<%BANNER%>

Skeletal Neutron Dose Response Functions

Permanent Link: http://ufdc.ufl.edu/UFE0041703/00001

Material Information

Title: Skeletal Neutron Dose Response Functions A New Protocol for Evaluating Dose to Active Marrow and Bone Endosteum
Physical Description: 1 online resource (105 p.)
Language: english
Creator: Bahadori, Amir
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: dose, endosteum, leukemia, marrow, neutron, osteosarcoma, skeleton
Nuclear and Radiological Engineering -- Dissertations, Academic -- UF
Genre: Nuclear Engineering Sciences thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Spongiosa in the adult human skeleton consists of AM, IM, and trabecular mineral bone. AM is considered to be the radiation target tissue for leukemia risk, while the 50 micrometer layer of total marrow adjacent to the bone surfaces, or TM sub 50, is considered to be the radiation target tissue for risk of bone cancer. For irradiation by sources external to the body, kerma to homogeneous spongiosa has been used as an estimator for dose to both of these target tissues, as direct dose calculations are not possible using a skeletal model that does not include sub-segmented spongiosa. Recent microCT imaging of a 40 year old male cadaver has allowed for the accurate modeling of the fine microscopic structure of spongiosa in many regions of the adult skeleton. This microstructure, along with associated masses and material compositions, was used to compute SAF values for protons originating in axial and appendicular bone sites. Using the calculated proton SAF values, bone masses and material compositions, and proton production cross-sections, neutron DRFs were calculated for AM and TM sub 50 targets in each bone site; kerma conditions were assumed for other resultant charged particles. For comparison purposes, AM, TM, and spongiosa kerma coefficients were calculated as well. At low incident neutron energies, AM kerma coefficient correlate well with AM DRF, while TM kerma coefficient correlate well with TM sub 50 DRF. At high incident neutron energies, all kerma coefficients and DRFs tend to converge as CPE was established. In the range of 10 eV to 100 MeV, substantial differences were observed among the kerma coefficients and DRF. As a result, it is recommended that the AM kerma coefficient be used to estimate AM DRF and the TM kerma coefficient be used to estimate TM sub 50 DRF below 10 eV. Between 10 eV and 100 MeV, the appropriate DRF should be used, and above 100 MeV, the spongiosa kerma coefficient applies well for estimating both DRF.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Amir Bahadori.
Thesis: Thesis (M.S.)--University of Florida, 2010.
Local: Adviser: Bolch, Wesley E.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-04-30

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041703:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041703/00001

Material Information

Title: Skeletal Neutron Dose Response Functions A New Protocol for Evaluating Dose to Active Marrow and Bone Endosteum
Physical Description: 1 online resource (105 p.)
Language: english
Creator: Bahadori, Amir
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: dose, endosteum, leukemia, marrow, neutron, osteosarcoma, skeleton
Nuclear and Radiological Engineering -- Dissertations, Academic -- UF
Genre: Nuclear Engineering Sciences thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Spongiosa in the adult human skeleton consists of AM, IM, and trabecular mineral bone. AM is considered to be the radiation target tissue for leukemia risk, while the 50 micrometer layer of total marrow adjacent to the bone surfaces, or TM sub 50, is considered to be the radiation target tissue for risk of bone cancer. For irradiation by sources external to the body, kerma to homogeneous spongiosa has been used as an estimator for dose to both of these target tissues, as direct dose calculations are not possible using a skeletal model that does not include sub-segmented spongiosa. Recent microCT imaging of a 40 year old male cadaver has allowed for the accurate modeling of the fine microscopic structure of spongiosa in many regions of the adult skeleton. This microstructure, along with associated masses and material compositions, was used to compute SAF values for protons originating in axial and appendicular bone sites. Using the calculated proton SAF values, bone masses and material compositions, and proton production cross-sections, neutron DRFs were calculated for AM and TM sub 50 targets in each bone site; kerma conditions were assumed for other resultant charged particles. For comparison purposes, AM, TM, and spongiosa kerma coefficients were calculated as well. At low incident neutron energies, AM kerma coefficient correlate well with AM DRF, while TM kerma coefficient correlate well with TM sub 50 DRF. At high incident neutron energies, all kerma coefficients and DRFs tend to converge as CPE was established. In the range of 10 eV to 100 MeV, substantial differences were observed among the kerma coefficients and DRF. As a result, it is recommended that the AM kerma coefficient be used to estimate AM DRF and the TM kerma coefficient be used to estimate TM sub 50 DRF below 10 eV. Between 10 eV and 100 MeV, the appropriate DRF should be used, and above 100 MeV, the spongiosa kerma coefficient applies well for estimating both DRF.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Amir Bahadori.
Thesis: Thesis (M.S.)--University of Florida, 2010.
Local: Adviser: Bolch, Wesley E.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-04-30

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041703:00001


This item has the following downloads:


Full Text

PAGE 1

1 SKELETAL NEUTRON DOSE RESPONSE FUNCTIONS: A NEW PROTOCOL FOR EVALUATING DOSE TO ACTIVE MARROW AND BONE ENDOSTEUM By AMIR ALEXANDER BAHADORI A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2010

PAGE 2

2 2010 Amir Alexander Bahadori

PAGE 3

3 To my family

PAGE 4

4 ACKNOWLEDGMENTS I thank Dr. Edward Dugan, Dr. Keith Eckerman, and Dr. Derek Jokisch for serving on my committee. I thank Dr. Wesley Bolch for providing guidance as the chair of my committee. I thank Perry Johnson, Badal Juneja, and Mike Wayson for helping me get started with the project. I thank Alexandra Kusnezov for listening to me pract ice my defense presentation multiple times and providing tips on how to make it better. Finally, I thank my family for providing love and support throughout my education.

PAGE 5

5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ...................................................................................................... 4 LIST OF TABLES ................................................................................................................ 6 LIST OF FIGURES .............................................................................................................. 8 LIST OF ABBREVIATIONS .............................................................................................. 11 LIST OF SYMBOLS .......................................................................................................... 13 ABSTRACT ........................................................................................................................ 15 CHAPTER 1 INTRODUCTION ........................................................................................................ 17 2 MATERIALS AND METHODS ................................................................................... 21 SAF Data ..................................................................................................................... 21 Photon DRFs and the Three -Factor Method ............................................................. 21 Neutron DRF Generalized Formulation ..................................................................... 22 Hydrogen Neutron DRF Formulation ......................................................................... 23 Neutron DRF Formulation for Other Elements .......................................................... 26 Complete Neutron DRF Definition .............................................................................. 27 3 RESULTS .................................................................................................................... 31 4 DISCUSSION .............................................................................................................. 40 5 CONCLUSIONS .......................................................................................................... 47 APPENDIX A AXIAL SKELETAL NEUTRON DRF DATA ................................................................ 49 B APPENDICULAR SKELETAL NEUTRON DRF DATA ............................................. 76 LIST OF REFERENCES ................................................................................................. 103 BIOGRAPHICAL SKETCH .............................................................................................. 105

PAGE 6

6 LIST OF TABLES Table page 2 -1 Skeletal tissue compositions (Generated using data from ICRU 1992) .............. 29 2 -2 Representative isotopes for elemen ts addressed in ICRU Report 63. (Generated using data from ICRU 2000) .............................................................. 29 3 -1 Thoracic vertebra DRF data................................................................................... 34 3 -2 Thoracic vertebra DRF data................................................................................... 35 3 -3 Thoracic vertebra dose-to kerma ratios ................................................................ 36 3 -4 Proximal humerus dose -to kerma ratios ............................................................... 37 A-1 Cervical vertebra DRF ............................................................................................ 50 A-2 Cl avicle DRF ........................................................................................................... 51 A-3 Cranium DRF .......................................................................................................... 52 A-4 Proximal femur DRF ............................................................................................... 53 A-5 Proxim al humerus DRF .......................................................................................... 54 A-6 Lumbar vertebra DRF ............................................................................................ 55 A-7 Mandible DRF ......................................................................................................... 56 A-8 Pelvis DRF .............................................................................................................. 57 A-9 Rib DRF .................................................................................................................. 58 A-10 Sacrum DRF ........................................................................................................... 59 A-11 Scapula DRF .......................................................................................................... 60 A-12 Sternum DRF .......................................................................................................... 61 A-13 Thoracic vertebra DRF ........................................................................................... 62 B-1 Ankle and foot DRF ................................................................................................ 77 B-2 Distal femur DRF .................................................................................................... 78 B-3 Proximal fibula DRF ............................................................................................... 79

PAGE 7

7 B-4 Distal fibula DRF .................................................................................................... 80 B-5 Distal humerus DRF ............................................................................................... 81 B-6 Patella DRF ............................................................................................................ 82 B-7 Proximal radius DRF .............................................................................................. 83 B-8 Distal radius DRF ................................................................................................... 84 B-9 Proximal tibia DRF ................................................................................................. 85 B-10 Dista l tibia DRF ....................................................................................................... 86 B-11 Proximal ulna DRF ................................................................................................. 87 B-12 Distal ulna DRF ...................................................................................................... 88 B-13 Wrist a nd hand DRF ............................................................................................... 89

PAGE 8

8 LIST OF FIGURES Figure page 2 -1 Angular distribution of neutrons from scatter interaction with hydrogen nuclei (Generated using data from NNDC 2006) ............................................................. 30 3 -1 Thoracic vertebra kerma coefficients and DRF s ................................................... 38 3 -2 Proximal humerus kerma coefficients and DRFs .................................................. 39 4 -1 Thoracic vertebra percent RD ................................................................................ 44 4 -2 Proximal humerus percent RD ............................................................................... 45 4 -3 Comparison between current and previous AM neutron DRF data for lumbar vertebra. (Generated using data from Kerr and Eckerman 1985) ........................ 46 A-1 Cervical vertebra kerma coefficients and DRFs .................................................... 63 A-2 Cervical vertebra percent RD ................................................................................ 63 A-3 Clavicle kerma coefficients and DRFs ................................................................... 64 A-4 Clavicle percent RD ............................................................................................... 64 A-5 Cranium kerma coefficients and DRFs .................................................................. 65 A-6 Cranium percent RD .............................................................................................. 65 A-7 Proximal femur kerma coefficients and DRFs ....................................................... 66 A-8 Proximal femur percent RD .................................................................................... 66 A-9 Proximal humerus kerma coefficients and DRFs .................................................. 67 A-10 Proximal humerus percent RD ............................................................................... 67 A-11 Lumbar vertebra kerma coefficients and DRFs .................................................... 68 A-12 Lumbar vertebra percent RD ................................................................................. 68 A-13 Mandible kerma coefficients and DRFs ................................................................. 69 A-14 Mandible percent RD ............................................................................................. 69 A-15 Pelvis kerma coefficients and DRFs ...................................................................... 70 A-16 Pelvis percent RD ................................................................................................... 70

PAGE 9

9 A-17 Rib kerma coefficients and DRFs .......................................................................... 71 A-18 Rib percent RD ....................................................................................................... 71 A-19 Sacrum kerma coefficients and DRFs ................................................................... 72 A-20 Sacrum percent RD ................................................................................................ 72 A-21 Scapula kerma coefficients and DRFs .................................................................. 73 A-22 Scapula percent RD ............................................................................................... 73 A-23 Ste rnum kerma coefficients and DRFs .................................................................. 74 A-24 Sternum percent RD .............................................................................................. 74 A-25 Thoracic vertebra kerma coefficients and DRFs ................................................... 75 A-26 Thoracic vertebra percent RD ................................................................................ 75 B-1 Ankle and foot kerma coefficients and DRF .......................................................... 90 B-2 Ankle and foot percent RD ..................................................................................... 90 B-3 Distal femur kerma coefficients and DRF .............................................................. 91 B-4 Distal femur percent RD ......................................................................................... 91 B-5 Proximal fibula kerma coefficients and DRF ......................................................... 92 B-6 Proximal fibula percent RD .................................................................................... 92 B-7 Distal fibula kerma coefficients and DRF .............................................................. 93 B-8 Distal fibula percent RD ......................................................................................... 93 B-9 Distal humerus kerma coefficients and DRF ......................................................... 94 B-10 Distal humerus percent RD .................................................................................... 94 B-11 Patella kerma coefficients and DRF ...................................................................... 95 B-12 Patella percent RD ................................................................................................. 95 B-13 Proximal radius kerma coefficients and DRF ........................................................ 96 B-14 Proximal radius percent RD ................................................................................... 96 B-21 Proximal ulna kerma coefficients and DRF ......................................................... 100

PAGE 10

10 B-22 Proximal ulna percent RD .................................................................................... 100 B-23 Distal ulna kerma coefficients and DRF .............................................................. 101 B-24 Distal ulna percent RD ......................................................................................... 101 B-25 Wrist and hand kerma coefficients and DRF ....................................................... 102 B-26 Wrist and hand percent RD .................................................................................. 102

PAGE 11

11 LIST OF ABBREVIATION S m m icrometer AF a bsorbed fraction AM a ctive m arrow b b arn CD c ompact disc CM c enter of mass CPE c harged particle equilibrium CSDA c ontinuously slowing down approximation DRF d ose response function DS86 Dosimetry System 1986 ENDF Evaluated Nuclear Data Fi le eV e lectron volt g g ram Gy g ray ICRU International Commission on Radiation Units and Measurements IM i nactive marrow keV o ne thousand electron volts km k ilometer m m eter meV o ne thousandth of one electron volt MeV o ne million electron volts microCT m icro -computed tomography NCRP National Council on Radiation Protection and Measurements NIST National Institute of Standards and Technology

PAGE 12

12 RD r elative difference SAF s pecific absorbed fraction TM t otal marrow TM50 b one endosteum

PAGE 13

13 LIST OF SYMBOLS d ose to AM k erma to homogeneous spongiosa r atio of mass energy absorption coefficients of AM and homogeneous spongiosa S(E) d ose enhancement factor En i ncident neutron energy u nit conversion factor Avogadros number a tom ic mass of nuclide j ( ) m ass of target region ( ) m ass of source region ( ) p ercent mass abundance of nuclide j in source region r ( ; ) AF for secondary charged particles of type I with energy from source region r to target region T ( ) p roduction cross -section for nuclide j and secondary charged particle i ( ) d istribution of secondary charged particle of type i from a neutron interaction with nuclide j ( ) c ross -section for neutron scatter on hydrogen ( ) e nergy distribution of recoil proton from neutron scatter on hydrogen r esultant particle energy E i ncident particle energy c osine of the CM scattering angle Q Q value for the scattering interaction

PAGE 14

14 A r atio of masses of stationary body and incident particle ( ; ) SAF for protons of energy from source region r to target region T ( ) d ifferential proton production cross -section ( ) k erma coefficient for a chosen bone region as a function of incident neutron energy ( ) ( ) DRF for a chosen bone region as a functi on of incident neutron energy.

PAGE 15

15 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the D egree of Master of Science SKELETAL NEUTRON DOSE RESPONSE FUNCTIONS: A NEW PROTOCOL FOR EVALUATING DOSE TO ACTIVE MARROW AND BONE ENDOSTEUM By Amir Alexander Bahadori May 2010 Chair: Wesley E. Bolch Major: Nuclear Engineering Sciences Spongiosa in the adult human skeleton consists of AM, IM, and trabecular mineral bone. AM is considered to be the radiation target tissue for leukemia risk, while the 50 m layer of total marrow adjacent to the bone surfaces, or TM50, is considered to be the radiation target tissue for risk of bone cancer. For irradiation by sources external to the body, kerma to homogeneous spongiosa has been used as an estimator for dose to both of these target tissues, as direct dose calculations are not possible using a skeletal model that does not include sub-segmented spongiosa. Recent microCT imaging of a 40 year old male cadaver has allowed for the accurate modeling of the fine microscopic structure of spongiosa in many regions of the adult skeleton. This microstructure, along w ith associated masses and material compositions, was used to compute SAF values for protons originating in axial and appendicular bone sites. Using the calculated proton SAF values, bone masses and material compositions, and proton production cross sectio ns, neutron DRFs were calculated for AM and TM50 targets in each bone site; kerma conditions were assumed for other resultant charged particles. For comparison purposes, AM, TM, and spongiosa kerma coefficients were calculated as well.

PAGE 16

16 At low incident neutron energies, AM kerma coefficient correlate well with AM DRF, while TM kerma coefficient correlate well with TM50 DRF. At high incident neutron energies, all kerma coefficients and DRFs tend to converge as CPE was established. In the range of 10 eV to 100 MeV, substantial differences were observed among the kerma coefficients and DRF. As a result it is recommended that the AM kerma coefficient be used to estimate AM DRF and the TM kerma coefficient be used to estimate TM50 DRF below 10 eV. Between 10 eV and 100 MeV, the appropriate DRF should be used, and above 100 MeV, the spongiosa kerma coefficient applies well for estimating both DRF.

PAGE 17

17 CHAPTER 1 INTRODUCTION Human exposure to neutrons occurs in a variety of environments. All humans are exposed to natural levels of background radiation including neutrons from cosmic sources. Occupationally, radiation workers may be exposed to significant neutron doses above background levels. Above an altitude of 10 km, neutrons can account for up to 50% of total dose equivalent, indicating that neutron dose is a concern for astronauts (ICRU 2000) Aircraft crews receive elevated neutron doses, although to a lesser extent (ICRU 2000). Generally, dosimetry is performed for individuals in these professions to characterize the dose received. Neutron dose can also be significant in medical applications, such as radiation therapy. In methods of therapy using neutron beams, such as boronneutron capture therapy, some neutrons will invariably interact in the patients healthy tissues. In high energy gamma therapy, photoneutron production may be signifi cant, exposing the patient to unintended neutron dose (Allen and Chaudhri 1988) Proton therapy may be performed on cancer patients when sharp distal fall off is required due to the proximity of the planning tumor volume to organs at -risk. Such therapies create a significant secondary neutron dose to the patient. Due to their large penetration distance and resulting secondary heavy charged particles, neutrons are of special concern in proton therapy (Xu et al 2008). Direct measurement of dose resulting from neutron irradiation is not practical, and for skeletal tissues, characterization of neutron dose through computational models is complicated greatly by the heterogeneous nature of these media. Human skeletal tissues are comprised of different regions and elements. Blood cell production takes

PAGE 18

18 place in AM which is one constituent of bone spongiosa. IM and trabecular mineral bone also comprise spongiosa. Depending on the bone site, different amounts of the three constituents are present. Irradiation of the active marrow is associated with leukemia risk, while irradiation of TM50, defined as the layer extending 50 m from the trabecular bone surface into the marrow cavity, is associated with risk of osteosarcomas (Eckerman et al 2007) The structure of spongiosa is complex and is not easily represented using simple geometric definitions. Currently, kerma to the spongiosa is used as a surrogate for the dose to active marrow and bone endosteum. However, the geometric structure and bone region composit ion differences lead to a lack of CPE (Eckerman et al 2007), and so the accuracy of using spongiosa kerma as a surrogate is called into question. To avoid the problems inherent in attempting to model the complex microstructure of skeletal tissues, DRFs ca n be utilized. Instead of performing full secondary particle transport, the user can score neutron fluence over the spongiosa of a particular bone site and implement the appropriate DRF to return the absorbed dose to AM or TM50. This method requires the calculation of the secondary charged particle absorbed fraction to the target tissue of interest. Previously, DRF s for photons have been calculated for skeletal tissues (Eckerman et al 2007) Using electron absorbed fraction data, target and source regi on masses, interaction probabilities, and secondary electron distributions, the photon DRF s were calculated for AM and TM50 for each bone site. Additionally, DRF s for neutrons have been calculated previously for the DS86 project for the atomic bomb surviv ors at Hiroshima and Nagasaki (Kerr and Eckerman 1985) However, these calculations considered only AM in a homogeneous skeletal model, and

PAGE 19

19 therefore did not separately calculate the DRF for TM50. Also, only recoil protons with energies less than 20 MeV were evaluated, and no anisotropic scattering was considered (Kerr and Eckerman 1985). Kerma response functions (also referred to as kerma coefficients) have been previously calculated for neutrons. K erma coefficients have been calculated for neutrons above 15 MeV (Brenner 1983). Due to a lack of experimental values at these high energies, nuclear interaction data are based on models of the nucleus However, the nuclear models used prior to this were general purpose in nature, which is not acceptable for lighter mass nuclides, such as those present in human tissues due to the lack of statistical behavior of nuclides with mass numbers less than 20 (Brenner 1983) Brenner used the intranuclear cascade model followed by Fermi breakup for t hese lighter nuclei, and obtained good results for incident neutron energies ranging from 16 to 80 MeV for carbon, nitrogen, and oxygen. Neutron kerma coefficients have also been calculated for incident neutron energies less than 30 MeV us ing cross-secti on data from ENDF (Caswell et al 1980). An important caveat was included in this investigation: below incident neutron energy around 30 eV, molecular interactions are significant, but are not addressed by the kerma coefficients (Caswell et al. 1980). ICR U Report 63, Nuclear Data for Neutron and Proton Radiotherapy and for Radiation Protection, presents cross-sections and kerma coefficients for elements of interest in radiotherapy. While previous neutron data was driven by explosives research and consider ed neutron energies up to 20 MeV, this report includes neutron data up to 150 MeV. To determine the cross -sections and kerma coefficients, the generated values from the GNASH code were compared with existing measurements (ICRU

PAGE 20

20 2000) It is important to e mphasize that the cross -section and kerma coefficient values stated in ICRU Report 63 are evaluated, meaning that they are a combination of experimental and theoretically derived data. Thus, if one calculates a kerma coefficient based upon the reported cr oss -sections, there will likely be some difference with the corresponding kerma coefficient as stated in the report. In the present study, skeletal neutron DRF s for AM and TM50 were calculated for all skeletal sites. The AM DRF s and TM50 DRF s were compared to kerma coefficients for AM, TM, and spongiosa. Based upon these comparisons, guidance is provided regarding the evaluation of dose to the two targets of interest. This protocol addresses incident neutron energies ranging from thermal to 150 MeV.

