SKELETAL NEUTRON DOSE RESPONSE FUNCTIONS: A NEW PROTOCOL FOR EVALUATING DOSE TO ACTIVE MARROW AND BONE ENDOSTEUM

Transcription

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

2 2010 Amir Alexander Bahadori 2

3 To my family 3

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 practice 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. 4

5 TABLE OF CONTENTS page ACKNOWLEDGMENTS... 4 LIST OF TABLES... 6 LIST OF FIGURES... 8 LIST OF ABBREVIATIONS LIST OF SYMBOLS ABSTRACT CHAPTER 1 INTRODUCTION MATERIALS AND METHODS SAF Data Photon DRFs and the Three-Factor Method Neutron DRF Generalized Formulation Hydrogen Neutron DRF Formulation Neutron DRF Formulation for Other Elements Complete Neutron DRF Definition RESULTS DISCUSSION CONCLUSIONS APPENDIX A AXIAL SKELETAL NEUTRON DRF DATA B APPENDICULAR SKELETAL NEUTRON DRF DATA LIST OF REFERENCES BIOGRAPHICAL SKETCH

6 LIST OF TABLES Table page 2-1 Skeletal tissue compositions. (Generated using data from ICRU 1992) Representative isotopes for elements addressed in ICRU Report 63. (Generated using data from ICRU 2000) Thoracic vertebra DRF data Thoracic vertebra DRF data Thoracic vertebra dose-to-kerma ratios Proximal humerus dose-to-kerma ratios A-1 Cervical vertebra DRF A-2 Clavicle DRF A-3 Cranium DRF A-4 Proximal femur DRF A-5 Proximal humerus DRF A-6 Lumbar vertebra DRF A-7 Mandible DRF A-8 Pelvis DRF A-9 Rib DRF A-10 Sacrum DRF A-11 Scapula DRF A-12 Sternum DRF A-13 Thoracic vertebra DRF B-1 Ankle and foot DRF B-2 Distal femur DRF B-3 Proximal fibula DRF

7 B-4 Distal fibula DRF B-5 Distal humerus DRF B-6 Patella DRF B-7 Proximal radius DRF B-8 Distal radius DRF B-9 Proximal tibia DRF B-10 Distal tibia DRF B-11 Proximal ulna DRF B-12 Distal ulna DRF B-13 Wrist and hand DRF

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

9 A-17 Rib kerma coefficients and DRFs A-18 Rib percent RD A-19 Sacrum kerma coefficients and DRFs A-20 Sacrum percent RD A-21 Scapula kerma coefficients and DRFs A-22 Scapula percent RD A-23 Sternum kerma coefficients and DRFs A-24 Sternum percent RD A-25 Thoracic vertebra kerma coefficients and DRFs A-26 Thoracic vertebra percent RD B-1 Ankle and foot kerma coefficients and DRF B-2 Ankle and foot percent RD B-3 Distal femur kerma coefficients and DRF B-4 Distal femur percent RD B-5 Proximal fibula kerma coefficients and DRF B-6 Proximal fibula percent RD B-7 Distal fibula kerma coefficients and DRF B-8 Distal fibula percent RD B-9 Distal humerus kerma coefficients and DRF B-10 Distal humerus percent RD B-11 Patella kerma coefficients and DRF B-12 Patella percent RD B-13 Proximal radius kerma coefficients and DRF B-14 Proximal radius percent RD B-21 Proximal ulna kerma coefficients and DRF

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

11 µm micrometer LIST OF ABBREVIATIONS AF AM b CD CM CPE CSDA DRF absorbed fraction active marrow barn compact disc center of mass charged particle equilibrium continuously slowing down approximation dose response function DS86 Dosimetry System 1986 ENDF ev g Gy ICRU IM kev km m mev MeV microct NCRP NIST Evaluated Nuclear Data File electron volt gram gray International Commission on Radiation Units and Measurements inactive marrow one thousand electron volts kilometer meter one thousandth of one electron volt one million electron volts micro-computed tomography National Council on Radiation Protection and Measurements National Institute of Standards and Technology 11

