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1 School of Engineering, City University, London EC1V 0HB, United Kingdom; and 2 Physiology Program, Harvard School of Public Health, Boston, Massachusetts 02115
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Current theories describe aerosol transport in the lung as a dispersive (diffusion-like) process, characterized by an effective diffusion coefficient in the context of reversible alveolar flow. Our recent experimental data, however, question the validity of these basic assumptions. In this study, we describe the behavior of fluid particles (or bolus) in a realistic, numerical, alveolated duct model with rhythmically expanding walls. We found acinar flow exhibiting multiple saddle points, characteristic of chaotic flow, resulting in substantial flow irreversibility. Computations of axial variance of bolus spreading indicate that the growth of the variance with respect to time is faster than linear, a finding inconsistent with dispersion theory. Lateral behavior of the bolus shows fine-scale, stretch-and-fold striations, exhibiting fractal-like patterns with a fractal dimension of 1.2, which compares well with the fractal dimension of 1.1 observed in our experimental studies performed with rat lungs. We conclude that kinematic irreversibility of acinar flow due to chaotic flow may be the dominant mechanism of aerosol transport deep in the lungs.
lung; deposition; chaos; fractal; particulate pollution
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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CONVECTION AND DIFFUSION ARE the two major mechanisms of mass transport for gas molecules and submicrometer aerosols in the pulmonary acinus. For gas transport, diffusion dominates at distances comparable to acinar size and over times comparable to breathing frequencies, and, therefore, theories based on diffusion are probably adequate. By contrast, the particle diffusivity of submicrometer-sized aerosols is very small, and, therefore, acinar convection, even though it is in a quasi-Stokes viscous flow regime (26), is correspondingly more important and may dominate aerosol transport. However, current theories describe aerosol transport as a dispersion (diffusion-like) process (e.g., Refs. 7, 10, 11, 19, 34). These theories are based on the following two key assumptions: 1) acinar flow is basically kinematically reversible (i.e., during expiration each fluid particle retraces the path taken during inspiration) (9, 45), and 2) all processes (including the coupling of Brownian diffusivity with the convective flow field and any kinematic irreversibility that may be present) that contribute to irreversible aerosol bolus spreading can be characterized as axial mixing with an effective longitudinal diffusivity (Deff). The first assumption is based on classical fluid mechanics (36), and the second assumption is substantially equivalent to Taylor dispersion (35). As most aerosol studies are currently interpreted in the framework of these dispersion theories, experimental data are often reduced and analyzed through the use of some Deff (e.g., Ref. 30), and many of the recent theoretical research efforts are focused on refining Deff for better fit to experimental data, through which new insights into acinar transport mechanisms are sought (e.g., Ref. 6).
Our laboratory's recent findings (37-41), as well as those of others (8, 18), however, have questioned the validity of the basic assumptions that formed the basis of the dispersive theories. We have demonstrated that, because of the peculiar geometry of the alveolated duct and its time-dependent motion associated with tidal breathing, under certain conditions, alveolar flow can be chaotic (16, 40). As a consequence, acinar flow can be kinematically irreversible, even though it is a low-Reynolds number viscous flow, and lung expansion and contraction are approximately self-similar and reversible (1, 13, 14, 24, 46). These findings are supported by a discovery in fluid mechanics that chaotic mixing can occur even in a viscous flow (2, 25). We have also developed a theoretical analysis (5) to show that chaotic mixing is radically different from diffusive mixing. In chaotic acinar flow, a tracer bolus undergoes cyclic stretch-and-fold deformation, resulting in the induction of finer and finer scales in tracer profile with repeated breaths. This process soon reaches a critical moment at which the lateral distance between adjacent tracer striations becomes comparable to the diffusion distance. A burst of mixing occurs at this moment, and mixing is quickly completed.
