radon concentrations are commonly expressed in terms of pCi/L or Bq/m3. However, another

unit of concentration that is sometimes used for radon progeny concentrations is the Working Level

(WL). It is defined as any combination of short-lived radon daughters in 1 liter of air that results in the

ultimate release of 1.3 x105 MeV of alpha energy (18). In a home with equilibrium fraction 0.4 the

concentration of radon progeny will be 0.004 WL for each pCi/L of radon. Cumulative exposure to

radon (and progeny) is sometimes quantified in Working Level Months (WLM), a unit designed for

occupational (miner) studies. It is defined as exposure to 1 WL for 170 hours. Some risk estimates

are expressed in WLM. In this study, all concentrations and calculations use pCi/L and Bq/m3.

Additionally, there exists another measure ofshort-lived progeny concentration known as poten­

tial alpha energy concentration. This accounts for all ofthe energy a concentration ofradon progeny

would be capable of releasing. For example, an atom of Po-218 would have a PAEC of 13.69 MeV

as it is considered responsible for the decay of Po-214 as well. For the Monte Carlo calculations

made in this study, each radioisotope effect was modeled separately.

2.3 Microdosimetry and Nanodosimetry StudiesAccording to the MELODI report in 2013, the main challenge facing the radiobiology field is

understanding the mechanisms that occur on a cellular and subcellular level (22) in irradiated tissue.

It is thought that damage to the cellular DNA is a pathway for cell mutation and possible cancer

development (23). The DNA is contained in chromosomal formations in the cell nucleus and is

considered the main sensitive volume affecting the cell survival cycle (24). On the subcellular level,

the dominant interactions that cause DNA damage are the inelastic collisions that occur along the

particle track length (24). The atoms that interact can become ionized and the distribution of these

interactions is called the track structure. Particles with high linear energy transfer (LET) have more

interactions along the track length causing more damage in a smaller interval compared to those with

low LET.

The literature cites a study by Brenner and Ward that showed a correlation between DNA double

strand breaks and ionization clusters ofwidth 2-3 nm (24). The nanodosimetric quantities are taken

into account in and around the DNA molecule to obtain the frequency distribution o f ionization

cluster sizes induced by a single ionizing particle in the sensitive volume (24) to estimate probable

double strand breaks (DSBs). At this scale the parameters for the dosimetry change and quanti­

10

ties like absorbed dose are no longer adequate. The research opportunities for linking biological

responses to track structures are rich, as the mechanics of neoplastic formation likely form the basis

of developing more effective treatments.

2.4 Computational ToolsMonte Carlo methods provide a way to estimate dose rates in humans with novel approaches

to modeling the geometries of the human body as well as the densities and materials of the various

tissues, the bones, and other formations of interest. These models provide an approximate view

of many scenarios involving exposure to ionizing radiation. These applications can have a range of

magnitudes including whole body dose estimates using human phantoms, organ doses from ingestion

or inhalation of radioactive materials, tumor doses for the planning of radiation treatments, as well

as models of cellular and subcellular interactions for the purpose of identifying mechanisms at work

in cell transformation.

There are nearly endless applications and many different codes from which to choose. The

literature mentions several Monte Carlo codes for researchers’ specific purposes. However, the

most widely used for general applications are MCNP and Geant4.

MCNP (Monte Carlo n-particle) is an export-controlled particle-tracking code distributed by

Los Alamos National Laboratory (7). It does specialize in criticality calculations but its use has

been extended to radiobiology simulations. The user has only to specify the geometry, materials,

and source description. Very little programming knowledge by the user is needed but the use of

the input file can be cumbersome for the novice. The MCNPX version has more features that

make it radiobiology friendly and there are methods to import geometries from imaging methods

like DICOM. Work or maintenance on MCNPX has been discontinued by LANL. Other codes are

required to import CT scans into MCNPX (Scan2MCNP).

Geant4 is a multipurpose, C++ object-oriented application that is open source and maintained by

CERN (8). Geant4 was initially developed for high-energy physics and in recentyears more modules

were added to account for biodosimetric analysis. Although there exists a DICOM application in

Geant4 available for importing CT scan files, no known studies include using these for assessing

the dose rates from radon exposure. This is true for MCNP as well. In Kendall and Smith, the

PLEIADES code was used to integrate kinetics and ICRP dosimetric model parameters (20). As

stated previously, the dose rates obtained from this study will be used for comparison to the Geant4

model.

Geant4-DNA has been developed by the European Space Agency as an experimentally vali­

dated simulation platform for the modeling of DNA damage induced by ionizing radiation (22).

11

Researchers from physics, chemistry, molecular and cellular biology, and computing have collabo­

rated on this Geant4-DNA expansion to provide an open source method for building computational

methodologies to analyze these special types of biodosimetry studies. The specific functionalities

include the ability to model the elementary physical interactions between ionizing particles and

biological media in the physical stage (22). These options are modified in the physics list class.

Additionally, there has been progress in implementing the physical-chemical and chemical stages

that simulate the excitations and dissociations of water into radical species and the interactions of

these radical species with DNA molecules (22). These features can be implemented with the Geant4

toolkit and its modeling capabilities. Geant4-DNA has been benchmarked with experimental data

for interactions of electrons, protons, and alphas in liquid water (25). The low energy electromag­

netic processes have been validated at energies 10 keV-40 MeV for alphas, 0.025 eV-1MeV for

electrons, and 1 keV-100 MeV for protons (26). Additionally, the tissue equivalent in this toolkit

is approximated by liquid water because the cellular composition, not to mention the human body,

is mostly water. The interactions of the ionizing radiation with water are well understood and this

approximation is accepted as adequate at this time (25).

The recent advances in the Geant4-DNA packages allow the user to explore dosimetry on a

small scale and at very low particle energies. At such low energies and small dimensions, event-

by-event tracking is applied without resorting to condensed history techniques leading to longer

simulation times (27). Users can benefit from features that describe interesting interactions like

the track structures and clustered damages caused by ionizing particles in and around the cell DNA

molecule. Chemical interactions are a novel part of the code system and provide a more complete

picture of the interactions of ionizing radiation with biological tissue. The ionizing radiation creates

chemical species (radicals like OH- ) in the water of the tissue that then scavenge charges from

sensitive organelles or molecules in the cell and present an opportunity for damages of the DNA

molecule (4). For the microscopic study, elements of these preliminary studies are used to describe

the alpha particles from the short-lived radon progeny in order to link the macroscopic doses to

cellular or biological effects.

CHAPTER 3

LUNG CANCER INCIDENCE AND MORTALITY:

RADON EXPOSURE IN UTAH

3.1 IntroductionRadon can be found in high levels from dwelling to dwelling anywhere in the world. Attempts to

quantify the risk involved in prolonged exposures fall on the shoulders of agencies and governments

so that they may recommend remediation levels and prevent unnecessary illness and death. The

EPA has found that smoking is a risk behavior that compounds the risk for lung cancer incidence

and mortality. Since smoking is the leading cause of lung cancer mortality, it can overshadow the

risks from residential radon exposure. Utah is an interesting place to study radon exposure as it has

the lowest smoking prevalence in the US (28) as well as areas of high radon concentrations. Figure

3.1 shows the predicted radon exposure in US states and counties. Zone 1 is the predicted highest

potential radon concentration (above 4 pCi/L). Zone 2 is considered moderate potential with radon

concentrations predicted to be between 2-4 pCi/L, while Zone 3 indicates low potential with less

than 2 pCi/L radon concentration. This figure represents a comparison across states and counties

but does not provide information on what an individual dwelling may contain. However, this map

gives a good representation of the general geographical regions that may have more or less radon

exposure potential.

3.2 Levels of Radon in UtahThe Utah Department of Environmental Quality (UDEQ) publishes radon levels every six months

(30). In each county radon concentrations are measured in a number of homes. In the most recent

study (December 2014) the UDEQ tested a total of 38,407 residences in the state of Utah and

calculated a statewide average radon concentration of 5.2 pCi/L. The maximum was 664 pCi/L with

36.8% of the data equal to or above the EPA recommended remediation level 4pCi/L, and 63.2%

under the remediation level (30).

The majority of the data is collected from Salt Lake County with a total of 19,492 tests conducted.

The average for the county was 4.2 pCi/L and the maximum found was 152.6 pCi/L with 33.3% equal

13

EPA Map of Radon Zones

u Zone l counties have a predicted avenge indoor radon screening level greater than 4 pCi. L fpicocuries per liter) (red zones)

Highest Potential

u Zone 2 counties have a predicted average indoor radon screening level between 2 and 4 pCi. L (orange zones)

Moderate Potential

Zone 3 counties have a predicted average indoor radon screening level less than 2 pCi I (yellow zones)

Low Potential

Fig. 3.1: EPA Indoor Radon Zones (29).

14

to or greater than the EPA limit and 66.7% less than the limit. Within each county the measurements

are further divided by zip code. For example, in Salt Lake County the zip code 84006 had the highest

average of 17.2 pCi/L with 28 tests collected. These levels can vary with many factors from house

to house: the pressure differential from a basement to the outdoors, any exposed soil in low areas

of the dwelling, and the amount of ventilation taking place (30). It is important to test for radon as

residents of Utah. As shown in Fig. 3.1, the potential for moderate or high radon concentrations

exists in every county in the state (29).

3.3 Utah Lung Cancer IncidenceWhile Utah has zones ofhigh radon concentration, it also has the lowest smoking prevalence in

the nation (28). The National Cancer Institute and the Center for Disease Control (CDC) maintain

the website cancer.gov that tracks cancer incidence and mortality by cancer type along with other

risk factors and demographics by US state and county. A few counties in Utah have a low smoking

prevalence with a higher lung cancer incidence/mortality: Tooele, Wasatch, and Kane Counties.

Wasatch County falls in the lowest smoking prevalence category but also registers in the third highest

lung cancer incidence and mortality categories. Wasatch County also has a high average indoor radon

concentration as shown in Table 3.1.

Figure 3.2 shows the data for smoking prevalence in each Utah county (28). The intervals are

percentages of current smokers of all races and sexes aged 18 or above. Figure 3.3 shows the lung

and bronchus cancer incidence for the above demographics of all ages from 2007-2011. Figure 3.4

shows the mortality rate for these types of cancers in the population from 2007-2011. Some of the

data for sparsely populated counties were suppressed for sampling reasons. As shown in Figs. 3.2,

3.3, and 3.4, smoking prevalence closely correlates to lung cancer incidence and mortality, especially

in Duchesne, Uintah, and Grand Counties. While not a robust way to correlate radon exposure to

lung cancer, these data do point to the possibilities available in epidemiological studies in Utah.

Table 3.1: Average radon concentrations in Utah counties of interest (30).

UT County Average Radon Concentration (pCi/L)Duchesne 6.2

Grand 2.3Kane 3.8

Tooele 5.7Uintah 4.4

Wasatch 9.7

15

Fig. 3.2 : Utah smoking prevalence by county (county names added) (28).

16

Fig. 3.3: Lung cancer incidence rates by Utah county (28).

17

Fig. 3.4: Lung cancer mortality rates by Utah county (28).

CHAPTER 4

MACROSCOPIC ANALYSIS OF RADON

EXPOSURE

4.1 IntroductionMonte Carlo codes provide a way to model the stochastic processes involved in radioactive decay

and particle transport. Of interest in this research are: MCNP (Monte Carlo N-Particle), an export

controlled code released by Los Alamos National Lab (7), and Geant4 (GEometry ANd Tracking), an

open source particle transport code produced at CERN and with contributors from all over the world

(8). Originally developed for high-energy physics applications, Geant4 now has many applications

in health and medical physics. There has been an increase in the development of medical applications

in recent releases of Geant4 and an example DICOM application exists with the appropriate C++

code to convert a patient CT scan to geometry for the Geant4 simulation (31).

On the other hand, to import CT image data into MCNP, an outside program must be used

(Scan2MCNP) and the resulting geometry is rigidly defined with lattice cells and corresponding

universes. Universes in MCNP describe a region in the geometry; in this case the lungs can be

analyzed separately from the rest of the phantom/CT scan data by virtue of their material, density,

and shape. The deposition of energy from ionizing radiation can be examined in different organs

or tissues, which is standard in dosimetric models. The morphological features o f the bronchial

airways are not visible in this conversion. The location of the airways could be estimated, but the

area of interest does not correspond to the same universe as the lungs, and modeling radon progeny

deposition in the bronchial bifurcation is not achievable in these circumstances. Still, there are some

insights to be gained from using both programs.

4.2 MCNPX Lung Model4.2.1 Short-Lived Rd-222 Progeny

The CT scan DICOM files were imported into Scan2MCNP in order to generate a lattice geom­

etry for use in MCNPX (32). The original file was created for a different purpose and modified in

this study to model the dosimetric effects of short-lived radon progeny in the lungs. This approach

19

assumes homogeneous volume source in the lungs ofalpha and beta particles ofenergies correspond­

ing to those associated with radon and radon progeny decay. The source is defined in the context o f

the lattice unit cell, which is the building block ofthe entire geometry, and the universe in which the

source-inhabited lattice is located as shown in Fig. 4.1. The source is distributed homogeneously

through the lung universe. The geometry definitions provided by the Scan2MCNP conversions do

not elucidate the details of the main bronchial airway. Furthermore, the portion of the geometry in

which the airway would be found is defined as another universe altogether. The right and left lobes

of the lung are specified to a particular lattice universe and the main airway structure falls into a

universe surrounding the lung as indicated in Fig. 4.1.

As described, the lung portion of the geometry is made up of lattice cells that are filled with

lung tissue. The dimensions of each voxel are shown in Fig. 4.1. This model is therefore an

oversimplification with respect to the source distribution; each lattice unit cell in the lung universe

contains an even distribution of source particles. The reality is that the radon progeny would be

expected to deposit in the airways.

The radon source is placed into the CT scan lung volume in the SDEF card, the portion of the

input file that allows the user to define the source type, energy, and position (Appendix A). The

MCNPX simulations were run with 107 source particles, the ionizing particles emitted by the radon

progeny. The source definition was configured in a variety of ways: all alpha and beta energies for

the short-lived radon progeny, only the alphas of the progeny, and only the betas of the radon progeny.

The source in the latest simulations was a single primary particle belonging to a single radioisotope;

107 alpha particles of energy 6 MeV belonging to 218Po were run in a simulation separate from

0.39 cm

0.39 cm

0.25 cm

Fig. 4.1 : MCNP plot of CT scan and voxel size.

20

the 214Po alpha of energy 7.69 MeV and the two beta particles. After all the iterations that were

implemented, this was an attempt to obtain the MCNPX calculated dose from each short-lived radon

daughter and sum the separated results.

The MCNP F6 tallies provide the absorbed dose (Gy) per each voxel per source particle. The

resulting dose tallies were plotted with a Python script that produces a heat map of the simulation

geometry (Appendix B). The application reads in the mctal text file that contains the absorbed dose

data from the MCNPX output: each voxel and the associated tally or dose value (Gy/particle). The

normalization/conversion factor required to obtain an equivalent dose rate is multiplied by each

absorbed dose value as follows:

Hrate = Da N 1CruFe FaVs37 par s 1 m 3 100 rad

Qaxs

yday

1 p C i/L I Gy \ day yr (4.1)

where D a is the MCNP absorbed dose in gray (mctal file value), N is the number of source

particles, CRn is the concentration of radon in pCi/L, Fe is the equilibrium fraction of radon progeny

to radon gas (taken to be 0.4), Fa is the fraction of the alpha (or beta) emitter present, Vs is the

source volume in m3, and Qa is the quality factor of the radiation (20 for alpha particles and 1 for

beta particles). The exposure time in this study was taken to be 18 hr/day over 365 days per year.

The ratio of the radon progeny to each other is 5:3:2:2 (218Po:214Pb:214Bi:214Po) (33). These are

values estimated by the NRC and can vary depending on the study and the radionuclides of interest.

The mctal file contains data for each voxel in the model. One quantity averaged over the whole

lung is needed to gain an understanding of the dose rates from inhalation of radon progeny. The

average equivalent dose was calculated by finding the mean value out of the nonzero voxel entries

in the mctal file and multiplying by the number of voxels that received dose (a total of 191,121

voxels in the lung universe). The voxel doses and their associated errors are shown in Figs. 4.2-4.5.

The average equivalent dose rates in the lung are listed in Table 4.1, together with the associated

mean error values for each run.

In Fig. 4.2 the equivalent dose rate from the 218Po alpha particle of 6 MeV is plotted in the

sagittal view in the left frame along with the associated error in the right frame. The color (or gray

scale value) represents dose deposit in each voxel and with high LET alpha particles (that have a

very short path length in tissue in each voxel), the dose is highly uniform over the lung. The error

is directly associated with the number of source particles; running 107 source particles resulted in a

mean error (over nonzero value voxels) of 14.9% (Table 4.1). As can be seen in the error image, the

voxels on the border of the lung organ show higher errors due to the lower sampling rate in voxels

that are receiving dose (34). In the majority of the lung volume, the error is about 10%. Increasing

voxe

l nu

mbe

r era

' vo

xcl

num

ber

21

Po-218 alpha equivalent dose rate (mrcm/yr)

/ “A ! \

/ '•( -y. I .

\if Y* I’ U - !

*3 «0 JOvoxel number

40 CO l>j ICO

voxel number

;. 4.2: Python map of MCNPX 6 MeV alpha equivalent dose rate per voxel (left) and associatederror (right).

Po-214 alpha equivalent dose rate (mrcm/yr) ■■0.000018 o.

A*0 60 00

voxel number

! \ i V \Irh ■

60 60 100 voxel number

I■ n

Fig. 4.3: Python map of MCNPX 7.69 MeV alpha equivalent dose rate per voxel (left) andassociated error (right).

voxe

l nu

mbe

r ̂

voxe

l nu

mbe

r

22

£ '*1

1 e-'

’ig. 4.4: Python map of MCNPX 0.7117 MeV beta dose rate (left) and associated error (right).

Fig. 4.5: Python map of MCNPX 2.13 MeV beta dose rate per voxel (left) and associated error(right).

23

Table 4.1: MCNPX equivalent dose rates from homogeneous distribution of radon progeny decayproducts in the lung.

MCNPX Model Per Voxel (mrem/yr) Average Equivalent Dose Rate in the Lung (mrem/yr) Mean Error

218Po a 1.2e-05 2.3 14.9%

214Pb $ 3.8e-08 0.007 10.2%

214Bi $ 2.5e-08 0.005 10.2%214Po a 6.1e-06 1.2 13.7%

the number of particles in these simulations would decrease the error, but it would not affect the

deviation of these values from the higher dose rates that are expected. These values are very low

considering the amount of background radiation an individual receives in a year and the fraction of

which is attributable to radon exposure (about 230 mrem/yr from radon) (29).

In Fig. 4.3 the equivalent dose rate from 214Po alpha emissions of 7.69 MeV is shown in the

sagittal view in the right frame with the associated error in the left frame. The color scale is the

same as that in Fig. 4.2 so that, visually, difference in equivalent dose rate from the two alpha

emitters is evident. This error frame in this plot also shows higher error along the edges of the lung

where the particle tracking is less accurate in the geometry. As expected, more energy is deposited

in tissue with the alpha source. It should be noted that gammas associated with radon and radon

progeny decay were neglected as they are more likely to escape the lung volume and contribute

relatively little to the lung dose (33). Figures 4.4 and 4.5 show the doses from beta decay of 214Pb

and 214Bi. The numerical dose rate scale in the Python plots for the beta dose is 1% that of the scale

for the alphas. This was scaled as such to provide some reference of the value for the beta dose in

comparison to the alpha doses in Figs. 4.2 and 4.3. Also included are the errors in the right hand

side frames. These were each run with 107 source particles; the mean error for both is 10.2%. The

values for the mean dose rates in the voxels as well as the mean dose rates in the lungs are included

in Table 4.1. These dose rates are almost three orders of magnitude lower than those from the alpha

emitters. Although this is to be expected, these doses are quite low because of the low lung material

density and the low LET of the beta particles. Much less energy would be deposited in such a case.

These doses obtained from the homogeneous sources of radon progeny decay products in the lungs

are much lower than would be expected. At least, the dose rate might be expected to be closer in its

value to the EPA-estimated average annual background dose rate in the US from radon exposure of

about 230 mrem/yr (29).

This dosimetric model does not adequately approximate the deposition of radon progeny in the

lungs. The CT scan DICOM files were imported with Scan2MCNP into an MCNP input file and

this affected both the visibility of the main bronchial airway as well as separating this structure from

24

the rest of the defined lung organ. Furthermore, by placing source particles in the lung, the ionizing

particles are traversing tissue that is, relative to other human tissues, low in density. Since absorbed

dose is dependent on the material receiving dose, this would reduce the amount of tissue available

for interaction and it follows that this would result in a lower than expected dose.

4.2.2 Radon Gas

The same properties of the MCNPX geometry structure that make it problematic for modeling

radon progeny in the bronchial bifurcation present an ideal opportunity for modeling the small doses

received by the decay of the radon gas. The assumption is that radon gas molecules would not deposit

or interact in the lung volume and thus could be modeled as a homogeneous source filling the lungs.

Since there is no deposition, any intake of radon would be exhaled. However, during the inhalation,

decay ofradon may take place. Although the dose is expected to be small, the contribution ofradon

gas can be calculated by determining the activity in the lungs during a cycle ofrespiration.

The radon alpha decay energy of 5.49 MeV is simulated in the lung volume using 108 alpha

source particles. Assuming a radon activity concentration of 4 pCi/L and an estimated respiration

rate of 15 L/min the activity passing through the lung in one minute is 60 pCi or 2.22 Bq. In one

minute the lungs are exposed to 2.22 decays per second. Therefore, in one minute there are about

135 alpha decays in the lungs. This will be the quantity by which the MCNP absorbed dose output

(Gy/par) is normalized. Recall, D a is the absorbed dose in Gy/par and for alpha particles the quality

factor 20 converts absorbed dose to equivalent dose.

rate = Da135 par 1080 min 365 day 100 rad 20 rem 103 m rem

m in day yr I Gy rad rem(4.2)

MCNPX provides the dose deposition in each voxel by scoring the energy deposition along each

short alpha track using the F6 tally. The lung tissue has density 0.26 g /c m 3 per the ICRU 46 report

so less dose is deposited than would be in a denser tissue (32). As an approximation, the lung

universe voxels contain a homogeneous distribution of source particles. The mean equivalent dose

was calculated in the Python script that plots the dose deposition. Table 4.2 shows the maximum

equivalent dose that was obtained by finding the maximum dose deposited in a voxel and applying

the normalization and conversion factor discussed previously. It also shows the mean equivalent dose

obtained by finding the mean dose deposit from the voxels that received dose. The mean standard

deviation is included and was calculated to be 7.5% for 108 source particles. These relatively small

equivalent doses are to be expected since the radon does not deposit in the lungs and any dose is

received from the small number ofdecays that may occur while the radon is present.

