Physics of respiration

The physics of respiration encompasses the physical principles and laws that govern gas exchange and breathing mechanics in living organisms. Respiration is fundamentally a biophysical process governed by classical gas laws, fluid dynamics, thermodynamics, and mechanics.

Overview

The respiratory system functions to exchange oxygen and carbon dioxide between the atmosphere and blood. This exchange depends entirely on pressure gradients, molecular diffusion, and mechanical forces. The physics of respiration can be analyzed through several fundamental domains: gas laws governing partial pressures, mechanics of breathing involving pressure-volume relationships, diffusion kinetics across membranes, fluid dynamics in airways, and surface tension effects in alveoli.

Gas laws in respiration

Dalton's law of partial pressures

states that in a mixture of non-reacting gases, the total pressure equals the sum of the partial pressures of individual gases:
This law explains how each gas in air contributes to total atmospheric pressure. At sea level, atmospheric pressure is approximately 760 mm Hg, and the partial pressure of oxygen is 160 mm Hg, yielding a fraction of oxygen of 0.21. On inspiration, air is warmed and moisturized to saturation in the human airways. The addition of water vapor decreases the partial pressure of other gasses. The partial pressure of oxygen within the upper airways is called inspired P_O₂ and is calculated:
where F_IO₂ is the fractional concentration of inspired oxygen, P_atm is atmospheric pressure, and P_H₂O is the partial pressure of water vapor in the upper airways. This yields a of approximately 150 mm Hg.
On inhalation, air passes through the upper airways until eventually reaching the alveoli in the lungs. The alveolar gas equation applies Dalton's law to calculate alveolar oxygen partial pressure:
where P_AO₂ is the partial pressure of alveolar oxygen, and P_ACO₂ is the partial pressure of alveolar carbon dioxide, and R is the respiratory quotient.

Henry's law

describes gas solubility in liquids, stating that the amount of dissolved gas is proportional to its partial pressure:
where C is the concentration of dissolved gas, k_H is Henry's constant, and P is the partial pressure. Different gases have different solubility coefficients in blood. Carbon dioxide is approximately 20 times more soluble in blood than oxygen, which has important physiological implications for gas transport.
In aerospace medicine, Henry's law underlies the development and treatment of decompression illness. Increases in altitude correspond to a decrease in the partial pressure of nitrogen, and corresponding decrease in dissolved nitrogen in the blood. If the nitrogen rapidly comes out of solution then it forms bubbles which can block off small capillaries and damage tissues. Cabin pressurization helps prevent this, but is not usually available in helicopters, requiring them to fly at lower altitudes safe for human physiology. Breathing gases used in high-altitude aircraft usually have a higher oxygen concentration in order to help remove nitrogen from the blood. This is also the reasoning for the usage of oxygen masks on airlines during sudden cabin depressurization. Although the partial pressure of oxygen also decreases with increases in elevation, since the majority of oxygen in the blood is bound to hemoglobin, it does not bubble out like nitrogen does.

Boyle's law

states that for a fixed amount of gas at constant temperature, pressure and volume are inversely related:
The lungs follow Boyle's law except near their maximum or minimum volumes when their compliance is low. During inhalation, the thoracic cavity expands, increasing lung volume and decreasing intrapulmonary pressure below atmospheric pressure, causing air to flow inward. During exhalation, the thoracic cavity decreases in volume, increasing pressure and forcing air outward.
The lungs exist within a negative pressure cavity called the pleural space. Under normal conditions the lungs expand to fill the pleural space. The pleural space directly expands or contracts with the thoracic cavity, causing the lungs to expand or contract with the thoracic cavity as well. However, if the pleural space accumulates blood or air then there is an increase in pressure within it, requiring a greater expansion of the thoracic cavity to inflate the lungs.
As a scuba diver descends, the pressure in their lungs increases, and in accordance to Boyle's law the volume within their lungs decreases. On ascent the inverse is true, and if a scuba diver doesn't exhale the increase in volume then they risk the overexpansion and rupture of their alveoli.

