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QUANTIFYING UNCERTAINTIES IN LUNG DOSIMETRY WITH APPLICATION TO PLUTONIUM OXIDE AEROSOLS By THOMAS EDWARD HUSTON 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 1995 Dedicated to Rhonda, my wife and friend without her encouragement this work would have been impossible. ACKNOWLEDGMENTS This work has been supported in part by Grant Number R23/CCR40976901 from the Centers for Disease Control and Prevention (CDC); however, its contents are solely the responsibility of the author and do not necessarily represent the official view of CDC. Preliminary portions of the research were performed under appointment to the Environmental Restoration and Waste Management Fellowship Program administered by Oak Ridge Institute for Science and Engineering for the United States Department of Energy. I am especially grateful to these agencies for providing the financial assistance necessary to complete this work. I wish to thank my supervisory committee membersDrs. William G. Vernetson (chair), W. Emmett Bolch (cochair), Marc Jaeger, David E. Hintenlang, William S. Properzio, and Wesley E. Bolchfor serving on the committee and for their guidance during the course of this study. I am especially thankful to Drs. William Vernetson, Emmett Bolch, and Marc Jaeger for their useful suggestions to improve content in early draft versions of the manuscript. I offer a special note of thanks to Dr. Emmett Bolch, who during the past two years provided me (through the resources of the CDC grant) with the financial backing to complete this research; his care for students is indeed a credit to his profession. I am thankful to several others with whom I have had the privilege of associating throughout various stages of this work. These persons include, among many others, Drs. Gen Roessler, John Till, Helen Grogan, Tony James, and Alan Birchall. Dr. Gen Roessler served as a point of contact for me during the early stages of this work. She introduced me to Dr. Till, who (along with colleagues from Radiological Assessments Corporation) expressed a need for quantitative information regarding uncertainties in lung dose predictions for plutonium. Dr. Till assisted during the early stages of this work by helping me obtain draft reports from the National Council on Radiation Protection and Measurements (NCRP) and the International Commission on Radiological Protection (ICRP). At that time, both agencies were in the process of releasing independent models for respiratory tract dosimetry. I appreciate the willingness of the ICRP and NCRP to release these draft reports to me before publication. Drs. Tony James and Alan Birchall provided me with many useful materials and encouragement. Dr. Helen Grogan provided several helpful comments throughout the work. I would like to thank my wife, Rhonda, for her constant encouragement throughout my "tenure" at the university. She kept me focused on my work, never complaining about the long hours I kept. She also helped organize the reference section of the manuscript. I have been truly blessed with a wonderful, caring wife and a best friend. I certainly look forward to spending the rest of my life (yes, I do plan to get one after graduation) with her. I want to thank our new son, Hayden Edward Huston (born only days ago on July 24, 1995), for bringing me happiness and wonder while I have prepared this manuscript. I would like to thank some (past and present) fellow students, Kaiss AlAhmady, Brian Birky, Thabet Tolaymat, George Harder, Louis Iselin, Susan Stanford, and Missy Jones, among others, for their friendship and stimulating discussions regarding the radiation sciences. I also appreciate the departmental staff in the Nuclear Engineering Sciences office (Barbara, Joan, Beth, Cess, and Donna) and the Environmental Engineering Sciences office (Sandy, Berdenia, and Shirley). Thanks also to Chuck, Al, Gene, and Gary for providing me with an outlet to this insanity by way of the Tuesday night trombone jazz sessions. Finally, but certainly not least, I am very thankful to all of my family and friends back home in Arkansas for giving me hope and encouragement throughout the many, many years of my education. I miss them all greatly. TABLE OF CONTENTS pAge ACKNOWLEDGMENTS ........................................ iii LIST OF TABLES ............ .................................. x LIST OF FIGURES ............................................... xiv ABSTRACT ........................................... ........ xviii CHAPTERS 1 INTRODUCTION ............................................ 1 1.1 Purpose of Study ....................................... 3 1.2. Background Information ................................ 4 1.2.1. Radiation Exposure Pathways ......................... 4 1.2.2. Internal Radiation Dosimetry, Reference Man, and Risk ...... 9 1.2.3. Advantages and Disadvantages of the Reference Man Approach 14 1.3. Previous Work ............ ... ................... 16 1.4. Description of Present Study .......................... 20 1.4.1. Assessment Problem Addressed .................. 20 1.4.2. Units of Exposure .................................. 22 1.4.3. Summary of the Research Approach .................... 24 2 METHODS FOR RESPIRATORY TRACT MODELING .............. 27 2.1. Introduction ............. ........................ ....... 27 2.2. Development of Respiratory Tract Dose Models ................. 31 2.3. Respiratory Tract Morphological Model ...................... 33 2.4. Respiratory Tract Deposition Model ........................ 35 2.5. Particle Size and Diffusion Characteristics ..................... 48 2.6. Respiratory Tract Clearance Model ........................... 51 2.7. Respiratory Tract Dose Model ............................. 63 2.8. Sum m ary ................................ ........... 70 page 3 METHODS FOR CONDUCTING PARAMETER UNCERTAINTY ANALYSES .............. .......... ................ 72 3.1. Introduction ............................................. 72 3.2. Quantifying Parameter Correlations and Uncertainties ............. 75 3.2.1. Parameter Correlations .............................. 75 3.2.2. Parameter Uncertainties ............................ 78 3.2.3. Testing the Fit of an Assigned Distribution ............... 84 3.2.4. Subjective Probability Judgements and Expert Opinion ...... 86 3.3. Propagation of Parameter Uncertainty ......................... 88 3.3.1. Simple Random Sampling ............................ 89 3.3.2. Latin Hypercube Sampling .......................... 91 3.4. Presentation of Uncertainties in Model Predictions ................ 96 3.5. Parameter Sensitivity Techniques ........................... 97 3.6. Description of the Lung Dose Uncertainty Code (LUDUC) ........ 102 3.7. Summary .................. ............ .. ....... 109 4 UNCERTAINTIES IN RESPIRATORY TRACT MODEL PARAMETERS 110 4.1 Deposition Model Parameters .............................. 112 4.1.1. BodyHeight .......................... ......... 112 4.1.2. BodyMassIndex ........... ...................... 116 4.1.3. Airway Diameters and Lengths ................... .... 123 4.1.4. Anatomical Dead Space ................... ......... 131 4.1.5. Regional Volumes of the Respiratory Tract ............... 135 4.1.6. Functional Residual Capacity ......................... 137 4.1.7. Vital Capacity ................................... 139 4.1.8. Ventilation Rate and Volumetric Flow Rate ............... 141 4.1.9. Tidal Volume ................................... 160 4.1.10. Fraction of Air Breathed Through the Nose ............... 169 4.1.11. Uncertainty in Particle Inhalability .................... 174 4.1.12. Regional Deposition Efficiency Uncertainty ............... 176 4.2. Clearance Model Parameters .............................. 179 4.2.1. Introduction ..................................... 179 4.2.2. Partition of Deposition in Clearance Model Compartments ... 180 4.2.3. Fractional Clearance Rate Constants .................... 188 4.2.4. Absorption Rate Constants ........................ .. 190 4.3. Dose Model Parameters .................................. 200 4.3.1. Introduction ..................................... 200 4.3.2. Measurements of the Bronchial Epithelium and Critical Cell Layers ............ ........... .......... 201 page 4.3.3. Extrathoracic Regions ................... ......... 207 4.3.4. Bronchial Region .................................. 207 4.3.5. Bronchiolar Region ............... ............... 214 4.3.6. Surface Area of Bronchial and Bronchiolar Regions ......... 219 4.3.7. AlveolarInterstitial Region ......................... 222 4.3.8. Total Lung Mass ......... ...... ................ 223 4.3.9. Mass of Lymph Nodes .............................. 225 4.3.10. Regional RiskApportionment Factors .................. 226 4.3.11. Summary of Methods for Dose Model Parameters .......... 228 5 APPLICATION OF LUDUC TO INHALED PLUTONIUM OXIDE AEROSOLS: RESULTS AND DISCUSSION .................. 231 5.1. Introduction ................. ....... .... .. ............ 231 5.2. Characteristics of P'PuO2 Aerosols ...................... 233 5.3. Dose Uncertainty Results for Inhaled "'PuO2 Aerosols ............. 237 5.3.1. Exposure Scenario and Notational Conventions ............ 237 5.3.2. Adult Males Exposed to "'PuO2 Aerosols ................ 239 5.3.3. Influence of Dose Integration Time ..................... 249 5.3.4. Influences of Age and Gender ........................ 252 5.3.5. Influences of Particle Size Dispersion .................. 256 5.4. Dose Sensitivity Results for Inhaled 9PuO, ..................... .264 5.4.1. Combined Lung Dose ............................ 266 5.4.2. Regional Tissue Doses ............ ............... 270 5.5. Deposition Sensitivity Results ..... .................... 279 5.5.1. Bronchial Region ............ .... .... ..... ....... 283 5.5.2. Bronchiolar Region .............................. 283 5.5.3. AlveolarInterstital Region .......................... 284 5.6. Implications of Dose Results and Comparison to Reference Man Dose 285 5.7. Summary of Results ................ ................... 292 6 CONCLUSIONS AND RECOMMENDATIONS ..................... 296 6.1. Summary of Research ................................ 296 6.2. Conclusions Based on Results for Plutonium Oxides .............. 300 6.3. Recommendations for Future Research ...................... 305 APPENDICES A COMPARISON OF ICRP AND NCRP MODELS .................... 311 B THE CLEARANCE MODEL: SYSTEM OF DIFFERENTIAL EQUATIONS ......................................... 323 C DOSE CALCULATIONS IN TRACHEOBRONCHIAL AIRWAYS ...... 330 D TIDAL VOLUMES FOR CHILDREN ........................... 355 E DOSE DATA FOR INHALATION OF PLUTONIUM OXIDE .......... 364 REFERENCES ................. ........ .... ................. 410 BIOGRAPHICAL SKETCH ......................................... 429 LIST OF TABLES Table page 11. Selected intaketodose conversion factors for inhalation of some plutonium isotopes and other transuranics .............................. 11 12. Organ and total risk per inhalation intake of plutonium compounds ....... 12 13. Specific information related to the assessment question and scenarios considered in this study ..................................... 21 21. Recommended parameters for use in model of regional deposition for the fraction of intake inhaled and exhaled through the nose for any subject as functions of respiratory variables and anatomical size. ............... 42 22. Recommended parameters for use in model of regional deposition for the fraction of intake inhaled and exhaled through the mouth for any subject, as functions of respiratory variables and anatomical size. ................ 43 23. Description of input parameters required by the revised ICRP deposition model. ................ ... .................. .............. 44 24. Other parameters of use in modeling particle deposition in the respiratory tract. .............. ................................. 46 25. Reference values for mechanical clearance rates in the particle transport aspect of the ICRP human respiratory tract model .................. 56 26. Reference values for partition of deposit among compartments in region. ... 56 27. Assignment of compartments to source regions for shortrange radiations in the revised ICRP respiratory tract model. ........................ 66 28. Riskapportionment factors recommended by the ICRP for weighting the dose to various respiratory tract target tissues .................. .. 69 31. Main steps involved in conducting a parameter uncertainty analysis ....... 74 Table page 32. Intervals paired for the Latin hypercube sample shown in Figure 36 ...... 95 33. Example of a hypothetical data set and its ranktransformed data set ...... 101 41. Selected height data from the Second National Health and Nutrition Examination Study (NHANES II) .............................. 113 42. Body mass index data from NHANES II ........................... 119 43. Correlations between height and BMI. .......................... 119 44. Dimensional model of the tracheobronchial tree in adult male ............ 126 45. Expressions relating airway lengths and diameters to body height ......... 127 46. Regression equations and related information for functional residual capacity. ............................................. 138 47. Regression equations and related information for vital capacity .......... 140 48. Regression equations and related data characterizing basal metabolic rates for given age and gender classes ............................... 152 49. Typical basal multiplier values for different activities .................. 155 410. Distributions assigned to basal multiplier for four physical exertion levels. .. 155 411. Summary of distributions and methods used to predict variabilities in VE. ... 157 412. Fraction ofventilatory airflow passing through the nose in normal augmenters and in mouth breathers. ............................ 172 413. Scaling constants used to account for uncertainties in regional deposition equations. ............................................. 178 414. Distributions and relationships describing partition of deposited material into compartments. ................. ...................... 182 415. Distributions adopted to describe uncertainties in fractional clearance rate constants used in mechanical clearance aspect. ..................... 189 Table aMe 416. Results of studies that examined longterm clearance of inhaled PuO2 aerosols from the lungs. ...................................... 191 417. Distributions and relationships adopted to describe the absorption clearance aspect for plutonium oxides. ................................. 199 418. Range of alpha particles in water for given energies .................... 201 419. Summary data for bronchial epithelium based on study by Gastineau et al. .. 204 420. Summary data for bronchial epithelium measurements based on study by Baldwin et al............................................ 205 421. Summary data for bronchial epithelium measurements based on study by Mercer et al. ............. ...... ........................... 206 422. Summary of distributions used to model uncertainty in source and target tissue dimensions in the BB and bb regions. ...................... 229 423. Summary of methods to model uncertainties in source and target tissue volumes and masses .............. ..... ..................... 230 424. Summary of distributions and relationships used to model uncertainties in risk apportionment factors. ................................... 230 51A. Combined equivalent dose to the lungs, HH/AE: Ranking of selected variables ........... ..... ........................ 268 51B. Combined equivalent dose to the lungs, HH/AE: Results of stepwise rank regression analysis ............... ................... .. 268 52A. Equivalent dose to BB secretary cell layer, H(BB,)/AE: Ranking of variables ............................................ 271 52B. Equivalent dose to BB secretary cell layer, H(BB.)/AE: Results of stepwise rankregression analysis ............. .... .......... 271 53A. Equivalent dose to BB basal cell layer, H(BBb)/AE: Ranking of variables 272 53B. Equivalent dose to BB basal cell layer, H(BB )/AE: Results of stepwise rankregression analysis ................ ................... 272 Table page 54A. Equivalent dose to bb secretary cell nuclei layer, H(bb,)/AE: Ranking of variables .................... ................. ........ 273 54B. Equivalent dose to bb secretary cell nuclei layer, H(bb,)/AE: Results of stepwise rankregression analysis ........................... 273 55A. Equivalent dose to AI tissue, H(AI)/AE: Ranking of variables ............ 274 55B. Equivalent dose to AI tissue, H(AI)/AE: Results of stepwise rankregression analysis ......................... ......................... 274 56A. Equivalent dose to thoracic lymph nodes (LNth), H(LNth)/AE: Ranking of input variables ........................... ............ 275 56B. Equivalent dose to LNth tissue, H(LNth)/AE: Results of stepwise rank regression analysis ...................................... 275 57. Ranking of the top ten input variables as determined by standardized rank regression coefficients for deposition fractions in respiratory tract regions ............... ...... ...................... 280 58A. Deposition fraction for BB region, DFBB: Results of stepwise rank regression analysis for the four topranked model parameters .......... 281 58B. Deposition fraction for bb region, DF,: Results of stepwise rankregression analysis for the four topranked model parameters .................. 281 58C. Deposition fraction for AI region, DFu: Results of stepwise rankregression analysis for the four topranked model parameters ................. 281 59. Summary comparison of typical dose predictions for exposure of various population groups ................... ................ 293 510. Summary list of the variables contributing the most to uncertainties in equivalent doses to thoracic target tissues. ...................... 295 511. Summary list of variables contributing the most to uncertainties in deposition fractions to thoracic regions. .................. ......... .. 295 LIST OF FIGURES Figure page 11. Factors to consider in radiological risk assessment .................... 6 12. Ratio of upper to lower 95% confidence bounds for committed effective dose equivalent per inhalation intake for adult male workers .............. 18 21. Components of a respiratory tract dosimetry model ................... 