Particle Toxicology - Chapter 20 docx

20 Biologically Based Lung Dosimetry and Exposure–Dose– Response Models for Poorly Soluble Inhaled Particles* Lang Tran Institute of Occupational Medicine Eileen Kuempel Risk Evaluation Branch, CDC NationalInstitutefor Occupational Safety and Health CONTENTS 20.1Introduction 352 20.1.1 Comparison of Human and Rodent Lung Structure and Physiology 352 20.1.2 Lung Dosimetry Models 353 20.2MathematicalModel of the Retention and ClearanceofParticles from the Rat Lungs 354 20.2.1 Structure of the RatBiomathematicalLung Model 355 20.2.1.1 Compartments of the Model 355 20.2.2 Mathematical Formulation of the Rat Lung Model 356 20.2.2.1 The Mathematical Description of the Normal (Non-Overload) Retention and Clearance of Particles 356 20.2.2.1.1 On the Alveolar Surface 356 20.2.2.1.2 In the Interstitium 358 20.2.2.1.3 At the Lymphatic Level 359 20.2.2.2 MathematicalDescription of Overload 359 20.2.2.3 MathematicalDescription of PMN Recruitment 361 20.2.2.4 Summary of Model Parameters 362 20.2.3 Model Parameters 363 20.2.3.1 Parameter Values 363 20.3Experimental Data 364 20.4Strategy for Model Calibration and Validation 366 20.5Model Extrapolation to Humans 367 20.5.1 Method for Extrapolation 367 20.5.2 Results 368 * Disclaimer: The findings and conclusions in this chapter are those of the authors and do not necessarily represent the view of the National Institute for Occupational Safety and Health. 351 © 2007 by Taylor & Francis Group, LLC 20.5.2.1 Results from Parameter Extrapolation 368 20.5.2.2 Simulation Results 368 20.6 Human Lung Dosimetry Model 369 20.6.1 Model Equations and Description 371 20.6.2 Model Parameter Description and Estimation 374 20.6.3 Application of Human Lung Dosimetry Modeling in Risk Assessment 375 20.7 Discussion 380 20.7.1 The Contribution of Dosimetric Modeling to Particle Toxicology 380 20.7.2 Issues in the Dosimetry of Nanoparticles 382 Acknowledgment 383 References 383 20.1 INTRODUCTION Inhaled airborneparticles may be deposited in the respiratory tract with aprobability that depends on the physical properties of the particles, the velocity of the air, and the structure of the airways. Oncedeposited, particles may be retained at the site of deposition, translocated elsewhere in the body, or cleared by the biological processes specific to each region of the respiratory tract. Themajor regions of the human respiratory tract include the extrathoracic (nasopharynx or head airways), thoracic (tracheobronchialairways),and alveolar(pulmonaryorgas-exchange) (ICRP 1994). These regions differ in structure and function (Miller 1999; McClellan 2000). The functions of the extrathoracic and thoracicregions include air conditioning and conducting, while the main function of the alveolarregion is the gas exchange. Clearance of particles depositing in the alveolarregion occursprimarily by alveolarmacrophage (AV)-mediated clearance to the thoracic region, where they are cleared viathe “mucociliaryescalator” and then expectorated or swallowed. All regions of the respiratory tract include lymphatic tissue. Theextrathoracic region drains to the extrathoracic lymph nodes, and the thoracic and alveolar regions drain to the thoracic (also called hilar) lymph nodes. Particles that are not cleared from the lungs may enter the lung interstitium and translocate to the lymph or blood circulation. Several terms have been adopted to describe particlesbased on their size and probability of deposition within the respiratory tract. Inhalable particles are those capable of depositing anywhere in the respiratory tract. Thoracic particles are those capable of depositing in the lung airways. Respi- rable particles are those capable of depositing in the gas exchange region of the lungs (ACGIH 2005). Therespirableparticlesize distribution includesthe ultrafine or nanoparticles (primaryparticle diameter ! 0.1 m m), fine particles ( ! 2.5 m m), and coarse particleswith diameters ! 