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Particle Transport and Deposition: Basic Physics of Particle Kinetics

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Abstract

The human body interacts with the environment in many different ways. The lungs interact with the external environment through breathing. The enormously large surface area of the lung with its extremely thin air‐blood barrier is exposed to particles suspended in the inhaled air. The particle‐lung interaction may cause deleterious effects on health if the inhaled pollutant aerosols are toxic. Conversely, this interaction can be beneficial for disease treatment if the inhaled particles are therapeutic aerosolized drugs. In either case, an accurate estimation of dose and sites of deposition in the respiratory tract is fundamental to understanding subsequent biological response, and the basic physics of particle motion and engineering knowledge needed to understand these subjects is the topic of this article. A large portion of this article deals with three fundamental areas necessary to the understanding of particle transport and deposition in the respiratory tract. These are: (i) the physical characteristics of particles, (ii) particle behavior in gas flow, and (iii) gas‐flow patterns in the respiratory tract. Other areas, such as particle transport in the developing lung and in the diseased lung are also considered. The article concludes with a summary and a brief discussion of areas of future research. © 2013 American Physiological Society. Compr Physiol 3:1437‐1471, 2013.

Keywords: Pulmonary embolism; Chronic thromboembolic pulmonary hypertension; Pulmonary arterial hypertension; Pulmonary arteriovenous malformations; Pulmonary vascular resistance

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Figure 1. Figure 1. A Skewed particle size distribution. Replotted, with permission, after Silverman et al. (1971) (284).
Figure 2. Figure 2. Lognormal particle size distribution. Replotted, with permission, after Silverman et al. (1971) (284).
Figure 3. Figure 3. Cumulative lognormal size distribution. Replotted, with permission, after Silverman et al. (1971) (284).
Figure 4. Figure 4. Cumulative particle size distribution plotted on logarithmic probability graph paper. The spread of the distribution of Fig. 2 or the geometric standard deviation (σg), is defined as the ratio of (84.13% size)/(50% size) or (50% size)/(15.87% size). Replotted, with permission, after Silverman et al. (1971) (284).
Figure 5. Figure 5. Smoluchowski's Brownian coagulation. Sphere of influence around test (fixed) particle of radius R in collision with moving particles of the same radius R. Once particles collide, perfect adhesion is assumed. Modified, with permission, after Probstein (1989) (261).
Figure 6. Figure 6. Total particle deposition in the human respiratory tract and corresponding fractions in the extrathoracic, bronchial, and alveolar region according to ICRP Publication 66 (1994) (153). Data are shown for two different breathing scenarios: exposure during sleeping (nose breathing) and exposure during heavy exercise (mouth breathing). Adapted, with permission, from Oberdörster, et al. (2007) (239).
Figure 7. Figure 7. Alevolar duct. Left: scanning electron micrograph of an alveolar duct surrounded by alveoli. From Gehr et al. (1978) (114), by permission. Middle: an axisymmetric alveolated duct model [i.e., a computationally two‐dimensional but physically three‐dimensional (3D) model] used in Tsuda et al. (1994a,b) (307,308). Right: rhythmically expanding and contracting 3D alveolar duct model used in Haber et al. [2000 (125), 2003 (127)].
Figure 8. Figure 8. Three‐dimensional reconstruction of the parenchyma tissue imaged by synchrotron X‐ray tomography. Upper: top view. Lower: side angle view. Adapted, with permission, from Tsuda et al. (2008a) (309).
Figure 9. Figure 9. Three‐dimensional finite element shell model of an alveolus viewed from different angles. Top: region of interest. Middle: top view (left); side view (middle); bottom view (right). Bottom: alveolar inside views (left and right). Adapted, with permission, from Tsuda et al. (2008) (309).
Figure 10. Figure 10. Heyder et al.'s seminal work (1988) (147). The presence of kinematical irreversibility in the acinus was demonstrated experimentally.
Figure 11. Figure 11. Alveolar recirculation. Top: computational predictions. Top Left: idealized model [modified, with permission, from Tsuda et al. (1995) (310)]. Top middle and right: synchrotron‐based realistic alveolar model. Adpated, with permission, from Filipovic et al. (2010) (95); Bottom: experimental observation of rotational flow patterns in the alveoli of excised rat lung. Bar = 100 μm. Adapted, with permission, from Tsuda et al. (2002) (315).
Figure 12. Figure 12. Poincaré sections of particle transport; each color represents a different trajectory. Left: stokes flow in a cavity—no perturbation present and seven particle paths shown. Right: the addition of a perturbation by wall motion creates islands in a sea of chaos; eight more particle paths have been added to the original seven for further detail. Modified, with permission, from Tsuda, Laine‐Pearson & Hydon (2011) (313).
Figure 13. Figure 13. Streamlines at peak inspiration (left) and the Poincaré map (right) on the symmetry mid‐plane of a hemispherical alveolar model with rhythmically expanding walls. The streamlines exhibit recirculations and a stagnation saddle point near the alveolar entrance. The Poincaré map shows that regions of stochasticity seem to appear bounded by quasiperiodic surfaces. Adapted, with permission, from Haber et al. (2000) (125).
Figure 14. Figure 14. Poincaré sections for a flow with Re = 1.0, showing the presence of chaos even in an alveolus with stationary walls. Adapted, with permission, from Henry et al. (2009) (144).
Figure 15. Figure 15. Complex convoluted “stretch‐and‐fold” flow patterns on the cross‐sections of large airways of rat lung. Adapted, with permission, from Tsuda, et al. (2002) (315).
Figure 16. Figure 16. Typical mixing pattern of two colors observed in ∼200μm acinar airway of adult rats after N = 1, 2, 3, and 4 cycles. Bar = 100 μm. Adapted, with permission, from Tsuda, et al. (2002) (315).
Figure 17. Figure 17. Comparison of Brownian tracer mixing between a system with pure diffusion and a system with stretch and fold convection and diffusion. (Top) Schematic view of these two systems. (Middle left) The slowly increasing length scale for mixing (δ) in pure diffusion. (Middle right) With stretch and fold convection, δ also increases slowly (but approaches an asymptotic value); by contrast, the folding length scale, w, decreases exponentially rapidly. (Bottom) Representation of the evolving extent of mixing corresponding to diffusion alone and to diffusion coupled with stretch and fold convection. At the time when the two length scales are comparable (vertical dotted line), there is sharp jump in mixing (entropy burst). [Adapted, with permission, from Tsuda et al., 2002 (315).]
Figure 18. Figure 18. Top: acinar structure of the immature lung of a 1‐day‐old rat (left) and the lung of a 21‐day‐old rat whose alveolar shape is nearly fully developed, but small in size (right) [adapted, with permission, from Schittny & Burri, 2008 (273)]. tb: terminal bronchioles, S: saccules, ad: alveolar ducts, arrows: secondary septa. Bottom: schematics of predicted patterns of particle‐laden inhaled airflow (shown in blue).
Figure 19. Figure 19. Formation of droplets at the level of small airways. At Ca above the critical values, a meniscus traveling along the airway thins and then disintegrates into small droplets. Re = 0.67, Ca = 1. See Malasheko et al. (2009) (214) for details.
Figure 20. Figure 20. A demonstration of multimodal imaging techniques: combined synchrotron radiation‐based X‐ray tomographic microscopy (SRXTM)‐based skeletonization technique, which locates an alveolus of interest within the acinar tree (129) and high‐resolution transmission electron microscopy (TEM), which is necessary to visualize nanosize particles in the alveolar structure. The concept is illustrated in this figure by the visualization of 700 nm gold particles (as surrogates for nanosize particles) instilled into an adult rat lung. First, a tissue sample was imaged by SRXTM and three‐dimensional (3D) reconstruction of the acinus was performed (315). Then, by using skeletonization techniques (129), an alveolus containing gold particles on its septal wall was identified in the distal region of the acinus (Panel A). The same particles were also identified in one section of a 3D stack of SRXTM images (Panel B). Using the registered coordinates of this region of interest, serial sectioning was performed in that area. The resulting TEM images of that alveolus and the gold particles located in it are shown in Panel C. A higher magnification of the regions A and B in Panel C are shown in Panel D and E, respectively. From Haberthür et al. (2009b) (130), Schittny et al. (2010) (274).