Mechanics of Breathing

Pressure-Volume Relationships

The mechanics of breathing involve coordinated changes in pressure and volume within the respiratory system. The key pressures involved are:

Atmospheric pressure : pressure of ambient air
Alveolar pressure : pressure within the alveoli
Intrapleural pressure : pressure in the pleural space
Transpulmonary pressure : difference between alveolar and intrapleural pressure

The transpulmonary pressure represents the distending pressure across the lung:
This pressure determines lung volume and is critical for understanding lung mechanics. The relationship between transpulmonary pressure and lung volume defines pulmonary compliance.

Compliance and elastance

Compliance is defined as the change in volume per unit change in pressure:
Normal lung compliance is approximately 200 mL/cm H₂O. Compliance is low when the lungs are nearly fully expanded or collapsed. As newborns are born with no air in their lungs, their initial lung compliance is low, requiring greater pressure to take their first breaths and inflate their lungs.
Diseases such as pulmonary fibrosis decrease compliance, while emphysema increases compliance.
Elastance is the reciprocal of compliance:
The lung and chest wall each have their own compliance values, and the total respiratory system compliance is determined by:

Work of breathing

The work of breathing represents the energy required to overcome elastic and resistive forces during ventilation. It can be calculated as:
This work has three components:

Elastic work: energy to overcome elastic recoil of lungs and chest wall
Resistive work: energy to overcome airway and tissue resistance
Inertial work: energy to accelerate gases and tissues
Gas diffusion

Fick's laws of diffusion

Gas exchange across the alveolar-capillary membrane is governed by Fick's first law of diffusion:
where:

V_gas is the rate of gas transfer
A is the surface area available for diffusion
D is the diffusion coefficient
P₁ - P₂ is the partial pressure difference across the membrane
T is the thickness of the membrane

This equation can be simplified to:
where D_L is the diffusing capacity of the lung, which incorporates surface area, membrane thickness, and diffusion properties.

Diffusion coefficients

The diffusion coefficient depends on:

Molecular weight: inversely proportional to the square root of molecular weight
Solubility: directly proportional to gas solubility in tissue
Temperature: increases with temperature

Carbon dioxide diffuses approximately 20 times faster than oxygen across the alveolar-capillary membrane due to its much higher solubility, despite its slightly larger molecular weight.

Diffusion limitation versus perfusion limitation

Gas transfer can be limited by either diffusion or perfusion:

Diffusion-limited: Transfer rate limited by membrane properties
Perfusion-limited: Transfer rate limited by blood flow
Airway resistance and fluid dynamics

Poiseuille's law

For laminar flow through cylindrical tubes, the Hagen-Poiseuille equation describes the relationship between flow rate and pressure:
where:

Q is flow rate
r is radius of the airway
ΔP is pressure difference
μ is viscosity of the gas
L is length of the airway

This equation demonstrates that flow is proportional to the fourth power of the radius, making airway radius the most critical determinant of resistance.
Airway resistance is defined as:
From Poiseuille's law:
Normal total airway resistance is approximately 1-2 cmH₂O/L/s. Disease states such as asthma and chronic obstructive pulmonary disease significantly increase airway resistance.

Laminar and turbulent flow

Flow patterns in airways depend on the Reynolds number :
where:

ρ is gas density
v is velocity
d is diameter
μ is viscosity
Laminar flow : smooth, organized flow following Poiseuille's law
Turbulent flow : chaotic, disorganized flow with higher resistance
Transitional flow : mixture of laminar and turbulent

In turbulent flow, resistance increases proportionally to the square of flow rate, rather than being independent of flow as in laminar conditions.

Surface tension and the Laplace law

Young-Laplace equation

Surface tension at the air-liquid interface in alveoli creates a pressure according to the Young-Laplace equation:
where:

P is pressure inside the alveolus
T is surface tension
r is radius of the alveolus

This equation predicts that smaller alveoli would have higher pressures and would tend to collapse into larger alveoli. This is prevented by pulmonary surfactant.

Pulmonary surfactant

is a complex mixture of lipids and proteins secreted by type II pneumocytes. It reduces surface tension from approximately 70 dyn/cm to as low as 5-10 dyn/cm.
Surfactant has two critical physical properties:

Reduces surface tension: Decreases the work of breathing
Provides stability: Surface tension varies with area, decreasing more in smaller alveoli, which prevents collapse

Without surfactant, the pressure required to inflate the lungs would be prohibitively high, and alveolar instability would result in atelectasis. Neonatal respiratory distress syndrome occurs when premature infants lack adequate surfactant production.