SKELETAL DOSIMETRY MODELS FOR ALPHA-PARTICLES FOR ...

SKELETAL DOSIMETRY MODELS FOR ALPHA-PARTICLES FOR USE IN MOLECULAR RADIOTHERAPY

By CHRISTOPHER J. WATCHMAN

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2005

Copyright 2005 by Christopher J. Watchman

ACKNOWLEDGMENTS I would like to take this opportunity to thank several people whose influence made this work possible. I would like to thank Dr. Wesley E. Bolch for his mentoring, encouragement and expertise over the last five years. I am grateful for the opportunities he has provided me. I am also grateful to my doctoral committee members, Drs. Edward Dugan, Benjamin Fregly, David Hintenlang, Mark Scarborough and George Sgouros for their willingness to share their time and knowledge with me. I would also like to thank the other members of the faculty and staff for their time and efforts on my behalf in my time at UF. I feel a deep debt of gratitude to the members of the Advance Laboratory for Radiation Dosimetry Studies who have been my colleagues and friends. My association with them has been most productive and rewarding. Finally I would like to thank my family for their continued support and patience with the whole doctoral process.

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TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................................................................................. iii LIST OF TABLES........................................................................................................... viii LIST OF FIGURES ........................................................................................................... xi ABSTRACT..................................................................................................................... xiv CHAPTER 1

INTRODUCTION ........................................................................................................1 Radionuclide Therapies or Molecular Radiotherapy....................................................1 Previous Skeletal Dosimetry Models............................................................................2 Target Cells...................................................................................................................5 Need for New Dosimetry Models.................................................................................8

2

ABSORBED FRACTIONS FOR ALPHA PARTICLES IN TISSUES OF TRABECULAR BONE: CONSIDERATIONS OF MARROW CELLULARITY WITHIN THE ICRP REFERENCE MALE...............................................................10 Introduction.................................................................................................................10 Materials and Methods ...............................................................................................12 Tissue Composition and Range-Energy Data......................................................13 Spatial Model for Marrow Tissue Transport .......................................................14 Chord-Based Model for Spongiosa Tissue Transport .........................................16 Results.........................................................................................................................19 Discussion...................................................................................................................20 Absorbed Fractions to the Active Bone Marrow.................................................20 Absorbed Fractions to the Bone Endosteum .......................................................22 Influence of Marrow Cellularity on Alpha-Particle Absorbed Fractions............24 Inter-Subject Variability in Alpha-Particle Absorbed Fractions .........................25 Skeletal-Averaged Absorbed Fractions for the ICRP Reference Male ...............26 Conclusion ..................................................................................................................27

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3

AGE AND IDIVIDUAL VARIABILITY IN ALPHA-PARTICLE ABSROBED FRACTIONS TO THE SKELETAL TISSUES .........................................................42 Introduction.................................................................................................................42 Materials and Methods ...............................................................................................43 Chord-Length Distributional Data.......................................................................43 Radiation Transport Methodology .....................................................................44 Results.........................................................................................................................45 Individual Variations with Trabecular Microstructure in the Adult....................45 Age Variations with both Trabecular Microstructure and Marrow Cellularity...47 Discussion...................................................................................................................50 Conclusion ..................................................................................................................52

4

ABSORBED FRACTIONS FOR ALPHA PARTICLES AND ELECTRONS IN TISSUES OF CORTICAL BONE..............................................................................61 Introduction.................................................................................................................61 Previous Dosimetric Models for Alpha Particles in Cortical Bone.....................62 Previous Dosimetric Model for Electrons in Cortical Bone................................64 Materials and Methods ...............................................................................................66 Tissue Composition and Range/Energy Data......................................................68 Chord-Based Model for Particle Transport in Cortical Bone..............................69 Stylized Bone Radiation Transport (SBoRT)......................................................73 Beta Particle Absorbed Fraction Calculation ......................................................75 Results.........................................................................................................................76 Discussion...................................................................................................................77 Alpha Particle Absorbed Fractions to the Cortical Bone Endosteum .................77 Electron Absorbed Fractions to the Cortical Bone Endosteum...........................80 Absorbed Fractions to Other Cortical Tissues.....................................................85 Conclusion ..................................................................................................................87

5

DERIVATION OF SKELETAL MASSES WITHIN THE CURRENT ICRP AGE SERIES: CONSIDERATIONS OF A 10-µM AND 50-µM ENDOSTEUM...........107 Introduction...............................................................................................................107 Marrow Masses .................................................................................................109 Bone and Endosteum Masses ............................................................................109 Bouchet and Bolch (1999).................................................................................110 Materials and Methods .............................................................................................111 Marrow Masses .................................................................................................112 Bone and Endosteum Masses ............................................................................115 Results and Discussion .............................................................................................119 Marrow Masses .................................................................................................119 Bone Masses......................................................................................................121 Endosteum Masses ............................................................................................122 Conclusion ................................................................................................................123

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ALPHA PARTICLE ABSORBED FRACTIONS IN THE SKELETAL TISSUES: CONSIDERATION OF A 50-µM ENDOSTEUM TARGET ...............133 Introduction...............................................................................................................133 Materials and Methods .............................................................................................135 Results.......................................................................................................................139 Disscusion.................................................................................................................140 Variations in the Definition of the Trabecular Endosteum Thickness ..............140 Bone Site Variability .........................................................................................143 Variation Due to Marrow Cellularity ................................................................145 Inter Subject Variability ....................................................................................148 Dosimetric Consequences of a 50 µm Trabecular Endosteum..........................148 Conclusion ................................................................................................................150

7

SPATIAL DISTRIBUTION OF CD34+ PRIMITIVE HEMATOPOEITIC CELLS AND BLOOD VESSELS WITH IN THE MARROW CAVITIES OF TRABECULAR BONE............................................................................................164 Introduction...............................................................................................................164 Materials and Methods .............................................................................................166 Slide Preparation ...............................................................................................167 Image Acquisition and Processing ....................................................................167 Results.......................................................................................................................170 Discussion.................................................................................................................172 Conclusion ................................................................................................................177

8

CONCLUSIONS AND FUTURE WORK...............................................................187 Conclusions...............................................................................................................187 Future Work..............................................................................................................189

APPENDIX A

A REVISED ALGORITHM FOR THE MAXIMUM ENDOSTEAL CHORD LENGTH ..................................................................................................................193

B

ALPHA PARTICLE ABSORBED FRACTIONS IN ICRP REFERENCE MALE 195

C

SBORT-CBICT DERIVATION ...............................................................................218

D

ALPHA AND BETA PARTICLE ABSORBED FRACTIONS IN CORTICAL BONE TISSUES.......................................................................................................220

E

MARROW CAVITY MODEL PROGRAM............................................................231

F

LOW CELLULARITY CAVITY MODEL PROGRAM.........................................240

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G

3D CHORD BASED INFINITE SPONGIOSA TRANSPORT COMPUTER CODE .......................................................................................................................246

H

CHORD BASED INFINITE CORTICAL TRANSPORT COMPUTER CODE ....302

LIST OF REFERENCES.................................................................................................332 BIOGRAPHICAL SKETCH ...........................................................................................345

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LIST OF TABLES Table

page

1-1

ICRP 30 alpha particle absorbed fractions .................................................................9

2-1

Candidate alpha-particle emitters for radionuclide therapy. ....................................35

2-2

Elemental composition of the tissues of skeletal spongiosa.....................................36

2-4

Ratios of alpha-particle absorbed fractions in the skeletal tissues of the lumbar vertebra….................................................................................................................38

2-5

Marrow cellularities and fractional tissue distributions in the skeleton of the ICRP Reference Male...............................................................................................39

2-6

Skeletal-averaged alpha-particle absorbed fractions in the ICRP Reference Male with explicit consideration of reference marrow cellularities (age 25y)..................40

2-7

Skeletal-averaged alpha-particle absorbed fractions in the ICRP Reference Male with explicit consideration of reference marrow cellularities (age 40y)..................41

3-1

Mean chord-lengths for marrow cavities and bone trabeculae for all subjects. .......58

3-2

Reference bone marrow cellularities as a function of age........................................59

3-3

Inter-subject variations in alpha-particle absorbed fractions at 100% marrow cellularity..................................................................................................................60

4-1

Reference alpha and beta particle absorbed fractions from ICRP 30. ...................102

4-2

Absorbed fractions for alpha and beta particles used in the OLINDA code..........103

4-3

Average transverse chord length distributions through haversian cavities and through cortical bone matrix of three difference skeletal sites. .............................104

4-4

Elemental composition of the tissues of cortical bone ...........................................105