Figure 1. A Skewed particle size distribution. Replotted, with permission, after Silverman et al. (1971) (284).


Figure 2. Lognormal particle size distribution. Replotted, with permission, after Silverman et al. (1971) (284).


Figure 3. Cumulative lognormal size distribution. Replotted, with permission, after Silverman et al. (1971) (284).


Figure 4. Cumulative particle size distribution plotted on logarithmic probability graph paper. The spread of the distribution of Fig. 2 or the geometric standard deviation (σg), is defined as the ratio of (84.13% size)/(50% size) or (50% size)/(15.87% size). Replotted, with permission, after Silverman et al. (1971) (284).


Figure 5. Smoluchowski's Brownian coagulation. Sphere of influence around test (fixed) particle of radius R in collision with moving particles of the same radius R. Once particles collide, perfect adhesion is assumed. Modified, with permission, after Probstein (1989) (261).


Figure 6. Total particle deposition in the human respiratory tract and corresponding fractions in the extrathoracic, bronchial, and alveolar region according to ICRP Publication 66 (1994) (153). Data are shown for two different breathing scenarios: exposure during sleeping (nose breathing) and exposure during heavy exercise (mouth breathing). Adapted, with permission, from Oberdörster, et al. (2007) (239).


Figure 7. Alevolar duct. Left: scanning electron micrograph of an alveolar duct surrounded by alveoli. From Gehr et al. (1978) (114), by permission. Middle: an axisymmetric alveolated duct model [i.e., a computationally two‐dimensional but physically three‐dimensional (3D) model] used in Tsuda et al. (1994a,b) (307,308). Right: rhythmically expanding and contracting 3D alveolar duct model used in Haber et al. [2000 (125), 2003 (127)].