10 m m. 20.1.1 C OMPARISON OF H UMAN AND R ODENT L UNG S TRUCTURE AND P HYSIOLOGY Humans and rodents have in common the major respiratory tract regions, but differ in the structural and physiologicaldetails of each region. For example, rats are obligatenose breathers, while humans breathe through either the mouth or nose, depending on the level of exertion and otherfactors. The nasal airways in rats are more extensive, and the particle deposition fractions in this region are greater than in humans. Conversely, particle deposition fractions in the tracheobronchial region are greater in humans than in rats. Deposition occurs primarily by particle-airway impaction in that region. Rats have an asymmetric (monopodial) branchingsystem of tracheobronchial airways, while primates including humans have asymmetric (bipodial or tripodial) branchingsystem (Crapo et al. 1990). Humans have respiratory bronchioles leading to the alveolarductswhile rats do not, insteadhaving terminal bronchioles leading directly to the alveolarducts. Yet, the alveolus structure,where gas exchange occurs, is similar in rodents, humans, and othermammals (Mauderly 1996). Becauseofthe structural andsizedifferences in thehuman andrat respiratorytract,the particle sizesthatare inhalable differ in rats and humans (Me ´ nache, Miller, and Raabe 1995). Particle Toxicology352 © 2007 by Taylor & Francis Group, LLC Humans also differ from rats in physiologicalfactors such as breathing and metabolic rates. Normalalveolarclearance is approximately10times faster in rats than in humans (Snipes1989). Tracheobronchial clearance is relatively rapid in both rats and humans (retention half-times from hours to days), although in humans it has been shownthat someparticles that depositinthe airways are clearedmore slowly(Stahlhofen, Scheuch, and Bailey 1995). The fraction of slowly cleared particlesfrom the lung airways has been showntoincreasewith decreasing particle size from 6to ! 1 m mgeometric diameter (Kreyling and Scheuch2000). This may be an important retention mechanism for nanoparticles, as well. The particle concentration in the lung airways (and particu- larly at airway bifurcations and centriacinar region)has been associated with both cancerand non-cancer lung diseases(Churg and Stevens 1988; Churg et al. 2003). Particles that deposit in the alveolar region are associated with the slowestclearance phase in both rats and humans, with normal retention half-times of approximately2months in rats and from months to yearsinhumans (Bailey, Fry, and James 1985). The rateofalveolarclearance can depend on the particle exposure concentration and duration in both rats and humans. For example, in coal miners,littleornoclearanceofparticleswas observed to occurafterretirementfrom mining (Freedmanand Robinson 1988; Kuempeletal. 1997).Inrats(andmiceand hamsters)with sufficiently high exposures, “overloading” of lung clearance has been observed at greater lung burdens and longer retention times than expected based on studies at lower exposures (Morrow 1988; Muhleetal. 1990; Elder et al. 2005). 20.1.2 L UNG D OSIMETRY M ODELS Thedifferences in human andrat lung structureand physiology that influence thekineticsof particle depositionand clearance canbedescribedusing biologically basedmathematical models.Also calledlung dosimetry models,these models describe the relationship between the externalexposure to airborneparticlesand the internal dose of particles in the lungs.Biomathe- matical models that describethe exposure–dose relationship of atoxicantover time are called toxicokineticmodels, while thosedescribingthe dose–responserelationshipare called toxico- dynamic models. Although less common,models that describe the exposure, dose, and response relationships are calledtoxicokinetic/toxicodynamic models. Lung dosimetry models have been developedfor several species,but mostly in ratsand humans. These models often focus separatelyonthe processesofparticle deposition or clearan- ce/retention, although some have been integrated in software programsfor humans (ICRP1994; NCRP 1997; CIIT and RIVM 2002)and rats (CIIT and RIVM 2002). In several earlier rat models, the lungs have beendescribed as asingle compartment, with adose-dependent clearance rate coefficient to account for overload (Yuetal. 