Dynamics: Setting the System in Motion

Flow Through Tubes: Application to the Lungs

Lung Resistance ↑

As you move air into the lungs, you have to overcome two types of resistance: airway resistance and tissue resistance. Airway resistance is determined by the principles we have just outlined for the general flow of air or liquid through tubes. Tissue resistance is a manifestation of the forces that must be overcome by virtue of moving molecules as you stretch the lungs. Airway resistance accounts for approximately 85% of the total resistance of the lungs.

If you move air rapidly into the lungs, that is, generate a high flow, a greater driving pressure is required to overcome the resistance in the lungs. Imagine the relationship between the volume of the lungs and pressure as you go you from one volume (V₁) to another (V₂) under infinitely slow (also called quasistatic) conditions (essentially a series of static measurements) (Fig. 4-7). Because we are under quasistatic conditions, we can essentially ignore the effects of resistance (resistance is only important when there is flow), and the relationship between volume and pressure is a straight line. The slope of the curve reflects only the compliance of the lung (recall that compliance is the change in volume divided by the change in pressure needed to produce the change in volume). Now move the air into the lung and expand it from V₁ to V₂ rapidly (i.e., under conditions of high flow). How do you think the relationship between pressure and volume will change? (Fig. 4-8)

To inflate the lung rapidly, you must overcome the resistance of the airways and the lung tissue. Initially, energy must be expended to accelerate the gas and to overcome the inertial forces of the lung. Thus, pressure changes with little change in volume at the outset of the inflation. As higher flows are achieved, volume changes more rapidly than pressure, as the momentum of the gas carries it into the alveoli, until the desired volume is reached.

Use Animated Figure 4-8 to observe how the speed of lung expansion affects the pressure-volume relationship and the amount of work involved in inflating the lung. Compare very slow expansion (quasistatic conditions) to very fast expansion and note how the pressure volume curve changes shape and how the amount of work increases in relation to the speed of expansion.

Determinants of the Cross-Sectional Area of the Airway ↑

As noted in Chapter 2, the larger, more central airways of the lung have cartilage and smooth muscle in their walls that helps determine their shape and size. The small airways in the periphery of the lung, however, have thin walls and are relatively compliant; their shape and size are affected to a greater degree by the pressure differential across the wall of the airway. Furthermore, the small airways are supported by a latticework of connective tissue (including the alveolar network) supplied by the surrounding lung. In a sense, the lung tethers open the small airways (Animated Figure 4-9).

Recall the example of the mesh stocking we discussed in Chapter 3. The network of the fibers forming the mesh is interconnected. Imagine a very flexible tube sewn into the mesh with the direction of the tube perpendicular to the plane of the mesh. As the mesh is stretched and the fibers pulled farther apart, the diameter of the tube passing through the mesh becomes larger. Similarly, as the lung expands, the diameter of the small airways increases; as the lung deflates, the caliber of the airway diminishes. Thus, lung size is one of the major determinants of the cross-sectional area of the small airways. Use Animated Figure 4-9 to view the change in diameter of a small airway during breathing. You can press the play button to watch the motion during inspiration and expiration or use the slider to control the animation yourself. Note how the small airway (shown in cross-section) runs through and is attached to the alveolar connective tissue network. Thus, during inspiration, when the lung inflates, expanding forces are transmitted from the pleura to the small airways via the intervening connective tissue.

The tethering effect just described can be related to the elastic properties of the lung tissue. If the elastic recoil of the lung is diminished and the tethering effect supplied by the lung is weakened, as occurs in emphysema, there will be a greater propensity for the small airways to narrow when the transmural pressure is negative (recall from Chapter 3 that transmural pressure is negative when the pressure outside the airway is greater than the pressure inside the airway). Thus, elastic recoil of the lung is a major determinant of the cross-sectional area of the small airways.

The medium-sized bronchi contain smooth muscle in their walls. The tone of these muscles is determined by the balance of the sympathetic and parasympathetic stimulation they receive. Recall that sympathetic activity leads to muscle relaxation and dilation of the airway while parasympathetic simulation leads to muscle constriction and narrowing of the airway. Thus, bronchial smooth muscle tone is a major determinant of the cross-sectional area of the medium-sized airways.

Airway smooth muscle tension for a given level of autonomic nervous system activity varies through the respiratory cycle and is different after inhalation than exhalation, that is, it shows hysteresis. The airways are wider at a given lung volume when the volume is reached during deflation (i.e., coming down from a higher lung volume) than they are when the volume is reached during inflation (i.e., coming up from a lower lung volume). Conceptually, this phenomenon is similar to the hysteresis we described for the lung as a whole in Chapter 3, but the mechanism that accounts for it is quite different. Airway hysteresis is believed to be the consequence of stress relaxation of the tissue. If you stretch tissue and hold it at that elongated position momentarily, the elastic forces relax just a bit. This effect appears to be accentuated when bronchomotor tone (smooth muscle tone) is increased, as during an asthma attack.