4-5

Measured long bone diameters and thicknesses.....................................................106

5-1

Surface to volume ratios used in trabecular bone calculation. ...............................127

5-2

Calculation of fraction of total skeleton mass in children......................................128 viii

5-3

Active marrow masses for all ages using cellularity method and density corrected Bouchet and Bolch .................................................................................129

5-4

Summary of bone masses for all ages. ...................................................................130

5-5

Summary of 10-µm endosteal masses for all ages. ................................................131

5-6

Trabecular endosteum masses for both 10-µm and 50-µm endosteum..................132

6-1

Descriptions and definitions of tissue used in this study. ......................................159

6-2

Ratios of absorbed fractions from TAM, TBS and TBV sources irradiating the TBE of a four adult subjects with respect to the ICRP 44-y reference male. ........160

6-3

S-values (mGy/MBq-s) for the cervical vertebrae, parietal bone and os coxae of a 66-y male subject for 211At, 212Bi, 213Bi and 223Ra..............................................162

6-4

Endosteum masses at 10 µm and 50 µm thickness in a 66-y male at reference marrow cellularities................................................................................................163

7-1

Characteristics of specimens used in present study. .............................................186

B-1 Absorbed fractions to TBE and TBV for α-emissions within the TBE of the Leeds 44y male.......................................................................................................195 B-2 Absorbed fractions to TBE and TBV for α-emissions on the TBS of Leeds 44y male. .......................................................................................................................196 B-3 Absorbed fractions to TBE and TBV for α-emissions within the TBV of the Leeds 44y male.......................................................................................................197 B-4 Absorbed fractions to active bone marrow (TAM) for α-emissions within the cervical vertebrae of the Leeds 44y male...............................................................198 B-5 Absorbed fractions to active bone marrow (TAM) for α-emissions within the femur head of the Leeds 44y male .........................................................................200 B-6 Absorbed fractions to active bone marrow (TAM) for α-emissions within the femur neck of the Leeds 44y male .........................................................................202 B-7 Absorbed fractions to active bone marrow (TAM) for α-emissions within the iliac crest of the Leeds 44y male....................................................................................204 B-8 Absorbed fractions to active bone marrow (TAM) for α-emissions within the lumbar vertebrae of the Leeds 44y male ................................................................206 B-9 Absorbed fractions to active bone marrow (TAM) for α-emissions within the parietal bone of the Leeds 44y male.......................................................................208 ix

B-10 Absorbed fractions to active bone marrow (TAM) for α-emissions within the ribs of the Leeds 44y male. ....................................................................................210 B-11 Absorbed fractions to TBE from α-emissions within the TAM of the Leeds 44y male .................................................................................................................212 B-12 Absorbed fractions to TBV from α-emissions within the TAM of the Leeds 44y male ........................................................................................................................215 D-1 Absorbed fractions to the cortical bone endosteum (CBE) for α-emissions within various source tissues..................................................................................220 D-2 Absorbed fractions to the cortical haversian space (CHS) for α-emissions within various source tissues .............................................................................................222 D-3 bsorbed fractions to the cortical bone volume (CBV) for α-emissions within various source tissues .............................................................................................224 D-4 Absorbed fractions to the cortical bone endosteum (CBE) for β-emissions within various source tissues .............................................................................................226 D-5 Absorbed fractions to the cortical haversian space (CHS) for β-emissions within various source tissues .............................................................................................227 D-6 Absorbed fractions to the cortical bone volume (CBV) for β-emissions within various source tissues .............................................................................................228 D-7 Absorbed fractions to the cortical bone cortex tissues for β-emissions within spongiosa tissues ....................................................................................................229 D-8 Absorbed fractions to the cortical bone cortex tissues for β-emissions within cortical bone cortex volume ...................................................................................230

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LIST OF FIGURES Figure

page

2-1

Histology slides of normal human bone marrow at two different marrow cellularities ...............................................................................................................30

2-2

Geometric model used to partition sampled marrow cavity chords into subtrajectories. ...............................................................................................................31

2-3

Absorbed fractions for an active marrow target.......................................................32

2-4

Absorbed fractions for an endosteum target from alpha sources. ............................33

2-5

Dependence of the active marrow absorbed fraction with changes in marrow cellularity within the lumbar vertebrae ....................................................................34

3-1

Inter-subject variations in alpha-particle absorbed fractions within the lumbar vertebrae at 100% marrow cellularity. .....................................................................54

3-2

Inter-subject variations in values of φ(TAM ← TAM) for alpha particles emitted within the iliac crest ....................................................................................55

3-3

Inter-subject variations in values of φ(TAM ← TBS) for alpha particles emitted within the iliac crest .................................................................................................56

3-4

Inter-subject variations in values of φ(TAM ← TBV) for alpha particles emitted within the iliac crest .................................................................................................57

4-1

Traverse chord-length distributions across (A) the osseous tissues (distances between haversian cavities), and (B) the haversian cavities (haversian space and endosteal layer) ........................................................................................................89

4-2

Range-energy plots for (A) alpha particles and (B) beta particles in tissues of cortical bone. ............................................................................................................90

4-3

Transverse view of the cortical bone microstructure ...............................................91

4-4

Diagram illustrating the transport method used for alpha particle tracking across a given osteon...........................................................................................................92

4-5

Diagram illustrating different source geometries the in transverse plane ................93

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4-6

CT image of a cadaver used in determination of nominal cortical thickness and medullary cavity diameter ........................................................................................94

4-7

Diagram showing the cylindrical geometry used in MCNP5 for the SBoRT calculation of macroscopic absorbed fractions in the long bones. ...........................95

4-8

Alpha particle absorbed fractions to the cortical bone endosteum...........................96

4-9

A comparison of the endosteum absorbed fraction from sources of the trabecular bone surface (TBS) and the cortical bone surface (CBV)........................................97

4-10 Absorbed fractions for the humerus cylindrical bone run in MCNP5 .....................98 4-11 Electron absorbed fractions to the cortical bone endosteum....................................99 4-12 Absorbed fraction in multiple layers of endosteum ...............................................100 4-13 Diagram illustrating the effects of curvature on the endosteal dose as a function of sampled transverse chord length. .......................................................................101 5-1

Error associated with S/V method..........................................................................125

5-2

Total bone masses as a function of age ..................................................................126

6-1

Diagram illustrating the placement of sampled chords occurring in the first endosteum region ...................................................................................................152

6-2

Illustration of how the sampled marrow cavity chord (dMC) is sampled for an active marrow source. ............................................................................................153

6-3

Plots showing the absorbed fraction in the sixth cervical vertebrae in a 66-y male…….. ..............................................................................................................154

6-4


6-5


6-6

Diagrams illustrating the variation in TBE absorbed fractions as function of bone site…..............................................................................................................157

6-7

Diagrams illustrating the variation in TBE absorbed fractions as function of marrow cellularity in the cervical vertebrae of a 66-y male...................................158

7-1

Images of bone marrow biopsies from iliac crest ..................................................179

7-2

Illustration of the imaged based area measurements of concentric layers from the bone surfaces. .........................................................................................................180 xii

7-3

Scatter plot illustrating the raw count data for CD34+ cells. Note the higher density of cells near the surface of the bone trabeculae. ........................................181

7-4

Histogram relating the frequency of CD34+ cells with respect to the bone trabeculae with area correction applied..................................................................182

7-5

Histogram relating the frequency of blood vessels with respect to the bone trabeculae with area correction applied..................................................................183

7-6

Histogram relating the frequency of CD34+ cells to blood vessel distances..........184

7-7

Figure presenting a stylized representation of a marrow cavity.............................185

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy SKELETAL DOSIMETRY MODELS FOR ALPHA-PARTICLES FOR USE IN MOLECULAR RADIOTHERAPY By Christopher J. Watchman December 2005 Chair: Wesley E. Bolch Major Department: Nuclear and Radiological Engineering Molecular radiotherapy is a cancer treatment methodology whereby a radionuclide is combined with a biologically active molecule to preferentially target cancer cells. Alpha-particle emitting radionuclides show significant potential for use in molecular radiotherapy due to the short range of the alpha-particles in tissue and their high rates of energy deposition. Current radiation dosimetry models used to assess alpha emitter dose in the skeleton were developed originally for occupational applications. In medical dosimetry, individual variability in uptake, translocation and other biological factors can result in poor correlation of clinical outcome with marrow dose estimates determined using existing skeletal models. Methods presented in this work were developed in response to the need for dosimetry models which account for these biological and patientspecific factors. Dosimetry models are presented for trabecular bone alpha particle dosimetry as well as a model for cortical bone dosimetry. These radiation transport models are the 3D chord-based infinite spongiosa transport model (3D-CBIST) and the chord-based infinite cortical transport model (CBICT), respectively. Absorbed fraction data for several xiv

skeletal tissues for several subjects are presented. Each modeling strategy accounts for biological parameters, such as bone marrow cellularity, not previously incorporated into alpha-particle skeletal dosimetry models used in radiation protection. Using these data a study investigating the variability in alpha-particle absorbed fractions in the human skeleton is also presented. Data is also offered relating skeletal tissue masses in individual bone sites for a range of ages. These data are necessary for dose calculations and have previously only been available as whole body tissue masses. A revised 3DCBIST model is also presented which allows for changes in endosteum thickness to account for revised target cell location of tissues involved in the radiological induction of bone cancer. In addition, new data are presented on the location of bone-marrow stem cells within the marrow cavities of trabecular bone of the pelvis. All results presented in this work may be applied to occupational exposures, but their greatest utility lies in dose assessments for alpha-emitters in molecular radiotherapy.