28 22. Anatomical representation of revised ICRP respiratory tract model ....... 34 23. Model of airway wall in the bronchial (BB) region .................... 36 24. Deposition model for the revised ICRP respiratory tract model .......... 37 25. Inhalability of particles as a function of the aerodynamic diameter for wind speeds ofU= 1, 5,and 10 m/s. .............................. 39 26. Particle transport model adopted by the ICRP to represent mucociliary and macrophage transport mechanisms to the gastrointestinal tract and lymph nodes ............................................ 52 27. Compartment model recommended by ICRP to represent dissolution and absorption to blood and lung tissues for materials deposited in the respiratory tract. ............... .................. ....... 57 28. Alternate form for the dissolution/absorption model ................... 59 29. Schematic of the overall compartment model to represent clearance of material from the respiratory tract by mechanical and absorptive processes. 61 3.1. Example of a uniform probability density function. ................ 80 3.2. Examples of triangular probability density functions ................... 81 33. Examples of two typical normal probability density functions. ........... 82 Figure page 34. Examples oflognormal probability density functions. .................. 83 35. Algorithm to generate a random number, on the interval (0,1) ......... 90 36. Example of a Latin hypercube sample. ............................. 94 37. Schematic diagram showing the flow of computations in the Lung Dose Uncertainty Code (LUDUC). ................................ 103 41. Average body height as a function of age for males and females .......... 115 42. Ratio of predicted to observed fractiles in body height for males .......... 117 43. Average body mass index as a function of age for males and females ...... 118 44. Ratio of predicted to observed fractiles in BMI for males ............... 122 45. Average airway length versus airway generation at three body heights and residual standard errors of the linear regression equations used to predict lengths ................ .......................... 128 46. Average airway diameter versus airway generation at three body heights and residual standard errors (RSE) of the linear regression equations used to predict diameters ................. .... .................. 128 47. Comparison of the cumulative probability for the observed residuals of ln(Vd) and the cumulative probability for Evd ...................... 133 48. Anatomical dead space as a function of body height ................... 134 49. Relationship between volumes at ambient temperature and pressure to volumes reported at body temperature and pressure ................. 143 410. Predicted average values for VE as a function of age for males and females .. 158 411. Comparison of ventilation rates at rest for males and females ............ 160 412. Tidal volume at various physical exertion levels for males and females ..... 167 413. Comparison of average resting tidal volumes in present study with other references ............ .................................... 169 Figr Rpage 414. Slowclearing fraction of material deposited in the tracheobronchial region as a function of the volumeequivalent particle diameter ........ 185 415. Normal probability plot of the residuals for the slowclearing thoracic deposit ................ .. ................ ............ 186 416. Total 239Pu disintegrations in the lung as a function of time for three values ofs, for the scenario specified ................. ............. 197 417. Surface area of the bronchial region as a function of height ............. 221 418. Surface area of the bronchiolar region as a function of height ............ 221 419. Total (bloodfilled) lung mass as a function of age for males and females ... 224 51. Fractiles predicted for the committed (50 year) equivalent dose per unit activity exposure to the lungs for a population group of 2534 yearold males at light exertion ....................... ......... .. 240 52. Dose quantities versus particle diameter in all thoracic target tissues for adult males exposed at light exertion ............................. .. 242 53. Equivalent dose to the lungs for adult males at four exertion levels: resting, sitting, light, and heavy exertion ....... ...... ... ..... 245 54. Estimated values of median dose to all thoracic targets for adult males at four exertion levels: resting, sitting, light, and heavy exertion ............. 247 55. Estimated values of the ratio of 95% to 5% dose fractiles for all thoracic targets for adult males at four exertion levels: resting, sitting, light, and heavy exertion .......... ............ .... ............ 248 56. Influence of integration time on dose uncertainties ................... 250 57. Influences of age and gender on dose uncertainties .................... 255 58. Estimated values of median dose to all thoracic targets for nine different age/gender groups at light exertion .......................... .. 257 59. Estimated values of the ratio of 95% to 5% dose fractiles for all thoracic targets for nine different age/gender groups at light exertion .......... 258 Figure page 510. Influence of activitysize dispersion on lung dose uncertainties ........... 260 511. Estimated values of median dose versus activity median diameter for thoracic tissues in adult males at four activitysize dispersion values ........... 262 512. Estimated values of the ratio of 95% to 5% dose fractiles versus activity median diameter for thoracic tissues in adult males at four activitysize dispersion values ....................................... 263 513. Lognormal probability plots for various equivalent doses in the respiratory tract .................................................. 286 514. Estimated values of the geometric standard deviation, GSD, of equivalent dose per activity exposure in various target tissues for males at four broad exertion levels ............. ....... ................... 288 515. Comparison of median dose values computed in this study to reference man dose values as predicted by LUDEP .......................... 290 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 QUANTIFYING UNCERTAINTIES IN LUNG DOSIMETRY WITH APPLICATION TO PLUTONIUM OXIDE AEROSOLS By Thomas Edward Huston August 1995 Chairperson: William G. Vernetson Cochair: W. Emmett Bolch Major Department: Nuclear Engineering Sciences A complete respiratory tract model for predicting lung dosimetry of inhaled radioactive aerosols involves several component models, including models for particle deposition in airways, biokinetic clearance and radiological decay of deposited materials, and radiological dose to critical target tissues. Each component depends on several parameters which can vary among members of a population group. The traditional approach has been to use reference values for parameters and to generate a single, deterministic reference dose. Based on conducting parameter uncertainty analyses, a methodology was developed in this study to incorporate parameter uncertainties into the respiratory tract modeling process. The methodology allows lung dose predictions to be determined as probability distributions, which better reflect the potential spread in doses for members of population groups than a single reference dose. The study involved xviii compilation and critical evaluation of previous studies to recommend defensible distributions representative of parameter uncertainties. Relationships were also identified to account for correlations between many model parameters. An interactive computer program, LUDUC (for LUng Dose Uncertainty Code), was developed to implement the methodology. Doses resulting from inhalation of plutonium oxide aerosols (aerodynamic diameters ranging from 0.1 to 50 microns) were investigated with LUDUC to demonstrate the methodology. This specific application of the methodology developed dose data which support an ongoing dose reconstruction study of plutonium released by the Rocky Flats Plant in Colorado. Resulting dose distributions followed a lognormal distribution shape for all scenarios examined. For many scenarios, the uncertainties in lung dose predictions were substantialwith geometric standard deviations approaching values of five. Uncertainties in doses increased by about a factor often from the smallest to the largest particle sizes. Differences in predicted dose distributions were small when comparing different age and gender groups from 2 to 35 years of age. Median doses for plutonium oxide generally agreed with reference dose values, providing some level of confidence in the referenceman approach. Parameter sensitivity analyses were conducted for inhaled plutonium oxides and revealed that dose uncertainties are generally attributable to only a few of the model parameters; parameter sensitivity depended on the inhaled particle diameter. CHAPTER 1 INTRODUCTION As knowledge of particle deposition, clearance, and radiation dosimetry in the human respiratory tract has increased, so have the sophistication and complexity of the conceptual and computational models used to describe these processes [e.g., International Commission on Radiological Protection (ICRP), 1960; Task Group on Lung Dynamics (TGLD), 1966; ICRP, 1979 and 1994]. In spite of recent advances in respiratory tract modeling, the reliability of model predictions should be addressed. A number of publications have focused on the techniques of model reliability assessment [e.g., Morgan and Henrion, 1990; International Atomic Energy Agency (IAEA), 1989; Organization for Economic Cooperation and Development (OECD), 1987; Hoffman and Gardner, 1983]. Although the general techniques of model reliability assessment can be applied to any mathematical model, past applications in the radiological dose assessment area (e.g., OECD, 1987; Desmet, 1988; Garten, 1980; Hoffman and Baes, 1979; Little and Miller, 1979) have primarily involved environmental transfer models (e.g., atmospheric, surface water, groundwater, and terrestrial/aquatic foodchain transport models). Similar techniques have also been applied to lightwater nuclear reactors to examine probabilities associated with accident scenarios (Rasmussen, 1975; Lewis, 1978). The current study extends the application of reliability assessment techniques to include anatomical and physiological models adopted to simulate the human respiratory tract. Several factors must be considered in a study of model reliability. According to a report by the International Atomic Energy Agency, model reliability is affected by: (1) uncertainty due to improper definition and conceptualization of the assessment problem or scenario, (2) uncertainty due to improper formulation of the conceptual model, (3) uncertainty involved in the formulation of the computational model, (4) uncertainty inherent within estimation of model parameter values, and (5) calculational and documentation errors in the production of results. (IAEA, 1989, p. 16) The assessment problem and scope of this study, item (1), are discussed in detail in a following section. Uncertainties in the formulation of the conceptual and computational (or mathematical) models, items (2) and (3), were not examined here. In regard to items (2) and (3), an underlying assumption in this research has been that the conceptual and computational models adopted for this study appropriately represent the anatomy and physiology of the human respiratory tract. This study has used the revised respiratory tract model recently issued (ICRP, 1994) by the International Commission on Radiological Protection (ICRP). The model is based on recommendations by an ICRP task group composed of experts in the field of respiratory tract dosimetry. The effect of uncertainties in respiratory tract model parameters on model predictions, item (4), has been the primary focus of this research. These uncertainties were examined in detail by implementing parameter uncertainty and parameter sensitivity analyses of the revised ICRP respiratory tract model. Calculational errors, item (5), were examined to some level, since the probabilistic computer code developed to implement parameter uncertainty analyses of the model was verified by comparison to a simpler, deterministic code, LUDEP, developed independently by the National Radiological Protection Board (Jarvis et al., 1993). 1.1 Purpose of Study The primary purpose of this study was to develop a computational methodology for quantifying uncertainties (including stochastic variabilities) in respiratory tract model dose predictions for exposure of population groups to radioactive aerosols. The study is based on parameter uncertainty analyses of recommended biological models describing the fate of inhaled, radioactive aerosols in the human respiratory tract. A probabilistic computer code, LUDUC (Lung Dose Uncertainty Code), was developed in this study to perform these analyses. A secondary purpose of this study was to demonstrate this computational methodology by application to various inhalation exposure scenarios for plutonium oxide aerosols (while also providing guidance for application to other radionuclides and chemical forms). An objective of this study was not to develop a new respiratory tract model or to validate existing models, but rather to use a model currently recommended by national and/or international scientific advisory bodies (NCRP, 1993; ICRP, 1994) as the basis for conducting parameter uncertainty analyses. In addition, parameter sensitivity analyses also were performed in the study to identify the parameters that most influence model predictions. The study was undertaken in an effort to improve current internal dose assessment methods by including parameter uncertainties in the dose modeling process. The methodology developed allows inhalation exposuretodose conversion factors (EDCFs), 4 among other assessment quantities, to be derived as probability distributions rather than as single, deterministic valueswhich are based solely on a reference human and do not account for parameter uncertainties arising from biological variability and lack of knowledge. Probabilistic characterization of respiratory tract model predictions is important for a many reasons. First, probabilistic characterization helps to demonstrate the reliability of models adopted to represent the anatomical and physiological characteristics of the human respiratory tract. Second, it helps to improve the credibility of dose assessment calculations by estimating the potential distribution or range of values (including descriptive statistics such as medians, fractiles, means, and standard deviations) for quantities of interest. Finally, probabilistic characterization, when performed in conjunction with sensitivity analyses, helps to distinguish the more influential model parameters (with respect to model predictions) from the less influential ones. This latter sensitivity information can help guide future research efforts in respiratory tract modeling. 1.2. Background Information 1.2.1. Radiation Exposure Pathways In scientific endeavors to quantify and predict human health risks from exposure to ionizing radiations, mathematical models are both appropriate and necessary. Numerous models exist for describing the release, environmental transport, foodchain propagation, human intake/usage, internal and external dosimetry, and subsequent health risks of radioactive materials (e.g., see Till and Meyer, 1983 and NCRP, 1984 for summary). An illustration of the major factors considered in radiological risk assessment is shown in Figure 11. The upper aspect of this figure (boxes 15) involves release conditions and environmental transport factors, while the lower aspect (boxes 68) involves human lifestyle and biological factors. As indicated by bold print in Figure 11, this study focuses on components in the risk assessment chain that are associated with usage rates and dose factors (boxes 6 and 7) for inhalation of radioactive aerosols. Within the context of inhalation of radioactivity, usage rates refer to the amounts of air and subsequently radioactivity inhaled per unit time by an individual. The amount of radioactivity inhaled per unit time is termed the inhalation intake rate. The time integral of the inhalation intake rate over the exposure duration is termed the inhalation intake (i.e., the total activity inhaled during the exposure period). Using the International System of units (SI), the inhalation intake is expressed in units ofbecquerels (Bq), where the becquerel is the special SI unit for radioactivity; one becquerel is equal to one radioactive disintegration (or transformation) per second. A quantity of interest in this study, related to usage rates, is the activity exposure. In this study activity exposure, denoted by AE and with units ofBqhr/m3, is defined as the time integral of the ambient activity concentration, C,(t) in Bq per m', over the exposure duration, D, in hours. Thus, D A =f C.