PAGE 21

21 CHAPTER 2 MATERIALS AND METHOD S SAF Data As previously stated, the calculation of a neutron DRF requires the AF of secondary charged particles to the target tissue of interest. AF can be calculated from the SAF which is simply the quotient of the AF and the mass of the target region. The SAF for AM and TM50 as a target were previously calculated for protons using path length distributions from microCT scans of spongiosa samples from a 40 year old male cadaver CSDA proton transport was used to generate SAF data. CSDA data were retrieved from NIST and scaled according to bone region composition (D. Jokisch, personal communication, December 9, 2008 ). The compositions for the three bone regions of interest ( AM trabecular m ineral bone, and IM ) were taken from ICRU Report 46, are shown in Table 2 1 These compositions were also used directly in the calculation of the neutron DRF s In addition, the neutron DRF calculation used a skeletal mass set that was entire ly consistent with that used to compile the SAF data. These masses were based on the same 40 year old male cadaver used to generate the path length distributions Photon DRFs and the Three -Factor Method Photon DRF have also been calculated using electron AF data generated from simulations based on the spongiosa microstructure of the 40 year old male cadaver. An alternative to explicitly calculating the photon DRF is to use the Three -Factor Method. Here, the dose to AM can be calculated from the dose to homogeneous spongiosa by (Lee et al. 2006) = ( ) [ 1 ]

PAGE 22

22 Energy dependence is implicit in the dose terms and the mass energy absorption coefficients. Since the properties of DRF follow the properties of dose, dose can be replaced by DRF in Equation 1. Therefore, for each bone, if the photon AM DRF is known, the dose enhancement factor can be found. The primary advantage to using the Three-Factor Method is the ease of use. If the dose to AM from photons is required, one can simply record dose over a homogeneous spongiosa volume and apply the corrections as in E quation 1 An easily implemented analogous method does not exist when addressing neutron DRF. In order to use a method similar to the Three-Factor Method with neutron dose and DRF, one would need to know the fraction of dose in the homogeneous spongiosa volume due to interaction from each resultant charged particle, with a corresponding dose enhancement factor. Thus, the large number of neutronproduced charged particle types (protons, deuterons, tritons, helium 3 nuclei, alphas, and recoil nuclei) precl udes the use of a neutron three-factor method. Instead, a dose-to kerma ratio can be calculated as the quotient of the calculated DRF and the spongiosa kerma coefficient of the corresponding bone site. This yields a dimensionless factor which can be ap plied to spongiosa kerma to yield absorbed dose to the target tissue of interest for a given bone site. Neutron DRF Generalized Formulation A general formulation for the neutron DRF should allow for consideration of all types of secondary charged particles resulting from neutron interactions. Neutron interactions are not represented by simple mathematical expressions Therefore, the calculation of neutron DRF relies on interaction probabilities, similar to the way kerma coefficients are calculated. In contrast with kerma coefficients, and similar to the photon

PAGE 23

23 DRF formulation, fractional energy deposition must be considered (Eckerman et al. 2007) For neutrons, the DRF formulation for a given skeletal site is ( ) ( ) = ( ) ( ) ( ) ( ; ) ( ) ( 0) [ 2 ] The value of the conversion factor is dependent upon the units used for the variables used to calculate the neutron DRF In general, mass will be expressed in grams, energy will be expressed in electronvolts, and cross -section will be expressed in barns. Therefore, after all operations excluding multiplication by the conversion factor are performed, the units are left i n the product of electronvolts and barns per gram. The desired units are gray -square meters Therefore, the conversion factor is given as =1 m21028 b 1 6022 10 19 J 1 eV 1000 g 1 kg = 1 6022 10 44 Gy m2b eV g 1 For incident neutrons, myriad charged particl es can result from interaction with a constituent nucleus. Theoretically, if AF data existed for all of these particles, a pure neutron DRF could be calculated. Hydrogen Neutron DRF Formulation Since specific absorbed fraction data is currently available for protons only a pure DRF is not practically calculated. Since the only resultant charged particle from a neutron interaction with hydrogen is a proton, it is the simplest element to address. In addition, due to the low relative abundance of deuterium and tritium, the neutron DRF formulation for hydrogen is simplified greatly by assuming that 1H comprises all of the hydrogen in the skeletal tissues The equation used to find the hydrogen component of the neutron DRF for each skeletal site is ( ) ( ) = ( ) ( ) ( ) ( ; ) ( ) ( 0) [ 3 ]

PAGE 24

24 In order to derive the energy distribution of protons resulting from neutron scatter on hydrogen, the angular distribution of neutrons aft er interaction with hydrogen must be used. This data is part of the ENDF, and is readily available from NNDC (NNDC 2006) The angular distribution of neutrons resulting from scatter on hydrogen is displayed in Figure 2-1 I t is evident that the assumption of isotropic scattering of neutrons on hydrogen is only valid up to incident neutron energy of 20 MeV. The anisotropy of scatter must be considered when calculating the hydrogen component of the neutron DRF. Now, it is necessary to convert the angular distribution of resultant neutrons to the energy distribution of recoil protons. First, the proton energy for a given incident energy and cosine of CM neutron scattering angle must be calculated. For the generalized case scatter on any stationary body, the energy of the recoil nucleus is given as (Shultis and Faw 2000) =1 2 ( 1 ) 1 1 + + + 1 [ 4 ] with 1 + 1 2, [ 5 ] and = ( 1 + ) [ 6 ] Clearly, for elastic scattering of a neutron on a hydrogen nucleus, the Q value is zero, and so equal s zero. Also, A can be approximated as unity, as a neutron and a proton are of nearly equal mass, yielding a value of zero for After considering these simplifications, the energy of the recoil proton is given as

PAGE 25

25 =1 2 ( 1 ) [ 7 ] Now, the angular distribution of scattered neutrons must be modified to yield the energy distribution of recoil protons. To do so, the chain rule must be applied as: ( ) = ( ) = ( ) = ( ) [ 8 ] Differentiating Equation 7 with respect to yields = 1 2 [ 9 ] Combining Equations 8 and 9 the energy distribution for recoil protons is given as ( ) = 2 ( ) [ 10 ] The negative sign in the formulation is a result of the inverse relationship between the cosine of the CM scattering angle and the recoil proton energy. To avoid negative values in a distribution, which are mathematically appropriate but not physically realizable, one may flip the distribution and the recoil proton energy, while leaving the incident neutron energy unaltered. This oper ation is numerically equivalent to interchanging the limits of integration. In order to ensure that the proper result is obtained, one can inspect the relative probabilities as a function of recoil proton energy for incident neutron energy of 150 MeV; for this energy, the most probable CM scattering angle cosine is -1, corresponding to a direct collision of the neutron with the hydrogen nucleus. This results in maximal energy transfer to the recoil proton. Thus, after the conversion of the angular distri bution of resultant neutrons to the energy distribution of recoil protons, the relative probability of a recoil proton with maximal energy should be greater than the

PAGE 26

26 relative probability of a recoil proton with zero energy, which results from a glancing co llision ( i.e., = 1). To perform the neutron DRF calculation, the computer program MATLABTM was used. Since the proton data was presented in SAF form, it was determined that the equations used to evaluate the neutron DRF should be modified to use the data in this form. Also, the equation was modified to minimize the number of numerical integrations performed, and the maximum proton energy is assumed to be the incident neutron energy. For hydrogen, the actual equation used to calculate the hydrogen component of the neutron DRF is ( ) ( ) = ( ) ( )( ; ) ( ) ( ,0) [ 11 ] To perform the integration, first the energy range was split into logarithmically equidistant divisions. Next, the summation was performed for the three source regions (active marrow, inactive marrow, trabecular bone). The product of the summation, the s cattering cross-section, and the recoil proton energy distribution was calculated for each incident neutron energy and recoil proton energy. The result was numerically integrated using the trapezoidal method. Finally, the conversion factor was applied to obtain a result in gray -square meters Neutron DRF Formulation for Other Elements The equation for the neutron DRF proton component associated with each target element is similar to Equation 11 the equation for the hydrogen component of the neutron DRF. For neutrons incident on an arbitrary element X, the proton component of the total neutron DRF is given as ( ) ( ) = ( ) ( )( ; ) ( )0 [ 12 ]

PAGE 27

27 The cross -sections and kerma c oefficients listed in ICRU Report 63 are for the major isotopes of elements considered important for biological or shielding reasons. These data are tabulated for incident neutron energies from 20 MeV to 150 MeV. The elements contained in ICRU Report 63, corresponding major isotopes, and natural abundances of the major isotopes are displayed in Table 22 According to ICRU Report 63 recommendations (ICRU 2000) when natural abundances of isotopes are assumed, the data for the major isotopes may be used a s representative of the element. The data included on the ICRU Report 63 data CD was used for the constituent elements of skeletal tissue. It should be noted that for iron, the kerma coefficients for the four major isotopes were included on the data CD, and so these were combined according to natural abundance in order to yield an elemental iron kerma coefficient. With the exception of protons, SAF data do not exist for charged particles resulting from neutron interactions in skeletal tissues. Therefore, partial kerma coefficients must be used for these resultant charged particles. Partial kerma coefficients for deuterons, 3He nuclei, alphas, and recoil nuclei are listed for the elements in ICRU Report 63. These were weighted by the appropr iate percent mass abundances and summed to yield the contribution of non-proton resultant charged particles. Assuming kerma conditions for charged particles other than protons will lead to some error in the estimation of the neutron DRF. However, the error is not exp ected to be significant since the heavier charged particles have a range in skeletal tissues that is much smaller than that for protons. Complete Neutron DRF Definition The final neutron DRF for each skeletal site was taken to be the hydrogenonly DRF for incident neutron energies up to 20 MeV Above 20 MeV, the neutron DRF was

PAGE 28

28 calculated for hydrogen and ICRU 63 elements. Any element not listed in ICRU 63 was not included in the calculation of the skeletal neutron DRF, primarily due to a lack of cross-se ction data. However, these elements make up less than one percent of the composition of active marrow, inactive marrow, and trabecular mineral bone and so their exclusion is not expected to cause appreciable error in the calculations.

PAGE 29

29 Table 2-1. Skeletal tissue compositi ons. (Generated using data from ICRU 1992) Element Composition by Mass (%) Active Marrow Trabecular Bone Mineral Inactive Marrow Hydrogen 10.5 3.4 11.5 Carbon 41.4 15.5 64.4 Nitrogen 3.4 4.2 0.7 Oxygen 43.9 43.5 23.1 Sodium* 0 0.1 0.1 Magnesium* 0 0.2 0 Phosphorous 0.1 10.3 0 Sulfur* 0.2 0.3 0.1 Chlorine* 0.2 0 0.1 Potassium* 0.2 0 0 Calcium 0 22.5 0 Iron 0.1 0 0 *These elements were not considered in the neutron DRF formulation. Table 2-2. Representative isotopes fo r elements addressed in ICRU Report 63. (Generated using data from ICRU 2000) Element Isotope Natural Percent Abundance Hydrogen 1 H 99.9885 Carbon 12 C 98.93 Nitrogen 14 N 99.632 Oxygen 16 O 99.757 Aluminum 27 Al 100 Silicon 28 Si 92.2297 Phosphorous 31 P 100 Calcium 40 Ca 96.941 Iron 56 Fe 91.754 Copper 63 Cu 69.17 Tungsten 184 W 30.64 Lead 208 Pb 52.4

PAGE 30

30 Figure 21 Angular distribution of neutrons from scatter interaction with hydrogen nuclei (Generated using data from NNDC 2006) (eV)

PAGE 31

31 CHAPTER 3 RESULTS AM and TM50 neutron DRF were calculated for the axial skeleton, which includes 13 bone sites. For each of the 13 bone sites of the appendicular skeleton, only the TM50 DRF was calculated, since no active marrow resides in these sit es. T he data generated are available in graphical and tabular form in Appendix A and Appendix B For comparison purposes, the neutron kerma coefficients for AM, TM, and spongiosa were also calculated for each axial bone site. Since the composition of AM for each axial bone site is the same, the AM kerma coefficients are all equal. Due to differences in cellularity and the percentage of spongiosa comprised of trabecular bone, the TM kerma coefficients and spongiosa kerma coefficients vary by bone site. Figure 3 -1 and Figure 3-2 show the AM kerma coefficient, TM kerma coefficient, spongiosa kerma coef ficient, AM DRF, and TM50 DRF for the thoracic vertebra and proximal humerus, respectively. The thoracic vertebra is a bone site where the differences among the kerma coefficients and DRF are small, while the proximal humerus is a bone site where the diff erences among the kerma coefficients and DRF are much more prominent. Corresponding DRF data are shown in Table 3 1 (thoracic vertebra) and Table 3 2 (proximal humerus). Dose-to -kerma ratios for the thoracic vertebra and the proximal humerus are shown in Table 3 3 and Table 3 4 respectively, as examples. Here, the dose-to kerma ratios were calculated using the DRF reported in this study and kerma coefficients given in ICRU Report 63. If dose -to kerma ratios are to be implemented in instances where the i ncident neutron energy exceeds 150 MeV, it is important that the user calculate kerma coefficients based upon the particular cross -section library for the transport

PAGE 32

32 program being utilized. Therefore, tabulated dose to kerma ratios are not provided for eac h bone site. While the differences between the thoracic vertebra and proximal humerus represent variation in terms of the spread among the kerma coefficients and DRF in the human skeleton, there are several similarities that are characteristic of every bon e site. At very low energies (less than 10 meV), the kerma coefficients and DRF change very little with incident neutron energy; an approximate value for the AM DRF is 3.1 x 1017 Gy m2, while the TM50 DRF ranges from a minimum 6.3 x 1018 Gy m2 for the appendicular skeletal sites to a maximum of 2.4 x 1017 Gy m2 for sites of high cellularity such as the vertebrae. The values then decrease to a minimum between 10 eV and 100 eV, and then increase with incident neutron energy. The maximum for values obse rved for the AM DRF are around 1.3 x 1014 Gy m2, while the maximum values for the TM50 DRF are between 1.2 x 1014 Gy m2 and 1.4 x 1014 Gy m2. At low incident neutron energies, the AM kerma coefficient accurately represents the AM DRF for all axial bone sites, while the TM kerma coefficient corresponds well with the TM50 DRF for both axial and appendicular bone sites. The convergence of these values at low incident neutron energies is expected, since secondary charged particles are unlikely to have enoug h energy to escape the region of their creation, imposing static CPE. At high incident neutron energies, all kerma coefficients and DRF converge, as dynamic CPE is established within the spongiosa region of each bone site. In the midrange incident neutr on energies (100 eV to 100 MeV), neither static nor dynamic CPE exist due to the interplay between th e size and shape of the bone tra beculae and marrow cavities and the ranges of the protons resulting from neutron

PAGE 33

33 interactions. This is manifested in large differences between the kerma coefficients and DRF when compared with the differences observed at energies outside of this range.

PAGE 34

34 Table 3 1 Thoracic vertebra DRF data Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) AM TM50 AM TM50 AM TM50 1.00E 03 3.08E 17 2.35E 17 1.00E+01 1.48E 18 1.16E 18 1.00E+05 6.67E 16 7.35E 16 1.50E 03 3.10E 17 2.36E 17 1.50E+01 1.28E 18 1.03E 18 1.50E+05 8.61E 16 9.51E 16 2.00E 03 3.12E 17 2.38E 17 2.00E+01 1.19E 18 9.74E 19 2.00E+05 1.02E 15 1.12E 15 3.00E 03 3.15E 17 2.40E 17 3.00E+01 1.11E 18 9.54E 19 3.00E+05 1.27E 15 1.40E 15 4.00E 03 3.17E 17 2.41E 17 4.00E+01 1.11E 18 9.91E 19 4.00E+05 1.52E 15 1.67E 15 5.00E 03 3.19E 17 2.43E 17 5.00E+01 1.15E 18 1.05E 18 5.00E+05 1.62E 15 1.80E 15 6.00E 03 3.20E 17 2.44E 17 6.00E+01 1.20E 18 1.13E 18 6.00E+05 1.76E 15 1.95E 15 8.00E 03 3.20E 17 2.44E 17 8.00E+01 1.34E 18 1.31E 18 8.00E+05 2.02E 15 2.23E 15 1.00E 02 3.19E 17 2.43E 17 1.00E+02 1.50E 18 1.50E 18 1.00E+06 2.38E 15 2.57E 15 1.50E 02 3.09E 17 2.35E 17 1.50E+02 1.96E 18 2.03E 18 1.50E+06 2.70E 15 2.90E 15 2.00E 02 2.92E 17 2.22E 17 2.00E+02 2.45E 18 2.57E 18 2.00E+06 3.09E 15 3.23E 15 3.00E 02 2.50E 17 1.90E 17 3.00E+02 3.45E 18 3.70E 18 3.00E+06 3.77E 15 3.78E 15 4.00E 02 2.18E 17 1.66E 17 4.00E+02 4.48E 18 4.83E 18 4.00E+06 4.31E 15 4.19E 15 5.00E 02 1.94E 17 1.48E 17 5.00E+02 5.51E 18 5.97E 18 5.00E+06 4.49E 15 4.26E 15 6.00E 02 1.77E 17 1.34E 17 6.00E+02 6.55E 18 7.11E 18 6.00E+06 4.68E 15 4.44E 15 8.00E 02 1.53E 17 1.17E 17 8.00E+02 8.62E 18 9.39E 18 8.00E+06 5.24E 15 5.02E 15 1.00E 01 1.37E 17 1.04E 17 1.00E+03 1.07E 17 1.17E 17 1.00E+07 5.63E 15 5.42E 15 1.50E 01 1.12E 17 8.55E 18 1.50E+03 1.58E 17 1.73E 17 1.50E+07 6.40E 15 6.32E 15 2.00E 01 9.72E 18 7.40E 18 2.00E+03 2.09E 17 2.28E 17 2.00E+07 6.79E 15 6.83E 15 3.00E 01 7.91E 18 6.03E 18 3.00E+03 3.08E 17 3.38E 17 3.00E+07 7.25E 15 7.37E 15 4.00E 01 6.86E 18 5.23E 18 4.00E+03 4.06E 17 4.46E 17 4.00E+07 7.64E 15 7.77E 15 5.00E 01 6.14E 18 4.68E 18 5.00E+03 5.02E 17 5.52E 17 5.00E+07 7.85E 15 7.99E 15 6.00E 01 5.61E 18 4.27E 18 6.00E+03 5.98E 17 6.57E 17 6.00E+07 8.11E 15 8.24E 15 8.00E 01 4.87E 18 3.71E 18 8.00E+03 7.88E 17 8.66E 17 8.00E+07 8.76E 15 8.90E 15 1.00E+00 4.35E 18 3.31E 18 1.00E+04 9.77E 17 1.07E 16 1.00E+08 9.58E 15 9.76E 15 1.50E+00 3.56E 18 2.72E 18 1.50E+04 1.45E 16 1.59E 16 1.50E+08 1.29E 14 1.32E 14 2.00E+00 3.09E 18 2.36E 18 2.00E+04 1.88E 16 2.06E 16 3.00E+00 2.53E 18 1.94E 18 3.00E+04 2.67E 16 2.93E 16 4.00E+00 2.21E 18 1.70E 18 4.00E+04 3.39E 16 3.72E 16 5.00E+00 1.99E 18 1.54E 18 5.00E+04 4.04E 16 4.44E 16 6.00E+00 1.83E 18 1.42E 18 6.00E+04 4.65E 16 5.11E 16 8.00E+00 1.62E 18 1.26E 18 8.00E+04 5.72E 16 6.30E 16

