(243d) A Computational Model of Dynamic Flow In the Respiratory System

Airflow in the pulmonary tract is important in terms of proper function of the respiratory system and adequate gas exchanger at the alveoli. In diseased states the inspired volume of air decreases and, in extreme cases, can lead to decreased in oxygen levels in the blood stream. Pulmonary airflow is also important in terms of particle transfer, deposition, and removal or penetration. The transfer and deposition of particles in the respiratory system is of major interest for the development of targeted local and systemic drug delivery formulations (Illum, 2006; Dalby and Suman, 2003, Azarmi et al., 2008). The effect of size and inhalation rate on particle transfer and deposition has been well studied for smooth spherical particles and steady inhalation. However, several issues remain to be elucidated including the deposition of non-spherical particles, dispersion and aggregation effects, the effect of particle charge and dynamic effects during a breathing cycle.

Deposited particles can undergo disaggregation, can release beneficial drugs, and, if sufficiently small, can penetrate into the bloodstream. The effective transfer and deposition of particles depends on the physiological state of the respiratory system, e.g. diseased or normal. Diseased physiological states can present constricted airflows, increased mucous layer thickness (due to overproduction or decreased clearance), and acute and chronic inflammation. The effective and targeted delivery of drugs in such diseased states remains a challenge to this day.  

The pulmonary system consists of approximately 24 generations of airway branches for a total of about 3 10⁷ branches. The dynamics of flow change dramatically from the bronchi to the alveoli as airway diameters decrease from 6mm to 100μm, velocities from 5m/s to 2.5mm/s, and local Reynolds numbers from about 1000 to 0.1. Consequently a full comprehensive (e.g., CFD) computational model of flow in the pulmonary system let alone a full realistic geometric representation is out of the question (Finlay, 2004). Consequently, approximate integrated models are being pursued. Integrated multi-scale physiological models of the respiratory system have been under development over the past few years (Burrowes et al., 2008). Integrative models often describe a small part of the pulmonary system (Martonen et al., 2002; Zhang et al., 2002) or employed sequences of branches or groups of branches to describe the flow from the bronchi to the alveoli (Nowak et al., 2003; Zhang et al., 2009). The necessity of an accurate geometric description of the URT has also become evident in recent simulations (van Ertbruggen et al.; 2007, Longest and Vinchurkar; 2007). Despite this progress, no computational models integrating the respiratory system from the bronchi to the alveoli nor any realistic models for dynamic flow have been reported.

To further improve our understanding of airflow as well as particle deposition during a breathing cycle a multi-level computational model of the respiratory system was developed that describes the dynamic airflow and motion of particles through the lungs. In this work airflow through the pulmonary system down to the alveolar sac and individual alveoli level is determined by dynamic and steady-state CFD simulations. The pulmonary system is separated into the upper respiratory tract, URT, consisting of 5-8 generations, the lower respiratory tract, LRT, consisting of multiple branching structures (bronchioles) and the alveolar sacs.

The URT is described by either a symmetrical branched geometry or a physiologically-realistic geometry. Airflow in the URT is described by a transitional SST k-ω turbulence model while particle depositions are described by a Lagrangian-particle/Eulerian-fluid approach. The lower respiratory tract, LRT, is described by a simplified laminar-flow model, with averaged resistances to flow. Deposition of inertial particles in the LRT is assumed to follow a dimensionless universal law dependent only on the local Stokes number (Zhang et al., 2009).

The alveolar sac model consists of spherical caps inflating and deflating instantaneously during a breathing cycle. According to this model, during inhalation the initial abrupt decrease in alveoli pressure drives the airflow towards the alveoli. During the inhalation stage inflowing air to the alveoli gradually increase the pressure reducing the driving force for flow. At the end of the inhalation period, the alveoli volume changes abruptly and the sudden increase in alveoli pressure drives exhalation. The transfer of pressure and airflow rates through the branched structure (i.e., from the alveoli to the URT) is described with a simple quasi-steady state laminar-flow model.

This paper reports on the effects of dynamic flow on airflow as well as the transfer and deposition of particles throughout the entire respiratory system for different inhalation rates and different sized inertial particles. The effects of pathophysiological conditions on resistance, airflow, and particle deposition is also shown.  

References

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