25

Table 4.2: Radon gas inhalation dose equivalent in MCNPX.

MCNPX Radon Simulation 4 pCi/L radon concentration and respiration rate of 15 L/min

Maximum equivalent dose rate (mrem/yr) 36±2.7Mean equivalent dose rate (mrem/yr) 25.5 ±1.9

The dose equivalent is plotted in the Python heat map in coronal as shown in Fig. 4.6, sagittal

as shown in Fig. 4.7, and axial views as shown in Fig. 4.8 along with the associated errors in the

right hand side frames. Slight variations in the dose deposition can be seen in Figs. 4.6-4.8 and the

degree of variation is evident in the difference between the maximum equivalent dose and the mean

equivalent dose summarized in Table 4.2.

In contrast to the radon progeny deposition scenario discussed previously, this model more

closely describes the effect of radon inhalation. The radon is inert gas and does not remain in the

lungs after exhalation. The dose received must be small since the number of decays in each breath

is also small. The low annual dose of approximately 25 mrem is a reasonable estimate as this is a

fraction of any equivalent dose contribution to background dose an individual might receive.

4.3 Geant4 DICOM Lung ModelObtaining dose estimates using CT scans allows for the use of unique, patient-specific geome­

tries. Developed as an open-source Monte Carlo particle tracking code by CERN, Geant4 has

grown into a multidisciplinary tool that includes code and toolkits for medical and health physics

applications. For dose assessment on an organ scale, the Geant4 DICOM code (31) allows the user

voxel number voxel number

Fig. 4.6: Python map of MCNPX equivalent dose rate for 5.49 MeV alpha particles (coronal view).

26

Equivalent dose rate from Rd-222 decay (mrcm/yr)■0.0000135 ° |

40 60 aovoxel number

1/ . i II I

<0 AO 100voxel number

Fig. 4.7: Python map of MCNPX equivalent dose rate for 5.49 MeV alpha particles (sagittal view).

Equivalent dose rate from Rd-222 (mrem/yr)

II 70

GO

SC

I40 CO 90

voxel number40 90 100voxel number

Fig. 4.8: Python map of MCNPX equivalent dose rate for 5.49 MeV alpha particles (axial view).

27

to input DICOM files that define the simulation geometry. Each DICOM file from a CT scan is a

slice of geometry in the z-direction and the Hounsfield unit values correspond to tissue densities and

materials defined by the user. In this case the material densities used are from the ICRU 46 report

(31). Source definitions are easily described and modified in a macro file and can be placed in areas

of interest by choosing the coordinates in a DICOM viewer. Figure 4.9 explains the steps of creating

a dosimetric model using the Geant4 DICOM methods.

An important part of building a dosimetric model based on a Monte Carlo model is an under­

standing of where the ingested/inhaled radionuclide will reside in the individual. This can become

difficult in cases where the radionuclide becomes mobile through absorption in the blood or by

uptake in various tissues. The short-lived radon progeny are most likely to deposit in the airways in

the main bronchial bifurcation as indicated in Fig. 4.10 and Fig. 4.11. This morphological feature is

easily identified in a DICOM viewer and DICOM coordinates can be obtained. Figure 4.10 shows

the axial view of the bifurcation where the x and y coordinates of a volume source can be estimated.

Figure 4.12 shows the OpenGL view of the DICOM CT scan geometry in the fixed axial perspective.

The set of DICOM files used in this study belongs to the CT scan of a typical adult female torso.

The file structure amounts to 133 slices of thickness 2.5 mm. The CT scan files available for this

study were in matlab format. To unpack these and convert them to DICOM files needed in Geant4, a

program called CERR (Computational Environment Radiotherapy Research) was used. To estimate

the absorbed or dose equivalent in the lungs due to inhalation of short-lived radon progeny, sources

of different types and shapes were placed in the DICOM geometry at the main bronchial bifurcation

as shown in Fig. 4.10 and Fig. 4.11 (35) (Appendix C).

The short-lived progeny are both alpha- and beta-emitters; to avoid a weighted quality factor

when normalizing the absorbed dose output, each type is simulated separately. The sources then

describe a) alphas of energies 6.0 and 7.69 MeV (corresponding to the decay energies of 218Po

and 214Po), and b) the intermediate beta particles from the decay of 214Pb and 214Bi of energies

r i

CT scan D IC O M files imported as geometry in

Geant4

Normalization and conversion

to equivalent dose rate

(mrem/yr)

Fig. 4.9: Geant4 CT scan based model: steps in creating the simulation physics models

28

Fig. 4.10: Axial view of bronchial bifurcation in DICOM viewer OsiriX.

Fig. 4.11: Coronal view of bronchial bifurcation in DICOM viewer OsiriX.

29

Fig. 4.12: Geant4 CT scan visual representation in OpenGL

30

0.7117 MeV and 2.13 MeV, respectively. The source shapes were chosen based on those found

in the literature (cylindrical) (36) as well as those that most closely approximated the bronchial

bifurcation geometry (ellipsoidal) from the CT image (Fig. 4.11). Figure 4.11 shows the airway

at the bifurcation and an ellipsoid more accurately describes the oblong width o f the airway. The

sources are placed to fill the airway above the bifurcation and to be a volumetric representation o f

particles that would deposit on the airway. This is a simplification ofthe deposition model; the air

flow and fluid mechanics ofrespiration are not taken into account. Instead, the assumption is that

the air above the bifurcation contains the same concentrations o f radon progeny as does the air in

the dwelling and that this region receives the majority of the deposition and the dose.

The Geant4 DICOM application scores each primary source particle emitted from the source

volume and the energy deposited in the detector (the CT scan geometry) is tallied in joules per

kilogram of tissue, or gray (Gy). This quantity is known as the absorbed dose and is dependent on

the medium being traversed by the charged particle. To understand the effects a type ofradiation has

in tissue relative to a low LET radiation, the primary particles are given a weight, or a quality factor

as described in detail in Chapter 2. In the case ofalpha particles traversing tissue, the quality factor

(weighting factor) for alpha radiation is assigned a value of 20 (37), which means that the biological

effect of the radiation is much greater than that of a low LET particle of the same energy (this is

also described in detail in Chapter 2). The alpha radiation deposits its energy in a very short track

compared to gamma or beta radiation that is usually assigned a quality factor of1 (37). This quality

factor represents a conversion from absorbed dose to equivalent dose, which gives a more accurate

value for the effects of alpha radiation in tissue and is often used in radiation protection situations.

The gray is related to an older quantity called the rad that, when multiplied by the quality factor, is

converted to the rem (roentgen equivalent man). Although rem is not an SI unit, it is used extensively

by US agencies to set exposure limits. The Sievert (Sv) is the SI equivalent dose unit and is different

only by a couple orders of magnitude. Since the EPA and NRC use rem in quoting background

exposures and other dosimetric measures, this work abides by that same standard. The following

equation shows the conversion from absorbed dose in Gy to rad which has units of100 erg/g:

Gy = J = = 104 e rg = 100 rad (4.3)kg 103g g

The equivalent dose is obtained by multiplying the radiation quality factor, w, by the absorbed

dose value. Multiplying an absorbed dose in Gy by the quality factor gives an equivalent dose in the

unit ofSievert whereas multiplying absorbed dose in rad by the quality factor gives the equivalent

dose in the unit of rem:

31

H (Sv) = wD (Gy)

H (rem) = wD (rad)

(4.4)

(4.5)

The equivalent dose rate from exposure to indoor radon concentration of 4pCi/L was calculated

using the absorbed dose calculated by the Geant4 DICOM (Table 4.3). These simulations contained

108 primary particles, N. The following equation is used to convert the absorbed dose in gray to

equivalent dose in mrem as well as normalize the simulation results to the dose from the expected

number of short-lived alpha or beta emitters in 4 pCi/L of radon:

Hrate = D a N 1CR,nFE FaVs37pars 1 m 3 100 rad

Qax sec y day

1 p C i/L I Gy \ day yr (4.6)

The absorbed dose must be normalized by the activity concentration expected and the number

of source particles. This is achieved by converting the 4 pCi/L to Bq/m3, or particles per second per

volume. This introduces the rate that will be needed to get the long-term rate of days, months, or

years. Then this is multiplied by source volume, Vs , to obtain the number of decay products expected

in a unit time. Taking into account the equilibrium fraction, FE, and the ratio of the short-lived

progeny to each other, Fa, the fractional concentration of alpha emitters is 34.5 Bq/m3 and the

fractional concentration of beta emitters is 24.8 Bq/m3 for an indoor radon concentration, CRn, of

148 Bq/m3 (4pCi/L). The time of exposure was set at 18 hours per day and 365 days per year. Many

of these parameters can be adjusted to fit each situation, especially the equilibrium fraction, the

radon concentration, and the time spent indoors.

The source volumes were varied in the simulations as the length of the main airway above the

bifurcation (as shown in Fig. 4.11). Volumes were chosen to approximate the progeny deposition

as radon concentrations are necessarily expressed in terms of volume. The shapes were determined

from the DICOM viewer to be dimensionally similar to an ellipsoid and a cylinder. It is the normal­

ization that reflects the increased doses, as an increase in the number of deposited particles would

Table 4.3: Equivalent dose rates (mrem/yr) obtained from Geant4 absorbed dose (C=cylindrical source and E=ellipsoidal source and all source volumes in mm3) .

Geant4 H r a t e C 817.2 E 817.6 C 1047.7 E 1047.8 C 2656.6 E 2658.7 C 3602.2 E 3602.2

218Po/214Po a 436.1 436.2 560.3 559.7 1420.7 1420.2 1926.4 1924.2214Pb/214 Bi $ 2.7 2.7 3.5 3.5 8.9 8.9 12.0 12.0

32

be expected. Increasing the source volume does not have any bearing on the number of source

particles. Table 4.3 shows the equivalent doses that were obtained with various sizes and shapes of

radon progeny sources. The values from the alphas and betas are listed separately.

There are a couple of ways that these values can be compared to existing dosimetric models. In

the study by Kendall and Smith, two models were compared that differentiated between absorption

rates of the radon decay products: one type assumed an absorption within 10 minutes of deposition

and the other assumed all deposited progeny decayed in the airways. With a radon concentration

of 200 Bq/m3 (5.4 pCi/L, the action level in UK), the annual committed effective dose rates were

estimated to be 5 mSv (500 mrem) for the absorption model and 20 mSv (2000 mrem) for the total

decay model with the effective dose in the lungs contributing more than 50% to the total effective

dose (20). If these values are extrapolated to the effective dose rates from exposure to 148 Bq/m3

the range is 318-1412 mrem/yr.

When the tissue-weighting factor 0.12 is applied to the dose rates obtained from Geant4 in Table

4.3 (ignoring the beta doses), then the effective dose contributions are between 52-231 mrem/yr.

It appears that the equivalent dose rates agree more with the literature as the source volumes in­

crease. The study by El-Hussein took into account parameters like attached/unattached fractions

and respiratory dynamics (5). Their predictions for effective dose rates from radon concentration

of 148 Bq/m3 (4 pCi/L, radon progeny alpha concentration 0.93 pCi/L) were between 227.7-662.4

mrem/year (5). These effective doses are estimated using different parameters such as attached

and unattached fractions (Chapter 1), breathing rates/habits (nose or mouth), and the absorption

characteristics of the radon decay products. Since the effective dose is a sum of doses received by

all of the tissues and organs in the body, a tissue-weighting factor of 0.12 is applied to the equivalent

dose received in the lung (18). The two largest source volumes agree with the lower ends fo these

estimates. However, only the lung airways are evaluated in this simplified CT scan model and no

estimates have been made with respect to other tissues and organs.

Another way to compare these lung equivalent doses obtained using Geant4 is to compare the

dose coefficients or dose conversion factors. Another convention put forth by the ICRP, dose

conversion factors express the equivalent or effective dose received per activity exposure. Numerous

studies have been done to estimate the dose conversion factors for various exposures: miners’

exposure to radon, atomic bomb survivors’ exposure to radiation, and indoor radon exposures (18).

In ICRP 65 report, the dose conversion factors for exposure to indoor radon were estimated for the

bronchial epithelium to be between 5-25 nGy (Bq*h*m-3)-1 (18). They used a tissue weighting

factor of 0.08 for the bronchial tissues and a weighting factor of 20 for the alpha particles and

obtained an effective dose coefficient of 6-15 nSv (Bq*h*m-3 )-1 (18). The dose coefficient is

33

then 9 nSv (Bq*h*m -3 ) - 1 as recommended by UNSCEAR (18). To compare the equivalent dose

rates from the Geant4 models to the dose coefficients listed by these reports, the following approach

is developed:

• First, the alpha dose in mrem to mSv is simply an order of magnitude change (from Table 4.3):

436 mrem=0.436 rem=0.00436 Sv.

• Then the activity concentration for the radon progeny is multiplied by the number of hours of

exposure in a year (18 h/day times 365 days per year):

0.4712

4 p C i/L37 B q /m 3 1 p C i/L

6570 h = 226, 884 Bq * h * m 3 (4.7)

• Therefore, 0.00436 Sv divided by 226,884 Bq*h*m-3 gives the equivalent dose coefficient of

19 nSv (Bq*h*m-3)-1 . However, to obtain the effective dose coefficient this quantity needs to

be multiplied by the tissue-weighting factor of 0.08 for a value of 1.5 nSv (Bq*h*m-3)-1 . For

the larger values of equivalent dose shown in Table 4.3 (of about 564 mrem/yr), an effective

dose coefficient of 2 nSv (Bq*h*m-3)-1 is obtained. Again, these are just shy of an order

of magnitude less than those quoted by the literature. This indicates that the volumes of the

sources used in these calculations are undersized and do not come close enough to containing

the true number of particles that would likely be deposited in the airway.

• The dose (corrected for tissue-weighting) needed to achieve the dose coefficient of 9 nSv

(Bq*h*m-3)-1 is about 2550 mrem/yr. The source volume in Geant4 needed for that equiva­

lent dose is about 4,768 mm3. This corresponds to an ellipsoid dimension of 12.5 mm x 9 mm

x 11.4 mm. The half-diameter of 12.5 mm of the bronchial tube in the case of this particular

CT scan is slightly larger than the actual dimensions for this patient (half-diameter is 10.5

mm). However, this is not unreasonable given that the average bronchial tube is 25 mm in

diameter (38). Therefore, a few different volumes were analyzed as shown in Table 4.3.

Table 4.3 shows the equivalent dose rates for the alpha-emitting progeny and the beta-emitting

progeny in different volumes. The volumes follow the source shape identifier (C for cylinder and E

for ellipsoid) and are expressed as mm3. Recall that the shapes were chosen to “fill” the bronchial

bifurcation region and each shape does so to a certain extent. The dose rates for same volumes and

different shapes vary only slightly. The dose rates increase with source volume because more radon

progeny are present in a larger volume. The volumes must be chosen based on the geometry and

this can lead to a large range of dose rates. The “right” volume is hard to predict because there are

many parameters contributing to particle deposition that cannot be modeled in Geant4. The previous

discussion on dose conversion factors is helpful because it indicates an equivalent dose that is needed

to obtain the “correct” or recommended value for the dose conversion factors. Additionally, the dose

34

rates obtained from the beta portion of the progeny decay did agree with the literature at less than

1% of the dose deposited by the alpha-emitters (16).

Table 4.4 compares the values of the dose coefficients obtained from the equivalent dose rates

of different source volumes. The volumes are approximate in order to compare both source shapes.

The source volumes are chosen based on the geometry coordinates in a DICOM viewer. The largest

volume shown in Table 4.4 is based on the maximum diameter of the bronchial airway and the

maximum height of the bronchial tube in the frame of Fig. 4.13.

As with the comparisons to the effective dose estimates in the literature, the dose conversion fac­

tors obtained with the two largest source volumes agree with the ranges set forth by the UNSCEAR

committee. Included in the UNSCEAR report is a comparison of indoor radon dose coefficients with

those of atomic bomb survivors. The dose coefficient for atomic bomb survivors was 18 mSv/WLM

or 28 nSv (Bq*h*m-3)- 1 which signifies much higher effective doses per time and activity exposure

(18).

The Geant4 DICOM codes do not provide error values. The purpose of running billions of

particles is to minimize the error associated with the calculations. In Chapter 7 this will be addressed

as one of the tasks for future work.

Table 4.4: Dose conversion factors per Geant4 source volume.

Geant4 Source Volume (mm3) Dose Conversion Factor (nSv (Bq*h*m 3) 1)817 1.5

1,048 22,657 53,602 7

y

I 1 11 118

Fig. 4.13: Maximum dimensions in the main bronchial bifurcation region in x and z directions.

35

4.4 Estimating Risk from Radon ExposureWhile some of the dose rates obtained from the Geant4 simulations agree with the literature,

they do not give any information about the biological effects of the radiation. Figure 4.14 shows the

equivalent dose rates for different indoor radon concentrations and different times of exposure. Since

the largest value of equivalent dose rate showed the best agreement with the values in the literature,

this was used as the benchmark for calculating different dose rates at different radon concentrations

and different exposure times. For example, an individual who spends 18 h/day in a house that has

radon concentration 8 pCi/L or 296 Bq/m3 will receive an annual equivalent dose in the lungs of

about 4000 mrem. This contribution to the person’s annual effective dose will be about 500 mrem.

The effective dose rate is the best value at which to compare other doses typically received by

radiation workers, individuals receiving a CT scan, or the average annual background dose in the

US. The value for a CT scan is a dose received over a short amount of time compared to annual doses

for radiation workers or annual background doses received by an individual. While not a precise

comparison, these values provide a reference for the analysis of higher radon doses. These reference

values are included in Fig. 4.15 as well as the average radon concentrations in several Utah counties.

The dashed lines connect Utah counties to their average indoor radon concentration. Equivalent dose

rates vary as radon concentration and time exposed. From Fig. 4.15 we can understand the following

14000

2 /7 4 4 /1 4 8 8 / 296 10 / 370 20 / 740Indoor R adon C oncentration (pCi/Ll/(Bq/in3)

Fig. 4.14: Equivalent dose rates in the lungs from various radon concentrations and exposure times.

36

correlations: 24 h/day in a house with radon concentration of 4 pCi/L is about equivalent to an extra

background dose of radon; 24 h/day in a house with radon concentration of 10 pCi/L is about the

same as a one-time CT scan effective dose. While these may seem routine, it is best practice to limit

these exposures and attempt to minimize the exposure to radiation when possible. Radiation worker

whole body limit is listed by the NRC as 5 rem per year and the dose limit to a single organ or tissue

is 50 rem per year. The risk associated with this exposure is an increase of 25% in developing cancer

per the LNT model (39).

This whole body limit is the effective dose, which is the sum contribution of all radiation expo­

sure weighted by tissue and organ type. In the example where the equivalent dose to the lungs is the

only quantity under consideration, an effective dose to the whole body could be found by weighting

the lung equivalent dose by a factor of 0.12 (18). There is a difference in the localized internal

exposure to alpha radiation and the external exposure to low LET particles. The alpha particles in

sensitive tissue will deposit their energy in a dense track. Low LET particles have a longer path

through air and tissue and will spread the energy loss through a greater mass of the media being

traversed. At the dose rate levels predicted by the Geant4 DICOM model, the biological effects are

Fig. 4.15: Effective dose contributions from the equivalent dose rates in the lungs with varyingradon concentrations and exposure times.

37

still stochastic and late effects may be observed after decades of exposure. However, to minimize

risks, homes can be tested for these higher levels of radon and remediate accordingly. According

to the ERR estimates given by the epidemiological studies, residents of Sevier County who dwell

in a home with the average radon concentration for that county (10.8 pCi/L or about 400 Bq/m3)

would be subject to an increase in relative risk of lung cancer mortality of 10-15% for every 100

Bq/m3 concentration of radon in the home, giving an ERR of 0.4 for lung cancer mortality. These

epidemiological estimates are fraught with high statistical uncertainties and it is difficult to reach a

robust conclusion from those estimates at this time (6).

In Utah there have been homes tested that contain much higher levels than those shown in Fig.

4.15. The Utah Department of Environmental Quality tests thousands of dwellings and publishes

the results every six months (30). The most recent results showed that some residences contain on

the order of hundreds of pCi/L radon concentration. These levels take an individual’s equivalent

dose rate to levels exceeding the low-dose threshold, 20 rem, and into the range where deterministic

effects may be observed (17).

The deposition of the radon progeny in the bifurcation does lead to a small amount of tissue

receiving most of the dose (40). This appears to be due to the attachment fraction (the portion of

radon progeny that condenses out to particles in the air) and the mean size of the particle. There is

deposition in different branches of the bronchial tubes, but the main bifurcation is a target site for the

deposition (40). Dosimetric models often treat the doses as if they were distributed over an entire

organ or body. The nonuniform and highly concentrated dose in a small section of tissue may have

effects on the cellular level that quantities like absorbed dose and equivalent dose cannot convey.

CHAPTER 5

MICROSCOPIC ANALYSIS OF RADON

EXPOSURE

5.1 IntroductionThe macroscopic analysis of radon exposure as presented in Chapter 4 provides the estimates

of the absorbed dose from internal radon related radiation exposures. In the low dose region, the

effects of radiation are quite unknown (1)(40)(41). Numerical estimates of dose depositions at the

cellular level provide additional information on the biological effects of ionizing radiation. The field

of nanodosimetry defines particle interaction quantities along particle tracks: the events that occur

along a particle’s journey through the short distance in which it deposits its energy and interacts with

the atoms/nuclei in a cell.

Geant4 can be used to track particles at the microscopic (cell) level at low energies. This

portion of the code is benchmarked for liquid water (a close approximation to the cellular material

composition) and is on target to simulate the first direct, physical interactions as well as the following

chemical and biological responses to interactions with ionizing radiation.