(t)dt = D*C. (11) 0 where E represents the timeaveraged ambient activity concentration over the exposure duration, D. The activity concentration represents the radioactivity per unit volume Figure 11. Factors to consider in radiological risk assessment. This study focuses on components represented by boxes 6 and 7 for inhalation. After NCRP 1984, Figure 1. (ambient air) as a function of time for a specified radionuclide and a specified particle activitysize distribution. The exposure duration, D, represents the time a group of subjects is exposed to the specified activity concentration (i.e., the time over which the inhalation intake occurs). The activitysize distribution characterizes the fraction of the airborne activity associated with aerosol particles in various size ranges. Particle size characteristics and activitysize distributions are discussed in section 2.6. As defined above, AE is useful when the activitysize distribution and the physical exertion level of the population group do not change significantly over the exposure duration for the specified radionuclide. These conditions have been assumed in conducting the present study. Throughout this study a simplifying assumption was to model the deposition of inhaled material as an acute event. This assumption is justified when the intake occurs over a relatively short exposure duration (during which ventilation rates remain relatively constant for individuals within the population group). For a long exposure duration (where ventilation and intake rates change), the mathematical model for biokinetic clearance requires mathematical expressions for the intake rates for individuals. Therefore, the methodology and results described herein are based on an acute activity deposition in the lungs. Dose factors for inhalation refer to the radiation dose delivered over a specified time period to a tissue, organ, or the whole body per unit of inhaled activity. Dose quantities of interest for an inhalation intake include the equivalent dose to various body organs (including, but not limited to, the lungs) and the effective dose to the whole body. These dose quantities are described in later sections of this dissertation. Generally, these dose quantities represent the amount of radiation energy absorbed per unit mass (of the target tissue) and include various weighting factors to account for the biological effectiveness of different radiation types and for the differential radiation sensitivities of organs in the body. The special SI unit for equivalent dose and effective dose is the sievert, abbreviated Sv. The sievert has more fundamental units ofjoules per kilogram. To compute radiation dose, the dose integration time must be specified. This integration time refers to the period, following the intake, over which the radiation dose is delivered. For radiation protection purposes, the ICRP (1991a) has recommended a dose integration time of 50 years for adults (18 years or older) and 70 years for children when 8 deriving equivalent and effective doses. However, for epidemiological studies or radiation litigation cases, other dose integration times might be desired. It is important to distinguish clearly the exposure duration, D, from the dose integration time. As described above, the exposure duration refers to the time over which the intake occurs. The dose integration time refers to the time over which the dose rate is integrated to compute radiation doses to various body tissues and organs. For radionuclides that deposit in the body, dose continues to be delivered (in some cases over many years) after the intake has occurred since material is retained by various tissues. Of the possible pathways for intake of a radionuclide into the body (i.e., inhalation, ingestion, absorption, and injection), inhalation is generally the most complex. Particles that deposit in the respiratory tract can undergo a number of processes including: (1) transport by mucociliary clearance to the gastrointestinal (GI) tract, (2) phagocytosis by alveolar macrophages accompanied by possible transport to the lungassociated lymph nodes (where particles can be retained throughout the remainder of a person's life) or the GI tract via the mucociliary escalator, and (3) dissolution accompanied by absorption from lung tissues to the blood circulatory system. Therefore, in addition to being a region of concern with respect to radiationinduced risk, the respiratory tract is also a portal for inhaled radionuclides to other body tissues and organ systems. For example, animal studies involving inhalation of a number of transuranic compounds have demonstrated increased incidences of fatal cancer to the bones, liver, and kidneys, as well as the lungs (ICRP 1980). 1.2.2. Internal Radiation Dosimetry, Reference Man, and Risk Radiation dose calculations for a given inhalation intake have traditionally involved deterministic techniques. In such techniques biological variabilities and uncertainties are ignored in the dose prediction yielding a single quantitative result. The traditional approach has been to define and apply anatomical and physiological models under the auspices of a reference or standard man, where reference man represents an individual comprising typical anatomical and physiological characteristics (e.g., ICRP, 1975, 1979). Such characteristics have been chosen by scientific consensus in order to provide a common (simplified and routine) basis for performing internal dose calculations. Acknowledging differences attributable to age and gender, the referenceman approach currently distinguishes between adult man, adult woman, and children of various ages (ICRP, 1989). Although a useful concept for simplifying computational effort, relatively few, if any, individuals in a given population group will match their reference man counterpart identically. Using the referenceman approach, tables of intaketodose conversion factors (or DCFs) have been compiled for a number of specific intake conditions (e.g., Eckerman et al., 1988; ICRP, 1979; ICRP, 1989; USNRC, 1992). Such tables are used extensively in the nuclear industry and affect many decisions regarding past and future exposures of both workers and the general public to potential internal radiation sources. Generally for internal dosimetry, the DCF represents either the radiation equivalent dose (to a tissue/organ) or the effective dose (to the whole body) per unit intake of radioactivity and has units of sieverts per becquerel (Sv/Bq). These quantities are defined in ICRP Publication 60 (1991 a). These dose quantities include a radiation weighting factor, WR, to account for the different biological effectiveness of various radiation types (e.g., photons, electrons, alpha particles, neutrons) per absorbed dose. When reflecting the effective dose, the DCF also incorporates tissue weighting factors, wT, which account for the different radiation sensitivities of organs/tissues to induction of detrimental diseases. Table 11 lists inhalation DCFs for some selected plutonium isotopes and transuranics. Except for Pu241, the dose from these radionuclides is due primarily to energy deposited by alpha particles. Values in all but the last column are from Eckerman et al. (1988) and are for a working, reference adult male. These values are based on the dose methodology described in ICRP Publication 30 and Supplements (ICRP, 1979). An aerosol with a 1 pm activity median aerodynamic diameter (AMAD, i.e., the diameter for which half of the activity is associated with particles of smaller aerodynamic diameter) with typical dispersion in size (i.e., geometric standard deviation or GSD < 3.5) has been used in deriving these values. The last column, labeled effective dose (denoted Hf), was derived using the organ equivalent doses from Eckerman et al. (1988) and the tissue weighting factors adopted in ICRP Publication 60 (ICRP, 1991a). The clearance class refers to the residence time of various chemical forms of the radionuclide in the lungs. Clearance classes D, W, and Y (defined in ICRP, 1979) refer to materials having residence times that are on the order of days, weeks, and years in the lungs, respectively. Generally, plutonium oxides, which are of interest in this study, are assigned to class Y, while other chemical forms of plutonium are assigned to class W. The term denoted f, corresponds to the fraction of the activity in the small intestine that is absorbed to the blood. An important point to note is that these tabulated DCFs have been listed without their associated uncertainties; the reason is that uncertainties in these DCFs have not been previously quantified. Table 11. Selected intaketodose conversion factors (in Sv/Bq) for inhalation of some plutonium isotopes and other transuranics based on an activity median aerodynamic diameter, AMAD, of 1 um. Inhaled Class"; Gonads' Lungs' Red Bone Bone Liver" Hfd Nuclide fb Marrow' Surfaces' Pu238 W;1.0E3 2.80E05 1.84E05 1.52E04 1.90E03 3.51E04 6.26E05 Y;1.0E5 1.04E05 3.20E04 5.80E05 7.25E04 1.37E04 6.15E05 Pu239 W;1.0E3 3.18E05 1.73E05 1.69E04 2.11E03 3.78E04 6.87E05 Y;1.0E5 1.20E05 3.23E04 6.57E05 8.21E04 1.51E04 6.48E05 Pu240 W;1.0E3 3.18E05 1.73E05 1.69E04 2.11E03 3.78E04 6.87E05 Y;1.0E5 1.20E05 3.23E04 6.57E05 8.21E04 1.51E04 6.48E05 Pu241 W;1.0E3 6.82E07 7.42E09 3.36E06 4.20E05 6.57E06 1.29E06 Y;1.0E5 2.76E07 3.18E06 1.43E06 1.78E05 3.01E06 9.37E07 Am241 W;1.0E3 3.25E05 1.84E05 1.74E04 2.17E03 3.91E04 7.08E05 Cm244 W;1.0E3 1.59E05 1.93E05 9.38E05 1.17E03 2.39E04 4.04E05 Source: All columns except last are from Eckerman et al. (1988). Last column is based on a weighted sum of organ/tissue doses with tissue weighting factors from ICRP (1991a). * "Class" refers to clearance class (D,W, or Y) as defined in ICRP Pub. 30 (ICRP 1979). b The term f, represents the fraction of activity absorbed from the small intestines to the blood. SOrgan/tissue equivalent dose in sieverts per becquerel (Sv/Bq). d Effective dose, HIf: sum of organ/tissue equivalent doses weighted by tissue weighting factors as described by ICRP (1991 a). For all of the transuranics listed in Table 11, the bone surfaces (endosteal tissues) are predicted to receive the greatest equivalent dose (per inhalation intake). For class W forms, the liver is predicted to receive the second highest equivalent dose followed by the red bone marrow. For class Y forms, the lungs are predicted to receive the second highest dose followed by the liver. In comparing organ DCFs, one should be aware that while DCFs indicate the typical equivalent doses to organs (of reference man), they do not necessarily reflect the radiationinduced health risks to these organs. As a means to compare organs on a risk basis, the ICRP (1991a, Table B20) has recommended organ/tissue risk factors. These risk factors quantify the additional probability (i.e., above the background or baseline probability) per organ equivalent dose that a person will experience a fatal cancer or contribute a severe genetic effect to offspring. The organ DCFs listed in Table 11 have been multiplied by respective organ risk factors (from Table B20 of ICRP, 1991a) to determine organ risks per intake. Table 12 lists results of these computations for some of the radionuclides in Table 11. For all radionuclides listed in Table 11 with clearance class W, the three organs having the greatest risk per unit intake (from highest to lowest risk) are: bone surfaces, red marrow, and liver; the lungs rank fifth and account for only about 5% of the total risk (based on data presented in Table 12). For clearance class Y, the order is lungs, bone surfaces, and red marrow; and the risk to the lungs contributes over 70% to the total risk from the intake. For both clearance classes, the order of organs as ranked by equivalent dose does not match the order as ranked by organ risk. The discrepancy is due to the fact that some organs are more sensitive to radiation than others. As a practical example of what the numbers in Table 12 reflect, consider the total risk per intake for class Y Pu239; the value is 3.84x106 per Bq. The annual limit on intake (ALI) for class Y Pu239 is about 300 Bq (ICRP, 1991b). If one million (106) people experienced a 300 Bq intake, then about 1000 out of the 106 people 13 [i.e., (300 Bq)*(3.84x106 Bq')*(106)] are predicted to develop a fatal cancer or pass on a severe genetic effect to offspring. It is predicted that 70% of those people, based on Table 12, would develop fatal lung cancers. A number of assumptions are implied in this methodology. The most important (and controversial) is that these risk factors, which are based on exposures of persons at high dose/high dose rate, are appropriate for the low dose/low dose rate exposures generally of interest in environmental exposure scenarios. Table 12. Organ and total risk (of fatal cancer or severe genetic disorder) per inhalation intake of plutonium compounds for working adult male. Risk per Inhalation Intake (x 106 Bq'') Pu238 Pu239 b Organ Class W Class Y Class W Class Y Lungs 0.156 (5.8%) 2.72 (73.7%) 0.147 (5.0%) 2.74 (71.4%) Bone 0.950 (35.2%) 0.290 (7.9%) 1.05 (35.5%) 0.410 (10.7%) Surfaces Red 0.760 (28.1%) 0.362 (9.8%) 0.845 (28.5%) 0.328 (8.5%) Marrow Liver 0.526 (19.5%) 0.205 (5.6%) 0.567 (19.2%) 0.226 (5.9%) Gonads' 0.280 (10.4%) 0.104 (2.8%) 0.318 (10.7%) 0.120 (3.1%) Total Riskd 2.70 (99.0%) 3.69 (99.8%) 2.96 (98.9%) 3.84 (99.6%) Notes: Values are based on product of dose factors from Eckerman et al. (1988) for working adult male (presented in Table 11) and organ risk factors from ICRP Pub. 60 (1991a, Table B.20). Values in parentheses represent percent contribution of respective organs to the total risk. Values for Am241 compounds are approximately equal to values for class W Pu238. b Values for Pu240 are equal to values for Pu239 (for respective classes). Risk of severe genetic effects for gonads. Risk of fatal cancer for other organs. d Total risk includes contributions from other organs (e.g., stomach, bladder, breast, etc.) not listed in the table. Parenthetical values represent the percent contribution from organs listed in the table. In summary, the above discussion indicates that inhalation of radioactive aerosols introduces risks to the lungs as well as to other body organs. Traditional methods provide 14 only point, deterministic predictions of organ dose/risk, not information on the uncertainty in these quantities. Regardless of which organs acquire higher risks after an inhalation intake, uncertainties in respiratory tract models are important and affect dose and dose based risk predictions. For certain inhaled radionuclides which pose the greatest risk to lung tissues (e.g., the class Y transuranics listed in Table 11), uncertainties in all aspects (i.e., deposition, clearance, and dosimetry) of the respiratory tract model are potentially important. For inhaled radionuclides that pose greater risks to tissues other than the lungs (e.g., class W transuranics listed in Table 11), uncertainties in the deposition and clearance aspects of the respiratory tract model are nonetheless important because they influence the amounts of radioactivity that reach these tissues. In the present study, the focus is only on uncertainty in radiation dose to the lungs. However, the methodology developed can also be useful for quantifying uncertainties in other organ doses (inasmuch as they are influenced by the lung model). 1.2.3. Advantages and Disadvantages of the ReferenceMan Approach As discussed, the referenceman approach for dose assessment results in single, quantitative deterministicc) dose estimates for a given intake scenario. In many circumstances such an approach is adequate and useful. For example, the following situations are well served by this approach: (1) if the purpose of the dose assessment were simply to demonstrate compliance with radiation protection standards and regulatory limits or, (2) if the purpose of the assessment were to perform screening calculations in order to identify doses (and dose pathways) which might result in serious health effects. 15 However, if the dose assessment study were being performed to assess actual radiological health risks either to an exposed individual or to an exposed population group (e.g., as in radiation litigation cases or epidemiological studies), it is difficult to justify the reference man approach (depending on the magnitude of the predicted risks). Individual and populationwide tissue doses might differ significantly from typical doses based on the referenceman methodology. In the former case, an exposed individual would likely differ from reference man with respect to anatomical and physiological characteristics. In the latter case, the problem is that the referenceman approach does not address the biological variabilities among individuals in a population group. Additionally, the referenceman approach does not include uncertainties due to lack of knowledge regarding model parameters. A number of major studies are underway in the United States whose tasks are to assess radiation doses and risks to population groups exposed to past releases of radioactive and hazardous materials from nuclear weaponsrelated production and testing sites. Facilities under study include the U.S. Department of Energy Hanford Site in Washington, Rocky Flats Plant in Colorado, Savannah River Site in South Carolina, and Oak Ridge National Laboratory in Tennessee, among others. A difficult issue that all of these studies face is one of incorporating uncertainties in dose and risk estimates. Some of these studies have attempted to include uncertainties in environmental transfer models (e.g., PNL, 1991a, 1991b; 1991c); however, none have conducted a detailed examination of the uncertainties in human biological models (describing the fate of the radionuclide after it enters the body). It would be beneficial to know whether variabilities in predicted 16 dose attributable to uncertainties in the human biological models are negligible compared to variabilities in dose attributable to uncertainties in environmental transfer models (i.e., uncertainties in sourceterm, atmospheric/hydrogeologic dispersion, and terrestrial/aquatic foodchain models). 