Lawrence Martin, MD, FACP, FCCP

1. The PCO2 Equation

The PCO2 equation puts into physiologic perspective one of the most common of all clinical observations: a patient's respiratory rate and breathing effort. The equation states that alveolar PCO2 (PACO2) is directly proportional to the amount of CO2 produced by metabolism and delivered to the lungs (VCO2) and inversely proportional to the alveolar ventilation (VA). While the derivation of the equation is for alveolar PCO2, its great clinical utility stems from the fact that alveolar and arterial PCO2 can be assumed to be equal. Thus:


The constant 0.863 is necessary to equate dissimilar units for VCO2 (ml/min) and VA (L/min) to PACO2 pressure units (mm Hg). Alveolar ventilation is the total amount of air breathed per minute (VE; minute ventilation) minus that air which goes to dead space per minute (VD). Dead space includes all airways larger than alveoli plus air entering alveoli in excess of that which can take part in gas exchange.

Even when alveolar and arterial PCO2 are not equal (as in states of severe ventilation-perfusion imbalance), the relationship expressed by the equation remains valid:


In the clinical setting we don't need to know the actual amount of CO2 production or alveolar ventilation. We just need to know if VA is adequate for VCO2; if it is, then PaCO2 will be in the normal range (35-45 mm Hg). Conversely, a normal PaCO2 means only that alveolar ventilation is adequate for the patient's level of CO2 production at the moment PaCO2 was measured.

From the PCO2 equation it is evident that a level of alveolar ventilation inadequate for CO2 production will result in an elevated PaCO2 (> 45 mm Hg; hypercapnia). Thus patients with hypercapnia are hypoventilating (the term hypoalveolarventilating would be more appropriate but hypoventilating is the conventional term). Conversely, alveolar ventilation in excess of that needed for CO2 production will result in a low PaCO2 (< 35 mm Hg; hypocapnia) and the patient will be hyperventilating. (Confusion sometimes arises because the prefix (hyper-, hypo-) differs for the same condition depending on whether one is describing a blood value or the state of alveolar ventilation.) For reasons that will be discussed below, the terms hypo- and hyper- ventilation refer only to high or low PaCO2, respectively, and should not be used to characterize any patient's respiratory rate, depth, or breathing effort.

From the PCO2 equation it follows that the only physiologic reason for elevated PaCO2 is a level of alveolar ventilation inadequate for the amount of CO2 produced and delivered to the lungs. 1 Thus arterial hypercapnia can always be explained by:

  1. not enough total ventilation (as may occur from central nervous system depression or respiratory muscle weakness); or
  2. too much of the total ventilation ending up as dead space ventilation (as may occur in severe chronic obstructive pulmonary disease, or from rapid, shallow breathing); or
  3. some combination of 1) and 2).

Excess CO2 production is omitted as a specific cause of hypercapnia because it is never a problem for the normal respiratory system unimpeded by a resistive load. During submaximal exercise, for example, where CO2 production is increased, PaCO2 stays in the normal range because VA rises proportional to the rise in VCO2. With extremes of exercise (beyond anaerobic threshold) PaCO2 falls as compensation for the developing lactic acidosis.2 In health PaCO2 may be reduced but is never elevated.

An important clinical corollary of the PaCO2 equation is that we cannot reliably assess the adequacy of alveolar ventilation - and hence PaCO2 - at the bedside. Although VE can be easily measured with a handheld spirometer (as tidal volume times respiratory rate), there is no way to know the amount of VE going to dead space or the patient's rate of CO2 production. A common mistake is to assume that because a patient is breathing fast, hard and/or deep he or she must be "hyperventilating." Not so, of course.

CASE 1. A house officer was called to the bedside of an elderly woman patient late at night. She was in hospital for evaluation of a pelvic mass. The patient was noted to be anxious and complaining of shortness of breath; her lung fields were clear to auscultation and vital signs were normal except for slight tachycardia and respiratory rate of 30/minute. A nurse commented that the patient "gets like this every night." The physician ordered a benzodiazepine drug for what he described as "hyperventilation and anxiety." Thirty minutes later the patient's breathing slowed considerably and she became cyanotic, whereupon she was transferred to the ICU.

Although nothing in the PCO2 equation directly relates respiratory rate or depth of breathing to PaCO2, physicians commonly (and mistakenly) use these observations to assess a patient's PaCO2. The error in this case was to assume the patient was hyperventilating (because she was breathing fast) and could tolerate the sedative; in fact she was hypoventilating - her PaCO2 was elevated (as will be explained further under Henderson-Hasselbalch, Equation 2).

Hypercapnia represents a failure of the respiratory system in some aspect and therefore a state of severe organ system impairment. In addition to this clinical fact there are three physiologic reasons why elevated PaCO2 is potentially dangerous. First, as PaCO2 increases, unless HCO3- also increases by the same degree pH will fall (see Henderson Hasselbalch, Equation 2). Second, as PaCO2 increases PAO2 (and hence PaO2) will fall unless inspired oxygen is supplemented (see Alveolar Gas, Equation 3). Third, the higher the PaCO2, the less defended is the patient against any further decline in alveolar ventilation.

This last point is graphically illustrated by plotting PaCO2 against alveolar ventilation (Figure 1). The higher the PaCO2 is to begin with, the more it will rise for any given decrement in alveolar ventilation. For example a decrease in alveolar ventilation of one L/minute (as may occur from anesthesia, sedation, congestive heart failure, etc.) will increase a baseline PaCO2 of 30 mm Hg to 36.3 mm Hg when VCO2 is 200 ml/min; the same one L/min decline in VA will raise a baseline PCO2 of 60 mm Hg to 92 mm Hg (Figure 1). Whereas the hyperventilating or normally- ventilating patient can almost always tolerate sedating drugs (without clinically important hypoventilation), even a small amount of sedative may be dangerous in the hypercapnic patient.

Note also from Figure 1 that an increase in CO2 production (e.g., from 200 to 300 ml/min) without concomitant increase in VA (as should occur normally) will cause PaCO2 to increase. This situation is sometimes seen in patients with severe chronic obstructive lung disease when they exercise, and in artificially-ventilated patients who are carbohydrate loaded (which increases CO2 production). The basic mechanism for hypercapnia in these and all other cases, however, is inadequate VA for the amount of CO2 delivered to the lungs.

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Copyright © 1996-2009 Lawrence Martin, M.D.