12 RD SAF TM TM 50 relative difference specific absorbed fraction total marrow bone endosteum 12

13 LIST OF SYMBOLS DD AAAA DD SSSS μμ eeee AAAA ρρ SSSS S(E) E n λλ NN AA AA jj mm(tt) mm(rr) ff jj (rr) φφ ii (TT rr; εε) σσ iiii pppppppp (EE nn ) nn iiii (εε, EE nn ) σσ nn,nn (EE nn ) nn pp (εε, EE nn ) εε E ωω cc Q dose to AM kerma to homogeneous spongiosa ratio of mass-energy absorption coefficients of AM and homogeneous spongiosa dose enhancement factor incident neutron energy unit conversion factor Avogadro s number atomic mass of nuclide j mass of target region mass of source region percent mass abundance of nuclide j in source region r AF for secondary charged particles of type I with energy εε from source region r to target region T production cross-section for nuclide j and secondary charged particle i distribution of secondary charged particle of type i from a neutron interaction with nuclide j cross-section for neutron scatter on hydrogen energy distribution of recoil proton from neutron scatter on hydrogen resultant particle energy incident particle energy cosine of the CM scattering angle Q-value for the scattering interaction 13

14 A Φ pp (TT rr; εε) σσ xxxx (εε, EE nn ) kk(ee nn ) DD(TT) ΦΦ(EE nn ) ratio of masses of stationary body and incident particle SAF for protons of energy εε from source region r to target region T differential proton production cross-section kerma coefficient for a chosen bone region as a function of incident neutron energy DRF for a chosen bone region as a function of incident neutron energy. 14

15 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science SKELETAL NEUTRON DOSE RESPONSE FUNCTIONS: A NEW PROTOCOL FOR EVALUATING DOSE TO ACTIVE MARROW AND BONE ENDOSTEUM Chair: Wesley E. Bolch Major: Nuclear Engineering Sciences By Amir Alexander Bahadori May 2010 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 µm layer of total marrow adjacent to the bone surfaces, or TM 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 crosssections, neutron DRFs were calculated for AM and TM 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. 15

16 At low incident neutron energies, AM kerma coefficient correlate well with AM DRF, while TM kerma coefficient correlate well with TM 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 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. 16

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 boron-neutron capture therapy, some neutrons will invariably interact in the patient s healthy tissues. In high energy gamma therapy, photoneutron production may be significant, 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 17

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 TM 50, defined as the layer extending 50 µm 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 composition 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 can 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 TM 50. This method requires the calculation of the secondary charged particle absorbed fraction to the target tissue of interest. Previously, DRFs for photons have been calculated for skeletal tissues (Eckerman et al. 2007). Using electron absorbed fraction data, target and source region masses, interaction probabilities, and secondary electron distributions, the photon DRFs were calculated for AM and TM 50 for each bone site. Additionally, DRFs for neutrons have been calculated previously for the DS86 project for the atomic bomb survivors at Hiroshima and Nagasaki (Kerr and Eckerman 1985). However, these calculations considered only AM in a homogeneous skeletal model, and 18

19 therefore did not separately calculate the DRF for TM 50. 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. Kerma 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 these 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 using cross-section 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). ICRU 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 considered 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 19

20 2000). It is important to emphasize 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 cross-sections, there will likely be some difference with the corresponding kerma coefficient as stated in the report. In the present study, skeletal neutron DRFs for AM and TM 50 were calculated for all skeletal sites. The AM DRFs and TM 50 DRFs 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. 20

21 CHAPTER 2 MATERIALS AND METHODS 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 TM 50 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 mineral 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 DRFs. In addition, the neutron DRF calculation used a skeletal mass set that was entirely 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 ) DD AAAA = DD SSSS μμ eeee AAAA SS(EE). [1] ρρ SSSS 21

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 Equation 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 neutron-produced charged particle types (protons, deuterons, tritons, helium-3 nuclei, alphas, and recoil nuclei) precludes 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 applied 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 22

