P-3a-120

MICRODOSIMETRIC IMPLICATIONS OF THE NONUNIFORMITY OFDEPOSITION PATTERNS OF INHALED RADIOACTIVE NUCLIDES

I. Balásházy1, W. Hofmann2 and J. Pálfalvi1

1Radiation and Environmental Physics Department, KFKI Atomic EnergyResearch Institute, P.O.Box 49, H-1525 Budapest 114, Hungary

2Institute of Physics and Biophysics, University of Salzburg,Hellbrunner Str. 34, A-5020 Salzburg, Austria

INTRODUCTIONAerosol deposition studies have demonstrated that deposition patterns of inhaled aerosols within airway

bifurcations are distinctly inhomogeneous during inhalation as well as exhalation. Current lung depositionmodels, however, employ analytical equations for the calculation of deposition efficiencies, which, by definition,cannot describe local inhomogeneities of deposition within airway bifurcations. In the present study, localdeposition patterns in airway bifurcations were computed by our recently developed numerical particledeposition model. To quantify the inhomogeneities of predicted deposition patterns, the whole surface of thebifurcation was scanned by a pre-specified surface element. Local deposition enhancement factors were thendetermined as the ratio of local to average deposition densities. In the present study, distributions ofenhancement factors and their corresponding maximum values were computed for a physiologically realisticbifurcation geometry in upper human bronchial airways (airway generations 3-4 in Weibel’s Model-A) assumingvarious surface element (patch) sizes (0.1 mm x 0.1 mm — 3 mm x 3 mm). Simulations were performed for awide range of particle sizes (1 nm - 20 µm) and flow conditions (flow rates of 10, 60 and 120 l/min).

Present lung dosimetry models for inhaled radionuclides and radon decay products are based ondeposition efficiencies for straight cylindrical airways, which is conceptually equivalent to the assumption thatinhaled particles are uniformly deposited in these airways (NRC 1991; Hofmann et al. 1996a). Furthermore,depth-dose distributions of radon progeny in bronchial epithelium are obtained by integrating the surfaceactivities over the surface of the cylindrical airways within the ranges of the alpha particles, thereby assumingagain that alpha particle sources are uniformly distributed on airway surfaces (Harley and Pasternack 1972; NRC1991). This assumption is supported by the view that Brownian motion in straight cylindrical tubes a prioriproduces uniform deposition patterns.

However, experimental studies about particle deposition in single pathway tracheobronchial airwaymodels (Martin and Jacobi 1972; Martonen et al. 1987; Shimo and Ohashi 1993), in airway casts of the humantracheobronchial tree (Schlesinger 1978; Cohen et al. 1988), and in single bronchial bifurcation models (Kim andFisher 1994; Kinsara et al. 1995) have demonstrated that diffusion-dominated particle deposition patterns arehighly nonuniform. Three main features of the deposition patterns within airway bifurcations have been observedin these experiments (Martonen et al. 1987): (i) deposition is enhanced at airway branching zones relative tocylindrical airway portions; (ii) deposition within a bifurcation is highest at the dividing spur; and, (iii)deposition is also enhanced at the inner sides of the daughter airways. Thus the observation of nonuniformdeposition patterns suggests that active particle transport by secondary flows (as opposed to passive transportdue to molecular diffusion) in human airway bifurcations may also play a significant role in particle deposition.Indeed, simulations of flow patterns in bronchial airway bifurcations have revealed that strong secondary flowsare produced at airway branching sites upon inspiration (Balásházy and Hofmann 1993a; Hofmann et al. 1996b).

Analytical solutions of the equations describing particle transport and deposition of inhaled particles inbronchial airway bifurcations can only be obtained for idealized airway geometries, and thus idealized airflowprofiles, and a limited number of physical deposition mechanisms acting simultaneously (Balásházy et al. 1991).Since these simplifications result in nearly uniform distributions of deposition sites, analytical deposition modelscannot a priori describe the strong local inhomogeneities of deposition patterns which have been observedexperimentally. Thus, the analysis of particle deposition in a realistic bifurcation geometry under realistic airflowconditions, or the simultaneous consideration of more than two deposition mechanisms, require the applicationof numerical modeling techniques (Gradon and Orlicki 1990; Balásházy and Hofmann 1993a; Balásházy 1994;Li and Ahmadi 1995).

