A MACROSCOPIC AND MICROSCOPIC STUDY OF RADON …
Transcript of 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
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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
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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
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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
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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,
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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
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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
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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).
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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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101
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103
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104
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1 1 2 13R 3 5R 2 10R 4 13R 2 3 2 8R 4 13R 2 2 3 2 5R 3 5R 22 3 3R 2 17R 1 16R1 1 2 13R 3 6R 2 9R 4 12R 3 3 2 lOR 4 12R 2 7R 3 7R 2 21R 1 1 16R1 2R 2 13R 3 6R 2 7R 4 13R 3 3R 2 4R 3 2 2R 4 11R 2 8R 3 8R 22 19R 1 17R1 2 R 2 1 6 R 3 3 R 2 5 R 3 2 4 1 2 R 3 3 2 3 2 R 2 2 R 3 3 2 2 R 4 1 1 R 22 7R 3 3R 2 24R 1 18R1 3R 2 16R 3 2R 2 5R 3 3 2 4 10R 3 3 2 3 4R 2 3 2R 2 2 3 3 44 8R 2 2R 3 2 4R 3 4R 2 24R 1 18R1 4R 2 15R 3 3R 2 4R 3 2 3R 4 8R 2 3 4R 2 2R 3 2 2 3 2 3 2R 24 6R 2 2R 3 2 4R 3 2R 2 2 3 3 2 22R 1 19R1 6R 2 13R 3 4R 2 9R 4 6R 2 2 3 3 2 3R 3 2 4R 3 5R 2 4 2R 22 8R 3 3 2 3R 3 2R 2 20R 1 20R1 8R 2 11R 3 5R 2 9R 4 3R 2 4R 3 2 10R 3 2 2 3 2R 2 18R 3 2R 22 17R 1 22R1 9R 2 11R 3 6R 2 3R 3 3 2 27R 3 4R 2 5R 3 2 7R 3 3 2 18R 1 1 22R1 9R 2 13R 3 2 7R 3 4R 2 34R 3 2 7R 3 2 19R 1 24R 1 10R 2 12R 3 2 6R 3 2R 2 35R 3 2 28R 1 26R 1 10R 2 21R 3 3 2 33R 3 3 2 27R 1 28R 1 11R 2 21R 3 3 2 30R 3 2R 2 26R 1 30R 1 12R 2 22R 3 2R 2 26R 3 3 2 27R 1 31R 1 14R 2 8R 3 3 2 11R 3 2 38R 3 3 2 13R 1 33R 1 15R 2 8R 3 2R 2 47R 3 2 13R 1 36R 1 16R 2 71R 1 38R 1 18R 2 66R 1 41R 1 20R 2 62R 1 43R 1 23R 2 20R 1 12R 2 21R 1 47R 1 29R 2 5R 1 91R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R 1 127R
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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125
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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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202
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203
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7R 3 2 57R 4 4 3 3 2 6R 1 37R 7R 3 2 58R 4 3 3 2 7R 1 36R 68R 4 4 3 2 7R 1 36R
4 2 8R 1 36R 4 2 8R 1 36R 4 2 8R 1 36R 4 2 8R 1 36R 3 3 2 7R 1 36R 3 2 7R 1 36R3 2 7R 1 36R4 2 8R 1 36R