23 DRF formulation, fractional energy deposition must be considered (Eckerman et al ). For neutrons, the DRF formulation for a given skeletal site is DD(TT) ΦΦ(EE nn ) = λλ NN AA jj mm (TT) AA rr ff jj (rr)mm(rr) ii φφ ii (TT rr; εε) σσ pppppppp jj iiii (EE nn )nn iiii (εε, EE 0 nn )εε dddd. [2] The value of the conversion factor λλ 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 electron-volts, and cross-section will be expressed in barns. Therefore, after all operations excluding multiplication by the conversion factor are performed, the units are left in the product of electron-volts and barns per gram. The desired units are gray-square meters. Therefore, the conversion factor is given as λ = 1 m J 1000 g = Gy m b 1 ev 1 kg b ev g 1. For incident neutrons, myriad charged particles 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 1 H 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 DD(TT) = λλ ΦΦ(EE nn ) HH NN AA mm(tt) AA rr ff HH (rr)mm(rr) φφ pp (TT rr; εε) σσ nn,nn (EE nn )nn pp (εε, EE HH 0 nn )εεεεεε. [3] 23

24 In order to derive the energy distribution of protons resulting from neutron scatter on hydrogen, the angular distribution of neutrons after 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. It 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) with and εε = 1 2 EE(1 αα) 1 ωω cc QQ AA+1, [4] αα AA 1 AA+1 2, [5] = QQ(1+AA) AAAA. [6] Clearly, for elastic scattering of a neutron on a hydrogen nucleus, the Q-value is zero, and so equals 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 αα. After considering these simplifications, the energy of the recoil proton is given as 24

25 εε = 1 EE(1 ωω 2 cc ). [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: nn(εε, EE) = dddd (EE) ddεε = dddd (EE) ddωω cc ddωω cc ddεε = nn(ωω cc, EE) ddωω cc ddεε. [8] Differentiating Equation 7 with respect to ωω cc yields ddεε = 1 EE. [9] ddωω cc 2 Combining Equations 8 and 9, the energy distribution for recoil protons is given as nn(εε, EE) = 2 nn(ωω EE cc, EE). [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 operation 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 distribution 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 25

26 relative probability of a recoil proton with zero energy, which results from a glancing collision (i.e., ωω cc = 1). To perform the neutron DRF calculation, the computer program MATLAB TM 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 DD(TT) = λλ NN AA ΦΦ(EE nn ) HH EE nn AA HH rr ff HH (rr)mm(rr) Φ pp (TT rr; εε) σσ nn,nn (EE nn )nn pp (εε, EE 0 nn )εεεεεε. [11] To perform the integration, first the energy range was split into logarithmicallyequidistant divisions. Next, the summation was performed for the three source regions (active marrow, inactive marrow, trabecular bone). The product of the summation, the scattering 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 DD(TT) ΦΦ(EE nn ) XX = λλ NN AA EE nn AA XX rr ff XX (rr)mm(rr) 0 Φ pp (TT rr; εε) σσ xxxx (εε, EE nn ) εεεεεε. [12] 26

27 The cross-sections and kerma coefficients 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 2-2. According to ICRU Report 63 recommendations (ICRU 2000), when natural abundances of isotopes are assumed, the data for the major isotopes may be used as 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, 3 He nuclei, alphas, and recoil nuclei are listed for the elements in ICRU Report 63. These were weighted by the appropriate 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 expected 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 hydrogen-only DRF for incident neutron energies up to 20 MeV. Above 20 MeV, the neutron DRF was 27

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-section 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. 28

29 Table 2-1. Skeletal tissue compositions. (Generated using data from ICRU 1992) Element Composition by Mass (%) Active Marrow Trabecular Bone Mineral Inactive Marrow Hydrogen Carbon Nitrogen Oxygen Sodium* Magnesium* Phosphorous Sulfur* Chlorine* Potassium* Calcium Iron *These elements were not considered in the neutron DRF formulation. Table 2-2. Representative isotopes for elements addressed in ICRU Report 63. (Generated using data from ICRU 2000) Element Isotope Natural Percent Abundance Hydrogen 1 H Carbon 12 C Nitrogen 14 N Oxygen 16 O Aluminum 27 Al 100 Silicon 28 Si Phosphorous 31 P 100 Calcium 40 Ca Iron 56 Fe Copper 63 Cu Tungsten 184 W Lead 208 Pb

