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# Alveolar Gas Equation

Editor: Bracken Burns Updated: 8/22/2022 8:03:54 PM

#### Introduction

The alveolar gas equation is used to calculate alveolar oxygen partial pressure, as it is impossible to collect gases directly from the alveoli. The equation is helpful in calculating and closely estimating the PAO2 inside the alveoli. The variables in the equation can affect the PAO2 inside the alveoli in different physiological and pathophysiological states.

Alveolar Gas Equation

• PAO2 = (Patm - PH2O) FiO2 - PaCO2/RQ

Patm is the atmospheric pressure (at sea level 760 mm Hg), and PH2O is the partial pressure of water (approximately 45 mm Hg). FiO2 is the fraction of inspired oxygen. PaCO2 is the partial pressure of carbon dioxide in alveoli (in normal physiological conditions around 40-45 mmHg). RQ is the respiratory quotient. The value of the RQ can vary depending on the type of diet and metabolic state. RQ is different for carbohydrates, fats, and proteins (the average value is around 0.82 for the human diet). Indirect calorimetry can provide better measurements of RQ by measuring the VO2 (oxygen uptake) and VCO2 (carbon dioxide production).

RQ = amount of CO2 produced/amount of oxygen consumed

At sea level, the alveolar PAO2 is:

• PAO2  = (760 - 47) 0.21 - 40/0.8 = 99.7 mm Hg.

The 3 major variables of the equation are the atmospheric pressure, amount of inspired oxygen, and levels of carbon dioxide. Each has an important clinical significance and can help explain physiological and pathophysiological states.[1]

#### Function

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#### Function

The function of the alveolar gas equation is in calculating the alveolar-arterial Ogradient (A-a gradient).

• Normal A-a gradient = (Age + 10) / 4
• A-a gradient increases 5 to 7 for every 10% increase in FiO2.

The arterial PO2 can be determined by obtaining an arterial blood gas. With the help of the alveolar gas equation, the partial pressure inside the alveoli can be calculated. Carbon dioxide is a very important variable in the equation. The PO2 in alveoli can change significantly with variations in blood and alveolar carbon dioxide levels. If the rise in CO2 is significant, it can displace oxygen molecules which causes hypoxemia. As atmospheric pressure reduces with increased altitude, the alveolar gas equation helps to calculate the PAO2 within the alveoli. This is significant in appropriately identifying the developed hypoxemia from decreased atmospheric pressure and treating it with appropriate supplemental oxygen levels.[2]

#### Issues of Concern

The derived alveolar gas equation is based on the assumption of a steady-state condition. The equation is only valid if the assumptions upon which it was constructed remain true. Low FiO2 conditions could violate the steady state. Thus, some physicians and scientists suggest using the detailed form of the equation. In clinical practice, the full alveolar gas equation does not convey relevant increased accuracy, and the abbreviated equation discussed above is sufficient in calculating the PO2 in alveoli.

#### Clinical Significance

Atmospheric Pressure

Increasing altitude decreases the atmospheric pressure; thus, for any given FiO2, there is a lower PO2  in the atmosphere and a lower PAO2  in alveoli. For example, breathing 21% oxygen at sea level would result in an alveolar PO2 close to 100 mm Hg, while breathing the same percentage of oxygen at Mount Everest (at atmospheric pressure of 263 mm Hg) would result in alveolar PO2 close to 0 mm Hg. As we ascend, barometric pressure goes down. This can lead to hypoxemia and trigger many physiologic changes.[1][2][3]

Symptoms (in decreasing order of frequency) include:

• Fatigue
• Nausea
• Vomiting
• Loss of appetite
• Dizziness
• Irritability
• Disturbed Sleep

A number of physiological changes occur which enable the body to function in a low-oxygen environment. This process of gradual adjustment is known as acclimatization. This increases the frequency and depth of breathing, cardiac output, blood pressure, and production of erythropoietin and 2,3-diphosphoglycerate (2,3 DPG). Without proper acclimatization and/or supplemental oxygen, one can have high-altitude cerebral edema, acute mountain sickness, and high-altitude pulmonary edema. On the other hand, increasing atmospheric pressure can have significant effects on the body by increasing the amount of dissolved oxygen in the blood. A hyperbaric oxygen chamber is used as a treatment for major carbon monoxide poisoning, decompression sickness, and non-healing ulcers.

Inspired Oxygen

Oxygen is used in the human body to perform oxidative phosphorylation and produce Adenosine Triphosphate (ATP), used in enzymatic reactions as a primary form of energy. Oxygen has a high redox potential and is the last acceptor of electrons within the electron transport chain. Hypoxemic patients typically present with shortness of breath and dyspnea. If hypoxia is severe, they may develop severe lactic acidosis, cyanosis, syncope, and arrhythmias.[4][5]

The alveolar gas equation helps us calculate the alveolar and arterial PO2 gradient (A-a) difference.

• Normal A-a gradient = (Age + 10) / 4

Every 10% rise in the inspired fraction of oxygen increases the partial pressure of available oxygen in the alveoli by approximately 60 to 70 mm Hg.[6] If more than required FiO2  is given, it can lead to an increase in PO2 within the alveoli, and if given for long periods of time, this can lead to lung injury. Higher levels of oxygen can be dangerous in end-stage chronic obstructive pulmonary disease patients, as their respiratory drive is dependent upon hypoxia (with a PO2 around 60 mm Hg).