The tendency of the solid decay products of radon to attach to aerosol particles and deposit

in bronchial bifurcations leads to higher energy deposition in very small sections of tissue (15).

Sensitive targets in the lungs include bronchial epithelial and bronchial secretory cells. To gather

the dosimetric data at this scale, quantities related to particle track structure like energy deposition,

step length, and interaction types along the track are of more interest than absorbed dose or dose

equivalent.

5.2 Geant4-DNA ModelThe microscopic effect of alpha particles of energies corresponding to those of the radon progeny

alpha-emitters was analyzed using the Geant4-DNA toolkit and the dnaphysics application (25).

Figure 5.1 shows a flow chart for the analysis of the particle track structure and the clustering

of ionization events for determination of DNA double strand break candidates. The ionization

events are gathered from the Geant4-DNA simulation and the events are clustered using a DBSCAN

39

Fig. 5.1: Small tissue volume particle track structure analysis based on Geant4-DNA and dataclustering.

algorithm in Python to determine the number of clusters that could constitute DSB candidates. As

described in Chapter 2, an ionization cluster (3 or more events) of size 3.2 nm that occurs in the

DNA molecule is considered a DSB candidate (42). Then, given the typical cell size, the probability

of the clusters occurring in the sensitive volume of the DNA molecule is found using the number of

cells traversed, the volume of the cell nucleus and the volume of the DNA molecule within the cell

nucleus.

A cube of liquid water of side length 100 represents a small section of tissue containing

cells of diameter ~15 ^m (38). A general particle source with random direction and starting location

traverses the cube and deposits its energy. Figure 5.2 (right) shows the trajectory for a 1 MeV alpha

particle and particle track structure (left). The particle track structure includes a large number of

elastic scattering interactions for electrons and ionizations for secondary electrons and the alpha

particle. As the alpha particle loses energy and gains negative electrical charge, ionization events

occur from the interactions of the alpha particle and then the Helium atom (Fig. 5.2). As the charge

decreases near the end of the particle path, the ionizing interactions are much fewer in number than

ionizations from the initial alpha particle. Figure 5.3 show the dominant interactions for the 6 MeV

alpha particle from 218Po and the 7.69 MeV alpha particle from 214Po.

As can be seen in Fig. 5.2, the alpha ionizations are more common compared to the alpha and

He ionizations; alpha excitations also contribute to the track structure. These occur as energy is

transferred to an atom and the electrons of the atom transition to an excited state. The general

particle source of alphas of energies 6.0 and 7.69 MeV are compared to a lower energy alpha particle

of 1 MeV to examine the track structure and accompanying interactions. The particle trajectory

through the geometry shown in Fig. 5.2 can be viewed in ROOT or OpenGL as a 3D object. The

track structure quantities are stored as n-tuples in ROOT. This makes it easy to extract the data

with commands in the source code. Energy deposition, position, and step length are some of the

other track structure quantities available in ROOT histograms. The Geant4-DNA simulations using

different energies of alpha particles in the microvolume of liquid water follow single alpha particle

40

Charged Particle Interactions ] MeV Alpha Particle Track Structure

In lcraftioB Type

Fig. 5.2: Sample ROOT output of 1 MeV alpha particle track structure (right) and dominantinteraction types (left).

Fig. 5.3: Dominant interactions for alpha particle emitted by Po-218 (6 MeV) and Po-214 (7.69MeV).

tracks to determine the interactions that occur in a small section of tissue. Geant4 allows for the

track structure to be examined for alphas of different energies. Each interaction along the particle

track is accounted for and stored as an n-tuple for evaluation in ROOT. In each energy category of

alphas, ionizations are a dominant interaction, especially as energy increases (Fig. 5.3).

5.3 Particle Track Structure AnalysisWhen the 218Po and 214Po atoms undergo decay, the alpha particles that are emitted lose energy

as they travel through the tissue. The main mechanisms of energy loss are elastic scattering and

ionization of atomic electrons in the medium. As the charged alpha particle interacts via the Coulomb

force, electrons are imparted with energy that releases them from their orbits creating ion pairs

41

(ionization) or elevates them to a higher energy state in the atom (excitation). Because of their

relatively large mass compared with the electron, the alpha particles experience very little recoil and

their track is more or less a straight path. The linear energy transfer is the amount of energy lost

per unit length along the track. Their high linear energy transfer (LET) gives alpha particles a short

range in tissue compared to the low LET beta or gamma particles. As the alpha particle slows to

lower energies, the particle picks up charges and stops abruptly as shown in the Bragg curve in Fig.

5.4.

The specific ionization of a charged particle is the number of ionization pairs produced per unit

length in a particular material. It can be found by dividing the stopping power by the energy required

to produce an ion pair in the material (4). The stopping power is similar to the LET except that it

refers to energy absorption property of the medium instead of the energy transfer property of the

particle. Figure 5.5 shows the stopping power for alpha particles in liquid water (43). The stopping

power is defined as: S = -d E /d x . The linear stopping power, S, is equal to the loss of energy, E,

along a path, x, in a specific medium.

For particles of higher energies, the Geant4 geometry volume was increased to (750 ^m)3 to

make sure the particles did not escape the volume before stopping. ASTAR tables from NIST were

consulted for the alpha particle range in liquid water and these ranges are listed in Table 5.1 (43). The

Distance of Penetration

Fig. 5.4: Bragg curve showing specific energy loss along the particle path.

42

Fig. 5.5 : ASTAR stopping power for liquid water (43).

Table 5.1: Ionization events and clusters of size 3.2 nm for alpha particle energies.

Alpha Energy (MeV) Approximate Range in Tissue (pm.) Ionization events Clusters <3.2 nm Cluster Yield

1 6 50,104 41 0.08%3 18 153,469 200 0.1%5 37 256,704 2,019 0.8%6 49 307,868 2,525 0.8%

7.69 73 394,754 3,062 0.8%9 95 462,515 3,488 0.7%10 113 514,274 3,700 0.7%

cluster yield is the percent of clusters formed per ionization event. The total number of ionization

events associated with each alpha track is found in Table 5.1 These are obtained from the Geant4

simulations; the total ionization events are from both the alpha particle and any secondary electrons

produced. The ionization events are of interest in examining the probability of double strand breaks

(DSBs) in the DNA molecule (42). The ionization events and their positions can be grouped into

clusters corresponding to the distance required to induce breaks within 10 base pairs in the DNA,

or 3.2 nm (26)(42). The Python code, sklearn.cluster.DBSCAN is freely available from scikit Learn

and contains the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) routine

that was used for this purpose (10). The DBSCAN algorithm has been successfully used in other

Monte-Carlo DNA simulations (26). The DBSCAN algorithm requires only two parameters: a

Euclidean distance and a number of points needed to form a cluster. The number of clusters along

the alpha particle track and their probability of interacting with the DNA molecule can be analyzed

to estimate the number of DSB candidates one might expect from the exposure to radon progeny.

43

In the dnaphysics example, the SteppingAction.cc file keeps track of each interaction along the

particle path, as well as its spatial coordinates (Appendix D). Script was added to this file to collect

each ionization event in the simulation along with its x,y,z location at the instance of ionization so a

separate text file with this information can be processed by the DBSCAN algorithm (Appendix E).

The DBSCAN script prints the total number of ionization events and the number of clusters of events

that agree with the parameters set in the script. The ionization events are clustered into groups of

three or more events within a distance of 3.2 nm of each other (Table 5.1). These clusters form DSB

candidates. No assumptions are made as to the position of cells or cell nuclei in the simulation tissue

volume so the clustering technique does not distinguish between clustered SSBs and clustered DSBs.

However, the DSB candidates do give a conservative estimate of the cellular damage inflicted by

222Rn progeny.

While the number of ionization events is approximately linear with alpha particle energy, the

number of clusters that match the criteria described above are not. Figure 5.6 shows the trend for

ionization clusters as alpha particle energy increases. There is a rapid increase from 3 MeV (200

clusters) and 5 MeV (2019 clusters). This is a consequence of the linear energy transfer of the

alpha particle and its range through the tissue. A longer particle track from a more energetic particle

necessarily spreads out the ionization events as the LET is lower along the beginning of the track and

dampens the probability of the events clustering in the neighborhood required for the DSB length.

As shown in the Bragg curve (Fig. 5.4), most of the particle energy is lost at the end of the path.

The number of cells a particle traverses is calculated using the estimated range of the particle. A

6 MeV alpha particle has a range of about 49 ^m in tissue and will therefore traverse about 3 cells

of diameter 15 ^m with an average of 842 clusters per cell traversed. Figure 5.7 shows an idealized

drawing of the cell structures.

The number of clusters along the particle track is divided between the cells the particle traverses.

The nucleus is estimated to fill 10% of the volume of the cell (38)(44) and the DNA molecule takes

about 0.5% of the volume of the nucleus (44). The number of ionization clusters in each cell, Nj,

is multiplied by the probability of hitting the nucleus, Pnuci, and the probability of hitting the DNA

molecule, Pd n a , as follows:

PdSB = PnudPDNANj (5.1)

The estimates for the number of cells traversed (taken from the particle range and the rough

diameter of a bronchial epithelial cell), the number of ionization clusters in each cell (taken from the

total number of ionization clusters), and the probability of a DNA hit based on these quantities are

44

Fig. 5.6 : Number of ionization clusters as a function of alpha particle energy.

Fig. 5.7: Cell sketch with DSB and SSB description.

45

contained in Table 5.2. The 6 MeV alpha particle causes more clusters per unit length because its

track is shorter than that of the 7.69 MeV alpha particle.

In Dos Santos et al. (42), a similar, small-scale study was described with protons of energy

0.5-50 MeV traversing a cell in Geant4-DNA. The geometry used in the Geant4-DNA is much more

complex in their study with the cell nucleus and DNA molecule placed and defined explicitly. They

found that for a 5 MeV proton (8.3 keV/ ^m) traversing a cellular volume, 0.242 DSB candidates

per proton per micrometer. The number of DSB’s increased with increasing LET. (For 6 MeV alpha

particles traversing ~49 micrometers the LET would be about 122 keV/ ^m). If the results from

Table 5.2 were also divided by micrometer, the results obtained for this study are much smaller than

those predicted by (42) (From Table 5.2: 0.42 hits per cell/15 micrometers per cell = 0.028 DSBs

per alpha particle per micrometer). This value is more similar to that of the 50 MeV proton from the

Dos Santos study of 0.021 DSB/proton per micrometer.

In a more recent study done by Dos Santos et al. (44), alpha particles were included in a similar

analysis (detailed DNA molecule with structure and dimension). The concept is similar: ionizing

radiation traversing a cell and the DNA damage by ionization clusters analyzed using DBSCAN

algorithm. The alpha particles in this study were of energy 5-50 MeV. The number of DSB’s per

alpha particle per micrometer was between 0.25-2.5 (44). The results obtained from Table 5.2 for

probable DNA hits by ionization clusters are about one order of magnitude smaller than these values.

These studies have been used to create more detailed geometries of the chromatin structure. It may

be that the simple small tissue volume (water cube) used in this study is not adequate to describe the

probability of DSB.

5.4 Merging the Geant4 ModelsThe probability of an alpha particle causing a DSB in a DNA molecule (Table 5.2) is useful when

linking the macro CT scan model to the cellular effects of 222Rn progeny exposure. The cell cycle,

or mitotic rate, is the time it takes a lung cell to cycle through its life and is taken to be 30 days (35).

For an activity concentration of alpha emitter, Ca (Bq/m3), source volume, VS, and cell cycle, tcea

in days, the number of alpha-emitting particles deposited, N dep, can be estimated with the following

relationship:

Table 5.2: Probability of DNA hits per cell from ionization clusters found using DBSCAN andGeant4-DNA and (5.2).

Alpha Particle Energy Cells Traversed Ionization Clusters per Cell Probability of DNA Hits6 MeV 3 842 0.42 per cell

7.69 MeV 5 612 0.31 per cell

46

(5.2)

The largest volume of source particles led to dose rate results that agreed best with the literature

(3602.2 mm3) as discussed in Chapter 4. Using the probability of DNA hits by an ionization cluster,

PDSB, defined in Table 5.2, the number of cells traversed by each alpha particle, N traversed and

time of 18 h/day, cell cycle time 30 days, the equilibrium factor 0.4, and the activity concentration

fraction of 0.42 for the 6 MeV alpha from 218Po and 0.17 for the 7.69 MeV alpha from 214Po, the

approximate upper limit of the number of DSBs in a cell cycle in the main bronchial bifurcation is

shown in Table 5.3.

Table 5.3 shows the total DSBs due to the deposition of alpha-emitters in a cell cycle of 30 days.

It is the result of applying Eq. (5.3) to Eq. (5.4). This takes into account the volumes that best

agreed with the literature described in Chapter 4 as well as the usual fractions of radon progeny

and time exposed. The smaller volume corresponds to a smaller number of particle depositions and

will have fewer DSBs as a result. The larger volume agrees best with the dose estimates from the

literature and is likely the best estimate of the radon progeny depostion on the airway. Figure 5.8

is a flow chart that describes the processes and results from both the macroscopic and microscopic

models and the connection that can be made from the source volume in the CT scan geometry to

the number of particle depositions, and thus, ionization clusters that may cause DSBs in the DNA

molecule. This chart summarizes the steps from Chapters 4 and 5 and visually describes the link

between the two models: the number of source particles deposited in the bronchial bifurcation and

the probability that these will cause DSBs in the cellular DNA.

N dep, an estimate can be made of the number of DSBs that occur in the tissue during a cell cycle as

follows:

N DSB — N depN traversedPDSB (5.3)

Using the same activity concentration of 148 Bq/m3 as used in the CT scan model, an exposure

47

Table 5.3: Number of DSBs per cell cycle using number of deposited alpha emitters from Geant4DICOM source volume.

Alpha Energy N d s b (Vs = 2657 m m 3) N DSB (Vs = 3602 m m 3)6 MeV 127 173

7.69 MeV 51 69Total DSBs per cell cycle 178 242

48

Fig. 5.8: Macroscopic and microscopic radon analysis flow chart.

CHAPTER 6

CONCLUSION

The objectives of this research were to 1) analyze the low-dose effects of radon exposure on

a macroscopic level using patient morphology in the form of CT scans and corresponding dose

rates from short-lived radon progeny and 2) estimate the cellular DNA damage inflicted by the

deposition of the same radon progeny in the bronchial bifurcation. CT scan DICOM files were

imported into a Geant4 application with a volume source of radon progeny decay products that

conform to the geometry above the main bronchial bifurcation. The sources were an approximation

of a concentration of radon progeny that might be found in the airway and deposited in the bronchial

bifurcation. The simulations in Geant4 resulted in equivalent dose rates of 436-1924 mrem/yr,

depending on source size shape. The largest value is in the range of the effective doses from

estimates found in the literature. This means that the larger volumes are better estimates of the

particle deposition in the bronchial airway. To verify that this was the case, an analysis was done on

the dose coefficients associated with each source volume. The largest source volume gave a dose

coefficient that was in the range predicted by the UNSCEAR 2006 committee. Additionally, the

contribution of beta-emitting progeny was found to be less than 1% of that of the alpha-emitters per

the literature estimates.

Since the mechanisms of cancer formation are not well known, the nanodosimetric quantities are

an important component of the study. Using Geant4-DNA toolkit, the alpha particles from the radon

short-lived radon progeny were tracked through a small tissue volume. Their interactions, especially

ionizations, were accounted for and further analyzed to determine how their placement could corre­

spond to DNA damages in a typical bronchial cell. The ionization events from the Geant4-DNA

simulations were extracted along with their spatial coordinates and clustered using a DBSCAN

algorithm. The ionization clusters were used to estimate the probability of an alpha-emitter causing

a double strand break in the DNA molecule. Although the geometry of the Geant4-DNA model is

simple and the clustering algorithm does not distinguish between clustered single strand breaks and

double strand breaks, this does offer an estimate for the number of DSBs expected in the tissue of a

person exposed to a particular concentration of indoor 222Rn.

50

Risk estimates are still being refined by researchers in many fields to further the understanding

of the effects of exposure to low-dose ionizing radiation. The patient-specific geometry used in

Geant4 and MCNPX leads to equivalent and effective doses received by exposure to short-lived

radon progeny. The results mentioned previously obtained in the macroscopic study were reasonable

compared to those estimates cited by organizations like the EPA for yearly background exposure as

well as those put forth by researchers in the field (5)(20)(29). The microscopic analysis gave results

that were lower than those estimates in the nanodosimetry studies (44). However, the advancements

that are being made in this field will lead to better tools with which to model the physical interactions

on the cell and molecular level. Together, these two models have the potential to promote further

understanding of the links between macroscopic quantities like dose rates and the biological effects

of low-dose radiation.

CHAPTER 7

FUTURE WORK

There are several aspects of the models used in this study that were approximations to the

conditions expected for radon exposure. These will all be discussed, but the most obvious item

that is missing is uncertainty analysis in the Geant4 applications. Billions of particles were used

in the DICOM simulations as the number of particles directly reduces the uncertainty of the cal­

culations. However, there was no code to calculate the uncertainty in each voxel as there exists in

MCNPX. Recall that running 108 particles resulted in a mean uncertainty of 7.5%. At this time, an

uncertainty calculation in the Geant4 DICOM does not exist but a motivated individual could add

it. In the Geant4-DNA dnaphysics application only one particle was run in each simulation; the step

calculations in this toolkit are on the order of nanometers and the particle goes through a very large

number of steps. The uncertainty analysis in this case would involve number of interactions instead

of number of particles. An attempt at running even 10 particles in simulations like this resulted in

output files that were unmanageable in size (32 GB).

7.1 Respiratory Dynamics and Attached/Unattached Fractions

The simulations in the Geant4 DICOM model involved only charged particle transport and

energy deposition. This is good for estimating the dose rates from a source that is confined by

the patient organ structure. However, there are complex systems at work in the lungs to keep the

organ from being harmed by inhaled particles. The breathing habits of an individual can affect the

inhalation and deposition of radon progeny. Fluid mechanics and flow modeling in the lung could be

coupled with the Monte Carlo methods to examine more closely the effects of these systems. Some

experimental work has been done on these aspects (5).

The radon progeny take different forms in the indoor environment: they can become attached to

aerosol particles of varying size, they can remain unattached, or they can cling to surfaces. There

are several experimental studies that examine the behavior of the progeny under these different

circumstances and their ability to deposit in the airways when inhaled. This study made no assump­

52

tions about the molecules to which the radon progeny may have been attached. The sources were

assumed to be samples of air that could be found anywhere in a dwelling that contained a particular

concentration of radon. Consequently, factors like equilibrium fraction were much more important

than the attached fraction. Coupled with the respiratory dynamics, an analysis of deposition based

on the attached/unattached fraction could prove useful in refining the DICOM model.

7.2 Chemical Reactions in the CellAs Geant4-DNA advances in its capabilities, the analysis of subsequent reactions in the cell after

a direct physical interaction of a charged particle with the cell will prove most useful in predicting

the effects of the radiation on the cell and the DNA. This study examined only the first interactions,

the ionization events that occurred while the alpha particles traversed the cell. Further interactions,

like hydrolysis, can occur and have detrimental effects. A more complete picture of the cell interac­

tions necessarily leads to more knowledge of the probable effects of radiation on health and cancer

development. As these developments are made in Geant4 it will be useful to examine the effects of

the short-lived radon progeny on the cellular level.