PAGE 35

35 Table 3 2 Thoracic vertebra DRF data Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) AM TM50 AM TM50 AM TM50 1.00E 03 3.08E 17 1.25E 17 1.00E+01 1.45E 18 7.02E 19 1.00E+05 4.17E 16 9.81E 16 1.50E 03 3.10E 17 1.25E 17 1.50E+01 1.24E 18 6.77E 19 1.50E+05 5.35E 16 1.26E 15 2.00E 03 3.12E 17 1.26E 17 2.00E+01 1.13E 18 6.90E 19 2.00E+05 6.30E 16 1.49E 15 3.00E 03 3.15E 17 1.27E 17 3.00E+01 1.03E 18 7.66E 19 3.00E+05 7.90E 16 1.85E 15 4.00E 03 3.17E 17 1.28E 17 4.00E+01 1.01E 18 8.73E 19 4.00E+05 9.72E 16 2.16E 15 5.00E 03 3.19E 17 1.29E 17 5.00E+01 1.01E 18 9.92E 19 5.00E+05 1.02E 15 2.35E 15 6.00E 03 3.20E 17 1.29E 17 6.00E+01 1.04E 18 1.12E 18 6.00E+05 1.11E 15 2.53E 15 8.00E 03 3.20E 17 1.29E 17 8.00E+01 1.13E 18 1.39E 18 8.00E+05 1.32E 15 2.84E 15 1.00E 02 3.19E 17 1.29E 17 1.00E+02 1.23E 18 1.66E 18 1.00E+06 1.67E 15 3.20E 15 1.50E 02 3.09E 17 1.25E 17 1.50E+02 1.55E 18 2.38E 18 1.50E+06 2.04E 15 3.62E 15 2.00E 02 2.92E 17 1.18E 17 2.00E+02 1.91E 18 3.10E 18 2.00E+06 2.52E 15 4.03E 15 3.00E 02 2.50E 17 1.01E 17 3.00E+02 2.64E 18 4.56E 18 3.00E+06 3.32E 15 4.68E 15 4.00E 02 2.18E 17 8.80E 18 4.00E+02 3.39E 18 6.03E 18 4.00E+06 3.93E 15 5.09E 15 5.00E 02 1.94E 17 7.85E 18 5.00E+02 4.14E 18 7.50E 18 5.00E+06 4.15E 15 5.13E 15 6.00E 02 1.77E 17 7.13E 18 6.00E+02 4.90E 18 8.97E 18 6.00E+06 4.38E 15 5.35E 15 8.00E 02 1.53E 17 6.19E 18 8.00E+02 6.40E 18 1.19E 17 8.00E+06 5.00E 15 5.88E 15 1.00E 01 1.37E 17 5.53E 18 1.00E+03 7.89E 18 1.49E 17 1.00E+07 5.43E 15 6.17E 15 1.50E 01 1.12E 17 4.54E 18 1.50E+03 1.15E 17 2.22E 17 1.50E+07 6.26E 15 6.90E 15 2.00E 01 9.72E 18 3.93E 18 2.00E+03 1.50E 17 2.95E 17 2.00E+07 6.62E 15 7.34E 15 3.00E 01 7.91E 18 3.20E 18 3.00E+03 2.18E 17 4.41E 17 3.00E+07 7.09E 15 7.78E 15 4.00E 01 6.86E 18 2.78E 18 4.00E+03 2.81E 17 5.87E 17 4.00E+07 7.52E 15 8.10E 15 5.00E 01 6.14E 18 2.49E 18 5.00E+03 3.43E 17 7.32E 17 5.00E+07 7.76E 15 8.27E 15 6.00E 01 5.61E 18 2.27E 18 6.00E+03 4.04E 17 8.75E 17 6.00E+07 8.02E 15 8.48E 15 8.00E 01 4.87E 18 1.98E 18 8.00E+03 5.24E 17 1.16E 16 8.00E+07 8.68E 15 9.13E 15 1.00E+00 4.34E 18 1.77E 18 1.00E+04 6.44E 17 1.44E 16 1.00E+08 9.40E 15 9.99E 15 1.50E+00 3.56E 18 1.46E 18 1.50E+04 9.41E 17 2.13E 16 1.50E+08 1.26E 14 1.36E 14 2.00E+00 3.08E 18 1.27E 18 2.00E+04 1.21E 16 2.77E 16 3.00E+00 2.53E 18 1.06E 18 3.00E+04 1.71E 16 3.94E 16 4.00E+00 2.20E 18 9.37E 19 4.00E+04 2.16E 16 5.00E 16 5.00E+00 1.98E 18 8.58E 19 5.00E+04 2.57E 16 5.98E 16 6.00E+00 1.82E 18 8.04E 19 6.00E+04 2.95E 16 6.87E 16 8.00E+00 1.60E 18 7.39E 19 8.00E+04 3.60E 16 8.44E 16

PAGE 36

36 Table 3 3 Thoracic vertebra dose-to kerma ratios Energy (eV) Dose to Kerma Ratio Energy (eV) Dose to Kerma Ratio Energy (eV) Dose to Kerma Ratio AM TM50 AM TM50 AM TM50 1.00E 03 1.161 0.884 1.00E+01 1.124 0.883 1.00E+05 1.072 1.182 1.50E 03 1.161 0.884 1.50E+01 1.115 0.896 1.50E+05 1.068 1.180 2.00E 03 1.161 0.884 2.00E+01 1.108 0.911 2.00E+05 1.065 1.178 3.00E 03 1.161 0.884 3.00E+01 1.098 0.942 3.00E+05 1.060 1.172 4.00E 03 1.161 0.885 4.00E+01 1.092 0.972 4.00E+05 1.062 1.166 5.00E 03 1.161 0.885 5.00E+01 1.088 0.997 5.00E+05 1.053 1.167 6.00E 03 1.161 0.885 6.00E+01 1.085 1.019 6.00E+05 1.048 1.160 8.00E 03 1.161 0.885 8.00E+01 1.083 1.055 8.00E+05 1.043 1.149 1.00E 02 1.161 0.885 1.00E+02 1.083 1.082 1.00E+06 1.046 1.131 1.50E 02 1.161 0.885 1.50E+02 1.083 1.120 1.50E+06 1.037 1.114 2.00E 02 1.161 0.885 2.00E+02 1.082 1.139 2.00E+06 1.043 1.092 3.00E 02 1.161 0.884 3.00E+02 1.083 1.159 3.00E+06 1.045 1.049 4.00E 02 1.161 0.884 4.00E+02 1.083 1.167 4.00E+06 1.041 1.011 5.00E 02 1.160 0.884 5.00E+02 1.082 1.172 5.00E+06 1.037 0.984 6.00E 02 1.160 0.884 6.00E+02 1.081 1.174 6.00E+06 1.030 0.976 8.00E 02 1.160 0.883 8.00E+02 1.080 1.176 8.00E+06 1.021 0.978 1.00E 01 1.159 0.883 1.00E+03 1.078 1.176 1.00E+07 1.015 0.978 1.50E 01 1.158 0.882 1.50E+03 1.075 1.176 1.50E+07 1.008 0.996 2.00E 01 1.158 0.882 2.00E+03 1.072 1.174 2.00E+07 0.999 1.005 3.00E 01 1.156 0.881 3.00E+03 1.064 1.167 3.00E+07 0.995 1.011 4.00E 01 1.155 0.880 4.00E+03 1.059 1.163 4.00E+07 0.995 1.011 5.00E 01 1.155 0.880 5.00E+03 1.055 1.159 5.00E+07 0.993 1.010 6.00E 01 1.154 0.879 6.00E+03 1.053 1.158 6.00E+07 0.992 1.008 8.00E 01 1.152 0.878 8.00E+03 1.056 1.161 8.00E+07 0.988 1.004 1.00E+00 1.151 0.878 1.00E+04 1.063 1.168 1.00E+08 0.997 1.015 1.50E+00 1.148 0.876 1.50E+04 1.079 1.185 1.50E+08 0.992 1.018 2.00E+00 1.146 0.875 2.00E+04 1.079 1.185 3.00E+00 1.141 0.874 3.00E+04 1.077 1.183 4.00E+00 1.139 0.875 4.00E+04 1.079 1.185 5.00E+00 1.136 0.875 5.00E+04 1.082 1.188 6.00E+00 1.133 0.876 6.00E+04 1.081 1.188 8.00E+00 1.128 0.879 8.00E+04 1.073 1.181

PAGE 37

37 Table 3 4 Proximal humerus dose-to -kerma ratios Energy (eV) Dose to Kerma Ratio Energy (eV) Dose to Kerma Ratio Energy (eV) Dose to Kerma Ratio AM TM50 AM TM50 AM TM50 1.00E 03 1.767 0.714 1.00E+01 1.586 0.768 1.00E+05 0.648 1.524 1.50E 03 1.767 0.714 1.50E+01 1.506 0.820 1.50E+05 0.641 1.513 2.00E 03 1.767 0.714 2.00E+01 1.431 0.873 2.00E+05 0.638 1.506 3.00E 03 1.767 0.714 3.00E+01 1.305 0.970 3.00E+05 0.639 1.495 4.00E 03 1.767 0.714 4.00E+01 1.209 1.048 4.00E+05 0.663 1.474 5.00E 03 1.767 0.714 5.00E+01 1.135 1.111 5.00E+05 0.638 1.473 6.00E 03 1.767 0.714 6.00E+01 1.079 1.161 6.00E+05 0.638 1.455 8.00E 03 1.768 0.714 8.00E+01 1.002 1.235 8.00E+05 0.659 1.415 1.00E 02 1.768 0.714 1.00E+02 0.953 1.285 1.00E+06 0.716 1.375 1.50E 02 1.768 0.714 1.50E+02 0.885 1.352 1.50E+06 0.755 1.345 2.00E 02 1.768 0.714 2.00E+02 0.851 1.385 2.00E+06 0.822 1.313 3.00E 02 1.767 0.714 3.00E+02 0.820 1.418 3.00E+06 0.885 1.249 4.00E 02 1.766 0.714 4.00E+02 0.805 1.433 4.00E+06 0.918 1.189 5.00E 02 1.765 0.713 5.00E+02 0.796 1.441 5.00E+06 0.936 1.156 6.00E 02 1.765 0.713 6.00E+02 0.790 1.446 6.00E+06 0.934 1.142 8.00E 02 1.763 0.713 8.00E+02 0.781 1.453 8.00E+06 0.946 1.112 1.00E 01 1.762 0.712 1.00E+03 0.774 1.456 1.00E+07 0.958 1.087 1.50E 01 1.760 0.712 1.50E+03 0.760 1.464 1.50E+07 0.957 1.056 2.00E 01 1.759 0.711 2.00E+03 0.749 1.469 2.00E+07 0.946 1.048 3.00E 01 1.755 0.710 3.00E+03 0.728 1.476 3.00E+07 0.944 1.036 4.00E 01 1.753 0.709 4.00E+03 0.710 1.482 4.00E+07 0.953 1.026 5.00E 01 1.750 0.709 5.00E+03 0.697 1.487 5.00E+07 0.958 1.022 6.00E 01 1.748 0.708 6.00E+03 0.688 1.491 6.00E+07 0.962 1.017 8.00E 01 1.744 0.708 8.00E+03 0.680 1.502 8.00E+07 0.962 1.011 1.00E+00 1.740 0.708 1.00E+04 0.677 1.514 1.00E+08 0.964 1.024 1.50E+00 1.730 0.708 1.50E+04 0.679 1.539 1.50E+08 0.949 1.026 2.00E+00 1.721 0.708 2.00E+04 0.674 1.540 3.00E+00 1.703 0.712 3.00E+04 0.668 1.539 4.00E+00 1.688 0.718 4.00E+04 0.666 1.542 5.00E+00 1.670 0.724 5.00E+04 0.665 1.545 6.00E+00 1.653 0.731 6.00E+04 0.662 1.544 8.00E+00 1.620 0.749 8.00E+04 0.653 1.529

PAGE 38

38 Figure 31 Thoracic vertebra kerma coefficient s and DRF s

PAGE 39

39 Figure 32 Proximal humerus kerma coefficient s and DRF s

PAGE 40

40 CHAPTER 4 DISCUSSION To quantitatively evaluate the use of a particular kerma coefficient for a DRF, the relative difference as a function of incident neutron energy was calculated. Explicitly, the RD is calculated as ( ) = ( ) ( ) ( ) ( ) ( ) [ 13 ] A positive RD value indicates that the kerma coefficient overestimates the DRF, while a negative RD value indicates that the kerma coefficient underestimates the DRF. The RD values in this study are reported as percentages. For the axial skeleton, the RD of the kerma coeff icient values with respect to the AM DRF and TM50 DRF were found, while the RD of the kerma coefficient values with respect to the TM50 DRF were calculated for the appendicular skeleton. The most pertinent comparisons for the axial skeletal sites are betw een AM kerma coefficient and AM DRF, TM kerma coefficient and TM50 DRF, Spongiosa kerma coefficient and AM DRF, and Spongiosa kerma coefficient and TM50 DRF. The first two comparisons are important for evaluating differences due to charged particle disequ ilibrium, while the last two comparisons indicate differences resulting from approximating dose to AM and TM50 by kerma to homogeneous spongiosa. Similarly, the most pertinent comparisons for the appendicular skeleton are between TM kerma coefficient and TM50 DRF, and Spongiosa kerma coefficient and TM50 DRF.

PAGE 41

41 Plots of the RD as a function of incident neutron energy for the thoracic vertebra and the proximal humerus are displayed in Figure 41 and Figure 42 respectively. Similar plots for all bone sites are available in Appendix A and Appendix B, along with tabular data. As one may infer from the plots of kerma coefficient and DRF, the RD of the AM kerma coefficient with respect to the AM DRF is low at low incident neutron energies. While theoretically the RD should be zero at low energies due to static CPE, small differences are observed due to the fact that the ICRU Report 63 data are evaluated, as explained in Chapter 1. The RD increases with increasing incident neutron energy from approximately 10 eV to 600 keV for the following bone sites: clavicle, cranium, proximal femur, proximal humerus, mandible, pelvis, and scapula. For the remaining axial bone sites, the maximum RD occurs at 20 MeV. The RD then decreases with energy and is within 10% for al l axial bone sites at 100 MeV. The AM kerma coefficient always overestimates the AM DRF. The TM kerma coefficient correlates well with the TM50 DRF at low incident neutron energies, as well. While theoretically the RD should be zero at low energies due to static CPE, small differences are observed due to the fact that the ICRU Report 63 data are evaluated, as explained in Chapter 1. For the axi al skeleton, the TM kerma coefficient tends to underestimate the TM50 DRF at intermediate incident neutron energies; substantial underestimation (greater than 10%) occurs for the clavicle, proximal femur, proximal humerus, mandible, and scapula. At around 10 MeV, the TM kerma coefficient overestimates TM50 DRF by the largest amount; the cranium is the most extreme case, with an overestimation of approximately 25%. The RD then decreases with increasing incident neutron energy. For the appendicular skeleton, the

PAGE 42

42 TM kerma coefficient is within 10% of the TM50 DRF until around 1 MeV, at which point the RD increases to a maximum and then decreases with increasing incident neutron energy. The maximum RD observed in the appendicular skeleton are 15% to 30%, and the RD is within 15% for all bone sites at 100 MeV. At low incident neutron energies, the spongiosa kerma coefficient underestimates the AM DRF (axial skeleton) and overestimates the TM50 DRF (axial and appendicular skeleton). These differences are driven solely by the differences in composition among AM, TM, and spongiosa. At intermediate incident neutron energies, the spongiosa kerma coefficient overestimates the AM DRF for the clavicle, proximal femur, proximal humerus, mandible, pelvis, and scapula. For the remainder of the axial bone sites, the spongiosa kerma coefficient continues to underestimate the AM DRF. The maximum RD for the spongiosa kerma coefficient as an estimator of the AM DRF ranges from 10% to 60%. For all axial and appendicular bone sites, the spongiosa kerma coefficient underestimates the TM50 DRF at intermediate incident neutron energies. Finally, the difference associated with approximating the AM DRF and TM50 DRF with the spongiosa kerma coefficient is low at energies greater than 100 MeV. Previously, AM neutron DRF have been calculated (Kerr and Eckerman 1985) A homogeneous skeleton was used, along with AF data generated from chord length distributions. It was determined that the AF data for lumbar vertebra could be used a s a surrogate for AF data for all other bone sites except for the parietal bone. Only isotropic scattering on hydrogen nuclei was considered for incident neutron energies ranging from 0.5 MeV to 20 MeV; kerma coefficients were applied for all other elemen ts.

PAGE 43

43 A comparison between the lumbar vertebra AM DRF calculated in this study and that calculated previously is displayed in Figure 43 The two datasets correspond well. Note that the newly -calculated DRF curve is slightly lower than that calculated by K err and Eckerman; the difference is small since the contribution from protonproducing interactions from elements other than hydrogen is almost zero in this energy range. The difference appears to be increasing towards the end of the energy range, as the relative importance of non -hydrogenous constituent elements begins to increase. In terms of implementation, the format of the response function to be used is dictated by the range of incident neutron energies. For cases in which the maximum incident neutron energy is less than 150 MeV, the fluence over spongiosa should be recorded. Next, the product of the DRF and the fluence is integrated to return absorbed dose. Neutron exposure situations in which this form should be used include occupational exposures at nuclear reactors (Shultis and Faw 2000) and proton therapy for tumors at relatively shallow depths, such as eye treatments. For cases in which the maximum incident neutron energy exceeds 150 MeV, the kerma to spongiosa should be recorded. Her e, two energy regimes must be considered separately kerma due to neutrons of incident energies under 150 MeV and exceeding 150 MeV. For the first regime, the product of the tabulated dose-to -kerma ratio and the recorded kerma is integrated; to return th e total absorbed dose, this value must be summed with the total kerma from neutrons of the second regime. This form should be used for secondary neutrons resulting from proton therapy for tumors at greater depths, such as prostate treatments, and for neut ron exposures in space (NCRP 2006) .

PAGE 44

44 Figure 41 Thoracic vertebra percent RD

PAGE 45

45 Figure 42 Proximal humerus percent RD

PAGE 46

46 Figure 43 Comparison between current and previous AM neutron DRF data for lumbar vertebra. (Generated using data from Kerr and Eckerman 1985)

PAGE 47

47 CHAPTER 5 CONCLUSIONS Kerma to spongiosa has been used in the past to characterize dose to AM and TM50 due to a lack of bone microstructure computational models. The availability of spongiosa samples from a human cadaver, along with the application of microCT imaging, has allowed for skeletal sub-segmentation and the explicit definition of spongiosa as a heterogeneous mixture of active marrow, inactive marrow, and trabecular mineral bone. Coupling path length distributions from skeletal subsegmentation with proton rangeenergy computations has led to the generation of proton SAF data with the various spongiosa constituents as sources and targets. In this case, the targets of -interest were the AM and the TM50. The results of this study indicate that large errors may be introduced by approximating dose to AM and TM50 by the kerma to spongiosa. For some bone sites, such as the thoracic vertebra, the error that occurs is small. For other bone sites, such as the proximal humerus, the error that occurs is large, exceeding 50%. In cases of uniform neutron irradiation of the body, the skeletal average dose to AM and TM50 are desired. Here, using kerma to spongiosa to estimate dose to TM50 results in errors exceeding 40%, while using kerma to spongiosa to estimate dose to AM results in errors exceeding 30%. The new skeletal neutron DRF improve upon previously -calculated skeletal neutron DRF in a number of ways. Firstly, the incident neutron energy range has been extended greatly. Secondly, secondary proton anisotropy is explicitly considered for neutron sca tter on hydrogen nuclei from energies ranging from thermal to 150 MeV. All

PAGE 48

48 proton -producing reactions are considered above incident neutron energy of 20 MeV. Finally, the new calculations consider bone -site -specific spongiosa composition. Future areas fo r improvement include considering resultant charged particles other than protons. While protons account for most of the difference between absorbed dose and kerma, assuming kerma conditions for the other charged particles introduces some error. Extending the energy range considered would be beneficial for confirming the existence of charged particle equilibrium above about 100 MeV. Explicitly accounting for neutron activation is another area of investigation not addressed in the current study, although i t does contribute to absorbed dose. Finally, the appropriateness of the infinite spongiosa approximation for proton transport should be validated using Monte Carlo simulation.

PAGE 49

49 APPENDIX A AXIAL SKELETAL NEUTR ON DRF DATA The following tables and plots present skeletal neutron DRF data and RD data for the axial skeleton. The skeletal sites addressed in this section are Cervical vertebra, Clavicle Cranium Proximal femur Proximal humerus Lumbar vertebra, Mandible Pelvi s Rib Sacrum Scapula, Sternum and Thoracic vertebra.

