Respiratory Deposition of Fibers in the Non-Inertial Regime—Development and Application of a Semi-Analytical Model

Abstract

A semi-analytical model describing the motion of fibrous particles ranging from nano-to micro scale was developed, and some important differences in respiratory tract transport and deposition between fibrous particles of various sizes and shapes were elucidated. The aim of this work was to gain information regarding health risks associated with inhalation exposure to small fibers such as carbon nanotubes. The model, however, is general in the sense that it can be applied to arbitrary flows and geometries at small fiber Stokes and Reynolds numbers. Deposition due to gravitational settling, Brownian motion and interception was considered, and results were presented for steady, laminar, fully developed parabolic flow in straight airways. Regarding particle size, our model shows that decrease in particle size leads to reduced efficiency of sedimentation but increased intensity of Brownian diffusion, as expected. We studied the effects due to particle shape alone by varying the aspect ratios and diameters of the microfibers simultaneously, such that the effect of particle mass does not come into play. Our model suggests that deposition both due to gravitational settling and Brownian diffusion decreases with increased fiber aspect ratio. Regarding the combined effect of fiber size and shape, our results suggest that for particles with elongated shape the probability of reaching the vulnerable gas-exchange region in the deep lung is highest for particles with diameters in the size range 10-100 nm and lengths of several micrometers. Note that the popular multi-walled carbon nanotubes fall into this size-range.

Modeling Transport and Deposition Efficiency of Oblate and Prolate Nano- and Micro-particles in a Virtual Model of the Human Airway

“…Comparing the results between the two rather different approaches given in Refs. [17] and [19], a good agreement is found. The Fokker-Planck equation for nonspherical particles was considered for fully developed pipe flow by Asgharian and Gradon [20].…”

“…The present study is a continuation of the previous work [17] in which particle tracking of prolate spheroids in different generations of the human lung was considered. Here, using the same method, we consider the particle tracking of the other type of spheroids called oblate spheroids.…”

“…For a prolate spheroid, d ? and d k are the Stokes diameters oriented perpendicular and parallel to the direction of motion, respectively, and are given by [17] Fig. 1 A representative sketch of the geometry used in the simulations with the initial position for an oblate and a prolate particle in the single particle runs Fig.…”

“…To extend the validity for the drag force from small Knudsen numbers Kn to large Kn, the Cunningham factors are applied with an adjusted radii as suggested by Dahneke [24]. The Cunningham factors for prolate spheroids are given by H€ ogberg et al [17]. Using the replacement b !…”

“…The error of the method when considering stochastic differential equations of this kind is of order O N À1=2 ð Þ [16]. This method has been successfully applied to derive the deposition of prolate micro-and nano-particles for a fully developed pipe flow [17]. The second approach is to utilize the Fokker-Planck equation to find solutions for the probability density function [16].…”