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CHAPTER 1 INTRODUCTION Radionuclide Therapies or Molecular Radiotherapy Traditionally, beta emitters have been used in radionuclide therapies (or molecular radiotherapy),1-8 but more recently, great interest has been shown in the use of alpha particle emitters for cancer therapy.7, 9-24 Alpha particles are attractive for this methodology as they demonstrate short ranges due to their high stopping power.18 A high linear energy transfer (LET) is achieved which can allow for large amounts of energy to be deposited at the target site, potentially resulting in cell death with a single traversal. The soft-tissue range of clinically relevant alpha-emitters is on the order of 5090 µm.25 These ranges relate to emission energies of approximately 5-9 MeV. Some of the alpha emitters investigated for use in radionuclide therapies have been 211At, 212Bi, 213

Bi, 212Pb, 225AC, 255Fm, 223Ra and 149Tb.18 Alpha-particle molecular radiotherapy involves the attachment of an alpha-

emitting radionuclide to a biologically active molecule. The goal is to improve the specificity and localized distribution of the alpha particle radioconjugate. One method involves combining the alpha emitter with biphosphonates for treatment of skeletal tumors. Another method combines a radionuclide with an antibody and is called radioimmunotherapy (RIT). Success has been achieved in combining 213Bi with HuM195(anti-CD33),6, 23 and 211At with biophospates.16, 24 Additionally, 211At has also been combined with monoclonal antibodies.16 Clinical trials of the 213Bi combination have been performed, and further clinical trials are in process or being planned. 1

2 Questions of marrow toxicity are of major concern in molecular radiotherapy. In radiological protection applications, alpha emitters tend to be of lower energy (≤5.5 MeV) while those of interest in molecular radiotherapy are of higher energy from ~5-9 MeV. Higher energy results in greater particle transport ranges. Current dosimetry models, as will be discussed in the next section, were designed with the shorter range alpha particles in mind. Medical alpha emitters also differ in comparison to those of interest in health physics applications in that they tend to have significantly shorter half lives (~hours or days vs. many years). Greater dose rates, due to the shorter half lives, further complicate dosimetry issues. Currently dosimetry methods do not correlate well with clinical bone marrow response;26 consequently, new approaches in alpha-emitter marrow dosimetry of skeletal tissues are warranted. Previous Skeletal Dosimetry Models Trabecular bone models currently used for many bone dosimetry applications are based upon the work of FW Spiers and his students at the University of Leeds during the period 1960 to 1980.27-40 This work is now thirty years old and is based upon modeling using the technology of the period. A 44-year old male trauma victim was used to obtain bone samples for this study, while data from Mechanik’s skeletal marrow mass publication was used to estimate marrow masses.41 Seven bone sites were obtained for this study including the femur neck, femur head, parietal bone, lumbar vertebrae, cervical vertebrae, rib and iliac crest. Modeling of these bone sites consisted of obtaining twodimensional physical slices of each trabecular bone site. An optical scanner was developed to measure chord-length distributions of bone and marrow spaces within these seven bone specimens. From these measurements, a frequency distribution of chord lengths was obtained. Using these chord-length distributions and range-energy

3 relationships, marrow absorbed fractions were calculated for several radionuclides. These radionuclides, 14C, 18F, 22Na, 32P, 45Ca, 90Sr, and 90Y, were chosen due to their application in health physics. Additionally, 226Ra, which is an alpha emitter, was also studied.42 Absorbed fractions and dose coefficients from this model were related in an approximate fashion to values appropriate in three dimensions. Furthermore, their modeling scheme did not consider the presence of adipocytes within the marrow cavities. Alpha particle bone dosimetry models used by the International Commission on Radiological Protection (ICRP) are based upon the assumption that the short range of the particle allows for simple modeling schemes. The models used by the ICRP in Publication 30,43 are based upon work by M.C. Thorne.44, 45 The ICRP uses an infinite two-dimensional planar model to describe marrow doses from emissions within the volume and on the surfaces of bone trabeculae. An absorbed fraction for active (or red) marrow self-irradiation simply assumes that 100% of the emission energy is locally deposited. Cortical bone tissue dosimetry follows similar planar modeling. Table 1-1 relates the ICRP 30 values for each irradiation source and target combination in skeletal dosimetry. Furthermore, this model assumes no energy dependency in the absorbed fraction with the exception of the 200 keV energy cutoff for electrons in trabecular bone. Recently newer modeling strategies have been proposed by Eckerman as published in Stabin and Siegel.46 The 2003 Eckerman model, which is used in the OLINDA/EXM 1.0 computer code, also used the Whitwell chord length data. Unlike previous models, Eckerman also allowed for energy variations in alpha particle absorbed fractions. Absorbed fractions in this model did display differences in comparison to the ICRP model. Note that each of the previously mentioned dosimetry models make no attempt,

4 with respect to alpha emitters, to address individual variability in the absorbed fraction, or to address issues related to inactive marrow (adipocytes) within bone marrow cavity. Other models used in marrow dosimetry rely upon microdosimetry techniques. These models use Monte Carlo methods to predict cell death based upon frequencies of alpha particle tracks traversing cell nuclei. These calculations involve describing a mathematical distribution of cells within an extracellular fluid matrix. Within the extracellular fluid, alpha particle emissions originate randomly through the use of Monte Carlo sampling. Particle track directions are then chosen randomly and the frequency of alpha particle tracks crossing cell nuclei is tallied. Based upon these frequencies, cell line outcomes are calculated. 3, 5, 7, 22, 47-53 Stichcombe and Roeske have proposed a method of combining this type of microdosimetric information with the MIRD schema.7, 52 Their method is further refined into S-values containing information concerning the single hit and multi-hit frequencies. Dosimetry estimates are currently limited to Phase I clinical trials and occasionally to Phase II trials. Phase I clinical trials involve a small number of patients where testing of safety, dose levels and clinical response are evaluated. Phase II trials are designed to evalulate anti-cancer effects of the proposed treatment methodology. Routine patientspecific dosimetry is not performed clinically at this time, as the dose estimates, obtained in Phase I trials, do not necessarily reflect the biological outcome as was previously mentioned. When done, the medical community uses macroscopic dose models described above, which were originally developed for occupational applications in radiological protection and health physics. This is done since these skeletal dosimetry models are the only available models to the clinical community. Better skeletal

5 dosimetry is needed if routine clinical dose estimates are to be performed as part of the therapeutic planning procedure as is the case in traditional radiation oncology. Target Cells The development of skeletal dosimetry models with the potential for improvements in dose-response correlations thus requires a better understand of the specific target tissues at risk from irradiation. Within the skeleton, two main radiosensitive tissues are designated as target tissues in skeletal dosimetry models. These are the hematopoietically active bone marrow and trabecular and cortical endosteum. Each tissue is important in dosimetry applications because each tissue has a replicating cell population. Dividing cell populations are more radiosensitive due to the increased potential for not only cell death but the introduction of errors in the DNA replication process. Of these cell populations, the least differentiated cell populations are at greatest risk with decreasing risk seen in each successive cell differentiation stage. Within bone marrow, the hematopoietic stem cell is the most primitive and undifferentiated cell. In the endosteum, a subset of tissues within the marrow cavity, the mesenchymal stem cells lining the bone trabeculae are also a primitive cell population. Each of these stem cell lines divides into two distinct cell populations, marrow tissues and osteonal tissues. Marrow tissues divide into multilineage progenitor cells, early progenitor cells, late progenitor cells, blast cells and lastly mature hematopoeitic or lymphoid cells.54 Mesenchymal stem cells within the marrow cavities develop into osteoprogenitor cells such as osteoblasts and osteoclasts. Other tissue committed stem cells are also found in the bone marrow which do not contribute to the previously named cell lines. There is evidence that these other stem cells are stored in bone marrow and then translocated to their specific committed tissue when needed. 55-58

