Airway radius

Figure 17.3 Airway obstruction, (a) Normal, patent airway with radial traction offered to it by surrounding airways. Resistance in this airway is low and air flows through it freely, (b) The airway is obstructed by the presence of excess mucus and airway resistance is increased. Airflow is reduced, (c) Thickening of the airway wall due to inflammation or edema narrows the lumen of the airway. The decrease in airway radius increases airway resistance and decreases airflow, (d) Destruction of surrounding airways results in the loss of interdependence, or radial traction. Without the structural support offered by surrounding airways, the central airway collapses and airflow through it is reduced.

Factors determining resistance to airflow are also analogous to those determining the resistance to blood flow and include viscosity, length of the airway, and airway radius. Under normal conditions, the viscosity of the air is fairly constant and the length of the airway is fixed. Therefore, airway radius is the critically important physiological factor determining airway resistance ... 

The probability of an inhaled particle being deposited by impaction is a function of the dimensionless Stokes number Stk, which relates particle properties (mass mP, diameter dP, and density, pP) to parameters of the airflow (air velocity vA, viscosity i)A, and airways radius rA) ... 

Cilia are thin cylindrical hair-like structures with a cross-sectional radius of 0.1 gm projecting from the apical epithelial surface of ciliated columnar cells. Ciliary length is thought to correspond to periciliary fluid depth and range from approximately 7 gm in proximal airways to roughly 5 gm in more distal airways.- Each ciliated epithelial cell supports approximately 200 cilia at a density of eight cilia/gm. Short microvilli, possibly associated with secretory functions, are interspersed among the cilia. 

Sedimentation of particles follows the principle outlined above [Eq. (1)] in which particles in the Stokes regime of flow have attained terminal settling velocity. In the airways this phenomenon occurs under the influence of gravity. The angle of inclination, t /, of the tube of radius R, on which particles might impact, must be considered in any theoretical assessment of sedimentation [14,19]. Landahl s expression for the probability, S, of deposition by sedimentation took the form ... 

Airway resistance is inversely proportional to the radius (r) of the airway to the fourth power. In other words, when the radius is reduced by a factor of two (50%), the airway resistance increases 16-fold. Several factors determine airway resistance, including ... 

Bronchial smooth muscle tone. Changes in bronchial smooth muscle tone are particularly important in the bronchioles compared to the bronchi. Recall that the walls of the bronchioles consist almost entirely of smooth muscle. Contraction and relaxation of this muscle has a marked effect on the internal radius of the airway. An increase in bronchial smooth muscle tone, or bron-choconstriction, narrows the lumen of the airway and increases resistance to... 

Figure 13. Growth curves for sulphuric acid droplets r, equilibrium radius ro, initial radius X0 initial concentration of sulphuric acid. Reprinted from Journal of Aerosol Science, 13, AT Cocks and RP Fernando, The growth of sulphate aerosols in the human airways, pp. 9-19, 1982, with kind permission from Elsevier Science Ltd...

Exposures to ambient particulate matter (PM), especially fine PM with an aerodynamic radius of 2.5 pm (PM2.5), have been consistently related to increases in mortality and morbidity (Dockery et al. 1993 Burnett et al. 1999). The effects of ambient PM exposures on certain vulnerable populations such as the elderly, those with compromised cardiopulmonary health and children are of particular concern. A number of studies have demonstrated, for instance, that exposure to air pollution is associated with reductions in lung function and growth, asthma, allergic rhinitis and respiratory infections in children (Janssen et al. 2003 Brauer et al. 2007). Among other things, their susceptibility can be attributed to the immaturity of their respiratory defence mechanisms and higher permeability of their airways to air pollutants compared to adults. 

Fig. 8. Scaled currents in the Rope-Walk model for airway trees of varying size. Here, r and L denotes the radius and length of branches in the tree used to model the total gas-exchanger area.

Representative velocity profiles derived from these expressions are shown in Figure 10.2 for two values of a, at four phases of the flow cycle. In these figures, the radial position, r, has been normalized by the tube radius, a. At a = 3 (Figure 10.2a), a value that under resting conditions can occur in the smallest arteries and larger arterioles as well as the middle airways, Stokes layers can occupy a significant fraction of the tube radius. The velocity at the wall is zero, as required by the no-slip condition, and as in steady flow the velocity varies smoothly with r, with no step change at any point. However, even at this... 

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