|By Lawrence Martin, M.D., FACP, FCCP
Associate Professor of Medicine
Case Western Reserve University School of Medicine
|3. Alveolar Gas Equation Top
The alveolar gas equation for calculating PAO2 is essential to understanding any PaO2 value and in assessing if the lungs are properly transferring oxygen into the blood. Is a PaO2 of 28 mm Hg abnormal? How about 55 mm Hg? 95 mm Hg? To clinically interpret PaO2 one has to also know the patient's PaCO2, FIO2 (fraction of inspired oxygen) and the PB (barometric pressure), all components of the equation for PAO2:
Despite this undisputed physiologic fact physicians sometimes make clinical decisions
PAO2 = FIO2(PB-47) - 1.2(PaCO2)
This young woman's PaO2 was initially judged 'normal' and so an abnormality in oxygen transfer was missed. The calculated PIO2 and PAO2 were 147 mm Hg and 110 mm Hg, respectively. Her P(A-a)O2 was elevated at 27 mm Hg (110 minus 83), indicating a state of V-Q imbalance, and therefore some parenchymal lung disease or abnormality. Indeed, she returned the next day with similar complaints, at which time a lung scan showed defects interpreted as high probability for pulmonary embolism.
*All pressures in mm Hg; Pike's Peak and Mt. Everest data from summits
If the climber maintained PaCO2 at 40 mm Hg his PAO2 would be minus 5 mm Hg, a value wholly incompatible with life! Ability to oxygenate blood at this altitude without supplemental oxygen is made possible (in large part) by extreme hyperventilation. On one expedition to the summit, 10 minutes after supplemental oxygen was removed a climber's end-tidal PCO2 (equivalent to PACO2) was measured at 7.5 mm Hg; assuming an R value of 0.85, the PAO2 was only 35 mm Hg.24 Based on a theoretical alveolar-arterial PO2 difference of 7 mm Hg, the climber's PaO2 at the summit was estimated at 28 mm Hg - very low but 'normal' under the circumstances.24
|4. Oxygen Content Equation Top
All physicians know that hemoglobin carries oxygen and that anemia can lead to severe hypoxemia. Making the necessary connection between PaO2 and O2 content requires knowledge of the oxygen content equation.
CaO2 = (SaO2 x Hb x 1.34) + .003(PaO2)
How much glucose is in the blood if the glucose level is 80 mm Hg? This question makes no sense, of course, because glucose is not a gas and therefore exerts no pressure in solution; any question regarding 'how much' is answered by determining its content, which in the case of glucose is usually reported as mg/dl blood. Oxygen is a gas and its molecules do exert a pressure but, like glucose, oxygen also has a finite content in the blood, in units of ml O2/dl blood. To remain viable tissues require a certain amount of oxygen per minute, a need met by a requisite oxygen content, not oxygen pressure. (Patients can and do live with very low PaO2 values, as long as their oxygen content and cardiac output are adequate.)
The oxygen carrying capacity of one gram of hemoglobin is 1.34 ml. With a hemoglobin content of 15 grams/dl blood and a normal hemoglobin oxygen saturation (SaO2) of 98%, arterial blood has a hemoglobin-bound oxygen content of 15 x .98 x 1.34 = 19.7 ml O2/dl blood. An additional small quantity of O2 is carried dissolved in plasma: .003 ml O2/dl plasma/mm Hg PaO2, or .3 ml O2/dl plasma when PaO2 is 100 mm Hg. Since normal CaO2 is 16-22 ml O2/dl blood, the amount contributed by dissolved (unbound) oxygen is very small, only about 1.4% to 1.9% of the total.
Given normal pulmonary gas exchange (i.e., a normal respiratory system), factors that lower oxygen content - such as anemia, carbon monoxide poisoning, methemoglobinemia, shifts of the oxygen dissociation curve - do not affect PaO2. PaO2 is a measurement of pressure exerted by uncombined oxygen molecules dissolved in plasma; once oxygen molecules chemically bind to hemoglobin they no longer exert any pressure.
PaO2 affects oxygen content by determining, along with other factors such as pH and temperature, the oxygen saturation of hemoglobin (SaO2). The familiar O2-dissociation curve can be plotted as SaO2 vs. PaO2 and as PaO2 vs. oxygen content (Figure 3). For the latter plot the hemoglobin concentration must be stipulated.
When hemoglobin content is adequate, patients can have a reduced PaO2 (defect in gas transfer) and still have sufficient oxygen content for the tissues (e.g., hemoglobin 15 grams%, PaO2 55 mm Hg, SaO2 88%, CaO2 17.8 ml O2/dl blood). Conversely, patients can have a normal PaO2 and be profoundly hypoxemic by virtue of a reduced CaO2. This paradox - normal PaO2 and hypoxemia - generally occurs one of two ways: 1) anemia, or 2) altered affinity of hemoglobin for binding oxygen.