1.3. Previous Work Upon conducting a literature search for previous work, three studies were found which dealt with uncertainties in inhalation radiation doses attributable to human respiratory tract models and associated parameters. Uncertainties have been examined for: (1) the effective dose (to whole body) due to inhaled U238, Th230, Ra226, and Pb 210 (Wise, 1985), (2) dose to basal cells of the bronchial epithelium due to inhalation of radon decay products (Hofmann and Daschil, 1986), and (3) dose to the lungs due to inhalation of radon decay products based on the revised ICRP lung model (Birchall and James, 1994). Based on measured deposition data from human experiments by Chan and Lippman (1980) and Yu et al. (1981), Wise (1985) examined uncertainties in the fitting parameters of empirical equations used to predict particle deposition in the respiratory tract. These uncertainties were propagated through the dose methodology recommended in ICRP Publication 30 (1979) to obtain uncertainty bounds for committedeffectivedose equivalents (i.e., dose integrated over 50 years post intake) for a number of selected inhalation scenarios. Uncertainties in organ committed dose to the lung were not presented; only the committed effective dose to the whole body. Selected statistics and uncertainty limits were tabulated for a number of particle aerodynamic diameters, radionuclides, and solubility classes. Wise did not directly account for stochastic variabilities in the input parameters of the lung deposition model such as airway dimensions, tidal volumes, ventilation rates, etc. Wise's study also neglected uncertainties in the clearance aspect of the lung dose model. Furthermore, variability in parameters involved in systemic and excretion models for anatomical and physiological systems beyond the respiratory tract were not included. Thus, the extent of the uncertainty in effective dose was underestimated. With the above limitations, Wise found that uncertainties in deposition model predictions lead to committed effective dose equivalents whose lower and upper 95% confidence limits differed by less than a factor of about 10. If a lognormal distribution is assumed for dose predictions, this factor corresponds to a geometric standard deviation, GSD, of about 1.8 (i.e., 101'4). Ratios of the upper 95% confidence bound to the lower 95% bound have been determined from results tabulated by Wise and are plotted in Figure 12. This plot represents a working adult male breathing (20 L/min) entirely through the nose. The ratio for the two largest particle sizes (5 and 6 Prm) are not shown for U238 since the lower 95% confidence limits were zero for these conditions. Wise also reported data for mouth breathers; the ratios obtained were slightly less than for nose breathers. While these results were important as a first attempt to quantify uncertainties in inhalation dose coefficients, they are incomplete. Hofmann and Daschil (1986) performed a parameter uncertainty analysis on the respiratory tract models for radon progeny (Hofmann, 1982a, 1982b) in order to derive 15 S U238(Y) 40 Th230 (Y) S10 Ra226 (W) S . Pb210 (D) 5  4T 0 1 2 3 4 5 6 Particle Aerodynamic Diameter (microns) Figure 12. Ratio of upper to lower 95% confidence bounds for committed effective dose equivalent per intake for adult male workers. Based on results from Wise (1985). The ratio is undefined for the largest two diameters (5 and 6 jpm) ofU238 because the lower bound was reported as zero. distributions in radiation dose to the basal cells of various airway generations of the bronchial epithelium. For the target cells considered (basal cells), Hofmann and Daschil examined uncertainty in more detail than Wise (1985) by accounting for variabilities in a number of model input parameters (including deposition fractions, total surface area of bronchial generations, amount of inhaled activity, mucociliary clearance rates, translocation rates to blood, and basal cell depths). However, the authors did not examine uncertainties in radiation doses arising in the pulmonary region of the lungs. Furthermore, doses were only examined for individual basal cells as the targets. While dose at the cellular level is of interest, the approach adopted in the revised ICRP lung model (ICRP, 1994) is to compute average doses for critical tissues (composed of many critical cells). The authors found that doses to basal cells of the bronchial epithelium under specified conditions were approximately lognormally distributed and that the 50% and 99% fractiles differed by about a factor of five depending on the tracheobronchial generation. This value corresponds to a GSD of about two. This dispersion is similar to that which can be deduced from results of the study by Wise (1985). Birchall and James (1994) recently performed an uncertainty analysis of the effective dose per unit exposure from radon progeny using the revised ICRP lung model (ICRP, 1994). This model is also used to conduct the present study. The primary purpose of their study was to reconcile dose factors derived from the revised lung model with those derived from epidemiological estimates. The study was performed for a working male with median ventilation rate of 20 L/min. Uncertainties were included for aerosol size characteristics, ventilation rate, deposition and clearance factors, source and target layer dimensions, and regional riskapportionment factors (discussed later in Chapter 2), among other variables. Here Birchall and James found that model predictions were influenced largely by the choice of values for the regional riskapportionment factors. Results indicated that effective dose per unit radon progeny exposure varied over about one order of magnitude based on parameter distributions selected. While the study by Wise (1985) did produce results of a useful form for whole body dose assessment activities, the results are incomplete since uncertainties only 20 pertained to the lung deposition portion of the dose model. Hofmann and Daschil (1986) produced results which accounted for more detail in the uncertainty and variability of lung model parameters but did not examine uncertainties in doses to the pulmonary region of the lungs. Consequently, it is difficult to apply results of that study to class Y materials such as plutonium oxides where a relatively large dose is expected to be delivered to the pulmonary region of the lungs. The study by Birchall and James (1994) included parameter uncertainties in the revised ICRP lung model but focused strictly on radon progeny. Furthermore, all of the above studies were performed for working reference mannot for other variants of the population (i.e., other age and gender groups). 1.4. Description of Present Study 1.4.1. Assessment Problem Addressed According to the IAEA (1989), the reliability of model predictions can only be properly examined within the context of a welldefined assessment problem. The assessment problem of interest throughout this study was the following: Determine the assessed quantity (per unit activity exposure, i.e., per Bqhr/m3) to an unspecified individual in a population group exposed under the following scenario: (a) specified age/gender of the population group, (b) specified exertion level (resting, sitting, light exertion, or heavy exertion) of the population group, (c) specified radionuclide/chemical form, (d) specified aerosol activitysize distribution (including related parameters such as particle mass density and particle shape factor, defined in section 2.5), (e) specified dose integration time, (f) specified ambient temperature and barometric pressure over exposure duration. The term assessed quantity in the above assessment problem serves simply as a placeholder for text describing specific quantities of interest in this study. Table 13 lists the assessed quantities and scenario information which were investigated in the present research. Quantities of interest included (1) the fraction of inhaled radioactivity that deposits in various respiratory tract (RT) regions, (2) the total number ofradionuclide transformations that occur in various RT source components as functions of time, and (3) the radiation dose delivered to various RT target tissues for a specified dose integration time. For item (3), the assessed quantity corresponds to a dose conversion factor, expressed per unit activity exposure (i.e., an exposuretodose conversion factor, or EDCF). These assessed quantities are discussed in more detail in Chapter 2. Table 13. Specific information related to the assessment question and scenarios considered in this study. Radionuclide/ Exertion Level Population Assessed Quantityb Chemical Form Age (years)" 239+20puO2 Resting (Sleeping) 2 Deposition Fraction Sitting (Awake) 5 (activity deposited in RT Light Exertion 10 regions) Heavy Exertion 15 1824 Number of Transformations 2534 (in RT source components) 3544 4554 Equivalent Dose 5564 (to RT target regions) Equivalent Dose (to lung: weighted sum) a Both males and females have been considered at these ages. b Quantities assessed in this study pertain to respiratory tract regions or to combinations of regions; other organs/tissues are not examined. Assessed quantities and respiratory tract regions are discussed in detail in Chapter 2. Since this assessment problem addresses unspecified individuals within a population group, it possesses a probabilistic rather than deterministic answer. In other words, stochastic variability exists in the assessed quantity among unspecified individuals in the population group. Therefore, the answer to the assessment question should be represented by a probability density function (distribution) rather than a single number. In performing demonstration calculations in this study, the scope of the assessment problem has been narrowed to include only inhaled PuO2laden aerosols with radionuclides Pu239 and Pu240. These particular radionuclides/chemical form was selected to support a dose reconstruction study underway by the Colorado Department of Public and Environmental Health. One purpose of that study is to predict population risks arising from historical releases of plutonium from the Rocky Flats Plant (a facility that produces and stores nuclear weapons components and is located about 20 from downtown Denver, Colorado). "2392PuO2 emits primarily alpha particles and is relatively insoluble in lung fluids; also as shown by predictions in Table 12, this material (depending on the magnitude of the intake) can result in potentially large risks to the lungs. As further limitation on the work, aerosol particles were assumed to be nonhygroscopic (i.e., particles do not increase in size upon entering saturated conditions of the respiratory tract) 1.4.2. Units of Exposure Traditional methods have predicted inhalation dose conversion factors per unit intake, where the intake represents the amount of radioactivity inhaled. However, in the assessment question defined above, the intake possesses stochastic variability among individuals of the exposed population. In order to account for these variabilities, an improved reference unit for dose predictions is the activity exposure, AE, defined earlier. At least three reasons exist for expressing dose factors per unit activity exposure rather than per unit activity intake. First, in assessing doses to humans from inspirable radionuclides released to the environment, atmospheric dispersion models are usually implemented to estimate airborne activity concentration, i.e., C,(t) in Bq m"3 at specific locations. By expressing dose factors in terms of activity exposure rather than intake, a more efficient coupling of the results of dispersion models and inhalation dose factors can be achieved. If dose factors were per unit intake, one would still need to determine the inhalation intake in order to use the dose factor. Second, intake depends on the human ventilation rate which is influenced by biological variability and lifestyle habits among members of a population. It is desirable in this study to account for variability in ventilation ( and subsequently the intake) as a contributor to uncertainties in dose factors. The activity exposure, AE, is not influenced by the ventilation rate. Third, the ventilation rate is a parameter in the deposition component of the lung dose model (it is proportional to the average inspiratory flow rate); so the dose coefficient (expressed per unit intake) is correlated with the intake since both are mutually dependent on ventilation rate. Therefore, in this study inhalation dose coefficients were derived per unit activity exposure and have units of Sv per Bqhrm"3. 1.4.3. Summary of the Research Approach As discussed in the opening section of this chapter, the reliability of model predictions is affected by several uncertainties introduced through the modeling process. This study examined the uncertainty in model predictions attributable to parameter uncertainties. The respiratory tract model issued recently by the ICRP (1994) was selected to perform this study. The study was divided into three phases: I, II, and III. Phase I involved development of a computer program to implement the adopted respiratory tract model and to couple the model with existing numerical random sampling programs. The program developed in this work accounts for all aspects of the RT model, including particle deposition, clearance, and radiation dosimetry. An existing program that performs Latin hypercube sampling (Iman and Shortencarier, 1984)which is a form of random number sampling used to select values for the model parameters from their respective, assigned, probability distributionswas coupled with the program for solving the respiratory tract model. Sampled model parameter values are combined to form input vectors (or realizations) which are propagated through the model to produce numerical distributions in model predictions. An overview of the RT model, and the techniques implemented to solve it, are provided in Chapter 2 and related appendices. Techniques employed in this study for generating random samples of the joint probability density function for the combined ranges of all parameters for propagating parameter uncertainties through the model structure are discussed in Chapter 3. That chapter also presents techniques used to examine parameter sensitivities in the model predictions. Phase H of the study involved quantifying uncertainties and variabilities in respiratory tract model parameters. Some of the general concepts involved in this phase of the study are discussed in Chapter 3. Based on an extensive literature review, Chapter 4 presents the specific parameter distributions adopted to perform uncertainty analyses in this study. This phase of the work was necessarily tedious since approximately seventy input parameters were assigned distributions in the RT model. Although many of these parameters were not primary input parameters, they were needed in order to account for correlations between and restrictions on the primary model parameters. Most of the parameter distributions presented in Chapter 4 are independent ofradionuclide and chemical form; so techniques developed in this study could be applied with minimal effort to other radionuclides/forms. For example, except for hygroscopic materials, all parameters related to the deposition component of the model are generally independent of radionuclide and physicochemical form. For the clearance model, only the parameters related to dissolution and absorption clearance processes and the radioactive decay constant depend on the radionuclide/form. For the dose model, all source and target geometrical dimensions are independent of nuclide/form; however, energy deposition computations do depend on the radionuclide decay scheme (radiation types, frequencies, and energies). Phase HI of the study involved application of the computational methodology (developed in Phase I) and recommended parameter distributions (developed in Phase II) to various assessment scenarios (i.e., substitution of entries in Table 13 into the assessment problem model). These scenarios involved inhalation exposures to plutonium 26 oxide aerosols by various population groups specified by age and gender. Equivalent doses to lung tissues and an overall, combined lung dose were examined for various particle sizes. This final phase also included sensitivity analyses with the primary model parameters to determine which parameters contributed most to the uncertainty in equivalent dose predictions for the lungs. The results of these activities are presented in Chapter 5. Chapter 6 presents a summary of the work, important conclusions and recommendations, and suggests future research to expand the methodology and the body of knowledge concerning uncertainties in human biologicalradiological dosimetry models. CHAPTER 2 METHODS FOR RESPIRATORY TRACT MODELING 2.1. Introduction In this study, parameter uncertainty analyses have been conducted with the new respiratory tract model recommended by the International Commission on Radiological Protection (ICRP, 1994). The National Council on Radiation Protection and Measurements (NCRP, 1993) has also been working to issue guidance on respiratory tract modeling (independently of the ICRP). However, a comparison of the two models (see Appendix A) revealed difficulties in implementing the NCRP model in the numerical strategy employed by this studywhich required solving the model repetitively and efficiently. In this study, Monte Carlo techniques have been employed to treat model parameters as random variables within the computational model recommended by the ICRP (these techniques are discussed in Chapter 3). The purpose of the current chapter is to provide an overview of the components of the new ICRP respiratory tract model and to outline the computational techniques for solving these components. A complete description of the model can be found in ICRP Publication 66 (ICRP, 1994). Although generally cited as a single entity, a respiratory tract model for dose assessment involves a number of component models arising from many specialized areas of study. As illustrated in Figure 21, the overall model can be divided into three primary componentsdeposition, clearance, and dosimetry models. Each component involves a number of input parameters which can depend on the exposure scenario. Topics which must be considered in developing the conceptual and computational models for the respiratory tract and in quantifying associated input parameters include respiratory tract morphology, radiation biology, and respiratory physiology. In this context, morphology refers to the anatomy and structure of the airways and associated tissues; radiation biology involves identification and sensitivities of various critical (target) cells in the respiratory tract; and respiratory physiology involves the functions and dynamics of the airways and associated tissues. Aerosol particle size characteristics must also be considered since they affect deposition mechanisms. Respiratory Tract Model User Input Parameters Deposition Model: (aerosol properties, particle impaction, sedimentation, and diffusion mehanisms) (Deposition Fractions) SClearance Model: (biological removal/retention radioactive decay processes) (Total Transrmations/Rates per Source Region) Dosimetric Model: (radioactive decay, Radiation Dose Estimates (e type and energy of emissions, sourcetarget geometries) Figure 21. Components of a respiratory tract dosimetry model. Particles deposit on airway walls by several interacting mechanisms including inertial impaction, gravitational sedimentation, Brownian diffusion, interception, and electrostatic attraction. The efficiencies of these deposition processes depend on a number of parameters including: particle physical characteristics (e.g., aerodynamic diameter, mass density, shape factor, and diffusion coefficient), airway diameters and lengths, airway branching and gravitational angles, tidal volume, functional residual capacity, and ventilation rate. Due to particle physical characteristics and air flow patterns in the lung, one or more of the above deposition mechanisms can dominate in various