1988; Yu andRappaport 1997; CIIT andRIVM 2002). Other rat models described the lung clearance of insoluble particlesduring chronic exposure in terms of clearance to the tracheobronchial region, transfer to lymph nodes, and sequestration within the alveolarregion (Vincentetal. 1987;Jones et al. 1988; Strom, Johnson, and Chan 1989; Sto ¨ ber, Morrow,and Hoover 1989; Sto ¨ ber, Morrow, and Morawietz1990a, Sto ¨ ber et al. 1990b). Of the human lung dosimetry models, many have focused on particle deposition. Thehumanmultiple path particledeposition (MPPD) model(CIIT andRIVM2002 includesoptions forlung morphology based on data by Yeh and Schum (1980), Mortensen et al. (1988),orKoblinger and Hofmann (1990).Other deposition models include an empirical (data-based) model of ultrafine aerosoldeposition in thehuman tracheobronchial airways (Zhang andMartonen 1997) anda stochastic modelofparticledeposition, with parameters described as statistical distributions based on experimental measurement, whichallowsfor intra-and inter-individual variation in deposition due to lung structure andgeometry(Koblingerand Hofmann1985). Humanlung dosimetry models have recently been reviewed by Martonen, Rosati, and Isaacs (2005). In this chapter,two biomathematicalmodels of the long-term clearance and retention of inhaled particlesinrats or humans are described in detail. These include abiologically based modelof Biologically Based Lung Dosimetry and Exposure–Dose–Response Models 353 © 2007 by Taylor & Francis Group, LLC exposure–dose–responseinrats(Tran et al.1999, 2000) andahuman exposure–dosemodel calibrated andvalidated usingdata fromtwo independentcohorts of coal minersinthe U.S. (Kuempel2000; Kuempel et al. 2001a, 2001b)and the U.K. (Tran andBuchanan2000).The features of each of thesemodels are unique comparedwith other existing models.The rat model is the only toxicokinetic/toxicodynamic model currently available for poorlysoluble particles. The humanmodel structure is biologicallybased andisthe only clearance/retentionmodel to be validated using humanparticle lung burden data.The structuresofthese humanand rat models are compatible, which facilitates biologically based extrapolation from the rat to the human for thoseparameters that are not available for humans. Finally, examples are provided of usingthese models in risk assessment of occupational exposure to poorlysoluble particles. 20.2 MATHEMATICAL MODEL OF THE RETENTION AND CLEARANCE OF PARTICLES FROM THE RATLUNGS Mathematically,the deposition and clearance process is adynamic system, which can be described as aseries of compartments. For example, in this model, X i represents the quantityoffree particles on the alveolar surface. Generally, the change in the particle burden in compartment i ,dX i /dt, is described by equations of the form d X i dt Z D C I ij K O ik (20.1) where D Z input from outside the system to compartment i , I ji Z input from compartment j to compartment i , O ik Z outputfrom compartment i to compartment k . Equation 20.1 is called the “mass balance” Equation (because, over aset of compartments, mass is preserved). If the rate of transfer of particlesfrom compartment j to compartment i is assumed to be directly proportional to the massofparticles residentincompartment j ,i.e., I ij Z k ij X j (20.2) then Equation 20.2 is calledthe “mass action” type and k ij the “transfer rate” is the fraction per unit time. For multipleinputs and outputs Equation 20.1 can be generalized as d X i dt Z D C X m j Z 1 I ji K X n k Z 1 O ik i Z 1 ; . ; l (20.3) where m is the number of compartments that output to compartment i , n is the number of compart- ments that receive output from compartment i and l is the total number of compartments which makeupthe system. Asystem of equations such as Equation 20.3 can represent the dynamicsofthe retention and clearance of particles/fibres in the alveolar region of the lung. 20.2.1 S TRUCTURE OF THE R AT B IOMATHEMATICAL L UNG M ODEL Themodel is defined by aset of differential equations, which describe the rates at which the quantities of particles in the various compartmentsare assumed to change.Below we describe Particle Toxicology354 © 2007 by Taylor & Francis Group, LLC these compartments, the scientific assumptions about the translocations between them, and the rate parameters governing theseprocesses. 