PAGE 50

50 Table A -1. Cervical vertebra DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) AM TM50 AM TM50 AM TM50 1.00E 03 3.08E 17 2.35E 17 1.00E+01 1.48E 18 1.16E 18 1.00E+05 6.69E 16 7.23E 16 1.50E 03 3.10E 17 2.36E 17 1.50E+01 1.28E 18 1.03E 18 1.50E+05 8.64E 16 9.34E 16 2.00E 03 3.12E 17 2.38E 17 2.00E+01 1.19E 18 9.70E 19 2.00E+05 1.02E 15 1.10E 15 3.00E 03 3.15E 17 2.40E 17 3.00E+01 1.11E 18 9.47E 19 3.00E+05 1.27E 15 1.38E 15 4.00E 03 3.17E 17 2.41E 17 4.00E+01 1.11E 18 9.83E 19 4.00E+05 1.52E 15 1.64E 15 5.00E 03 3.19E 17 2.43E 17 5.00E+01 1.15E 18 1.04E 18 5.00E+05 1.62E 15 1.77E 15 6.00E 03 3.20E 17 2.44E 17 6.00E+01 1.20E 18 1.12E 18 6.00E+05 1.77E 15 1.92E 15 8.00E 03 3.20E 17 2.44E 17 8.00E+01 1.34E 18 1.29E 18 8.00E+05 2.02E 15 2.20E 15 1.00E 02 3.19E 17 2.43E 17 1.00E+02 1.50E 18 1.48E 18 1.00E+06 2.38E 15 2.54E 15 1.50E 02 3.09E 17 2.35E 17 1.50E+02 1.96E 18 1.99E 18 1.50E+06 2.70E 15 2.86E 15 2.00E 02 2.92E 17 2.22E 17 2.00E+02 2.45E 18 2.53E 18 2.00E+06 3.07E 15 3.19E 15 3.00E 02 2.50E 17 1.90E 17 3.00E+02 3.46E 18 3.63E 18 3.00E+06 3.73E 15 3.73E 15 4.00E 02 2.18E 17 1.66E 17 4.00E+02 4.49E 18 4.75E 18 4.00E+06 4.24E 15 4.11E 15 5.00E 02 1.94E 17 1.48E 17 5.00E+02 5.52E 18 5.86E 18 5.00E+06 4.39E 15 4.15E 15 6.00E 02 1.77E 17 1.34E 17 6.00E+02 6.56E 18 6.98E 18 6.00E+06 4.55E 15 4.30E 15 8.00E 02 1.53E 17 1.17E 17 8.00E+02 8.63E 18 9.22E 18 8.00E+06 5.05E 15 4.84E 15 1.00E 01 1.37E 17 1.04E 17 1.00E+03 1.07E 17 1.14E 17 1.00E+07 5.39E 15 5.22E 15 1.50E 01 1.12E 17 8.54E 18 1.50E+03 1.58E 17 1.70E 17 1.50E+07 6.11E 15 6.08E 15 2.00E 01 9.72E 18 7.40E 18 2.00E+03 2.09E 17 2.24E 17 2.00E+07 6.51E 15 6.58E 15 3.00E 01 7.91E 18 6.03E 18 3.00E+03 3.09E 17 3.31E 17 3.00E+07 6.98E 15 7.12E 15 4.00E 01 6.86E 18 5.23E 18 4.00E+03 4.07E 17 4.37E 17 4.00E+07 7.40E 15 7.54E 15 5.00E 01 6.14E 18 4.68E 18 5.00E+03 5.03E 17 5.41E 17 5.00E+07 7.63E 15 7.77E 15 6.00E 01 5.61E 18 4.27E 18 6.00E+03 5.99E 17 6.44E 17 6.00E+07 7.91E 15 8.05E 15 8.00E 01 4.87E 18 3.71E 18 8.00E+03 7.90E 17 8.50E 17 8.00E+07 8.58E 15 8.73E 15 1.00E+00 4.35E 18 3.31E 18 1.00E+04 9.81E 17 1.05E 16 1.00E+08 9.44E 15 9.63E 15 1.50E+00 3.56E 18 2.72E 18 1.50E+04 1.45E 16 1.56E 16 1.50E+08 1.28E 14 1.31E 14 2.00E+00 3.09E 18 2.36E 18 2.00E+04 1.88E 16 2.03E 16 3.00E+00 2.53E 18 1.94E 18 3.00E+04 2.68E 16 2.88E 16 4.00E+00 2.21E 18 1.70E 18 4.00E+04 3.40E 16 3.66E 16 5.00E+00 1.99E 18 1.53E 18 5.00E+04 4.06E 16 4.37E 16 6.00E+00 1.83E 18 1.42E 18 6.00E+04 4.67E 16 5.03E 16 8.00E+00 1.62E 18 1.26E 18 8.00E+04 5.75E 16 6.20E 16

PAGE 51

51 Table A -2. Clavicle DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) AM TM50 AM TM50 AM TM50 1.00E 03 3.08E 17 1.44E 17 1.00E+01 1.46E 18 7.77E 19 1.00E+05 4.69E 16 8.92E 16 1.50E 03 3.10E 17 1.45E 17 1.50E+01 1.26E 18 7.30E 19 1.50E+05 5.99E 16 1.16E 15 2.00E 03 3.12E 17 1.46E 17 2.00E+01 1.16E 18 7.28E 19 2.00E+05 7.02E 16 1.37E 15 3.00E 03 3.15E 17 1.47E 17 3.00E+01 1.07E 18 7.80E 19 3.00E+05 8.71E 16 1.71E 15 4.00E 03 3.17E 17 1.48E 17 4.00E+01 1.05E 18 8.67E 19 4.00E+05 1.06E 15 2.00E 15 5.00E 03 3.19E 17 1.49E 17 5.00E+01 1.07E 18 9.70E 19 5.00E+05 1.11E 15 2.17E 15 6.00E 03 3.20E 17 1.50E 17 6.00E+01 1.11E 18 1.08E 18 6.00E+05 1.21E 15 2.36E 15 8.00E 03 3.20E 17 1.50E 17 8.00E+01 1.22E 18 1.32E 18 8.00E+05 1.42E 15 2.67E 15 1.00E 02 3.19E 17 1.49E 17 1.00E+02 1.35E 18 1.57E 18 1.00E+06 1.76E 15 3.01E 15 1.50E 02 3.09E 17 1.45E 17 1.50E+02 1.73E 18 2.21E 18 1.50E+06 2.13E 15 3.42E 15 2.00E 02 2.92E 17 1.37E 17 2.00E+02 2.14E 18 2.87E 18 2.00E+06 2.60E 15 3.80E 15 3.00E 02 2.50E 17 1.17E 17 3.00E+02 2.99E 18 4.20E 18 3.00E+06 3.39E 15 4.37E 15 4.00E 02 2.18E 17 1.02E 17 4.00E+02 3.86E 18 5.54E 18 4.00E+06 3.99E 15 4.72E 15 5.00E 02 1.94E 17 9.09E 18 5.00E+02 4.73E 18 6.88E 18 5.00E+06 4.23E 15 4.67E 15 6.00E 02 1.77E 17 8.26E 18 6.00E+02 5.60E 18 8.22E 18 6.00E+06 4.46E 15 4.78E 15 8.00E 02 1.53E 17 7.17E 18 8.00E+02 7.34E 18 1.09E 17 8.00E+06 5.04E 15 5.21E 15 1.00E 01 1.37E 17 6.40E 18 1.00E+03 9.05E 18 1.35E 17 1.00E+07 5.45E 15 5.44E 15 1.50E 01 1.12E 17 5.25E 18 1.50E+03 1.32E 17 2.01E 17 1.50E+07 6.19E 15 6.20E 15 2.00E 01 9.72E 18 4.55E 18 2.00E+03 1.73E 17 2.67E 17 2.00E+07 6.52E 15 6.65E 15 3.00E 01 7.91E 18 3.70E 18 3.00E+03 2.50E 17 3.95E 17 3.00E+07 6.91E 15 7.14E 15 4.00E 01 6.86E 18 3.21E 18 4.00E+03 3.23E 17 5.22E 17 4.00E+07 7.24E 15 7.50E 15 5.00E 01 6.14E 18 2.88E 18 5.00E+03 3.94E 17 6.48E 17 5.00E+07 7.39E 15 7.69E 15 6.00E 01 5.61E 18 2.63E 18 6.00E+03 4.64E 17 7.73E 17 6.00E+07 7.59E 15 7.90E 15 8.00E 01 4.87E 18 2.29E 18 8.00E+03 6.01E 17 1.02E 16 8.00E+07 8.19E 15 8.49E 15 1.00E+00 4.34E 18 2.04E 18 1.00E+04 7.37E 17 1.28E 16 1.00E+08 8.96E 15 9.28E 15 1.50E+00 3.56E 18 1.68E 18 1.50E+04 1.07E 16 1.90E 16 1.50E+08 1.20E 14 1.27E 14 2.00E+00 3.09E 18 1.46E 18 2.00E+04 1.38E 16 2.48E 16 3.00E+00 2.53E 18 1.21E 18 3.00E+04 1.94E 16 3.54E 16 4.00E+00 2.21E 18 1.07E 18 4.00E+04 2.44E 16 4.50E 16 5.00E+00 1.98E 18 9.75E 19 5.00E+04 2.90E 16 5.39E 16 6.00E+00 1.82E 18 9.09E 19 6.00E+04 3.32E 16 6.20E 16 8.00E+00 1.61E 18 8.27E 19 8.00E+04 4.05E 16 7.65E 16

PAGE 52

52 Table A -3. Cranium DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) AM TM50 AM TM50 AM TM50 1.00E 03 3.08E 17 1.56E 17 1.00E+01 1.47E 18 8.14E 19 1.00E+05 6.05E 16 7.53E 16 1.50E 03 3.10E 17 1.57E 17 1.50E+01 1.28E 18 7.49E 19 1.50E+05 7.73E 16 9.74E 16 2.00E 03 3.12E 17 1.58E 17 2.00E+01 1.18E 18 7.33E 19 2.00E+05 9.04E 16 1.15E 15 3.00E 03 3.15E 17 1.60E 17 3.00E+01 1.11E 18 7.62E 19 3.00E+05 1.11E 15 1.43E 15 4.00E 03 3.17E 17 1.61E 17 4.00E+01 1.11E 18 8.29E 19 4.00E+05 1.32E 15 1.69E 15 5.00E 03 3.19E 17 1.62E 17 5.00E+01 1.14E 18 9.12E 19 5.00E+05 1.39E 15 1.83E 15 6.00E 03 3.20E 17 1.62E 17 6.00E+01 1.19E 18 1.01E 18 6.00E+05 1.50E 15 1.99E 15 8.00E 03 3.20E 17 1.63E 17 8.00E+01 1.33E 18 1.21E 18 8.00E+05 1.72E 15 2.27E 15 1.00E 02 3.19E 17 1.62E 17 1.00E+02 1.49E 18 1.42E 18 1.00E+06 2.05E 15 2.60E 15 1.50E 02 3.09E 17 1.57E 17 1.50E+02 1.94E 18 1.98E 18 1.50E+06 2.36E 15 2.96E 15 2.00E 02 2.92E 17 1.48E 17 2.00E+02 2.41E 18 2.56E 18 2.00E+06 2.76E 15 3.30E 15 3.00E 02 2.50E 17 1.27E 17 3.00E+02 3.40E 18 3.72E 18 3.00E+06 3.43E 15 3.85E 15 4.00E 02 2.18E 17 1.10E 17 4.00E+02 4.41E 18 4.89E 18 4.00E+06 3.94E 15 4.19E 15 5.00E 02 1.94E 17 9.86E 18 5.00E+02 5.42E 18 6.07E 18 5.00E+06 4.08E 15 4.15E 15 6.00E 02 1.77E 17 8.96E 18 6.00E+02 6.44E 18 7.24E 18 6.00E+06 4.22E 15 4.26E 15 8.00E 02 1.53E 17 7.77E 18 8.00E+02 8.46E 18 9.58E 18 8.00E+06 4.68E 15 4.68E 15 1.00E 01 1.37E 17 6.94E 18 1.00E+03 1.05E 17 1.19E 17 1.00E+07 4.98E 15 4.93E 15 1.50E 01 1.12E 17 5.69E 18 1.50E+03 1.55E 17 1.77E 17 1.50E+07 5.64E 15 5.70E 15 2.00E 01 9.72E 18 4.93E 18 2.00E+03 2.03E 17 2.34E 17 2.00E+07 6.06E 15 6.26E 15 3.00E 01 7.91E 18 4.02E 18 3.00E+03 2.99E 17 3.45E 17 3.00E+07 6.59E 15 6.89E 15 4.00E 01 6.86E 18 3.48E 18 4.00E+03 3.91E 17 4.55E 17 4.00E+07 7.06E 15 7.36E 15 5.00E 01 6.14E 18 3.12E 18 5.00E+03 4.82E 17 5.64E 17 5.00E+07 7.35E 15 7.66E 15 6.00E 01 5.61E 18 2.85E 18 6.00E+03 5.72E 17 6.71E 17 6.00E+07 7.68E 15 7.99E 15 8.00E 01 4.87E 18 2.48E 18 8.00E+03 7.50E 17 8.85E 17 8.00E+07 8.44E 15 8.75E 15 1.00E+00 4.35E 18 2.21E 18 1.00E+04 9.27E 17 1.10E 16 1.00E+08 9.41E 15 9.80E 15 1.50E+00 3.56E 18 1.82E 18 1.50E+04 1.36E 16 1.63E 16 1.50E+08 1.30E 14 1.37E 14 2.00E+00 3.09E 18 1.58E 18 2.00E+04 1.76E 16 2.11E 16 3.00E+00 2.53E 18 1.31E 18 3.00E+04 2.49E 16 3.01E 16 4.00E+00 2.21E 18 1.15E 18 4.00E+04 3.14E 16 3.82E 16 5.00E+00 1.99E 18 1.04E 18 5.00E+04 3.73E 16 4.56E 16 6.00E+00 1.83E 18 9.69E 19 6.00E+04 4.27E 16 5.24E 16 8.00E+00 1.62E 18 8.74E 19 8.00E+04 5.23E 16 6.46E 16

PAGE 53

53 Table A -4. Proximal femur DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) AM TM50 AM TM50 AM TM50 1.00E 03 3.08E 17 1.25E 17 1.00E+01 1.46E 18 6.95E 19 1.00E+05 4.50E 16 8.82E 16 1.50E 03 3.10E 17 1.25E 17 1.50E+01 1.25E 18 6.66E 19 1.50E+05 5.75E 16 1.14E 15 2.00E 03 3.12E 17 1.26E 17 2.00E+01 1.15E 18 6.76E 19 2.00E+05 6.75E 16 1.34E 15 3.00E 03 3.15E 17 1.27E 17 3.00E+01 1.06E 18 7.45E 19 3.00E+05 8.40E 16 1.67E 15 4.00E 03 3.17E 17 1.28E 17 4.00E+01 1.04E 18 8.44E 19 4.00E+05 1.03E 15 1.95E 15 5.00E 03 3.19E 17 1.29E 17 5.00E+01 1.06E 18 9.56E 19 5.00E+05 1.08E 15 2.12E 15 6.00E 03 3.20E 17 1.29E 17 6.00E+01 1.09E 18 1.08E 18 6.00E+05 1.18E 15 2.29E 15 8.00E 03 3.20E 17 1.29E 17 8.00E+01 1.19E 18 1.33E 18 8.00E+05 1.38E 15 2.59E 15 1.00E 02 3.19E 17 1.29E 17 1.00E+02 1.31E 18 1.59E 18 1.00E+06 1.71E 15 2.91E 15 1.50E 02 3.09E 17 1.25E 17 1.50E+02 1.68E 18 2.27E 18 1.50E+06 2.08E 15 3.32E 15 2.00E 02 2.92E 17 1.18E 17 2.00E+02 2.07E 18 2.95E 18 2.00E+06 2.54E 15 3.70E 15 3.00E 02 2.50E 17 1.01E 17 3.00E+02 2.88E 18 4.33E 18 3.00E+06 3.30E 15 4.34E 15 4.00E 02 2.18E 17 8.79E 18 4.00E+02 3.71E 18 5.72E 18 4.00E+06 3.89E 15 4.75E 15 5.00E 02 1.94E 17 7.85E 18 5.00E+02 4.55E 18 7.11E 18 5.00E+06 4.10E 15 4.77E 15 6.00E 02 1.77E 17 7.13E 18 6.00E+02 5.38E 18 8.49E 18 6.00E+06 4.31E 15 4.97E 15 8.00E 02 1.53E 17 6.19E 18 8.00E+02 7.04E 18 1.12E 17 8.00E+06 4.91E 15 5.50E 15 1.00E 01 1.37E 17 5.53E 18 1.00E+03 8.69E 18 1.40E 17 1.00E+07 5.35E 15 5.78E 15 1.50E 01 1.12E 17 4.53E 18 1.50E+03 1.27E 17 2.08E 17 1.50E+07 6.16E 15 6.61E 15 2.00E 01 9.72E 18 3.93E 18 2.00E+03 1.66E 17 2.74E 17 2.00E+07 6.58E 15 7.10E 15 3.00E 01 7.91E 18 3.20E 18 3.00E+03 2.40E 17 4.05E 17 3.00E+07 7.11E 15 7.61E 15 4.00E 01 6.86E 18 2.78E 18 4.00E+03 3.11E 17 5.33E 17 4.00E+07 7.54E 15 7.99E 15 5.00E 01 6.14E 18 2.48E 18 5.00E+03 3.79E 17 6.60E 17 5.00E+07 7.77E 15 8.21E 15 6.00E 01 5.61E 18 2.27E 18 6.00E+03 4.46E 17 7.85E 17 6.00E+07 8.03E 15 8.46E 15 8.00E 01 4.87E 18 1.98E 18 8.00E+03 5.78E 17 1.03E 16 8.00E+07 8.72E 15 9.13E 15 1.00E+00 4.34E 18 1.77E 18 1.00E+04 7.10E 17 1.28E 16 1.00E+08 9.52E 15 1.00E 14 1.50E+00 3.56E 18 1.45E 18 1.50E+04 1.03E 16 1.90E 16 1.50E+08 1.28E 14 1.37E 14 2.00E+00 3.09E 18 1.27E 18 2.00E+04 1.33E 16 2.47E 16 3.00E+00 2.53E 18 1.05E 18 3.00E+04 1.86E 16 3.52E 16 4.00E+00 2.21E 18 9.34E 19 4.00E+04 2.34E 16 4.48E 16 5.00E+00 1.98E 18 8.54E 19 5.00E+04 2.78E 16 5.35E 16 6.00E+00 1.82E 18 7.99E 19 6.00E+04 3.18E 16 6.16E 16 8.00E+00 1.60E 18 7.33E 19 8.00E+04 3.88E 16 7.58E 16

PAGE 54

54 Table A -5. Proximal humerus DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) AM TM50 AM TM50 AM TM50 1.00E 03 3.08E 17 1.25E 17 1.00E+01 1.45E 18 7.02E 19 1.00E+05 4.17E 16 9.81E 16 1.50E 03 3.10E 17 1.25E 17 1.50E+01 1.24E 18 6.77E 19 1.50E+05 5.35E 16 1.26E 15 2.00E 03 3.12E 17 1.26E 17 2.00E+01 1.13E 18 6.90E 19 2.00E+05 6.30E 16 1.49E 15 3.00E 03 3.15E 17 1.27E 17 3.00E+01 1.03E 18 7.66E 19 3.00E+05 7.90E 16 1.85E 15 4.00E 03 3.17E 17 1.28E 17 4.00E+01 1.01E 18 8.73E 19 4.00E+05 9.72E 16 2.16E 15 5.00E 03 3.19E 17 1.29E 17 5.00E+01 1.01E 18 9.92E 19 5.00E+05 1.02E 15 2.35E 15 6.00E 03 3.20E 17 1.29E 17 6.00E+01 1.04E 18 1.12E 18 6.00E+05 1.11E 15 2.53E 15 8.00E 03 3.20E 17 1.29E 17 8.00E+01 1.13E 18 1.39E 18 8.00E+05 1.32E 15 2.84E 15 1.00E 02 3.19E 17 1.29E 17 1.00E+02 1.23E 18 1.66E 18 1.00E+06 1.67E 15 3.20E 15 1.50E 02 3.09E 17 1.25E 17 1.50E+02 1.55E 18 2.38E 18 1.50E+06 2.04E 15 3.62E 15 2.00E 02 2.92E 17 1.18E 17 2.00E+02 1.91E 18 3.10E 18 2.00E+06 2.52E 15 4.03E 15 3.00E 02 2.50E 17 1.01E 17 3.00E+02 2.64E 18 4.56E 18 3.00E+06 3.32E 15 4.68E 15 4.00E 02 2.18E 17 8.80E 18 4.00E+02 3.39E 18 6.03E 18 4.00E+06 3.93E 15 5.09E 15 5.00E 02 1.94E 17 7.85E 18 5.00E+02 4.14E 18 7.50E 18 5.00E+06 4.15E 15 5.13E 15 6.00E 02 1.77E 17 7.13E 18 6.00E+02 4.90E 18 8.97E 18 6.00E+06 4.38E 15 5.35E 15 8.00E 02 1.53E 17 6.19E 18 8.00E+02 6.40E 18 1.19E 17 8.00E+06 5.00E 15 5.88E 15 1.00E 01 1.37E 17 5.53E 18 1.00E+03 7.89E 18 1.49E 17 1.00E+07 5.43E 15 6.17E 15 1.50E 01 1.12E 17 4.54E 18 1.50E+03 1.15E 17 2.22E 17 1.50E+07 6.26E 15 6.90E 15 2.00E 01 9.72E 18 3.93E 18 2.00E+03 1.50E 17 2.95E 17 2.00E+07 6.62E 15 7.34E 15 3.00E 01 7.91E 18 3.20E 18 3.00E+03 2.18E 17 4.41E 17 3.00E+07 7.09E 15 7.78E 15 4.00E 01 6.86E 18 2.78E 18 4.00E+03 2.81E 17 5.87E 17 4.00E+07 7.52E 15 8.10E 15 5.00E 01 6.14E 18 2.49E 18 5.00E+03 3.43E 17 7.32E 17 5.00E+07 7.76E 15 8.27E 15 6.00E 01 5.61E 18 2.27E 18 6.00E+03 4.04E 17 8.75E 17 6.00E+07 8.02E 15 8.48E 15 8.00E 01 4.87E 18 1.98E 18 8.00E+03 5.24E 17 1.16E 16 8.00E+07 8.68E 15 9.13E 15 1.00E+00 4.34E 18 1.77E 18 1.00E+04 6.44E 17 1.44E 16 1.00E+08 9.40E 15 9.99E 15 1.50E+00 3.56E 18 1.46E 18 1.50E+04 9.41E 17 2.13E 16 1.50E+08 1.26E 14 1.36E 14 2.00E+00 3.08E 18 1.27E 18 2.00E+04 1.21E 16 2.77E 16 3.00E+00 2.53E 18 1.06E 18 3.00E+04 1.71E 16 3.94E 16 4.00E+00 2.20E 18 9.37E 19 4.00E+04 2.16E 16 5.00E 16 5.00E+00 1.98E 18 8.58E 19 5.00E+04 2.57E 16 5.98E 16 6.00E+00 1.82E 18 8.04E 19 6.00E+04 2.95E 16 6.87E 16 8.00E+00 1.60E 18 7.39E 19 8.00E+04 3.60E 16 8.44E 16

