Numerical modelling and analysis of peripheral airway asymmetry and ventilation in the human adult lung.

We present a new one-dimensional model of gas transport in the human adult lung. The model comprises asymmetrically branching airways, and heterogeneous interregional ventilation. Our model differs from previous models in that we consider the asymmetry in both the conducting and the acinar airways in detail. Another novelty of our model is that we use simple analytical relationships to produce physiologically realistic models of the conducting and acinar airway trees. With this new model, we investigate the effects of airway asymmetry and heterogeneous interregional ventilation on the phase III slope in multibreath washouts. The model predicts the experimental trend of the increase in the phase III slope with breath number in multibreath washout studies for nitrogen, SF(6) and helium. We confirm that asymmetrical branching in the acinus controls the magnitude of the first-breath phase III slope and find that heterogeneous interregional ventilation controls the way in which the slope changes with subsequent breaths. Asymmetry in the conducting airways appears to have little effect on the phase III slope. That the increase in slope appears to be largely controlled by interregional ventilation inhomogeneities should be of interest to those wishing to use multibreath washouts to detect the location of the structural abnormalities within the lung.

The simultaneous role of an alveolus as flow mixer and flow feeder for the deposition of inhaled submicron particles.

In an effort to understand the fate of inhaled submicron particles in the small sacs, or alveoli, comprising the gas-exchange region of the lung, we calculated the flow in three-dimensional (3D) rhythmically expanding models of alveolated ducts. Since convection toward the alveolar walls is a precursor to particle deposition, it was the goal of this paper to investigate the streamline maps' dependence upon alveoli location along the acinar tree. On the alveolar midplane, the recirculating flow pattern exhibited closed streamlines with a stagnation saddle point. Off the midplane we found no closed streamlines but nested, funnel-like, spiral, structures (reminiscent of Russian nesting dolls) that were directed towards the expanding walls in inspiration, and away from the contracting walls in expiration. These nested, funnel-like, structures were surrounded by air that flowed into the cavity from the central channel over inspiration and flowed from the cavity to the central channel over expiration. We also found that fluid particle tracks exhibited similar nested funnel-like spiral structures. We conclude that these unique alveolar flow structures may be of importance in enhancing deposition. In addition, due to inertia, the nested, funnel-like, structures change shape and position slightly during a breathing cycle, resulting in flow mixing. Also, each inspiration feeds a fresh supply of particle-laden air from the central channel to the region surrounding the mixing region. Thus, this combination of flow mixer and flow feeder makes each individual alveolus an effective mixing unit, which is likely to play an important role in determining the overall efficiency of convective mixing in the acinus.

Radial transport along the human acinar tree.

A numerical model of an expanding asymmetric alveolated duct was developed and used to investigate lateral transport between the central acinar channel and the surrounding alveoli along the acinar tree. Our results indicate that some degree of recirculation occurs in all but the terminal generations. We found that the rate of diffusional transport of axial momentum from the duct to the alveolus was by far the largest contributor to the resulting momentum in the alveolar flow but that the magnitude of the axial momentum is critical in determining the nature of the flow in the alveolus. Further, we found that alveolar flow rotation, and by implication chaotic mixing, is strongest in the entrance generations. We also found that the expanding alveolus provides a pathway by which particles with little intrinsic motion can enter the alveoli. Thus, our results offer a possible explanation for why submicron particles deposit preferentially in the acinar-entrance region.

Hamiltonian chaos in a model alveolus.