The objectives of the studies reported here are, through numerical simulations of bolus experiments, to provide key data showing that the behavior of particles in a rhythmically expanding, multiply alveolated duct flow, with a saddle point and associated vortexes in each air pocket, does not satisfy the fundamental assumptions of any dispersion theory and that the shape of a tracer bolus evolves to a stretch-and-fold fractallike pattern, similar to those found in flow visualization experiments in rat lungs (Tsuda A, Butler JP, and Rogers RA, unpublished observations). The results suggest that 1) kinematic irreversibility is the origin of aerosol transport, 2) axial transport cannot be characterizable by an effective diffusivity, and 3) fractal trajectories can occur in most of the alveoli in the acinar tree. The alternative mechanism of aerosol transport that we propose here may, in fact, be the dominant mechanism determining deposition of submicrometer particles deep in the lung.
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METHODS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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In a previous investigation (40), we used the
single-alveolus model to explore the basic physics operating in a
viscous flow subjected to cyclic alveolar wall motion. The alveolus
model used in the present investigation is also axisymmetric but
comprises a central circular channel around which are placed nine tori, equispaced in the axial direction (Fig.
1A). Details of a typical cell
are given in Fig. 2. The duct and
alveolar walls move in a perfectly kinematically reversible, simple
sinusoidal manner with a specific volume excursion C of 25%
[C = (Vmax 
Vmin)/Vmin, where Vmax and
Vmin are the maximum and minimum volumes of the model,
respectively] and a cycle period T of 3 s. These
correspond roughly to typical tidal ventilation and respiratory period
in human. Any length scale L of the model changes as
L(t) = 
/T, and K = (
1)/( + 1), where 
/R
is the volume flow rate and RD is the
duct radius. The root mean square (RMS) Reynolds number
ReRMS = URMS
, where URMS is the RMS U and equals
Umax/
is the kinematic viscosity. ReRMS ranges
from 0.006 to 0.728 in the alveolated region of the model. Using a
closed-end duct has the added advantage of avoiding the difficulty of
defining appropriate boundary conditions at the downstream boundary of
the alveolated section. Typically, LD/RD is >100, and,
hence, it can be assumed that the end of the closed-end duct was
sufficiently far from the downstream boundary of the alveolated section
so as not to affect the flow across this boundary adversely. As a
further refinement to the original model, the sharp corner at the
intersection between the alveolus and the duct is replaced by a more
natural circular section. For comparative purposes, two other cases are
also simulated. One is the flow in an isolated alveolus model (Fig.
1B), similar to that used in Tsuda et al. (40),
and the other is the flow in a nonalveolated, rhythmically expanding
straight tube (Fig. 1C).
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The flow field is defined by the full, incompressible Navier-Stokes equations, which are solved numerically on a multiblock, body-fitted moving grid using the finite volume code CFX-4 (CFDS, AEA Technology, Harwell, UK). This general-purpose, pressure-correction code offers a variety of discretization schemes and solution techniques. In these calculations, central differencing is used to model the convection terms, and the implicit backward Euler method is used to advance the solution in time. A combination of the SIMPLEC pressure-correction method (44) and the Rhie-Chow (28) algorithm to eliminate pressure oscillations on the collocated gird (12) is used in the formulation of the discrete equations. Stone's method (33) is used to solve the discrete velocity equations, and the method of preconditioned conjugate gradients (see, for example, Ref. 22) is used to solve the discrete pressure correction equation. At the inlet, a constant-pressure boundary is defined. The value of the pressure on this boundary is set arbitrarily to zero, and, as for incompressible flow, only the pressure gradient is of importance. The no-slip condition is enforced on all solid surfaces, which, in the case of moving walls, means that the fluid matches the wall velocity at the fluid-wall interface. Tests were carried out to ensure that the solutions are grid independent and converged. For example, increasing the number of grid cells by 30% above that which was eventually used produces an increase of only 0.16% in the predicted maximum velocity. The final 73-block grid had a total of 38,349 active cells. With the use of a measure of error due to using backward Euler time stepping, suggested by Roache (29), a time step of T/240 is found to give sufficiently accurate results in that further reductions in the size of the time step used does not produce any significant reduction in the error. These simulations are computationally intensive, with one breathing cycle taking ~350 h on a Sun Ultra 10.