regions of the respiratory tract. Deposition generally does not depend on the radionuclide or its chemical form (except for hygroscopic materials). Predictions of the deposition component of the respiratory tract model include the fractions of inhaled activity which deposit in various respiratory tract regions. These deposition fractions are subsequently inputs to the clearance model. Clearance of deposited materials refers to their biological and radiological removal from the respiratory tract. Three primary mechanisms exist for biological clearance in the respiratory tract: (1) mucociliary clearance of material to the gastrointestinal tract, (2) phagocytosis by alveolar macrophages followed by subsequent translocation to lymph nodes or to the mucociliary escalator, and (3) dissolution of material accompanied by absorption to airway tissues and/or to the blood circulatory system. When the material is radioactive a fourth removal mechanism existsradioactive decay. Depending on the region of deposition and the physicochemical form of the deposited material, various clearance mechanisms/patterns can occur. To model clearance, the respiratory tract is compartmentalized and is traditionally described by a system of firstorder, linear differential equations with respect to time. Except in very unique circumstances, deposition and clearance models are not intended solely for radioactive materials. From both a biological and mathematical perspective, the only difference between a radioactive and nonradioactive material with respect to deposition and clearance is the accommodation of radioactive decay as one removal mechanism. Two predictions are generally of interest for the clearance model as applied to inhaled radionuclides. One is the total number of radioactive transformations (or disintegrations) that occur in individual model compartments over a specified integration time; the other is the transformation rate (or activity) of the radionuclide in individual model compartments at a specified time. The latter model prediction is related to the radiation dose rate while the former is related to the radiation dose (i.e., the timeintegrated dose rate). The dosimetry component of a respiratory tract model is unique to radioactive materials. The radiation dose rate attributable to shortrange radiation types (e.g., alpha particles, beta particles, and electrons) is directly related to the amount of radioactivity present in lungs; this activity is determined by solving the clearance model for the intake scenario of concern. For gamma rays and other penetrating radiation types, activity in other body organs can also contribute to the lung dose. The radiation dose is the integral of the dose rate over time and is related to the total number of radioactive transformations that occur in organs in the specified time interval. The dosimetry aspect depends on the radionuclide since different decay schemes (radiation types, frequencies, and energies) are characteristic of different radionuclides. Furthermore, for shortrange radiations, the dose to critical lung tissues is very sensitive to the sourcetarget geometry. This geometry refers to the spatial relationship between tissues that contain the radioactive material (source regions) and tissues that contain the critical cells (target regions). 2.2. Development of Respiratory Tract Dose Models A brief summary of the evolution of the model used in this study has been given by the ICRP (1994). The first coherent model integrating respiratory tract deposition, clearance, and dosimetry was issued in ICRP Publication 2 (ICRP, 1960). Prior to that publication, discussions and recommendations concerning respiratory tract dosimetry were made at various conferences, such as the Tripartite Conferences on Radiation Protection held from 19491953 (Taylor, 1983). The model reported in ICRP Publication 2 assumed that, lacking specific data, 75% of inhaled aerosol particles would deposit in the respiratory tract (50% deposited in upper airways; 25% deposited in the lungs; and 25% was exhaled). Concerning clearance, the model classified materials as either soluble or insoluble. Soluble materials that deposited in the lungs were assumed to be absorbed completely (by the blood) and translocated to other body tissues. For insoluble materials that deposited in the lungs, half of the material was assumed to clear (to the GI tract) with a biological half time of 24 hours (presumably to the GI tract); the other half was assumed to clear with a biological half time of 120 days (radiological decay would affect the overall clearance time). In 1966, a revised lung model was published (TGLD, 1966) by the ICRP Task Group on Lung Dynamics. A slightly modified version of this model was ultimately 32 published by the ICRP in Publication 30 (ICRP, 1979). Most of the current annual intake limits ofradionuclides for workers (e.g., USNRC, 1992) are based upon the Publication 30 model, which is a considerable improvement over the Publication 2 model. The ICRP Publication 30 model divides the thoracic region of the lungs into two regions (tracheobronchial and pulmonary) and includes a deposition model that accounts for particle size influences. The Publication 30 model incorporates an improved clearance model which provides guidance for classifying materials into three (compared to only two in the former model) clearance classes. Clearance to lymph nodes, blood, and the gastrointestinal tract are all included in the model. The model is based on an adult lung morphology for deposition and on both human and animal data for clearance of materials. Dosimetry calculations are based on averaging energy deposition over the total lung mass. In December of 1994, the ICRP issued a new respiratory tract model as ICRP Publication 66 (ICRP, 1994). Among the reasons for revising the model were: (1) to provide a means for calculating doses to the nasal and oral passages; (2) to compute more biologically significant doses to critical target regions rather than simply averaging dose over the total lung mass; (3) to provide more flexibility for selecting various clearance rates so that predicted clearance patterns better match observed patterns; (4) to incorporate new data on particle deposition below 0.1 Pm particle diameter; (5) to incorporate new knowledge and data on particle retention and clearance in various regions of the respiratory tract; and (6) to construct a model that applies to all members of the world's population consistent with age, gender, and race. A principal feature of the 33 revised lung model is that the relative radiosensitivities of various respiratory tract tissues are taken into account when combining regional doses to obtain an overall lung dose. As discussed in the opening paragraph, the NCRP (1993) has also been working, independently of the ICRP, to issue new guidance on respiratory tract modeling. Many of the items listed above for the ICRP Publication 66 model are also addressed in the model adopted in principle, but not yet published, by the NCRP. The conceptual and computational models recommended by the NCRP and the ICRP (1994) differ in several ways. Differences exist in the deposition model resolution, specification of fractional clearance rates, and specification of target regions in the dosimetry model. Some of these differences between the models are discussed in more detail in Appendix A. 2.3. Respiratory Tract Morphological Model The anatomical representation of the revised ICRP (1994) respiratory tract model is shown schematically in Figure 22. Based on structure and function, the model divides the respiratory tract into the following five primary regions: (1) the extrathoracic region comprising the anterior nasal passages, ET,, (2) the extrathoracic region comprising the posterior nasal passages, larynx, pharynx, and mouth, ET2, (3) the bronchial region, BB, comprising airway generations 0 through 8 (trachea through the bronchi), (4) the bronchiolar region, bb, comprising airway generations 9 through 15, and (5) the alveolarinterstitial region, AI, comprising the first respiratory bronchioles through the alveolar sacs and including interstitial connective tissues. Thoracic Bronchial Bronchioles bb / Bronchiolar \/ i Al Alveolar Interstitial bb \ Bronchioles Terminal Bronchioles AJ Respiratory Bronchioles Alveolar Duct + Alveoli Figure 22. Anatomical representation of the revised ICRP respiratory tract model. The respiratory tract is divided into five primary regions (ETI, ET2, BB, bb, and AI) and two lymph node regions (not shown). Reproduced by permission from ICRP Publication 66 (ICRP, 1994, p. 9). In addition two lymph node regions are identified to represent the lymph nodes (LNET) which drain the extrathoracic regions (ET, and ET2) and the lymph nodes (LNTH) which drain the thoracic regions (i.e., BB, bb, AI). To account for the morphological variation of the respiratory tract with respect to age, gender, and race, scaling factors are used in the deposition model. These factors allow regional deposition to be computed for any subject by scaling certain aspects of the model based on the ratio of subject airway dimensions to those of reference man. Scaling factors are based on the diameters of the trachea and airway generations 8 and 15. The thickness and cellular structure of surface and epithelial tissues in ET, BB, bb, AI regions are taken to be invariant with age, gender, and body size; however the surface area of the various airway regions does depend on body size and is accommodated in this study. For ET, BB, and bb regions, the airways are modeled as cylinders. Source and target tissues residing within the airway wall are considered to be cylindrical shells. Figure 23 is a schematic of the cross sectional view of a typical airway wall for the bronchial region. Although there are some differences in thicknesses and tissue layer structure, similar geometries are used in the model to represent bb and ET airway wall tissues. 2.4. Respiratory Tract Deposition Model The clearance pattern and regional doses are influenced by the amounts of radioactive material which deposit in the various respiratory tract regions. To compute the fraction of inhaled radioactivity which deposits in the five broad respiratory tract regions, the basic approach of the ICRP (1994) is to model the respiratory tract as a series 36 of filters, as illustrated in Figure 24. The first filter in the figure represents the inhalability of the aerosoldiscussed below. The other filters represent the respiratory tract regions described above. Because deposition occurs during both inhalation and exhalation, some respiratory regions appear more than once in the filter chain. 5 5n ~.. ".." ..+.Mucus (Gel Layer) 6pm Cilia + Sol Layer 10 am Nuclei of Secretory 35 pm Cells 30 pm i (Target) I I Nuclei of Basal Cells 5 Basal Cell Basement (Target) Membrane 5j m Lamina O10 Propria Subepithelial Layer <500 pm of Tissue /Alveolar Interstitiu Figure 23. Model of airway wall in the bronchial (BB) region. Targets in this region include secretary cell nuclei and basal cell nuclei. The region is separated from the alveolar interstitium by a layer of subepithelial connective tissue. Reproduced with permission from ICRP Publication 66 (ICRP, 1994, p. 15). Region Na Pa Extrathoracic sal thway F Environment (ambient air) Inhalability Inhaled Air ,A Bronchial Bronchiolar AlveolarInterstitial Bronchiolar Bronchial Extrathoracic E Exhaled Air hm(ET2), hin(ET2) hil(BB) hin(bb) h(AI) hex(bb) he(BB) hex(ET2), heET2m) hexETl) Exhaled Air Figure 24. Representation of the deposition component of the revised ICRP respiratory tract model. The respiratory tract is modeled as a series of filters with characteristic volumes and deposition efficiencies. After Figure 8 in ICRP(1994). Filfration Filtration Efficiency h,( NhTinT) Two pathways are considered for air flow in and out of the thoracic regionthe nasal pathway (i.e., air inhaled via the nose) and the oral pathway (i.e., air inhaled via the mouth). Both pathways can coexist during breathing. The fraction of air inhaled which passes through the nose is denoted by F,. These pathways are distinguished because the nasal pathway generally results in more filtration of particles than the oral. Each deposition region (or filter) possesses two characteristic parametersits volume, V, and its deposition (or filtration) efficiency, h. The deposition efficiency represents the overall efficiency of the region for removing aerosol particles (h = 1  output/input particles). Denoting the tidal volume of the flow by VT and the (dead space) volume of thejth filter by Vj, the volumetric fraction of the tidal air which reaches filter is given by: 1 for j = 0 Sj1 S 1 Vi for 1 : j (N+1)/2 (21) VT, iO 4Nj+ for (N+3)/2 j N where a value of zero for j denotes the inhalability (a virtual filter with Vo = 0; discussed in following paragraph); N is the total number of filters (not counting inhalability) considered for the complete breathing cycle (inhalation and exhalation). Note that N = 9 for nose breathing, and N = 7 for mouth breathing. The middle component of Eq. 21 represents the fraction of air reaching filter during inhalation. The bottom component represents the fraction of air reaching filter during exhalation and assumes that the volume of air traversing a filter during inhalation equals the volume during exhalation. Inhalability (the first "filter" in the chain) refers to the efficiency with which particles of a given diameter are able to be inspired by the nose and mouth. Inhalability effects arise due to the complex flow of particles around the human head and torso and is important only for particles with aerodynamic diameters larger than about 0.5 pm. For increased wind speeds and larger particles, the inhalability can be greater than one; this effect is attributable to nonisokinetic sampling conditions of the human head. Based on the model recommended by the ICRP (1994), the inhalability is plotted in Figure 25 as a function of the particle aerodynamic diameter. In the deposition model, inhalability can be regarded as a virtual filter which acts to remove particles from the air before they actually enter the airways. 2 1.8 h = 0.5 (1 [7.6x104 d ae + l] ) + 1.0xl0"5 U275 exp(0.055d a) 1.6 1.2  0.6 0.4 U= 1 m/s 0.2 0 0 10 20 30 40 50 60 70 80 90 100 dae (microns) Figure 25. Inhalability of particles as a function of the aerodynamic diameter for various wind speeds ofU = 1, 5, and 10 m/s. In this sequential filtration system, the index corresponds to a respiratory tract region as it is encountered by air during the respiratory cycle (both inspiration and expiration). The fraction of material inhaled which deposits in filter, DEj, is given by an expression involving the filtration efficiencies, hi, of the preceding filters and the volumetric correction factor, jI DE = hjjH (1 h) (22) iO0 Deposition in each respiratory region results from both aerodynamic and thermodynamic processes. Aerodynamic processes include inertial impaction and gravitational settling; thermodynamic processes include particle diffusion and Brownian motion. Aerodynamic deposition mechanisms generally dominate for particles with aerodynamic diameter larger than about 0.2 pm while thermodynamic mechanisms dominate for particles less than this size. The model assumes that particles in the aerosol carry no net chargei.e., electrostatic deposition mechanisms are not accommodated. Denoting h, as the aerodynamic deposition efficiency and h, as the thermodynamic deposition efficiency, James et al. (1994b) have represented the combined deposition efficiency of region j by the quadratic expression: hj = (h 2 + hh2)1 (23) James et al. (1994b) provide a detailed discussion of the mathematical expressions used to estimate h. and h. for the various respiratory tract regions/filters. The expressions for extrathoracic regions are based upon regression analyses of experimental data involving both persons (e.g., Stahlhofen et al., 1989; Rudolf et al., 1986) and hollow 41 casts (e.g., Swift et al., 1992). Expressions for thoracic regions are based upon regression analyses of deposition data predicted by an underlying, more sophisticated, theoretical model developed by Egan and Nixon (1985), Nixon and Egan, 1987, and Egan et al. (1989). The equations adopted by the ICRP (1994) for regional deposition efficiencies are listed in Tables 21 and 22. Expressions presented in Table 21 are for air inhaled and exhaled through the nose; those in Table 22 are for air inhaled and exhaled through the mouth. The primary difference between nose and mouth breathing is that the anterior nasal passages (region ET1) are not part of the flow pathway for mouth breathing. The equations apply over a wide particle size rangefrom a 0.001 pm thermodynamic particle diameter to a 100 pm aerodynamic particle diameter. As shown in Tables 21 and 22, the deposition model depends on a number of parameters. Parameters required as direct input to the deposition model are listed along with brief descriptions in Table 23. Reference values for parameters have been presented in ICRP Publication 66 (ICRP, 1994) and are specified for various age and gender groups. Many of the parameters described in Table 23 depend on other, more fundamental, parameters such as body height, weight, and age. Other parameters, investigated during the course of this work to account for correlations between the direct input parameters, are listed in Table 24. Uncertainties and variabilities in these parameters are examined in detail in Chapter 4. The outputs of the deposition model are the fractions of activity that deposit in the various respiratory tract regionsET,, ET2, BB, bb, and AI. The deposition model does 0 a 4) a 0 o 0 I 0. c ) o .9 O j) f a, 0 o L0 I 4) r ri C4 V) r*  N . o^ + 1 0_ t0 ON L0. C' 6O N I n 1T Km K Ka K Ii\o lol  c0 4 I W 4) c o Sm > : p >  Va 10 C.. . IIII 00 t 0 0 4) + 00 e CM '.6 4  C C  1 a A C. C V: .0 I 03 0 . ., +P .d a, .40 'C. 0 .4d Bvv'v .