In the pulmonary acinus, the airflow Reynolds number is usually much less than unity and hence the flow might be expected to be reversible. However, this does not appear to be the case as a significant portion of the fine particles that reach the acinus remains there after exhalation. We believe that this irreversibility is at large a result of chaotic mixing in the alveoli of the acinar airways. To test this hypothesis, we solved numerically the equations for incompressible, pulsatile, flow in a rigid alveolated duct and tracked numerous fluid particles over many breathing cycles. The resulting Poincare sections exhibit chains of islands on which particles travel. In the region between these chains of islands, some particles move chaotically. The presence of chaos is supported by the results of an estimate of the maximal Lyapunov exponent. It is shown that the streamfunction equation for this flow may be written in the form of a Hamiltonian system and that an expansion of this equation captures all the essential features of the Poincare sections. Elements of Kolmogorov-Arnol'd-Moser theory, the Poincare-Birkhoff fixed-point theorem, and associated Hamiltonian dynamics theory are then employed to confirm the existence of chaos in the flow in a rigid alveolated duct.

Simulation of flow through a Miller cuff bypass graft.

Unnatural temporal and spatial distributions of wall shear stress in the anastomosis of distal bypass grafts have been identified as possible factors in the development of anastomotic intimal hyperplasia in these grafts. Distal bypass graft anastomoses with an autologus vein cuff (a Miller cuff) interposed between the graft and artery have been shown to alleviate the effects of intimal hyperplasia. In this study, pulsatile flow through models of a standard end-to-side anastomosis and a Miller cuff anastomosis are computed and the resulting wall shear stress and pressure distributions analysed. The results are inconclusive, and could be taken to suggest that the unnatural distributions of shear stress that do occur along the anastomosis floor may not be particularly important in the development of intimal hyperplasia. However, it seems more likely that the positive effects of the biological and material properties of the vein cuff, which are not considered in this study, somehow outweigh the negative effects of the shear stress distributions predicted to occur on the floor of the Miller-cuff graft.

Kinematically irreversible acinar flow: a departure from classical dispersive aerosol transport theories.

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.

Flow in a simple model skeletal muscle ventricle: comparison between numerical and physical simulations.

Flow patterns generated during ventricular filling have been investigated for three different combinations of flow rate and injection volume. The numerical solutions from a commercially available computational fluid dynamics package were compared with observations made under identical flow conditions in a physical model for the purpose of code validation. Particle pathlines were generated from the numerical velocity data and compared with corresponding flow-visualization pictures. A vortex formed at the inlet to the ventricle in both cases: During the filling phase, the vortex expanded and traveled toward the apex of the ventricle until, at the end of filling, the vortex occupied the full radial extent of the ventricle; the vortex continued to travel once the filling process had ended. The vortices in vitro were more circular in shape and occupied a smaller volume than those generated by the numerical model. Nevertheless, comparison of the trajectories of the vortex centres showed that there was good agreement for the three conditions studied. Postprocessing of velocity data from the numerical solution yielded wall shear-stress measurements and particle pathlines that clearly illustrate the mass-transport qualities of the traveling vortex structure. For the cases considered here, the vortex transit produced a time-dependent shear stress distribution that had a peak value of 20 dynes cm-2, with substantially lower levels of shear stress in those regions not reached by the traveling vortex. We suggest that vortex formation and travel could reduce the residence time of fluid within a skeletal muscle ventricle, provided that the vortex travels the complete length of the ventricle before fluid is ejected at the start of the next cycle.

Numerical investigation of steady flow in proximal and distal end-to-side anastomoses.

Steady flow in model proximal and distal end-to-end bypass anastomoses were simulated numerically. The predictions were compared to whole field measurements of the flow in in vitro models, and were shown to match well the general features of the measured flows. The predictions confirmed that the flows in end-to-side anastomoses are complex and three dimensional, and contain areas that could allow long residence times. Careful examination of the predictions revealed certain features of the flows not seen easily in the experiments. Shear stress and pressure on the vessel walls were predicted, and areas known to be prone to intimal hyperplasia were shown to correspond to areas of high spatial gradient of shear stress. Two anastomosis angeles, 30 and 45 deg, were considered, and it was shown that the more acute angle may have some benefit in terms of the levels of shear gradients and the power required to drive the flow through the anastomosis.

Formation and travel of vortices in model ventricles: application to the design of skeletal muscle ventricles.