Particle trajectories are calculated in all three models using a special-purpose tracking routine. This routine reads a full cycle of flow field and grid data produced by CFX-4 and uses this data repeatedly, cycle after cycle, and a predictor and corrector method to track individual particles (fluid elements) over as many cycles as required. The time step used in the particle tracking routine is set independently of that for the flow-field solution. Before the particle track is advanced to the next time, the time step is recalculated, using local flow conditions, to ensure that the particle does not step out of the solution domain. At each particle-track time, a grid and flow field are created from the CFX-4 data using bicubic interpolation in space (27) and linear interpolation in time. For numerical efficiency, the routine solves the particle tracks in a stationary computational space, and, at each time step, the particle position is mapped back to physical space before it is written to an output file. The maximum error in the predicted particle position is estimated to be 0.2% of the distance traveled by the particle, and, in most cases, the error is considerably smaller than this.
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Flow patterns.
Solving the velocity field of the carrier gas on a moving grid over the
physiologically relevant range of flow parameters (ReRMS < 1) in a rhythmically expanding and
contracting, multiply alveolated duct, we often detected the presence
of slowly rotating recirculation in each alveolus (see Fig.
3, A and B). The
size of the recirculation flow depends on the ratio between the
alveolar flow (A) (i.e., flow produced by the volume
change of the alveolus) and the volumetric ductal flow
(D) (A/D).
Similar to our previous study (40), we found that the
smaller the A/D, the larger the
alveolar recirculation. When A/D
is larger than ~0.1, however, the alveolar flow is largely radial
without recirculation (Fig. 3C). Because, under normal
breathing conditions or during moderate exercise, the value of
A/D is usually <0.05 in the
majority of alveoli along the acinar tree (from the respiratory bronchioles to the last few generations) (37), we expect
that most of the alveoli are likely to possess recirculation in their flow field. Importantly, the presence of alveolar recirculation in the
cyclically expanding alveoli is topologically associated with the
existence of a stagnation saddle point in each alveolar flow field
(40), implying that chaotic mixing could originate in most
of the alveoli (see DISCUSSION).
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Interalveolar kinematic mixing.
To demonstrate the effects of a series of saddle points on fluid flow
irreversibility, the motion of massless particles was tracked over one
ventilation cycle in a nine-cell alveolar model for three different
ranges of A/D (0.0050 < A/D < 0.0053, 0.040 < A/D < 0.069, and 0.081 < A/D < 0.577 shown in Fig.
4, A, B, and
C, respectively). The particles were initially placed on
radial lines across the duct midway between alveoli at three different
initial axial locations (shown as three different colors, brown, green,
and pink, in Fig. 4). As soon as inspiration begins, particles near the
center line convect distally, proportionally to the bulk mean
velocities (see t/T = 0.25 in Fig. 4). The lines of particles quickly approach each other and comigrate along the central channel, particularly in the cases of smaller
A/D (Fig. 4, A or
B). The particles that were located initially near the
alveolar opening enter the alveolus (Fig. 4). The depth of particle
penetration into the alveolus during inspiration depends on the size of
alveolar recirculation. When the alveolar recirculation is large (Fig.
4A), the particles penetrate deep into the alveoli, and the
particles from the three different lines appear to be mixed during
inspiration (see t/T = 0.25 and 0.5 in Fig.
4A).
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Motion of interface between inhaled tracer fluid and the host
alveolar residual fluid.
Regarding massless tracer particles as marked fluid elements, the
interface between one fluid and another can be approximated by chords
connecting initially adjacent particles (Fig.