For obvious experimental reasons, deposition experiments in bronchial airway models and lung castsare restricted to large bronchial airways. Fortunately, this region where limited experimental data are availablecoincides with the region in which the majority of bronchial carcinomas have been detected (Spencer 1977).Furthermore, Martin and Jacobi (1972) observed enhanced deposition at airway branching sites only in the first 6

P-3a-120

bronchial airway generations. Based on these experimental and pathological observations, the bronchial airwaybifurcation models used in the present study correspond to airway generations 3-4 (segmental bronchi) inWeibel´s (1963) Model A.

In an earlier attempt, experimentally observed deposition enhancement within bronchial airwaybifurcations upon inspiration was characterized by a “bifurcation enhancement factor”, which was related to thecentral bifurcation zone and the two daughter airways (Martonen 1991). These bifurcation enhancement factorswere subsequently applied to the deposition of inhaled radon progeny (Hofmann et al. 1990). The goal of thepresent study is to quantify the nonuniformity of theoretically predicted deposition patterns by local depositionenhancement factors, which are related to the whole bifurcation (Balásházy et al. 1997).

First, inspiratory particle deposition patterns of spherical unit density particles within three-dimensionalmodels of segmental bronchial airway bifurcations are simulated by a numerical fluid dynamics and particletrajectory model. Second, local deposition enhancement factors are computed by scanning along the surface ofthe bifurcation with a prespecified surface area element. The maxima and the distributions of the localenhancement factors are studied as functions of bifurcation geometry, size of the scanning element, particle size,and flow rate. Upon inhalation, deposition efficiencies are higher and deposition patterns are moreinhomogeneous than upon exhalation (Balásházy and Hofmann 1993a,b). Hence, the present analysis isrestricted to inspiratory particle deposition patterns.

MODELING OF PARTICLE DEPOSITIONIn the this study, human segmental bronchial airway branchings are represented by a “physiologically

realistic bifurcation” (PRB) model, with a smooth transition zone and a rounded carinal ridge (Heistracher andHofmann 1995). This PRB model provides a quite realistic description of in vivo particle deposition in humanlungs. For subsequent numerical fluid dynamics calculations, the geometries of these bronchial bifurcationmodels are set up by the FIRE® (AVL, Graz, Austria) commercial CFD program package.

B

A

η=8.1 %

dp=1 nm

Qp=7.5 l min-1Qp=7.5 l min-1

B

A

η=2.0 %

dp=200 nm

Qp=1.25 l min-1

B

A

η=14 %

dp=1 nm

Qp=1.25 l min-1

B

A

η=1.1 %

dp=200 nm

Figure 1. Spatial deposition patterns of 1 nm and 200 nm diameter particles, dp, at two flow rates, Qp, in physiologicallyrealistic bifurcation model with the related deposition efficiencies, η, based on 100,000 randomly selected particles.Linear dimensions approximate to airway generations 3-4 in Weibel’s Model (1963). The parabolic inlet flow withflow rates of 7.5 and 1.25 l min-1 in the parent branch correspond to inspiratory flow rate of 60 and 10 l min-1,respectively.

P-3a-120

Three-dimensional airflow patterns in these bifurcation models are computed by solving the Navier-Stokes and continuity equations with the FIRE® CFD code, applying finite volume methods. Parabolic velocityprofiles at the inlet and constant pressure conditions at the outlet boundary are applied. The air is considered asan incompressible fluid and the flow is stationary and laminar. The flow rate in the parent airway is 15, 7.5 or1.25 l min-1, which corresponds to a 120, 60 or 10 l min-1 flow rate in the trachea (or a 60, 30 or 5 l min-1

respiratory minute volume), respectively. These three flow rates are characteristic of heavy and light physicalactivites or resting breathing conditions, respectively (ICRP 1994).

For the computation of particle deposition within the bifurcation model, inspired particles are selectedrandomly by Monte Carlo techniques at the inlet of the parent branch in accordance with the assumed parabolicair velocity profile. Aerosol particle trajectories are then simulated by considering the concomitant effects ofBrownian motion, inertial impaction, gravitational settling, and interception. A particle trajectory ends if ittouches the surface of the bifurcation (i.e., the particle is being deposited) or leaves the bifurcation at the outletof the daughter branches (i.e., no deposition event). Having simulated a large number of particle trajectories,deposition patterns and related deposition efficiencies can be determined.

A more detailed description of the fluid dynamics and particle deposition calculations has beenpublished elsewhere (Balásházy 1994; Balásházy and Hofmann 1993a,b, 1995).In all subsequent computations,the position of the main plain of the bifurcation is horizontal, and the number of selected particle trajectories is100,000 (note: this large number of trajectories is necessary for the statistical analysis of local depositionenhancement factors).

