5.1: Fundamentals of Airflow

To generate flow in the airways, so far we have looked at how the pressure differential is generated and the factors affecting the compliance of the lung. Now we will look at the factors that cause resistance to airflow and how mechanical and neural influences affect it.

The first factor we must consider when thinking about airflow is the type of flow that is occurring.

The most efficient form of flow is laminar (i.e., laminar flow takes the lowest pressure differential for flow to occur). In laminar flow the molecules are moving in an orderly manner, those at the side of the tube moving a little slower due to contact with tube walls and those in the middle moving fastest (figure 5.1).

Figure 5.1: Laminar flow.

When velocity increases or tube radius decreases then this organization is lost. Collisions between molecules and with the tube wall are now more frequent and movement is more chaotic, and the flow becomes turbulent (figure 5.2). At this point some molecules are at times moving against the pressure gradient due to these collisions. Consequently, to generate the same amount of molecule movement (i.e., flow) from one end of the tube to another, a greater pressure differential is needed when flow becomes turbulent. Turbulent flow is more common in the large airways where velocity and airway radius are high.

Figure 5.2: Turbulent flow.

In reality, the vast majority of the airways are branching small tubes, so we see a mixture of the two above—mostly laminar flow but some turbulence generated at the branch (or transitional) points (figure 5.3).

Figure 5.3: Transitional flow.

For our purposes though we are going to look at the factors that affect flow when it is laminar—the dominant form of flow in the majority of airways. These factors are described by Poiselle’s equation. We will now break down Poiselle’s equation in relation to flow of air down airways. Although initially an intimidating equation, there are some things we can generally ignore.

\[\dot{\mathrm{V}}=\frac{\Delta \mathrm{P} \times \pi \times \mathrm{r}^{4}}{8 \mathrm{n} \times \mathrm{L}} \label{Poiselle’s equation} \]

First, Poiselle says that flow decreases when length of the tube increases; because the airways have constant length, we do not have to worry about it.

Then there is the viscosity of the gas. This is not usually a concern either when breathing humidified air at a constant biological temperature. It does become important when breathing other gas mixtures, however, such as a helium/oxygen blend that has a lower viscosity and is given to respiratory patients or deep water divers to increase flow. But we will assume it is another constant. Pi (π) is also a constant.

So the two remaining variables are the important ones to understand. The pressure differential created by expansion and relaxation of the lung generates a proportional flow, and we have dealt with this in previous chapters.

What we will look at more closely now is airway radius as this has a profound effect on flow. Radius is critical for two main reasons. First it is variable, as the caliber of an airway changes with lung volume and by the action of airway smooth muscle. Second, it has a very powerful effect on flow; as you can see in Poiselle’s equation, radius is to the fourth power. This means a small increase in radius has a large effect on flow. For example, if the radius of an airway is doubled from 1 mm to 2 mm, the flow rate through the tube increases sixteenfold, which of course is two to the fourth power (i.e., 2x2x2x2). The inverse is of course true—halve the radius and flow reduces sixteenfold.

So far we have couched everything in terms of flow, but really we need to look at airway resistance. Because resistance is simply the reciprocal (or opposite) of flow, we can flip Poiselle’s equation upside down to describe resistance, and we now see that a reduction in radius (r) causes a large increase in resistance (R).

\[\mathrm{R}=\frac{8 n \times \mathrm{L}}{\Delta \mathrm{P} \times \pi \times r^{4}} \nonumber \]