# Dynamic Lung Mechanics

## Objectives

• 1.

Describe how a pressure gradient is created.

• 2.

Define airway resistance and its measurement.

• 3.

Discuss three factors that contribute to or regulate airway resistance in health and disease.

• 4.

Describe the concepts of flow limitation, the equal pressure point, and dynamic airway compression.

• 5.

Define work of breathing and the factors that contribute to work of breathing.

Dynamic lung mechanics studies the lung in motion. To cause air to move from the outside of the body into the distal airways, three opposing forces must be overcome: (1) the elastic recoil of the lungs and chest wall, (2) the frictional resistances of the airways and of the tissues of the lung and chest wall, and (3) the inertance or impedance of acceleration of the respiratory system. The elastic forces of the lung and chest wall ( Chapter 2 ) depend on lung volume and are not affected by motion. Inertance depends on the rate of airflow but is negligible during quiet breathing. Thus the major force that must be overcome to achieve airflow is frictional resistance. Frictional resistance is determined by flow and not by a change in lung volume.

## How a Pressure Gradient is Generated

Gases move from regions of higher pressure to regions of lower pressure. The movement of air in and out of the lungs requires the creation of a pressure gradient from the inside of the alveoli to the outside world. Pressure changes within the airways are, by convention, referenced to barometric pressure and are either greater than or less than barometric pressure. Because the absolute barometric pressure is different at different altitudes, again by convention, the pressure surrounding the chest wall (the barometric pressure) is referenced to zero when pressure gradients are being measured. Inspiration occurs when negative pressure is generated inside the alveoli—that is to say, when alveolar pressure is lower than atmospheric pressure.

Alveoli are not capable of expanding on their own. They will expand only when there is an increase in the distending pressure across their walls. The distending pressure across the alveolar wall is called the transmural (mural, meaning any wall) or transpulmonary (across the lung; that is, from the alveolus to the pleura) pressure gradient and it is generated by the muscles of inspiration. Before airflow begins, the pressure inside the alveoli is the same as atmospheric pressure, which by convention is equal to 0 cm H 2 O. An important principle of respiration is that pressures at the pleural surface generated by the muscles of respiration are transmitted through the alveolar walls to the more centrally located alveoli and small airways. Thus alveolar units are structurally interdependent.

During inspiration, as the muscles of inspiration contract, the pressure inside the airways decreases relative to barometric pressure (that is, it becomes less than atmospheric pressure or “negative” relative to the “zero” atmospheric pressure) according to Boyle’s law (see Appendix C). Thus if the pressure in the alveoli decreases, the volume in the alveoli must increase. For example, during inspiration the pressure inside the airways is −5 cm H 2 O. That is, it is 5 cm H 2 O less than atmospheric pressure (zero), but the actual pressure, assuming that you are at sea level, would be 760 mm Hg − 5 cm H 2 O (note the different units) or 760 mm Hg − ∼4 mm Hg. During exhalation, the process is reversed, and the pressure inside the airways becomes greater than atmospheric pressure. The important principle to remember is that gases always flow from an area of higher pressure to an area of lower pressure.

## Resistance

The pressure flow characteristics of laminar flow (Appendix C) were first described by the French physician Poiseuille. In straight circular tubes, the flow rate ( <SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='V˙’>V˙
V ˙
; the dot above the letter V signifies a change in volume with respect to time—that is, a flow rate) is given by:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml='V˙=Pxr48nl’>V˙=Pxr48nlV˙=Pxr48nl
V ˙ = Pxr 4 8 nl
where P is the driving pressure, r is the radius, n is the viscosity, and l is the length. Thus it can be seen that the driving pressure (P) is proportional to the flow rate ( <SPAN role=presentation tabIndex=0 id=MathJax-Element-3-Frame class=MathJax style="POSITION: relative" data-mathml='V˙’>V˙
V ˙
)—that is, P = k × <SPAN role=presentation tabIndex=0 id=MathJax-Element-4-Frame class=MathJax style="POSITION: relative" data-mathml='V˙’>V˙
V ˙
. The flow resistance, R, across a set of tubes is defined as the change in driving pressure (ΔP) divided by the flow rate, or
<SPAN role=presentation tabIndex=0 id=MathJax-Element-5-Frame class=MathJax style="POSITION: relative" data-mathml='R=ΔPV˙=8nlπr4′>R=?PV˙=8nl?r4R=ΔPV˙=8nlπr4
R = Δ P V ˙ = 8 nl π r 4

The units of resistance are cm H 2 O/L ⋅ sec. A number of important observations can be made based on this equation, including the role of the radius in determining resistance. If the radius of the tube is reduced in half, the resistance will increase 16-fold. If, however, the length is increased twofold, the resistance will only increase twofold. Thus the radius of the tube primarily determines resistance. Stated another way, resistance is inversely proportional to the fourth power of the radius and directly proportional to the length of the tube and the gas viscosity. The radius is thus the main factor that affects resistance. The smaller the airway, the greater the resistance of that airway.