PAGE 55

55 Table A -6. Lumbar vertebra DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) AM TM50 AM TM50 AM TM50 1.00E 03 3.08E 17 2.35E 17 1.00E+01 1.48E 18 1.16E 18 1.00E+05 6.68E 16 7.27E 16 1.50E 03 3.10E 17 2.36E 17 1.50E+01 1.28E 18 1.03E 18 1.50E+05 8.63E 16 9.40E 16 2.00E 03 3.12E 17 2.38E 17 2.00E+01 1.19E 18 9.72E 19 2.00E+05 1.02E 15 1.11E 15 3.00E 03 3.15E 17 2.40E 17 3.00E+01 1.11E 18 9.51E 19 3.00E+05 1.27E 15 1.39E 15 4.00E 03 3.17E 17 2.41E 17 4.00E+01 1.11E 18 9.87E 19 4.00E+05 1.52E 15 1.65E 15 5.00E 03 3.19E 17 2.43E 17 5.00E+01 1.15E 18 1.05E 18 5.00E+05 1.62E 15 1.77E 15 6.00E 03 3.20E 17 2.44E 17 6.00E+01 1.20E 18 1.12E 18 6.00E+05 1.76E 15 1.92E 15 8.00E 03 3.20E 17 2.44E 17 8.00E+01 1.34E 18 1.30E 18 8.00E+05 2.02E 15 2.20E 15 1.00E 02 3.19E 17 2.43E 17 1.00E+02 1.50E 18 1.49E 18 1.00E+06 2.38E 15 2.54E 15 1.50E 02 3.09E 17 2.35E 17 1.50E+02 1.96E 18 2.01E 18 1.50E+06 2.70E 15 2.86E 15 2.00E 02 2.92E 17 2.22E 17 2.00E+02 2.45E 18 2.55E 18 2.00E+06 3.08E 15 3.18E 15 3.00E 02 2.50E 17 1.90E 17 3.00E+02 3.46E 18 3.67E 18 3.00E+06 3.74E 15 3.70E 15 4.00E 02 2.18E 17 1.66E 17 4.00E+02 4.48E 18 4.79E 18 4.00E+06 4.25E 15 4.07E 15 5.00E 02 1.94E 17 1.48E 17 5.00E+02 5.52E 18 5.92E 18 5.00E+06 4.40E 15 4.11E 15 6.00E 02 1.77E 17 1.34E 17 6.00E+02 6.55E 18 7.05E 18 6.00E+06 4.57E 15 4.26E 15 8.00E 02 1.53E 17 1.17E 17 8.00E+02 8.63E 18 9.30E 18 8.00E+06 5.08E 15 4.81E 15 1.00E 01 1.37E 17 1.04E 17 1.00E+03 1.07E 17 1.15E 17 1.00E+07 5.43E 15 5.19E 15 1.50E 01 1.12E 17 8.55E 18 1.50E+03 1.58E 17 1.71E 17 1.50E+07 6.17E 15 6.04E 15 2.00E 01 9.72E 18 7.40E 18 2.00E+03 2.09E 17 2.26E 17 2.00E+07 6.55E 15 6.52E 15 3.00E 01 7.91E 18 6.03E 18 3.00E+03 3.08E 17 3.34E 17 3.00E+07 6.99E 15 7.03E 15 4.00E 01 6.86E 18 5.23E 18 4.00E+03 4.06E 17 4.40E 17 4.00E+07 7.37E 15 7.42E 15 5.00E 01 6.14E 18 4.68E 18 5.00E+03 5.03E 17 5.45E 17 5.00E+07 7.57E 15 7.62E 15 6.00E 01 5.61E 18 4.27E 18 6.00E+03 5.99E 17 6.49E 17 6.00E+07 7.82E 15 7.86E 15 8.00E 01 4.87E 18 3.71E 18 8.00E+03 7.89E 17 8.55E 17 8.00E+07 8.44E 15 8.48E 15 1.00E+00 4.35E 18 3.31E 18 1.00E+04 9.79E 17 1.06E 16 1.00E+08 9.24E 15 9.30E 15 1.50E+00 3.56E 18 2.72E 18 1.50E+04 1.45E 16 1.57E 16 1.50E+08 1.24E 14 1.26E 14 2.00E+00 3.09E 18 2.36E 18 2.00E+04 1.88E 16 2.04E 16 3.00E+00 2.53E 18 1.94E 18 3.00E+04 2.67E 16 2.90E 16 4.00E+00 2.21E 18 1.70E 18 4.00E+04 3.39E 16 3.68E 16 5.00E+00 1.99E 18 1.53E 18 5.00E+04 4.05E 16 4.40E 16 6.00E+00 1.83E 18 1.42E 18 6.00E+04 4.66E 16 5.06E 16 8.00E+00 1.62E 18 1.26E 18 8.00E+04 5.74E 16 6.24E 16

PAGE 56

56 Table A -7. Mandible DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) AM TM50 AM TM50 AM TM50 1.00E 03 3.08E 17 1.56E 17 1.00E+01 1.47E 18 8.27E 19 1.00E+05 5.46E 16 8.71E 16 1.50E 03 3.10E 17 1.57E 17 1.50E+01 1.27E 18 7.68E 19 1.50E+05 6.98E 16 1.13E 15 2.00E 03 3.12E 17 1.58E 17 2.00E+01 1.17E 18 7.58E 19 2.00E+05 8.19E 16 1.33E 15 3.00E 03 3.15E 17 1.60E 17 3.00E+01 1.09E 18 7.99E 19 3.00E+05 1.01E 15 1.65E 15 4.00E 03 3.17E 17 1.61E 17 4.00E+01 1.08E 18 8.78E 19 4.00E+05 1.22E 15 1.94E 15 5.00E 03 3.19E 17 1.62E 17 5.00E+01 1.10E 18 9.74E 19 5.00E+05 1.29E 15 2.11E 15 6.00E 03 3.20E 17 1.62E 17 6.00E+01 1.15E 18 1.08E 18 6.00E+05 1.40E 15 2.29E 15 8.00E 03 3.20E 17 1.63E 17 8.00E+01 1.27E 18 1.31E 18 8.00E+05 1.62E 15 2.59E 15 1.00E 02 3.19E 17 1.62E 17 1.00E+02 1.41E 18 1.54E 18 1.00E+06 1.96E 15 2.93E 15 1.50E 02 3.09E 17 1.57E 17 1.50E+02 1.83E 18 2.17E 18 1.50E+06 2.31E 15 3.34E 15 2.00E 02 2.92E 17 1.48E 17 2.00E+02 2.27E 18 2.80E 18 2.00E+06 2.74E 15 3.72E 15 3.00E 02 2.50E 17 1.27E 17 3.00E+02 3.18E 18 4.09E 18 3.00E+06 3.49E 15 4.34E 15 4.00E 02 2.18E 17 1.10E 17 4.00E+02 4.12E 18 5.39E 18 4.00E+06 4.06E 15 4.73E 15 5.00E 02 1.94E 17 9.85E 18 5.00E+02 5.06E 18 6.69E 18 5.00E+06 4.28E 15 4.74E 15 6.00E 02 1.77E 17 8.96E 18 6.00E+02 5.99E 18 7.99E 18 6.00E+06 4.49E 15 4.91E 15 8.00E 02 1.53E 17 7.77E 18 8.00E+02 7.87E 18 1.06E 17 8.00E+06 5.09E 15 5.40E 15 1.00E 01 1.37E 17 6.94E 18 1.00E+03 9.72E 18 1.32E 17 1.00E+07 5.49E 15 5.70E 15 1.50E 01 1.12E 17 5.69E 18 1.50E+03 1.43E 17 1.96E 17 1.50E+07 6.31E 15 6.53E 15 2.00E 01 9.72E 18 4.93E 18 2.00E+03 1.88E 17 2.60E 17 2.00E+07 6.70E 15 7.00E 15 3.00E 01 7.91E 18 4.02E 18 3.00E+03 2.74E 17 3.87E 17 3.00E+07 7.15E 15 7.49E 15 4.00E 01 6.86E 18 3.48E 18 4.00E+03 3.57E 17 5.12E 17 4.00E+07 7.54E 15 7.86E 15 5.00E 01 6.14E 18 3.12E 18 5.00E+03 4.38E 17 6.36E 17 5.00E+07 7.73E 15 8.06E 15 6.00E 01 5.61E 18 2.85E 18 6.00E+03 5.18E 17 7.60E 17 6.00E+07 7.96E 15 8.28E 15 8.00E 01 4.87E 18 2.48E 18 8.00E+03 6.78E 17 1.01E 16 8.00E+07 8.60E 15 8.93E 15 1.00E+00 4.34E 18 2.21E 18 1.00E+04 8.36E 17 1.25E 16 1.00E+08 9.36E 15 9.76E 15 1.50E+00 3.56E 18 1.82E 18 1.50E+04 1.23E 16 1.86E 16 1.50E+08 1.25E 14 1.33E 14 2.00E+00 3.09E 18 1.58E 18 2.00E+04 1.58E 16 2.42E 16 3.00E+00 2.53E 18 1.31E 18 3.00E+04 2.24E 16 3.45E 16 4.00E+00 2.21E 18 1.15E 18 4.00E+04 2.82E 16 4.39E 16 5.00E+00 1.99E 18 1.05E 18 5.00E+04 3.36E 16 5.25E 16 6.00E+00 1.83E 18 9.77E 19 6.00E+04 3.84E 16 6.05E 16 8.00E+00 1.61E 18 8.84E 19 8.00E+04 4.71E 16 7.46E 16

PAGE 57

57 Table A -8. Pelvis DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) AM TM50 AM TM50 AM TM50 1.00E 03 3.08E 17 1.81E 17 1.00E+01 1.47E 18 9.25E 19 1.00E+05 6.15E 16 7.90E 16 1.50E 03 3.10E 17 1.82E 17 1.50E+01 1.28E 18 8.41E 19 1.50E+05 7.89E 16 1.02E 15 2.00E 03 3.12E 17 1.83E 17 2.00E+01 1.18E 18 8.14E 19 2.00E+05 9.27E 16 1.21E 15 3.00E 03 3.15E 17 1.85E 17 3.00E+01 1.10E 18 8.29E 19 3.00E+05 1.15E 15 1.51E 15 4.00E 03 3.17E 17 1.86E 17 4.00E+01 1.10E 18 8.90E 19 4.00E+05 1.37E 15 1.79E 15 5.00E 03 3.19E 17 1.87E 17 5.00E+01 1.13E 18 9.69E 19 5.00E+05 1.45E 15 1.94E 15 6.00E 03 3.20E 17 1.88E 17 6.00E+01 1.19E 18 1.06E 18 6.00E+05 1.57E 15 2.11E 15 8.00E 03 3.20E 17 1.88E 17 8.00E+01 1.32E 18 1.26E 18 8.00E+05 1.81E 15 2.41E 15 1.00E 02 3.19E 17 1.87E 17 1.00E+02 1.48E 18 1.47E 18 1.00E+06 2.14E 15 2.75E 15 1.50E 02 3.09E 17 1.81E 17 1.50E+02 1.92E 18 2.03E 18 1.50E+06 2.47E 15 3.15E 15 2.00E 02 2.92E 17 1.71E 17 2.00E+02 2.39E 18 2.61E 18 2.00E+06 2.88E 15 3.52E 15 3.00E 02 2.50E 17 1.46E 17 3.00E+02 3.37E 18 3.79E 18 3.00E+06 3.60E 15 4.12E 15 4.00E 02 2.18E 17 1.28E 17 4.00E+02 4.37E 18 4.98E 18 4.00E+06 4.16E 15 4.52E 15 5.00E 02 1.94E 17 1.14E 17 5.00E+02 5.37E 18 6.16E 18 5.00E+06 4.36E 15 4.56E 15 6.00E 02 1.77E 17 1.04E 17 6.00E+02 6.37E 18 7.35E 18 6.00E+06 4.56E 15 4.74E 15 8.00E 02 1.53E 17 8.99E 18 8.00E+02 8.38E 18 9.73E 18 8.00E+06 5.15E 15 5.28E 15 1.00E 01 1.37E 17 8.03E 18 1.00E+03 1.04E 17 1.21E 17 1.00E+07 5.56E 15 5.62E 15 1.50E 01 1.12E 17 6.58E 18 1.50E+03 1.53E 17 1.80E 17 1.50E+07 6.37E 15 6.49E 15 2.00E 01 9.72E 18 5.70E 18 2.00E+03 2.02E 17 2.37E 17 2.00E+07 6.77E 15 6.98E 15 3.00E 01 7.91E 18 4.64E 18 3.00E+03 2.96E 17 3.52E 17 3.00E+07 7.23E 15 7.50E 15 4.00E 01 6.86E 18 4.03E 18 4.00E+03 3.88E 17 4.64E 17 4.00E+07 7.63E 15 7.89E 15 5.00E 01 6.14E 18 3.60E 18 5.00E+03 4.79E 17 5.76E 17 5.00E+07 7.84E 15 8.10E 15 6.00E 01 5.61E 18 3.29E 18 6.00E+03 5.69E 17 6.87E 17 6.00E+07 8.09E 15 8.34E 15 8.00E 01 4.87E 18 2.86E 18 8.00E+03 7.46E 17 9.10E 17 8.00E+07 8.75E 15 9.00E 15 1.00E+00 4.35E 18 2.56E 18 1.00E+04 9.23E 17 1.13E 16 1.00E+08 9.55E 15 9.85E 15 1.50E+00 3.56E 18 2.10E 18 1.50E+04 1.36E 16 1.69E 16 1.50E+08 1.28E 14 1.34E 14 2.00E+00 3.09E 18 1.82E 18 2.00E+04 1.76E 16 2.20E 16 3.00E+00 2.53E 18 1.50E 18 3.00E+04 2.49E 16 3.14E 16 4.00E+00 2.21E 18 1.32E 18 4.00E+04 3.15E 16 3.99E 16 5.00E+00 1.99E 18 1.20E 18 5.00E+04 3.76E 16 4.77E 16 6.00E+00 1.83E 18 1.11E 18 6.00E+04 4.31E 16 5.49E 16 8.00E+00 1.62E 18 9.98E 19 8.00E+04 5.29E 16 6.77E 16

PAGE 58

58 Table A -9. Rib DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) AM TM50 AM TM50 AM TM50 1.00E 03 3.08E 17 2.35E 17 1.00E+01 1.48E 18 1.16E 18 1.00E+05 6.67E 16 7.33E 16 1.50E 03 3.10E 17 2.36E 17 1.50E+01 1.28E 18 1.03E 18 1.50E+05 8.61E 16 9.45E 16 2.00E 03 3.12E 17 2.38E 17 2.00E+01 1.19E 18 9.73E 19 2.00E+05 1.02E 15 1.12E 15 3.00E 03 3.15E 17 2.40E 17 3.00E+01 1.11E 18 9.52E 19 3.00E+05 1.27E 15 1.39E 15 4.00E 03 3.17E 17 2.41E 17 4.00E+01 1.11E 18 9.88E 19 4.00E+05 1.52E 15 1.65E 15 5.00E 03 3.19E 17 2.43E 17 5.00E+01 1.15E 18 1.05E 18 5.00E+05 1.62E 15 1.78E 15 6.00E 03 3.20E 17 2.44E 17 6.00E+01 1.20E 18 1.12E 18 6.00E+05 1.76E 15 1.94E 15 8.00E 03 3.20E 17 2.44E 17 8.00E+01 1.34E 18 1.30E 18 8.00E+05 2.02E 15 2.22E 15 1.00E 02 3.19E 17 2.43E 17 1.00E+02 1.50E 18 1.49E 18 1.00E+06 2.37E 15 2.56E 15 1.50E 02 3.09E 17 2.35E 17 1.50E+02 1.96E 18 2.01E 18 1.50E+06 2.69E 15 2.89E 15 2.00E 02 2.92E 17 2.22E 17 2.00E+02 2.45E 18 2.56E 18 2.00E+06 3.08E 15 3.21E 15 3.00E 02 2.50E 17 1.90E 17 3.00E+02 3.45E 18 3.67E 18 3.00E+06 3.75E 15 3.74E 15 4.00E 02 2.18E 17 1.66E 17 4.00E+02 4.48E 18 4.80E 18 4.00E+06 4.28E 15 4.12E 15 5.00E 02 1.94E 17 1.48E 17 5.00E+02 5.52E 18 5.93E 18 5.00E+06 4.44E 15 4.16E 15 6.00E 02 1.77E 17 1.34E 17 6.00E+02 6.55E 18 7.06E 18 6.00E+06 4.61E 15 4.32E 15 8.00E 02 1.53E 17 1.17E 17 8.00E+02 8.62E 18 9.33E 18 8.00E+06 5.14E 15 4.87E 15 1.00E 01 1.37E 17 1.04E 17 1.00E+03 1.07E 17 1.16E 17 1.00E+07 5.50E 15 5.26E 15 1.50E 01 1.12E 17 8.55E 18 1.50E+03 1.58E 17 1.72E 17 1.50E+07 6.24E 15 6.14E 15 2.00E 01 9.72E 18 7.40E 18 2.00E+03 2.09E 17 2.27E 17 2.00E+07 6.62E 15 6.64E 15 3.00E 01 7.91E 18 6.03E 18 3.00E+03 3.08E 17 3.36E 17 3.00E+07 7.07E 15 7.17E 15 4.00E 01 6.86E 18 5.23E 18 4.00E+03 4.06E 17 4.42E 17 4.00E+07 7.46E 15 7.57E 15 5.00E 01 6.14E 18 4.68E 18 5.00E+03 5.03E 17 5.48E 17 5.00E+07 7.67E 15 7.79E 15 6.00E 01 5.61E 18 4.27E 18 6.00E+03 5.98E 17 6.53E 17 6.00E+07 7.93E 15 8.04E 15 8.00E 01 4.87E 18 3.71E 18 8.00E+03 7.88E 17 8.61E 17 8.00E+07 8.56E 15 8.69E 15 1.00E+00 4.35E 18 3.31E 18 1.00E+04 9.78E 17 1.07E 16 1.00E+08 9.38E 15 9.55E 15 1.50E+00 3.56E 18 2.72E 18 1.50E+04 1.45E 16 1.58E 16 1.50E+08 1.26E 14 1.30E 14 2.00E+00 3.09E 18 2.36E 18 2.00E+04 1.88E 16 2.06E 16 3.00E+00 2.53E 18 1.94E 18 3.00E+04 2.67E 16 2.93E 16 4.00E+00 2.21E 18 1.70E 18 4.00E+04 3.39E 16 3.72E 16 5.00E+00 1.99E 18 1.53E 18 5.00E+04 4.05E 16 4.44E 16 6.00E+00 1.83E 18 1.42E 18 6.00E+04 4.65E 16 5.11E 16 8.00E+00 1.62E 18 1.26E 18 8.00E+04 5.73E 16 6.29E 16

PAGE 59

59 Table A -10. Sacrum DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) AM TM50 AM TM50 AM TM50 1.00E 03 3.08E 17 2.37E 17 1.00E+01 1.48E 18 1.17E 18 1.00E+05 6.68E 16 7.08E 16 1.50E 03 3.10E 17 2.39E 17 1.50E+01 1.28E 18 1.03E 18 1.50E+05 8.62E 16 9.17E 16 2.00E 03 3.12E 17 2.40E 17 2.00E+01 1.19E 18 9.72E 19 2.00E+05 1.02E 15 1.09E 15 3.00E 03 3.15E 17 2.42E 17 3.00E+01 1.11E 18 9.45E 19 3.00E+05 1.27E 15 1.36E 15 4.00E 03 3.17E 17 2.44E 17 4.00E+01 1.11E 18 9.76E 19 4.00E+05 1.52E 15 1.63E 15 5.00E 03 3.19E 17 2.45E 17 5.00E+01 1.15E 18 1.03E 18 5.00E+05 1.62E 15 1.76E 15 6.00E 03 3.20E 17 2.46E 17 6.00E+01 1.20E 18 1.10E 18 6.00E+05 1.76E 15 1.91E 15 8.00E 03 3.20E 17 2.47E 17 8.00E+01 1.34E 18 1.27E 18 8.00E+05 2.02E 15 2.21E 15 1.00E 02 3.19E 17 2.46E 17 1.00E+02 1.50E 18 1.45E 18 1.00E+06 2.38E 15 2.56E 15 1.50E 02 3.09E 17 2.38E 17 1.50E+02 1.96E 18 1.95E 18 1.50E+06 2.70E 15 2.93E 15 2.00E 02 2.92E 17 2.25E 17 2.00E+02 2.45E 18 2.47E 18 2.00E+06 3.09E 15 3.29E 15 3.00E 02 2.50E 17 1.92E 17 3.00E+02 3.45E 18 3.54E 18 3.00E+06 3.77E 15 3.86E 15 4.00E 02 2.18E 17 1.68E 17 4.00E+02 4.48E 18 4.63E 18 4.00E+06 4.31E 15 4.27E 15 5.00E 02 1.94E 17 1.50E 17 5.00E+02 5.51E 18 5.71E 18 5.00E+06 4.49E 15 4.33E 15 6.00E 02 1.77E 17 1.36E 17 6.00E+02 6.55E 18 6.80E 18 6.00E+06 4.67E 15 4.49E 15 8.00E 02 1.53E 17 1.18E 17 8.00E+02 8.62E 18 8.97E 18 8.00E+06 5.22E 15 5.03E 15 1.00E 01 1.37E 17 1.05E 17 1.00E+03 1.07E 17 1.11E 17 1.00E+07 5.60E 15 5.42E 15 1.50E 01 1.12E 17 8.64E 18 1.50E+03 1.58E 17 1.65E 17 1.50E+07 6.35E 15 6.30E 15 2.00E 01 9.72E 18 7.48E 18 2.00E+03 2.09E 17 2.18E 17 2.00E+07 6.74E 15 6.79E 15 3.00E 01 7.91E 18 6.09E 18 3.00E+03 3.08E 17 3.21E 17 3.00E+07 7.21E 15 7.31E 15 4.00E 01 6.86E 18 5.29E 18 4.00E+03 4.06E 17 4.23E 17 4.00E+07 7.60E 15 7.72E 15 5.00E 01 6.14E 18 4.73E 18 5.00E+03 5.02E 17 5.24E 17 5.00E+07 7.82E 15 7.95E 15 6.00E 01 5.61E 18 4.32E 18 6.00E+03 5.98E 17 6.24E 17 6.00E+07 8.09E 15 8.22E 15 8.00E 01 4.87E 18 3.75E 18 8.00E+03 7.88E 17 8.26E 17 8.00E+07 8.75E 15 8.89E 15 1.00E+00 4.35E 18 3.35E 18 1.00E+04 9.78E 17 1.03E 16 1.00E+08 9.59E 15 9.77E 15 1.50E+00 3.56E 18 2.75E 18 1.50E+04 1.45E 16 1.53E 16 1.50E+08 1.29E 14 1.33E 14 2.00E+00 3.09E 18 2.38E 18 2.00E+04 1.88E 16 1.99E 16 3.00E+00 2.53E 18 1.96E 18 3.00E+04 2.67E 16 2.84E 16 4.00E+00 2.21E 18 1.72E 18 4.00E+04 3.39E 16 3.60E 16 5.00E+00 1.99E 18 1.55E 18 5.00E+04 4.05E 16 4.29E 16 6.00E+00 1.83E 18 1.43E 18 6.00E+04 4.65E 16 4.93E 16 8.00E+00 1.62E 18 1.27E 18 8.00E+04 5.73E 16 6.07E 16

