In this lesson, you’ll discover what airway resistance means and learn two different ways of calculating it. You’ll also uncover issues with calculating a true airway resistance.

What Is Airway Resistance?

Riddle me this: It’s something you can’t touch but you can hold, and every living animal has it. What is it?

The answer is breath!

How do we breathe? Well, with our lungs, of course. Although we breathe all the time, there are actually many factors involved in a simple breath.

One is the resistance to airflow in the lung, known as airway resistance, which in science and medicine is abbreviated as Raw. In order for air to move into or out of your lungs, it has to want to, and it has to overcome friction, the force that stops two things from sliding past each other. Yes, even air has friction. Airway resistance is thus a measure of the resistance to lung airflow caused by friction.

The resistance of your lung to airflow is a determinant of how easy it is to breathe; therefore, scientists like to measure it. Knowing the airway resistance helps doctors tell if your lungs are functioning normally.

1st Formula for Airway Resistance

Why does air want to move in the first place? The answer is the difference in pressure.

Imagine a rubber band holding a bundle of toothpicks. What happens if you pull on two sides of the rubber band? The pressure of the rubber band that was holding the toothpicks together decreases. This makes the toothpicks loosen and move. If you release the rubber band, it moves back into place, putting pressure back on the toothpicks and tightening them.

A similar event occurs in your lungs. Your muscles pull the lung (rubber band) open, decreasing the pressure and leaving air free to flow inside (the loosened toothpicks). Upon exhaling, your muscles relax, no longer pulling the lung, thereby increasing the pressure (retightening the toothpicks). The increased pressure forces the air to leave the lungs.

The first formula for airway resistance involves determining the change in pressure from where air enters (your mouth) to where it ends up, the part of the lung called the alveoli. The pressure of the lung where air enters is the same as the pressure of the atmosphere (PB), while the pressure of the alveoli (Palv) is determined by other factors.

The most common unit of pressure used for the lung is centimeters of water (cmH2O).

So, now we know one part of the equation: change in pressure. The other part involves flow rate (V dot), or how fast air flows.

Imagine you’re in a room full of people and see an empty room nearby. You go in there to escape the crowd, but people follow you. If you measure the number of people who’ve moved into the room over time, you’ll get the flow rate of people. For example, 10 people in 10 minutes = 1 person per minute. Since air isn’t a solid, it’s most often measured by how much volume in liters (L) it occupies, and since it moves so fast, time’s usually measured in seconds (sec).

One formula for airway resistance then is a ratio of the change in pressure to the flow rate of air. To calculate the change in pressure, all we need to do is subtract the alveolar pressure from the atmospheric pressure. Normal airway resistance is around 2 cmH2O per L per sec.

2nd Formula for Airway Resistance

What happens if you can’t measure flow or pressure?

French physicist Jean L;onard Marie Poiseuille developed an equation to describe flow in a tube. Since it looks at changes in pressure and flow rate, and your lungs are a bunch of connecting tubes, the equation can be adapted to determine airway resistance based on lung structure. The main factors involved are the length of the tube (l), the radius of the tube (r) and another factor called viscosity (mu).

Viscosity is like a gooeyness factor. Imagine the difference between water and syrup. Syrup is more viscous than water. It’s harder to run your fingers through syrup than water, right?

Now that we know the main players, all we need is the basic equation, which is: 8 times length times viscosity all divided by pi times the radius to the 4th power. The viscosity stays pretty much the same throughout the lung, so 8, pi, and mu are basically constants. The only factors that will majorly affect the resistance are length and radius.

Issues with Formulas

There are a few issues with these formulas. First, the formulas are based on a smooth, even, straight airflow, or laminar flow. However, air doesn’t flow down a straight path, but has to make many twists and turns inside the lung, creating a chaotic, turbulent flow. Other, more complex equations involving more variables like air density have been developed to account for this flow variance.

In reality, there’s more resistance in the bigger airways (trachea and bronchus) than smaller, so even inside the lung airway resistance varies. Other factors, including lung elasticity and obstruction, also affect resistance. Even each breath alters multiple factors and changes airway resistance. Thus, the equations give a simplified glimpse of true airway resistance.

Lesson Summary

Airway resistance (Raw) is the lung’s resistance to airflow due to friction. There are two equations that can be used to measure resistance. The first equation is a ratio of the change in pressure to flow rate of air. The change in pressure (deltaP) is the pressure where air enters (atmospheric pressure or PB) minus ending or alveolar pressure (Palv).The first equation is:

Raw = (deltaP) / V dot.

The second equation involves airway length (l), viscosity (mu), and radius (r) and is:

Raw= 8 * l * (mu) / (pi) * r^4

These equations assume laminar airflow, whereas in our lungs, airflow is sometimes turbulent and involves more complex computations. And, of course, the bigger airways have more resistance than smaller ones. The main variables influencing actual airway resistance are changes in pressure, airflow, viscosity, air density, airway length, and radius.