('n 0* (4 c 0 .2 a)  rA i aO c a. 4 2f < < 4 "('4 :> rsC ^^S ^ gf ef .b~~~ "gS0t S __ d" X. z N N 0 V.4 , a~ .: 0 0~ 0P *,  TTT?1tII. 0 o '6 o0 M 0*  u (N e~ l v V .C ~ (. c 0 a I. o SI < t to r o g >~z> U co + o 0  o ^ 0 *a (N a a ( *^, ____ __ __ _^ [ 's ao ^ o *5 S 0 0 c .0 I .0 II 0 IC o5 s on g Table 23. Description of input parameters required by the revised ICRP deposition model. Quantity (units) Symbol Description/Comments Aerodynamic Diameter d, Diameter of a unit density sphere with same settling (pmn) velocity as the particle of interest. Used to quantify aerodynamic deposition mechanisms (important for particles larger than about 0.2 pm). Thermodynamic d, Diameter of spherical particle with same diffusion Diameter (ipm) coefficient as the particle of interest. Diffusion coefficient D Physical constant for particle characterizing its (cm2/s) diffusivity in specified medium (air in this case); depends on particle size, air temperature, and pressure, among other quantities. Used to quantify thermodynamic deposition mechanisms (important for particles smaller than about 0.2 pm). Volumetric Flow Rate VF Total flow rate of air entering the respiratory tract (mL/s) (nasal + oral pathways). Nasal Volumetric VF. Flow rate for air entering by nose; V,=VFF; Flow Rate (mL/s) F,= fraction of air inhaled by nasal pathway. Oral Volumetric Flow VFm Flow rate for air entering by mouth; VFm=VF(1F) Rate (mL/s) Tracheal Scaling SF, Scaling factor to relate regional deposition efficiencies Factor in ET and BB regions of subject of interest to reference man. SF, = 1.65/do (do = diameter of trachea in subject, cm). Bronchiolar Scaling SFb Scaling factor to relate regional deposition efficiencies Factor in bb region of subject of interest to reference man. SFb = 0.165/d, (d8 = diameter of airway generation 8 in subject, cm). Alveolar Scaling SFA Scaling factor to relate regional deposition efficiencies Factor in AI region of subject of interest to reference man. SFA = 0.051/d16 (di6 = diameter of generation 16 in subject, cm). Residence time in tB Time constant for conduction of air through BB BB Region (sec) region. The ICRP has recommended the following expression to compute tB from other quantities: _tB = VD(BB) (1 + 0.5 VT/FRC)/V Table 23 continued. Quantity Symbol Description/Comments Residence time in tb Time constant for conduction of air through bb bb Region (sec) region. ICRP has recommended the following expression to compute tb from other quantities: tb = VD(bb) (1 + 0.5 VT/FRC)/VF. Residence time in tA Time constant for residence of air in the alveolar AI region (sec) region. ICRP has recommended the following expression to compute tA from other quantities: tA = [VT VD]i[1 + 0.5 VT/FRC]/VF where VD= VD(ET) + VD(BB) + VD(bb). Tidal Volume (mL) VT Volume of air inhaled or exhaled per breath; depends on temperature and saturation conditions. Tidal volume is specified at body temperature, ambient pressure, and saturated with water vapor. Volume of ET Region VD(ET) The (dead space) volume of the ET region airways (mL) (anterior nose + oro/nasopharynx+larynx). Volume of BB Region VD(BB) The (dead space) volume of the BB region airways (mL) (trachea + airway generations 18). Volume of bb Region VD(bb) The (dead space) volume of the bb region airways (mL) (generations 9 to 15). Functional Residual FRC Volume of air remaining in the lungs at the end of a Capacity (mL) It normal exhalation. Table 24. Other parameters of use in modeling particle deposition in the respiratory tract. Quantity Symbol Description/Comments Age (y) A Age of subject of interest in years. Body Height (cm) Ht Height of subject of interest. Body Mass (kg) Wt Body mass (or weight) of subject of interest. Body Mass Index (kg/m2) BMI MI = (Wt)/(Ht2) Anatomical Dead Space VD Total volume of the conducting airways including (mL) extrathoracic region: VD = VD(ET) + VD(BB) + VD(bb) Ventilation Rate (L/min) VE Amount of air inhaled or exhaled per unit time. Oxygen Consumption Vo2 The amount of oxygen consumed by the body per unit Rate (mL/min) time. Ventilatory Equivalent VQ Ratio of the ventilation rate to the oxygen consumption Ratio rate, VQ = V/V02. Basal Metabolic Rate BMR Energy consumption rate needed to sustain basic life (MJ/day) activities. Basal Multiplier Bmt Multiplication factor to relate the metabolic rate at a specified exertion level to the basal metabolic rate. Oxygen Consumption Hoy Amount of oxygen needed to produce 1 kJ of energy. Factor (L/kJ) Vital Capacity (mL) VC The amount of air present in lungs at maximal inhalation. not depend on the total activity inhaled, only on the fraction of the total activity that is associated with a given particle size. The fraction of activity associated with given particle sizes are quantified by the activitysize distribution, where size in this case refers to either the aerodynamic diameter or the thermodynamic particle diameter. These distributions are probability density functions which express the fraction of activity associated with particles in an incremental size range. Generally, measurements have shown that particles are lognormally distributed with respect to size. Therefore, the size distributions are usually characterized by a geometric mean aerodynamic (or thermodynamic) diameter and a geometric standard deviation (GSD). The activity median aerodynamic (or thermodynamic) diameter, denoted by AMAD (or AMTD) is the diameter of the particle for which half of the activity is associated with particles less than that diameter. The ICRP (1994) has suggested four physical exertion levels be used to classify the physical activities of persons. The levels are: resting (or sleeping), sitting awake, light exertion, and heavy exertion. Based on these four exertion levels, the ICRP has recommended age and genderspecific reference values characterizing the ventilation rate, tidal volume, respiratory frequency, and fraction of time spent in these levels. The present study considers all of these parameters except the fraction of time spent in various levels; subsequently, computations developed in this work assume a subjects are exposed while at only one of these four levels over the duration of the exposure. More details concerning the types of activities assigned to exertion levels in this study are given in Chapter 4. 2.5. Particle Size and Diffusion Characteristics This section presents some of the relationships needed to compute parameters in the deposition model which are related to particle size. Most of these relationships have been discussed in more detail in Hinds (1982). The two parameters required by the model that depend on particle size (and air temperature and pressure) are the aerodynamic diameter, d,, and the particle diffusion coefficient, D. Other quantities that are used to relate these two parameters are the equivalent volume diameter, d,, and the thermodynamic diameter, dt, which are discussed below. For a dispersiontype aerosol (e.g., windborne surface soil), the aerodynamic diameter (or more generally the distribution of aerodynamic diameters) would likely be determined from measurements, for example, employing cascade impactors. For an aerosol produced by a chemical reaction (e.g., oxidation processes), the thermodynamic diameter (or more generally the distribution of thermodynamic diameters) would likely be determined from measurements, for example, employing graded screen arrays or diffusion batteries. The aerodynamic diameter, d., of a particle (defined as the diameter of a unit density sphere with the same settling velocity as the particle) is related to the equivalent volume diameter, d, (defined as the diameter of a sphere with the same volume as the particle), by the following expression: d. d [ pC(d) /(24) S X PoC(d) I 49 where X is the particle (dynamic) shape factor; p is the mass density of the particle; p, is unit density (1 g/cm3); C(d,) and C(d.) are particle slip correction factors (Hinds, 1982). If d. is given, d, can be computed from Equation 24. The particle mass density is difficult to measure, especially for aggregates (clusters of particles attached as a result of thermal coagulation). Generally, if the source of the aerosol particles is known, the mass density of the particulates is assumed equal to the mass density of the bulk material. James et al. (1994b) have suggested a reference value of 3 g cm3 for environmental aerosols because it is typical of many natural materials. The slip correction factor generally depends on air temperature and pressure. For particles in the respiratory tract (saturated air at 37C ) at atmospheric pressure P (cm Hg), the slip factor has been reported by James et al. (1994b) as: C(d ,P) = 1 +[13.57 +4.31 exp(0.102 Pd.)]/[PdJ (25) The slip factor for d., C(d.), is also computed with Equation 25 by replacing d, with da. The particle (dynamic) shape factor, X, is the ratio of the actual drag force on an irregular particle, FD, to the drag force predicted by Stoke's law, Fs, using the particle's equivalent volume diameter, d,; F FD x = (26) Fs 3 arud 50 where tj is the viscosity of air in the respiratory tract and u is the particle velocity. For a spherical particle X = 1; typical values of X range from 1 to 2 (Hinds, 1982). Shape factors must generally be determined experimentally. The diffusion coefficient, D (cm2/s), for a particle is estimated by the following expression (Hinds, 1982): C(d )kT D =C(d (27) 3x t dh where k is Boltzmann's constant, T is the absolute temperature (K), and d, is the thermodynamic diameter (diameter of sphere with same thermal diffusivity as particle of interest). Consistent units must be used for quantities in Equation. 27. Based on the discussion in James et al. (1994b), the following expression determines the value of the thermodynamic diameter to be used in Equation 27 (d4 and d, in ipm): d. for d.> 0.005 pm d, = (28) d,[l+3 exp(2.20x103d)] for d.0.005im The lower portion of Equation (28) is based on recommendations, by Ramamurthi and Hopke (1989), that a correction be made to Eq. 27 for particles less than about 2 nm. A value of 5 nm was chosen as the application point for their results in this study, since it can be shown that the error in assuming da equals d, is less than 0.01% for d, > 5 nm. Solving Eqs. 24 and 25 for d, involves an iterative approach since the solution cannot be obtained analytically. James et al. (1994b) have recommended an approximate, initial solution by setting d, = d,(x/p)'"; convergence to the correct value by iteration is reportedly rapid (usually requiring less than 10 iterations). 2.6. Respiratory Tract Clearance Model The clearance model adopted by the ICRP (1994) is based on an approach introduced by Cuddihy and colleagues (Cuddihy, 1976, 1984; Cuddihy et al., 1979; Cuddihy and Yeh, 1988). In this approach clearance from various regions is based on competitive clearance processes. In all regions but the anterior nasal passages, ET,, clearance is achieved (1) by mechanical translocation processes (such as macrophage uptake and transport in fluids over surfaces by mucociliary action to the gastrointestinal tract), (2) by transport to lymph nodes, and (3) by dissolution and absorption to lung tissues and/or to blood. Radioactive decay can also be considered a form of removal. These processes compete to remove material from various regions. In the anterior extrathoracic region (ETI) material is removed by external pathways (such as nose blowing, sneezing, or coughing) and by radioactive decay. Three major working assumptions have been made in the clearance model (discussed by Bailey and Roy, 1994). These assumptions are as follows: (1) clearance rates due to mechanical transport processes (mucociliary and macrophage transport) and dissolution/absorption processes (to blood) are independent; therefore, the overall fractional clearance rate from a model compartment is represented by the sum of the rates due to individual processes; (2) mechanical transport rates are the same for all materials; i.e., the chemical form of the material does not influence the fractional clearance rate due to particle transport processes; and (3) the dissolution/absorption rate of a material to blood is the same for all regions of the respiratory tract except the anterior nasal passages ET,, where no absorption is assumed to occur. The compartment model which has been adopted by the ICRP (1994) to represent mechanical clearance processes (including particle transport by the mucociliary mechanism and by alveolar macrophages) to the gastrointestinal tract and lymph nodes is shown in Figure 26. This figure does not include absorption pathways. Arrows represent routes (and directions) for particle transport in the clearance model. According to the second assumption above, these routes and their associated fractional clearance rates are generally independent of the chemical form of the material. Anterior Extrathoraci Region NasalT Boar B 2 13 12 11 GITract Thoradic Region Bronchi se2 BB ! 9 87 Bronchioles LNh bb bb bb 6 AS 4 Alveolar Interstitim _Al AI A 10 3 3 2 I I [L Squeatered in tissue Available for surface transport Figure 26. Representation of particle transport model recommended by the ICRP (1994) for mucociliary and macrophage transport mechanisms to the gastrointestinal tract and lymph nodes (no absorption pathways shown). Material that deposits in the respiratory tract is assigned to those compartments which that are shaded in Figure 26. The deposition model predicts the overall amount of material that deposits in a given broad region (i.e., ETi, ET,, BB, bb, and AI; represented by the grouped boxes in Fig. 26). This regional deposition is then partitioned among the shaded compartments within the region to account for observed clearance patterns. An exception to the second assumption exists for the BB and bb regions. For these regions the partition of the deposition to regional compartments is based on particle size. This aspect of the model is discussed in more detail in Chapter 4. Clearance of materials from respiratory tract regions does not always occur at a constant rate with respect to time. To accommodate timevarying clearance rates in a practical manner, the model designers have represented the broad respiratory regions (ET, BB, bb, and AI) by a number of compartments (representing materials in different clearance states) clearing at different rates. Uncertainties in the fraction of the initial deposition assigned to these states (or compartments) and in clearance rates for these compartments are discussed in section 4.2 and are included in parameter uncertainty analyses. These compartments are discussed below. The ET, region is modeled by a single compartment in which all material is deposited and cleared at a constant rate. The ET2 region is modeled by two compartments, ET2 and ET,. Based on animal data, the ICRP (1994) has suggested that 0.05% of the regional deposition be associated with ET. and the rest (99.95%) with the ET2 compartment. The ET, compartment represents material that is sequestered by the airway walls in the ET2 region and can only be cleared to lymph nodes or to blood (as do all following compartments subscripted by seq). Mechanical clearance from the BB region is represented by three compartments, BB,, BB2, and BBq. Based on animal data, the ICRP (1994) recommends that 0.7% of the material deposited in BB be assigned to the BB, compartment. The rest is partitioned between BBI (a fastclearing compartment) and BB2 (a slowclearing compartment) based on particle size. The bb region is represented in an analogous manner by compartments labeled bbl, bb2, bbq. These bb compartments are assumed to receive the same partition of deposition as their BB region counterparts. Mechanical clearance from the AI region is modeled by three compartments, AI,, AI2, and Al3, representing compartments that clear fast, slow, and very slow, respectively. The ICRP (1994) recommends partitioning the overall deposition in AI by fractions of 0.3, 0.6, and 0.1 for compartments AI,, AI2, and Al3, respectively. These values, along with reference values for all other compartments, are subject to uncertainties and variabilities which are addressed in Chapter 4. In the conceptual model structure, the mechanical clearance rates for compartments in Figure 26 are taken to be independent of particle size and physico chemical form of the deposited material. For reference, the compartments in Fig. 26 have been numbered. Denoting the mechanical clearance rate from compartment i to compartment in Fig. 26 as m,j, the ICRP (1994) reference values for mechanical clearance rates are listed in Table 25. One interpretation of these rates is that they represent the fraction of material in compartment i that passes from compartment i toj per unit time by the specified pathway. Denoting the fraction of the regional deposition assigned to a compartment as fd, Table 26 lists reference values for the partition of deposition among compartments. Unlike particle transport mechanisms represented by the compartment scheme in Fig. 26, absorptive processes do depend on the physicochemical properties of the radionuclide. Such properties include solubility of material within, and transportability through, lung tissues. The model adopted by the task group to describe these processes is shown in Figure 27. According to the third assumption listed in the beginning of this section, absorption rates are taken to be the same from all regions (except ETi where no absorption is assumed) and depend on the chemical form of the radionuclide. Similar to the processes represented in Figure 26, experimental evidence suggests that for some materials the fractional absorption rate of materials to blood is timevarying. Rather than using timevarying clearance rates (which would lead to a system of differential equations with timevarying coefficients), the ICRP (1994) has modeled absorption to blood by multiple compartments with constant fractional absorption rates. In the model, particles are deposited into "initial state" compartments. These initialstate compartments correspond to the shaded compartments in Fig. 26. After deposition, competing mechanisms act either to remove material from a location or to change the state of the material. Material deposited in the initial state can be 56 Table 25. Reference values for (fractional) mechanical clearance rates in the particle transport aspect of the ICRP human respiratory tract model. Pathway From To Rate (d') Half Time" m,4 AI, bb, 0.02 35 d m2, AI2 bb, 0.001 700 d m3,4 Al3 bb, 0.0001 7000 d ...n ............ I ............. ..........0.00002......... mn4, bb, BBI 2 8h ms,7 bb2 BBI 0.03 23 d ... 0.......01 ...................0.01 ... ,o....................b.b ..,....... L.N ....................... ...................................................................................... mi7, BBi ET, 10 100 min ms,11 BB2 ET2 0.03 23 d .. L N0 .0 1 7 0.................... .......... ....................... 