Modeling Deposition of Inhaled Particles - Aerosols: Measurement, Dosimetry, and Health Effects - page 88

diameter. The model, which was based on previous empirical models, 20 considered data from a wide
variety of deposition experiments; theoretical relationships were used for particle sizes for which no
data were available. The empirical ICRP respiratory tract dosimetry model 21 was developed by the
International Commission on Radiological Protection. This model can be used to estimate regional
deposition in the lungs as a function of particle characteristics and ventilatory conditions via a
number of algebraic equations based on the work of Rudolf et al. 20,22-24 Other empirical deposition
models have been developed for the head, 25,26 TB, 25-27 and alveolar 28 regions, and the entire lung. 29
Empirical models have been combined with pharmacokinetic models, 30 and modeling predic-
tions derived from empirical relationships have been used to validate and conirm results from
mechanistic deposition models. 9,31
5.3.1.2 Deterministic Models
Deterministic models are developed using an engineering approach to the simulation of air and par-
ticle motion. In deterministic models, simplifying assumptions about airway geometries and airlow
conditions are made in order to derive expressions for particle trajectories from particle momentum
equations. Such models vary in complexity; deterministic modeling efforts may range from simple
analytical expressions that can be solved algebraically to systems of nonlinear ordinary or partial
differential equations. In addition, deterministic models may describe particle deposition in a single
airway, a bifurcation, or a complete branching network of respiratory airways.
Martonen 7,32 has developed deterministic models of particle deposition in human lungs. These
models were formulated by modeling the airways of the lung as either straight or curved smooth-
walled tubes, and assuming a ixed (laminar or turbulent) velocity proile in each airway generation.
Other deterministic models of particle deposition in the respiratory system have been developed by
Gradón and Orlicki, 33 Yu et al., 34,35 Egan and Nixon, 36 Anjilvel and Asgharian, 37 Asgharian et al., 38
Phalen et al., 39,40 and Choi and Kim. 41
In deterministic models, the simulated particle deposition patterns are determined solely by the
input parameters to the model. Therefore, for any set of model input parameters, the same deposi-
tion pattern is found. This is not necessarily true of the next class of models, stochastic models.
5.3.1.3 Stochastic Models
Models of particle deposition are categorized as stochastic if the morphological description of the
lung is considered to vary in a random manner, within prescribed limits. The concept of stochastic
deposition modeling, irst introduced by Koblinger and Hofmann, 42 has been used by Hofmann
and coworkers to simulate aerosol particle deposition in both human 42-45 and rat 46-48 lungs. Radon
progeny, 49 cigarette smoke, 50 and diesel exhaust 51 deposition have been speciically addressed.
In stochastic deposition modeling, the morphometric parameters describing the geometry of the
lung are not given constant values, but are described instead by statistical (e.g., lognormal) distribu-
tions, which are in turn based on experimental measurements. These morphometric parameters may
include airway diameters, lengths, and branching angles. Other, less obvious, parameters (such as
ratios of parent airway cross-sectional area to the sum of daughter airway cross-sectional areas) may
also be stochastically deined. Then, as each modeled particle enters the lungs, its pathway is deter-
mined by a random selection of values for each of the required morphometric parameters within
their corresponding lognormal distribution. For example, the properties of the daughter airways are
randomly assigned for each bifurcation. 52 The average resulting deposition in each airway is then
calculated from the behavior of the entire ensemble of particles.
5.3.1.4 Computational Fluid-Particle Dynamics
Computational luid-particle dynamics (CFPD) refers to the study of the motion of particles as
determined by CFD simulations. In CFPD studies of particle deposition, CFD solutions of luid
velocities are coupled with the solution of particle trajectory equations developed from Newton's
Second Law. 53 Particles are deposited when their trajectory intersects with an airway wall.