20.2.1.1 Compartmen ts of the Model Our mathematical model describes the progress over time of the retention of particlesand the alveolarmacrophage (AM)-mediated clearance process in the pulmonary region, together with the particle redistributionand theoverloadphenomena. Figure 20.1 showsthe nine conceptual compartmentsdescribingthe locationofinhaledparticles,plusthe main translocation routes betweenthem, including AM-mediated clearance (Tran et al. 1999, 2000). In Figure 20.1,inhaled particles in the respirable size range can reach the alveolarregion of the lung, where they come intocontact with epithelial cells. Themass (mg) of free particleson thealveolarsurfaceisrepresented by compartment X 1 .Asthe result of this contact, these particles are readily transferred into the interstitium (compartment X 5 represents the amount of free particles in the interstitium). This process is likely to be dependent on particle size (Ferin,Oberdo ¨ rster, andPenney1992; Oberdo ¨ rster, Ferin, andLehnert 1994;Geiser et al. 2005).However,the particle-epithelial cellcontactalsogenerates chemotacticsignals that attractAMs to thesite of particle deposition(Warheit et al.1988; Reynolds2005). The ensuing phagocytosis by AMs endeavors to clear the alveolarsurface of particles (and thus prevent interstitialisation). Subsequently, the ingested particles are removed by migrating AMs to the mucociliary escalator. (Compartment X 2 represents the amount of particles inside mobile, active AMs.) However, these cells have afinite lifespan. AMs eventually decay and become inactive (compartment X 5 represents the amount of particles inside decayed AMs) and release D X 1 X 2 X 3 X 6 X 5 X 8 X 9 X 7 X 4 cl Free particles Mobile alveolar macrophages (AM) Mobile interstitial macrophages (IM) Interstitial granuloma Decayed &inactive IMs Free particles Lymph node burden Alveolar sequestration Alveolar surface Interstitium Lymph nodes Decayed &inactive AMs r A r I i ee r A r I d A d I f AM-mediated clearance FIGURE 20.1 Schema of the compartments ( X 1 – X 9 )and the transfer rates between compartments. Biologically Based Lung Dosimetry and Exposure–Dose–Response Models 355 © 2007 by Taylor & Francis Group, LLC their particle load onto the alveolar surface for re-phagocytosis by other, more effective, AMs. Free particles that cross the alveolar epithelium intothe interstitium may encounter interstitial macrophages (IMs) and the same events, as described above, are repeated(compartment X 6 representsthe amount of particles inside mobileIMs and X 7 representsthe particle amount inside decayed IMs).However,fromthe interstitium, some particles(both free andinside IMs)are removed to the lymph nodes (represented by compartment X 9 ). As the particle-epithelial cells contact progresses, AMsbecome increasingly retained in the alveolarregion where theyphagocytose until they become overloaded.AsoverloadedAMs decay,thisload becomes increasingly difficult to redistributetomore effective AMs (i.e., the macrophagesthatingest this particleloadwill,inturn, become overloaded).Gradually,a “sequestration” pool of particles emerges, consisting of particles in overloaded AMs. This is represented by compartment X 4 .Similarly, interstitial granulomas are assumed to be derived from overloaded IMs.The amountofparticles sequestered in granulomas is represented by compartment X 8 in the model. Table 20.1 givesasummary description of each of the compart- ments. Theretention of particle-laden AMsoccurs togetherwith therecruitment of polymorphonuclear leukocyte(PMN) cells into theaffectedregion—this is thehallmarkof the inflammatory process (Donaldson and Tran 2002). 