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Appendix the Alveolar Gas Equation Is Used to Estimate The [Posted as supplied by author] Appendix The alveolar gas equation is used to estimate the alveolar PO 2 at any given level of inspired oxygen and alveolar PCO 2. The simplified version of the alveolar gas equation states: PAO2 = P IO2 – PACO 2/R [1;2] where P AO2 represents the alveolar oxygen tension, P ACO 2 the alveolar CO 2 tension, R is the ‘respiratory exchange ratio’ (ratio of CO 2 production to oxygen uptake, usually assumed to average 0.8) and P IO2 the inspired oxygen tension. P IO2 breathing air at sea level and body temperature and humidity is approximately 20kPa. In the classical model of pulmonary gas exchange, alveolar PCO 2 is approximated to arterial PCO 2 and therefore is obtained from arterial blood gas analysis. The A-a gradient (calculated by subtracting PaO 2 from P AO2) is an index of the efficiency of oxygen uptake in the lungs and under normal physiological conditions is < 2.0kPa. It widens with increased ventilation-perfusion mismatching in pathological conditions such as COPD. Importantly, the A-a gradient also widens if alveolar PO 2 increases (as when supplemental oxygen is breathed), while it narrows when alveolar PO 2 decreases (as occurs with hypercapnia, since alveolar, as well as arterial PCO 2 increases).[3] PIO2 can only be estimated accurately if the fractional concentration of inspired oxygen is known (as with breathing room air or via a Venturi-type mask where the percentage of oxygen is specified). Unfortunately, this does not apply with a patient breathing via nasal cannulae as the concentration of oxygen inspired is not predictable from the flow rate. In the present case, therefore, the alveolar gas equation can only be meaningfully applied to specimens A, C, E and F from Figure/Table 1, these are presented separately in Table 2. In A (obtained previously in a stable clinical state) and F (obtained after recovery) the calculated A-a gradients of 5.7 and 5.2kPa are markedly elevated, implying severely deranged pulmonary gas exchange. If, in the situation illustrated by blood gas specimen B, oxygen therapy is suddenly withdrawn, P ACO 2 and PaCO 2 remain high initially because of the body’s large CO 2 stores, while P AO2, and therefore PaO 2, will fall precipitately to levels well below those present before oxygen therapy was commenced. In specimen C, the A-a gradient is numerically less but is, in fact, grossly abnormal at the prevailing severely reduced alveolar PO 2. As no arterial blood gas specimen was taken on admission to hospital, we have used the subsequent stable blood gases as an indicator of the patient’s usual state. Admittedly, it is likely that admission values in this case would have been worse, but the general principle illustrated here is not affected as, for a given inspired oxygen concentration, a higher arterial PCO 2 will inevitably be accompanied by a lower arterial PO 2. The reciprocal relationship between oxygen and CO 2 in the alveoli, plus the differential body stores of the two gases imply that removing oxygen completely from a patient who has developed worsening hypercapnia is likely to result in dangerously low PaO 2. Table 1 Arterial blood gas measurements † A B C D E F When At callout 30 minutes 14 hours later 16 hours later 2 weeks stable* later later Inspired Gas Room 4L/min Room 1L/min Room Air Room Air Nasal Air Nasal Air Oxygen Oxygen pH 7.40 7.22 7.28 7.31 7.36 7.41 (7.35-7.45) PaCO 2 (KPa) 5.2 12.4 10.9 9.6 8.1 6.3 (4.5-6.0) PaO 2 (KPa) 7.8 19.8 4.2 11.3 5.7 6.9 (12.0-15.0) Bicarbonate 24.3 36.9 37.0 35.0 33.2 29.5 (21.0 – 28.0) O2 Saturation 90.6 99.2 59.6 96.4 79.2 86.5 (95-98%) *Stable gases were measured 15 months prior to hospital admission. †Normal ranges according to the Salford Royal Foundation Trust laboratory are shown in parentheses Table 2 Calculated Alveolar-arterial oxygen gradients whilst breathing room air Blood specimen A C E F PIO2 kPa 20 20 20 20 PaCO 2 kPa 5.2 10.9 8.1 6.3 Estimated 13.5 6.4 9.9 12.1 PAO2 kPa* PaO 2 kPa 7.8 4.2 5.7 6.9 Estimated 5.7 2.2 4.2 5.2 A-aPO 2 kPa *Using the alveolar gas equation [1] Campbell EJ. The J. Burns Amberson Lecture. The management of acute respiratory failure in chronic bronchitis and emphysema. Am Rev Respir Dis 1967 Oct;96(4):626- 39. [2] Fenn WO, Rahn H, Otis AB. A theoretical study of the composition of the alveolar air at altitude. Am J Physiol 1946 Aug 1;146(5):637-53. [3] Hoffstein V, Duguid N, Zamel N et al. Estimation of changes in alveolar-arterial oxygen gradient induced by hypoxia. J Lab Clin Med 1984 Nov;104(5):685-92. .
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