B

A

η = 2.3%

dp = 10 nm

B

A

η = 41.6%

dp = 10 µm

B

A

η = 8.7 %

dp = 5 µm

B

A

η = 2.1 %

dp = 1 µm

Figure 2. Spatial deposition patterns of 10 nm — 10 µm diameter particles at a flow rate of 7.5 l min-1 in the parent branch inphysiologically realistic bifurcation model with the related deposition efficiencies, η, based on 100,000 randomlyselected particles. Linear dimensions as in Fig. 1.

Deposition patterns of 1 nm and 200 nm diameter unit density particles are presented in Fig. 1 for aflow rate of 7.5 l min-1 (upper panels) and 1.25 l min-1 (bottom panels) in the parent branch (light physical activityand resting conditions), illustrating significant differences between attached and unattached radon progeny. For 1nm particles, deposition is relatively uniform throughout the whole bifurcation, except in the central bifurcationzone, where deposition is enhanced in the vicinity of the carinal ridge. In contrast, deposition of 200 nm particlesis distinctly inhomogeneous in the central bifurcation zone and the two daughter airways due to the action ofsecondary flows: hot spots are formed at the top and bottom parts of the central bifurcation zone where the cross-section is decreasing and in the daughter branches downstream of the carina over and bottom of the main planeof the bifurcation and in the case of the higher flow rate along the main plane of the bifurcation, as well.

P-3a-120

Comparing the deposition patterns of 1nm and 200 nm particles, the following observations can be made: (i) atthe higher flow rate: the deposition efficiency, η, is 8.1 % for the unattached and 2.0 % for the attached radonprogeny (an increasing deposition efficiency with decreasing particle size is consistent with deposition bydiffusion); (ii) comparing these values to the corresponding deposition efficiencies at lower flow rate: η is 14 %for the unattached and 1.1 % for the attached radon progenies; (iii) the deposition pattern is much morehomogeneous in case of the smaller particle size, emphasizing again the dominant role of diffusion; (iv)deposition of the larger particle size in the central bifurcation zone and the daughter airways is stronglyinfluenced by the strong local secondary flows. Here the deposition mechanisms are not strong enough toovercome these secondary flows at the carinal ridge. It is the reason why there is no deposition in this region atall at low flow rate and 200 nm particle size.

In Figure 2, computed deposition patterns are displayed for 10 nm, 1µm, 5 µm and 10 µm diameterparticles at the 60 l min-1 inspiratory flow rate (light physical activity breathing condition, Qp=60 l min-1). Boththe deposition efficiencies and the deposition patterns are similar in the case of 10 nm and 1 µm particles to thecase of the 200 nm particles (attached radon progeny), η is about 2 %. However, in the case of large particles (5and 10 µm) the inertial impaction is strong enough to overcome the effect of the secondary flows in the vicinityof the carinal ridge and there are hot spots even at the carinal ridge and downstream of the carina in the mainplane of the branching, as well. The deposition efficiency is 8.7 % at 5 µm particles and 42 % at 10 µm particles.

ENHANCEMENT FACTORSFor the quantification of inhomogeneities of deposition patterns illustrated in Figs 1 - 2, the local

deposition densitiy, i.e., the number of particles deposited per unit surface area, is determined by scanning thewhole surface of the bifurcation with a prespecified surface element (or patch) (Balásházy et al. 1998). The localdeposition density in a specified surface element relative to the average deposition density is then defined as thelocal deposition enhancement factor, EF:

EF deposition density in a surface elementdeposition density in the whole bifurcation

= .

By this definition, EF = 1 in case of a uniform deposition, while EF > 1 characterizes inhomogeneousdeposition patterns.

A computer code has been developed which scans the surface of the bifurcation with a prespecifiedsurface element and computes local deposition enhancement factors for each patch (Balásházy et al. 1998). Sincethe deposition enhancement factor is the ratio of two statistical variables, the resulting relative standard deviation(coefficient of variation), sef, is given by:

,(%),/1/1100 dbdeef nns −=where, nde and ndb are the number of particles deposited in a given surface element and in the whole bifurcation,respectively.

If the distribution of deposition sites within a bifurcation is very inhomogeneous, then the computedenhancement factor is sensitive to the size of the pre-specified surface element (patch size). From amicrodosimetric point of view, the patch size should be as small as possible. Since the presence of severalneighboring biological cells seems to be necessary for the development of a tumor (Crawford-Brown andHofmann 1996; Trosko 1996), a patch size of about 100 µm x 100 µm (i.e., about 10 x 10 epithelial cells) hasbeen selected here as the smallest surface element. However, from a statistical point of view, the larger thesurface element the smaller is the standard deviation of the related enhancement factor.