20.2.2 M ATHEMATICAL F ORMULATION OF THE R AT L UNG M ODEL 20.2.2.1 TheMathematical Description of the Normal (Non-Overload) Retention and Clearance of Particles 20.2.2.1.1 On the Alveolar Surface The rate of change of the mass of free particles(in mg day K 1 )consists primarily of the deposition of particlesfrom the aerosol, the phagocytosis by AMs, and the interstitialisation of these particles, and secondarily, of the release of particles from macrophages which reach the end of their lifecycle TABLE 20.1 TheCompartmentsinthe ModelRepresenting the Location of Particles and the Level of Inflammation Symbol Location of Particles On the alveolar surface X 1 Free on alveolar surface X 2 Successfully phagocytosed by alveolar macrophages X 3 In inactive alveolar macrophages, can be released for re-phagocytosis X 4 Sequestered in overloaded, immobile alveolar macrophages In the interstitium X 5 Free in interstitium X 6 Successfully phagocytosed by interstitial macrophages X 7 Attached to inactive interstitial macrophages, can be re-released for phagocytosis X 8 Interstitial granuloma At the lymph nodes X 9 Thoracic lymph nodes PMN recruitment PMN Number of PMN cells in the alveolar region Particle Toxicology356 © 2007 by Taylor & Francis Group, LLC d X 1 d t Z D K r A X 1 K iX 1 C d A X 3 (20.4a) where X 1 is the mass(mg) of free particlesremaining on the alveolarsurface; D is the dose rate of particlesdeposited on the alveolar surface (mg day K 1 ), calcu- lated from Equation 2.4b; r A is the rate of phagocytosis by AMs (day K 1 ); i is the rate of interstitialisation (day K 1 ); X 3 is themass(mg)ofparticles in macrophagesinthe inactivephase of their lifecycle; and d A is the deathrate for inactive macrophages. The deposited dose rate D of deposited particles(in mg day K 1 )iscalculated as D Z Concentration! Ventilation rate! DailyExposureperiod ! Alveolar deposition fraction ! ð 5 = 7 Þ ! ð 6 = 100Þ (20.4b) where Concentration is the aerosol concentration (mg m K 3 ); Ventilation rate is the breathing ventilation rateofthe rat ( l minute K 1 ); Daily Exposure period is the duration of each daily exposure (hr day K 1 ); Alveolar deposition fraction is the fraction of the inhaled particlesofagiven size de- posited in the alveolarregion; (5/7)convertsthe concentration forafive-days-per-week inhalationpatternintothe equivalent average concentration for the 7-daysweek; and (6/100)converts the units of the breathingrate to match the time and volume units of the concentration and exposure period. The alveolar deposition fraction, used in Equation 20.4b, was derived in two ways: (i) from the assumption that inhaled particlesare of the (Mass Median Aerodynamic Diameter) MMAD size, andalso(ii)fromthe measured particlesize distribution,and usingexperimental data on the alveolardeposition efficiency for particle inhaled (Raabe et al. 1988). The transfer rate coefficients ( D , r A , i ,etc.) in these equations are shown in Figure 20.1 next to their translocation routes. The coefficients i , d A are approximately constant whenthe lung burden is low, but at higherlung burden the macrophage mediated clearance becomes impaired and the transferrates becomefunctions of the alveolar particle surface area, s alv ,and the form of this dependence is described later. This assumesthatthe dependence is on thesum of particles which areavailabletothe AMs, i.e.,dependenceon s alv Z s ( X 1 C X 2 C X 3 C X 4 ), where s is particle-specific surface area (in unit of area per unit of mass). The phagocytosis rate is left constant for the range of particlestobemodeledpresently. However, it is envisaged that phagocytosis will become less effective as AMsare expected to clear larger epithelial areas, (covered by particles with larger surface areas). This is likely to be true for nanoparticles. However, data is currently lacking for areasonably accurate model. Equation 20.4a, with these coefficients writtenasfunctions of s alv ,becomes d X 1 d t Z D K r A X 1 K i ð s alv Þ X 1 C d A ð s alv Þ X 3 (20.4c) Biologically Based Lung Dosimetry and Exposure–Dose–Response Models 357 © 2007 by Taylor & Francis Group, LLC Particles that have been phagocytosed by macrophages will subsequently either be removed from the alveolar region by way of macrophage migration and the mucociliary escalator or be released onto the alveolar surface upon the necrosis of AMs. So the rate of change of the mass of phagocytosed particles in active AMs(i.e., X 2 )is d X 2 d t Z r A X 1 K clð S alv Þ X 2 K r A X 2 (20.5) where cl is the AM-mediated clearance rate (day K 1 ), r A is the phagocytosis rate (day K 1 ), and r A is the transfer rate (day K 1 )from active AMs to inactive AMs. When this clearance is unaffected by overload,clisestimated to be 0.015 day K 1 (Sto ¨ ber, Morrow,and Hoover 1989). When clearance is affectedbyoverload,thenthe dependence of cl on s alv is describedbyEquation 20.13. The phagocytosis rate r A is assumedtobeindependent of theparticlesurface area as AMsare assumed to be locally mobile in the alveolar region and able to phagocytose particles. Also, r A is assumed to be unaffected by the particle surface area. Themass of particles inside inactive AMs, X 3 ,isdescribed by d X 3 d t Z r A X 2 K d A ð s alv Þ X 3 K f ð s alv Þ X 3 (20.6) where d A is the release rate of particles from inactive AMs back to the alveolar surface and f is the rate of transfer into the alveolarsequestration compartment. Note that for acertain choice of d A and f , d A C f Z constant. Equations 20.4 through Equation 20.6 describethe dynamics of translocation of particles on the alveolar surface when the lung defenses are not overloaded. The fourth compartment on the alveolarsurface, X 4 ,becomes involved once the lung becomes overloaded with particles. The rate of change of the amount of particles in the alveolar sequestration compartment ( X 4 ), representing the massofparticles trapped inside overloaded macrophages, is d X 4 d t Z f ð s alv Þ X 3 (20.7) 20.2.2.1.2 In the Interstitium Once particles areinterstitialised, they will be phagocytosed readilybyIMs.Interstitialised particles that escape phagocytosis, together with the particlesphagocytosed by Ims, may eventually be removed to the lymph nodes. Let X 5 be the massoffreeparticles that are interstitialised, then d X 5 d t Z i ð s alv Þ X 1 K e ð s inst Þ X 5 K r I X 5 C d I ð s inst Þ X 7 (20.8) where e is the removal rate (day K 1 )ofparticles to the lymph nodes; r I and d I ,respectively, the rates of phagocytosis by macrophages and release from inactive macrophages, are assumed to have the same valuefor IMs as for AMs; and s inst is the interstitial burdeninunit of surface area, i.e. s inst Z s ( X 5 C X 6 C X 7 C X 8 ). Equation 20.8 for IMs is comparable to Equation 20.4c for AMs—the first term on the right hand side of Equation 20.8 is the transfer from alveolar surface (instead of deposition in Equation 20.4c),the second and third terms include X 5 insteadof X 1 ,and the last term includes X 7 insteadof Particle Toxicology358 © 2007 by Taylor & Francis Group, LLC X 3 .Similarly, the mass of particles phagocytosed by IMs is d X 6 d t Z r I ð s inst Þ X 5 K e ð S inst Þ X 6 K r I X 6 (20.9) where the removal rate to lymph nodes ( e )isassumed to be the same for IMs as for interstitialised free particles. The mass of particles trapped in interstitial granulomas is described by d X 7 d t Z r I X 6 K d ð s inst Þ X 7 K y ð s inst Þ X 7 (20.10) where the transfer rate of particles from active IMs to inactive IMs ( r I )and the release ratefrom inactive IMs ( d I )are also assumed to have the same dependence on the relevantburden(interstitial or alveolar particle surface area), and also the samenon-overload values as for AMs; y is the rate (day K 1 )ofinterstitial granuloma formation which occurs when the IM defense of the interstitium becomes impaired. The conditions relating to the transfer of particles to interstitial granuloma ( X 8 )are linked with overloadand thereforeare described in the sectiononoverload (later). However, themassof particlestrapped in interstitial granulomas is described by d X 8 d t Z y ð s inst Þ X 7 (20.11) 20.2.2.1.3 At the Lymphatic Level The mass of particles accumulated in the mediastinal lymph nodes is the sum of the transfer from free interstitialised particles(X 5 )and particles in IMs ( X 6 ) d X 9 d t Z e ð X 5 C X 6 Þ (20.12) 20.2.2.2 Mathematical Description of Overload As describedearlier,the impairmentofpulmonary clearance during exposure duetooverload correlated with the increase in the rate of recruitment of PMNs. The PMN level, in turn, correlated with particle surface area.This impairment of clearance can be described mathematically as a function, q ,ofalveolar particle burden(in terms of mass or surface area), which