6 For dosimetry purposes, knowledge of the location of the primitive cells within the marrow cavity may allow for more accurate dosimetry models. Current practice in bone marrow dosimetry is to assume that the hematopoeitic stem cells, and all other hematopoeitic cells at risk, are located uniformly within marrow cavities. This assumption allows for the averaging of the absorbed dose across the entire marrow cavity and as a result over all marrow tissue regions of trabecular spongiosa. Work by Charlton, Utteridge and Beddoe59 is used to support this uniform assumption. In their work, stem cells were stained using a CD34 antibody. Distance measurements were then made from the stained cells to the surface of fat cells within the marrow cavities. Compilation of these measurements indicated a uniform distribution of stem cells to adipocyte distances with in the marrow cavities. Work by Shah et al.60 has shown that adipocytes in bone marrow are also randomly distributed within the marrow cavity. The Charlton et al. study assumes that if the adipocytes are randomly distributed in the cavity and if the stem cells are uniformly located from the adipocytes, then the stem cells must also be randomly located throughout the marrow cavity. They did not account for the spatial location of the stem cells with respect to the surfaces of the bone trabeculae. Since their objective was to address stem cell dose from radon daughter alpha-emissions from marrow adipocytes, their data were appropriately applied in their study. Had other sources such as active bone marrow, bone trabeculae surfaces or bone trabeculae volumes been used, their assumption of uniformity may not have applied. In contrast to this work, Lord and his collaborators61-66 have found spatial gradients in hematopoietic cells, identified by cytokine expression, within the medullary cavity of the mouse femur. Their results demonstrated that the most primitive cells were

7 preferentially located closer to the interior bone surfaces, while the most mature cells tended to be located closer to the central portion of the marrow cavity. Note that this work represents murine data and not human data as did the Charlton et al. study. Despite this fact, if a spatial gradient does exist in human bone marrow, then using the uniformity assumption will incorrectly assess risk to the radiosensitive tissues of the bone marrow. When the endosteum tissues are considered, the traditional definition of this target tissue has been to consider a layer of osteoprogenitor cells located within 10 µm from the bone surfaces (in both trabecular and cortical bone). This definition was first proposed in ICRP Publication 26.67 Using this definition, Eckerman68, 69 has considered the endosteum to be a sub-tissue target within the bone marrow. In contrast, Bolch70-80 and his collaborators have treated the endosteum as a completely separate target from the active bone marrow. Recently, studies of the relevant cells for the induction of radiogenic bone cancers have led to a questioning of the current ICRP definition of endosteum. In two review papers, Gössner et al.,81, 82 have presented a strong case indicating that irradiation of cells, as deep as 50 µm into the marrow cavity, may develop into bone cancers. Irradiation of not only the mesenchymal stem cells but also the other osteoprogenitor cells, which tend to be ~10-50 µm in diameter, seems to be responsible for these cancers. Note that the 50 µm layer of tissues is well within the range of therapeutic alpha emitter particle ranges. The data reviewed by Gössner et al. indicate that by only determining the absorbed dose to the current 10 µm endosteum, dose estimates are incorrectly determining dose to the target cells at risk of radiation induced bone cancer.

8 Need for New Dosimetry Models The current poor correlation of calculated marrow absorbed doses with marrow toxicity and clinical response indicates the need for new dosimetry approaches for alpha emitters. The work presented in this dissertation has led to the development of models which better incorporate our understanding of tissue histology in skeletal tissues. Two radiation transport models, the 3D Chord Based Infinite Spongiosa Transport (Chapter 2) and Chord Based Infinite Cortical Transport (Chapter 4), have been developed to better incorporate many of the issues mentioned earlier. In Chapter 3, an investigation quantifying the individual and age variability of alpha particle absorbed fractions in spongiosa tissues is presented. In Chapter 5, skeletal tissue masses for several bone sites within the body are developed from data in the ICRP literature as needed for the application to the results of Chapter 2 (trabecular bone) and Chapter 4 (cortical bone). Chapter 6 deals with the dosimetry consequences of the adoption of a 50 µm endosteum layer, while Chapter 7 presents data regarding the spatial density of stem cells within the marrow cavities of human bone marrow. Each of these chapters presents methods for improved skeletal dosimetry calculations and gives support data for their applications in either health physics or medical physics. The methods presented may potentially provide a pathway for improved patient-specific dosimetry in molecular radiotherapy with corresponding improvements in the correlation of tissue dose and clinical response.

9 Table 1-1. ICRP 30 alpha particle absorbed fractions Source Target Absorbed Fraction TBS TBV 0.025 TBS TBS 0.25 TAM TBV 0.05 TAM TBS 0.5 TAM TAM 1.0 TAM CBS 0.0 TAM CBV 0.0 CBS CBV 0.01 CBS CBS 0.25 TBS - trabecular bone surface, TBV - trabecular bone volume, TAM - trabecular active marrow, CBS - cortical bone surface, CBV - cortical bone volume

CHAPTER 2 ABSORBED FRACTIONS FOR ALPHA PARTICLES IN TISSUES OF TRABECULAR BONE: CONSIDERATIONS OF MARROW CELLULARITY WITHIN THE ICRP REFERENCE MALE1 Introduction Beta-particle emitters have played a prominent role in the development of radionuclide-based cancer therapy. More recently, increased interest has been shown in the potential of alpha-emitters for radioimmunotherapy, particularly for leukemia and micrometastases.20, 23, 83 Alpha particles provide an attractive alternative to beta-particles owing to their higher collisional stopping power (providing increased absorbed dose to tumor cells) and correspondingly shorter range (providing increased sparing of nontargeted tissues). Examples of alpha-emitters under clinical investigation for radionuclide therapy are listed in Table 2-1.18 When alpha-emitters are localized at low activity concentrations in targeted tissues, techniques of microdosimetry are generally required to characterize the frequency distribution of absorbed dose to individual target cells. At high activity concentrations, as would be expected in clinical alpha-particle radioimmunotherapy, the variation in cellular dose is small, and macroscopic dosimetry techniques may be applied as formulated under the MIRD schema. 84 At present, standardized values of absorbed fraction (φ) for alpha particles in the skeletal tissues are limited to two principle sources: the International Commission on 1

This chapter has been published in the Journal of Nuclear Medicine. CJ Watchman, DW Jokish, PW Patton, DA Rajon, G Sgouros and WE Bolch. Absorbed Fractions for Alpha Particles in Tissues of Trabecular Bone: Considerations of Marrow Cellularity within the ICRP Reference Male. J Nuc Med; 46:117-1185.

10

11 Radiological Protection (ICRP) in their Publication 30,85 and the 2003 Eckerman model as published by Stabin and Siegel60 for use in the OLINDA code. While the ICRP has provided many important updates to both physiological and anatomical reference values for the skeleton, 86, 87 no fundamental updates to its skeletal dosimetry model have been issued. The ICRP 30 bone model, developed to provide a conservative dosimetric framework for radiation protection of the skeletal tissues, gives values of alpha-particle absorbed fraction that are independent of both particle energy and skeletal site. Literature sources cited as references for the ICRP 30 model include studies by Thorne44, 45 and by Mays and Sears88 in which simple geometrical configurations were adopted such as infinite parallel planes (representing the bone-marrow interface) and spheres (representing the marrow space with an endosteum layer on its surface). The beta particle results of Whitwell and Spiers28 are also used as reference values for alpha particles irradiating the active marrow from bone volume sources. In the 2003 Eckerman model, an energy dependence is introduced for some source-target tissue combinations, while for others, values from the ICRP 30 model are adopted. In the present study, an expanded model of alpha-particle transport in the skeletal tissues is given that explicitly accounts for absorbed fraction variations with, not only particle energy, but with skeletal site and marrow cellularity. Each parameter is potentially important in improving the patient-specificity of the skeletal dose estimate. As shown in Table 2-1, alpha energies of clinically relevant radionuclides range from ~5.5 to 9 MeV. In contrast, those of interest in occupational radiation protection (for which the ICRP 30 model was established) range from only ~4 to 5.5 MeV. Furthermore, when bone-site-specific radionuclide therapies are applied, variations in the