APPENDIX A

MCNPX INPUT FILE

MESSAGE: IXR o u tp = ra d o n _ x .tx t ptrac=bOOO.pccc ++++++++++++++++++++++++++++++++++++++++++++++++++++++ cc C e l ls cc ++++++++++++++++++++++++++++++++++++++++++++++++++++++

c F i l l i n g U n iv e rse s c1 0 - 1 u = 12 2 -1 .0 2 0 0 0 0 - l u = 23 3 -1 .8 5 0 0 0 0 - l u = 34 5 -0 .2 6 0 0 0 0 - l u = 4 $ lung5 5 -0 .2 6 0 0 0 0 - l u = 5 cc L a t t i c e U n it C e ll c6 0 -27 26 -17 16 38 -37 u = 7 l a t = 1 f i l l = 0 :127 0 :127 0 :1321 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R1 39R 2 7R 1 79R1 36R 2 13R 1 76R1 35R 2 4R 3 3R 2 7R 1 74R1 34R 2 2 3 12R 2 3R 1 73R1 33R 2 2 3 15R 2 2R 1 72R1 32R 2 2 3 3R 2 3 2 7R 3 3R 2 2 1 72R1 32R 2 2 3 2R 2 17R 1 71R1 32R 2 2 3 3 2 18R 1 71R1 32R 2 2 3 3 2 19R 1 70R1 31R 2 2R 3 2R 2 19R 1 69R1 31R 2 2R 3 2R 2 20R 1 68R1 31R 2 2R 3 2R 2 21R 1 63R 3 1 2R1 31R 2 2R 3 2R 2 23R 1 58R 2 2R 3 1 2R1 31R 2 2R 3 2R 2 24R 1 55R 2 3R 3 3 1 2R1 2R 2 3R 1 24R 2 2R 3 2R 2 HR 4 2 12R 1 53R 2 2R 3 3R 1 2R1 2R 3 2 4R 1 22R 2 3R 3 3 2 25R 1 46R 2 8R 3 2 3 3R 1 1

54

1 1 3 3R 2 4R 1 20R 2 3R 3 3 2 12R 4 2R 2 10R 1 43R 2 12R 3 3 2R 1 11 1 3 3R 2 5R 1 19R 2 3R 3 3 2 H R 4 2R 2 12R 1 40R 2 8R 3 3 22 3R 3 2R 1 11 1 3 3R 2 7R 1 17R 2 4R 3 3 2 26R 1 39R 2 7R 3 4R 2 2R 3 3R 1 11 1 3 2R 2 9R 1 16R 2 4R 3 2R 2 13R 3 2R 2 9R 1 36R 2 8R 3 7R 23 4R 11 3 3R 2 10R 1 16R 2 4R 3 3 2 12R 3 3R 2 9R 1 35R 2 15R 3 7R 1 1 3 5R 2 10R 1 14R 2 5R 3 2 12R 3 3R 2 9R 1 33R 2 15R 3 9R 1 1 3 7R 2 10R 1 12R 2 15R 3 2 2R 3 3 2 4R 3 2 6R 1 31R 2 14R 3 3 10R 11 3 8R 2 11R 1 11R 2 15R 3 2 7R 3 3 2 6R 1 30R 2 12R 3 14R 1 1 3 9R 2 11R 1 10R 2 15R 3 3 2 6R 3 2 7R 1 29R 2 15R 3 12R 1 1 3 10R 2 HR 1 9R 2 15R 3 2R 2 14R 1 28R 2 16R 3 5R 2 3 5R 1 1 3 3R 2 3 5R 2 12R 1 9R 2 32R 1 27R 2 17R 3 12R 1 1 3 3R 2 2R 3 3R 2 12R 1 9R 2 20R 3 2 10R 1 27R 2 22R 3 8R 1 3 7R 2 15R 1 10R 2 19R 3 2 10R 1 26R 2 24R 3 7R 1 3 5R 2 17R 1 10R 2 30R 1 27R 2 30R 3 3 1 3 5R 2 17R 1 11R 2 29R 1 28R 2 29R 3 3 1 3 5R 2 17R 1 12R 2 27R 1 29R 2 29R 3 3 1 3 5R 2 17R 1 13R 2 25R 1 31R 2 26R 1 3R 1 3 5R 2 16R 1 16R 2 21R 1 34R 2 22R 1 6R 1 3 5R 2 16R 1 16R 2 19R 1 36R 2 20R 1 8R 1 3 5R 2 15R 1 18R 2 17R 1 38R 2 17R 1 10R 1 3 6R 2 13R 1 19R 2 15R 1 41R 2 14R 1 12R 1 3 2 4R 3 2 11R 1 20R 2 14R 1 44R 2 11R 1 14R 1 3 2 15R 1 22R 2 12R 1 50R 2 4R 1 17R 1 3 2 14R 1 25R 2 7R 1 76R 1 3 2 12R 1 28R 2 3R 1 79R 1 3R 2 9R 1 113R 1 7R 2 3R 1 115R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R1 127R1 127R1 127R1 127R

JJ

1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R1 39R 2 5R 1 81R 1 36R 2 12R 1 77R 1 35R 2 4R 3 3 2 3 2R 2 4R 1 75R 1 34R 2 2 3 12R 2 2R 1 74R 1 33R 2 2 3 14R 2 2R 1 73R 1 33R 2 2 3 3R 2 13R 1 73R 1 32R 2 2 3 3R 2 15R 1 72R 1 32R 2 2 3 2R 2 17R 1 71R 1 32R 2 2 3 2R 2 18R 1 70R 1 31R 2 2R 3 3 2 20R 1 69R 1 31R 2 2R 3 3 2 21R 1 68R 1 31R 2 2R 3 3 2 22R 1 67R1 31R 2 2R 3 2R 2 9R 3 2R 2 9R 1 60R 2 2 3 1 2R 1 31R 2 2R 3 3 2 9R 3 3 2 13R 1 56R 2 3R 3 1 2R 1 2R 2 2 1 26R 2 2R 3 2R 2 25R 1 53R 2 5R 3 1 2R 1 2R 2 4R 1 24R 2 2R 3 3 2 25R 1 47R 2 9R 3 3R 1 11 1 3 3R 2 3R 1 22R 2 2R 3 3 2 12R 4 2R 2 10R 1 43R 2 12R 32 3 3 1 11 1 3 4R 2 4R 1 20R 2 2R 3 3 2 10R 4 3R 2 HR 1 41R 2 15R 33 3 1 11 1 3 3R 2 6R 1 19R 2 3R 3 3 2 26R 1 38R 2 7R 3 2R 2 5R 3 3R 1 11 1 3 2R 2 9R 1 17R 2 4R 3 2 15R 3 3 2 8R 1 37R 2 8R 3 6R 22 3 4R 11 3 3R 2 10R 1 16R 2 19R 3 2R 2 10R 1 34R 2 14R 3 9R 1 1 3 4R 2 12R 1 13R 2 19R 3 5R 2 7R 1 33R 2 15R 3 9R 1 1 3 7R 2 11R 1 12R 2 18R 3 7R 2 6R 1 30R 2 16R 3 10R 1 1 3 8R 2 11R 1 11R 2 15R 3 2 7R 3 2R 2 5R 1 29R 2 13R 3 14R 11 3 9R 2 12R 1 9R 2 14R 3 3R 2 5R 3 3 2 6R 1 28R 2 15R 3 7R 22 3 3R 11 3 10R 2 11R 1 10R 2 14R 3 2R 2 4R 3 2 8R 1 27R 2 16R 3 6R 22 2R 3 2R 11 3 10R 2 12R 1 9R 2 21R 3 2 9R 1 26R 2 17R 3 5R 2 3R 3 3R 1 1 3 2R 2 2R 3 4R 2 13R 1 9R 2 18R 3 3 2 10R 1 26R 2 22R 3 9R 1 3 4R 2 19R 1 9R 2 19R 3 2 10R 1 25R 2 25R 3 7R 1 3 5R 2 18R 1 10R 2 18R 3 2 10R 1 25R 2 28R 3 4R 1 3 4R 2 19R 1 10R 2 29R 1 27R 2 30R 3 3 1 3 5R 2 18R 1 11R 2 28R 1 27R 2 31R 3 1 3 5R 2 18R 1 12R 2 26R 1 29R 2 28R 1 2R 1 3 5R 2 17R 1 15R 2 22R 1 32R 2 24R 1 5R 1 3 5R 2 17R 1 16R 2 20R 1 33R 2 22R 1 7R 1 3 5R 2 16R 1 17R 2 18R 1 36R 2 19R 1 9R 1 3 5R 2 15R 1 17R 2 17R 1 39R 2 16R 1 11R 1 3 3 2 3 3R 2 13R 1 17R 2 16R 1 42R 2 13R 1 13R 1 3 2 17R 1 19R 2 14R 1 46R 2 9R 1 15R1 3 2 15R 1 23R 2 9R 1 75R1 3 2 13R 1 26R 2 5R 1 78R1 2R 2 10R 1 28R 2 2 1 82R1 5R 2 6R 1 114R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R

56

1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 39R 21 36R 21 34R 21 33R 21 33R 21 32R 21 32R 21 32R 21 32R 21 32R 21 32R 21 32R 21 32R 21 32R 21 32R 21 2R 2 c11 1 3 211 1 3 3111 1 3 2111 1 3 211 3 2R ^1 3 3R i1 3 4R i1 3 8R i1 3 9R i1 3 lOR3 2R 1

3R 2 14R 1 73R 2R 2 16R 1 72R 2R 2 17R 1 71R 3 2 19R 1 70R 3 2 20R 1 69R 3 2 22R 1 67R3 2 10R 3 3R 2 8R 1 61R 2 3 1 2R 2R 2 8R 3 2 13R 1 58R 2 2R 3 1 2R 2R 2 7R 3 2 15R 1 55R 2 5R 1 2R25R 2 2R 3 3 2 7R 3 2 4R 4 2 lOR 1 47R 2 lOR 3 2R 1

3R 2 5R 1 20R 2 3R 3 3 2 9R 4 4R 2 lOR 1 41R 2 15R 3 2R 1

2R 2 7R 1 19R 2 3R 3 3 2 9R 4 2 15R 1 38R 2 16R 3 3R 1

I 1 17R 2 32R 1 36R 2 13R 3 3 2 2R 3 4R 12 12R 1 16R 2 19R 3 3R 2 2 3 2 5R 1 34R 2 H R 3 12R 12 13R 1 14R 2 18R 3 5R 2 3 2 5R 1 32R 2 15R 3 lOR 12 3 2 12R 1 12R 2 18R 3 7R 2 6R 1 30R 2 15R 3 11R 12 12R 1 10R 2 16R 3 3 2 5R 3 2R 2 5R 1 28R 2 15R 3 13R 12 12R 1 lOR 2 14R 3 2R 2 5R 3 2R 2 5R 1 27R 2 15R 3 14R 1

lOR 2 12R 1 9R 2 14R 3 2R 2 14R 1 26R 2 16R 3 6R 2 3R 3

57

1 3 10R 2 12R 1 10R 2 16R 3 2 13R 1 25R 2 17R 3 5R 2 4R 3 3R 11 3 2R 2 2R 3 4R 2 13R 1 9R 2 20R 3 2 9R 1 24R 2 18R 3 2 2 32 2 3 9R1 3 2R 2 4R 3 2R 2 13R 1 9R 2 19R 3 2 10R 1 24R 2 26R 3 7R 1 3 5R 2 18R 1 10R 2 30R 1 24R 2 27R 3 6R 1 3 5R 2 18R 1 10R 2 30R 1 25R 2 32R 3 1 3 5R 2 18R 1 HR 2 28R 1 26R 2 32R 3 1 3 5R 2 18R 1 13R 2 25R 1 28R 2 30R 1 1 1 3 5R 2 18R 1 14R 2 24R 1 29R 2 26R 1 4R 1 3 5R 2 17R 1 16R 2 21R 1 31R 2 24R 1 6R 1 3 6R 2 15R 1 16R 2 20R 1 34R 2 21R 1 8R 1 3 6R 2 14R 1 16R 2 19R 1 36R 2 19R 1 10R 1 3 3 2 3 3R 2 13R 1 16R 2 18R 1 39R 2 16R 1 12R 1 3 2 18R 1 18R 2 16R 1 42R 2 12R 1 14R 1 3 2 16R 1 21R 2 12R 1 47R 2 8R 1 16R 1 3 2 13R 1 25R 2 8R 1 76R 1 2R 2 10R 1 27R 2 4R 1 80R 1 5R 2 5R 1 115R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R

58

1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 39R 2 2 1 85R1 36R 2 10R 1 79R1 34R 2 5R 3 3R 2 4R 1 77R1 33R 2 2R 3 10R 2 2R 1 76R1 33R 2 2 3 11R 2 3R 1 75R1 32R 2 2R 3 3R 2 12R 1 74R1 32R 2 2 3 3R 2 13R 1 74R1 32R 2 2 3 2R 2 15R 1 73R1 32R 2 2 3 2R 2 16R 1 72R1 32R 2 2 3 3 2 19R 1 70R1 32R 2 2 3 3 2 20R 1 69R1 32R 2 2 3 3 2 21R 1 68R1 32R 2 2 3 2R 2 8R 3 3R 2 9R 1 66R1 32R 2 2 3 2R 2 23R 1 59R 2 2R 1 2R1 32R 2 2R 3 3 2 7R 3 2 15R 1 56R 2 4R 11 2R 2 3R 1 25R 2 2R 3 3 2 6R 3 2 4R 4 4 2 10R 1 53R 2 6R 3 1 11 1 3 2 5R 1 23R 2 2R 3 3 2 6R 3 2 3R 4 2R 2 4 2 9R 1 43R 22 12R 3 2R 1 11 1 3 3R 2 5R 1 20R 2 3R 3 3 2 5R 3 2 2R 4 4R 2 lOR 1 41R 22 14R 3 2R 1 11 1 3 3R 2 6R 1 20R 2 lOR 3 2 2R 4 2 15R 1 38R 2 15R 3 4R 1 11 1 3 2R 2 9R 1 18R 2 31R 1 36R 2 13R 3 2 2R 3 5R 1 1 3 3R 2 11R 1 16R 2 19R 3 3R 2 8R 1 33R 2 13R 3 11R 11 3 3R 2 13R 1 14R 2 18R 3 5R 2 2 3 2 4R 1 31R 2 15R 3 5R 22 2 3 2R 11 3 4R 2 14R 1 13R 2 16R 3 6R 2 8R 1 29R 2 15R 3 7R 2 3 3R 1 1 3 8R 2 12R 1 11R 2 14R 3 2R 2 14R 1 27R 2 16R 3 13R 1 1 3 9R 2 12R 1 10R 2 14R 3 2R 2 6R 3 3 2 5R 1 26R 2 16R 3 14R 1 1 3 10R 2 12R 1 9R 2 14R 3 2R 2 5R 3 2 7R 1 25R 2 16R 3 15R 1 1 3 10R 2 13R 1 9R 2 31R 1 24R 2 16R 3 7R 2 5R 3 2R 1 1 3 2R 2 2R 3 5R 2 12R 1 9R 2 31R 1 23R 2 18R 3 5R 2 5R 3 4R 1 3 2R 2 4R 3 2R 2 14R 1 9R 2 30R 1 23R 2 25R 3 9R 1 3 6R 2 18R 1 9R 2 30R 1 23R 2 27R 3 7R 1 3 5R 2 19R 1 10R 2 29R 1 23R 2 34R 3 1 3 5R 2 19R 1 11R 2 28R 1 24R 2 33R 3 1 3 6R 2 18R 1 12R 2 26R 1 25R 2 33R 1 1 3 6R 2 17R 1 14R 2 24R 1 27R 2 29R 1 3R 1 3 6R 2 16R 1 15R 2 23R 1 29R 2 25R 1 6R 1 3 6R 2 16R 1 14R 2 23R 1 31R 2 22R 1 8R 1 3 6R 2 15R 1 14R 2 22R 1 33R 2 21R 1 9R 1 3 3 2 3 3R 2 13R 1 15R 2 21R 1 36R 2 19R 1 10R 1 3 2 3R 3 2 13R 1 16R 2 21R 1 37R 2 15R 1 13R1 3 2 16R 1 19R 2 17R 1 41R 2 13R 1 14R1 3 2 14R 1 22R 2 13R 1 47R 2 8R 1 16R1 1 2 13R 1 23R 2 10R 1 76R1 4R 2 7R 1 27R 2 2 1 84R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R

59

1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 39R 2 1 86R1 36R 2 8R 1 81R1 34R 2 4R 3 4R 2 2 1 2 1 78R1 33R 2 2R 3 9R 2 2R 1 77R1 32R 2 2R 3 10R 2 3R 1 76R1 32R 2 2R 3 3R 2 11R 1 75R1 32R 2 2 3 4R 2 12R 1 74R1 32R 2 2 3 3R 2 14R 1 73R1 32R 2 2 3 2R 2 16R 1 72R1 32R 2 2 3 3 2 18R 1 71R1 32R 2 2 3 3 2 19R 1 70R1 32R 2 2 3 3 2 21R 1 68R1 32R 2 2 3 3 2 22R 1 67R1 32R 2 2 3 2R 2 7R 3 2 14R 1 59R 21 33R 2 2 3 3 2 24R 1 56R 2 4R 1 2R1 2R 2 2R 1 27R 2 2 3 3 2 6R 3 2 4R 4 4 2 10R 1 54R 2 5R 3 1 11 1 3 2 5R 1 24R 2 2R 3 2 HR 4 2R 2 11R 1 44R 2 14R 3 1 1 1 1 3 3 2 6R 1 22R 2 10R 3 2 2R 4 3R 2 11R 1 41R 2 15R 3 2R 1 11 1 3 2R 2 7R 1 20R 2 31R 1 38R 2 15R 3 4R 1 1 1 1 3 2R 2 9R 1 18R 2 31R 1 36R 2 16R 3 6R 1 1 3 3R 2 11R 1 16R 2 20R 3 3 2 9R 1 33R 2 16R 3 8R 11 3 3R 2 14R 1 14R 2 17R 3 4R 2 2R 3 2 4R 1 31R 2 13R 3 6R 22 2 3 3R 11 3 4R 2 15R 1 12R 2 17R 3 4R 2 9R 1 28R 2 16R 3 4R 2 4R 3 2R 1 1 3 8R 2 12R 1 11R 2 14R 3 6R 2 10R 1 26R 2 17R 3 5R 2 3R 33 2R 11 3 9R 2 13R 1 10R 2 13R 3 3 2 7R 3 3 2 5R 1 24R 2 17R 3 15R 11 3 10R 2 12R 1 10R 2 13R 3 2R 2 14R 1 23R 2 17R 3 3R 2 3 3R 22 3R 3 2R 11 3 11R 2 12R 1 9R 2 13R 3 2R 2 14R 1 22R 2 17R 3 7R 2 6R 33 3 11 3 3R 2 2 3 5R 2 13R 1 8R 2 31R 1 22R 2 19R 3 4R 2 6R 3 4R 1 3 3 2 5R 3 3R 2 13R 1 9R 2 31R 1 20R 2 24R 3 3 2 3 9R 1 3 3 2 3 2R 2 19R 1 9R 2 31R 1 20R 2 27R 3 2 3 7R 1 3 6R 2 18R 1 10R 2 30R 1 20R 2 36R 3 1 3 5R 2 19R 1 12R 2 27R 1 22R 2 35R 3 1 3 6R 2 18R 1 12R 2 27R 1 23R 2 35R 1 3 4R 2 20R 1 13R 2 25R 1 25R 2 30R 1 3R 1 3 6R 2 17R 1 14R 2 24R 1 27R 2 27R 1 5R 1 3 6R 2 16R 1 14R 2 24R 1 28R 2 25R 1 7R 1 3 6R 2 15R 1 13R 2 25R 1 30R 2 22R 1 9R 1 3 3 2 3 3R 2 14R 1 13R 2 25R 1 31R 2 21R 1 10R 1 3 2 2R 3 2R 2 13R 1 13R 2 25R 1 33R 2 18R 1 12R

1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111

60

3 2 15R 1 20R 2 18R 1 39R 2 13R 1 15R1 2 13R 1 22R 2 14R 1 45R 2 8R 1 18R4R 2 9R 1 24R 2 3R 1 83R7R 2 2 1 30R 2 1 85R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R35R 2 8R 1 82R 34R 2 4R 3 3R 2 2 1 81R 33R 2 2R 3 8R 2 2R 1 78R 32R 2 2R 3 7R 2 5R 1 77R 32R 2 2 3 4R 2 10R 1 76R

61

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62

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75

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85

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86

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88

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89

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91

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92

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94

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95

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96

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97

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98

1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R1 48R 2 7R 1 70R1 44R 2 13R 1 68R1 22R 2 12R 1 5R 2 18R 1 66R1 20R 2 42R 1 10R 2 13R 1 38R1 18R 2 33R 4 2 37R 1 35R1 16R 2 35R 4 4 2 37R 1 34R1 13R 2 37R 4 2R 2 38R 1 33R1 11R 2 39R 4 2R 2 44R 1 27R1 9R 2 27R 3 3 2 11R 4 2R 2 47R 1 24R1 7R 2 28R 3 2R 2 64R 1 22R1 6R 2 28R 3 2R 2 30R 3 3 2 34R 1 20R1 6R 2 36R 4 4R 2 3R 3 2R 2 13R 3 2R 2 35R 1 18R1 5R 2 35R 4 6R 2 2R 3 4R 2 4R 4 2R 2 5R 3 2R 2 15R 3 3 2 21R 11 12R1 4R 2 33R 3 2 4 7R 2 2 3 3 2 2 3 2R 2 2R 4 4R 2 5R 3 2 14R 33 4R 2 21R 1 11R1 3R 2 10R 3 3R 2 17R 3 2R 4 8R 2 2 3 5R 2 3 3 2 4 6R 2 3 3 22 7R 3 3 2 4R 3 2 2 3 5R 2 19R 1 11R1 2R 2 10R 3 5R 2 15R 3 2 4 10R 2 2 3 5R 2 3 3 4 8R 2 3 3 22 5R 3 2R 2 3R 3 2 2R 3 2 3 3R 2 19R 1 11R

2 12R 3 5R 2 17R 4 10R 2 2 3 3 2 2 3 3 2 2R 4 9R 2 8R 3 3 2 11R2 2R 3 3 2 2R 3 2 2R 4 9R 2 8R 3 3 2 10R2 1 1 R 4 9 R 2 8 R 3 3 2 4 R 3 2 6 R 3 3 2

12 3R 3 2 5R 3 2R 2 19R 11 2 11R 3 6R 2 16R 4 10R2 3R 3 2 5R 3 2R 2 20R 11 2 11R 3 6R 2 15R 4 11R2 18R 1 11R1 2 12R 3 5R 2 14R 4 12R 3 2R 2 8R 4 9R 2 7R 3 2R 2 4R 3 2 6R 33 2 18R 1 12R1 2 13R 3 3R 2 2 3 2 9R 3 2 4 12R 2 3 2 3 2 8R 4 9R 2 7R 3 3R 22 2R 3 2 6R 3 3 2 18R 1 12R1 2 1 4 R 3 3 2 2 3 3 2 9 R 3 2 2 4 1 1 R 2 2 R 3 2 4 R 3 2 3 3 4 9 R 23 3 2 4R 3 6R 2 8R 3 2 18R 1 13R1 2 14R 3 7R 2 11R 4 10R 2 2R 3 2 3R 3 3 2 2 3 4 8R 2 2 3 3 22 3R 3 7R 2 2 3 2 23R 1 14R1 2 14R 3 11R 2 7R 4 9R 2 2R 3 2R 2 2 3 3R 2 2R 4 6R 2 9R 32 2R 3 3R 2 2R 3 2 22R 1 14R1 1 2 14R 3 10R 2 7R 4 8R 2 3R 3 3R 2 3 2 2 3 3 2 2R 4 4R 2

99

2 15R 3 3 2 25R 1 15R1 2R 2 17R 3 5R 2 8R 4 7R 2 6R 3 2R 2 3R 3 3 2 3R 4 2R 2 43R 1 1 15R1 3R 2 17R 3 4R 2 5R 3 3 2 2 4 5R 2 8R 3 3 2 10R 3 3 2 43R 1 1 15R1 4R 2 15R 3 3 2 3R 3 3 2 3R 3 3 2 7R 3 3 2 6R 3 2 12R 3 3R 22 13R 3 2 23R 1 17R1 6R 2 12R 3 2R 2 5R 3 2 11R 3 3 2 22R 3 2 16R 3 3 2 21R 1 18R 1 7R 2 11R 3 2R 2 16R 3 2R 2 40R 3 2R 2 20R 1 19R 1 8R 2 11R 3 3 2 8R 3 2 4R 3 3 2 43R 3 3 2 19R 1 21R 1 9R 2 11R 3 2 9R 3 2 33R 3 2 13R 3 3 2 19R 1 22R 1 9R 2 24R 3 2 30R 3 2 34R 1 24R 1 10R 2 70R 3 2 17R 1 26R 1 11R 2 67R 3 3 2 14R 1 30R 1 12R 2 10R 3 2 69R 1 32R 1 14R 2 77R 1 34R 1 15R 2 74R 1 36R 1 17R 2 68R 1 40R 1 19R 2 26R 1 6R 2 30R 1 42R 1 22R 2 17R 1 18R 2 5R 1 61R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R1 127R1 127R1 127R1 127R1 127R