varies between0 and 1. As q is amultiplier of the rate parameters, theseparameters are fully functioningwhen q z 1. Mathematicalexpressions were developed to describe this progressive impairment.Similar equations were used in other models (e.g., Yu et al. 1988; Sto ¨ ber, Morrow,and Hoover 1989; Tran, Jones,and Donaldson1997). Note that all of thesefunctional forms are essentially chosenfor practical reasons (i.e., they integrate well with the models in which they form apart). For example, Tran, Jones,and Donaldson 1997 used an exponential decay form q ð m alv Þ Z e K l : ð m alv K m crit Þ b for m alv O m crit q ð m alv Þ Z 1for m alv % m crit where m alv is the particle mass in the alveolarregion and m crit is the criticalmassfrom which impairment begins to manifest. l and b are parameters controlling the rate and form of decay.This Biologically Based Lung Dosimetry and Exposure–Dose–Response Models 359 © 2007 by Taylor & Francis Group, LLC functionhas twolimitations. First, theparameters of this function cannot be related to some tangible entity, such as mass or surface area. So, it is difficult to judge the plausibility of different values which ( l and b )give agood fit with data. Finally, there is adeterministic boundary at m crit belowwhich there is no impairment—i.e.,the equationabove provides an abruptswitch over to impairment of clearance. While there is some evidence that this might be the case (Muhle et al. 1990), it is more plausiblethatimpairment wouldlikely progress continuously. Thus,anew functional form for q in terms of alveolar surface burden, s alv ,isintroduced q ð s alv Þ Z 1 K 1 1 C s 1 = 2 s alv  b  (20.13) This functional form is similar to that used by Yu and Rappaport (1997) to describeretardation of clearance of insoluble dust. The function is dependent on two parameters, namely s 1/2 and b .The former, s 1/2 ,represents the level of particle surface area such that the impairment is half of its originalvalue; while the latter, b ,controlsthe steepnessofthe impairment.Figure 20.2 showsthe behavior of q for two different sets of values for b and s 1/2 over arange of values of s alv .One advantage this function has over the earlier functions from the literature is that one of its para- meters, s 1/2 ,isreadily interpretableand will be usefulinthe comparison of the effects of different dustsontheir retention and clearance. Since particle surface area affects clearance by mobilemacrophages, we assumehere that the clearance rate is modified as clð s alv Þ Z q ð s alv Þ cl (20.14) where cl,onthe right-hand sideofEquation 20.14, is the time-independentrate forlow lung burdens. Thus, as the particle burden on the alveolar surface (in terms of surface area)increases, mobilemacrophages are increasingly retained on the alveolar surface,asdescribed by Equation 20.14. During this phase,particles released by inactive AMs upon death will be less likelytobe removed by mobile AMstothe mucociliary escalator (i.e., the transfer rate d A ,back to the alveolar surface to be re-phagocytosed and then clearedbyAMs,decreaseswith increasing alveolarlung burden). Instead,these particlesare re-phagocytosed by retained AMsleading to transfer at arate, 100 200 300 400 500 600 700 0 0.2 0.4 0.6 0.8 1 b =15 b =0.94 s 1/2 =387cm 2 s 1/2 =679cm 2 Alveolar burden surface area, s alv (cm 2 ) Impairment function θ (0− 1) FIGURE 20.2 The impairment function for particle surface area between 0and 750 cm 2 and two different sets of values for ( b , s 1/2 ). Particle Toxicology360 © 2007 by Taylor & Francis Group, LLC [...]... TiO2 0 20 40 60 80 100 120 140 160 180 200 0 0 20 40 60 80 100 120 140 160 180 200 FIGURE 20. 4 Mean lymph node burden during exposure and model predictions (lines) © 200 7 by Taylor & Francis Group, LLC 366 Particle Toxicology 12 50 mg m−3 25 mg m−3 TiO2 10 Number of PMNs (×106) Number of PMNs (×106) 12 8 6 4 2 0 0 20 40 60 80 10 8 6 4 2 0 0 100 120 140 160 180 200 75 mg m−3 37.5 mg m−3 BaSO4 20 40 60... build-up of particles in the alveolar compartment is determined by the rates of particle deposition, AM-mediated clearance, and particle transfer into the interstitium (Equation 20. 