PAGE 60

60 Table A -11. Scapula DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) AM TM50 AM TM50 AM TM50 1.00E 03 3.08E 17 1.56E 17 1.00E+01 1.47E 18 8.17E 19 1.00E+05 5.73E 16 8.06E 16 1.50E 03 3.10E 17 1.57E 17 1.50E+01 1.27E 18 7.54E 19 1.50E+05 7.32E 16 1.04E 15 2.00E 03 3.12E 17 1.58E 17 2.00E+01 1.18E 18 7.40E 19 2.00E+05 8.58E 16 1.24E 15 3.00E 03 3.15E 17 1.60E 17 3.00E+01 1.10E 18 7.71E 19 3.00E+05 1.06E 15 1.54E 15 4.00E 03 3.17E 17 1.61E 17 4.00E+01 1.09E 18 8.41E 19 4.00E+05 1.27E 15 1.82E 15 5.00E 03 3.19E 17 1.62E 17 5.00E+01 1.12E 18 9.28E 19 5.00E+05 1.34E 15 1.97E 15 6.00E 03 3.20E 17 1.62E 17 6.00E+01 1.17E 18 1.02E 18 6.00E+05 1.45E 15 2.14E 15 8.00E 03 3.20E 17 1.63E 17 8.00E+01 1.30E 18 1.23E 18 8.00E+05 1.67E 15 2.44E 15 1.00E 02 3.19E 17 1.62E 17 1.00E+02 1.45E 18 1.45E 18 1.00E+06 2.00E 15 2.78E 15 1.50E 02 3.09E 17 1.57E 17 1.50E+02 1.88E 18 2.03E 18 1.50E+06 2.34E 15 3.18E 15 2.00E 02 2.92E 17 1.48E 17 2.00E+02 2.34E 18 2.62E 18 2.00E+06 2.76E 15 3.56E 15 3.00E 02 2.50E 17 1.27E 17 3.00E+02 3.29E 18 3.82E 18 3.00E+06 3.48E 15 4.16E 15 4.00E 02 2.18E 17 1.10E 17 4.00E+02 4.26E 18 5.02E 18 4.00E+06 4.04E 15 4.57E 15 5.00E 02 1.94E 17 9.85E 18 5.00E+02 5.23E 18 6.23E 18 5.00E+06 4.23E 15 4.58E 15 6.00E 02 1.77E 17 8.96E 18 6.00E+02 6.20E 18 7.44E 18 6.00E+06 4.44E 15 4.74E 15 8.00E 02 1.53E 17 7.77E 18 8.00E+02 8.15E 18 9.85E 18 8.00E+06 5.02E 15 5.23E 15 1.00E 01 1.37E 17 6.94E 18 1.00E+03 1.01E 17 1.23E 17 1.00E+07 5.41E 15 5.55E 15 1.50E 01 1.12E 17 5.69E 18 1.50E+03 1.48E 17 1.82E 17 1.50E+07 6.19E 15 6.35E 15 2.00E 01 9.72E 18 4.93E 18 2.00E+03 1.95E 17 2.41E 17 2.00E+07 6.57E 15 6.84E 15 3.00E 01 7.91E 18 4.01E 18 3.00E+03 2.85E 17 3.58E 17 3.00E+07 7.03E 15 7.37E 15 4.00E 01 6.86E 18 3.48E 18 4.00E+03 3.73E 17 4.73E 17 4.00E+07 7.43E 15 7.75E 15 5.00E 01 6.14E 18 3.12E 18 5.00E+03 4.58E 17 5.87E 17 5.00E+07 7.63E 15 7.97E 15 6.00E 01 5.61E 18 2.85E 18 6.00E+03 5.43E 17 7.01E 17 6.00E+07 7.89E 15 8.21E 15 8.00E 01 4.87E 18 2.48E 18 8.00E+03 7.10E 17 9.29E 17 8.00E+07 8.56E 15 8.87E 15 1.00E+00 4.34E 18 2.21E 18 1.00E+04 8.76E 17 1.16E 16 1.00E+08 9.36E 15 9.74E 15 1.50E+00 3.56E 18 1.82E 18 1.50E+04 1.29E 16 1.72E 16 1.50E+08 1.26E 14 1.33E 14 2.00E+00 3.09E 18 1.58E 18 2.00E+04 1.66E 16 2.25E 16 3.00E+00 2.53E 18 1.31E 18 3.00E+04 2.34E 16 3.20E 16 4.00E+00 2.21E 18 1.15E 18 4.00E+04 2.96E 16 4.07E 16 5.00E+00 1.99E 18 1.04E 18 5.00E+04 3.52E 16 4.87E 16 6.00E+00 1.83E 18 9.71E 19 6.00E+04 4.03E 16 5.60E 16 8.00E+00 1.62E 18 8.77E 19 8.00E+04 4.94E 16 6.91E 16

PAGE 61

61 Table A -12. Sternum DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) AM TM50 AM TM50 AM TM50 1.00E 03 3.08E 17 2.35E 17 1.00E+01 1.48E 18 1.15E 18 1.00E+05 6.64E 16 7.15E 16 1.50E 03 3.10E 17 2.36E 17 1.50E+01 1.28E 18 1.02E 18 1.50E+05 8.57E 16 9.28E 16 2.00E 03 3.12E 17 2.37E 17 2.00E+01 1.19E 18 9.62E 19 2.00E+05 1.01E 15 1.10E 15 3.00E 03 3.15E 17 2.40E 17 3.00E+01 1.11E 18 9.35E 19 3.00E+05 1.26E 15 1.38E 15 4.00E 03 3.17E 17 2.41E 17 4.00E+01 1.11E 18 9.66E 19 4.00E+05 1.51E 15 1.65E 15 5.00E 03 3.19E 17 2.43E 17 5.00E+01 1.15E 18 1.02E 18 5.00E+05 1.61E 15 1.78E 15 6.00E 03 3.20E 17 2.43E 17 6.00E+01 1.20E 18 1.09E 18 6.00E+05 1.75E 15 1.94E 15 8.00E 03 3.20E 17 2.44E 17 8.00E+01 1.34E 18 1.26E 18 8.00E+05 2.01E 15 2.23E 15 1.00E 02 3.19E 17 2.43E 17 1.00E+02 1.50E 18 1.44E 18 1.00E+06 2.36E 15 2.59E 15 1.50E 02 3.09E 17 2.35E 17 1.50E+02 1.96E 18 1.93E 18 1.50E+06 2.69E 15 2.96E 15 2.00E 02 2.92E 17 2.22E 17 2.00E+02 2.44E 18 2.45E 18 2.00E+06 3.08E 15 3.33E 15 3.00E 02 2.50E 17 1.90E 17 3.00E+02 3.45E 18 3.51E 18 3.00E+06 3.77E 15 3.91E 15 4.00E 02 2.18E 17 1.66E 17 4.00E+02 4.48E 18 4.59E 18 4.00E+06 4.32E 15 4.33E 15 5.00E 02 1.94E 17 1.48E 17 5.00E+02 5.51E 18 5.67E 18 5.00E+06 4.51E 15 4.41E 15 6.00E 02 1.77E 17 1.34E 17 6.00E+02 6.54E 18 6.75E 18 6.00E+06 4.71E 15 4.59E 15 8.00E 02 1.53E 17 1.17E 17 8.00E+02 8.61E 18 8.91E 18 8.00E+06 5.28E 15 5.17E 15 1.00E 01 1.37E 17 1.04E 17 1.00E+03 1.07E 17 1.11E 17 1.00E+07 5.68E 15 5.55E 15 1.50E 01 1.12E 17 8.54E 18 1.50E+03 1.58E 17 1.64E 17 1.50E+07 6.47E 15 6.43E 15 2.00E 01 9.72E 18 7.40E 18 2.00E+03 2.08E 17 2.17E 17 2.00E+07 6.87E 15 6.92E 15 3.00E 01 7.91E 18 6.02E 18 3.00E+03 3.08E 17 3.22E 17 3.00E+07 7.33E 15 7.43E 15 4.00E 01 6.86E 18 5.23E 18 4.00E+03 4.05E 17 4.25E 17 4.00E+07 7.72E 15 7.83E 15 5.00E 01 6.14E 18 4.67E 18 5.00E+03 5.01E 17 5.27E 17 5.00E+07 7.93E 15 8.05E 15 6.00E 01 5.61E 18 4.27E 18 6.00E+03 5.96E 17 6.28E 17 6.00E+07 8.20E 15 8.31E 15 8.00E 01 4.87E 18 3.71E 18 8.00E+03 7.86E 17 8.29E 17 8.00E+07 8.85E 15 8.97E 15 1.00E+00 4.35E 18 3.31E 18 1.00E+04 9.75E 17 1.03E 16 1.00E+08 9.67E 15 9.83E 15 1.50E+00 3.56E 18 2.72E 18 1.50E+04 1.44E 16 1.53E 16 1.50E+08 1.30E 14 1.33E 14 2.00E+00 3.09E 18 2.36E 18 2.00E+04 1.87E 16 1.99E 16 3.00E+00 2.53E 18 1.94E 18 3.00E+04 2.66E 16 2.83E 16 4.00E+00 2.21E 18 1.70E 18 4.00E+04 3.38E 16 3.60E 16 5.00E+00 1.99E 18 1.53E 18 5.00E+04 4.03E 16 4.31E 16 6.00E+00 1.83E 18 1.41E 18 6.00E+04 4.63E 16 4.96E 16 8.00E+00 1.62E 18 1.26E 18 8.00E+04 5.70E 16 6.12E 16

PAGE 62

62 Table A -13. Thoracic vertebra DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) AM TM50 AM TM50 AM TM50 1.00E 03 3.08E 17 2.35E 17 1.00E+01 1.48E 18 1.16E 18 1.00E+05 6.67E 16 7.35E 16 1.50E 03 3.10E 17 2.36E 17 1.50E+01 1.28E 18 1.03E 18 1.50E+05 8.61E 16 9.51E 16 2.00E 03 3.12E 17 2.38E 17 2.00E+01 1.19E 18 9.74E 19 2.00E+05 1.02E 15 1.12E 15 3.00E 03 3.15E 17 2.40E 17 3.00E+01 1.11E 18 9.54E 19 3.00E+05 1.27E 15 1.40E 15 4.00E 03 3.17E 17 2.41E 17 4.00E+01 1.11E 18 9.91E 19 4.00E+05 1.52E 15 1.67E 15 5.00E 03 3.19E 17 2.43E 17 5.00E+01 1.15E 18 1.05E 18 5.00E+05 1.62E 15 1.80E 15 6.00E 03 3.20E 17 2.44E 17 6.00E+01 1.20E 18 1.13E 18 6.00E+05 1.76E 15 1.95E 15 8.00E 03 3.20E 17 2.44E 17 8.00E+01 1.34E 18 1.31E 18 8.00E+05 2.02E 15 2.23E 15 1.00E 02 3.19E 17 2.43E 17 1.00E+02 1.50E 18 1.50E 18 1.00E+06 2.38E 15 2.57E 15 1.50E 02 3.09E 17 2.35E 17 1.50E+02 1.96E 18 2.03E 18 1.50E+06 2.70E 15 2.90E 15 2.00E 02 2.92E 17 2.22E 17 2.00E+02 2.45E 18 2.57E 18 2.00E+06 3.09E 15 3.23E 15 3.00E 02 2.50E 17 1.90E 17 3.00E+02 3.45E 18 3.70E 18 3.00E+06 3.77E 15 3.78E 15 4.00E 02 2.18E 17 1.66E 17 4.00E+02 4.48E 18 4.83E 18 4.00E+06 4.31E 15 4.19E 15 5.00E 02 1.94E 17 1.48E 17 5.00E+02 5.51E 18 5.97E 18 5.00E+06 4.49E 15 4.26E 15 6.00E 02 1.77E 17 1.34E 17 6.00E+02 6.55E 18 7.11E 18 6.00E+06 4.68E 15 4.44E 15 8.00E 02 1.53E 17 1.17E 17 8.00E+02 8.62E 18 9.39E 18 8.00E+06 5.24E 15 5.02E 15 1.00E 01 1.37E 17 1.04E 17 1.00E+03 1.07E 17 1.17E 17 1.00E+07 5.63E 15 5.42E 15 1.50E 01 1.12E 17 8.55E 18 1.50E+03 1.58E 17 1.73E 17 1.50E+07 6.40E 15 6.32E 15 2.00E 01 9.72E 18 7.40E 18 2.00E+03 2.09E 17 2.28E 17 2.00E+07 6.79E 15 6.83E 15 3.00E 01 7.91E 18 6.03E 18 3.00E+03 3.08E 17 3.38E 17 3.00E+07 7.25E 15 7.37E 15 4.00E 01 6.86E 18 5.23E 18 4.00E+03 4.06E 17 4.46E 17 4.00E+07 7.64E 15 7.77E 15 5.00E 01 6.14E 18 4.68E 18 5.00E+03 5.02E 17 5.52E 17 5.00E+07 7.85E 15 7.99E 15 6.00E 01 5.61E 18 4.27E 18 6.00E+03 5.98E 17 6.57E 17 6.00E+07 8.11E 15 8.24E 15 8.00E 01 4.87E 18 3.71E 18 8.00E+03 7.88E 17 8.66E 17 8.00E+07 8.76E 15 8.90E 15 1.00E+00 4.35E 18 3.31E 18 1.00E+04 9.77E 17 1.07E 16 1.00E+08 9.58E 15 9.76E 15 1.50E+00 3.56E 18 2.72E 18 1.50E+04 1.45E 16 1.59E 16 1.50E+08 1.29E 14 1.32E 14 2.00E+00 3.09E 18 2.36E 18 2.00E+04 1.88E 16 2.06E 16 3.00E+00 2.53E 18 1.94E 18 3.00E+04 2.67E 16 2.93E 16 4.00E+00 2.21E 18 1.70E 18 4.00E+04 3.39E 16 3.72E 16 5.00E+00 1.99E 18 1.54E 18 5.00E+04 4.04E 16 4.44E 16 6.00E+00 1.83E 18 1.42E 18 6.00E+04 4.65E 16 5.11E 16 8.00E+00 1.62E 18 1.26E 18 8.00E+04 5.72E 16 6.30E 16

PAGE 63

63 Figure A 1 Cervical vertebra kerma coefficients and DRFs Figure A 2 Cervical vertebra percent RD

PAGE 64

64 Figure A 3. Clavicle kerma coefficients and DRFs Figure A 4. Clavicle percent RD

PAGE 65

65 Figure A 5. Cranium kerma coefficients and DRFs Figure A6. Cranium percent RD

PAGE 66

66 Figure A 7. Proximal femur kerma coefficients and DRFs Figure A 8. Proximal femur percent RD

PAGE 67

67 Figure A 9. Proximal humerus kerma coefficients and DRFs Figure A 10. Proximal humerus percent RD

PAGE 68

68 Figure A11. Lumbar vertebra kerma coefficients and DRFs Figure A 12. Lumbar vertebra percent RD

PAGE 69

69 Figure A 13. Mandible kerma coefficients and DRFs Figure A 14. Mandible percent RD

PAGE 70

70 Figure A 15. Pelvis kerma coefficients and DRFs Figure A 16. Pelvis percent RD

PAGE 71

71 Figure A 17. Rib kerma coefficients and DRFs Figure A 18. Rib percent RD

PAGE 72

72 Figure A 19. Sacrum kerma coefficients and DRFs Figure A 20. Sacrum percent RD

PAGE 73

73 Figure A 21. Scapula kerma coefficients and DRFs Figure A 22. Scapula percent RD

PAGE 74

74 Figure A 23. Sternum kerma coefficients and DRFs Figure A 24. Sternum percent RD

PAGE 75

75 Figure A 25. Thoracic vertebra kerma coefficients and DRFs Figure A 26. Thoracic vertebra percent RD

PAGE 76

76 APPENDIX B APPENDICULAR SKELETAL NEUTRON DRF DATA The following tables and plots present skeletal neutron DRF data and RD data for the appendicular skeleton. The skeletal sites addressed in this section are Ankle and foot, Distal femur, Proximal fibula, Distal fibula, Distal humerus, Patella, Proximal radius, Distal radius, Proximal tibia Distal tibia, Proximal ulna, Distal ulna, and Wrist and hand.

