Dynamic Lung and Chest Wall Mechanics

Patterns of Airflow

There are two major patterns of airflow in the airways—laminar and turbulent. Laminar flow is parallel to the airway walls and is present at low flow rates. As the flow rate increases and particularly as the airways divide, the flow stream becomes unsteady and small eddies develop. At higher flow rates the flow stream is disorganized, and turbulence occurs.

The pressure-flow characteristics of laminar flow were first described by the French physician Poiseuille and apply to both liquids and air. In straight circular tubes the flow rate ( $\dot{V}$ ) is defined by the following equation:

where P is the driving pressure, r is the radius of the tube, η is the viscosity of the fluid, and l is the length of the tube. It can be seen that driving pressure (P) is proportional to the flow rate ( $\dot{V}$ ); thus the greater the pressure, the greater the flow.

The flow resistance (R) across a set of tubes is defined as the change in driving pressure (ΔP) divided by the flow rate, or:

The units of resistance are cm H ₂ O/L•second. This equation is for laminar flow and demonstrates that the radius of the tube is the most important determinant of resistance. If the radius of the tube is reduced by half, the resistance will increase 16-fold. If, however, tube length is increased twofold, the resistance will increase only twofold. Thus, the radius of the tube is the principal determinant of resistance. Stated another way, resistance is inversely proportional to the fourth power of the radius, and it is directly proportional to the length of the tube and to the viscosity of the gas. To increase flow, increase the radius of the tube, shorten the tube, or decrease the viscosity of the flowing compound.

In turbulent flow, gas movement occurs both parallel and perpendicular to the axis of the tube. Pressure is proportional to the flow rate squared. The viscosity of the gas increases with increasing gas density, and therefore the pressure drop increases for a given flow. Overall, gas velocity is blunted because energy is consumed in the process of generating eddies and chaotic movement. As a consequence, higher driving pressure is needed to support a given turbulent flow than to support a similar laminar flow.

Whether flow through a tube is laminar or turbulent depends on the Reynolds number. The Reynolds number (R _e ) is a dimensionless value that expresses the ratio of two dimensionally equivalent terms (kinematic/viscosity), as seen in the equation:

where d is the fluid density, v is the average velocity, r is the radius, and η is the viscosity. In straight tubes, turbulence occurs when the Reynolds number is greater than 2000. From this relationship it can be seen that turbulence is most likely to occur when the average velocity of the gas flow is high and the radius is large. In contrast, a low-density gas such as helium is less likely to cause turbulent flow. This is clinically relevant in states of increased airway resistance where a decrease in gas density can improve airflow (e.g., by substituting helium for nitrogen in inspired air with a compound called Heliox). The increased rate of airflow also causes audible changes in voice pitch when breathing helium.

Although these relationships apply well to smooth cylindrical tubes, application of these principles to a complicated system of tubes such as the airways is difficult. As a result, much of the flow in the airways demonstrates characteristics of both laminar and turbulent flow. In the trachea, for example, even during quiet breathing the Reynolds number is greater than 2000. Hence turbulent flow occurs in the trachea even during quiet breathing. Turbulence is also promoted by the glottis and vocal cords, which produce some irregularity and obstruction in the airways. As gas flows distally, the total cross-sectional area increases dramatically, and gas velocities decrease significantly. As a result, gas flow becomes more laminar in the smaller airways even during maximal ventilation. Overall, the gas flow in the larger airways (nose, mouth, glottis, and bronchi) is turbulent, whereas the gas flow in the smaller airways is laminar. Breath sounds heard with a stethoscope reflect turbulent airflow. Laminar flow is silent, which is why it is difficult to “hear” small airway disease with a stethoscope.