20) The deposition of particles in the alveolar compartment is assumed to occur at a rate proportional to the concentration in inhaled air, i.e., a first-order process (Equation 20. 21) AM-mediated clearance is © 200 7 by Taylor... of change of particle mass in the interstitium (MI) at any time (t) is defined as dMI =dt Z RI KRLN (20. 25) where RI is defined in Equation 20. 20 and Equation 20. 25 RLN is the translocation rate (mg/yr) of particles from the interstitium to the lung-associated (hilar) lymph nodes, as follows RLN Z KLN !365 !MI (20. 26) where KLN is the first-order rate coefficient (dK1) for translocation of particles from... increase, (Figure 20. 3) consistent with overload, lymph node burdens were higher for TiO2 (Figure 20. 4) Mean numbers of PMNs (inflammation) also increased more rapidly for TiO2 (Figure 20. 5) However, TiO2 16 50 mg m−3 25 mg m−3 12 Lung burden (mg) Lung burden (mg) 14 75 mg m−3 37.5 mg m−3 BaSO4 10 8 6 4 2 0 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 FIGURE 20. 3 Mean lung... micrometer-sized particles (Semmler et al 200 4) Comparison of observed vs model-predicted lung burdens in rats show that some rat lung dosimetry models (Tran et al 200 0; Tran, Graham, and Buchanan 200 1; Tran et al 200 2; CIIT and RIVM 200 2) predict reasonably well the retained mass lung burdens in rats exposed by chronic inhalation to ultrafine or fine poorly soluble particles (Kuempel et al 200 6) More... are described in Table 20. 10 The optimized parameter values and statistical model fit are shown in Table 20. 11 The model with the best fit (lowest mean squared error) was the three-compartment model with interstitial-sequestration compartment but with no dose-dependent decline in AM-mediated clearance From Table 20. 11, the optimal choice, i.e., the three-compartment model with first-order interstitialisation... constant rate (Equation 20. 24); this will occur even at low lung dust burdens, below the estimated human-equivalent dose associated with overloading of alveolar clearance The buildup of particles in the interstitium is described by the difference in the rates of particles entering from the alveoli and particles leaving to the lung-associated lymph nodes (Equation 20. 25) The rate of particle translocation... nodes FIGURE 20. 10 Three-compartment human lung dosimetry model (From Kuempel, E D., O’Flaherty, E J., Stayner, L T., Smith, R J., Green, F H Y., and Vallyathan, V., Reg Toxicol Pharmacol., 34, 69–87, 200 1a With permission.) where KI is the first-order rate coefficient (dK1) for transfer of particles from the interstitium to the lung-associated (hilar) lymph nodes MA is defined in Equation 20. 20; and 365... assumed) (Jarabek et al 200 5) (Table 20. 13) The estimated critical lung dose as particle surface © 200 7 by Taylor & Francis Group, LLC Biologically Based Lung Dosimetry and Exposure–Dose–Response Models 377 45 Deposited 40 Predicted burden (g) 35 Cleared 30 25 20 Lungs 15 10 Interstitium 5 0 Alveoli 20 25 30 35 40 45 50 Time (year) 55 Lymph nodes 60 65 70 75 FIGURE 20. 11 Predicted mass of particles retained... 1.50 1.50 1.31 1.54 1.28 —e C9.9 K7.8 K5.7 C6.4 C6.4 K7.1 C9.2 K9.2 a © 200 7 by Taylor & Francis Group, LLC Particle Toxicology FD, fractional deposition; first-order rate coefficients; KT, alveolar macrophage-mediated clearance of particles to the tracheobronchi; KI, transfer of particles to the interstitium; KLN, translocation of particles to the hilar lymph nodes b Output is mean predicted lung burden . 3 Duration of experiment203 days 119 days 0 20 40 60 80 100 120 140 160 180 200 BaSO 4 75 mgm − 3 37.5 mgm − 3 0 20 40 Lung burden (mg) Lung burden (mg) 60 80 100 120 140 160 180 200 0 2 4 6 8 10 12 14 16 TiO 2 50. 200 0 2 4 6 8 10 12 14 16 TiO 2 50 mgm − 3 25 mgm − 3 FIGURE 20. 3 Mean lung burdens during exposure and model predictions (lines). 0 20 40 60 80 100 120 140 160 180 200 0204 06080100 120 140 160 180 200 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 TiO 2 50. Dosimetric Modeling to Particle Toxicology 380 20. 7.2 Issues in the Dosimetry of Nanoparticles 382 Acknowledgment 383 References 383 20. 1 INTRODUCTION Inhaled airborneparticles may be deposited