79R 1 36R39R 3 3 2 37R 1 36R36R 3 4R 2 36R 1 36R35R 3 6R 2 35R 1 36R34R 3 7R 2 35R 1 36R34R 3 8R 2 24R 3 2 8R 1 36R8R 3 2 24R 3 7R 2 25R 3 2 8R 1 36R8R 3 2 24R 3 6R 2 35R 1 36R8R 3 2 24R 3 3 2 2 3 3 2 36R 1 36R41R 3 2 32R 1 37R33R 3 2 4R 3 2 34R 1 37R31R 3 3 2 3R 3 3 2 2 3 2 30R 1 38R31R 3 2 3 R 3 2 R 2 2 3 2 29R 1 38R33R 3 3 2 33R 1 39R30R 3 3 2 34R 1 40R7R 3 2 20R 3 2 20R 3 2 11R 1 41R7R 3 2R 2 37R 3 3 2 11R 1 42R45R 3 2 11R 1 44R55R 1 45R51R 1 47R47R 1 49R42R 1 52R13R 1 3R 2 18R 1 54R 3R 1 13R 2 11R 1 57R
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204
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205
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9R 1 88R16R 1 15R 2 15R 1 52R 24R 1 4R 2 23R 1 49R 57R 1 47R 61R 1 45R28R 3 2 2 3 3 2 29R 1 44R30R 3 6R 2 27R 1 43R14R 4 5R 2 10R 3 2 3 2R 2 29R 1 42R10R 3 2 2 4 11R 2 41R 1 42R12R 4 5 R 2 3 R 4 4 2 4 2 30R 4 2 10R 1 41R9R 3 2 4 2R 2 42R 4 4 3 3 2 8R 1 40R10R 4 4 2 45R 4 4 3 3 2 7R 1 40R10R 4 2 47R 4 2R 2 9R 1 39R59R 4 2R 2 9R 1 39R6R 3 2 4 2 49R 4 3R 2 8R 1 39R6R 3 3 4 2 50R 4 4R 2 3 2 6R 1 38R6R 3 2 4 2 50R 4 4R 3 2 7R 1 38R62R 4 2R 2 3 2 6R 1 38R63R 4 3R 2 7R 1 38R64R 4 2R 2 8R 1 37R65R 4 4 2 8R 1 37R6R 3 2 57R 4 4 3 3 2 6R 1 37R7R 3 2 58R 4 2 3 2 6R 1 37R68R 4 3 2 6R 1 37R68R 4 2 8R 1 36R68R 4 2 8R 1 36R68R 4 2 8R 1 36R79R 1 36R79R 1 36R7R 3 2 61R 3 2 7R 1 36R6R 3 2 70R 1 36R78R 1 36R78R 1 36R78R 1 36R38R 3 2 38R 1 36R36R 3 4R 2 36R 1 36R35R 3 6R 2 35R 1 36R35R 3 6R 2 35R 1 36R34R 3 6R 2 35R 1 36R7R 3 2 24R 3 7R 2 25R 3 2 8R 1 36R33R 3 7R 2 34R 1 37R31R 3 3R 2 2 3 3R 2 33R 1 37R30R 3 3R 2 4R 3 2R 2 32R 1 37R29R 3 2 3 3 2 4 R 3 2 R 2 32R 1 37R28R 3 2 2 3 3 2 3R 3 3 2 2 3 2 30R 1 38R26R 3 2 9R 3 3 2 2 3 2 29R 1 38R23R 3 3 2 15R 3 3 2 26R 1 39R35R 3 2 4R 3 2 11R 3 2 11R 1 40R
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206
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7 R 3 2 4 2 R 3 2 1 1 R 1 41R7R 3 3 2 39R 3 2 11R 1 42R58R 1 44R55R 1 45R51R 1 47R47R 1 49R43R 1 51R13R 1 3R 2 18R 1 54R 3R 1 13R 2 11R 1 57R
5R 1 90R15R 1 15R 2 14R 1 53R 24R 1 2R 2 24R 1 50R 56R 1 48R 59R 1 46R31R 3 2 5R 3 2 21R 1 45R31R 3 3 2 2 3 2 2R 3 2 22R 1 44R14R 4 5R 2 44R 1 43R10R 3 2 2 4 11R 2 41R 1 42R9R 3 2 4 3R 2 40R 4 3 3 2 8R 1 41R11R 4 4 2 43R 4 4 2 3 2 7R 1 41R10R 4 2 45R 4 2R 2 9R 1 40R10R 4 2 46R 4 3R 2 8R 1 40R59R 4 2R 2 9R 1 39R
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210
12R 213R 213R 214R 215R 215R 216R 239R18R 220R 221R 223R 225R 227R 229R 232R 235R 238R 2127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R127R28R 225R 223R 221R 2
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211
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213
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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)
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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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