100

1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R1 48R 2 6R 1 71R 1 44R 2 13R 1 68R1 22R 2 14R 1 2R 2 19R 1 16R 2 5R 1 43R1 20R 2 43R 1 6R 2 17R 1 37R1 18R 2 72R 1 35R1 16R 2 35R 4 4 2 37R 1 34R1 13R 2 37R 4 2R 2 38R 1 33R1 11R 2 26R 3 3 2 10R 4 2R 2 43R 1 28R1 9R 2 27R 3 2R 2 10R 4 2R 2 46R 1 25R1 7R 2 28R 3 2R 2 13R 4 2 13R 3 2R 2 30R 1 24R1 6R 2 29R 3 2 30R 3 2R 2 32R 1 22R1 6R 2 35R 4 5R 2 4R 3 3 2 13R 3 2R 2 33R 1 20R1 5R 2 34R 4 8R 2 2 3 2 2 3 3 2 3R 4 3R 2 5R 3 3 2 15R 3 3R 22 15R 1 17R1 5R 2 32R 3 4 9R 2 2 3 2 2R 3 3 2 2 4 5R 2 21R 3 5R 2 19R 1 1 12R1 3R 2 32R 3 3 4 10R 2 3 5R 2 2R 4 8R 3 3 2 8R 3 3 2 4R 3 7R 22 18R 1 12R1 2R 2 11R 3 3R 2 18R 4 10R 2 2 3 5R 2 3 2 4 9R 2 3 2 7R 3 22 3R 3 2 2 3 6R 2 18R 1 12R1 1 2 11R 3 5R 2 16R 4 11R 2 2 3 5R 2 2R 4 9R 2 8R 3 3 2 4R 32 3R 3 4R 2 18R 1 12R1 2 12R 3 5R 2 15R 4 11R 2 2 3 6R 2 2R 4 9R 2 8R 3 3 2 4R 32 5R 3 2R 2 18R 1 12R1 2 12R 3 4R 2 15R 4 12R 3 4R 2 2 3 3 2 2R 4 9R 2 8R 3 3 2 4R 32 4R 3 3R 2 18R 1 12R1 2 12R 3 4R 2 14R 4 13R 3 3R 2 6R 4 11R 2 6R 3 2R 2 4R 3 22 4R 3 2R 2 17R 1 13R1 2 11R 3 4R 2 2R 3 2 8R 3 3 2 4 13R 3 2R 2 5R 3 2 4 11R 2 6R 33 2R 2 3R 3 2 5R 3 3 2 17R 1 14R1 2 1 3 R 3 3 2 2 3 2 R 2 8 R 3 3 2 4 1 2 R 2 2 R 3 2 4 R 3 2 3 4 1 1 R 2 3 3 2 3 R 3 6 R 2 2 3 2 5 R 3 2 17R 1 14R1 2 14R 3 6R 2 HR 4 11R 2 2R 3 2 3R 3 3 2 3 2 4 9R 2 2 3 3 22 2R 3 7R 2 2 3 2 22R 1 15R1 1 2 13R 3 8R 2 9R 4 10R 2 2R 3 3 2 3R 3 3 2 2R 4 8R 2 8R 33 7R 2 2R 3 2 20R 1 15R1 1 2 14R 3 9R 2 7R 4 10R 2 2R 3 2R 2 2 3 4R 2 2 4 7R 2 14R 3 3 3 2 23R 1 16R1 2R 2 17R 3 5R 2 7R 4 8R 2 5R 3 4R 2 7R 4 4R 2 42R 1 16R1 3R 2 16R 3 5R 2 4R 3 3 2 2 4 6R 2 3 2 5R 3 2R 2 10R 4 4 22 8R 3 2 31R 1 17R1 4R 2 15R 3 6R 2 4R 3 2 3R 4 3R 2 3 3 2 6R 3 2 14R 3 2R 2 13R 32 22R 1 18R1 6R 2 12R 3 2R 2 3R 3 2R 2 11R 3 2R 2 6R 3 2 14R 3 3 2 14R 33 2 20R 1 19R1 7R 2 11R 3 2R 2 6R 3 2 8R 3 2R 2 29R 3 2 9R 3 2R 2 19R 1 20R 1 8R 2 11R 3 3 2 7R 3 2 4R 3 3R 2 28R 3 3 2 11R 3 2 20R 1 21R 1 9R 2 11R 3 2 9R 3 2 2R 3 3 2 28R 3 2R 2 11R 3 2 19R 1 23R 1 9R 2 23R 3 2 31R 3 3 2 32R 1 25R1 10R 2 24R 3 2 28R 3 2 32R 11 11R 2 67R 3 3 2 14R 1 30R1 12R 2 10R 3 2 53R 3 2 14R 11 14R 2 9R 3 '2 66R 1 34R1 15R 2 74R 1 36R1 17R 2 69R 1 39R1 19R 2 28R 1 2R 2 32R 1 42R1 21R 2 21R 1 13R 2 22R 1 46R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R

101

1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R1 49R 2 5R 1 71R1 27R 2 2R 1 13R 2 13R 1 68R1 22R 2 38R 1 11R 2 11R 1 41R1 20R 2 68R 1 37R1 18R 2 72R 1 35R1 17R 2 34R 4 2 38R 1 34R1 13R 2 38R 4 4 2 38R 1 33R1 11R 2 26R 3 3 2 10R 4 2R 2 42R 1 29R1 9R 2 27R 3 2R 2 10R 4 2R 2 12R 3 3 2 30R 1 26R1 7R 2 28R 3 2R 2 11R 4 2R 2 12R 3 2R 2 30R 1 25R1 6R 2 37R 4 4 2 21R 3 2R 2 31R 1 23R1 6R 2 35R 4 6R 2 19R 3 3 2 32R 1 22R1 5R 2 33R 4 10R 2 2 3 2 3 2 4R 4 3R 2 23R 3 3R 2 13R 1 20R 1 5R 2 31R 3 3 4 10R 2 3 3 2 4R 4 7R 2 20R 3 5R 2 15R 1 17R 1 4R 2 30R 3 3 2 4 10R 2 2 3 4R 2 2 4 9R 3 2R 2 14R 3 7R 2 16R 1 1 14R1 2R 2 12R 3 2 3 2 17R 4 12R 2 3 5R 2 2 4 10R 2 3 2 13R 3 8R 22 17R 1 13R1 1 2 12R 3 3R 2 17R 4 11R 2 2 3 5R 2 2 4 11R 2 14R 3 2 2 33 4R 2 18R 1 13R1 2 12R 3 4R 2 16R 4 11R 2 2 3 6R 2 2 4 11R 2 14R 3 2 4R 3 2R 22 17R 1 13R1 2 12R 3 4R 2 15R 4 12R 2 2 3 6R 2 2 4 11R 2 14R 3 2 3R 3 3R 22 17R 1 13R1 2 13R 3 2R 2 14R 4 14R 3 3R 2 2 3 3 2 2R 4 11R 2 14R 3 2 2R 33 3R 2 17R 1 14R1 2 1 1 R 3 2 2 3 2 2 R 3 3 2 8 R 3 2 4 1 4 R 2 3 3 2 4 R 3 3 2 4 12R 22 5 R 3 3 2 4 R 3 3 2 4 R 3 3 2 17R 1 14R1 2 16R 3 3R 2 8R 3 2 2 4 12R 2 2R 3 2 4R 3 2R 4 12R 2 3 3 22 2R 3 5R 2 2 3 2 5R 3 2 16R 1 15R1 2 14R 3 6R 2 10R 4 12R 2 2R 3 2 3R 3 2 2R 4 11R 2 2 3 2 3R 3

102

3 6R 2 2 3 3 2 2R 3 2 17R 1 15R1 1 2 13R 3 7R 2 9R 4 12R 2 2 3 3 2 3R 3 3 2 2R 4 9R 2 7R 33 7R 2 2R 3 2R 2 17R 1 16R1 1 2 14R 3 8R 2 7R 4 10R 2 2R 3 2R 2 2R 3 2R 2 2R 4 9R 2 9R 33 2 2 3 3R 2 22R 1 16R1 2R 2 16R 3 5R 2 7R 4 10R 3 2 2R 3 2R 2 3 2R 2 5R 4 6R 2 40R 1 1 16R1 3R 2 16R 3 4R 2 4R 3 3 2 2 4 8R 3 3 2 3R 3 4R 2 7R 4 5R 22 6R 3 3 2 29R 1 18R1 4R 2 15R 3 6R 2 3R 3 2 3R 4 5R 2 3 2R 2 3R 3 2R 2 14R 3 2R 22 2R 3 2 31R 1 18R1 6R 2 13R 3 2R 2 3 2R 2 9R 4 2R 2 2 3 3R 2 4R 3 2 15R 3 2 3R 33 2 7R 3 3 2 21R 1 19R1 8R 2 10R 3 3R 2 3R 3 3 2 9R 3 2R 2 8R 3 2 19R 3 2 9R 3 3 22 18R 1 21R1 8R 2 10R 3 2R 2 7R 3 2 3R 3 5R 2 9R 3 2 17R 3 3 2 10R 3 22 18R 1 22R1 9R 2 25R 3 2R 2 29R 3 2R 2 10R 3 2 18R 1 24R 1 9R 2 23R 3 2 32R 3 3 2 11R 3 2 18R 1 25R 1 10R 2 23R 3 3 2 28R 3 3 2 30R 1 28R 1 11R 2 24R 3 2 27R 3 2 29R 1 30R 1 12R 2 10R 3 2 53R 3 3 2 13R 1 32R 1 14R 2 9R 3 2 66R 1 34R 1 15R 2 74R 1 36R 1 17R 2 69R 1 39R 1 18R 2 66R 1 41R 1 21R 2 22R 1 12R 2 23R 1 45R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R

103

1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R1 50R 2 3R 1 72R 1 26R 2 6R 1 11R 2 12R 1 68R 1 22R 2 38R 1 7R 2 15R 1 41R 1 20R 2 68R 1 37R 1 18R 2 72R 1 35R 1 17R 2 74R 1 34R1 13R 2 25R 3 3 2 10R 4 4 2 38R 1 33R1 11R 2 26R 3 2R 2 9R 4 2R 2 12R 3 2 27R 1 30R1 9R 2 27R 3 2R 2 10R 4 2R 2 12R 3 3 2 29R 1 27R1 8R 2 42R 4 2R 2 12R 3 2R 2 30R 1 25R1 7R 2 35R 4 2R 2 21R 3 3 2 31R 1 24R1 6R 2 34R 4 7R 2 11R 4 2R 2 38R 1 23R1 5R 2 33R 4 11R 2 8R 4 4R 2 22R 3 3R 2 12R 1 21R1 5R 2 31R 3 3 4 10R 2 3 3R 2 2R 4 8R 2 19R 3 5R 2 13R 1 19R1 4R 2 30R 3 3 4 12R 2 3 4R 2 2 4 9R 2 3 3 2 14R 3 7R 2 14R 11 16R1 3R 2 32R 4 12R 2 3 5R 2 2 4 11R 2 14R 3 8R 2 16R 1 15R 1 1 2 33R 4 12R 2 2 3 5R 2 2 4 11R 2 14R 3 8R 2 17R 1 14R 1 1 2 13R 3 3 2 16R 4 13R 2 3 6R 2 2 4 11R 2 14R 3 8R 2 17R 1 1 13R1 2 14R 3 2 16R 4 13R 3 2 3 6R 2 2 4 12R 2 13R 3 8R 2 17R 1 1 13R1 2 29R 3 2 4 14R 2 3 9R 4 12R 2 13R 3 8R 2 17R 1 14R 1 2 16R 3 2R 2 8R 3 3 2 4 14R 2 2 3 3 2 2R 3 2R 2 4 13R 2 12R 33 3 2 4R 3 2 16R 1 15R1 2 15R 3 4R 2 8R 3 2 4 13R 2 2R 3 2 3R 3 2 3 3 4 12R 2 3 3 22 6R 3 3 2 2 3 2R 2 3R 3 2 16R 1 15R1 2 14R 3 5R 2 11R 4 12R 2 11R 4 12R 2 2 3 2 3R 3 6R 2 2R 32 2 3 3 2 16R 1 16R1 1 2 13R 3 6R 2 10R 4 1 2 R 2 7 R 3 2 2 R 4 1 1 R 2 7 R 3 8 R 2 2 R 32 18R 1 16R1 1 2 14R 3 7R 2 7R 4 12R 3 2 3 2R 2 2R 3 3 2 3R 4 10R 2 7R 33 7R 2 21R 1 17R1 2 R 2 1 6 R 3 4 R 2 7 R 4 1 1 R 3 2 2 3 2 R 2 2 R 3 3 2 4 R 4 8 R 2 9 R 32 28R 1 17R1 3R 2 16R 3 4R 2 4R 3 3 2 4 9R 3 3 2 3R 3 3 2 3 3 2 6R 4 7R 22 5R 3 3R 2 27R 1 18R1 4R 2 15R 3 4R 2 4R 3 2 3R 4 6R 2 3 3R 2 2R 3 2R 2 8R 4 5R 22 3 2 3R 3 2R 2 4R 3 2 22R 1 19R1 6R 2 13R 3 5R 2 9R 4 4R 2 3 3R 2 3R 3 3 2 6R 3 3 2 12R 3 3 22 5R 3 3 2 20R 1 20R1 8R 2 10R 3 7R 2 9R 4 2 2R 3 2 8R 3 2 7R 3 2R 2 9R 3 2 7R 33 3 2 19R 1 21R1 8R 2 12R 3 3 2 4R 3 2 4R 3 3 2 2 3 2R 2 9R 3 2 18R 3 3 2 8R 33 2 18R 1 23R1 9R 2 12R 3 2 10R 3 4R 2 11R 3 2 17R 3 3 2 9R 3 2 18R 1 24R 1 9R 2 22R 3 2 17R 3 2 15R 3 3 2 29R 1 26R1 10R 2 22R 3 2R 2 29R 3 2R 2 28R 1 28R1 11R 2 22R 3 2R 2 27R 3 3 2 28R 1 30R1 12R 2 10R 3 2 HR 3 3 2 26R 3 2 11R 31 14R 2 8R 3 3 2 51R 3 2 14R 1 33R1 15R 2 74R 1 36R1 17R 2 69R 1 39R1 18R 2 66R 1 41R1 20R 2 25R 1 6R 2 28R 1 44R1 24R 2 17R 1 16R 2 18R 1 48R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R

104

1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 51R 2 1 74R1 25R 2 10R 1 8R 2 12R 1 16R 2 2R 1 48R1 21R 2 41R 1 2R 2 19R 1 40R1 20R 2 68R 1 37R1 18R 2 72R 1 35R1 17R 2 74R 1 34R1 14R 2 24R 3 2R 2 50R 1 33R1 11R 2 26R 3 2R 2 10R 4 4 2 11R 31 9R 2 27R 3 2R 2 10R 4 2R 2 11R 31 8R 2 42R 4 2R 2 12R 3 2R 2 29R 1 26R1 7R 2 35R 4 2R 2 4R 4 2R 2 46R 1 25R1 6R 2 34R 4 8R 2 10R 4 3R 2 37R 1 23R1 5R 2 31R 3 3 4 11R 2 8R 4 5R 2 22R 3 2R 2 11R 1 22R

3 2 27R 1 30R 2R 2 28R 1 28R

2 2R 4 8R 2 2 3 2 16R 3 5R 2 11R 1

2 4 11R 3 2R 2 13R 3 7R 2 12R 1

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105

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106

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108

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109

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110

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112

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158

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159

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5R 2 20R 4 12R 2 12R 1 33R 2R 2 2 4 11R 2 19R 4 12R 2 12R 1 33R 2R 2 2 4 12R 2 17R 4 3R 2 4 7R 2 13R 1 33R 1R 2 4 4R 2 15R 4 13R 2 14R 1 32R 4 21R 2 4 4R 2 14R 4 2R 2 2 4 9R 2 14R 1 32R 27R 2 9R 4 19R 3 2 13R 1 32R

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186

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187

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188

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189

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190

1 29R 2 4R 1 92R1 24R 2 14R 1 25R 2 12R 1 48R1 21R 2 20R 1 19R 2 18R 1 45R1 19R 2 24R 1 14R 2 23R 1 43R1 18R 2 26R 1 11R 2 26R 1 42R1 16R 2 30R 1 7R 2 29R 1 41R1 15R 2 70R 1 40R1 14R 2 72R 1 39R1 14R 2 73R 1 38R1 13R 2 32R 3 3 2 4R 3 2 33R 1 38R1 12R 2 20R 4 3R 2 8R 3 3 2 4R 3 2 12R 4 4 2 19R1 12R 2 15R 3 2 2 4 8R 2 27R 4 3R 3 3 2 14R 1 3711 12R 2 14R 3 3 4 13R 2 26R 4 3R 2 3 2 13R 1 36R1 11R 2 15R 4 19R 2 23R 4 3R 2 14R 1 36R1 11R 2 14R 4 20R 2 24R 4 3R 2 13R 1 36R1 11R 2 13R 4 20R 2 26R 4 3R 2 12R 1 36R1 11R 2 13R 4 19R 2 27R 4 4R 2 12R 1 35R1 11R 2 10R 3 2 4 20R 2 28R 4 3R 2 3 2 10R 1 35R1 11R 2 9R 3 2 4 20R 2 29R 4 4R 2 11R 1 35R1 11R 2 10R 4 21R 2 29R 4 4R 3 3 2 9R 1 35R1 10R 2 11R 4 13R 2 5R 4 2 30R 4 5R 2 10R 1 35R1 10R 2 11R 4 9R 2 41R 4 5R 2 10R 1 35R1 10R 2 10R 4 9R 2 42R 4 5R 2 10R 1 35R1 10R 2 9R 3 4 7R 2 43R 4 6R 2 10R 1 35R1 10R 2 10R 4 6R 2 44R 4 6R 3 2 9R 1 35R1 9R 2 11R 4 5R 2 45R 4 6R 2 10R 1 35R 1 9R 2 11R 4 5R 2 44R 4 7R 2 10R 1 35R 1 9R 2 11R 4 4R 2 45R 4 7R 2 10R 1 35R 1 9R 2 10R 4 5R 2 44R 4 8R 2 10R 1 35R 1 9R 2 9R 3 2 4 4R 2 43R 4 9R 3 2 9R 1 35R 1 9R 2 9R 3 4 4R 2 43R 4 10R 3 3 2 8R 1 35R 1 8R 2 11R 4 4R 2 22R 4 4 2 20R 4 8R 2 11R 1 34R 1 8R 2 11R 4 4R 2 19R 4 4R 2 22R 4 6R 2 11R 1 34R 1 9R 2 11R 4 3R 2 19R 4 4R 2 22R 4 6R 2 11R 1 34R 1 9R 2 11R 4 3R 2 18R 4 5R 2 7R 4 2R 2 12R 4 5R 2 11R 1 34R 1 9R 2 11R 4 3R 2 18R 4 4R 2 8R 4 4 2 13R 4 4R 2 12R 1 34R 1 9R 2 10R 3 4 3R 2 17R 4 4R 2 9R 4 4 2 13R 4 4R 2 3 2 10R 1 1 33R1 9R 2 10R 3 4 4R 2 16R 4 3R 2 2R 3 2 6R 4 4 2 13R 4 4R 3 3 22 9R 1 34R1 9R 2 10R 3 2 4 3R 2 16R 4 2R 2 2 3 4R 2 3R 4 2R 2 13R 4 4R 32 11R 1 34R1 9R 2 12R 4 3R 2 15R 4 3R 2 3 6R 2 2R 4 2R 2 13R 4 4R 2 12R 1 1 33R1 9R 2 12R 4 4R 2 14R 4 3R 2 3 6R 2 2R 4 2R 2 13R 4 4R 2 12R 1 1 33R1 10R 2 H R 4 4R 2 14R 4 3R 2 3 6R 2 2 4 3R 2 12R 4 4R 2 13R 1 1 33R1 10R 2 12R 4 4R 2 13R 4 2R 2 2 3 6R 2 4 4R 2 11R 4 5R 2 13R 1 1 33R1 10R 2 12R 4 5R 2 H R 4 3R 2 2 3 6R 2 4 5R 2 9R 4 5R 2 14R 11 33R1 1 1 R 2 1 2 R 4 5 R 2 9 R 4 4 R 2 3 2 R 2 2 3 2 R 2 2 4 4 R 2 8 R 4 6 R 22 12R 1 35R1 12R 2 11R 4 7R 2 6R 4 5R 3 2R 2 3R 3 2R 2 4 6R 2 4R 4 7R 22 13R 1 35R1 13R 2 11R 4 8R 2 3R 4 5R 2 3 2 3 2 3R 3 2 3 2 4 19R 3 2 12R 1 1 35R1 14R 2 9R 3 3 4 16R 3 4R 2 3R 3 3 2 3 2 4 17R 3 3 2 12R 1 36R 1 15R 2 9R 3 2 4 14R 3 4R 2 3 2 2 3 4R 2 2 4 15R 2 3 2 12R 1 1 36R1 16R 2 9R 3 2 4 12R 2 3 3 R 2 7 R 3 3 2 2 R 4 13R 2 14R 1 38R 1 18R 2 11R 4 8R 3 3R 2 5R 3 3 2 3R 3 2 2 3 2 2 4 9R 2 15R 1 1 38R1 19R 2 19R 3 3 2 8R 3 2 8R 3 3 2 2 4 4R 2 16R 1 40R 1 21R 2 14R 3 2R 2 10R 3 2 10R 3 2R 2 19R 1 41R 1 23R 2 60R 1 42R 1 25R 2 56R 1 44R 1 27R 2 51R 1 47R 1 29R 2 46R 1 50R 1 32R 2 39R 1 54R 1 35R 2 15R 1 1 2 15R 1 57R 1 58R 2 6R 1 61R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R