12 trabecular micro-architecture (bone trabeculae and marrow cavity sizes) may alter patterns of alpha energy deposition beyond that predicted by a single skeletal-averaged set of absorbed fractions. Finally, marrow cellularity can vary greatly among different patients,89 and is not considered in either of the two existing models. As shown in Figure 2-1, adipocytes localized along the trabecular surfaces at low marrow cellularities can significantly reduce the alpha-particle energy available for deposition to active bone marrow. Materials and Methods In this study, alpha-particle transport in the skeletal tissues is accomplished using techniques similar to those developed for electrons in models published by Eckerman and Stabin69 and by Bouchet et al.70 In the Eckerman and Stabin model stochastic sampling of chord-length distributions from bone samples was used to deterministically transport electrons using range-energy data. Bouchet et al, on the other hand, used the EGS4 transport code to calculate energy deposition while still incorporating the chord-length data in the transport geometry. The 3D microstructure of individual bone trabeculae and marrow cavities, used in this study, are taken from the chord-length distributions published by Whitwell28, 90 at the University of Leeds for seven skeletal sites from a 44-year male subject. The unique feature of the present model, however, is the use of a supplemental 3D spatial model of the active and inactive tissues within the marrow space. Through the use of range-energy relationships, absorbed fractions to active marrow, as well as bone endosteum and bone trabeculae are calculated for alpha-particle emissions up to 10 MeV. The details of this 3D chord-based infinite spongiosa transport (3D-CBIST) model for skeletal dosimetry are outlined below. In the model, we adopt the following nomenclature to define various

13 source and target tissues: TBV – trabecular bone volume, TBE – trabecular bone endosteum, TBS – trabecular bone surfaces, TAM – trabecular active (“red”) marrow, and TIM – trabecular inactive (“yellow”) marrow. The modifying phrase “infinite spongiosa transport” indicates that we are only considering alpha transport within the tissues of trabecular spongiosa (marrow, endosteum, and bone trabeculae), and any crossfire from cortical bone and the interior spongiosa regions of the skeletal site is ignored. While this assumption is rarely valid for higher-energy beta particles in the skeleton75, the model is considered to be quite adequate for alpha particles even at energies approaching 10 MeV. For TBV sources, the radiopharmaceutical is assumed to be distributed uniformly within the volume of the bone trabeculae. Future extensions of the model may accommodate its variation with depth when the physical half-life exceeds bone remodeling half-times. Generally, however, TBS and TBE sources would be more appropriate for bone-seeking agents in radionuclide therapy. The former would correspond to agents initially incorporated in the osseous tissues at bone-remodeling sites, while the latter would correspond to agents directly targeting osteoblasts and/or osteoclasts. Tissue Composition and Range-Energy Data Elemental compositions and mass densities for the tissues of trabecular spongiosa were taken from Report 46 of the International Commission on Radiological Units and Measurements (ICRU)91 (see Table 2-2). Range-energy functions were calculated for active (red) marrow, inactive (yellow) marrow, and trabecular endosteum using the Bragg-Kleeman rule92 with liquid water93 as the reference media for range scaling:

RT = RH2O

ρH2O ρT

AT , AH2O

(2-1)

14 where RT is the CSDA (continuous slow-down approximation) range in the desired tissue (TAM, TIM, or TBE), RH2O is the corresponding linear range in water, and ρT and ρH20 are their respective mass densities. In Eq. 2-1, the effective atomic number of these tissues, AT (as well as AH2O), is calculated as: ⎛ w AT = ⎜ ∑ i ⎜ i A i ⎝

-1

⎞ ⎟ , ⎟ ⎠

(2-2)

where wi is the mass fraction for the ith element within that tissue. Trabecular bone was similarly scaled using ICRU 49 compact bone as the reference tissue93. Tabular data for CSDA range versus particle energy were thus created for all tissues for use in the energy deposition calculation. Ranges at intermediate energies were assessed via interpolation of tabular values. Spatial Model for Marrow Tissue Transport As previously noted by Bolch et al.,94 the chord-based skeletal models of both Eckerman and Stabin69 and of Bouchet et al.70 were constructed in such a fashion that considerations of marrow cellularity could not be made explicitly during particle transport (only via energy-independent scaling of absorbed fractions following particle transport). To permit such considerations during alpha-particle transport, a spatial model of the marrow tissues was created as demonstrated schematically in Figure 2. Each model consists of two regions: (1) an inner sphere of marrow in which randomly selected marrow chords are started (each representing the potential trajectory of an alpha particle track emitted within the active marrow or emerging from the endosteal layer into the marrow space), and (2) a buffer region in which marrow chords (and thus the alphaparticle tracks) may terminate, but not begin. The buffer region (scaled to the active

15 marrow range of 10-MeV alpha particles) thus ensures that the sampled marrow-cavity chord will always fully lie within tissues of the marrow spatial model. The 1000-µm diameter of the marrow spatial model corresponds roughly to the nominal chord-length seen for marrow cavities in the Leeds 44-year male. As shown in Figure 2-2, regions of inactive (or yellow) marrow are simulated as a series of randomly placed spherical fat cells (adipocytes). Adipocyte diameters are randomly sampled from a five-bin histogram (92, 72, 56, 40, and 20 µm) that approximate the Gaussian distribution of sizes reported by Reverter et al.95 in normal human bone marrow (mean diameter of 56.7 ± 5.6 µm). Marrow models of varying marrow cellularity (from 10% to 100%) are generated by increasing the number of randomly placed adipocytes within the marrow sphere. For marrow cellularities greater than 50%, adipocyte overlap is prohibited as cell clustering is only prominent at cellularities below 50%.60 For marrow cellularities below 50%, the 50% cellularity model is modified through step-wise increases in adipocyte diameter (5% each) and by abandoning the restriction on adipocyte overlap. Adipocyte diameter increases (representing multicellular adipocyte clusters) are continued until the desired overall marrow cellularity is achieved. Transverse views through marrow models at cellularities of 70% (no cell clusters), 40% (few cell clusters), and 20% (multiple cell clusters) are shown in the lower portion of Figure 2-2. Note that in all 3D spatial models of the marrow space, neither the bone trabeculae for the trabecular endosteum are represented – their influence on particle transport is handled separately by chord-based techniques described below.

16 Chord-Based Model for Spongiosa Tissue Transport Alpha-particle transport in the present study is performed through random and alternate sampling of cumulative density functions (CDFs) for µ-random (external) chord lengths across bone trabeculae (dT) and the marrow cavities (dMC) in each of the seven skeletal sites of the Leeds 44-year male. Corresponding distributions under I-randomness (interior) are applied in regions of alpha-particle source emissions.96 For consistency with the sample preparation and scanning methods of the Leeds studies, we make a distinction between the marrow cavity (MC - total volume of tissue between bone trabeculae inclusive of the endosteal layer) and the marrow space (MS - total marrow tissue volume between bone trabeculae exclusive of the endosteal layer). Explicit treatment of the endosteal layer, as well as the active and inactive tissues of the bone marrow, is discussed below. The transport methodology is best described by first considering an alpha-emitter uniformly distributed within the tissues of the bone trabeculae (i.e., TBV source). The transport code first randomly samples a bone chord-length dTmax from the I-random cumulative density function CDFI (dTmax) for the skeletal site of interest (e.g., cervical vertebra). This sampled chord length is treated as the maximum possible distance that an alpha particle may travel within its bone trabecula prior to entering the endosteal layer. The transport distance actually taken, dT, is thus uniformly sampled across this interval: [0, dTmax]. The range-energy function for alpha particles in bone tissue is then used to determine the total energy expended by the particle within that bone trabecula. If residual kinetic energy remains, the particle is further transported into (and potentially across) the adjacent endosteal layer.

17 For the alpha particle emerging from a bone trabecula, a random marrow-cavity chord length dMC is sampled under µ-randomness (CDFµ) for the same skeletal site. The value of dMC is at most composed of two endosteal chord lengths (near and far side of the marrow cavity) and an intervening chord length across the marrow space: dMC = dE1 + dMS + dE2.

(2-3)

Values of dE1 and dE2 (and thus dMS) are determined through uniform sampling of the cosine of the entry angle (η) across each 10-µm endosteal layer: η1 ∈ [0 : 1] with d E1 = (10 µm) η1

and

η2 ∈ [0 : 1] with d E2 = (10 µm) η2

and

(d

E1

(2-4)

+ d E2 ) ≤ dEmax .

The assignment of dEmax in this and in other chord-based skeletal models is discussed in Appendix A. If (dE1 + dE2) < dEmax, then dMS = dMC – (dE1 + dE2)

with

dMS ≥ 0.