Figure 8. Three‐dimensional reconstruction of the parenchyma tissue imaged by synchrotron X‐ray tomography. Upper: top view. Lower: side angle view. Adapted, with permission, from Tsuda et al. (2008a) (309).


Figure 9. Three‐dimensional finite element shell model of an alveolus viewed from different angles. Top: region of interest. Middle: top view (left); side view (middle); bottom view (right). Bottom: alveolar inside views (left and right). Adapted, with permission, from Tsuda et al. (2008) (309).


Figure 10. Heyder et al.'s seminal work (1988) (147). The presence of kinematical irreversibility in the acinus was demonstrated experimentally.


Figure 11. Alveolar recirculation. Top: computational predictions. Top Left: idealized model [modified, with permission, from Tsuda et al. (1995) (310)]. Top middle and right: synchrotron‐based realistic alveolar model. Adpated, with permission, from Filipovic et al. (2010) (95); Bottom: experimental observation of rotational flow patterns in the alveoli of excised rat lung. Bar = 100 μm. Adapted, with permission, from Tsuda et al. (2002) (315).


Figure 12. Poincaré sections of particle transport; each color represents a different trajectory. Left: stokes flow in a cavity—no perturbation present and seven particle paths shown. Right: the addition of a perturbation by wall motion creates islands in a sea of chaos; eight more particle paths have been added to the original seven for further detail. Modified, with permission, from Tsuda, Laine‐Pearson & Hydon (2011) (313).


Figure 13. Streamlines at peak inspiration (left) and the Poincaré map (right) on the symmetry mid‐plane of a hemispherical alveolar model with rhythmically expanding walls. The streamlines exhibit recirculations and a stagnation saddle point near the alveolar entrance. The Poincaré map shows that regions of stochasticity seem to appear bounded by quasiperiodic surfaces. Adapted, with permission, from Haber et al. (2000) (125).


Figure 14. Poincaré sections for a flow with Re = 1.0, showing the presence of chaos even in an alveolus with stationary walls. Adapted, with permission, from Henry et al. (2009) (144).


Figure 15. Complex convoluted “stretch‐and‐fold” flow patterns on the cross‐sections of large airways of rat lung. Adapted, with permission, from Tsuda, et al. (2002) (315).


Figure 16. Typical mixing pattern of two colors observed in ∼200μm acinar airway of adult rats after N = 1, 2, 3, and 4 cycles. Bar = 100 μm. Adapted, with permission, from Tsuda, et al. (2002) (315).


Figure 17. Comparison of Brownian tracer mixing between a system with pure diffusion and a system with stretch and fold convection and diffusion. (Top) Schematic view of these two systems. (Middle left) The slowly increasing length scale for mixing (δ) in pure diffusion. (Middle right) With stretch and fold convection, δ also increases slowly (but approaches an asymptotic value); by contrast, the folding length scale, w, decreases exponentially rapidly. (Bottom) Representation of the evolving extent of mixing corresponding to diffusion alone and to diffusion coupled with stretch and fold convection. At the time when the two length scales are comparable (vertical dotted line), there is sharp jump in mixing (entropy burst). [Adapted, with permission, from Tsuda et al., 2002 (315).]


Figure 18. Top: acinar structure of the immature lung of a 1‐day‐old rat (left) and the lung of a 21‐day‐old rat whose alveolar shape is nearly fully developed, but small in size (right) [adapted, with permission, from Schittny & Burri, 2008 (273)]. tb: terminal bronchioles, S: saccules, ad: alveolar ducts, arrows: secondary septa. Bottom: schematics of predicted patterns of particle‐laden inhaled airflow (shown in blue).


Figure 19. Formation of droplets at the level of small airways. At Ca above the critical values, a meniscus traveling along the airway thins and then disintegrates into small droplets. Re = 0.67, Ca = 1. See Malasheko et al. (2009) (214) for details.


Figure 20. A demonstration of multimodal imaging techniques: combined synchrotron radiation‐based X‐ray tomographic microscopy (SRXTM)‐based skeletonization technique, which locates an alveolus of interest within the acinar tree (129) and high‐resolution transmission electron microscopy (TEM), which is necessary to visualize nanosize particles in the alveolar structure. The concept is illustrated in this figure by the visualization of 700 nm gold particles (as surrogates for nanosize particles) instilled into an adult rat lung. First, a tissue sample was imaged by SRXTM and three‐dimensional (3D) reconstruction of the acinus was performed (315). Then, by using skeletonization techniques (129), an alveolus containing gold particles on its septal wall was identified in the distal region of the acinus (Panel A). The same particles were also identified in one section of a 3D stack of SRXTM images (Panel B). Using the registered coordinates of this region of interest, serial sectioning was performed in that area. The resulting TEM images of that alveolus and the gold particles located in it are shown in Panel C. A higher magnification of the regions A and B in Panel C are shown in Panel D and E, respectively. From Haberthür et al. (2009b) (130), Schittny et al. (2010) (274).
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Akira Tsuda, Frank S. Henry, James P. Butler. Particle Transport and Deposition: Basic Physics of Particle Kinetics. Compr Physiol 2013, 3: 1437-1471. doi: 10.1002/cphy.c100085