5A). In our studies, this piecewise linear approximation to
the interface can represent the front of incoming tidal gas or a tracer
bolus facing the host alveolar residual gas. As we have demonstrated in
Fig. 4, A and B, the kinematically irreversible
deformation of the tracer interface seems to be due to its association
with alveolar recirculation flow over the respiratory cycle. Thus
characteristics (e.g., size and strength) of the alveolar recirculation
may be major determinants in these processes. Our studies described
here focus on the situation that presumably occurs deep in the acinus, where the alveolar flow exhibits a medium- to small-sized recirculation (Fig. 3B). Larger alveolar recirculation flow (Fig.
3A) is likely to occur near the entrance of acinus (e.g.,
respiratory bronchioles), and that case is discussed elsewhere
(38).
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2) of distribution of particles was
computed and plotted vs. cycle number (N) as a family in the
P employed (Fig. 6). The
results show that 2 is independent of P and
grows exponentially with increasing N [2 = 0.0474(e0.457N 1)]. It is
important to note that 2 does not increase linearly with
N; this observation is fundamentally inconsistent with the
predictions of the classical dispersion theory (discussed below).
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L/Lo = (L
Lo)/Lo, where
Lo (=
xk|; xk is the
kth particle position) is the initial length of the tracer,
and L
(= Xk|; Xk is the
kth particle's mapped position) is the tracer length at end
expiration] and the pattern of the tracer.
L/Lo was plotted vs. N
as a family in P (Fig. 7). The
results show that the length of the tracer dramatically increases with
increasing N and that this increase in
L/Lo is strongly depended on the P used to approximate the interface. (Note that this
behavior is different from the axial phenomena in which the growth of
2 is essentially independent of the P.)
Furthermore, the tracer length grows exponentially with N if
a large P (P > 4,096) is used for
simulation. Because the reciprocal of P is a parameter related to scale resolution in our simulation, the fact that the increase in L/Lo with N
strongly depends on P suggests that the resulting pattern of
the tracer is fractal. To test this possibility, we examined the
spatial pattern of all of the particles (~16,000) used for the
simulation described above at the end of every cycle by employing the
fractal analysis method of box-counting technique popularized by Glenny
(15). Briefly, the test section of interest (usually the
most particle-dense area) (Fig. 8,
inset) was covered by M square boxes, each with
an edge length E. Denoting the particle concentration in the
ith box by µi and the overall mean concentration by 
(µi 0.21, 0.25, and 0.25 for
N = 1, 2, and 3, respectively (Fig. 8B).
This indicates a power law relationship between the tracer particle
distribution and the resolution of the analysis and that, therefore,
the tracer pattern resulting from kinematically irreversible acinar
fluid mechanics may indeed be fractal with a fractal dimension
D
1.2 (D = 1 slope; Ref.
3). Remarkably, this dimension is close to that found in
our animal experiments (unpublished observations, also see
DISCUSSION).
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DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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The principal findings of this study are that 1)
chaotic fluid motion occurring in a rhythmically expanding and
contracting, multiply alveolated duct induces substantial kinematic
irreversibility in the acinus, even under low-Reynolds number flow
conditions, and 2) mixing due to this kinematic
irreversibility is fundamentally different from the mixing described in
dispersive processes.1 A
tracer (bolus) subjected to the chaotic flow field is deformed both
axially and laterally. The 2 of particle distribution
increases exponentially, rather than linearly, with increasing cycle
time; thus axial bolus spreading does not obey the basic rules
described in classical diffusive transport theories (35).
The cycle-by-cycle evolution of lateral particle distribution is even
more complex. The tracer forms fingerlike protrusions, even after one
cycle. The tracer length exponentially increases as N
increased, forming characteristic stretch-and-fold fractal-like patterns.
Chaotic mixing in the pulmonary acinus.