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191

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2 13R 1 27R 2 lOR 1 49R2 19R 1 20R 2 17R 1 46R2 22R 1 16R 2 22R 1 43R2 26R 1 11R 2 26R 1 42R2 29R 1 7R 2 29R 1 41R2 69R 1 40R2 71R 1 39R2 72R 1 39R2 33R 3 2 4R 3 2 33R 1 !2 16R 3 2 2 4 3R 2 5R 32 18R 4 7R 2 29R 4 2R 32 14R 3 2 4 14R 2 2 4 22 14R 4 19R 2 24R 4 2R i2 14R 4 20R 2 24R 4 3R i2 13R 4 20R 2 26R 4 3R i2 13R 4 19R 2 27R 4 4R i2 10R 3 3 4 20R 2 28R 42 9R 3 3 4 20R 2 29R 4 <2 10R 4 9R 2 8R 4 2R 2 12 10R 4 7R 2 43R 4 4R 22 11R 4 6R 2 44R 4 5R 22 10R 4 6R 2 45R 4 5R 22 9R 3 4 5R 2 45R 4 6R i2 10R 4 4R 2 47R 4 5R 32 10R 4 4R 2 46R 4 6R 2

3 2 43R 1 37R 3 2 14R 1 37R 23R 4 2R 3 3 2 12R 1 37R

4R 3 2 9R 1 36R IR 3 3 2 8R 1 36R >9R 4 4R 2 10R 1 36R lOR 1 36R 9R 1 36R 9R 1 36R

2 9R 1 35R lOR 1 35R

9R 2 11R 4 3R 2 46R 4 7R 2 lOR 1 35R 9R 2 11R 4 3R 2 45R 4 8R 2 10R 1 35R 9R 2 9R 3 4 4R 2 45R 4 8R 2 10R 1 35R 9R 2 9R 3 4 3R 2 45R 4 9R 2 3 2 8R 1 35R

2 10R 4 3R 2 47R 4 7R 2 3 2 8R 1 35R2 10R 4 3R 2 48R 4 6R 2 10R 1 35R2 lOR 4 3R 2 22R 4 2R 2 23R 4 5R 2 11R 1 34R2 11R 4 2R 2 22R 4 2R 2 24R 4 4R 2 11R 1 34R2 11R 4 2R 2 21R 4 3R 2 7R 4 2 15R 4 4R 2 11R 1 34R2 11R 4 2R 2 20R 4 3R 2 8R 4 4 2 14R 4 3R 2 3 2 10R 1 34R2 10R 3 4 2R 2 20R 4 2R 2 9R 4 4 2 14R 4 3R 3 3 2 10R 1

33R9R 2 lOR 3 4 2R 2 19R 4 2R 2 lOR 4 2 15R 4 3R 3 3 2 lOR 1 33R9R 2 11R 4 3R 2 18R 4 4 2 2 3 3R 2 4R 4 4 2 15R 4 3R 2 12R 1 33R9R 2 12R 4 2R 2 18R 4 4 2 33RlOR 2 11R 4 2R 2 17R 4 2R 33R10R 2 11R 4 3R 2 16R 4 2R

3 6R 2 2R 4 4 2 15R 4 3R 2 12R 1

2 3 6R 2 2R 4 4 2 15R 4 3R 2 12R 1

2 3 6R 2 2 4 4 2 16R 4 2R 2 13R 1

192

1 33R1 10R 2 12R1 33R1 11R 2 11R1 34R1 11R 2 12R

4 2R 2 16R 4 4 2 2 3 6 R 2 4 3 R 2 14R 4 3R 2 13R 1

4 3R 2 15R 4 4 2 2 3 6 R 2 4 3 R 2 13R 4 4R 2 12R 1

4 3 R 2 1 3 R 4 2 R 2 2 3 3 2 2 3 2 R 2 2 4 3 R 2 1 1 R 44 3R 2 13R 1 35R1 12R 2 11R 4 4R 2 11R 4 2R 2 2 3 3 2 3R 3 3 2 2 4 3R 2 10R 4 4 3R 3 3 2 12R 1 35R1 13R 2 9R 3 3 4 4R 2 9R 4 3R 2 2R 3 2 4R 3 2 2 4 5R 2 6R 4 4 5R 3 3 2 11R 1 36R

4 3R 2 2R 3 3 2 3R 3 2 3R 4 17R 2 3

3 3R 2 2 3 2R 2 3R 4 15R 2 14R 1 37R 2 3R 3 2 2R 3 3 2 2R 4 13R 2 14R 1

2 3 2 9R 3 2 4R 4 9R 2 15R 1 39R 2 4 3R 2 16R 1 40R 2 10R 3 2R 2 19R 1 41R

1 14R 2 9R 5( :2 4 5R 2 6R <2 12R 1 36R1 15R 2 9R 5( :2 4 14R 2 2R1 16R 2 11R 4 11R 5! 3R 3 51 37R1 18R 2 11R 4 8R 2 3 3 2 ;1 19R 2 17R 3 2R 2 22R 3 i1 21R 2 13R 3 2 R 2 11R 3 i1 23R 2 41R 3 2R 2 15R 1 t1 25R 2 56R 1 44R1 27R 2 51R 1 47R1 29R 2 46R 1 50R1 32R 2 39R 1 54R1 35R 2 14R 1 2R 2 16R 1 {1 58R 2 7R 1 60R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R

193

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1 22R 2 18R 1 21R 2 15R 1 47R1 20R 2 22R 1 16R 2 21R 1 44R1 19R 2 25R 1 11R 2 25R 1 43R1 17R 2 29R 1 7R 2 28R 1 42R1 16R 2 68R 1 41R1 15R 2 70R 1 40R1 15R 2 71R 1 39R1 14R 2 32R 3 2 3 2 37R 1 38R1 13R 2 20R 4 2R 2 33R 3 2 15R 1 38R1 13R 2 17R 4 7R 2 30R 4 4 3 3 2 14R 1 37R1 12R 2 16R 4 17R 2 23R 4 2R 3 2 13R 1 37R1 12R 2 14R 4 19R 2 24R 4 2R 2 13R 1 37R1 12R 2 13R 4 20R 2 25R 4 2R 2 13R 1 36R1 12R 2 12R 4 20R 2 26R 4 3R 2 12R 1 36R1 11R 2 11R 3 4 21R 2 27R 4 3R 2 11R 1 36R1 11R 2 10R 3 3 4 20R 2 28R 4 3R 3 2 10R 1 36R1 11R 2 11R 4 7R 2 10R 4 4 2 29R 4 4R 2 3 2 8R 1 36R1 11R 2 11R 4 6R 2 43R 4 4R 2 10R 1 36R1 11R 2 10R 4 5R 2 45R 4 4R 2 10R 1 36R1 11R 2 10R 4 4R 2 46R 4 5R 2 9R 1 36R1 10R 2 10R 4 4R 2 47R 4 5R 2 9R 1 36R1 10R 2 10R 4 4R 2 47R 4 5R 3 2 8R 1 36R1 10R 2 10R 4 3R 2 48R 4 5R 2 9R 1 36R1 10R 2 10R 4 2R 2 48R 4 6R 2 10R 1 35R1 10R 2 10R 4 2R 2 47R 4 7R 2 10R 1 35R1 9R 2> 9R 3 2 4 2R 2 46R 4 8R 2 10R 1 35R1 9R 2> 9R 3 4 2R 2 46R 4 9R 3 3 2 8R 1 35R1 9R 2 10R 4 2R 2 48R 4 7R 3 3 2 8R 1 35R 1 9R 2 lOR 4 2R 2 50R 4 5R 2 lOR 1 35R 1 9R 2 lOR 4 2R 2 51R 4 4R 2 lOR 1 35R 1 9R 2 lOR 4 2R 2 25R 4 2 24R 4 4R 2 lOR 1 35R 1 9R 2 11R 4 4 2 24R 4 4 2 25R 4 3R 2 lOR 1 35R 1 9R 2 11R 4 4 2 23R 4 2R 2 25R 4 3R 2 11R 1 34R 1 9R 2 9R 3 2 4 4 2 22R 4 2R 2 8R 4 2 16R 4 3R 3 2 10R 1 34R 1 9R 2 H R 4 4 2 22R 4 4 2 9R 4 2 16R 4 2R 2 3 2 10R 1 34R 1 9R 2 11R 4 4 2 21R 4 4 2 9R 4 4 2 16R 4 2R 2 3 2 10R 1 34R 1 9R 2 11R 4 4 2 21R 4 2 2 3 3R 2 4R 4 2 17R 4 2R 2 12R 1 34R 1 10R 2 11R 4 4 2 19R 4 4 2 3 5R 2 3R 4 2 17R 4 2R 2 12R 1 34R 1 10R 2 11R 4 4 2 19R 4 4 2 3 6R 2 2R 4 2 17R 4 2R 2 12R 1 34R 1 10R 2 11R 4 2R 2 18R 4 4 2 3 6R 2 2 4 4 2 17R 4 2R 2 12R 1 1 33R1 10R 2 12R 4 4 2 18R 4 2 2 3 6 R 2 4 2 R 2 16R 4 2R 2 12R 1 35R1 11R 2 11R 4 4 2 17R 4 4 2 2 3 2R 2 3 2R 2 2 4 4 2 15R 4 3R 22 11R 1 35R1 1 1 R 2 1 2 R 4 4 2 1 6 R 4 4 2 2 3 3 2 2 3 2 R 2 2 4 2 R 2 1 4 R 4 4 4 2 13R 1 35R1 12R 2 10R 3 4 2R 2 15R 4 2 2R 3 2 3R 3 3 2 2 4 2R 2 12R 44 3R 3 2 12R 1 35R1 13R 2 9R 3 2 4 2R 2 13R 4 4 2 2R 3 2 4R 3 2 2R 4 2R 2 10R 44 3R 2 3 2 11R 1 36R1 14R 2 9R 3 2 4 3R 2 10R 4 4 2 2R 3 3 2 3R 3 3 2 2R 4 4R 22 5R 4 5R 2 14R 1 36R1 15R 2 11R 4 3R 2 7R 4 2R 2 3R 3 2R 2 2 3 2R 2 3R 4 15R 2 14R 1 1 36R1 17R 2 11R 4 10R 2 3R 3 3 2 2R 3 3 2 2R 3 3 2 3R 4 12R 2 14R 1 1 37R1 18R 2 11R 4 7R 2 5R 3 2 9R 3 2 4R 4 9R 2 15R 1 39R 1 19R 2 13R 4 4 2 3 2 3 2 25R 4 3R 2 16R 1 40R 1 21R 2 12R 3 3R 2 24R 3 3 2 19R 1 41R 1 23R 2 9R 3 3 2 29R 3 2R 2 15R 1 42R 1 25R 2 56R 1 44R 1 27R 2 51R 1 47R 1 29R 2 46R 1 50R 1 31R 2 41R 1 53R 1 35R 2 14R 1 2R 2 16R 1 56R 1 58R 2 7R 1 60R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R1 127R

194

1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 27R 2 8R 1 32R 2 2R 1 54R1 23R 2 16R 1 23R 2 13R 1 48R1 21R 2 20R 1 17R 2 20R 1 45R1 19R 2 25R 1 12R 2 24R 1 43R1 18R 2 28R 1 7R 2 28R 1 42R1 17R 2 67R 1 41R1 16R 2 69R 1 40R1 15R 2 70R 1 40R1 14R 2 17R 3 2 12R 3 3 2 38R 1 39R1 14R 2 17R 3 2 37R 3 2 15R 1 38R1 13R 2 14R 3 2 2 4 7R 2 31R 4 2 3 2 13R 1 38R1 13R 2 15R 4 16R 2 25R 4 4 2 14R 1 37R1 12R 2 14R 4 19R 2 24R 4 2R 2 13R 1 37R1 12R 2 13R 4 20R 2 25R 4 2R 2 12R 1 37R1 12R 2 10R 3 2 4 20R 2 26R 4 3R 2 12R 1 36R1 12R 2 10R 3 4 21R 2 27R 4 3R 2 11R 1 36R1 11R 2 10R 3 2 4 6R 2 9R 4 3R 2 28R 4 3R 2 31 11R 2 11R 4 5R 2 44R 4 4R 2 10R 1 36R1 11R 2 11R 4 4R 2 45R 4 4R 2 10R 1 36R1 11R 2 10R 4 4R 2 46R 4 4R 2 10R 1 36R1 11R 2 7R 3 2 2 4 3R 2 47R 4 5R 2 9R 1 36R1 11R 2 9R 4 3R 2 48R 4 5R 3 2 8R 1 36R1 10R 2 10R 4 2R 2 50R 4 4R 3 2 8R 1 36R1 10R 2 10R 4 2R 2 49R 4 5R 2 3 2 7R 1 36R1 10R 2 10R 4 4 2 49R 4 6R 2 9R 1 36R1 10R 2 10R 4 4 2 48R 4 7R 2 10R 1 35R1 10R 2 8R 3 2 4 4 2 47R 4 8R 3 2 9R 1 35R1 9R 2 9R 3 4 4 2 49R 4 7R 3 3 2 8R 1 35R1 9R 2 10R 4 4 2 51R 4 5R 3 3 2 8R 1 35R1 9R 2 lOR 4 4 2 52R 4 4R 2 lOR 1 35R1 9R 2 lOR 4 4 2 53R 4 3R 2 lOR 1 35R1 9R 2 lOR 4 4 2 53R 4 3R 2 lOR 1 35R1 9R 2 11R 4 2 26R 4 2 26R 4 2R 2 lOR 1 35R1 9R 2 11R 4 2 25R 4 4 2 26R 4 2R 2 lOR 1 35R1 9R 2 9R 3 3 4 2 24R 4 4 2 27R 4 2R 3 2 9R 1 35R1 9R 2 9R 3 3 4 2 23R 4 4 2 28R 4 2R 3 2 9R 1 35R1 9R 2 11R 4 2 23R 4 2 9R 4 2 18R 4 2R 2 lOR 1 35R1 lOR 2 lOR 4 4 2 21R 4 2 2R 3 2R 2 4R 4 2 18R 4 2R 2 lOR 11 34R1 lOR 2 11R 4 2 21R 4 2 3 5R 2 23R 4 4 2 11R 1 35R 1 10R 2 11R 4 2 21R 4 2 3 6R 2 22R 4 4 2 11R 1 35R 1 10R 2 11R 4 4 2 20R 4 2 3 6R 2 2 4 2 18R 4 2R 2 11R 1 35R 1 11R 2 10R 4 4 2 19R 4 2 2 3 6R 2 4 4 2 18R 4 4 2 12R 1 35R 1 11R 2 11R 4 2 19R 4 2 2 3 6R 2 4 4 2 17R 4 2R 2 12R 1 35R1 11R 2 12R 4 2 18R 4 2 2 3 3 2 2R 3 3 2 2 4 4 2 16R 4 4 2 32 11R 1 35R1 12R 2 9R 3 3 4 4 2 16R 4 2 2R 3 2 4R 3 2 2 4 4 2 15R 4 2R 33 2 11R 1 35R1 13R 2 9R 3 2 4 4 2 25R 3 2 2R 4 4 2 12R 4 3R 2 3 2 11R 1 36R1 14R 2 11R 4 4 2 13R 4 2 2R 3 3 2 4R 3 2 3R 4 2R 2 9R 4 3R 2

195

1 15R 2 11R 4 2R 2 9R 4 2 4R 3 2R 2 2 3 3R 2 3R 4 3R 2 3R 44 5R 2 14R 1 37R1 17R 2 11R 4 2R 2 5R 4 4 2 3R 3 2 3R 3 3 2 2R 3 3 2 3R 4 12R 22 13R 1 38R1 18R 2 11R 4 7R 2 11R 3 2 10R 4 8R 2 15R 1 39R1 19R 2 13R 4 4 2 28R 4 4R 2 16R 1 40R1 21R 2 12R 3 3R 2 46R 1 41R1 23R 2 9R 3 3 2 29R 3 3R 2 13R 1 43R1 25R 2 56R 1 44R1 27R 2 51R 1 47R1 29R 2 46R 1 50R1 31R 2 41R 1 53R1 35R 2 15R 1 1 2 16R 1 56R1 58R 2 8R 1 59R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 28R 2 6R 1 91R 1 24R 2 14R 1 24R 2 11R 1 50R 1 21R 2 20R 1 18R 2 17R 1 47R 1 20R 2 23R 1 13R 2 22R 1 45R 1 18R 2 28R 1 7R 2 27R 1 43R 1 17R 2 66R 1 42R 1 16R 2 68R 1 41R 1 15R 2 70R 1 40R1 14R 2 17R 3 2 12R 3 2R 2 3R 3 3 2 13R 3 2 16R 1 39R 1 14R 2 32R 3 2 4R 3 2 16R 3 3 2 13R 1 39R 1 13R 2 17R 4 8R 2 30R 4 3 3 2 13R 1 38R

196

1 13R 2 14R 4 17R 2 25R 4 2R 2 13R 1 37R1 12R 2 13R 4 18R 2 27R 4 2R 2 12R 1 37R1 12R 2 10R 3 2 4 20R 2 27R 4 2R 2 3 2 9R 1 37R1 12R 2 10R 3 4 7R 2 7R 4 4R 2 28R 4 3R 2 10R 1 37R1 12R 2 11R 4 4R 2 44R 4 3R 2 3 2 8R 1 37R1 12R 2 10R 4 4R 2 45R 4 4R 2 10R 1 36R1 11R 2 11R 4 3R 2 46R 4 4R 2 10R 1 36R1 11R 2 8R 3 2 4 3R 2 47R 4 4R 2 10R 1 36R1 11R 2 10R 4 2R 2 48R 4 5R 2 9R 1 36R1 11R 2 9R 4 2R 2 50R 4 4R 2 9R 1 36R1 11R 2 9R 4 2R 2 49R 4 5R 3 2 8R 1 36R1 10R 2 10R 4 4 2 49R 4 6R 2 9R 1 36R1 10R 2 10R 4 4 2 48R 4 7R 2 9R 1 36R1 10R 2 10R 4 2 49R 4 7R 2 9R 1 36R1 10R 2 8R 3 2 4 2 50R 4 6R 3 3 2 8R 1 35R1 9R 2 9R 3 4 4 2 52R 4 4R 3 3 2 8R 1 35R1 9R 2 10R 4 4 2 53R 4 3R 2 3 2 8R 1 35R1 9R 2 10R 4 4 2 53R 4 3R 2 10R 1 35R1 9R 2 10R 4 2 55R 4 2R 2 10R 1 35R1 9R 2 10R 4 2 55R 4 2R 2 10R 1 35R1 9R 2 10R 4 2 55R 4 2R 2 10R 1 35R1 9R 2 9R 3 2 4 2 26R 4 2 27R 4 4 3 2 9R 1 35R1 9R 2 9R 3 3 4 2 25R 4 2 28R 4 4 2 10R 1 35R1 9R 2 9R 3 2 4 2 55R 4 4 2 10R 1 35R1 10R 2 10R 4 2 23R 4 2 30R 4 4 2 10R 1 35R1 10R 2 10R 4 2 25R 3 4R 2 24R 4 4 2 10R 1 35R1 10R 2 10R 4 2 22R 4 2 3 5R 2 24R 4 2 11R 1 35R1 10R 2 11R 4 2 21R 4 2 3 6R 2 22R 4 4 2 11R 1 35R1 10R 2 11R 4 2 21R 4 2 3 6R 2 2 4 2 19R 4 4 2 11R 1 35R1 11R 2 10R 4 2 23R 3 6R 2 4 4 2 19R 4 2 12R 1 35R1 11R 2 11R 4 2 19R 4 2 2 3 6R 2 2 4 2 18R 4 4 2 12R 1 35R1 12R 2 9R 55 4 2 19R 4 2 2 3 3 2 2 3 2R 2 2 4 2 17R 4 4 3 3 22 10R 1 35R1 12R 2 9R 51 3 4 2 2 1 R 3 2 4 R 3 2 2 4 4 2 16R 4 4 2 3 2 10R 11 35R1 13R 2 9R 55 2 4 2 30R 4 4 2 14R 4 4 2 3 2 1 1 R 1 36R1 14R 2 11R 4 2 14R 4 2 2R 3 2 10R 4 4 2 11R 4 2R 2 13R 1 37R1 15R 2 11R 4 4 2 16R 3 2R 2 2 3 2R 2 4R 4 2R 2 7R 4 3R 2 14R1 36R1 17R 2 11R 4 2 13R 3 2 3R 3 3 2 8R 4 12R 2 14R 1 38R1 18R 2 11R 4 7R 2 11R 3 2 10R 4 8R 2 15R 1 39R1 19R 2 13R 4 4 2 28R 4 4R 2 16R 1 40R1 21R 2 10R 3 4R 2 28R 3 2 2 3 2 14R 1 41R1 23R 2 9R 51 3 2 29R 3 3R 2 13R 1 43R1 25R 2 56R 1 44R1 27R 2 51R 1 47R1 29R 2 46R 1 50R1 31R 2 41R 1 53R1 35R 2 15R 1 1 2 17R 1 55R1 58R 2 8R 1 59R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R1 127R

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197

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198

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199

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200

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201

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202

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2R 1 13R 2 10R 1 58R

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203

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204

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205

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206

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48R

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218

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74R 1 38R4R 3 2 68R 1 38R5R 3 2 68R 1 38R69R 3 2 4R 1 38R76R 1 37R76R 1 37R76R 1 37R76R 1 37R76R 1 37R76R 1 37R76R 1 37R5R 3 2 29R 3 3R 2 28R 3 2 5R 1 37R 5R 3 2 28R 3 5R 2 27R 3 2 5R 1 37R 34R 3 2 3R 3 3 2 27R 3 2 5R 1 37R 40R 3 2 33R 1 37R 74R 1 38R 74R 1 38R35R 3 2R 2 35R 1 38R 73R 1 38R 72R 1 39R 71R 1 39R7R 3 2 28R 3 2 22R 3 2 7R 1 40R7R 3 2 20R 3 2R 2 2R 3 3 2 21R 3 2 8R :28R 3 3R 2 3 2R 2 30R 1 41R30R 3 3R 2 30R 1 42R13R 3 2R 2 13R 3 2 32R 1 42R11R 3 3 2 30R 3 2R 2 13R 1 43R58R 1 44R54R 1 46R51R 1 47R47R 1 48R43R 1 50R12R 1 6R 2 17R 1 53R2 1 15R 2 12R 1 55R 2R 1 60R