1 .................... 7.. ........................................... ma1i, ET2 GI tract 100 10 min m1,13 ET, LN, 0.001 700 d m,I ,1 ET, Environment 1 17 h Source: ICRP (1994, Table 17A). 'Half times are approximate since they are based on rounded values for the rates (halftime = ln(2)/rate). No halftime is reported for m3,0; the rate for this route was chosen simply to direct the desired amount of material to the lymph nodes. Units: d = day; h = hour; min = minutes. Table 26. Reference values for partition of deposition among compartments in region. Respiratory Tract Clearance Fraction, fd, of Regional Deposition Region Compartment Assigned to Compartment" ET2 ET2 fd(ET2) = 0.9995 ET f(Tq=............ f~ ). = 0.0005 ........................................................ .. T ..................................... fdf .T.. ....... = O...0005................................. BB BBI fd(BB,) =0.993 f, BB2 fd(BB2) =f, ....................................................... .. ........ .........................f () ......... = ..0 7 ................................... bb bb, fd(bbl) = 0.993 f bb2 fd(bb2) = ................. .. ......... (b .......... ................................... AI All fd(AIi) = 0.3 AI2 fd(A12) = 0.6 AI, f&(AI,) = 0.1 Source: ICRP (1994, Table 17B). ' The term f, represents the slowclearing fraction of particles deposited in the tracheobronchial airways; it depends on particle size (discussed in section 4.2.2.1). PARTICLES IN INITIAL STATE MATERIAL IN TRANSFORMED STATE (Depoited Particle) . (ComparmnUts: 1, 2, 3,..., 14) pt (Compartmnat: IT, 2T, 3T, .13T) fbp xbst (lfbi (fb P MATERIAL IN BOUND STATE (f t (Compartment: AI(b), bb(b), BB(b) ET(b), LNet(b), LNth(b)) V tb BLOOD Figure 27. Compartment model recommended by ICRP (1994) to represent dissolution and absorption to blood and lung tissues for materials deposited in the respiratory tract. (1) transported mechanically between initial state compartments by the pathways indicated in Figure 26, (2) transformed to a different clearance state (i.e., "transformed state") represented by a different compartment although in the same spatial location, or (3) absorbed from the initial state to either a "bound state" or to the blood. The bound state represents material that chemically binds to the tissues in the airway wall after dissolving in lung fluids. The total fractional clearance rate for materials from initial state compartments to the blood and to the bound state is denoted by sp. The fraction of material that clears from the initial state to the bound state is given by fb so that the net fractional clearance rates to the bound state and the blood are fbSp and (1fb)sp, respectively. The transformed state represents material that is absorbed to the blood and bound state at a different rate, s, than initial state material. The fractional clearance rate from initial state to transformed state is represented by s,. According to the clearance model adopted by the ICRP (1994), material in the transformed state can either be (1) transported mechanically among transformed state compartments by assuming the same pathways apply as in Figure 26 or (2) absorbed to the blood and bound state. The total fractional clearance rate for materials from the transformed state to the blood and the bound state is denoted by s,. The fraction of material that clears from the transformed state to the bound state is given by fb (assumed to equal the fraction to bound state from initial state) so that the net fractional clearance rates to the bound state and the blood are fbs, and (lfb)s, respectively. The ICRP (1994) has also examined an alternate form for the absorption model which has parameters that are generally easier to determine from experimental data than the model shown in Figure 27. This alternate model is depicted in Figure 28. In this alternate form, material is assumed to be deposited in either a rapid dissolution state (or rapid absorption phase) or a slow dissolution state (or slow absorption phase). The fraction of material in the rapid phase is denoted by f (so that the fraction in the slow phase is 1). Fractional clearance rates from the rapid and slow states to the blood and bound states are given by s, and s,, respectively. As before, fb represents the fraction of cleared material that goes to the bound state. Concerning the amount of material that is absorbed to blood over a specified time period, this alternate form provides the same (1fY Sr Bound Material Blood Figure 28. Alternate form for the dissolution/absorption model. This model form is related to the form in Figure 27 through Equation 29. numerical results as the form in Figure 27. The following expressions can be derived which relate the two models: sp = s. + f,, s.) s, = (1 f)( Sr s,) (29) s, = s, When reliable human data exist, the absorption aspect of the model can use observed rates of absorption to blood; when data is not available, the absorption rate is classified as slow, moderate andfast (denoted S, M, and F) and is based on reference values recommended by the ICRP. In the present study, literature related to absorption of plutonium oxides was investigated (section 4.2.4) to develop distributions for the absorption rate constants for that specific material. Upon coupling the absorption model of Figure 27 with the particle transport model of Figure 26, the overall compartmental clearance model is obtained; it is represented schematically in Figure 29. The overall clearance model is presented in its complete mathematical form (i.e., as a system of firstorder differential equations) in Appendix B, where the mathematical form of the older ICRP Publication 30 lung model (ICRP, 1979) is also presented for comparison. The revised lung model possesses 33 compartments compared to only 10 for the older model. Since the mathematical form of the clearance model involves linear, firstorder differential equations with constant coefficients, the model can be solved analytically for simple exposures of interest. Due to mathematical complexity in accounting for changes in activity intake rates over time (e.g., due to changes in ventilation rate with level of physical exertion), this study has focused on an acute intake scenario. For an acute activity intake, material is deposited instantaneously at time to in the respective initial state compartments (shaded regions in Fig. 26). This assumption simplifies the solution to the differential equations presented in Appendix B for the clearance model. This simplifying assumption is appropriate when ventilation rates remain relatively constant over the exposure duration (which is less at most a few hours) and when the exposure duration is much less than the dose integration time. A relatively simple solution to the differential equations also exists for relatively constant, nonacute intakes however, such scenarios are reserved for future study. N fin vim o\ e 15 0 I I c4 0 E t 0 0 o 4 8 4 o I SCO o C Sc& .0 ~I. Several methods are available for solving clearance models represented by systems of linear firstorder differential equations in this exposure situation. In this study, a computational algorithm described by Birchall (1986) has been employed. This algorithm is based on analytical equations (socalled Bateman equations) presented by Skrable et al. (1974), which originate from equations first suggested by Bateman (1910). The algorithm is restricted to firstorder, nonrecycling compartment models, such as the clearance model described here. Nonrecycling models are those which do not allow material to reenter clearance compartments (i.e., routes do not allow material to return to previous compartments of residence). The algorithm can solve the clearance model for both acute and constant, chronic activity intake scenarios. Given the initial number of atoms deposited into initial state compartments, the algorithm can solve the clearance model for two quantities: (1) the number of atoms remaining in compartments at time 1, and (2) the total number of radioactive transformations occurring in compartments over an integration time r. For a compartment of interest, the algorithm operates by first finding all pathways that lead to that compartment. For each pathway leading to the compartment the algorithm uses the Bateman equations to compute the contribution made to (1) the activity in compartment at time, I and (2) to the total transformations in compartment over time r. Contributions from all pathways are then summed. Provisions are included to avoid duplicating contributions from overlapping pathways. A complete description of the algorithm and a listing of the source code for computer implementation can be found in the original paper by Birchall (1986). 2.7. Respiratory Tract Dose Model Dose calculations in the revised ICRP respiratory tract model are based on the methodology presented in ICRP Publication 30 (ICRP, 1979) for radiation workers and later expanded for exposures to the general population in ICRP Publication 56 (ICRP, 1989). In that methodology, the committed equivalent dose to a tissue T, denoted HT(r) with special SI unit of Sv, is the timeintegrated equivalent dose rate for that tissue, where r is the integration time. For radiation protection purposes the ICRP (1989 and 1991a) has recommended an integration time of r = 50 years for adults and r = 70 years for children. However, other integration times can be specified if desired. The equivalent dose rate at time t for target tissue Tis given by: HT(t) = c q,(t) SEE (TS;t)j (210) j where c is a constant accounting for conversion of units, qj(t) is the activity of radionuclidej in source region S for a subject at time t; SEE(T S; t) represents the specific effective energy for tissue T irradiated by radionuclidej in source S and is defined below. Due to sourcetarget geometry effects, the SEE generally depends on the age of the subject at time t. The summation over s is over all source regions, S, that irradiate the target. The summation over is over all radionuclides in source region S. The double summation over s andj then accounts for all radionuclides in all source regions that affect the target tissue. The specific effective energy, SEE(T+ S)j for radionuclidej is expressed by: w,E,Y,YAF(TS;t), SEE (TS;t) = E wEYAF(TS;t) (211) R MT(t) where w. is the radiation weighting factor for radiation type R emitted from radionuclide j; ER is the energy of radiation R; YR is the yield of radiation type R per transformation of radionuclidej; AF(TS; t)R is the fraction of energy of radiation R emitted by source S that is absorbed in target T and depends, among other things, on the age of subject at time t; and MT(t) is the mass of target tissue T for the subject at time t. Assuming an acute intake at time to, the committed equivalent dose at time t due to the intake is computed as: HT(t) = fH(tdt' = c f q(t )SEE (TS;t j (212) to to If the SEE is assumed to be independent of time t (e.g., for adults where growth is negligible), the term enclosed in brackets becomes: j j SEE (TS;t Idt = U(r) SEE (TS) (213) to where U j() = f q(t)dt' (214) to and where U,(zr) equals the total number of transformations of radionuclidej that occur in source region S over an integration time of r = t to When a respiratory tract region is the source, Uf(t) depends on both the deposition and clearance models described above and is determined by integrating, with respect to time, the solutions to the differential equations that are presented in Appendix B. The present study focuses on doses to various lung tissues as the targets. The scope of the present study has been limited to include only source regions within the respiratory tract. The scope is further limited to include only those doses which are contributed by alpha particles. For an inhalation of primarily alphaemitting radionuclides with negligible photon, electron, and beta emissionssuch as Pu238, Pu 239, Pu240the dose to lung tissues is due almost exclusively to alpha particles which originate within the lung tissues. To justify this statement, the computer program LUDEP (Jarvis et al., 1993) has been run for a class S (insoluble) "Puladen aerosol having an AMAD of 5 pmr and a GSD of 2.5; the scenario involved a reference adult male at light exertion. The lung model described here and the ICRP (1979) metabolic models for other organ systems were used with reference values for all parameters. Results indicated negligible contributions to the lung dose from source organs other than the lungs (<<0.1%) and from radiations other than alpha particles that originated within the lungs (<<0.1%). Methods developed in this study are applied to Pu239 and Pu240 oxides in Chapter Five; for these radionuclides doses contributed by radiations other than alpha particles are negligible. For shortrange alpha, beta, and electron emitters, source regions in the lungs are identified in Table 27. In total the ICRP (1994) has identified 17 source components to be considered for shortrange radiation emitters. These regions have been modeled to correspond with anatomical regions in the airway wall as shown earlier in Fig. 23. The 66 thicknesses and depths of various source and target layers are important determinants of the fraction of energy that can reach the target layers. These dimensions are examined in more detail in Chapter 4. Table 27. Assignment of compartments to source regions for shortrange radiations in the revised ICRP respiratory tract model. Target" Source Region Clearance Compartments Comprising Sources in the Respiratory Tractb ETSurface d it .................... .. 14 ET2 Surface fluid 11 + 1T Particles sequestered in airway wall 12 + 12T Bound material ET(b) LN All transformations in LN ........................... 13. +1..3T..+..LN.(bnd)...................................... BB Mucous gel layer 7 + 7T Mucous sol layer 8 + 8T Particles sequestered in airway wall 9 + 9T Bound material BB(b) Alveolarinterstitium 1 + 2 + 3 + IT + 2T + 3T + AI(bnd) bb Mucous gel 4 + 4T Mucous sol 5 + 5T Particles sequestered in airway wall 6 + 6T Bound material bb(bnd) Alveolarinterstitium 1 + 2 + 3 + IT + 2T + 3T + AI(bnd) AI All transformations in AI and LNth 1 + 2 + 3 + IT + 2T + 3T + AI(bnd) + ........................................................................................................l..... 1..... ....n.. ... .................................. LNth All transformations in LNth 10 + 10T + LN,(bnd) Source: ICRP (1994) Target cell nuclei layers in respective respiratory tract regions are discussed in text. b See Figs. 26 and 27 and Appendix B for additional clarification of model compartments. Target tissues in the revised model include the following tissue and cell layers. For the extrathoracic tissues the target regions are: (1) the basal cell nuclei layer in the epithelium of region ET,; (2) the basal cell nuclei layers in the epithelium of the naso oropharynx and larynx in region ET2; and (3) the total mass of the extrathoracic lymph nodes, LNT. For the thoracic tissues (or lungs) the target tissues are: (1) the secretary cell nuclei layer in the epithelium of the BB region; (2) the basal cell nuclei layer in the epithelium of the BB region; (3) the secretary cell nuclei layer in the epithelium of the bb region; (4) the total mass of the alveolarinterstitial tissues, AI; and (5) the total mass of the thoracic lymph nodes, LNa. This aspect of the revised model (computing doses to target regions within the lungs) differs from the ICRP Publication 30 model (ICRP, 1979) in which a single dose was computed to the lung by averaging over the total lung mass. Based on a review of human epidemiological studies, Masse and Cross (1989) have suggested that target tissues in the respiratory tract be assigned varying degrees of radiation sensitivity in the new model. To account for varying sensitivities, the revised respiratory tract model (ICRP, 1994) has incorporated regional weighting factors to partition the risk from irradiation of lung tissues. The approach adopted in the model specifies that combined equivalent doses to extrathoracic and thoracic (lung) tissues be computed by the following expressions: HT(ET) = HT,ET(I) AET(I) + HT,ET(2) AET(2) + HT,LN(ET) ALN(ET) (215) HT(TH) = HBB ABB + HT,b Ab + HT, AA + HT,LN ALN (216) where HT(ET) and HT(TH) are the detrimentadjusted equivalent doses to the extrathoracic and thoracic (lung) tissues, respectively; HT,ET(1),..., etc., are the equivalent doses to targets in the extrathoracic regions; HT BB,..., etc., are equivalent doses to targets in the thoracic regions; AET(I),..., etc., are detriment apportionmentfactors for the partition of risk in ET tissues; and ABB,..., etc., are detriment apportionment factors for the partition of risk in the thoracic (lung) tissues. The detriment apportionment factors are used to weight the doses to the individual regions and reflect the relative sensitivity of the target regions to radiation induced effects. The values recommended by the ICRP in Publication 66 are listed below in Table 28; it is important to note that these values are quite uncertain. Concerning the values reported in the table, the following statement was made: It was concluded that there was no basis for deriving factors to represent regional differences in radiation sensitivity with any acceptable degree of confidence. Therefore, the weighting factors given in Table 31 [Table 28] are recommended. These factors may be revised by the Commissions as better information becomes available. Revisions can be made without changing the respiratory tract dosimetry model itself. (ICRP, 1994, p. 114) Based on this statement, the focus of this study has been more toward regional doses than an overall, combined lung dose. Uncertainties in the apportionment factors do not influence regional doses (only their interpretation on a radiological risk basis). Nonetheless, the methodology developed in this study (1) predicts uncertainties in the combined lung dose and (2) provides a means to change the detrimentapportionment (actually their assigned uncertainties) for the thoracic region with little effort. It is noted that although methods are provided for predicting doses to the extrathoracic tissues, these tissues are not included in the list of organs that receive tissue weighting factors in the ICRP (1991a) system of radiological protection. Consequently, these tissues do not receive as much emphasis in this study. Table 28. Riskapportionment factors recommended by the ICRP for weighting the dose to various respiratory tract target tissues. Extrathoracic Detriment Thoracic Detriment Regions Apportionment Regions Apportionment Factors (A)" Factors (A) ET, 0.001 BB 0.333 ET2 1 bb 0.333 LNET 0.001 AI 0.333 LN, 0.001 Total = 1.002 Total = 1.000 Source: ICRP (1994). * Values are as listed in the reference; do not sum to one. Masses for target layers associated with ET, BB, and bb regions can be estimated from the products of the regional surface area and the target layer thickness. The regional surface areas are both age and sexdependent and must generally be estimated from airway dimensions, which depend on body size. Absorbed fractions for shortrange radiations in ET, BB, and bb tissues depend primarily on the source and target layer thicknesses and depths. Measurements (e.g., Gehr, 1987) suggest that dimensions for source and target layers in the airways are independent of age or body size. Furthermore, computations have shown that the airway diameter is of secondary importance to absorbed fractions. Based on these findings, the ICRP (1994) has suggested that absorbed fractions for shortrange radiations in the lung are independent of age. The computational methods used to compute energy absorption in BB and bb target tissues in this study are discussed in detail in Appendix C. The approach for ET regions has been to use the simplified expressions for the absorbed fractions, AF, as 70 presented by James et al. (1994a). For ET regions, the uncertainties in source and target dimensions are not included in the present study since these regions are relatively resistant to radiation effects and for reasons discussed above. For AI and lymph node tissues, the absorbed fractions suggested by the ICRP(1994) for shortrange radiations are used to compute doses. These absorbed fractions (AF) in these regions for alpha particles may be summarized as: AF(AI BB) = AF(AI bb) = AF(AI ET)= 0 (217) AF(AI AI) = AF (LNr. LNm) = AF(LNET LNET) = 1. (218) Equation 217 simply states that alpha particles emitted from sources in the BB, bb, or ET regions deposit a negligible amount of energy in the AI region. Equation 217 has been suggested by the ICRP since the additional energy deposited in the AI region from sources in other respiratory tract regions is negligible compared to the energy deposited in the AI region due to sources in the AI region (due primarily to the thickness of tissues separating these regions and to large surface area and mass of the AI region). Equation 218 states that alpha particles emitted by the AI and lymph node tissues (as source regions) are completely absorbed by the those regions (as target tissues). 