Resistance to airflow in the respiratory system is composed of three individual resistances; airway resistance, pulmonary (parenchyma or lung tissue) resistance, and chest wall resistance. Airway resistance is defined as the frictional resistance of the entire system of airways from the tip of the nose (for nasal breathing) or mouth (for mouth breathing) to the alveoli. Pulmonary resistance (or lung resistance) is defined as the frictional resistance afforded by the lungs and the airways combined. Chest wall resistance is the frictional resistance of the chest wall and abdominal structures. In turn, airway resistance is composed of the resistance of the upper airway (from nose to glottis) and the resistance of the lower airways (from glottis to alveoli).

Approximately 25% to 40% of the total resistance to airflow is located in the upper airways—namely the nose, nasal turbinates, oropharynx, nasopharynx, and larynx ( Fig. 3.1 ). Respiratory system resistance is thus higher when breathing through the nose than when breathing through the mouth. During V t breathing, the vocal cords open slightly during inspiration and close slightly during exhalation. During inspiration, airways inside the chest are surrounded by a negative intrathoracic (pleural) pressure, and airways outside the chest (extrathoracic airways) are surrounded by atmospheric pressure. As a result, the pressure surrounding the extrathoracic airways is greater than the pressure inside the airways, and these extrathoracic airways are pulled inward, resulting in partial or complete airway obstruction, especially during deep inspirations.

This inward pulling of extrathoracic airways during inspiration is most easily demonstrated in the nose. Making a rapid inspiratory effort while breathing through the nose results in collapse of the anterior portion of the nose (a “sniff”). Counteracting the collapse of the extrathoracic airways during inspiration are the muscles of the oropharynx that contract during inspiration. Reflex contraction of these pharyngeal dilator muscles dilates and stabilizes the upper airway. In the anterior nose, active contraction of the alae nasi minimizes the collapse associated with sniffing. Failure of these muscles to contract can occur, especially during sleep, and can result in airway obstruction and obstructive sleep apnea (see Chapter 10 ).

Airflow resistance in the lower airways (Raw) can be divided between the resistance in the large airways (≥4 mm in diameter: first four airway generations), the medium-sized airways (subsegmental bronchi, 1–4 mm in diameter), and the small airways (bronchioles, <1 mm in diameter). Therefore Raw is equal to the sum of each of these individual resistances; that is,

<SPAN role=presentation tabIndex=0 id=MathJax-Element-6-Frame class=MathJax style="POSITION: relative" data-mathml='Raw=Rlarge+Rmedium+Rsmall’>Raw=Rlarge+Rmedium+RsmallRaw=Rlarge+Rmedium+Rsmall
Raw = R large + R medium + R small

From Poiseuille’s equation you might conclude that the major site of resistance in the airways is in the smallest airways. For many years this was thought to be true. In fact, however, the major site of resistance along the bronchial tree is the large bronchi. The smallest airways contribute little to the overall total resistance of the bronchial tree even though their individual resistance is high. The reason for this is interrelated and twofold. First, for the whole lung, the airways are a complex combination of tubes of different sizes arranged both in parallel and in series. As gas flows into more distal airways, the airway number increases faster than the decrease in individual airway size. As a result, there is a large increase in total airway cross-sectional area and airflow velocity becomes very low as the effective cross-sectional area increases ( Fig. 3.2 ). Second, at the same time that individual airways are becoming smaller with each generation and the resistance from generation to generation is additive (airways in series where R tot = Rgen 1 + Rgen 2 + Rgen 3 + …), the increase in airway number and airways now in parallel is increasing faster and the resistance within a generation where the airways are in parallel is decreasing (e.g., in generation 10, 1/R 10 = 1/Rbranch 1 + 1/Rbranch 2 + 1/Rbranch 3 + …). Thus the resistance of the airway generations with small airways is small. As an example, assume that there are three tubes each with a resistance of 3 cm H 2 O/L ⋅ sec ( Fig. 3.3 ). If the tubes are in series, the total resistance (R tot ) is the sum of the individual resistances:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-7-Frame class=MathJax style="POSITION: relative" data-mathml='RTOT=R1+R2+R3=3+3+3=9cmH2O/Lsec’>RTOT=R1+R2+R3=3+3+3=9cmH2O/LsecRTOT=R1+R2+R3=3+3+3=9cmH2O/Lsec
R TOT = R 1 + R 2 + R 3 = 3 + 3 + 3 = 9 cm H 2 O / L sec

If the tubes are in parallel (as they are in small airways), the total resistance is the sum of the inverse of the individual resistances (see Fig. 3.3 ).

<SPAN role=presentation tabIndex=0 id=MathJax-Element-8-Frame class=MathJax style="POSITION: relative" data-mathml='1/RTOT=1/R1+1/R2+1/R3=1/3+1/3+1/3=1cmH2O/Lsec’>1/RTOT=1/R1+1/R2+1/R3=1/3+1/3+1/3=1cmH2O/Lsec1/RTOT=1/R1+1/R2+1/R3=1/3+1/3+1/3=1cmH2O/Lsec
1 / R TOT = 1 / R 1 + 1 / R 2 + 1 / R 3 = 1 / 3 + 1 / 3 + 1 / 3 = 1 cm H 2 O / L sec   Get Clinical Tree app for offline access 