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229

13R 2 74R 1 38R13R 2 34R 3 4R 2 34R 1 38R13R 2 33R 3 6R 2 33R 1 38R13R 2 33R 3 6R 2 33R 1 38R13R 2 33R 3 7R 2 32R 1 38R13R 2 33R 3 7R 2 32R 1 38R14R 2 32R 3 7R 2 32R 1 38R14R 2 32R 3 3 2 2R 3 2R 2 31R 1 39R14R 2 6R 3 2 22R 3 2 40R 1 39R15R 2 5R 3 2 21R 3 2 33R 3 2 6R 1 39R15R 2 6R 3 2 19R 3 2 41R 1 40R16R 2 25R 3 3 2 2 R 3 3 2 2 R 3 2 3 R 3 3 2 26R 1 40R16R 2 30R 3 5R 2 4R 3 3 2 24R 1 41R17R 2 32R 3 2 33R 1 41R18R 2 31R 3 2 32R 1 42R19R 2 10R 3 3 2 38R 3 2 11R 1 42R20R 2 48R 3 3 2 11R 1 43R21R 2 60R 1 44R23R 2 26R 3 2 29R 1 45R26R 2 53R 1 46R29R 2 48R 1 48R32R 2 43R 1 50R35R 2 11R 1 8R 2 17R 1 52R59R 2 11R 1 55R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R

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230

127R127R38R 2 28R 1 59R 33R 2 36R 1 56R 30R 2 42R 1 53R 28R 2 45R 1 52R27R 2 9R 3 2 4R 3 2 19R 3 2 11R 1 49R25R 2 52R 1 48R24R 2 53R 1 48R23R 2 3R 3 3 2 49R 1 47R22R 2 4R 3 2 45R 3 3 2 3R 1 46R22R 2 3R 3 2 38R 4 4 2 6R 3 2 3R 1 46R21R 2 43R 4 4R 2 10R 1 45R20R 2 60R 1 45R19R 2 62R 1 44R19R 2 63R 1 43R18R 2 64R 1 43R18R 2 2R 3 2 56R 3 2 3R 1 42R17R 2 3R 3 2 57R 3 2 2R 1 42R17R 2 67R 1 41R16R 2 68R 1 41R16R 2 69R 1 40R15R 2 70R 1 40R15R 2 70R 1 40R15R 2 3R 3 2 66R 1 39R14R 2 4R 3 2 60R 3 2 4R 1 39R14R 2 72R 1 39R14R 2 73R 1 38R13R 2 74R 1 38R13R 2 74R 1 38R13R 2 74R 1 38R13R 2 74R 1 38R13R 2 4R 3 2 68R 1 38R13R 2 4R 3 2 68R 1 38R13R 2 36R 3 2 36R 1 38R13R 2 34R 3 4R 2 34R 1 38R13R 2 33R 3 6R 2 33R 1 38R13R 2 33R 3 7R 2 32R 1 38R13R 2 32R 3 8R 2 32R 1 38R13R 2 32R 3 8R 2 32R 1 38R14R 2 31R 3 8R 2 32R 1 38R14R 2 32R 3 3 2 2R 3 2R 2 24R 3 2 5R 1 39R14R 2 6R 3 2 56R 3 2 6R 1 39R15R 2 5R 3 2 21R 3 2 33R 3 2 6R 1 39R15R 2 27R 3 2 41R 1 40R16R 2 25R 3 3 2 3 R 3 2 2 R 3 2 32R 1 40R16R 2 30R 3 5R 2 4R 3 3 2 24R 1 41R17R 2 32R 3 2 33R 1 41R18R 2 31R 3 2 32R 1 42R18R 2 11R 3 2 18R 3 2 19R 3 2 10R 1 43R20R 2 29R 3 2 18R 3 2 11R 1 43R21R 2 28R 3 2 30R 1 44R23R 2 26R 3 2 29R 1 45R26R 2 53R 1 46R29R 2 48R 1 48R31R 2 44R 1 50R35R 2 11R 1 8R 2 17R 1 52R59R 2 11R 1 55R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R

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231

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2 70R 1 40R2 24R 3 3 2 4R 3 2 2R 3 2 32R 12 31R 3 4R 2 5R 3 3 2 23R 1 41R2 31R 3 2R 2 8R 3 2 22R 1 41R2 10R 3 2 19R 3 2 32R 1 42R2 10R 3 2 18R 3 2 19R 3 3 2 9R :2 29R 3 2 18R 3 2 11R 1 43R2 28R 3 2 30R 1 44R2 25R 3 2 29R 1 45R2 53R 1 46R2 48R 1 48R2 44R 1 50R2 11R 1 8R 2 17R 1 52R2 11R 1 55R

127R

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232

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12R 1 1 2 14R 1 59R36R 1 56R41R 1 53R44R 1 52R48R 1 50R50R 1 49R52R 1 48R3R 3 3 2 48R 1 47R4R 3 2 45R 3 2 2R 1 47R3R 3 2 36R 4 4R 2 5R 3 2 3R 141R 4 7R 2 3R 3 2 4R 1 45R59R 1 45R61R 1 44R62R 1 44R2R 3 2 59R 1 43R2R 3 2 56R 3 2 3R 1 42R65R 1 42R66R 1 42R67R 1 41R68R 1 41R69R 1 40R70R 1 40R3R 3 2 66R 1 39R3R 3 2 60R 3 2 4R 1 39R

46R

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233

14R 2 72R 1 39R14R 2 73R 1 38R14R 2 73R 1 38R13R 2 74R 1 38R13R 2 74R 1 38R13R 2 4R 3 2 68R 1 38R13R 2 4R 3 2 62R 3 2 4R 1 38R13R 2 74R 1 38R13R 2 74R 1 38R13R 2 34R 3 3 2 37R 1 38R13R 2 33R 3 2R 2 3R 3 2 32R 1 38R13R 2 32R 3 3 2 3 3 2 2R 3 2 32R 1 38R13R 2 32R 3 4R 2 2R 3 2 32R 1 38R14R 2 31R 3 8R 2 32R 1 38R14R 2 5R 3 2 25R 3 7R 2 24R 3 2 5R 1 39R14R 2 37R 3 3 2 25R 3 2 5R 1 39R14R 2 6R 3 2 56R 3 2 6R 1 39R15R 2 70R 1 40R15R 2 70R 1 40R16R 2 24R 3 2 4R 3 2 4R 3 2 31R 1 40R16R 2 22R 3 2 6R 3 2R 2 3 2R 2 30R 1 41R17R 2 31R 3 3R 2 7R 3 2 22R 1 41R18R 2 9R 3 3 2 19R 3 2 32R 1 42R19R 2 10R 3 2 18R 3 2 19R 3 3 2 9R 1 43R20R 2 29R 3 2 18R 3 2 11R 1 43R21R 2 28R 3 2 30R 1 44R24R 2 25R 3 2 29R 1 45R26R 2 53R 1 46R29R 2 48R 1 48R31R 2 44R 1 50R35R 2 11R 1 9R 2 16R 1 52R60R 2 10R 1 55R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R

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234

127R127R127R127R127R127R127R127R127R127R37R 2 11R 1 3R 2 13R 1 59R33R 2 36R 1 56R31R 2 41R 1 53R29R 2 44R 1 52R27R 2 31R 3 2 15R 1 50R26R 2 50R 1 49R25R 2 52R 1 48R24R 2 3R 3 2 49R 1 47R23R 2 3R 3 3 2 35R 4 4 2 6R 3 2 3R 1 47R22R 2 40R 4 5R 2 5R 3 2 3R 1 46R22R 2 39R 4 8R 2 3R 3 2 3R 1 46R21R 2 59R 1 45R20R 2 61R 1 44R20R 2 61R 1 44R19R 2 2R 3 2 59R 1 43R18R 2 2R 3 3 2 55R 3 2 2R 1 43R18R 2 60R 3 2 3R 1 42R17R 2 66R 1 42R17R 2 67R 1 41R17R 2 67R 1 41R16R 2 69R 1 40R16R 2 3R 3 2 64R 1 40R15R 2 71R 1 39R15R 2 71R 1 39R14R 2 72R 1 39R14R 2 73R 1 38R14R 2 73R 1 38R14R 2 73R 1 38R13R 2 4R 3 2 68R 1 38R13R 2 4R 3 2 62R 3 2 4R 1 38R13R 2 4R 3 2 62R 3 2 4R 1 38R13R 2 74R 1 38R13R 2 35R 3 2R 2 35R 1 38R13R 2 33R 3 6R 2 33R 1 38R13R 2 33R 3 7R 2 32R 1 38R13R 2 33R 3 2 39R 1 38R14R 2 73R 1 38R14R 2 73R 1 38R14R 2 5R 3 2 25R 3 2 3 2R 2 27R 3 2 5R 1 39R14R 2 65R 3 2 5R 1 39R15R 2 5R 3 2 64R 1 39R15R 2 70R 1 40R15R 2 70R 1 40R16R 2 23R 3 2 5R 3 2 4R 3 2 31R 1 40R16R 2 22R 3 2 5R 3 2R 2 2R 3 2R 2 29R 1 41R17R 2 30R 3 5R 2 6R 3 3 2 21R 1 41R18R 2 9R 3 3 2 18R 3 2R 2 20R 3 2 9R 1 42R19R 2 10R 3 2 18R 3 2 19R 3 3 2 9R 1 43R20R 2 29R 3 2 31R 1 43R21R 2 28R 3 2 30R 1 44R24R 2 25R 3 2 29R 1 45R27R 2 52R 1 46R28R 2 49R 1 48R31R 2 44R 1 50R35R 2 11R 1 9R 2 16R 1 52R60R 2 10R 1 55R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R

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235

127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R37R 2 10R 1 5R 2 12R 1 59R33R 2 36R 1 56R31R 2 40R 1 54R29R 2 44R 1 52R27R 2 14R 3 2 32R 1 50R26R 2 40R 3 2 8R 1 49R25R 2 52R 1 48R24R 2 47R 3 2 4R 1 48R23R 2 4R 3 2 34R 4 2R 2 5R 3 3 2 3R 1 47R23R 2 38R 4 6R 2 5R 3 2 3R 1 46R22R 2 39R 4 8R 2 8R 1 46R21R 2 47R 4 2 lOR 1 45R20R 2 61R 1 44R20R 2 61R 1 44R19R 2 2R 3 2 59R 1 43R19R 2 2R 3 2 55R 3 2 2R 1 43R18R 2 60R 3 2 3R 1 42R18R 2 65R 1 42R17R 2 67R 1 41R17R 2 67R 1 41R16R 2 69R 1 40R16R 2 3R 3 2 64R 1 40R15R 2 4R 3 2 65R 1 39R15R 2 71R 1 39R14R 2 72R 1 39R14R 2 73R 1 38R14R 2 73R 1 38R14R 2 73R 1 38R13R 2 4R 3 2 68R 1 38R13R 2 4R 3 2 68R 1 38R13R 2 68R 3 2 4R 1 38R13R 2 74R 1 38R13R 2 35R 3 2R 2 35R 1 38R13R 2 33R 3 6R 2 33R 1 38R13R 2 33R 3 7R 2 32R 1 38R13R 2 32R 3 8R 2 32R 1 38R14R 2 31R 3 8R 2 32R 1 38R14R 2 31R 3 8R 2 32R 1 38R14R 2 5R 3 2 25R 3 7R 2 24R 3 2 5R 1 39R14R 2 65R 3 2 5R 1 39R15R 2 71R 1 39R15R 2 70R 1 40R15R 2 31R 3 2 4R 3 2 31R 1 40R16R 2 29R 3 3 2 4R 3 3 2 30R 1 40R16R 2 21R 3 3 2 5R 3 2R 2 2R 3 2R 2 29R 1 41R17R 2 9R 3 2 17R 3 3R 2 3 3R 2 6R 3 2 21R 1 41R18R 2 9R 3 3 2 18R 3 2R 2 19R 3 3 2 9R 1 42R19R 2 30R 3 2 19R 3 3 2 9R 1 43R20R 2 29R 3 2 31R 1 43R21R 2 28R 3 2 30R 1 44R

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236

24R 2 25R 3 2 29R 1 45R27R 2 52R 1 46R28R 2 49R 1 48R30R 2 45R 1 50R35R 2 11R 1 9R 2 16R 1 52R60R 2 10R 1 55R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R37R 2 9R 1 7R 2 11R 1 59R33R 2 36R 1 56R31R 2 40R 1 54R29R 2 44R 1 52R28R 2 47R 1 50R26R 2 40R 3 2 8R 1 49R25R 2 52R 1 48R24R 2 47R 3 2 4R 1 48R24R 2 38R 4 3R 2 5R 3 2 4R 1 47R23R 2 38R 4 7R 2 9R 1 46R22R 2 38R 4 9R 2 8R 1 46R21R 2 59R 1 45R20R 2 61R 1 44R20R 2 2R 3 2 57R 1 44R19R 2 2R 3 2 54R 3 2 3R 1 43R19R 2 2R 3 2 59R 1 43R

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237

18R 218R 217R 217R 216R 216R 215R 215R 214R 214R 214R 214R 213R 213R 213R 213R 213R 213R 213R 214R 214R 214R 214R 214R 215R 215R 216R 216R 217R 217R 218R 219R 220R 221R 224R 226R 228R 230R 235R 260R 2127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R

17R 4 2 46R 1 42R 65R 1 42R 67R 1 41R 67R 1 41R 69R 1 40R3R 3 2 58R 3 2 4R 1 40R4R 3 2 65R 1 39R71R 1 39R72R 1 39R73R 1 38R73R 1 38R73R 1 38R4R 3 2 68R 1 38R4R 3 2 68R 1 38R68R 3 2 4R 1 38R74R 1 38R35R 3 2R 2 35R 1 38R33R 3 6R 2 33R 1 38R33R 3 7R 2 32R 1 38R31R 3 8R 2 32R 1 38R31R 3 8R 2 32R 1 38R5R 3 2 24R 3 8R 2 32R 1 38R5R 3 2 25R 3 7R 2 24R 3 2 5R 1 39R38R 3 2 25R 3 2 5R 1 39R71R 1 39R70R 1 40R30R 3 2 4R 3 2 31R 1 40R29R 3 3 2 4R 3 3 2 30R 1 40R20R 3 3 2 5R 3 2R 2 2R 3 2R 2 29R 1 41R9R 3 3 2 16R 3 3R 2 2 3 2R 2 6R 3 2 21R 1 41R10R 3 2 23R 3 2 8R 3 2 6R 3 3 2 9R 1 42R51R 3 2 10R 1 43R62R 1 43R28R 3 2 30R 1 44R56R 1 45R52R 1 47R49R 1 48R45R 1 50R11R 1 9R 2 16R 1 52R 10R 1 55R

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238

127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R37R 2 8R 1 8R 2 11R 1 59R33R 2 36R 1 56R31R 2 40R 1 54R29R 2 44R 1 52R28R 2 46R 1 51R26R 2 40R 3 3 2 7R 1 49R25R 2 51R 1 49R24R 2 53R 1 48R24R 2 37R 4 5R 2 10R 1 47R23R 2 37R 4 8R 2 8R 1 47R22R 2 38R 4 9R 2 8R 1 46R21R 2 59R 1 45R21R 2 59R 1 45R20R 2 2R 3 2 57R 1 44R19R 2 2R 3 2 54R 3 2 3R 1 43R19R 2 2R 3 2 54R 3 2 3R 1 43R18R 2 17R 4 2 46R 1 42R18R 2 65R 1 42R17R 2 67R 1 41R17R 2 67R 1 41R16R 2 69R 1 40R16R 2 3R 3 2 58R 3 2 4R 1 40R15R 2 4R 3 2 64R 1 40R15R 2 71R 1 39R14R 2 72R 1 39R14R 2 21R 4 2 50R 1 38R14R 2 22R 4 2 49R 1 38R14R 2 73R 1 38R13R 2 4R 3 2 62R 3 2 4R 1 38R13R 2 4R 3 2 62R 3 2 4R 1 38R13R 2 74R 1 38R13R 2 74R 1 38R13R 2 35R 3 2R 2 35R 1 38R13R 2 34R 3 5R 2 33R 1 38R13R 2 33R 3 7R 2 32R 1 38R14R 2 31R 3 8R 2 32R 1 38R14R 2 31R 3 8R 2 32R 1 38R14R 2 5R 3 2 24R 3 8R 2 32R 1 38R14R 2 5R 3 2 25R 3 7R 2 24R 3 2 5R 1 39R14R 2 32R 3 2 4R 3 2 25R 3 2 5R 1 39R15R 2 71R 1 39R15R 2 38R 3 2 30R 1 40R16R 2 29R 3 3 2 4R 3 3 2 30R 1 40R16R 2 29R 3 3 2 4R 3 3 2 30R 1 40R17R 2 20R 3 2 6R 3 2R 2 2R 3 2R 2 29R 1 41R17R 2 9R 3 3 2 15R 3 3R 2 2R 3 2R 2 28R 1 42R18R 2 10R 3 2 23R 3 2 8R 3 3 2 5R 3 3 2 9 R 1 42R19R 2 63R 1 43R20R 2 61R 1 44R21R 2 60R 1 44R24R 2 56R 1 45R26R 2 52R 1 47R28R 2 49R 1 48R30R 2 45R 1 50R34R 2 11R 1 10R 2 16R 1 52R61R 2 9R 1 55R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R

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239

127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R37R 233R 231R 229R 228R 226R 225R 225R 224R 223R 222R 221R 221R 220R 219R 219R 218R 218R 217R 217R 216R 216R 215R 215R 214R 214R 214R 214R 213R 213R 213R 213R 213R 213R 213R 214R 214R 214R 214R 214R 215R 215R 2

8R 1 9R 2 10R 1 59R36R 1 56R40R 1 54R44R 1 52R46R 1 51R49R 1 50R51R 1 49R52R 1 48R36R 4 6R 2 lOR 1 47R37R 4 8R 2 8R 1 47R37R 4 lOR 2 8R 1 46R59R 1 45R59R 1 45R2R 3 2 57R 1 44R2R 3 3 2 53R 3 2 2R 1 44R2R 3 2 59R 1 43R64R 1 43R65R 1 42R66R 1 42R67R 1 41R68R 1 41R3R 3 2 58R 3 2 4R 1 40R 4R 3 2 64R 1 40R 71R 1 39R 72R 1 39R20R 4 4 2 50R 1 38R 22R 4 2 49R 1 38R 73R 1 38R4R 3 2 62R 3 2 4R 1 38R 4R 3 2 62R 3 2 4R 1 38R 74R 1 38R 74R 1 38R35R 3 2R 2 35R 1 38R34R 3 5R 2 33R 1 38R33R 3 6R 2 33R 1 38R32R 3 7R 2 32R 1 38R32R 3 7R 2 32R 1 38R5R 3 2 25R 3 7R 2 32R 1 38R5R 3 2 25R 3 7R 2 24R 3 2 5R :32R 3 2 4R 3 2 32R 1 39R71R 1 39R30R 3 3 2 4R 3 3 2 30R 1 40R

39R

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240

16R 2 29R 3 3 2 4R 3 2R 2 29R 1 40R16R 2 28R 3 2R 2 4R 3 2R 2 28R 1 41R17R 2 19R 3 3 2 5R 3 3R 2 2R 3 3R 2 28R 1 41R17R 2 9R 3 3 2 15R 3 3R 2 2R 3 2R 2 17R 3 2 9R 1 42R18R 2 35R 3 2 9R 3 3 2 4R 3 3 2 9 R 1 42R19R 2 63R 1 43R20R 2 61R 1 44R21R 2 59R 1 45R24R 2 55R 1 46R26R 2 52R 1 47R28R 2 49R 1 48R30R 2 45R 1 50R33R 2 12R 1 10R 2 16R 1 52R61R 2 8R 1 56R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R37R 2 7R 1 lOR 2 lOR 1 59R33R 2 36R 1 56R31R 2 40R 1 54R29R 2 44R 1 52R28R 2 46R 1 51R27R 2 6R 3 2 40R 1 50R26R 2 50R 1 49R25R 2 37R 4 2 13R 1 48R

241

1 24R 2 36R 4 6R 2 10R 1 47R1 23R 2 37R 4 8R 2 8R 1 47R1 22R 2 37R 4 9R 2 9R 1 46R1 21R 2 59R 1 45R1 21R 2 59R 1 45R1 20R 2 2R 3 2 57R 1 44R1 20R 2 2R 3 2 53R 3 2 2R 1 44R1 19R 2 2R 3 2 59R 1 43R1 19R 2 63R 1 43R1 18R 2 65R 1 42R1 17R 2 66R 1 42R1 17R 2 67R 1 41R1 16R 2 68R 1 41R1 16R 2 3R 3 2 58R 3 2 4R 1 40R1 15R 2 70R 1 40R1 15R 2 71R 1 39R1 14R 2 19R 4 2 51R 1 39R1 14R 2 20R 4 2R 2 48R 1 39R1 14R 2 22R 4 2 49R 1 38R1 14R 2 73R 1 38R1 13R 2 4R 3 2 62R 3 2 4R 1 38R1 13R 2 68R 3 2 4R 1 38R1 13R 2 74R 1 38R1 13R 2 74R 1 38R1 13R 2 35R 3 2R 2 35R 1 38R1 13R 2 34R 3 5R 2 33R 1 38R1 14R 2 32R 3 6R 2 33R 1 38R1 14R 2 32R 3 7R 2 32R 1 38R1 14R 2 32R 3 7R 2 25R 3 2 5R 1 38R1 14R 2 5R 3 2 25R 3 7R 2 32R 1 38R1 14R 2 5R 3 2 25R 3 3 2 2 3 2R 2 25R 3 2 5R 1 39R1 15R 2 31R 3 2 4R 3 2 32R 1 39R1 15R 2 71R 1 39R1 15R 2 30R 3 3 2 4R 3 3 2 30R 1 40R 1 16R 2 25R 3 6R 2 2R 3 3R 2 29R 1 40R 1 16R 2 28R 3 3 2 6R 3 3R 2 26R 1 41R 1 17R 2 19R 3 2 6 R 3 3 2 6 R 3 3 2 28R 1 41R 1 17R 2 lOR 3 2 15R 3 3 2 6R 3 2 17R 3 2 9R 1 42R 1 18R 2 47R 3 2 4R 3 2 lOR 1 42R 1 19R 2 63R 1 43R 1 20R 2 61R 1 44R 1 21R 2 59R 1 45R 1 24R 2 55R 1 46R 1 26R 2 52R 1 47R 1 28R 2 49R 1 48R 1 30R 2 45R 1 50R 1 33R 2 13R 1 9R 2 16R 1 52R 1 61R 2 8R 1 56R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R cc C e ll C onta in ing L a t t ic e c8 0 16 -19 26 -2 9 -3 7 39 f i l l = 7 cc O utside o f V oxels c9 0 -1 6 : 19 : -2 6 : 29 : 37 : -39 cc Tumor volume cc 10 10 -1 .1 2 -2c ++++++++++++++++++++++++++++++++++++++++++++++++++++++ cc S u rfaces cc ++++++++++++++++++++++++++++++++++++++++++++++++++++++