Hyperoxygenation, by increasing the PO2  within the alveoli and plasma during the process of intubation or procedural conscious sedation, is very helpful and can be easily understood with the help of the alveolar gas equation. For example, at sea level, with no additional supplemental oxygen and a normal physiological state, the PO2 inside the alveoli calculates at approximately 100 mm Hg.

• PAO2 = (Patm - PH2O) FiO2 - PaCO2/RQ

For 100% oxygen:

• PAO= (760 - 47) x 1 - (40 / 0.8) = 663 mm Hg

However, if a patient is given 100% oxygen in the same situation, the PO2 can be as high as 663 mm Hg. In normal physiological conditions, this gives a clinician 8 to 9 minutes to successfully intubate before a patient’s partial pressure of oxygen falls below 60 mm Hg and desaturation on pulse oximetry becomes evident.

In pathological conditions where diffusion is impaired (congestive heart failure, pneumonia, alveolar hemorrhage), without pre-oxygenation, the clinician may have a few seconds to a few minutes before the patient desaturates. In these severe pathological conditions, it is recommended that an experienced clinician attempt the intubation. In these conditions, bilevel positive airway pressure (BIPAP) can be used to pre-oxygenate and even hyperventilate the patient as long as they are hemodynamically stable, alert, awake, and able to protect the airway.

Carbon Dioxide

Carbon dioxide is the end product of carbohydrate metabolism. It is transported by red blood cells, mostly bound to the hemoglobin, to the lungs from peripheral tissues, where it diffuses out and allows hemoglobin to bind to oxygen (Bohr and Haldane effects). It is important to note that any increase in carbon dioxide must result in a decrease in the PO2. For example, if a patient is on room air with 0.21 FiO2  and is at sea level, as PaCO2 rises from 40 to 80, the PAO2  decreases from 100 to approximately 60, and the patient becomes hypoxemic. This emphasizes the importance of continuous capnography and pulse oximetry, especially during procedures where conscious sedation is used.

In hypoxic conditions, the normal response is hyperventilation and increasing the minute ventilation to exhale more carbon dioxide, which decreases the partial pressure of carbon dioxide and increases PO2  to some extent. For example, a 10 mm Hg PCO2 decrease in alveoli increases the PO2 by approximately 10 to 12 mm Hg, which can be significant in acute and chronic disease processes. This is very important as an adaptation for survival.[7]

#### Other Issues

The alveolar gas equation has limitations, especially in low atmospheric pressures and low-inspired FiO2. With acclimatization, severe acidosis, and carbon monoxide poisoning, the body’s physiology and pathophysiology change substantially, and the equation cannot be used reliably.

#### Enhancing Healthcare Team Outcomes

The alveolar gas equation is used to calculate alveolar oxygen partial pressure, as it is impossible to collect gases directly from the alveoli. The equation is helpful in calculating and closely estimating the PaO2 inside the alveoli.

#### References

[1]

Diehl JL, Mercat A, Pesenti A. Understanding hypoxemia on ECCO(2)R: back to the alveolar gas equation. Intensive care medicine. 2019 Feb:45(2):255-256. doi: 10.1007/s00134-018-5409-0. Epub 2018 Oct 15     [PubMed PMID: 30324288]

Level 3 (low-level) evidence

[2]

Bashar FR, Vahedian-Azimi A, Farzanegan B, Goharani R, Shojaei S, Hatamian S, Mosavinasab SMM, Khoshfetrat M, Khatir MAK, Tomdio A, Miller AC, MORZAK Collaborative. Comparison of non-invasive to invasive oxygenation ratios for diagnosing acute respiratory distress syndrome following coronary artery bypass graft surgery: a prospective derivation-validation cohort study. Journal of cardiothoracic surgery. 2018 Nov 27:13(1):123. doi: 10.1186/s13019-018-0804-8. Epub 2018 Nov 27     [PubMed PMID: 30482210]

Level 1 (high-level) evidence

[3]

Van Iterson EH, Olson TP. Use of 'ideal' alveolar air equations and corrected end-tidal PCO(2) to estimate arterial PCO(2) and physiological dead space during exercise in patients with heart failure. International journal of cardiology. 2018 Jan 1:250():176-182. doi: 10.1016/j.ijcard.2017.10.021. Epub 2017 Oct 7     [PubMed PMID: 29054325]

[4]

Zavorsky GS, Hsia CC, Hughes JM, Borland CD, Guénard H, van der Lee I, Steenbruggen I, Naeije R, Cao J, Dinh-Xuan AT. Standardisation and application of the single-breath determination of nitric oxide uptake in the lung. The European respiratory journal. 2017 Feb:49(2):. pii: 1600962. doi: 10.1183/13993003.00962-2016. Epub 2017 Feb 8     [PubMed PMID: 28179436]

[5]

Conkin J. Equivalent Air Altitude and the Alveolar Gas Equation. Aerospace medicine and human performance. 2016 Jan:87(1):61-4. doi: 10.3357/AMHP.4421.2016. Epub     [PubMed PMID: 26735235]

[6]

Roy TK, Secomb TW. Theoretical analysis of the determinants of lung oxygen diffusing capacity. Journal of theoretical biology. 2014 Jun 21:351():1-8. doi: 10.1016/j.jtbi.2014.02.009. Epub 2014 Feb 20     [PubMed PMID: 24560722]

[7]

Nose H. [Conditions under which alveolar air equations are modified and the compensation terms of saturated water vapor in those equations]. Masui. The Japanese journal of anesthesiology. 2005 Apr:54(4):427-35     [PubMed PMID: 15852634]