In the present study, we therefore computed enhancement factors for six different patch sizes:3 mm x 3 mm, 2 mm x 2 mm, 1 mm x 1 mm, 0.5 mm x 0.5 mm, 0.25 mm x 0.25 mm, and 0.1 mm x 0.1mm(Figure 3). As always square surface elements will be used here, the size of an input patch is identified by onlyone dimension, e.g. 3 mm or 0.1 mm. As the figure illustrate, maximum enhancement factors strongly increasewith diminishing patch size, which proves the distinct inhomogeneity of local particle deposition patterns for allparticle sizes.

The minimum patch size in the scanning code is the size of one cell of the computational grid whichwas generated for the CFD calculations. This cell size is not uniform on the surface of the bifurcation: thecomputational grid is denser (i.e., cells are smaller) in the central zone of the bifurcation than in the vicinity ofthe inlet and outlets. In that area of the bifurcation where the highest deposition density is expected, the cellshave a 0.02 - 0.04 mm2 size, while the average value is about 0.06 mm2, which refers to a linear dimension of0.245 mm. Thus, the 0.1 mm input patch size is generally smaller than the size of one cell on the surface of thefinite volume mesh, which may lead to an underestimation of the computed enhancement factors.

Two different methods have been developed to scan the surface of the finite volume mesh (Balásházyand Hofmann 1998): (i) a “nonoverlapping” scan, in which the surface element is moved by the defined patch

P-3a-120

size along the surface of the computational grid (i.e., adjacent patches lie next to each other); and, (ii) an“overlapping” scan, in which the patch is moved only by one cell of the computational mesh on the surface. Forsufficiently large patch sizes, a given patch will always contain several cells; thus the spatial resolution of theoverlapping scan is much finer that by the nonoverlapping scan. Consequently, an overlapping scan will be usedto detect the maximum values of the deposition enhancement factors. However, for the analysis of thedistribution of enhancement factors, an overlapping scan could assign a given deposition event to more than onepatch. Hence, the nonoverlapping scan will be applied here to avoid multiple counting. If the linear dimensionsof the selected patch sizes are smaller than or equal to those of the computational grid, then there is no differencebetween overlapping and nonoverlapping scans.

1E-3 0,01 0,1 1 100

20

40

60

80

100

120Patch sizes:

Particle size (µm)

3 mm 2 mm 1 mm 0.5 mm 0.25 mm 0.1 mm

Max

imum

enh

ance

men

t fac

tor

Figure 3. Maximum local deposition enhancement factor as a function of particle size at Qp = 7.5 l min-1 flow rate, computedby overlapping scan for different patch sizes in physiologically realistic bifurcation model.

Two dosimetric parameters of the computed local deposition enhancement factors will be derived toillustrate the inhomogeneity of the deposition pattern: (i) maximum enhancement factors, which can be related tothe highest local doses delivered within a bronchial bifurcation; and, (ii) frequency distributions of theenhancement factors, which can be related to the distribution of local doses, contrasting the common assumptionof a uniform nuclide distribution in current lung dosimetry models.

Maximum of enhancemnent factorsMaximum deposition enhancement factors, EFmax, for 1 nm – 20 µm particles at three flow rates

corresponding to high and light physical activities and resting breathing condition in a physiologically realisticbronchial bifurcation model (airway generations 3-4, Weibel's 1963 Model A) are presented in Figure 4. TheFigure presents the maxima of enhancement factors in the case of 0.1 mm patch size computed by overlappingscan. Inspection of the figure indicates that the maxima of enhancement factors increase near linearly withparticle size in the size range of 1nm - 1 µm. Depending upon the flow rate, their values are between 40 and 120.However, for even larger particle sizes, the enhancement factor maximum increases very rapidly, up to amaximum, until it decreases again sharply down to a value of around 50. The maximum values of these curvesare between 300 and 400, depending on the applied flow rate. At higher flow rates, the maximum of these curvesis higher and occurs at a smaller particle size. Regarding the absolute values of the maximum enhancementfactors, airway cells located at the carinal ridge or at the inner sides of the two daughter branches may receivemassive local doses, which can be up to two orders of magnitude larger than the average dose for a givenbifurcation. The dependence of the maximum enhancement factor on particle size, as illustrated in Figure 4, isdetermined by the ratio of the maximum number of particles deposited on a surface element (Nel,max) to the totalnumber of particles deposited in the whole bifurcation. While both numbers increase with particle size todifferent extents, the abrupt increase of Nel,max for particles between 1 to 4 µm produces a distinct peak in thissize range. Likewise, the dependence of the deposition enhancement factors on flow rate reflects the changingratio of the relative deposition efficiencies in the selected surface element and the whole bifurcation.

