BIOC34H3 Lecture Notes - Lecture 10: Ideal Gas Law, Transpulmonary Pressure, Gas Constant
Lecture 10: Lung Mechanics (continued) and Spirometry
1. The Ideal Gas Law
The Ideal Gas Law is as follows:
PV = nRT
Where P is gas pressure, V is the volume in which the gas is contained, n is the number of moles
of gas, R is the universal gas constant, and T is temperature in degrees Kelvin. Pressure can be
calculated by the equation P = nRT/V. Boyle's Law, which states that for a given quantity of gas
in a chamber, the gas pressure is inversely proportional to the volume of the chamber.
There are three main pressures associated with pulmonary mechanics as well as two important
pressure differentials. Atmospheric pressure, inter-alveolar pressure, and inter-pleural
pressure are the three pressure values, and the important pressure differentials are between the
former two (which is the driving force for moving air in and out of the lungs) and between the
latter two (called transpulmonary pressure, which is the driving force for lung expansion).
Air flow in and out of the lungs is caused by differences between atmospheric pressure and
pressure inside the lungs (inter-alveolar pressure). If the former pressure is higher than the latter,
air will flow into the lungs, and vice versa. We can calculate air flow via this equation:
Air Flow = (atmospheric pressure – inter-alveolar pressure) / Resistance
We consider (in this case) atmospheric pressure to be constant (atmospheric pressure changes are
primarily due to changes in altitude).
2. Pressure and Volume Changes during Inspiration and Expiration
As the lung expands, inter-alveolar pressure will decrease. As inter-alveolar pressure falls lower
relative to atmospheric pressure, the lungs will begin to fill with molecules of air. As the lungs
fill, pressure begins to increase again, and when it reaches equilibrium with the pressure of air
outside the lungs, air flow will cease. Even though Palv relative to Patm goes down and up during
inspiration, breath volume increases during this entire time period until equilibrium is reached
(i.e., Palv relative to Patm is zero).
During expiration, as the lungs recoil to the “resting state”, inter-alveolar pressure increases
relative to atmospheric pressure forcing air out of the lungs. When enough air has been exhaled,
pressure will begin to decrease again, until it reaches equilibrium and the process begins again. If
one were to graph inter-alveolar pressure relative to atmospheric pressure during the process of a
breath, it would resemble a sine wave: a shallow dip down and a shallow curve up, and back
3. Pressure and Volume Changes during Inspiration – A More Detailed Look
Motor activity in the phrenic nerve causes the diaphragm to contract and move downward
causing the chest wall to expand. This causes a pull on the interpleural fluid leading to a decrease
in intrapleural pressure. As intrapleural pressure decreases (with no immediate change in intra-
alveolar pressure), transpulmonary pressure increases. This causes the lungs to expand and
therefore lung volume increases. As lung volume increases, inter-alveolar pressure decreases
leading to an increase in the atmospheric pressure – inter-alveolar pressure difference. This
causes air to flow into the lungs.
4. Surface Tension and Pulmonary Surfactant
Recall that compliance is a measure of how easy it is to expand, in this case, the lungs. The inner
walls of the alveoli have a thin fluid layer on their surface. As such, when the lungs expand,
work is required to expand both the lungs (alveoli) and this fluid layer. The fluid layer exerts a
surface tension due to its interaction with the lung tissue and other fluid molecules. This surface
tension causes a reduction in lung compliance.
Consider a soap bubble to be a model of a single alveoli. There is a layer of fluid on the inside
surface of the bubble. This fluid layer exerts a surface tension that pulls the inner surface of the
bubble inward causing it to collapse. At the same time, the air pressure within the bubble
(distending pressure) is exerting an outward force preventing the bubble from collapsing. When
the surface tension pulling the bubble inward is balanced by the distending pressure pushing
outward, the bubble will “settle” on a final volume.
LaPlace’s Law states that the pressure (P) required to prevent an alveoli from collapsing (at rest)
is equal to two times the surface tension (T) divided by the radius (r): P = 2T/r. This relationship
means that a smaller alveoli requires a larger pressure to prevent it from collapsing than does a