(2-5)

If, however, (dE1 + dE2) > dEmax, then both near and far endosteal chord-lengths are iteratively rescaled: ⎛ d E 1 ⎞ max dE 1 = ⎜ ⎟ dE ⎝ dE 1+ dE 2 ⎠ dE 2 = d Emax − dE 1

and and

(2-6)

dMS = d MC − ( dE 1 + dE 2 ) .

The alpha-particle range-energy function in endosteal tissues is then used to determine the kinetic energy lost within the first endosteal layer. If residual kinetic energy still exists, and dMS > 0, the alpha particle is further transported within the tissues of the marrow space. At this point, the chord-length dMS is placed at a random location and direction within the transport region of the marrow spatial model (shown in Fig. 2-2). Consider for

18 the moment that dMS is given as chord A−B. This marrow space chord thus represents the potential trajectory of the alpha particle emerging from the surface of the bone endosteum in which the first tissue encountered is active marrow. In this particular case, however, the particle has only sufficient kinetic energy to carry it from starting point A to point B* in the marrow tissues. During its traversal, the alpha particle traverses a single adipocyte. Consequently, the particle trajectory A−B* can be divided into three marrow subtrajectories: dM1 (distance from point A to the adipocyte entry point), dM2 (distance across the adipocyte), and dM3 (distance from the adipocyte exit point to the particle termination point B*). Energy deposition to active marrow for this particle would be recorded only across active-marrow sub-trajectories dM1 and dM3. As another example, another sampled chord-length dMS might be positioned at chord C−D in Figure 2-2. In this case, the alpha particle “sees” an adipocyte immediately upon its emergence from the bone endosteum, and must expend some kinetic energy within that fat cell before it enters (and then stops) within the active marrow tissues. As the fat fraction of the geometrical model increases (marrow cellularity decreases), this scenario becomes more and more prevalent, thus simulating the presence and increased loss of alpha-particle energy in the first-fat layer for particles emerging from the trabecular endosteum. Furthermore, the alpha particle in this example is able to fully travel the sampled chord-length dMS. In this case, residual kinetic energy still remains at point D and the particle is then transported across the endosteal chord-length dE2 on the far side of the marrow space (via methods described previously). For a TAM source, transport calculations are performed as described above except that the starting value of dMC is selected from an I-random cumulative density function

19 CDFI(dMC). The corresponding marrow-space chord, dMS, is then placed within the marrow spatial model at a point external to the adipocytes, and partitioned into subtrajectories as described earlier. For TBE sources, a transport chord length is selected uniformly across the interval [0,dE1] followed by transport in either bone (dT) or marrow tissues (dMS), depending upon the emission angle. Similarly, for TBS sources of alpha particles, they may be directed either within the adjacent bone trabeculae (dT) or across the full chord-length of the endosteal layer (dE1). If residual energy is still present at various tissue interfaces, the transport techniques described above are continued. Results Tabulated values of absorbed fraction are presented in Appendix B (Tables B1 to B12). A representative tabulation of this data is given in Table 2-3 for alpha-particle emissions within the various source tissues of the lumbar vertebrae of the Leeds 44y male subject. For each source-target combination, energy deposition is tracked within the primary tissue (e.g., TAM←TAM), secondary tissue (e.g., TAM←TBE or TBS), or tertiary tissue (e.g., TAM←TBV) depending on the emission energy (and resulting CSDA range) of the alpha particle. Coefficients of variation (COVs) are ≤1% for primary targets and ≤ 5% for secondary targets. Errors in absorbed fractions to tertiary targets vary according to the source-target geometry and marrow cellularity selected. Values of COV for φ(TAM←TBV) and φ(TBV←TAM) (both separated by the bone endosteum) are below 20% for alpha-particle energies >2.5 MeV. Endosteal and surface sources for alpha-particle emission yield absorbed fractions with COVs below 3% for both secondary and tertiary target tissues. For each source region, computation times for

20 the 100% cellularity model are noted to be only ~5 minutes on a 1-GHz Pentium V workstation, and are ~1 hour on the same system at low cellularities approaching 10%. Discussion Absorbed Fractions to the Active Bone Marrow Figures 2.3A to 2.3D display values of absorbed fraction to active bone marrow as a function of alpha-particle energy within three of the seven skeletal sites of the Leeds 44-year male. While the energy range of clinical interest extends down to only ~5.5 MeV, values at very low energies are displayed as well for visual confirmation of the model (e.g., values of φ should approach unity when the source and target tissue are the same). In each case, the marrow cellularity is set to 100%, and thus differences in energy dependence of the absorbed fraction are strictly related to differences in the trabecular microstructure of these bone sites. Their dependence on marrow cellularity is discussed separately. The absorbed fraction for self-irradiation of the active bone marrow, φ(TAM←TAM), is shown in Figure 2-3A for the ribs, cervical vertebra, and parietal bone. At low energies, the absorbed fraction in each bone site is ~1.0 and thus is closely approximated by the energy-independent value assumed under both the ICRP 30 and 2003 Eckerman bone models. As the particle energy increases, however, an increasing amount of kinetic energy is lost to the bone trabeculae and endosteum, leaving less energy available for deposition to bone marrow. The parietal bone demonstrates the greatest divergence from the ICRP 30 and 2003 Eckerman models at all energies (~0.90 at 6 MeV and ~0.80 at 10 MeV), as this particular bone site is characterized by relatively small marrow cavities and thick bone trabeculae.27

21 Energy-dependent absorbed fractions to active bone marrow (100% cellular) are shown in Figures 2-3B for alpha-particles emitted uniformly within the 10-µm tissue layer of the bone endosteum (a source region not considered in the other two bone models). For this source tissue, the absorbed fraction to bone marrow is shown to be 0.043 at the lowest energy considered (500 keV) and increases to values of 0.48, 0.46, and 0.45 at 10 MeV in the ribs, cervical vertebra, and parietal bone, respectively. When the alpha-emitter is localized within the surfaces of the bone trabeculae (Fig. 2-3C), values of absorbed fraction to the marrow tissues are reduced at all energies as compared to a TBE source. In this case, the alpha particle must exceed ~2 MeV for it to have sufficient energy to penetrate the endosteal layer. In contrast, the ICRP 30 and 2003 Eckerman bone models assign a value of 0.5 to φ(TAM←TBS) independent of the alpha-particle emission energy (based upon a planar half-space transport geometry). Furthermore, these models do not explicitly treat the endosteum and bone marrow as independent target tissues. At an emission energy of 6 MeV, for example, the ICRP 30 and 2003 Eckerman bone models predicts an alphaparticle dose to bone marrow 1.9, 1.9, and 2.1 times higher in the ribs, cervical vertebra, and parietal bone, respectively, than given in the present study. However, when energy deposition to the endosteal layer is separately accounted for in the 2003 Eckerman model (dashed curve in Fig. 2-3C), excellent agreement is noted between the two model predictions. Finally, energy-dependent values of φ(TAM←TBV) are shown in Figure 3D for alpha particles emitted uniformly within the volume of the bone trabeculae. The ICRP 30 model applies an energy-independent value 0.05 to this source-target combination. Our

22 3D-CBIST model predicts values of φ(TAM←TBV) less than 0.05 at alpha energies below ~8 MeV in the ribs and cervical vertebra, with higher absorbed fractions to bone marrow seen at energies exceeding 8 MeV. The ICRP 30 model is shown to be overly conservative with regard to values of φ(TAM←TBS) in the parietal bone at all energies considered. Improved agreement is seen between energy-dependent values of the present study (for the ribs and cervical vertebra), and those from the 2003 Eckerman model provided that their target definition is again revised to exclude the endosteal layer [i.e., difference between φ(TAM←TBS)2003Eckerman and φ(TBE←TBS)2003Eckerman]. Absorbed Fractions to the Bone Endosteum Figures 2-4A to 2-4D display values of absorbed fraction to the trabecular endosteum as a function of alpha particle energy at three of the seven skeletal sites in the Leeds 44-year male subject. In each case, the marrow cellularity is set to 100%, and thus differences in energy dependence are strictly related to differences in trabecular microstructure. The fraction of alpha-particle energy deposited within the endosteal layers of trabecular bone is shown in Figure 2-4A for emissions within the marrow space. Transport results given by the 3D-CBIST skeletal model show values of absorbed fraction to endosteal tissues that begin at ~0.001-0.007 (500 keV) and increase to values of 0.074, 0.032, and 0.018 (10 MeV) for the parietal bone, cervical vertebra, and ribs, respectively. This particular source-target combination is not discussed in ICRP 30, while an energy- and bone-independent value of 0.09 is assigned for φ(TBE←TAM) in the 2003 Eckerman model. At 6 MeV, the 2003 Eckerman value is 1.56, 3.88, and 7.50 times higher than those given by the present model in the parietal bone, cervical vertebra,