Viscous flow has been considered kinematically reversible if the
boundary motion is reversible (36, 45). In the mid-1980s, however, there was a breakthrough discovery in fluid mechanics, namely,
that even Stokes flow can be kinematically irreversible if the
structure of the flow is chaotic (2, 25). In the last several years, applying this new concept to respiratory fluid mechanics, our laboratory has been studying the role of chaotic flow
phenomena in the experimentally observed, yet theoretically unexplained, convective mixing occurring in the lung periphery (5, 16, 37, 40). In our laboratory's previous numerical study (16, 40), we reported that chaotic flow and chaotic mixing can occur in the alveolated duct because of its peculiar geometry and time-dependent motion associated with tidal breathing. We
found that acinar flow was often slowly rotating in the alveolar air
pocket, and the velocity field near the alveolar opening was complex
with a stagnation saddle point typical of chaotic flow structure.
Performing Lagrangian fluid particle tracking, we further demonstrated
that, in such a flow structure, the motion of fluid, x(t), could be highly complex, irreversible, and
unpredictable even though it was governed by simple deterministic
equations [x(t) = 
v(x,t)dt,
x(0) = xo, where
v(x,t) denotes Eulerian velocity field].
Fingerlike protrusion. In this study, a line of massless particles was introduced in the alveolated duct to represent a fluid-fluid interface (Figs. 4 and 5A). The behavior of this interface, such as its reversibility and irreversibility, changes in its shape and size and contains crucial information for understanding the mechanism of mixing between inhaled particles and alveolar residual gas. By tracking the motion of the tracer particles, we have followed the motion of this interface over several cycles. Because the boundary of this line, shown as the point Q in Fig. 5A, is stationary on the wall because of the no-slip condition, the line expands when the alveolar walls expand during inspiration, and the line also tends to contract when the walls contract during expiration. However, the reversibility of this process depended on the nature of the flow fields sampled during expansion and contraction. The segments of the line near the channel center line are enormously stretched axially (see Fig. 4) and sample mostly reversible Poiseuille-like ductal flow fields (Fig. 3). Consequently, the interfacial line near the center line also shows approximately reversible behavior (Fig. 5B). By contrast, the segments of the lines near the walls (e.g., segments s1, s2, and s3 in Fig. 5A) sample a series of irreversible alveolar flow fields (e.g., Alv-1, Alv-2, and Alv-3, respectively, in Fig. 5A) and, consequently, do not return to their original positions (Fig. 5B). Each of these line segments, separated by points that sample approximately reversible flow fields between alveoli (e.g., R1, R2, and R3) basically form one finger after a cycle (Fig. 5B). The number of "fingers," therefore, roughly matches the number of alveoli distal to the initial position. Although, in the present computational model, the number of alveoli that the tracer samples is limited to six (due to computational constraints), in a real acinus, the inhaled bolus is expected to encounter a larger number of alveoli (~200) along the acinar longitudinal pathway. This implies that the acinar airways are likely to be filled with many longitudinal fingers after a few breathing cycles. This prediction has been confirmed experimentally in our laboratory's recent flow visualization studies performed in rat acini (39).
The size of each finger depended on its resident time in alveolar recirculation. The line segments that were closer to the side walls (e.g., s1 and s2) spent more time in recirculation (Alv-1 and Alv-2, respectively) and produced longer fingers. As the N increased, the tracer repeatedly encountered alveolar recirculation; the number of fingers rapidly increased, and they propagated toward the channel center line. This global evolution of the tracer pattern (i.e., rapid increase in the number of fingers, cycle-by-cycle lateral propagation), together with progressively finer scale tracer striations (discussed below in detail), are important observations because they indicate a substantial net enhancement of lateral particle transport for deposition.Axial phenomena-a departure from the conventional dispersion
theory.
In current theories, aerosol transport in the pulmonary acinus is
described as a dispersion (diffusion-like) process, and the mixing
phenomena are couched in the language of a Deff.
The most important feature of this approach is that, in any process that is dispersive in the sense that it can be characterized by an
effective diffusivity, the variance of a bolus asymptotically increases
linearly in time (or N). Phrased differently, the variance is an additive function over time. The reduction of experimental data
through the use of some Deff has thus been the
framework by which many aerosol studies have been conducted (e.g., Ref. 30). For instance, bolus spreading in the tracheobronchial
tree is commonly characterized by the difference between the inhaled and exhaled variances (proportional to H2, where
H is the bolus width at half height), given by
2
of bolus particle distribution grows faster than linearly in time, in
contrast to the linear growth predicted by all theories that are
characterized by a
Deff.2
It is important to emphasize here that mixing of kinematic origin (e.g., chaotic flow in the acinus) has a fundamentally different nature
from mixing described in dispersive mechanisms; thus it cannot be
described by any Deff.
