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# Alveolar gas equation: Altitude

The alveolar gas equation estimates alveolar oxygen content given a few readily measurable variables. The pAO2 derived from performing the calculation can then be used to discern the degree of shunt present in a patient. Practical simplification of the complex formula allows for the following equation:

pAO2 = FiO2 (Patm – pH20) – (paCO2/RER)

Where in the average person the respiratory exchange ratio (RER) (or respiratory quotient) is typically considered to be 0.8 (varies depending on the diet and primary source of fuel the patient is utilizing such as fat, protein or carbohydrates)

At sea level, the atmospheric pressure is 760 mmHg and the vapor pressure of water at body temperature is 47 mmHg. Plugging these rough numbers into the aforementioned equation leads to the following simplification at sea level:

pAO2 = (FiO2 x 713 mmHg) – (paCO2/0.8)

Given that increasing altitude decreases the atmospheric pressure, for any given FiO2 you would expect a lower pAO2 and, consequently, a lower paO2. For example, whereas breathing 100% oxygen at sea level would result in an alveolar pO2 of 663 mmHg, breathing 100% oxygen on Mt. Everest at a barometric pressure of 263 mmHg would result in a pAO2 of 166 mmHg (assuming the pH2O, paCO2 and RER to be the same). This results in hypoxia which triggers all manner of physiologic changes that can include but are not limited to: respiratory alkalosis (as seen in acute mountain sickness), mental status changes, increased heart rate and cardiac output, decreased systemic vascular resistance, pulmonary vasoconstriction/hypertension (as seen in chronic mountain sickness with potential evolution of cor pulmonale), and cerebral edema, among others.

Conversely, increasing the barometric pressure can have significant effects by increasing the amount of dissolved oxygen. It is for this reason that hyperbaric oxygen therapy has been implemented for the treatment of nonhealing wounds, decompression sickness, and carbon monoxide poisoning, among others.

Though not specific to altitude necessarily, the alveolar gas equation illustrates that, by definition, hypoventilation (and increases in PaCO2) will result in a relative hypoxemia given all other variables in the equation are held steady. For any given patient, this fact may or may not have any clinical relevance.

Most variable bypass canisters can compensate for adjustment in atmospheric pressure automatically. So you will not have to adjust the percent concentration for isoflurane or sevoflurane at different altitudes. The partial pressure of the anesthetic gases will remain the same.

However, you will have to make adjustments for desflurane. The percent of desflurane delivered will not change with altitude, but the partial pressure will. A desflurane vaporizer is kept at a constant temperature (39 degrees Celsius) which maintains a constant vapor pressure of 2atm. At higher altitudes, the total pressure decreases. Dalton’s law states that the total pressure equals the sum of the partial pressures, so if the percent concentration is constant, the partial pressure will decrease proportionally at a lower atmospheric pressure. Because potency of an anesthetic agent is related to its partial pressure rather than its percent concentration, you would need to increase the dial of percent concentration of a volatile anesthetic to achieve the same MAC at a higher altitude.

Required dial setting = desired % x (760mmHg/current atmospheric pressure)