Transmural Pressure and the Size of Airways During Forced Exhalation ↑

The transmural pressure of the airways—the pressure inside minus the pressure outside the airway (i.e., the pleural pressure)—is always positive during relaxed breathing at rest because pleural pressure is more negative than airway pressure throughout the respiratory cycle. Recall that a positive transmural pressure is called a distending pressure (this term is applicable any time the transmural pressure is positive, even as an airway decreases in diameter during exhalation; during exhalation, a positive transmural pressure across the airway means that the airway is not being compressed, even if pleural pressure becomes positive).

During conditions in which ventilation is elevated and expiratory flow must be increased, such as exercise, expiratory muscles may be recruited to push out air, and pleural pressure during expiration is often positive (i.e., greater than atmospheric pressure). If the pleural pressure is higher than the pressure inside the airway, transmural pressure becomes negative and the airway, if we are describing a small airway without smooth muscle or cartilage in its wall, may collapse. In the normal lung, whether or not the transmural pressure in the small airways becomes negative during exhalation is determined partly by how quickly the pressure in the airway declines as air travels from the alveolus to the mouth.

Exhalation begins when the inspiratory muscles relax and alveolar pressure becomes positive. Air begins to move out of the alveolus and flows toward the mouth. As the air moves down the airways, flow is constant. To sustain flow, pressure is dissipated because of the interplay of the factors we described earlier in this chapter as we examined the physical properties of flow through tubes.

First, pressure is lost as the resistance of the airways is overcome. The energy is dissipated as heat. Second, as you move from the periphery of the lung to the mouth, you go from millions of small airways in parallel ultimately to a single tube, the trachea. The total cross-sectional area of the airways diminishes. To maintain a constant flow, the velocity of the gas molecules must increase. In accord with Bernoulli's principle, this process leads to an additional decrease in pressure within the airway. Third, as you move from the periphery to the central airways, you go from conditions of laminar flow to turbulent flow. To sustain a constant flow with this change in conditions, more work must be done; pressure decreases some more.

Given that the pressure in the airways must decrease as air flows from the alveolus to the mouth, what determines whether or not transmural pressure becomes negative and the forces on the airway predispose it to narrow or collapse? To answer this question, let us consider the flow of water through an infinitely flexible tube, that is, a tube that will completely collapse as soon as the pressure outside the tube is greater than the pressure inside the tube (this type of tube is called a Starling resistor).

As you can see in Animated Figure 4-10A, water in tank A is flowing through a tube and ultimately empties on the ground. The tube that exits the container, however, must pass through a second container of water,tank B. The water that exits container A has a pressure, P_I (the pressure inside the tube) that is initially proportional to the height of the water above the tube in tank A. As the water flows through the tube, the pressure inside the tube, P_I, falls because of resistance in the tube. The point at which transmural pressure of the tube is zero is called the equal pressure point (EPP) because the pressure inside and outside the tube are now the same. If P_I becomes less than the pressure surrounding the tube (P_S) in tank B, the tube collapses (transmural pressure is negative). When the tube collapses, flow stops. Use Animated Figure 4-10A to view this sequence up to the initial tube closure. What are the factors that determine the location of the point of collapse? What would happen if the animation were to continue? Think about these questions before reading on and finding out the answers.

In the absence of flow (with the tube collapsed), we are now back in static conditions, and the pressure in the tube at the point of collapse is now proportional to the height of the water in tank A. P_I is now greater than P_S, the transmural pressure is positive, and the tube opens and flow is reestablished. However, as soon as flow is reestablished, we are back in dynamic conditions and must deal with resistance in the tube. P_I again decreases, and collapse occurs. This cycle is repeated until sufficient water has exited the tube to make the height of the water in tank A equal to the height in tank B. Use Animated Figure 4-10B to view this sequence and observe the cycle of flow, pressure decrease, tube collapse, and static conditions leading to tube reopening and reestablishment of flow. You can use the slider to move slowly back and forth through the animation.

Whether or not the P_S is greater than P_I before the tube exits tank B depends on two factors: the differential in the height of the water in tank A versus tank B and the resistance of the tube. If we use this model as an analogy for the ventilatory pump, tank A represents the alveolus, the tube represents the airways, and the pressure in tank B, P_S, represents pleural pressure during a forced exhalation. For a given airway resistance and rate of decrease in pressure in the airway, the factor that determines whether transmural pressure (in this case P_I minus P_S) becomes negative in the airway is the difference between alveolar pressure and pleural pressure. As you recall from Chapter 3:

and

where = alveolar pressure; = elastic recoil pressure; and = pleural pressure. Thus, the elastic recoil of the lung is a critical factor in determining whether airways collapse in the lung during exhalation.

Of course, the airways in the lungs are not Starling resistors, and the tendency of the small airways to collapse in the presence of a negative transmural pressure is offset, to some degree, by the tethering effect of the surrounding tissue, which is also a reflection of the elastic recoil of the lung. Furthermore, the pressure surrounding the alveolus and the airway in the thorax is the pleural pressure, which is essentially equal throughout the thorax (with minor differences based on gravity, as we discussed in Chapter 3). There is no true equivalent for the pleural pressure, with respect to its effect on alveolus and airway, within the Starling model. Nevertheless, the concepts represented by the Starling resistor are important in understanding the notion of flow limitation in the lungs, both in normal individuals and in those with diseases of the airways.