P-3a-120

1E-3 0,01 0,1 1 100

100

200

300

400

Flow rate during inhalation:

Q = 120 l/min Q = 60 l/min Q = 10 l/min

Enha

ncem

ent f

acto

r max

imum

Particle size (µm)Figure 4. Maximum local deposition enhancement factors as a function of particle size at three inspiratory flow rates,

computed by overlapping scan with 100 µm x 100 µm patch sizes in physiologically realistic bifurcation model.Linear dimensions correspond to generations 3-4 in Weibel’s (1963) Model-A.

Distributions of enhancement factorsFrequency distribution of enhancement factors and number of particles deposited on a given patch for

1 nm particles at 60 l min-1 inspiratory flow rate (Qp = 7.5 l min-1) in a physiologically realistic bifurcation modelwhere the linear dimensions correspond to airway generations 3-4 in Weibel's (1963) Model A, are plotted inFigure 5 for the smallest (0.1 mm) and the largest (3 mm) input patch sizes, computed by nonoverlapping scan.

0 10 20 30 400

1000

2000

3000

4000

5000

"0.1mm patch"No. of patch = 8832EFmax = 41EFmin = 0

Enhancement factor

Freq

uenc

y

0 1 2 3 4 50

2

4

6

8

10

12

"3mm patch"No. of patch = 73EFmax = 5.2EFmin = 0.046

Enhancement factor

Freq

uenc

y

0 2 4 6 8 100

1000

2000

3000

4000

5000

"0.1mm patch" Nmax = 10

Freq

uenc

y

No. of dep. particles on a patch0 100 200 300 400 500

0

2

4

6

dp=1 nm Qp = 7.5 l/min

"3mm patch" Nmax= 540

Freq

uenc

y

No. of dep. particles on a patch

Figure 5. Distribution of enhancement factors for 0.1 and 3 mm patch sizes and number of particles deposited on thesepatches for the inhalation of 1 nm particles at a flow rate of Qp = 7.5 l min-1 in the a physiologically realisticbifurcation model ( EFmin: EF in that patch which has the lowest value in the whole bifurcation; Nmax: maximumnumber of particles deposited in a given patch).

P-3a-120

The high degree of inhomogeneity of enhancement factors (upper panels) and number of particlesdeposited on the specified surface elements (bottom panels) are illustrated in the figure (the deposition efficiencyis 8.1 %). While there is no deposition at all in 54 % of the scanned 0.1 mm surface elements (left panels), i.e.,the minimum deposition enhancement factor, EFmin, is zero, all scanned 3 mm patches (right panels) containdeposited particles.

0 10 20 300

1000

2000

3000

"0.1mm patch"

No. of patch = 8832EFmax = 38EFmin = 0

Enhancement factor

Freq

uenc

y

0 1 2 3 4 5 60

2

4

6

8

10 "3mm patch"

No. of patch = 73EFmax = 5.9EFmin = 0.188

Enhancement factorFr

eque

ncy

0 2 4 6 8 10 12 14 16 180

1000

2000

3000

"0.1mm patch"

Nmax = 19

Freq

uenc

y

No. of dep. particles on a patch0 200 400 600 800 1000

0

2

4

dp=1 nm Qp=1.25 l/min

"3mm patch"

Nmax = 927

Freq

uenc

y

No. of dep. particles on a patch

Figure 6. Distribution of enhancement factors for 0.1 and 3 mm patch sizes and number of particles deposited on thesepatches for the inhalation of 1 nm particles at a low flow rate of Qp = 1.25 l min-1 in the a physiologically realisticbifurcation model ( EFmin and Nmax, see Fig.5.)

Corresponding distributions of enhancement factors for the low flow rate, presented in Figure 6, aresimilar in shape to those obtained for the 60 l min-1 flow rate. Due to the efficiency of the diffusion depositionmechanism at the low flow rate, deposition is much more uniform here than for the higher flow rate. This is alsoillustrated by the four times higher EFmin (0.188 vs. 0.046) in the case of the 3 mm patch. While maximumenhancement factors are very similar for both flow rates, the maximum number of deposited particles in a patch,Nmax, is about two times higher at the low flow rate due to the higher deposition efficiency.