242

c py P lanes c16 py -50 .04882817 py -49 .658203 19 py -0 .048854cc px P lanes c26 px -25 .04882827 px -24 .658203 29 px 24.951146cc pz P lanes c37 pz 21.87500038 pz 21.62500039 pz -11 .375000 cc Sphere f o r F i l l i n g U n iverses c 1 s -24 .853516 -49 .853516 21.750000 1.171874 c R ectangu lar P a r a l le lp ip e d1 rpp -25 .048828 -24 .658203 -50 .048828 -49 .658203 2 1 .625 21.875 cc MTT cc 2 arb 7 .7 0 -3 1 .6 3 -1 .6 3 10.1 -2 9 .2 9 -1 .6 3 7 .0 9 -3 0 -6 .3 5 c 8 .4 7 -2 8 .2 7 -4 .8 8 7 .7 8 -2 8 .5 4 -1 .6 0 7 .41 -2 8 .2 7 -5 .3 4 c 5 .7 4 -3 0 .1 5 -1 .6 3 5 .7 9 -3 0 .3 1 -5 .5 9 1234 2546 5768 c 1783 1752 3864c ++++++++++++++++++++++++++++++++++++++++++++++++++++++ cc M a teria ls cc ++++++++++++++++++++++++++++++++++++++++++++++++++++++ cc M a teria l 2 P rologu e c Name Female S o ft T issu e c D ensity 1.02000 (gm/cm"3) c C ategory ICRU 46 cc From ICRU 46c Mat 2 : 1.000000 * 4(Fem ale S o f) c Boron Cone = 1 .25 u g /g cm21001.70c -1 .05988E -01 1002.70c -1 .21900E -05 6 000 .70c -3 .15000E -01 7 014 .70c -2 .39126E -02 7 015 .70c -8 .73599E -05 8 016 .70c -5 .46999E -01 11023.70c -9 .99999E -04 15031.70c -2 .00000E -03 16032.70c -1 .89980E -03 16033.70c -1 .50000E -05 16034.70c -8 .49999E -05 16036.70c -2 .00000E -07 17035.70c -7 .57599E -04 17037.70c -2 .42400E -04 19039.70c -1 .86516E -03 19040.70c -2 .34000E -07 19041.70c -1 .34604E -04 5 010 .70c -1 .25000E -06 mt2 lw tr .lO t cc M a teria l 3 P rologu e c Name Bone, Compact c D ensity 1 .850000 (gm/cm"3) c C ategory p h y s ic s .n is t .g o v cc From ICRU 46c Mat 3 : 1.000000 * 5 (B one, Comp) cm31001.70c -0 .063984 6 000 .70c -0 .2 7 8 7 014 .70c -0 .0 2 7 8 016 .70c -0 .410016 12000.42c -0 .0 0 2 15031.70c -0 .0 7 16032.70c -0 .0 0 2 2 0040.70c -0 .1 4 7 mt3 lw tr .lO t cc M a teria l 4 P rologu e c Name A ir (D ry, Sea L evel) c D ensity 0 .001048 (gm/cm"3) c C ategory Gas cc From p h y s ic s .n is t .g o v c Mat 4 : 1.000000 * 2

243

m46000.70c -0 .000124 7014 .70c -0 .755268 8016 .70c -0 .231781 18000.42c -0 .012827 cc M a teria l 5 P rologu e c Name Lung ( in f la t e d ) c D ensity 0 .260000 (gm/cm"3) c C ategory ICRU 46 cc From ICRU 46c Mat 5 : 1.000000 * 3(Lung ( i n f l ) ) cm51001.70c -0 .1 0 3 6000 .70c -0 .1 0 5 7014 .70c -0 .0 3 1 8016 .70c -0 .7 4 9 11023.70c -0 .0 0 2 15031.70c -0 .0 0 2 16032.70c -0 .0 0 3 17035.70c -0 .0 0 3 19039.70c -0 .0 0 2 mt5 lw tr .lO t cc M a teria l 10 P rologu e c Name MTTc D ensity 1 .122 (gm/cm"3) c T:H = 8 :1c Boron Cone = 10 u g /g cmlO1001.70c -9 .89876E -02 1002.70c -1 .13849E -05 6000 .70c -2 .68997E -01 7014 .70c -4 .48358E -02 7015 .70c -1 .63798E -04 8016 .70c -5 .68994E -01 11023.70c -1 .97998E -03 15031.70c -3 .95996E -03 16032.70c -4 .78745E -03 16033.70c -3 .77996E -05 16034.70c -2 .14198E -04 16036.70c -5 .03995E -07 17035.70c -2 .31823E -03 17037.70c -7 .41737E -04 19039.70c -3 .69298E -03 19040.70c -4 .63315E -07 19041.70c -2 .66513E -04 5010 .70c -1 .00000E -05 mtlO lw tr .lO t CC ***SECTI0N 3 PARTICLE PHYSICS AND VARIANCE REDUCTION CLCA 8J 1 1 CMODE A E $ H D T S # P CUT:A J 0 0 0 0 CUT:E J 0 0 0 0 C CUT:P J 0 0 0 0 C CUT:H J 0 0 0 0 C CUT:D J 0 0 0 0 C CUT:T J 0 0 0 0 C CUT:S J 0 0 0 0 C CUT:# J 0 0 0 0 CPHYS:A 22 0 -1 J 0 J 1 3J 0..99 $alpha tra n sp o rt (5 th e n try = s t r a g g lin g m odel)PHYS:E 22 0 -1 J 0 J 1 3J 0..99 $ e le c t r o n tra n sp o rt (5 th e n try = s t r a g g lin g model)C PHYS :P 22 0 ■-1 J 0 J 1 6J 0 .99C PHYS :H 22 0 ■-1 J 0 J 1 6J 0 .9 9 $ proton tra n sp o rt (5 th e n try = s t r a g g lin g model)C PHYS :D 22 0 ■-1 J 0 J 1 6J 0 .9 9 $deuteron tra n sp o rt (5 th e n try = s t r a g g lin g model)C PHYS :T 22 0 ■-1 J 0 J 1 6J 0 .9 9 $ t r i t o n tra n sp o rt (5 th e n try = s t r a g g lin g model)C PHYS :S 22 0 ■-1 J 0 J 1 6J 0 .9 9 $3He tra n sp o rt (5 th e n try = s t r a g g lin g m odel)C PHYS :# 22 0 ■-1 J 0 J 1 6J 0 .9 9 $4He tra n sp o rt (5 th e n try = s t r a g g lin g m odel)CIMP:A 5R 1 0IMP:E 5R 1 0C IMP P 1 5R 1 0C IMP N 1 6R 1 1C IMP H 1 6R 1 1C IMP D 1 6R 1 1C IMP T 1 6R 1 1C IMP S 1 6R 1 1C IMP # 1 6R 1 1CC Radon S h o r t - l iv e d Progeny Volume SourceCSDEF PAR=A ERG=5.49 CEL=D3 X=D4 Y=D5 Z=D6 EFF=0.01 $ P a r t ic l e d i s t Energy d is t CC SI1 L 34 3 3 34 C SP1 .25 .25 .25 .25 CC SI2 L 6 .0 0 .7117 2 .1318 7 .6 9

244

C SP2 .25 .25 .25 .25 $ P a r t ic le energy s h o r t - l iv e d C513 L (4<6<8)SP3 1C514 H -25 .048828 -24 .658203 SP4 D 0 1C515 H -50 .048828 -49 .658203 SP5 D 0 1C516 H 21.625 21.875 SP6 D 0 1CC SI7 L 1 .8 3 e l0 1 .7 9 1 e l l 2 .9 7 3 e l l 2 .9 7 30 00 1 64 e ll C SP7 C .061554 .602422 .999999 1C * * * = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

C *** ABSORBED DOSE TALLY ( a l l p a r t i c l e s )C *** -------------------------------------FC1006 Absorbed Dose ( a l l p a r t i c l e s ) $ Shows t a l l y type in p r in to u t +F1006 (6 < 6 [0 :1 2 7 0 :1 2 7 0 :1 3 2 ] < 8)FM1006 1.602E-10 $ MeV/g t o Gy (J /k g )SD1006 0.038147 2179071R $Volume and rep eat C

CC * * * = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

c *** 4He-Alpha (4He2+) DOSE, RBE AND RELATED TALLIESC *** -------------------------------------FC5016 4He-Alpha (4He2+) Absorbed Dose F5016:A (6 < 6 [0 :1 2 7 0 :1 2 7 0 :1 3 2 ] < 8)FM5016 1.602E-10 SD5016 0.038147 2179071R C CC ***SECTI0N 7 SIMULATION CONTROL AND DEBUG PARAMETERS CTALNPPRDMP 1E+08 1E+06 1 1 J NPS 1E+08

APPENDIX B

PYTHON SCRIPT

from __future__ import with_statement#change input file below as needed

with open('mctal_rd.txt') as f:

# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # ######################### MCTAL variables ########################

# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #X=float(133) #enter number of voxels in Z

Y=float(128) #enter number of voxels in X Z=float(128) #enter number of voxels in Y

T=float(X*Y*Z) #enter total number of lattice elements (voxels)

V=float(T/4) #lines of mean and SEM = total voxels divided by four

# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #

##################### radiobiological variables ###################### ################################################################ alphax=float(0.0700) #alpha reference (Co-60 gammas) abx=float(2.91) #alpha/beta reference

betax=float(alphax/abx) #beta (don't change)D=float(l) #prescription dose (Gy)

x=float(2.8423) #DSB Gy~-1 DSB~-1 Co-60

y=float(0.0020) #ZF Co-60

kappa=float(2*betax/x**2) theta=float((alphax-kappa*y*x**2)/x)#r is a variable used to help find the point where the results start.

#one line after 'vals' is the mean and SEM values (4 per line)

r = str('vals')

#import necessary libraries and functions

import numpy as np

import matplotlib.pyplot as pitimport math from mpl_toolkits.axes_gridl

import make_axes_locatable from mpl_toolkits.mplot3dimport Axes3D

# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # ########################### Tally 1: 1006 ##########################

# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #

c = 0

while c != r: line = f.readline()

c = line.stripO

meanl = [] #Initialize list variables

SEMI = []b=0 #Initialize variable used in loopwhile b < V:

a=0

line = f.readline() #Reads the line of the first tally

data = line.strip().split() #Separates the line at each space and assigns it to the list data.

meanl.extend((float(data[a]), float(data[a+2]), float(data[a+4]), float(data[a+6]))) SEMl.extend((float(data[a+l]), float(data[a+3]), float(data[a+5]), float(data[a+7])))

b=b+l #Adds to the value b so that while loop reads and extracts the data for each tally.

# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # ########################### Tally 2: 9016 ##########################

################################################################

c = 0

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while c != r:

line = f.readlineQ

c = line.stripO mean2 = []SEM2 = []

b=0 while b < V:

a=0

line = f.readline()data = line.strip().split()

mean2.extend((float(data[a]), float(data[a+2]), float(data[a+4]), float(data[a+6]))) SEM2.extend((float(data[a+l]), float(data[a+3]), float(data[a+5]), float(data[a+7])))

b=b+l

# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # ######################## Write data to a table ######################## # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #dosel = [x*3.57862e7 for x in meanl]dose2 = [x*3.57862e7 for x in mean2]

errl = [x*100 for x in SEMI]

err2 = [x*100 for x in SEM2]

print "max equivalent dose (mrem/yr) = " + str(max(dosel))

print "equivalent dose mean(mrem/yr) = " + str(np.mean(filter(lambda a: a != 0.0, dosel)))

print "alpha dose max (mrem/yr) = " + str(max(dose2))print "alpha dose mean (mrem/yr) = " + str(np.mean(filter(lambda a: a != 0.0, dose2)))

print "mean error(0/0) = " + str(np.mean(filter(lambda a: a != 0.0, errl))) # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # ###################### Create matrices from lists #####################

################################################################ matrixl = np.reshape(dosel, (X, Y, Z))

matrix5 = np.reshape(errl, (X, Y, Z))

matrix2 = np.reshape(dose2, (X, Y, Z))

matrix6 = np.reshape(err2, (X, Y, Z)) # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # ###################### Create slices of matrices ###################### # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #

slicel = matrixl[:, :, 64]slice2 = matrix5[:, :, 64]slice3 = matrix2[64, :]

slice4 = matrix6[64, :]

# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #

##################### Plot 2D and 3D matrices ######################

################################################################

zl = np.arange(l, 51) z2 = np.arange(l, 101)########################## Plot Figurel ###########################

plt.figure(l)

plt.subplot(121)

plt.title('Equivalent dose from RD-222 decay (mrem/yr)', fontsize = 16)im = plt.imshow(slicel, vmax=0.000014) plt.xlabel('voxel number',fontsize = 12)

plt.ylabel('voxel number', fontsize = 12)

plt.minorticks_on() divider = make_axes_locatable(plt.gca())

cax = divider.append_axes("right", "5%", pad="30/0") plt.colorbar(im, orientation='vertical', cax=cax)

plt.subplot(122)

plt.title('error (%)', fontsize = 16) im = plt.imshow(slice2) plt.xlabel('voxel number',fontsize = 12)

plt.ylabel('voxel number', fontsize = 12)

plt.minorticks_on() divider = make_axes_locatable(plt.gca())

cax = divider.append_axes("right", "5%", pad="30/0") plt.colorbar(im, orientation='vertical', cax=cax)

'''plt.subplot(223)

plt.title('proton biological dose (Gy)', fontsize = 8) im = plt.imshow(slice4, vmin = 0, vmax = 6e-14)

plt.xlim(0, 50)

plt.ylim(100, 0)

plt.xlabel('x (mm)', fontsize = 8) plt.ylabel('depth (mm)', fontsize = 8)plt.minorticks_on() divider = make_axes_locatable(plt.gca())

cax = divider.append_axes("right", "5%", pad="30/0") plt.colorbar(im, orientation='vertical', cax=cax)

247

plt.subplot(224)

plt.title('photon dose (Gy)', fontsize = 8)

im = plt.imshow(slice5, vmin = 0, vmax = 6e-14) plt.xlim(0, 50)

plt.ylim(100, 0)plt.xlabel('x (mm)', fontsize = 8) plt.ylabel('depth (mm)', fontsize = 8)

plt.minorticks_on() divider = make_axes_locatable(plt.gca())

cax = divider.append_axes("right", "5%", pad="30/0")

plt.colorbar(im, orientation='vertical', cax=cax)

plt.tight_layout() print('Figure 1 created')

########################## Plot Figure 2 ###########################plt.figure(2)

plt.subplot(221)

plt.title('total physical dose (Gy)', fontsize = 8)im = plt.imshow(slice6, vmin = 0, vmax = 4e-13) #vmax = 6e-14 for MIT-FCB

plt.xlim(0, 50) plt.ylim(0, 50)

plt.xlabel('x (mm)', fontsize = 8)

plt.ylabel('y (mm)', fontsize = 8)

plt.minorticks_on() divider = make_axes_locatable(plt.gca())

cax = divider.append_axes("right", "5%", pad="30/0") plt.colorbar(im, orientation='vertical', cax=cax)

plt.subplot(222)

plt.title('proton physical dose (Gy)', fontsize = 8)

im = plt.imshow(slice7, vmin = 0, vmax = 4e-13) plt.xlim(0, 50)

plt.ylim(0, 50)

plt.xlabel('x (mm)', fontsize = 8)

plt.ylabel('y (mm)', fontsize = 8)

plt.minorticks_on() divider = make_axes_locatable(plt.gca())

cax = divider.append_axes("right", "5%", pad="30/0") plt.colorbar(im, orientation='vertical', cax=cax) plt.subplot(223)

plt.title('proton biological dose (Gy)', fontsize = 8) im = plt.imshow(slice8, vmin = 0, vmax = 4e-13)

plt.xlim(0, 50)

plt.ylim(0, 50)

plt.xlabel('x (mm)', fontsize = 8)

plt.ylabel('y (mm)', fontsize = 8)plt.minorticks_on() divider = make_axes_locatable(plt.gca())

cax = divider.append_axes("right", "5%", pad="30/0") plt.colorbar(im, orientation='vertical', cax=cax)

plt.subplot(224)plt.title('photon dose (Gy)', fontsize = 8)

im = plt.imshow(slice9, vmin = 0, vmax = 4e-13)

plt.xlim(0, 50)

plt.ylim(0, 50)

plt.xlabel('x (mm)', fontsize = 8) plt.ylabel('y (mm)', fontsize = 8)

plt.minorticks_on() divider = make_axes_locatable(plt.gca())

cax = divider.append_axes("right", "5%", pad="30/0") plt.colorbar(im, orientation='vertical', cax=cax)

plt.tight_layout() print('Figure 2 created')'''

plt.show()

APPENDIX C

GEANT4 DICOM MACRO

# S. Chauvie## Macro file recommended for the use with DICOM example and built-in physic list.# This macro uses the physics list already contained in the Geant4 distribution## # # # # # # # # # # # # # # # # # # # # # # # ## Set of the verboses#/control/verbose 1 /tracking/verbose 0 /run/verbose 1 /event/verbose 0 # # # # # # # # # # # # # # # # # # # # # # # # # ## Random#/random/setDirectoryName ./random/setSavingFlag 1#/random/resetEngineFrom currentEvent.rndml # # # # # # # # # # # # # # # # # # # # # # # # # ## Initialisation procedure##/geometry/textInput/verbose 3#/dicom/intersectWithUserVolume 0. 0. 0. 45.*deg 0. 0. TUBE 0. 150. 100. /gps/pos/type Volume /gps/pos/shape Ellipsoid /gps/pos/centre -50.5 mm,2.5 mm,88.75 mm /gps/pos/halfx 8.0 mm /gps/pos/halfy 5.0 mm /gps/pos/halfz 3.75 mm /gps/pos/type Volume /gps/pos/shape Cylinder /gps/pos/centre -50.5 mm,2.5 mm,88.75 mm /gps/pos/radius 6.5 mm /gps/pos/halfz 3.75 mm #/gps/pos/type Surface #/gps/pos/shape Square #/gps/pos/centre -50.5 mm,11.48 mm,75 mm /gps/source/add .4375 /gps/particle alpha /gps/energy 6.00 MeV /gps/ang/type cos /gps/source/add .2625 /gps/particle e­/gps/energy .7117 MeV /gps/ang/type cos /gps/source/add .175 /gps/particle e­/gps/energy 2.13 MeV /gps/ang/type cos /gps/source/add .175 /gps/particle alpha /gps/energy 7.69 MeV /gps/ang/type cos /gps/source/multiplevertex true /run/beamOn 100000000

APPENDIX D

GEANT4-DNA MACRO

#/control/execute vis.mac

/tracking/verbose 0 /run/verbose 2

# use /run/initialize before calling /dna/det/setMat

# in this example, this is done in dnaphysics.cc

#/dna/det/setMat G4_WATER_M0DIFIED

/dna/det/setMat G4_WATER

#/gps/particle e- #/gps/particle proton

#/gps/particle hydrogen

/gps/particle alpha #/gps/particle alpha+

#/gps/particle helium

#/gps/particle ion

#/gps/ion 14 28

/gps/energy 7.69 keV

/process/em/auger true /run/beamOn 1

APPENDIX E

DBSCAN SCRIPT

print(__doc__)

import numpy as npfrom sklearn.cluster import DBSCAN

from sklearn import metrics

from sklearn.datasets.samples_generator import make_blobs

from sklearn.preprocessing import StandardScaler

# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #

# Generate sample data#centers = [ [ 1 , 1 , 1 ] , [ - 1 , - 1 , - 1 ] , [ 1 , - 1 , 1 ] ]

#X, labels_true = make_blobs(n_samples=750, centers=centers, cluster_std=0.4,

# random_state=0, n_features=3)

#

#X = StandardScaler().fit_transform(X)

#print X

#print labels_true

# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #

#GET ALL THE DATA!X = □with open("bigboxl0.txt") as f:

for line in f:if line.startswith("G4WT0 > ") and line.count(",") == 2:

tmp = line.strip().replace("G4WT0 > ", "").split(",")

tmp[0] = float(tmp[0])

tmp[l] = float(tmp[l])

tmp[2] = float(tmp[2])

X.append(tmp)

print str(len(X)) + " Points"

X = StandardScaler().fit_transform(X)

print X# Compute DBSCAN

db = DBSCAN(eps=0.0000000032, min_samples=3).fit(X)

core_samples_mask = np.zeros_like(db.labels_, dtype=bool)

core_samples_mask[db.core_sample_indices_] = True

labels = db.labels_# Number of clusters in labels, ignoring noise if present.

n_clusters_ = len(set(labels)) - (1 if -1 in labels else 0)

print('Estimated number of clusters: 0/Od' % n_clusters_)

#print("Homogeneity: 0/O0.3f" 0/0 metrics.homogeneity_score(labels_true, labels)) #print("Completeness: 0/O0.3f" 0/0 metrics.completeness_score(labels_true, labels))

#print("V-measure: 0/O0.3f" 0/0 metrics.v_measure_score(labels_true, labels))

#print("Adjusted Rand Index: o/0O.3f"# 0/0 metrics.adjusted_rand_score(labels_true, labels))

#print("Adjusted Mutual Information: o/0O.3f"# 0/0 metrics.adjusted_mutual_info_score(labels_true, labels))

#print("Silhouette Coefficient: o/0O.3f"# % metrics.silhouette_score(X, labels))

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