PAGE 77

77 Table B -1. Ankle and foot DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) TM50 TM50 TM50 1.00E 03 6.33E 18 1.00E+01 4.00E 19 1.00E+05 7.41E 16 1.50E 03 6.37E 18 1.50E+01 4.09E 19 1.50E+05 9.57E 16 2.00E 03 6.40E 18 2.00E+01 4.37E 19 2.00E+05 1.13E 15 3.00E 03 6.46E 18 3.00E+01 5.19E 19 3.00E+05 1.41E 15 4.00E 03 6.51E 18 4.00E+01 6.16E 19 4.00E+05 1.66E 15 5.00E 03 6.54E 18 5.00E+01 7.20E 19 5.00E+05 1.82E 15 6.00E 03 6.57E 18 6.00E+01 8.28E 19 6.00E+05 1.99E 15 8.00E 03 6.58E 18 8.00E+01 1.05E 18 8.00E+05 2.28E 15 1.00E 02 6.55E 18 1.00E+02 1.28E 18 1.00E+06 2.59E 15 1.50E 02 6.34E 18 1.50E+02 1.85E 18 1.50E+06 3.01E 15 2.00E 02 5.99E 18 2.00E+02 2.43E 18 2.00E+06 3.37E 15 3.00E 02 5.13E 18 3.00E+02 3.60E 18 3.00E+06 3.98E 15 4.00E 02 4.47E 18 4.00E+02 4.76E 18 4.00E+06 4.36E 15 5.00E 02 3.99E 18 5.00E+02 5.92E 18 5.00E+06 4.36E 15 6.00E 02 3.63E 18 6.00E+02 7.08E 18 6.00E+06 4.58E 15 8.00E 02 3.15E 18 8.00E+02 9.39E 18 8.00E+06 5.18E 15 1.00E 01 2.81E 18 1.00E+03 1.17E 17 1.00E+07 5.52E 15 1.50E 01 2.31E 18 1.50E+03 1.73E 17 1.50E+07 6.53E 15 2.00E 01 2.00E 18 2.00E+03 2.29E 17 2.00E+07 7.12E 15 3.00E 01 1.63E 18 3.00E+03 3.37E 17 3.00E+07 7.72E 15 4.00E 01 1.41E 18 4.00E+03 4.43E 17 4.00E+07 8.11E 15 5.00E 01 1.27E 18 5.00E+03 5.48E 17 5.00E+07 8.33E 15 6.00E 01 1.16E 18 6.00E+03 6.52E 17 6.00E+07 8.55E 15 8.00E 01 1.01E 18 8.00E+03 8.61E 17 8.00E+07 9.24E 15 1.00E+00 9.02E 19 1.00E+04 1.07E 16 1.00E+08 1.01E 14 1.50E+00 7.46E 19 1.50E+04 1.59E 16 1.50E+08 1.39E 14 2.00E+00 6.54E 19 2.00E+04 2.08E 16 3.00E+00 5.49E 19 3.00E+04 2.96E 16 4.00E+00 4.93E 19 4.00E+04 3.76E 16 5.00E+00 4.57E 19 5.00E+04 4.49E 16 6.00E+00 4.34E 19 6.00E+04 5.16E 16 8.00E+00 4.10E 19 8.00E+04 6.36E 16

PAGE 78

78 Table B -2. Distal femur DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) TM50 TM50 TM50 1.00E 03 6.33E 18 1.00E+01 4.00E 19 1.00E+05 7.41E 16 1.50E 03 6.37E 18 1.50E+01 4.09E 19 1.50E+05 9.57E 16 2.00E 03 6.40E 18 2.00E+01 4.37E 19 2.00E+05 1.13E 15 3.00E 03 6.46E 18 3.00E+01 5.19E 19 3.00E+05 1.41E 15 4.00E 03 6.51E 18 4.00E+01 6.16E 19 4.00E+05 1.66E 15 5.00E 03 6.54E 18 5.00E+01 7.20E 19 5.00E+05 1.82E 15 6.00E 03 6.57E 18 6.00E+01 8.28E 19 6.00E+05 1.99E 15 8.00E 03 6.58E 18 8.00E+01 1.05E 18 8.00E+05 2.28E 15 1.00E 02 6.55E 18 1.00E+02 1.28E 18 1.00E+06 2.59E 15 1.50E 02 6.34E 18 1.50E+02 1.85E 18 1.50E+06 3.01E 15 2.00E 02 5.99E 18 2.00E+02 2.43E 18 2.00E+06 3.37E 15 3.00E 02 5.13E 18 3.00E+02 3.60E 18 3.00E+06 3.98E 15 4.00E 02 4.47E 18 4.00E+02 4.76E 18 4.00E+06 4.36E 15 5.00E 02 3.99E 18 5.00E+02 5.92E 18 5.00E+06 4.36E 15 6.00E 02 3.63E 18 6.00E+02 7.08E 18 6.00E+06 4.58E 15 8.00E 02 3.15E 18 8.00E+02 9.39E 18 8.00E+06 5.18E 15 1.00E 01 2.81E 18 1.00E+03 1.17E 17 1.00E+07 5.52E 15 1.50E 01 2.31E 18 1.50E+03 1.73E 17 1.50E+07 6.53E 15 2.00E 01 2.00E 18 2.00E+03 2.29E 17 2.00E+07 7.12E 15 3.00E 01 1.63E 18 3.00E+03 3.37E 17 3.00E+07 7.72E 15 4.00E 01 1.41E 18 4.00E+03 4.43E 17 4.00E+07 8.11E 15 5.00E 01 1.27E 18 5.00E+03 5.48E 17 5.00E+07 8.33E 15 6.00E 01 1.16E 18 6.00E+03 6.52E 17 6.00E+07 8.55E 15 8.00E 01 1.01E 18 8.00E+03 8.61E 17 8.00E+07 9.24E 15 1.00E+00 9.02E 19 1.00E+04 1.07E 16 1.00E+08 1.01E 14 1.50E+00 7.46E 19 1.50E+04 1.59E 16 1.50E+08 1.39E 14 2.00E+00 6.54E 19 2.00E+04 2.08E 16 3.00E+00 5.49E 19 3.00E+04 2.96E 16 4.00E+00 4.93E 19 4.00E+04 3.76E 16 5.00E+00 4.57E 19 5.00E+04 4.49E 16 6.00E+00 4.34E 19 6.00E+04 5.16E 16 8.00E+00 4.10E 19 8.00E+04 6.36E 16

PAGE 79

79 Table B -3. Proximal fibula DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) TM50 TM50 TM50 1.00E 03 6.33E 18 1.00E+01 4.02E 19 1.00E+05 7.38E 16 1.50E 03 6.37E 18 1.50E+01 4.11E 19 1.50E+05 9.53E 16 2.00E 03 6.40E 18 2.00E+01 4.41E 19 2.00E+05 1.13E 15 3.00E 03 6.46E 18 3.00E+01 5.24E 19 3.00E+05 1.41E 15 4.00E 03 6.51E 18 4.00E+01 6.23E 19 4.00E+05 1.66E 15 5.00E 03 6.54E 18 5.00E+01 7.28E 19 5.00E+05 1.82E 15 6.00E 03 6.57E 18 6.00E+01 8.38E 19 6.00E+05 1.99E 15 8.00E 03 6.58E 18 8.00E+01 1.06E 18 8.00E+05 2.28E 15 1.00E 02 6.55E 18 1.00E+02 1.29E 18 1.00E+06 2.59E 15 1.50E 02 6.34E 18 1.50E+02 1.88E 18 1.50E+06 3.02E 15 2.00E 02 5.99E 18 2.00E+02 2.46E 18 2.00E+06 3.36E 15 3.00E 02 5.13E 18 3.00E+02 3.64E 18 3.00E+06 3.96E 15 4.00E 02 4.47E 18 4.00E+02 4.82E 18 4.00E+06 4.34E 15 5.00E 02 3.99E 18 5.00E+02 6.00E 18 5.00E+06 4.35E 15 6.00E 02 3.63E 18 6.00E+02 7.16E 18 6.00E+06 4.59E 15 8.00E 02 3.15E 18 8.00E+02 9.49E 18 8.00E+06 5.23E 15 1.00E 01 2.81E 18 1.00E+03 1.18E 17 1.00E+07 5.60E 15 1.50E 01 2.31E 18 1.50E+03 1.75E 17 1.50E+07 6.65E 15 2.00E 01 2.00E 18 2.00E+03 2.30E 17 2.00E+07 7.23E 15 3.00E 01 1.63E 18 3.00E+03 3.38E 17 3.00E+07 7.80E 15 4.00E 01 1.41E 18 4.00E+03 4.43E 17 4.00E+07 8.19E 15 5.00E 01 1.27E 18 5.00E+03 5.46E 17 5.00E+07 8.39E 15 6.00E 01 1.16E 18 6.00E+03 6.49E 17 6.00E+07 8.59E 15 8.00E 01 1.01E 18 8.00E+03 8.57E 17 8.00E+07 9.26E 15 1.00E+00 9.02E 19 1.00E+04 1.07E 16 1.00E+08 1.01E 14 1.50E+00 7.46E 19 1.50E+04 1.59E 16 1.50E+08 1.38E 14 2.00E+00 6.54E 19 2.00E+04 2.07E 16 3.00E+00 5.50E 19 3.00E+04 2.95E 16 4.00E+00 4.94E 19 4.00E+04 3.75E 16 5.00E+00 4.58E 19 5.00E+04 4.48E 16 6.00E+00 4.35E 19 6.00E+04 5.15E 16 8.00E+00 4.11E 19 8.00E+04 6.34E 16

PAGE 80

80 Table B -4. Distal fibula DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) TM50 TM50 TM50 1.00E 03 6.33E 18 1.00E+01 4.00E 19 1.00E+05 7.40E 16 1.50E 03 6.37E 18 1.50E+01 4.09E 19 1.50E+05 9.56E 16 2.00E 03 6.40E 18 2.00E+01 4.37E 19 2.00E+05 1.13E 15 3.00E 03 6.46E 18 3.00E+01 5.19E 19 3.00E+05 1.41E 15 4.00E 03 6.51E 18 4.00E+01 6.16E 19 4.00E+05 1.66E 15 5.00E 03 6.54E 18 5.00E+01 7.20E 19 5.00E+05 1.82E 15 6.00E 03 6.57E 18 6.00E+01 8.27E 19 6.00E+05 1.99E 15 8.00E 03 6.58E 18 8.00E+01 1.05E 18 8.00E+05 2.28E 15 1.00E 02 6.55E 18 1.00E+02 1.27E 18 1.00E+06 2.59E 15 1.50E 02 6.34E 18 1.50E+02 1.85E 18 1.50E+06 3.01E 15 2.00E 02 5.99E 18 2.00E+02 2.43E 18 2.00E+06 3.36E 15 3.00E 02 5.13E 18 3.00E+02 3.59E 18 3.00E+06 3.96E 15 4.00E 02 4.47E 18 4.00E+02 4.76E 18 4.00E+06 4.33E 15 5.00E 02 3.99E 18 5.00E+02 5.92E 18 5.00E+06 4.33E 15 6.00E 02 3.63E 18 6.00E+02 7.08E 18 6.00E+06 4.55E 15 8.00E 02 3.15E 18 8.00E+02 9.38E 18 8.00E+06 5.14E 15 1.00E 01 2.81E 18 1.00E+03 1.17E 17 1.00E+07 5.47E 15 1.50E 01 2.31E 18 1.50E+03 1.73E 17 1.50E+07 6.49E 15 2.00E 01 2.00E 18 2.00E+03 2.28E 17 2.00E+07 7.08E 15 3.00E 01 1.63E 18 3.00E+03 3.37E 17 3.00E+07 7.65E 15 4.00E 01 1.41E 18 4.00E+03 4.43E 17 4.00E+07 8.04E 15 5.00E 01 1.27E 18 5.00E+03 5.48E 17 5.00E+07 8.25E 15 6.00E 01 1.16E 18 6.00E+03 6.52E 17 6.00E+07 8.46E 15 8.00E 01 1.01E 18 8.00E+03 8.61E 17 8.00E+07 9.15E 15 1.00E+00 9.02E 19 1.00E+04 1.07E 16 1.00E+08 1.00E 14 1.50E+00 7.46E 19 1.50E+04 1.60E 16 1.50E+08 1.38E 14 2.00E+00 6.54E 19 2.00E+04 2.08E 16 3.00E+00 5.49E 19 3.00E+04 2.96E 16 4.00E+00 4.93E 19 4.00E+04 3.76E 16 5.00E+00 4.57E 19 5.00E+04 4.49E 16 6.00E+00 4.34E 19 6.00E+04 5.16E 16 8.00E+00 4.10E 19 8.00E+04 6.35E 16

PAGE 81

81 Table B -5. Distal humerus DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) TM50 TM50 TM50 1.00E 03 6.33E 18 1.00E+01 4.00E 19 1.00E+05 7.42E 16 1.50E 03 6.37E 18 1.50E+01 4.09E 19 1.50E+05 9.58E 16 2.00E 03 6.40E 18 2.00E+01 4.38E 19 2.00E+05 1.13E 15 3.00E 03 6.46E 18 3.00E+01 5.19E 19 3.00E+05 1.41E 15 4.00E 03 6.51E 18 4.00E+01 6.17E 19 4.00E+05 1.67E 15 5.00E 03 6.54E 18 5.00E+01 7.21E 19 5.00E+05 1.82E 15 6.00E 03 6.57E 18 6.00E+01 8.29E 19 6.00E+05 1.99E 15 8.00E 03 6.58E 18 8.00E+01 1.05E 18 8.00E+05 2.28E 15 1.00E 02 6.55E 18 1.00E+02 1.28E 18 1.00E+06 2.60E 15 1.50E 02 6.34E 18 1.50E+02 1.85E 18 1.50E+06 3.02E 15 2.00E 02 5.99E 18 2.00E+02 2.43E 18 2.00E+06 3.37E 15 3.00E 02 5.13E 18 3.00E+02 3.60E 18 3.00E+06 3.98E 15 4.00E 02 4.47E 18 4.00E+02 4.77E 18 4.00E+06 4.36E 15 5.00E 02 3.99E 18 5.00E+02 5.93E 18 5.00E+06 4.35E 15 6.00E 02 3.63E 18 6.00E+02 7.09E 18 6.00E+06 4.58E 15 8.00E 02 3.15E 18 8.00E+02 9.40E 18 8.00E+06 5.18E 15 1.00E 01 2.81E 18 1.00E+03 1.17E 17 1.00E+07 5.51E 15 1.50E 01 2.31E 18 1.50E+03 1.73E 17 1.50E+07 6.52E 15 2.00E 01 2.00E 18 2.00E+03 2.29E 17 2.00E+07 7.11E 15 3.00E 01 1.63E 18 3.00E+03 3.38E 17 3.00E+07 7.69E 15 4.00E 01 1.41E 18 4.00E+03 4.44E 17 4.00E+07 8.09E 15 5.00E 01 1.27E 18 5.00E+03 5.49E 17 5.00E+07 8.31E 15 6.00E 01 1.16E 18 6.00E+03 6.54E 17 6.00E+07 8.53E 15 8.00E 01 1.01E 18 8.00E+03 8.63E 17 8.00E+07 9.23E 15 1.00E+00 9.02E 19 1.00E+04 1.08E 16 1.00E+08 1.01E 14 1.50E+00 7.46E 19 1.50E+04 1.60E 16 1.50E+08 1.39E 14 2.00E+00 6.54E 19 2.00E+04 2.08E 16 3.00E+00 5.49E 19 3.00E+04 2.96E 16 4.00E+00 4.93E 19 4.00E+04 3.76E 16 5.00E+00 4.58E 19 5.00E+04 4.49E 16 6.00E+00 4.35E 19 6.00E+04 5.17E 16 8.00E+00 4.10E 19 8.00E+04 6.36E 16

PAGE 82

82 Table B -6. Patella DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) TM50 TM50 TM50 1.00E 03 6.33E 18 1.00E+01 4.00E 19 1.00E+05 7.41E 16 1.50E 03 6.37E 18 1.50E+01 4.09E 19 1.50E+05 9.57E 16 2.00E 03 6.40E 18 2.00E+01 4.37E 19 2.00E+05 1.13E 15 3.00E 03 6.46E 18 3.00E+01 5.19E 19 3.00E+05 1.41E 15 4.00E 03 6.51E 18 4.00E+01 6.16E 19 4.00E+05 1.66E 15 5.00E 03 6.54E 18 5.00E+01 7.20E 19 5.00E+05 1.82E 15 6.00E 03 6.57E 18 6.00E+01 8.28E 19 6.00E+05 1.99E 15 8.00E 03 6.58E 18 8.00E+01 1.05E 18 8.00E+05 2.28E 15 1.00E 02 6.55E 18 1.00E+02 1.28E 18 1.00E+06 2.59E 15 1.50E 02 6.34E 18 1.50E+02 1.85E 18 1.50E+06 3.01E 15 2.00E 02 5.99E 18 2.00E+02 2.43E 18 2.00E+06 3.37E 15 3.00E 02 5.13E 18 3.00E+02 3.60E 18 3.00E+06 3.98E 15 4.00E 02 4.47E 18 4.00E+02 4.76E 18 4.00E+06 4.36E 15 5.00E 02 3.99E 18 5.00E+02 5.92E 18 5.00E+06 4.36E 15 6.00E 02 3.63E 18 6.00E+02 7.08E 18 6.00E+06 4.58E 15 8.00E 02 3.15E 18 8.00E+02 9.39E 18 8.00E+06 5.18E 15 1.00E 01 2.81E 18 1.00E+03 1.17E 17 1.00E+07 5.52E 15 1.50E 01 2.31E 18 1.50E+03 1.73E 17 1.50E+07 6.53E 15 2.00E 01 2.00E 18 2.00E+03 2.29E 17 2.00E+07 7.12E 15 3.00E 01 1.63E 18 3.00E+03 3.37E 17 3.00E+07 7.72E 15 4.00E 01 1.41E 18 4.00E+03 4.43E 17 4.00E+07 8.11E 15 5.00E 01 1.27E 18 5.00E+03 5.48E 17 5.00E+07 8.33E 15 6.00E 01 1.16E 18 6.00E+03 6.52E 17 6.00E+07 8.55E 15 8.00E 01 1.01E 18 8.00E+03 8.61E 17 8.00E+07 9.24E 15 1.00E+00 9.02E 19 1.00E+04 1.07E 16 1.00E+08 1.01E 14 1.50E+00 7.46E 19 1.50E+04 1.59E 16 1.50E+08 1.39E 14 2.00E+00 6.54E 19 2.00E+04 2.08E 16 3.00E+00 5.49E 19 3.00E+04 2.96E 16 4.00E+00 4.93E 19 4.00E+04 3.76E 16 5.00E+00 4.57E 19 5.00E+04 4.49E 16 6.00E+00 4.34E 19 6.00E+04 5.16E 16 8.00E+00 4.10E 19 8.00E+04 6.36E 16

PAGE 83

83 Table B -7. Proximal radius DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) TM50 TM50 TM50 1.00E 03 6.33E 18 1.00E+01 4.00E 19 1.00E+05 7.40E 16 1.50E 03 6.37E 18 1.50E+01 4.09E 19 1.50E+05 9.56E 16 2.00E 03 6.40E 18 2.00E+01 4.37E 19 2.00E+05 1.13E 15 3.00E 03 6.46E 18 3.00E+01 5.19E 19 3.00E+05 1.41E 15 4.00E 03 6.51E 18 4.00E+01 6.17E 19 4.00E+05 1.66E 15 5.00E 03 6.54E 18 5.00E+01 7.20E 19 5.00E+05 1.82E 15 6.00E 03 6.57E 18 6.00E+01 8.28E 19 6.00E+05 1.99E 15 8.00E 03 6.58E 18 8.00E+01 1.05E 18 8.00E+05 2.27E 15 1.00E 02 6.55E 18 1.00E+02 1.28E 18 1.00E+06 2.58E 15 1.50E 02 6.34E 18 1.50E+02 1.85E 18 1.50E+06 2.98E 15 2.00E 02 5.99E 18 2.00E+02 2.43E 18 2.00E+06 3.31E 15 3.00E 02 5.13E 18 3.00E+02 3.60E 18 3.00E+06 3.85E 15 4.00E 02 4.47E 18 4.00E+02 4.76E 18 4.00E+06 4.14E 15 5.00E 02 3.99E 18 5.00E+02 5.93E 18 5.00E+06 4.06E 15 6.00E 02 3.63E 18 6.00E+02 7.08E 18 6.00E+06 4.21E 15 8.00E 02 3.15E 18 8.00E+02 9.39E 18 8.00E+06 4.72E 15 1.00E 01 2.81E 18 1.00E+03 1.17E 17 1.00E+07 5.02E 15 1.50E 01 2.31E 18 1.50E+03 1.73E 17 1.50E+07 5.97E 15 2.00E 01 2.00E 18 2.00E+03 2.28E 17 2.00E+07 6.50E 15 3.00E 01 1.63E 18 3.00E+03 3.37E 17 3.00E+07 7.08E 15 4.00E 01 1.41E 18 4.00E+03 4.42E 17 4.00E+07 7.45E 15 5.00E 01 1.27E 18 5.00E+03 5.47E 17 5.00E+07 7.63E 15 6.00E 01 1.16E 18 6.00E+03 6.50E 17 6.00E+07 7.80E 15 8.00E 01 1.01E 18 8.00E+03 8.59E 17 8.00E+07 8.39E 15 1.00E+00 9.02E 19 1.00E+04 1.07E 16 1.00E+08 9.15E 15 1.50E+00 7.46E 19 1.50E+04 1.59E 16 1.50E+08 1.25E 14 2.00E+00 6.54E 19 2.00E+04 2.07E 16 3.00E+00 5.49E 19 3.00E+04 2.95E 16 4.00E+00 4.93E 19 4.00E+04 3.75E 16 5.00E+00 4.57E 19 5.00E+04 4.48E 16 6.00E+00 4.34E 19 6.00E+04 5.16E 16 8.00E+00 4.10E 19 8.00E+04 6.35E 16

PAGE 84

84 Table B -8. Distal radius DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) TM50 TM50 TM50 1.00E 03 6.33E 18 1.00E+01 4.01E 19 1.00E+05 7.42E 16 1.50E 03 6.37E 18 1.50E+01 4.11E 19 1.50E+05 9.58E 16 2.00E 03 6.40E 18 2.00E+01 4.40E 19 2.00E+05 1.13E 15 3.00E 03 6.46E 18 3.00E+01 5.23E 19 3.00E+05 1.41E 15 4.00E 03 6.51E 18 4.00E+01 6.21E 19 4.00E+05 1.67E 15 5.00E 03 6.54E 18 5.00E+01 7.26E 19 5.00E+05 1.83E 15 6.00E 03 6.57E 18 6.00E+01 8.35E 19 6.00E+05 1.99E 15 8.00E 03 6.58E 18 8.00E+01 1.06E 18 8.00E+05 2.29E 15 1.00E 02 6.55E 18 1.00E+02 1.29E 18 1.00E+06 2.60E 15 1.50E 02 6.34E 18 1.50E+02 1.87E 18 1.50E+06 3.02E 15 2.00E 02 5.99E 18 2.00E+02 2.46E 18 2.00E+06 3.37E 15 3.00E 02 5.13E 18 3.00E+02 3.63E 18 3.00E+06 3.99E 15 4.00E 02 4.47E 18 4.00E+02 4.81E 18 4.00E+06 4.37E 15 5.00E 02 3.99E 18 5.00E+02 5.98E 18 5.00E+06 4.38E 15 6.00E 02 3.63E 18 6.00E+02 7.15E 18 6.00E+06 4.61E 15 8.00E 02 3.15E 18 8.00E+02 9.48E 18 8.00E+06 5.24E 15 1.00E 01 2.81E 18 1.00E+03 1.18E 17 1.00E+07 5.62E 15 1.50E 01 2.31E 18 1.50E+03 1.75E 17 1.50E+07 6.63E 15 2.00E 01 2.00E 18 2.00E+03 2.30E 17 2.00E+07 7.22E 15 3.00E 01 1.63E 18 3.00E+03 3.39E 17 3.00E+07 7.82E 15 4.00E 01 1.41E 18 4.00E+03 4.46E 17 4.00E+07 8.21E 15 5.00E 01 1.27E 18 5.00E+03 5.51E 17 5.00E+07 8.40E 15 6.00E 01 1.16E 18 6.00E+03 6.55E 17 6.00E+07 8.61E 15 8.00E 01 1.01E 18 8.00E+03 8.64E 17 8.00E+07 9.28E 15 1.00E+00 9.02E 19 1.00E+04 1.07E 16 1.00E+08 1.01E 14 1.50E+00 7.46E 19 1.50E+04 1.60E 16 1.50E+08 1.39E 14 2.00E+00 6.54E 19 2.00E+04 2.08E 16 3.00E+00 5.50E 19 3.00E+04 2.96E 16 4.00E+00 4.94E 19 4.00E+04 3.76E 16 5.00E+00 4.58E 19 5.00E+04 4.49E 16 6.00E+00 4.35E 19 6.00E+04 5.17E 16 8.00E+00 4.11E 19 8.00E+04 6.37E 16