Lateral phenomena (fractal patterns). The results of our study show that complex flow phenomena can occur in the lateral direction. Because of alveolar flow irreversibility, the tracer (i.e., a series of line segments, s1, s2, etc., in Fig. 5A) deforms at every cycle, forming fine characteristic stretch-and-fold striation patterns (see Fig. 5B, insets), on top of the global fingerlike protrusion (Fig. 5B). Consequently, an enormously large lateral diffusion surface (which is represented as a stretched tracer line in our study) evolves over every cycle, suggesting a substantial enhancement of lateral particle transport and subsequent deposition on the acinar walls. Interestingly, we found that exact estimation of tracer length L was not possible because L was strongly dependent on the number of particles forming the tracer (Fig. 7). At sufficiently fine scales (i.e., when the number of test particles used is sufficiently large), the apparent L of the tracer increases exponentially with increasing N.
The analysis of potentially fractal patterns by the well-known method of box counting (32) was employed. The analysis shows that the distribution of tracer particles evolve in a fractal-like manner, with D 1.2. The fact that the tracer pattern exhibits fractal characteristics is not entirely surprising, because the origin
of particle irreversibility is due to chaotic alveolar flow, and
deterministic chaos often manifests a fractal geometry (23,
32). On the other hand, it is important and remarkable that the
fingerlike protrusions (i.e., global pattern) found in these
simulations are strikingly similar to those found in the longitudinal
airway section of our experiments performed with rat lungs
(39). Moreover, our initial finding that D
1.2 obtained in finer scale stretch-and-fold striations in the present
numerical study is close to D 1.1 found in those rat
experiments (unpublished observations) is encouraging. Although further
detailed analyses will be necessary to determine the dependence of the
fractal dimension (or indeed if the pattern remains fractal) on model
parameters, these similarities suggest that our numerical simulation,
although based on highly idealized assumptions, does, in fact, capture the essential features of the underlying mixing mechanism, namely, that
low-Reynolds number chaotic flow in the acinus determines particle
transport in the lung.
Physiological origins of mixing. Our laboratory has recently proposed two possible origins of "stretch-and-fold" kinematics in the pulmonary acinus: first, that induced by a small departure (asynchrony) from kinematically reversible motion of alveolar walls (16, 41), and, second, that due to the presence of saddle points associated with alveolar recirculation flows in the acinar flow field (40). With respect to the first mechanism, Miki et al. (24) reported the presence of a small but consistent geometric hysteresis (i.e., temporal asynchrony) in lung expansion during normal tidal ventilation in live rabbits. By matching this degree of geometric hysteresis, we have generated physiologically realistic asynchrony in physical models (41) and computational models (16), which demonstrated that geometrical hysteresis, even if small, can produce stretch-and-fold patterns and, consequently, induce substantial acinar flow irreversibility. In a related work, Smaldone et al. (31), using gravitational sedimentation of aerosol particles to estimate mean linear intercepts, showed significant geometric hysteresis in excised lungs with large-volume excursions from minimal volume and interpreted their data in terms of respiratory unit recruitment and derecruitment. Those studies, however, being restricted to single-volume histories, did not address the issue of mixing during cyclic ventilation and so are not strictly comparable to the present work. Finally, flow/volume hysteresis (different flow magnitudes at isovolume points on inspiration and expiration) can lead to differences in the velocity profiles in the central airways; this, in turn, can cause a difference in aerosol deposition between inspiration and expiration (4).