23 and ribs, respectively. If one additionally permits alpha emissions in the endosteal layer itself (as is done in the 2003 Eckerman model), revised estimates of φ(TBE←TAM + TBE) from the 3D-CBIST model are given as shown by dot-dashed lines in Figure 2-4A. Here, we see that the additional contributions from endosteal self-dose increase estimates of φ(TBE←TAM) at very low alpha energies for the ribs and parietal bone (where TBE accounts for 0.7% and 0.8% of the revised source mass), but negligibly impact their values at clinically relevant energies (5.5 to 8 MeV). In contrast, the endosteal layer in the cervical vertebrae accounts for up to 8.5% of the combined source mass, and thus the endosteal self-dose is more prominent, even at the higher alpha energies, although still smaller than predicted under the 2003 Eckerman model. Values of φ(TBE←TBE) and φ(TBE←TBS) are given in Figures 2-4B and 2-4C, respectively. For these source-target combinations, the 3D-CBIST model predicts that the absorbed fraction is negligibly influenced by differences in trabecular microarchitecture across different skeletal sites. In Figure 2-4B, the absorbed fraction for the self-irradiation of the trabecular endosteum is shown to approach unity for very lowenergy alpha emissions, and to approach values of ~0.10 to 0.12 at 10 MeV. When the source of alpha emissions is localized to the surfaces of the bone trabeculae (Fig. 2-4C), the half-space assumption is shown to be valid for alpha particles less than ~2 MeV, above which the absorbed fraction to trabecular endosteum declines to values of ~0.13 to 0.15 at 10 MeV. These values are compared to the energy-independent assignment of φ(TBE←TBS) = 0.25 under the ICRP 30 bone model. Consequently, for low-energy alpha emitters, the dose to trabecular endosteum is under-estimated within the ICRP 30

24 model according to our calculations. Comparisons with the 2003 Eckerman model, on the other hand, demonstrate excellent agreement over the energy range 3 - 8 MeV. Finally, Figure 2-4D displays absorbed fractions to TBE for alpha sources localized uniformly within the bone trabeculae. For alpha energies exceeding ~3.0 MeV, the ICRP 30 assumption of φ(TBE←TBV) = 0.025 is shown to under-estimate the energy deposited within the trabecular endosteum of the ribs and cervical vertebra. This same model is shown to over-estimate energy deposition to TBE within the parietal bone at alpha particle energies up to ~6 MeV. Values of φ(TBE←TBV) given by the 2003 Eckerman model show good agreement with those of the present study in 2 of the 3 skeletal sites shown (ribs and cervical vertebra). Influence of Marrow Cellularity on Alpha-Particle Absorbed Fractions In Figures 2-5A – 2-5D, the same four source-target combinations shown in Figures 2-3A – 2-3D are again considered. In this case, however, we focus on a single bone site (lumbar vertebra) and allow the marrow cellularity to range from 100% to 20%. For the self-irradiation of the active marrow (Fig. 2-5A), the ICRP 30 and 2003 Eckerman bone models are shown to closely approximate values of φ(TAM←TAM) given by the 3D-CBIST model only for marrow that is 100% cellular. As adipocyte concentrations increase (marrow cellularities decrease), less alpha-particle energy is deposited within active marrow, and a greater divergence of φ(TAM←TAM) from the unity assumption is noted at all energies. Furthermore, at a given alpha energy below 10 MeV, values of φ(TAM←TAM) at different marrow cellularities are shown not to scale as simple ratios of their corresponding cellularities; consequently full 3D transport is thus required to accurately report values of alpha-particle absorbed fraction.

25 Shielding effects of increased adipocyte concentration are noticeably demonstrated in Figures 2-5B and 2-5C for alpha sources localized within the bone endosteum or on the bone surfaces, respectively. As marrow cellularity decreases, alpha particles emerging from the endosteal layer increasingly encounter adipocytes along the endosteal surface; values of both φ(TAM←TBE) and φ(TAM←TBS) thus decline in value at all energies. Consequently, energy deposition to active marrow is increasingly overestimated in the ICRP 30 and 2003 Eckerman bone models as the marrow becomes less and less cellular. At 6 MeV, for example, the ICRP 30 model over-estimates the energy deposited to active marrow for TBS emissions by factors of 1.9, 3.0, and 9.2 at marrow cellularities of 100%, 60%, and 20%, respectively. The influence of marrow cellularity on values of φ(TAM←TBV) is demonstrated in Figure 5D for the lumbar vertebra. At marrow cellularities of 100%, 80%, and 60%, the ICRP 30 bone model value of φ(TAM←TBV) = 0.05 is not reached until alpha emission energies approach ~7.5 MeV, 8.3 MeV, and 9.3 MeV, respectively. At lower marrow cellularities (e.g., 40% and 20%), the ICRP 30 bone model conservatively estimates the energy deposited to active marrow at all energies considered (≤ 10 MeV). The 2003 Eckerman model is shown to closely match results from the 3D-CBIST model at 100% cellularity, if one accounts for energy lost to the TBE in their definition of the active marrow target. Inter-Subject Variability in Alpha-Particle Absorbed Fractions Chord-length distributions for the 44-year male subject in the Leeds studies form the basis for both the present model, and that of the 2003 Eckerman model of the OLDINA/EXM code. It is of clinical interest to explore the degree to which alpha-

26 particle absorbed fractions can potentially vary with corresponding changes in trabecular microstructure seen in different patients. Four additional chord-length distributions are available from the Leeds studies of the lumbar vertebra which can be used for just such a comparison: those from a 25y male, 55y female, 70y female and a 85y female. 90 Table 2-4 displays 3D-CBIST values of absorbed fractions of both active marrow and endosteum for the 44-year male subject at 100% cellularity. Ratios of these same values are then shown between each subject and the Leeds 44-year male. For TAM targets (left side of Table 2-4), variations of less than 1% are noted for alpha emissions in the TAM and on the TBS, while ~12% inter-subject variations are seen for TBV sources. These variations seen reasonable considering the short ranges of alpha particles in the skeletal tissues, and the fixed nature of the endosteal layer chord-length algorithm in the 3DCBIST model. Inter-subject variations in bone trabeculae thickness thus translate to increased inter-subject variations in values of φ(TAM←TBV) over φ(TAM←TAM) or φ(TAM←TBS). For the TBE as the target tissue, 6 MeV), and for φ(TBE←TBV) at low energies (~3 MeV for ribs and cervical vertebra). In cases of high marrow cellularity (~100%), good agreement in values of φ(TAM←TBS) and φ(TAM←TBV) are noted between the 3D-CBIST and 2003 Eckerman models, but only for a equivalent definition of the active marrow (e.g., exclusive of the endosteal layer). In contrast, the energy-independent assumption of unity for φ(TAM←TAM) in the 2003 Eckerman model is seen to be overly conservative in regard to its dependence on both skeletal site (Fig. 2-3A) and marrow cellularity (Fig. 2-5A). Excellent model agreement is also seen for values of φ(TBE←TBS) and φ(TBE←TBV). Energy-dependent values of φ(TBE←TAM) given by the 3D-CBIST code, however, are found to be very much lower than φ(TBE←TAM) = 0.09 assumed under the 2003 Eckerman model. It has been shown that invasive or non-invasive measurements of marrow cellularity can be clinically important to improvements in patient-specific dose estimates to active bone marrow.89, 94, 97 Explicit consideration of marrow cellularity and its role in modifying values of absorbed fraction under the MIRD schema has been made for betaparticle emitters either by use of reference cellularity values by skeletal site,69, 98 or by permitting marrow cellularity to be a running variable in the dosimetry model.94 Results

29 presented here provide a firmer basis for patient-specific dosimetry in alpha-emitter radionuclide therapies through the explicit consideration of absorbed fraction variations with particle energy, skeletal site, and marrow cellularity. While results given here utilize the University of Leeds chord-length distributions for a single 44-year male subject (ICRP Reference Male), the 3D-CBIST code can be easily extended to other individuals (i.e., cadavers) for which chord-length distributions are available from 3D microimaging of sectioned samples of trabecular spongiosa.74, 99

30

Marrow at 80% cellularity

Bone trabeculae

300 µm

Adipocytes

Active marrow

First fat layer

Marrow at 30% cellularity Figure 2-1.