PAGE 85

85 Table B -9. Proximal tibia DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) TM50 TM50 TM50 1.00E 03 6.33E 18 1.00E+01 4.01E 19 1.00E+05 7.41E 16 1.50E 03 6.37E 18 1.50E+01 4.11E 19 1.50E+05 9.56E 16 2.00E 03 6.40E 18 2.00E+01 4.40E 19 2.00E+05 1.13E 15 3.00E 03 6.46E 18 3.00E+01 5.23E 19 3.00E+05 1.41E 15 4.00E 03 6.51E 18 4.00E+01 6.22E 19 4.00E+05 1.66E 15 5.00E 03 6.54E 18 5.00E+01 7.27E 19 5.00E+05 1.82E 15 6.00E 03 6.57E 18 6.00E+01 8.36E 19 6.00E+05 1.99E 15 8.00E 03 6.58E 18 8.00E+01 1.06E 18 8.00E+05 2.28E 15 1.00E 02 6.55E 18 1.00E+02 1.29E 18 1.00E+06 2.60E 15 1.50E 02 6.34E 18 1.50E+02 1.87E 18 1.50E+06 3.02E 15 2.00E 02 5.99E 18 2.00E+02 2.46E 18 2.00E+06 3.37E 15 3.00E 02 5.13E 18 3.00E+02 3.64E 18 3.00E+06 3.99E 15 4.00E 02 4.47E 18 4.00E+02 4.81E 18 4.00E+06 4.38E 15 5.00E 02 3.99E 18 5.00E+02 5.99E 18 5.00E+06 4.39E 15 6.00E 02 3.63E 18 6.00E+02 7.16E 18 6.00E+06 4.63E 15 8.00E 02 3.15E 18 8.00E+02 9.48E 18 8.00E+06 5.26E 15 1.00E 01 2.81E 18 1.00E+03 1.18E 17 1.00E+07 5.62E 15 1.50E 01 2.31E 18 1.50E+03 1.75E 17 1.50E+07 6.64E 15 2.00E 01 2.00E 18 2.00E+03 2.30E 17 2.00E+07 7.23E 15 3.00E 01 1.63E 18 3.00E+03 3.39E 17 3.00E+07 7.82E 15 4.00E 01 1.41E 18 4.00E+03 4.45E 17 4.00E+07 8.22E 15 5.00E 01 1.27E 18 5.00E+03 5.49E 17 5.00E+07 8.43E 15 6.00E 01 1.16E 18 6.00E+03 6.52E 17 6.00E+07 8.65E 15 8.00E 01 1.01E 18 8.00E+03 8.61E 17 8.00E+07 9.34E 15 1.00E+00 9.02E 19 1.00E+04 1.07E 16 1.00E+08 1.02E 14 1.50E+00 7.46E 19 1.50E+04 1.59E 16 1.50E+08 1.40E 14 2.00E+00 6.54E 19 2.00E+04 2.07E 16 3.00E+00 5.50E 19 3.00E+04 2.96E 16 4.00E+00 4.94E 19 4.00E+04 3.76E 16 5.00E+00 4.58E 19 5.00E+04 4.49E 16 6.00E+00 4.35E 19 6.00E+04 5.17E 16 8.00E+00 4.11E 19 8.00E+04 6.37E 16

PAGE 86

86 Table B -10. Distal tibia DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) TM50 TM50 TM50 1.00E 03 6.33E 18 1.00E+01 4.01E 19 1.00E+05 7.42E 16 1.50E 03 6.37E 18 1.50E+01 4.11E 19 1.50E+05 9.59E 16 2.00E 03 6.40E 18 2.00E+01 4.40E 19 2.00E+05 1.13E 15 3.00E 03 6.46E 18 3.00E+01 5.24E 19 3.00E+05 1.41E 15 4.00E 03 6.51E 18 4.00E+01 6.22E 19 4.00E+05 1.67E 15 5.00E 03 6.54E 18 5.00E+01 7.28E 19 5.00E+05 1.83E 15 6.00E 03 6.57E 18 6.00E+01 8.37E 19 6.00E+05 2.00E 15 8.00E 03 6.58E 18 8.00E+01 1.06E 18 8.00E+05 2.29E 15 1.00E 02 6.55E 18 1.00E+02 1.29E 18 1.00E+06 2.60E 15 1.50E 02 6.34E 18 1.50E+02 1.87E 18 1.50E+06 3.02E 15 2.00E 02 5.99E 18 2.00E+02 2.46E 18 2.00E+06 3.38E 15 3.00E 02 5.13E 18 3.00E+02 3.64E 18 3.00E+06 3.99E 15 4.00E 02 4.47E 18 4.00E+02 4.82E 18 4.00E+06 4.37E 15 5.00E 02 3.99E 18 5.00E+02 6.00E 18 5.00E+06 4.37E 15 6.00E 02 3.63E 18 6.00E+02 7.17E 18 6.00E+06 4.60E 15 8.00E 02 3.15E 18 8.00E+02 9.50E 18 8.00E+06 5.21E 15 1.00E 01 2.81E 18 1.00E+03 1.18E 17 1.00E+07 5.59E 15 1.50E 01 2.31E 18 1.50E+03 1.75E 17 1.50E+07 6.60E 15 2.00E 01 2.00E 18 2.00E+03 2.31E 17 2.00E+07 7.18E 15 3.00E 01 1.63E 18 3.00E+03 3.40E 17 3.00E+07 7.78E 15 4.00E 01 1.41E 18 4.00E+03 4.46E 17 4.00E+07 8.17E 15 5.00E 01 1.27E 18 5.00E+03 5.51E 17 5.00E+07 8.38E 15 6.00E 01 1.16E 18 6.00E+03 6.55E 17 6.00E+07 8.59E 15 8.00E 01 1.01E 18 8.00E+03 8.65E 17 8.00E+07 9.27E 15 1.00E+00 9.02E 19 1.00E+04 1.08E 16 1.00E+08 1.01E 14 1.50E+00 7.46E 19 1.50E+04 1.60E 16 1.50E+08 1.39E 14 2.00E+00 6.54E 19 2.00E+04 2.08E 16 3.00E+00 5.50E 19 3.00E+04 2.96E 16 4.00E+00 4.94E 19 4.00E+04 3.76E 16 5.00E+00 4.58E 19 5.00E+04 4.50E 16 6.00E+00 4.35E 19 6.00E+04 5.17E 16 8.00E+00 4.11E 19 8.00E+04 6.38E 16

PAGE 87

87 Table B -11. Proximal ulna DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) TM50 TM50 TM50 1.00E 03 6.33E 18 1.00E+01 4.00E 19 1.00E+05 7.43E 16 1.50E 03 6.37E 18 1.50E+01 4.09E 19 1.50E+05 9.60E 16 2.00E 03 6.40E 18 2.00E+01 4.38E 19 2.00E+05 1.13E 15 3.00E 03 6.46E 18 3.00E+01 5.21E 19 3.00E+05 1.41E 15 4.00E 03 6.51E 18 4.00E+01 6.18E 19 4.00E+05 1.67E 15 5.00E 03 6.54E 18 5.00E+01 7.23E 19 5.00E+05 1.83E 15 6.00E 03 6.57E 18 6.00E+01 8.31E 19 6.00E+05 1.99E 15 8.00E 03 6.58E 18 8.00E+01 1.05E 18 8.00E+05 2.29E 15 1.00E 02 6.55E 18 1.00E+02 1.28E 18 1.00E+06 2.60E 15 1.50E 02 6.34E 18 1.50E+02 1.86E 18 1.50E+06 3.02E 15 2.00E 02 5.99E 18 2.00E+02 2.44E 18 2.00E+06 3.37E 15 3.00E 02 5.13E 18 3.00E+02 3.61E 18 3.00E+06 3.98E 15 4.00E 02 4.47E 18 4.00E+02 4.78E 18 4.00E+06 4.36E 15 5.00E 02 3.99E 18 5.00E+02 5.95E 18 5.00E+06 4.34E 15 6.00E 02 3.63E 18 6.00E+02 7.11E 18 6.00E+06 4.55E 15 8.00E 02 3.15E 18 8.00E+02 9.43E 18 8.00E+06 5.14E 15 1.00E 01 2.81E 18 1.00E+03 1.17E 17 1.00E+07 5.47E 15 1.50E 01 2.31E 18 1.50E+03 1.74E 17 1.50E+07 6.48E 15 2.00E 01 2.00E 18 2.00E+03 2.30E 17 2.00E+07 7.06E 15 3.00E 01 1.63E 18 3.00E+03 3.39E 17 3.00E+07 7.66E 15 4.00E 01 1.41E 18 4.00E+03 4.45E 17 4.00E+07 8.07E 15 5.00E 01 1.27E 18 5.00E+03 5.50E 17 5.00E+07 8.28E 15 6.00E 01 1.16E 18 6.00E+03 6.55E 17 6.00E+07 8.51E 15 8.00E 01 1.01E 18 8.00E+03 8.64E 17 8.00E+07 9.20E 15 1.00E+00 9.02E 19 1.00E+04 1.08E 16 1.00E+08 1.01E 14 1.50E+00 7.46E 19 1.50E+04 1.60E 16 1.50E+08 1.39E 14 2.00E+00 6.54E 19 2.00E+04 2.08E 16 3.00E+00 5.50E 19 3.00E+04 2.96E 16 4.00E+00 4.94E 19 4.00E+04 3.76E 16 5.00E+00 4.58E 19 5.00E+04 4.50E 16 6.00E+00 4.35E 19 6.00E+04 5.18E 16 8.00E+00 4.10E 19 8.00E+04 6.38E 16

PAGE 88

88 Table B -12. Distal ulna DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) TM50 TM50 TM50 1.00E 03 6.33E 18 1.00E+01 4.00E 19 1.00E+05 7.42E 16 1.50E 03 6.37E 18 1.50E+01 4.08E 19 1.50E+05 9.60E 16 2.00E 03 6.40E 18 2.00E+01 4.37E 19 2.00E+05 1.14E 15 3.00E 03 6.46E 18 3.00E+01 5.19E 19 3.00E+05 1.42E 15 4.00E 03 6.51E 18 4.00E+01 6.16E 19 4.00E+05 1.67E 15 5.00E 03 6.54E 18 5.00E+01 7.19E 19 5.00E+05 1.83E 15 6.00E 03 6.57E 18 6.00E+01 8.27E 19 6.00E+05 2.00E 15 8.00E 03 6.58E 18 8.00E+01 1.05E 18 8.00E+05 2.29E 15 1.00E 02 6.55E 18 1.00E+02 1.27E 18 1.00E+06 2.60E 15 1.50E 02 6.34E 18 1.50E+02 1.85E 18 1.50E+06 3.01E 15 2.00E 02 5.99E 18 2.00E+02 2.43E 18 2.00E+06 3.37E 15 3.00E 02 5.13E 18 3.00E+02 3.59E 18 3.00E+06 3.97E 15 4.00E 02 4.47E 18 4.00E+02 4.76E 18 4.00E+06 4.34E 15 5.00E 02 3.99E 18 5.00E+02 5.92E 18 5.00E+06 4.34E 15 6.00E 02 3.63E 18 6.00E+02 7.08E 18 6.00E+06 4.57E 15 8.00E 02 3.15E 18 8.00E+02 9.38E 18 8.00E+06 5.18E 15 1.00E 01 2.81E 18 1.00E+03 1.17E 17 1.00E+07 5.53E 15 1.50E 01 2.31E 18 1.50E+03 1.73E 17 1.50E+07 6.52E 15 2.00E 01 2.00E 18 2.00E+03 2.29E 17 2.00E+07 7.08E 15 3.00E 01 1.63E 18 3.00E+03 3.37E 17 3.00E+07 7.67E 15 4.00E 01 1.41E 18 4.00E+03 4.44E 17 4.00E+07 8.06E 15 5.00E 01 1.27E 18 5.00E+03 5.49E 17 5.00E+07 8.27E 15 6.00E 01 1.16E 18 6.00E+03 6.53E 17 6.00E+07 8.49E 15 8.00E 01 1.01E 18 8.00E+03 8.63E 17 8.00E+07 9.17E 15 1.00E+00 9.02E 19 1.00E+04 1.08E 16 1.00E+08 1.00E 14 1.50E+00 7.46E 19 1.50E+04 1.60E 16 1.50E+08 1.38E 14 2.00E+00 6.54E 19 2.00E+04 2.08E 16 3.00E+00 5.49E 19 3.00E+04 2.97E 16 4.00E+00 4.93E 19 4.00E+04 3.77E 16 5.00E+00 4.57E 19 5.00E+04 4.50E 16 6.00E+00 4.34E 19 6.00E+04 5.17E 16 8.00E+00 4.10E 19 8.00E+04 6.37E 16

PAGE 89

89 Table B -13. Wrist and hand DRF Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) Energy (eV) DRF (Gy m 2 ) TM50 TM50 TM50 1.00E 03 6.33E 18 1.00E+01 4.00E 19 1.00E+05 7.42E 16 1.50E 03 6.37E 18 1.50E+01 4.09E 19 1.50E+05 9.58E 16 2.00E 03 6.40E 18 2.00E+01 4.38E 19 2.00E+05 1.13E 15 3.00E 03 6.46E 18 3.00E+01 5.19E 19 3.00E+05 1.41E 15 4.00E 03 6.51E 18 4.00E+01 6.17E 19 4.00E+05 1.67E 15 5.00E 03 6.54E 18 5.00E+01 7.21E 19 5.00E+05 1.82E 15 6.00E 03 6.57E 18 6.00E+01 8.29E 19 6.00E+05 1.99E 15 8.00E 03 6.58E 18 8.00E+01 1.05E 18 8.00E+05 2.28E 15 1.00E 02 6.55E 18 1.00E+02 1.28E 18 1.00E+06 2.60E 15 1.50E 02 6.34E 18 1.50E+02 1.85E 18 1.50E+06 3.02E 15 2.00E 02 5.99E 18 2.00E+02 2.43E 18 2.00E+06 3.37E 15 3.00E 02 5.13E 18 3.00E+02 3.60E 18 3.00E+06 3.98E 15 4.00E 02 4.47E 18 4.00E+02 4.77E 18 4.00E+06 4.36E 15 5.00E 02 3.99E 18 5.00E+02 5.93E 18 5.00E+06 4.35E 15 6.00E 02 3.63E 18 6.00E+02 7.09E 18 6.00E+06 4.58E 15 8.00E 02 3.15E 18 8.00E+02 9.40E 18 8.00E+06 5.18E 15 1.00E 01 2.81E 18 1.00E+03 1.17E 17 1.00E+07 5.51E 15 1.50E 01 2.31E 18 1.50E+03 1.73E 17 1.50E+07 6.52E 15 2.00E 01 2.00E 18 2.00E+03 2.29E 17 2.00E+07 7.10E 15 3.00E 01 1.63E 18 3.00E+03 3.38E 17 3.00E+07 7.69E 15 4.00E 01 1.41E 18 4.00E+03 4.44E 17 4.00E+07 8.09E 15 5.00E 01 1.27E 18 5.00E+03 5.49E 17 5.00E+07 8.31E 15 6.00E 01 1.16E 18 6.00E+03 6.54E 17 6.00E+07 8.53E 15 8.00E 01 1.01E 18 8.00E+03 8.63E 17 8.00E+07 9.23E 15 1.00E+00 9.02E 19 1.00E+04 1.08E 16 1.00E+08 1.01E 14 1.50E+00 7.46E 19 1.50E+04 1.60E 16 1.50E+08 1.39E 14 2.00E+00 6.54E 19 2.00E+04 2.08E 16 3.00E+00 5.49E 19 3.00E+04 2.96E 16 4.00E+00 4.93E 19 4.00E+04 3.76E 16 5.00E+00 4.58E 19 5.00E+04 4.49E 16 6.00E+00 4.35E 19 6.00E+04 5.17E 16 8.00E+00 4.10E 19 8.00E+04 6.36E 16

PAGE 90

90 Figure B 1. Ankle and foot kerma coefficients and DRF Figure B 2. Ankle and foot percent RD

PAGE 91

91 Figure B 3. Distal femur kerma coefficients and DRF Figure B 4. Distal femur percent RD

PAGE 92

92 Figure B 5. Proximal fibula kerma coefficients and DRF Figure B 6. Proximal fibula percent RD

PAGE 93

93 Figure B 7. Distal fibula kerma coefficients and DRF Figure B 8. Distal fibula percent RD

PAGE 94

94 Figure B 9. Distal humerus kerma coefficients and DRF Figure B 10. Distal humerus percent RD

PAGE 95

95 Figure B 1 1. Patella kerma coefficients and DRF Figure B 12. Patella percent RD

PAGE 96

96 Figure B 13. Proximal radius kerma coefficients and DRF Figure B 14. Proximal radius percent RD

PAGE 97

97 Figure B 15. Distal radius kerma coefficients and DRF Figure B 16. Distal radius percent RD

PAGE 98

98 Figure B 17. Proximal tibia kerma coefficients and DRF Figure B 18. Proximal tibia percent RD

PAGE 99

99 Figure B 19. Distal tibia kerma coefficients and DRF Figure B 20. Distal tibia percent RD

PAGE 100

100 Figure B 21. Proximal ulna kerma coefficients and DRF Figure B 22. Proximal ulna percent RD

PAGE 101

101 Figure B 23. Distal ulna kerma coefficients and DRF Figure B 24. Distal ulna percent RD

PAGE 102

102 Figure B 25. Wrist and hand kerma coefficients and DRF Figure B 26. Wrist and hand percent RD

PAGE 103

103 LIST OF REFERENCES Akkurt H and Eckerman K F 2007 Development of PIMAL: Mathematical p h antom with m oving a rms and l egs (Oak Ridge, TN: Oak Ridge National Laboratory ) Allen P D and Chaudhri M A 1998 Photoneutron production in tissue during high ener gy bremsstrahl ung radiotherapy Physics in Medicine and Biology 33 10171036 Brenner D J 1983 Neutron kerma values above 15 MeV calculated with a nuclear mo del applicable to light nuclei Physics in Medicine and Biology 29 437441 Caswell R S, Coyne J J and Randolph M L 1980 Kerma Factors for Neutron Energies below 30 MeV Radiation Research 83 217254 Eckerman K F, Bolch W E, Zankl M and Petoussi -Henss N 2007 Response functions for computing absorbed dose to skeletal t issues from photon irradiation Radiation Prote ction Dosimetry 127 187191 ICRU 1992 Photon, electron, proton and neutron int eraction data for body tissues ICRU Report 46 (Bethesda, MD: International Commission on Radiati on Units and Measurements) ICRU 2000 Nuclear data for neutron and p roton r adioth erapy and for radiation Protection ICRU Report 63 (Bethesda, MD: International Commission on Radiation Units and Measurements) Kerr G D and Eckerman K F 1985 Neutron and photon fluence -to dose conversion factors for active marrow of the skeleton Proceedings of the Fifth Symposium on Neutron Dosimetry 133-145 (Luxembourg: CEC) Lee C, Lee C, Shah A P and Bolch W E 2006 An assessment of bone marrow and bone endosteum dosimetry methods for photon sources Physics in Medicine and Biology 51 5391 5407. NCRP 2006 Information Needed to Make Radiation Protection Recommendations for Space Missions Beyond Low -Earth Orbit NCRP Report No. 153 (Bethesda, MD: National Commission on Radiation Protection and Measurements) NNDC 2006 Angular distribution of neutrons: 1-H -1(n,elastic) Accessed November 13, 2008 http://www.nndc.bnl.gov/sigma/getMF4Data.jsp Shultis J K and Faw R E 2000 Radiation Shielding (La Grange Park, IL: American Nuclear Society, Inc .) Turner J E 1995 Atoms, Radi ation, and Radiation Protection 2nd Edition (New York: John Wiley & Sons, Inc .)

PAGE 104

104 Xu X G, Bednarz B and Paganetti H 2008 A review of dosimetry studies on external beam radiation treatment with resp ect to second cancer induction Physics in Medicine and Biolog y 53 R193-R241 Zheng Y, Klein W and Low D 2009 Monte Carlo simulation of the neutron spectral fluence and dose equivalent for use in shielding a proton therapy vault Physics in Medicine and Biology 54 6943 -6957

PAGE 105

105 BIOGRAPHICAL SKETCH Amir Alexander Bahadori was born in Kansas City, Kansas The oldest of four children, he attended Sumner Academy of Arts and Sciences graduating in 2003 He earned his B.S. in m echanical e ngineering with n uclear e ngineering o ption and his B.S. m athematics at Kansas State University, both in 200 8. Upon completion of his M.S. program, Amir will be entering the medical physics Ph.D. program at the University of Florida.