30 (ev) Figure 2-1. Angular distribution of neutrons from scatter interaction with hydrogen nuclei. (Generated using data from NNDC 2006) 30

31 CHAPTER 3 RESULTS AM and TM 50 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 TM 50 DRF was calculated, since no active marrow resides in these sites. The 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 coefficient, AM DRF, and TM 50 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 differences 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 incident neutron energy exceeds 150 MeV, it is important that the user calculate kerma coefficients based upon the particular cross-section library for the transport 31

32 program being utilized. Therefore, tabulated dose-to-kerma ratios are not provided for each 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 bone 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 Gy m 2, while the TM 50 DRF ranges from a minimum 6.3 x Gy m 2 for the appendicular skeletal sites to a maximum of 2.4 x Gy m 2 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 observed for the AM DRF are around 1.3 x Gy m 2, while the maximum values for the TM 50 DRF are between 1.2 x Gy m 2 and 1.4 x Gy m 2. 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 TM 50 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 enough 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 mid-range incident neutron energies (100 ev to 100 MeV), neither static nor dynamic CPE exist due to the interplay between the size and shape of the bone trabeculae and marrow cavities and the ranges of the protons resulting from neutron 32

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. 33

34 Table 3-1. Thoracic vertebra DRF data (ev) AM TM50 (ev) AM TM50 (ev) AM TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 34

35 Table 3-2. Thoracic vertebra DRF data (ev) AM TM50 (ev) AM TM50 (ev) AM TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 35

36 Table 3-3. Thoracic vertebra dose-to-kerma ratios Energy Dose-to-Kerma Ratio Energy Dose-to-Kerma Ratio Energy Dose-to-Kerma Ratio (ev) AM TM50 (ev) AM TM50 (ev) AM TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

37 Table 3-4. Proximal humerus dose-to-kerma ratios Energy Dose-to-Kerma Ratio Energy Dose-to-Kerma Ratio Energy Dose-to-Kerma Ratio (ev) AM TM50 (ev) AM TM50 (ev) AM TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

38 Figure 3-1. Thoracic vertebra kerma coefficients and DRFs 38

39 Figure 3-2. Proximal humerus kerma coefficients and DRFs 39

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 RRRR(EE nn ) = kk(ee nn ) DD (TT) ΦΦ (EEnn ) DD(TT) ΦΦ (EEnn ) [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 coefficient values with respect to the AM DRF and TM 50 DRF were found, while the RD of the kerma coefficient values with respect to the TM 50 DRF were calculated for the appendicular skeleton. The most pertinent comparisons for the axial skeletal sites are between 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 disequilibrium, while the last two comparisons indicate differences resulting from approximating dose to AM and TM 50 by kerma to homogeneous spongiosa. Similarly, the most pertinent comparisons for the appendicular skeleton are between TM kerma coefficient and TM 50 DRF, and Spongiosa kerma coefficient and TM 50 DRF. 40

41 Plots of the RD as a function of incident neutron energy for the thoracic vertebra and the proximal humerus are displayed in Figure 4-1 and Figure 4-2, 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 all axial bone sites at 100 MeV. The AM kerma coefficient always overestimates the AM DRF. The TM kerma coefficient correlates well with the TM 50 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 axial skeleton, the TM kerma coefficient tends to underestimate the TM 50 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 TM 50 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 41

42 TM kerma coefficient is within 10% of the TM 50 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 TM 50 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 TM 50 DRF at intermediate incident neutron energies. Finally, the difference associated with approximating the AM DRF and TM 50 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 as 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 elements. 42

43 A comparison between the lumbar vertebra AM DRF calculated in this study and that calculated previously is displayed in Figure 4-3. The two datasets correspond well. Note that the newly-calculated DRF curve is slightly lower than that calculated by Kerr and Eckerman; the difference is small since the contribution from proton-producing 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. Here, 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 the 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 neutron exposures in space (NCRP 2006). 43

44 Figure 4-1. Thoracic vertebra percent RD 44

45 Figure 4-2. Proximal humerus percent RD 45

46 Figure 4-3. Comparison between current and previous AM neutron DRF data for lumbar vertebra. (Generated using data from Kerr and Eckerman 1985) 46