An additional parameter characterizing the distribution of enhancement factors of the 1 nm particles inthe vicinity of the maximum value are the 90th and 80th percentiles of EFmax: (i) at the high flow rate, there aretwo patches over the 90th percentile (and 5 over the 80th percentile) in the case of the 0.1 mm patch size, and onlyone patch and five patches, respectively, for the 3 mm patch size; (ii) at the low flow rate, the correspondingvalues are: two patches each over the 90th and 80th percentiles for the 0.1 mm patch size, and one patch each incase of the 3 mm patch size.

The distributions of enhancement factors were also analyzed for 10 nm – 10 µm diameter unit densityparticles. In the size range of 10 nm – 200 nm the distributions of enhancement factors are similar to each otherat all input patch sizes and flow rates. However, for particles larger than 200 nm, the inhomogeneity increaseswith the particle size. Figure 7 and Figure 8 present the corresponding enhancement factor maxima distributionsfor ultrafine (10nm) and for large particles (10µm) at the 60 l min-1 flow rate.

In summary, the analysis of the distribution of enhancement factors has revealed that the degree ofinhomogeneity is rather high for all analyzed particle sizes and flow rates. As it is expected, the inhomogeneityis the smallest at the nanoparticle size at lowest flow rate. However it is interesting that there is a sharpmaximum of the enhancement factor maximum versus particle size function, at all flow rates.

P-3a-120

0 10 20 30 40 500

2000

4000

6000

8000

0.1 mm patch

No. of patches = 8832EF

max

= 52

EFmin

= 0

Enhancement factor

Freq

uenc

y

0 1 2 3 40

5

10

15

20

3 mm patch

No. of patches = 73EFmax = 4.7EFmin = 0

dp = 0.01µm Q

p = 7.5 l/min

Enhancement factor

Freq

uenc

y

0 2 4 6 80

2000

4000

6000

8000

0.1 mm patch

Nmax

= 9

Freq

uenc

y

No. of p. dep. on a patch0 50 100 150

0

5

10

15

20

3 mm patch

Nmax

= 166

Freq

uenc

y

No. of p. dep. on a patch

Figure 7. Distribution of enhancement factors for 0.1 and 3 mm patch sizes and number of particles deposited on thesepatches for the inhalation of 0.01 µm particles at a flow rate of Qp = 7.5 l min-1 in the a physiologically realisticbifurcation model ( EFmin and Nmax, see Fig.5.)

0 50 1000

2000

4000

6000

8000

0.1 mm patchNo. of patches = 8832

EFmax = 113EFmin = 0

Enhancement factor

Freq

uenc

y

0 5 10 150

10

20

30

40

503 mm patchNo. of patches = 73

EFmax

= 15EFmin = 0

Enhancement factor

Freq

uenc

y

0 5 10 15 200

2000

4000

6000

8000

0.1 mm patch

Nmax

= 22

Freq

uenc

y

No. of p. dep. on a patch0 200 400 600 800

0

10

20

30

40

50

3 mm patch

N max = 904

dp = 10µm Q

p = 7.5 l/min

Freq

uenc

y

No. of p. dep. on a patch

Figure 8. Distribution of enhancement factors for 0.1 and 3 mm patch sizes and number of particles deposited on thesepatches for the inhalation of 10 µm particles at a flow rate of Qp = 7.5 l min-1 in the a physiologically realisticbifurcation model ( EFmin and Nmax, see Fig.5.)

P-3a-120

SUMMARY AND CONCLUSIONComputed air velocity fields and particle trajectories demonstrated the significant role of secondary

flows for particle deposition. In the case of inspiration, areas of enhanced deposition were formed primarily inthe vicinity of the carinal ridge or at the inner sides of the daughter branches. The sizes of these deposition hotspots depend on particle size, flow rate and bifurcation geometry. For example, enhanced deposition areas forlarge particles were much more intense than those found for ultrafine particles. The computed local depositionenhancement factors exhibited strong local inhomogeneities for all particle sizes and flow rates considered here(except for nanometer-sized particles at very low flow rates). The maximum values of the enhancement factorsin a bifurcation strongly increased with decreasing patch size, thus illustrating the high degree ofinhomogeneities of the deposition patterns in upper human airways. The computed maximum enhancementfactors were as high as several hundreds, suggesting that epithelial cells located at these sites will receivemassive doses relative to the assumption of a uniform nuclide distribution.

Since the prevalent philosophy of inhalation risk assessment is based upon the assumption of a uniformparticle deposition pattern, the incorporation of deposition enhancement factors within airway bifurcations willprovide more realistic estimates of radiation doses and resulting carcinogenic risk. Such microdosimetricconsiderations are particularly important for inhaled alpha-emitting radionuclides, such as the short-lived radonprogeny, where cellular doses are strongly correlated with the emission sites of alpha particles.