300 µm Histology slides of normal human bone marrow at two different marrow cellularities. At the lower cellularity, a greater proportion of bone trabecular surface is covered by adipocytes (i.e., the first fat layer).

31

α-track ≥ sampled marrow chord

Transport radius (380 µm)

D

Buffer region (120 µm)

C Active (red) marrow

B B Adipocytes (yellow marrow)

A

α-track < sampled marrow chord

70% Figure 2-2.

40%

20%

Geometric model used to partition sampled marrow cavity chords into sub-trajectories of the alpha particle through active (red) marrow and inactive (yellow) marrow, the latter represented by individual adipocytes (white spheres).

B

1.00 ICRP 30 and 2003 Eckerman models

0.95

0.90

0.85

φ (TAM ← TAM) Ribs

0.80

0.50 0.45

Absorbed fraction to TAM


A

0.40 0.35 0.30 0.25 0.20

φ (TAM ← TBE)

0.15

Ribs

0.10

Cervical vertebra

Cervical vertebra

Parietal bone 0.05

Parietal bone

0.00

0.75

0

0.50

10

0

12

D

ICRP 30 and 2003 Eckerman Models

0.12

0.30

φ (TAM ← TBS)

0.25

Ribs 0.20

Cervical vertebra

0.15

Parietal bone

0.10

2003 Eckerman Model

10

12

Parietal Bone

0.08 0.07

2003 Eckerman M odel

0.06 0.05 0.04 ICRP 30 M odel

0.03 2003 Eckerman M odel (Revised target: TAM - TBE)

0.01

0.00

8

Cervical Vertebra

0.09

0.02

(Revised target: TAM - TBE)

0.05

6 α-energy (MeV)

Ribs

0.10

0.35

4

φ (TAM ← TBV)

0.11

0.40

2

32

0.45


4 6 8 α-particle energy (MeV)


C

2

0.00

0

Figure 2-3.

2

4

6 α-energy (MeV)

8

10

12

0

2

4

6 α-energy (MeV)

8

10

12

Absorbed fractions for an active marrow target (100% cellularity) from (A) an active marrow source (TAM), (B) a trabecular bone endosteum source (TBE), (C) a trabecular bone surface source(TBS), and (D) a trabecular bone volume source (TBV).

0.09

φ (TBE ← TAM)

Cervical vertebra

0.07

Parietal bone

φ (TBE ← TBE)

0.90

0.06 0.05 Source: TBE + TAM

0.04 0.03 Source: TAM only

0.02

Ribs

0.80

Cervical vertebra

0.70

Parietal bone

0.60 0.50 0.40 0.30 0.20 0.10

ICRP 30 (source-target combination not explicitly considered)

0.00

1.00

2003 Eckerman model

0.08

0.01

0.00

0

C

B

Ribs

Absorbed fraction to TBE


A

2

4

6 α-energy (MeV)

8

10

12

0

D

0.60

2

4

6 α-energy (MeV)

8

10

12

0.07

φ (TBE ← TBV) Absorbed fraction to TBE


2003 Eckerman model

0.40

0.30

ICRP 30

0.20

φ (TBE ← TBS) Ribs

0.10

Parietal bone

Figure 2-4.

Cervical vertebra 0.05

Parietal bone 2003 Eckerman model

0.04 0.03 0.02

ICRP 30

0.00

0.00

2

Ribs

0.01

Cervical vertebra

0

33

0.06

0.50

4

6 α-energy (MeV)

8

10

12

0

2

4

6 α-energy (MeV)

8

10

12

Absorbed fractions for an endosteum target from alpha sources emitted within the (A) the TAM, (B) the TBE, (C) the TBS, and (D) the TBV.

B

1.0


ICRP 30 and 2003 Eckerman models

0.8 0.7 0.6

φ (TAM ← TAM)

0.5

100% 80% 60% 40% 20%

0.4 0.3

100% 80% 60% 40% 20%

0.40 0.35 0.30 0.25 0.20 0.15 0.10

0.00

0

2

4

6 α-energy (MeV)

8

0.35 0.30

D

0.12

(Revised target: TAM - TBE)

0.25 0.20 0.15

8

10

12

60%

0.08

40%

0.07

20%

0.06 0.05 0.04

ICRP 30

0.03 2003 Eckerman M odel (Revised target: TAM - TBE)

0.01

0.05

6 α-energy (MeV)

2003 Eckerman model

80%

0.09

0.02

0.10

4

100%

0.10 2003 Eckerman M odel

2

φ (TAM ← TBV)

0.11


100% 80% 60% 40% 20%

0

12

ICRP 30 and 2003 Eckerman models

φ (TAM ← TBS)

0.40

10

34

0.50 0.45


φ (TAM ← TBE)

0.05

0.2

C

0.50 0.45

0.9


A

0.00

0.00

0

0

Figure 2-5.

2

4

6 α-energy (MeV)

8

10

12

2

4

6 α-energy (MeV)

8

10

12

Dependence of the active marrow absorbed fraction with changes in marrow cellularity within the lumbar vertebrae. (A) TAM source, (B) TBE source, (C) TBS source, and (D) TBV source.

35 Table 2-1. Candidate alpha-particle emitters for radionuclide therapy. The relevant energy range of their alpha-particle emissions is from ~5.5 to 9 MeV. Radionuclide Daughters Bi-213

Po-213 Tl-209 Pb-209 Bi-209 Bi-212

Half-Life

Yield* (%)

Emission Particle

Particle Energy†

45.6 m

2 98 17 98 2 100

α β− γ α β− β−

5.9 MeV 444 keV 440 keV 8.4 MeV 659 keV 198 keV

36 64 64 36 8 31 36

α β− α β− γ γ γ

6.0 MeV 492 keV 8.8 MeV 560 keV 510 keV 580 keV 2.6 MeV

42 19 58 24 41 31

α γ α γ γ γ

5.9 MeV 80 keV 7.4 Mev 70 keV 570 keV 1 MeV

100 100 10 100

α α γ α

5.8 MeV 6.4 MeV 218 keV 7.1 MeV

100 40 14 100 10 100 100 16 84 13 100

α γ γ α γ α β− α α γ β−

5.7 MeV 80 keV 270 keV 6.8 MeV 270 keV 7.4 MeV 447 keV 6.3 MeV 6.6 MeV 350 keV 493 keV

4.2 µs 2.2 m 3.25 h stable 1.0 h

Po-212 Tl-208

298 ns 3.05 m

Pb-208

stable

At-211

7.21 h

Po-211 Bi-207

516 ms 32 y

Pb-207

stable

Ac-225 Fr-211

10 d 4.9 m

At-217 Bi-213 Ra-223

32.3 ms see Bi-213 11.4 d

Rn-219

4s

Po-215 Pb-211 Bi-211

1.8 ms 36.1 m 2.1 m

Tl-207 Pb-207

4.8 m stable

* Percent emitted per decay of parent radionuclide †

Mean β energy and approximate α and γ energies are listed.

36 Table 2-2. Elemental composition of the tissues of skeletal spongiosa. Data taken from ICRU Publication 46. Tissues of Trabecular Spongiosa Active Marrow Inactive Marrow Endosteum † ‡ (TIM) (TBE) (TAM)* 10.5 11.5 10.5 41.4 64.4 25.6 3.4 0.7 2.7 43.9 23.1 60.2 ---0.1 0.1 ---------0.1 ---0.2 0.2 0.1 0.3 0.2 0.1 0.2 0.2 ---0.2 ---------0.1 -------

Element H C N O Na Mg P S Cl K Ca Fe -3

Mass Density (g cm ) 1.03 Source: ICRU Report 46 - Appendix A *TAM - "adult red marrow" † TIM - "adult yellow marrow" ‡ TBE - "adult ICRU-44 soft tissue (male)" § TBV - "adult cortical bone"

0.98

1.03

Trabeculae § (TBV) 3.4 15.5 4.2 43.5 0.1 0.2 10.3 0.3 ------22.5 ---1.92

37 Table 2-3. Absorbed fractions to active bone marrow (TAM) for α-emissions within the iliac crest of the Leeds 44-year male for various source tissues and marrow cellularities.

Energy (MeV) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0

Energy (MeV) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0

100%

90%

80%

9.98E-01 9.97E-01 9.96E-01 9.94E-01 9.93E-01 9.90E-01 9.88E-01 9.86E-01 9.83E-01 9.80E-01 9.77E-01 9.74E-01 9.70E-01 9.67E-01 9.62E-01 9.59E-01 9.55E-01 9.50E-01 9.46E-01 9.41E-01



100%

90%

80%




Lumbar Vertebrae φ (TAM