2.8. Summary The purpose of this chapter has been to provide an overview of the new ICRP respiratory tract model (ICRP, 1994). In this chapter, the deposition, clearance, and dosimetry components of the respiratory tract model have been presented, and model parameters have been introduced. The following chapter presents the methods 71 employed to treat model parameters and associated quantities as random variables within the (computational) model framework. Chapter 4 examines the respiratory tract model parameters in greater detail by providing results of a formidable literature review undertaken to assign probability distributions to parameters and to account for relationships (or correlations) among parameters. CHAPTER 3 METHODS FOR CONDUCTING PARAMETER UNCERTAINTY ANALYSES 3.1. Introduction A computational methodology has been developed to quantify uncertainties in lung dose quantities for population groups exposed to radioactive aerosols. This methodology is based on conducting parameter uncertainty analyses using the revised ICRP respiratory tract model described in Chapter 2 within the scope of the assessment problem defined in Chapter 1. The purpose of a parameter uncertainty analysis is to quantify variabilities in model predictions attributable to uncertainties (including stochastic variability and lack of knowledge) in model parameters. Additionally, parameter sensitivity analyses of the model are desired in order to determine the relative importance of parameters in affecting model predictions (i.e., which parameters contribute most to variability of the predictions). Specific methods involved in performing such analyses for complex mathematical models have been the subject of many studies and reports (IAEA, 1989; Morgan and Henrion, 1990; OECD, 1987; Hoffman and Gardner, 1983; Iman and Helton, 1985; Iman and Conover, 1982; Hamby, 1995; Iman and Helton, 1988; Nowak and Hofer, 1987; Paschoa and Wrenn, 1987). The purpose of this chapter is to provide a description of methods used in the current study to perform such analyses with the selected respiratory tract model. 73 The International Atomic Energy Agency (IAEA, 1989) has listed the main steps involved in conducting a parameter uncertainty/sensitivity analysis. These steps are repeated in Table 31 and have been followed in the current study. To examine the concepts and techniques associated with these steps, this chapter is divided into five additional sections. In section 3.2 parameter uncertainties and correlations are addressed. Section 3.3 involves a discussion of the numerical methods used to sample the joint probability density function (i.e., the probability density for combined parameter values) and to propagate this joint density function through the model. In section 3.4, some measures of model prediction uncertainty and formats for presenting results are discussed. Section 3.5 provides a discussion of techniques employed to determine parameter sensitivities in the model (i.e., methods to determine dominant parameters and their contributions to model prediction uncertainty). Section 3.6 provides a description of the computer code developed to implement the respiratory tract model and to integrate it with the methods described in this chapter. Due to the mathematical nature of the respiratory tract model and the large number of model parameters involved, a numerical approach has been adopted for propagating parameter uncertainties through the model. A Latin hypercube sampling technique (McKay et al., 1979; described in section 3.3) has been used in this study to generate a numerical representation of the joint probability density function for the combined range of parameter values. This technique involves numerical generation ofn values from each of the m hypothesized parameter distributions. A special pairing process is then implemented to combine values randomly for the m model parameters into n input vectors which can be used to solve the model for n output values for each desired model prediction. Various aspects of the technique are discussed in more detail in the following sections of this chapter. Table 31. Main steps involved in conducting a parameter uncertainty analysis. (1) List all of the parameters that are potentially important contributors to uncertainty in the final model prediction. (2) For each parameter listed, specify the maximum reasonable range of applicable alternative values. (3) Specify the degree of belief (in percentage) that the appropriate parameter value is not larger than specific values selected from the range established in Step 2 above and select a probability distribution that best fits the quoted degrees of belief. (4) Account for dependencies among model parameters by introducing suitable restrictions, by incorporating appropriate conditional degrees of belief, or by specifying suitable measures of degree of association. (5) Set up a subjective probability density function (pdf) for the combined range of parameter values. This will subsequently be referred to as a joint pdf. Propagate this joint pdf through the model to generate a subjective probability distribution of predicted values. (6) Derive quantitative statements about the effects of parameter uncertainties on the model prediction. (7) Rank the parameters with respect to their contribution to the uncertainty in the model prediction [sensitivity of parameters]. (8) Present and interpret the results of the analysis. Source: IAEA (1989, pp. 3132) with minor alterations. 3.2. Quantifying Parameter Correlations and Uncertainties The first four steps listed in Table 31 involve identifying model input parameters and quantifying their correlations and uncertainties. Primary input parameters for the respiratory tract model have been identified in Chapter 2. In this section, the techniques used to account for parameter correlations and uncertainties are discussed. Chapter 4 contains a detailed discussion of individual respiratory tract model parameters, focusing on the distributions and relationships adopted in this study to accommodate parameter uncertainties and correlations. 3.2.1. Parameter Correlations Two approaches for accommodating parameter correlations/dependencies have been considered. One approach involves specifying and using a rank correlation matrix and is implemented during the pairing process for the m parameter values. The other approach involves using regression equations along with random error terms. The latter approach generally accounts for correlations directly by incorporating detailed relationships between parameters into the uncertainty analysis; consequently, this approach is used here and is more heavily weighted in the following discussion. However, the methodology accommodates the rank correlation matrix approach (as discussed below and in section 3.6). The correlation matrix approach uses a restricted pairing technique (Iman and Conover, 1982) to induce correlation between the ranks of two numerically sampled input variables. Iman and Shortencarier (1984) have developed a computer code which implements this approach within the Latin hypercube sampling scheme (discussed in section 3.3). Use of the code requires the user to specify rank correlation coefficients for pairs of parameters. If an appropriately sampled data set exists for two parameters, for example parameters X and Y, then the rank correlation coefficient (also known as Spearman's correlation coefficient) can be estimated by the sample correlation coefficient of the ranktransformed data. The rank correlation coefficient expresses the degree of linear relationship between the ranks of X and Y (i.e., it is a measure of the monotonic relationship between parameters). For example, if an increase in X always results in an increase in Y, the rank correlation coefficient would be (positive) one. If an increase in X always resulted in a decrease in Y, the rank correlation coefficient would be negative one. This approach is discussed in more detail by Iman and Conover (1982) and by Liebetrau and Doctor (1987). A second approach for accommodating relationships between parameters (and the one used in this study) is to use reported regression equations which predict the value of one variable (or input parameter) as a function of another variable (or input parameter). Consider a hypothetical example involving two variables, X and Y. Assume a literature survey has revealed that Y can be predicted (to some degree) by a regression equation relating Y to X; for example, Y = aX (i.e., a power function with fitting parameters a and b determined, for example, by the least squares method). This expression is equivalent to InY = In(a) + b*ln(X), and the associated coefficient of determination, R2, provides a measure of the variance in Y that is unexplained by the variance in X. For example, a value ofR2 = 0.90 means that 90% of the variance in Y is explained by the regression. A 77 residual, or random, error term can be introduced to explain the remaining uncertainty in Y. For this example, the expression above could be multiplied by an error term, Eyx so that Y = (aXb)*Ex; equivalently, InY = In(a) + b*ln(X) + In(Ey,). A distribution for Y, that accounts for its correlation with X, is then obtained by sampling values from a distribution for X and from a distribution for Ex. The parameter Y does not, in this case, need to be assigned a distribution of its own since it is determined by sampled values for X and Ex. The choice of the distribution shape for the residual error term depends on the type of regression equation used. For linear, quadratic, and higherorder polynomial regression models the error term is customarily added to the regression expression and assigned a normal distribution with mean value of zero and standard deviation estimated by the standard deviation of the residual errors. The residual errors are given by the differences between the observed values of Y and the values predicted by the regression equation without the random error term. For exponential and powerfunction regression models, the error term is customarily multiplied into the regression expression and assigned a lognormal distribution with geometric mean of one and geometric standard deviation estimated by the sample standard deviation of the log residuals, where log residuals refer to the differences between In(observed Y) and In(predicted Y). The term In refers to the natural logarithm. Given the data set for the residuals or log residuals, the assigned distribution for the residuals can be subjected to various statistical tests (section 3.2.3) to determine whether the assigned (or hypothesized) distribution is accepted or rejected based on the data. Throughout this study, parameter correlations have been handled directly (when possible) by using reported regression equations and accompanying residual error terms. This approach allows all random variables to be sampled independently in the Latin hypercube sampling scheme, improving computational efficiency. More details are given for specific model parameters in Chapter 4, where literature is reviewed, parameter uncertainties and regression relationships are discussed, and distributions are assigned. Although a mechanism exists in the methodology for its inclusion (see section 3.6), the rank correlation pairing approach for inducing parameter correlations has not been employed in this study. 3.2.2. Parameter Uncertainties Uncertainties in respiratory tract model parameters are accommodated by introducing continuous random variables. Such variables can attain any real value within their allowed range. Associated with each random variable is a probability density function, orpdf. The pdfcharacterizes uncertainties (and variabilities) of the random variable by describing the probability associated with a specified range of values for the random variable. For a continuous random variable, a continuous probability density function is used. All of the parameters investigated in this study possess uncertainties due both to lack of knowledge and to stochastic variability. Since lack of knowledge exists, thepdfs generally incorporate some subjective information. One interpretation of the distributions assigned in Chapter 4 is that all represent subjective prior distributions in which distribution parameters (e.g., mean and standard deviation) are Bayesian estimators (Morgan and Henrion, 1990, p. 83). Future information and data for model parameters can be used to update these prior distributions by employing Bayesian statistics (DeGroot, 1970) to compute the posterior distributions. Notwithstanding these issues, one must work in the present with limited data sets and attempt to assign, on a case by case basis, distributions to model parameters that realistically reflect the current state of knowledge (as perceived by the assessor). If measured data exist for model parameters, graphical and statistical tests can be used to determine whether to reject an assigned (hypothesized) pdf, however, no tests exist which can unequivocally prove that an assigned distribution is the correct one. Many distribution shapes can be used to represent parameter uncertainties. Among thepdfs considered in this study are the uniform (or rectangular), triangular, normal, and lognormal probability density functions. The choice of distribution depends on the information available for the specific parameter being considered. A description of each of these distribution shapes follows. The uniform pdf represents the simplest distribution shape for continuous random variables. For this pdf the random variable has an equal probability of assuming any value between a specified minimum and maximum value. If the minimum value is represented by a and the maximum by b, thepdffor the uniform distribution is given as: 1 f(x) = asx b (31) (b a) where x refers to a specific value of the random variable, denoted as X. The integral of the pdf over a specified range of values Ax is the probability of X taking on a value in that range. A typical uniform distribution is shown in Figure 31. This distribution shape is useful when the only information known about the parameter is the range of possible values and when no other sufficiently detailed information exists to justify one of the other Spriori pdfs. 0.15 0 a= ,b= 10 5 0 5 10 1 x Figure 31. Example of a uniform probability density function with a = 0 and b = 10. The triangular probability density function has three parameters, the minimum value a, the mode (or most probable value) b, and the maximum value c. Three cases can be identified for triangular distributions. For case one, a < b < c; for case two, a = b < c; and for case three, a < b = c. Typical distribution shapes associated with these cases are shown in Figure 32. Functions representing the pdf are given by the following equations for these three cases: Case one (a < b < c): 2(x a) (c a)(b a) f(x) = * 2(c x) (c a)(c b) b sxe (32) Case two (a = b < c): Case three (a < b = c): f(x) = 2(c x) axc (c a)2 f(x) = 2(x a) axc (c a)2 (33) (34) This distribution shape is useful for model parameters with values that tend toward a single most likely value (i.e., stochastic variability is not expected to be large), but the paucity of data precludes that value from being specified exactly. a) Case 1: a a=0, b = 3, c= 10 0 5 10 1 b) Case 2: a = b < c a = b =0, c = 10 0 5 10 15 x c) Case 3: a < b = c a=0, b = c = 10 0 5 10 15 x Figure 32. Examples of triangular probability densities for the three possible cases discussed in text: (a) Case one: a The normal (or Gaussian) probability density function is specified by two parameters, p and a, where p represents the mean value and a represents the standard deviation. The pdf for the normal distribution is: 1 ^ ( _ f(x) = 1 (xI ) ,(2; o 2o ) (35) 