Regarding the effect of local particle deposition on the resulting lung cancer risk, one has to bear inmind that local deposition enhancement factors derived in this paper refer to initial particle deposition patterns.There are two effects reducing the degree of inhomogeneity of the initial deposition patterns: (i) Upon deposition,particles are subsequently cleared from the initial deposition sites by mucociliary action. However, mucustransport is significantly impaired at the carinal ridge (Hofmann et al., 1990), i.e., at those sites where themaximum deposition enhancement could be found. Thus for short-term responses (e.g. in the time range of aboutone hour), such as the decay of the short-lived radon progeny, mucociliary clearance may only slightly reducemaximum enhancement factors. (ii) Due to the isotropic emission of alpha particles on the surface of bronchialairways, the near wall dose primarily reflects the nonuniformity of the surface activities, while the far wall doseis only slightly affected by the activity pattern. Assuming that near wall dose and far wall dose contributions areapproximately equal (Harley and Pasternack 1972), about half of the exposed cells experience the effect of localenhancement factors.

In conclusion, knowledge of the degree of inhomogeneity of particle deposition patterns will allow amore reliable assessment of the carcinogenic risk of inhaled radon progeny. The results presented in this paperdemonstrate that airway cells located at the carinal ridge or at the inner sides of the two daughter branches mayreceive massive local doses, which can be up to two orders of magnitude larger than the average dose for a givenbifurcation. In current dosimetric models, the implicit assumption of a uniform deposition on bronchial airwaysurfaces is equivalent to the notion that all epithelial cells will receive the same average dose. In contrast, wepropose to replace the average dose concept by (i) the fraction of the surface without any particles beingdeposited there (i.e., the dose is zero), and (ii) the remaining fraction, which will have many more particles thanindicated by the average deposition density. Since it has recently been suggested that the number of multiplecellular hits may play a crucial role in the extrapolation of lung cancer risk from occuptional to domesticenvironments (Brenner 1992), maximum enhancement factors may serve as a measure of the probability ofmultiple hits.The developing measuring techniques (e.g. Czitrovszy et al., 1996,1998, Jani et al., 1996,1998) will may make itpossible to compare some of our computed results with experimental findings in the near future.

ACKNOWLEDGMENTSThis research was supported by: OMFB-01790/98 Hungarian Contract, Hungarian-Austrian TéT

Contract: A-8/98, Hungarian OTKA T 030571 Project, and CEC Contract No. FI4P-CT95-0025.

REFERENCES1. I.Balásházy, W.Hofmann, and T.B.Martonen, Inspiratory particle deposition in airway bifurcation models. J.

Aerosol Sci. 22, 15-30 (1991).2. I.Balásházy and W.Hofmann, Particle deposition in airway bifurcations: I. Inspiratory flow. J. Aerosol Sci.

24, 745-772 (1993a).3. I.Balásházy and W.Hofmann, Particle deposition in airway bifurcations: II. Expiratory flow. J. Aerosol Sci.

24, 773-786 (1993b).4. I.Balásházy and W.Hofmann, Deposition of aerosols in asymmetric airway bifurcations. J. Aerosol Sci. 26,

273-292 (1995).

P-3a-120

5. I.Balásházy, Simulation of particle trajectories in bifurcating tubes. J. Comput. Phys. 110, 11-22 (1994).6. I.Balásházy, T.Heistracher and W.Hofmann, Deposition enhancement factors for inhaled radon decay

products in bronchial airway bifurcations. J. Aerosol Sci. 28, S597-S598 (1997).7. I.Balásházy, W.Hofmann and T.Heistracher, Computation of local enhancement factors for the

quantification of particle deposition patterns in airway bifurcations. J. Aerosol Sci. 30(2), 185-203(1999).

8. D.J. Brenner, Radon: current challenges in cellular radiobiology. Int. J. Radiat. Biol. 61, 3-13 (1992).9. B.S.Cohen, N.H.Harley, R.B.Schlesinger and M.Lippmann, Nonuniform particle deposition on

tracheobronchial airways: Implications for lung dosimetry. Ann. Occup. Hyg. 32(Sl), 1045-1053 (1988).10. D.J.Crawford-Brown and W.Hofmann, The role of variability of dose in dose-response relationships for

alpha emitting radionuclides. Radiat. Prot. Dosim. 28, 283-290 (1989).11. D.J.Crawford-Brown and W.Hofmann, The testing of radiobiological models of radon carcinogenesis

