THE FOUR MOST IMPORTANT EQUATIONS IN CLINICAL PRACTICE
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:
- not enough total ventilation (as may occur
from central nervous system depression or
respiratory muscle weakness); or
- 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
- 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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