47 CHAPTER 5 CONCLUSIONS Kerma to spongiosa has been used in the past to characterize dose to AM and TM 50 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 range-energy 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 TM 50. The results of this study indicate that large errors may be introduced by approximating dose to AM and TM 50 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 TM 50 are desired. Here, using kerma to spongiosa to estimate dose to TM 50 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 scatter on hydrogen nuclei from energies ranging from thermal to 150 MeV. All 47

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 for 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 it does contribute to absorbed dose. Finally, the appropriateness of the infinite spongiosa approximation for proton transport should be validated using Monte Carlo simulation. 48

49 APPENDIX A AXIAL SKELETAL NEUTRON 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, Pelvis, Rib, Sacrum, Scapula, Sternum, and Thoracic vertebra. 49

50 Table A-1. Cervical vertebra DRF (ev) AM TM50 (ev) AM TM50 (ev) AM TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 50

51 Table A-2. Clavicle DRF (ev) AM TM50 (ev) AM TM50 (ev) AM TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 51

52 Table A-3. Cranium DRF (ev) AM TM50 (ev) AM TM50 (ev) AM TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 52

53 Table A-4. Proximal femur DRF (ev) AM TM50 (ev) AM TM50 (ev) AM TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 53

54 Table A-5. Proximal humerus DRF (ev) AM TM50 (ev) AM TM50 (ev) AM TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 54

55 Table A-6. Lumbar vertebra DRF (ev) AM TM50 (ev) AM TM50 (ev) AM TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 55

56 Table A-7. Mandible DRF (ev) AM TM50 (ev) AM TM50 (ev) AM TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 56

57 Table A-8. Pelvis DRF (ev) AM TM50 (ev) AM TM50 (ev) AM TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 57

58 Table A-9. Rib DRF (ev) AM TM50 (ev) AM TM50 (ev) AM TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 58

59 Table A-10. Sacrum DRF (ev) AM TM50 (ev) AM TM50 (ev) AM TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 59

60 Table A-11. Scapula DRF (ev) AM TM50 (ev) AM TM50 (ev) AM TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 60

61 Table A-12. Sternum DRF (ev) AM TM50 (ev) AM TM50 (ev) AM TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 61

62 Table A-13. Thoracic vertebra DRF (ev) AM TM50 (ev) AM TM50 (ev) AM TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 62

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

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

65 Figure A-5. Cranium kerma coefficients and DRFs Figure A-6. Cranium percent RD 65

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

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

68 Figure A-11. Lumbar vertebra kerma coefficients and DRFs Figure A-12. Lumbar vertebra percent RD 68

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

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

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

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

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

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

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

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. 76

77 Table B-1. Ankle and foot DRF (ev) TM50 (ev) TM50 (ev) TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 77

78 Table B-2. Distal femur DRF (ev) TM50 (ev) TM50 (ev) TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 78

79 Table B-3. Proximal fibula DRF (ev) TM50 (ev) TM50 (ev) TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 79

80 Table B-4. Distal fibula DRF (ev) TM50 (ev) TM50 (ev) TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 80

81 Table B-5. Distal humerus DRF (ev) TM50 (ev) TM50 (ev) TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 81

82 Table B-6. Patella DRF (ev) TM50 (ev) TM50 (ev) TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 82

83 Table B-7. Proximal radius DRF (ev) TM50 (ev) TM50 (ev) TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 83

84 Table B-8. Distal radius DRF (ev) TM50 (ev) TM50 (ev) TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 84

85 Table B-9. Proximal tibia DRF (ev) TM50 (ev) TM50 (ev) TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 85

86 Table B-10. Distal tibia DRF (ev) TM50 (ev) TM50 (ev) TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 86

87 Table B-11. Proximal ulna DRF (ev) TM50 (ev) TM50 (ev) TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 87

88 Table B-12. Distal ulna DRF (ev) TM50 (ev) TM50 (ev) TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 88

89 Table B-13. Wrist and hand DRF (ev) TM50 (ev) TM50 (ev) TM E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-16 89

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

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

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

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

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

95 Figure B-11. Patella kerma coefficients and DRF Figure B-12. Patella percent RD 95

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

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

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

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

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

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