needed for in vitro to in vivo extrapolations. Environ. Int. 22(Sl), 985-994 (1996).12. A.Czitrovszky, P.L.Csonka, P.Jani, A.Ringelhann and J.Bobvos, Comparison of different measurement

methods of airborne dust pollution within the city of Budapest. J. Aerosol Sci. 27, 19-20 (1996).13. A.Czitrovszky, A.Nagy, T.Mosoni, P.Jani, K.Bodnár and Á.Illés, A new sizing method for liquid-borne

particles with high dynamic range. SPIE 3573, 225-229 (1998).14. L.Gradon and D.Orlicki, Deposition of inhaled aerosol particles in a generation of the tracheo-bronchial

tree. J. Aerosol Sci. 21, 3-19 (1997).15. N.H.Harley and B.S.Pasternack, Alpha absorption measurements applied to lung dose from radon daughters.

Health Phys. 23, 771-782 (1972).16. T.Heistracher and W.Hofmann, Physiologically realistic models of bronchial airway bifurcations. J. Aerosol

Sci. 26, 497-509 (1995).17. T.Heistracher, I.Balásházy and W.Hofmann, The significance of secondary flows for localized particle

deposition in bronchial airway bifurcations. J. Aerosol Sci. 26(Sl), 615-616 (1995).18. W.Hofmann, T.B.Martonen and M.G.Ménache, A dosimetric model for localised radon progeny

accumulations at tracheobronchial bifurcations. Radiat. Prot. Dosim. 30, 245-259, (1990).19. W.Hofmann, G.Mainelis, A.Mohamed, I.Balásházy, J.Vaupotic and I.Kobal, Comparison of different

modeling approaches in current lung dosimetry models. Environ. Int. 22(Sl), 965-976,(1996a).20. W.Hofmann, I.Balásházy, T.Heistracher and L.Koblinger, The significance of particle deposition patterns in

bronchial airway bifurcations for extrapolation modeling. Aerosol Sci. Technol. 25, 305-327 (1996b).21. International Commission on Radiological Protection (ICRP), Human respiratory tract model for

radiological protection. Oxford: Pergamon Press; ICRP Publication 66, Ann. ICRP 24 (1994).22. P.Jani, A.Nagy and A.Czitrovszky, Aerosol particle size determination using a photon correlation laser

Doppler anemometer. J. Aerosol Sci. 27 531-532 (1996).23. P.Jani, A.Nagy and A.Czitrovszky . Single nanoparticle size measurement algorithm using photon

correlation techniques. J. Aerosol Sci. 29, 419-420 (1998).24. C.S.Kim and D.M.Fisher, Deposition of ultrafine particles in the bifurcating airway models. In: Flagan,

R.C., ed. Abstracts. 4th International Aerosol Conference. Vol. 2. Cincinnati, OH, American Association forAerosol Research; 888-889 (1994).

25. A.A.Kinsara, S.K.Loyolka, R.V.Tompson, W.H.Miller and R.F.Holub, Deposition patterns of molecularphase radon progeny (218Po) in lung bifurcations. Health. Phys. 68, 371-382 (1995).

26. A.Li and G.Ahmadi, Computer simulation of particle deposition in the upper tacheobronchial tree. AerosolSci. Technol. 23, 201-223 (1995).

27. D.Martin and W.Jacobi, Diffusion deposition of small-sized particles in the bronchial tree. Health Phys. 23,23-29 (1972).

28. T.B.Martonen, W.Hofmann and J.E.Lowe, Cigarette smoke and lung cancer. Health Phys. 52, 213-217(1987).

29. T.B.Martonen, Aerosol therapy implications of particle deposition patterns in simulated human airways. J.Aerosol Med. 4, 25-40 (1991).

30. National Research Council (NRC), Comparative dosimetry of radon in mines and homes. Washington, DC:National Academy Press (1991).

31. R.B.Schlesinger and M.Lippmann, Selective particle deposition and bronchogenic carcinoma. Environ. Res.15, 424-431 (1978).

32. M.Shimo and A.Ohashi, Deposition of unattached RaA atoms in the tracheobronchial region. In: Cross,F.T., ed. Indoor radon and lung cancer: reality or myth. Part 1. Richland, WA: Battelle Press, 201-210(1993).

33. H.Spencer, Pathology of the lung. 3rd ed. New York: Pergamon Press (1977).34. J.E.Trosko, Role of low-level ionizing radiation in multi-step carcinogenic process. Health Phys. 70, 812-

822 (1996).

P-3a-120

35. E.R.Weibel, Morphometry of the human lung. Berlin: Springer (1963).