A common misconception is that anemia affects PaO2 and/or SaO2; if the respiratory system is normal, anemia affects neither value. (In the presence of a right to left intrapulmonary shunt anemia can lower PaO2 by lowering the mixed venous oxygen content; when mixed venous blood shunted past the lungs mixes with oxygenated blood leaving the pulmonary capillaries, lowering the resulting PaO2.25 With a normal respiratory system mixed venous blood is fully oxygenated - as much as allowed by the alveolar PO2 - as it passes through the pulmonary capillaries.)
Obviously, however, the lower the hemoglobin content the lower the oxygen content. It is not unusual to see priority placed on improving a chronically hypoxemic patient's low PaO2 when a blood transfusion would be far more beneficial.
Anemia can also confound the clinical suspicion of hypoxemia since anemic patients do not generally manifest cyanosis even when PaO2 is very low. Cyanosis requires a minimum quantity of de-oxygenated hemoglobin to be manifest - approximately 5 grams% in the capillaries.26,27 A patient whose hemoglobin content is 15 grams% would not generate this much reduced hemoglobin in the capillaries until the SaO2 reached 78% (PaO2 44 mm Hg); when hemoglobin is 9 grams% the threshold SaO2 for cyanosis is lowered to 65% (PaO2 34 mm Hg).27
Altered hemoglobin affinity may occur from shifts of the oxygen dissociation curve (e.g., acidosis, hyperthermia), from alteration of the oxidation state of iron in the hemoglobin (methemoglobinemia), or from carbon monoxide poisoning.
This patient's true SaO2 would have been much lower than 98% had it been measured on the first ER visit instead of just calculated. The physician missed hypoxemia as a cause of headache and dyspnea because of the 'normal' calculated SaO2.
|TRUE-FALSE QUIZ -- based on "THE FOUR MOST IMPORTANT EQUATIONS IN CLINICAL PRACTICE"
Lawrence Martin, M.D., FACP, FCCP
Directions: This quiz is designed to test your understanding of information in the review paper, The Four Most Important Equations in Clinical Practice. For each of the following five numbered statements or questions, there are five lettered responses (a-e), each of which may be true or false. Circle the correct or true responses. Answers immediately follow the quiz.
1. Normal range for PaCO2 is 35-45 mm Hg. A change in PaCO2 from normal
to 28 mm Hg means the subject
2. The arterial PO2 is predicted to be reduced to some extent from
3. To obtain a reasonable idea of the acid-base state of a patient's blood,
4. Arterial blood gas data (pH, PaCO2, PaO2, SaO2) are related in some simple
5. There are some "truisms" in terminology and physiology for proper blood gas interpretation. They include which of the following?
A N S W E R S
|R E F E R E N C E S|
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23. Harris EA, Kenyon AM, Nisbet HD, et al. The normal alveolar-arterial oxygen tension gradient in man. Clin Sci Mol Med 1974;46:89-104.
24. West JB, Hackett PH, Maret KH, et al. Pulmonary gas exchange on the summit of Mount Everest. J Appl Physiol 55:678-87, 1983.
25. Dantzker, DR. Cardiopulmonary Critical Care. Grune & Stratton, Orlando, 1986; page 39.
26. Lundsgaard C, Van Slyke DD. Cyanosis. Medicine 1923;2:1-76.
27. Martin L and Khalil H. How much reduced hemoglobin is necessary to generate central cyanosis? Chest 1990;97:182-85.
28. Hampson NB. Arterial oxygenation in carbon monoxide poisoning (Letter). Chest 1990;98:1538-9.
29. Gothgen IH, Siggaard-Andersen O, Kokholm G. Variations in the hemoglobin- oxygen dissociation curve in 10079 arterial blood samples. Scand J Clin Lab Invest 1990;50 (Suppl) 203:87-90.
30. Barker SJ, Tremper KK. The effect of carbon monoxide inhalation on pulse oximetry and transcutaneous PO2. Anesthesiology 1987;66:677-79.
31. Raemer DN, Elliott WR, Topulos G, et al. The theoretical effect of carboxyhemoglobin on the pulse oximeter. J Clin Monit 1989;5:246-249.
32. Ralston AC, Webb RK, Runciman WB. Potential errors in pulse oximetry. III: Effects of interferences, dyes, dyshaemoglobins and other pigments. Anaesthesia 1991;46:291-5.
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36. Barker SJ, Tremper KK, Hyatt J. Effects of methemoglobinemia on pulse oximetry and mixed venous oximetry. Anesthesiology 1989;70:112-17.
37. Watcha MF, Connor MT, Hing AV. Pulse oximetry in methemoglobinemia. Amer J Dis Child 1989;143:845-47.
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