Vortex-ring production was studied in axisymmetric elastomeric ventricles designed to stimulate flow in a cardiovascular assist device. A flow visualization technique was used to investigate the effects of reducing the inlet diameter and predilating the ventricle on vortex travel in two ventricles of different shape and size. In most cases, vortex rings formed during the filling phase. They were bounded by the incoming jet of fluid and the ventricular wall. The velocity of their centres during the filling period was proportional to the inflow velocity. During filling, vortex velocity was substantially independent of the shape and diameter of the two ventricles studied. It was dependent mainly on orifice diameter: a narrower inlet led to greater inflow velocities and proportionately greater vortex velocities. At the end of the filling phase, each vortex increased in size to occupy the full radial extent of the ventricle. This process was associated with a decrease in the axial velocity and strength of the vortex. At low flow rates, these losses resulted in the arrest of the vortex at end filling. Vortex motion in ventricles is particularly important in the design of a cardiovascular device such as the skeletal muscle ventricle (SMV), where small ejection fractions may leave blood at the apex of the ventricle relatively undisturbed. It is suggested that inlet diameter could be selected to favour the formation and travel of vortices, with a resultant reduction in apical residence time and hence a reduced risk of thrombus formation.

Aerosol transport and deposition in the rhythmically expanding pulmonary acinus.

Little is known about factors controlling the dynamics of aerosol dispersion and deposition in the lung periphery, though this knowledge becomes increasingly important in many fields such as environmental and occupational exposure, diagnostic applications, and therapeutic deliver of drugs via aerosols. For the last several years, we have been studying aerosol behavior in the pulmonary acinus, where the airway structure and the associated fluid mechanics are distinctly different from those in the conducting airways. Our major research efforts have been focused on the basic physics underlying acinar fluid mechanics and particle dynamics, which are likely to be conditioned by the two key geometric factors of acinar airways: structural alveolation and rhythmic expansion and contraction of the alveolar walls. A combination of computational and experimental analyses revealed that due to these unique geometric features acinar flow can be extremely complex despite the low Reynolds number, and can have substantial effects on particle dynamics. In particular, chaotic mixing can occur in the lung periphery. In the course of such a mixing process, the inhaled aerosol particles quickly mix with the residual alveolar gas in a manner that is radically different from the previously considered classical diffusion process. The objective of this paper is to briefly review our current understanding of these processes, to discuss existing deposition models, and to describe our ongoing research efforts toward a basic understanding of aerosol behavior in the pulmonary acinus.

Chaotic mixing of alveolated duct flow in rhythmically expanding pulmonary acinus.

We examined the effects of rhythmic expansion of alveolar walls on fluid mechanics in the pulmonary acinus. We generated a realistic geometric model of an alveolated duct that expanded and contracted in a geometrically similar fashion to simulate tidal breathing. Time-dependent volumetric flow was generated by adjusting the proximal and distal boundary conditions. The low Reynolds number velocity field was solved numerically over the physiological range. We found that for a given geometry, the ratio of the alveolar flow (QA) to the ductal flow (QD) played a major role in determining the flow pattern. For larger QA/QD (as in the distal region in the acinus), the flow in the alveolus was largely radial. For small QA/QD (as in the proximal region in the acinus), the flow in the alveolus was slowly rotating and the velocity field near the alveolar opening was complex with a stagnation saddle point typical of chaotic flow structures. Performing Lagrangian fluid particle tracking, we demonstrated that in such a flow structure the motion of fluid could be highly complex, irreversible, and unpredictable even though it was governed by simple deterministic equations. These are the characteristics of chaotic flow behavior. We conclude that because of the unique geometry of alveolated duct and its time-dependent motion associated with tidal breathing, chaotic flow and chaotic mixing can occur in the lung periphery. Based on these novel observations, we suggest a new approach for studying acinar fluid mechanics and aerosol kinetics.