2.1 Gas Laws in Transport Medicine

Gas Laws in Critical Care Transport

Critical care transport occurs in a dynamic physical environment where barometric pressure decreases exponentially as altitude increases. Understanding the physical behavior of gases under changing pressures, volumes, and temperatures is paramount for the flight clinician. These behaviors are governed by the gas laws, which have direct physiological consequences and guide clinical management of patients in flight.

Boyle's Law: Pressure and Volume

Boyle's Law states that at a constant temperature, the volume of a gas is inversely proportional to the pressure exerted upon it:

$\text{P}_1 \text{V}_1 = \text{P}_2 \text{V}_2$

In flight medicine, this is the most critical law for understanding the behavior of gases in closed spaces. As an aircraft climbs, barometric pressure decreases, causing any trapped gas to expand. Conversely, during descent, pressure increases, causing gas volume to contract.

Clinical Calculations: Dry vs. Wet Gas

Consider a patient at sea level (barometric pressure [P₁] = 760 mmHg) with a pneumothorax containing 100 mL of air. If the transport aircraft climbs to a cabin altitude of 8,000 feet (where barometric pressure [P₂] is approximately 564 mmHg), we can calculate the new volume using the dry gas formula:

$\text{V}_2 = \frac{\text{P}_1 \times \text{V}_1}{\text{P}_2} = \frac{760 \times 100}{564} \approx 134.8 \text{ mL}$

This represents a 35% increase in the volume of the pneumothorax.

However, in the human body, gases are saturated with water vapor. Water vapor pressure (PH₂O) is constant at 47 mmHg at normal body temperature (37°C). Because water vapor pressure does not change with altitude, the expansion of wet (saturated) gases is greater than predicted by dry gas calculations. The physiological formula for wet gas expansion is:

$\text{V}_2 = \text{V}_1 \times \frac{\text{P}_1 - 47}{\text{P}_2 - 47}$

Using the same scenario:

$\text{V}_2 = 100 \times \frac{760 - 47}{564 - 47} = 100 \times \frac{713}{517} \approx 137.9 \text{ mL}$

Due to saturation, the pneumothorax actually expands by 38% at 8,000 feet. This highlights the severity of gas expansion in vivo.

Clinical Applications and Mitigation

---

Dalton's Law: Partial Pressures

Dalton's Law states that the total pressure of a gas mixture is the sum of the partial pressures of its individual components:

$\text{P}_{\text{total}} = \text{P}_1 + \text{P}_2 + \text{P}_3 + \dots$

The atmosphere is composed of approximately 78% Nitrogen, 21% Oxygen, and 1% trace gases. The fractional concentration of oxygen (FiO₂) remains constant at 21% up to approximately 70,000 feet. However, as barometric pressure (PB) drops with altitude, the partial pressure of oxygen (PO₂) drops proportionally:

$\text{P}_{\text{O}_2} = \text{F}_{\text{iO}_2} \times \text{P}_{\text{B}}$

• Sea level: PO₂ = 0.21 × 760 mmHg = 159.6 mmHg
• 10,000 feet: PO₂ = 0.21 × 523 mmHg = 109.8 mmHg

This reduction in ambient PO₂ decreases the pressure gradient driving oxygen across the alveolar-capillary membrane, which leads directly to hypoxemic hypoxia. To maintain adequate arterial oxygen tension, the flight clinician must increase the FiO₂ to compensate for the reduced barometric pressure. The relationship is described by the simplified Alveolar Gas Equation:

$\text{P}_{\text{A}} \text{O}_2 = \text{F}_{\text{iO}_2} (\text{P}_{\text{B}} - 47) - \frac{\text{P}_{\text{a}} \text{CO}_2}{\text{R}}$

Where PAO₂ is alveolar oxygen tension, PaCO₂ is arterial carbon dioxide tension, and R is the respiratory quotient (typically 0.8).

---

Charles's Law: Temperature and Volume

Charles's Law states that at a constant pressure, the volume of a gas is directly proportional to its absolute temperature (measured in Kelvin):

$\frac{\text{V}_1}{\text{T}_1} = \frac{\text{V}_2}{\text{T}_2}$

According to the standard environmental temperature lapse rate, ambient temperature decreases by approximately 2°C (3.5°F) for every 1,000 feet of ascent.

Clinical Applications

1. Oxygen Cylinder Pressure: Portable oxygen cylinders stored in unheated exterior compartments will show lower pressures when exposed to cold temperatures at cruising altitudes. A tank that read "full" (e.g., 2,000 psi) on a hot tarmac will show a lower pressure reading at altitude. Clinicians must calculate tank duration based on these temperature-induced changes.
2. Tidal Volume Expansion: Cold gases delivered from a ventilator will warm to body temperature (37°C) once inhaled. As the temperature rises, the volume of the gas expands. High-quality transport ventilators must calibrate volumes to Body Temperature, Pressure, Saturated (BTPS) conditions to avoid volutrauma or barotrauma.

---

Henry's Law: Gas Solubility

Henry's Law states that the amount of gas dissolved in a liquid is directly proportional to the partial pressure of that gas in contact with the liquid:

$\text{C} = k \times \text{P}$

Where C is the concentration of dissolved gas, k is the solubility constant, and P is the partial pressure of the gas.

Decompression Sickness (DCS)

At sea level, nitrogen is dissolved in body tissues and blood. As an aircraft climbs and ambient barometric pressure decreases, nitrogen becomes less soluble. If the ascent is rapid, nitrogen gas bubbles out of solution, forming microemboli in blood vessels, lymphatics, and joint spaces, a condition known as decompression sickness ("the bends").

Clinical Action

To prevent DCS in high-risk patients (such as commercial divers or patients undergoing high-altitude transfer), clinicians must pre-oxygenate the patient with 100% oxygen for at least 30 minutes. This washes out (denitrogenates) dissolved nitrogen from the tissues. If a patient develops DCS in flight, the clinician must immediately administer high-flow oxygen, request the pilot descend to the lowest safe altitude (or cabin altitude of sea level), and coordinate transport directly to a hyperbaric oxygen therapy facility.

---

Graham's Law: Rate of Diffusion

Graham's Law states that the rate of diffusion of a gas through a membrane or medium is inversely proportional to the square root of its molecular weight:

$\text{Rate} \propto \frac{1}{\sqrt{\text{Molecular Weight}}}$

Physiological Gas Exchange

Lighter molecules diffuse faster than heavier ones. In physiology, Graham's Law interacts with Henry's Law of solubility, which is formulated as Fick's Law of Diffusion.

Although carbon dioxide (CO₂, molecular weight ≈ 44) is heavier than oxygen (O₂, molecular weight ≈ 32) and should diffuse slower according to Graham's Law, CO₂ is 24 times more soluble in plasma than oxygen. Consequently, CO₂ diffuses approximately 20 times faster than oxygen across the alveolar-capillary membrane. This explains why patients with alveolar capillary thickening (e.g., ARDS, pulmonary edema) develop severe hypoxemia long before they develop hypercapnia.

Heliox (a mixture of helium and oxygen) utilizes Graham's Law to treat severe reactive airway diseases. Because helium has a low molecular weight and density, Heliox promotes laminar airflow, reducing airway resistance and the patient's work of breathing.