In contrast to these studies, which focus primarily on differing geometric features between inspiration and expiration, in this paper we investigate the second mechanism mentioned above. We believe that the presence of saddle points may be an equally fundamental mixing mechanism responsible for convective mixing in the acinus. Note that such saddle point singularities do not exist in rigid wall models of acinar flow but, through their association with alveolar recirculation, are necessarily linked to the cyclic motion of the alveolar walls. To distinguish clearly this mechanism from the former one (caused by geometric hysteresis), we used only kinematically reversible wall motion in these studies. The present paper extends our previous work (40), which was restricted to a saddle point in a single alveolar space, by considering the effect of multiple saddle points in a multiply alveolated channel. In practice, we believe that both mechanisms, asynchrony and saddle points, coexist in the pulmonary acinus, mutually enhancing each other in producing stretch-and-fold mixing.Significance and conclusions.
It is well established that exposure to environmental aerosol
pollutants is associated with health risks, ranging from mild to life
threatening (47). The exposure and pathophysiological consequences are clearly linked by two independent and separate causal
pathways: the exposure-dose relationship (i.e., given an aerosol
concentration in the ambient air, what is the actual dose delivered to
the lung) and the dose-response relationship (i.e., for a given
deposited dose or burden, what is the biological consequence). Despite
the large literature on exposure assessment methodologies as well as on
the pathophysiological consequences of short- and long-term exposures,
there is much less known about the mechanisms contributing to the first
of these links, and much deposition and mixing data are inconsistent
with previous theories of mixing deep in the lung. It is important,
therefore, to identify new potential mechanisms that may dominate
aerosol transport, even when boundary motion is approximately
reversible. We argue in this paper that chaotic mixing is such a
candidate. We have shown, through realistic numerical simulation of the
low-Reynolds number alveolated duct flow (and by comparison with
experimental results in rat lungs; unpublished observations), that the
peculiar geometry of the alveolated duct structure within the pulmonary
acinus and its cyclic motion during breathing can give rise to
1) a chaotic type of mixing associated with the presence of
saddle points, 2) slow recirculatory flow within the
alveoli, and 3) stretching and folding of stream surfaces.
These, in turn, can significantly increase mixing, especially
laterally, and will also contribute to an increasing 2
(which increases faster than linearly with breath number, an observation that is inconsistent with any dispersal mechanism that can
be characterized by an effective axial diffusivity). We suggest that
chaotic mixing may be the dominant mechanism of aerosol transport and
deposition deep in the lung.
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ACKNOWLEDGEMENTS |
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This study was supported by National Heart, Lung, and Blood Institute Grants HL-47428 and HL-54885 and, in part, by Environmental Protection Agency Research Award R827353.
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FOOTNOTES |
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Address for reprint requests and other correspondence: A. Tsuda, Physiology Program, Harvard School of Public Health, Huntington Ave., Boston, MA 02115 (E-mail: atsuda{at}hsph.harvard.edu).
1 It is unlikely that the results on kinematic irreversibility in this paper are important to ventilation-perfusion matching, but a quantitative assessment of this remains open.
2 In a recent theoretical study in fluid mechanics, Jones and Young (21) showed that the axial variance of tracer fluid elements in low-Reynolds number chaotic flow in a twisted pipe grows faster than linearly with time. They also pointed out that the resulting distribution of the tracer particles exhibited a fractal pattern (20). Experimentally, whether variances are in fact additive or not in real lungs, there do not appear to be any data on the growth of bolus variance as a function of breath number. [This point should not be confused with the observation that there is an essentially linear relationship between bolus width and volume of penetration in the bronchial tree (18)].
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
10.1152/japplphysiol.00385.2001
Received 23 April 2001; accepted in final form 22 October 2001.
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REFERENCES |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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(= 60°), alveolar half-opening angle;
CL, duct center line. Note that the alveolar corners were
rounded with the corner radius = 0.02 RD.
,
P = 512; 
, P = 1,024;
, P = 2,048; 
,
P = 4,098; 
, P = 8,192;
dashed and dotted lines show linear growth (
