THE FOUR MOST IMPORTANT EQUATIONS IN CLINICAL PRACTICE
Lawrence Martin, MD, FACP, FCCP
4. Oxygen Content Equation
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.
CASE 4. A 54-year-old man came to the emergency room (ER)
complaining of headaches and shortness of breath. On room air
his PaO2 was 89 mm Hg, PaCO2 38 mm Hg, pH 7.43; hematocrit
was 44%. SaO2 was not directly measured but instead calculated
at 98% for this PaO2, based on a standard oxygen dissociation
curve. After some improvement he was scheduled for a brain CAT
scan two days later, and discharged from the ER. He was brought
back to the ER the next evening, unconscious. Ambulance
attendants alerted the ER physician to a possible faulty heater in
the patient's house. This time carbon monoxide and SaO2 were
measured along with routine arterial blood gases. The results:
PaO2 79 mm Hg, PaCO2 31 mm Hg, pH 7.36, SaO2 53%,
carboxyhemoglobin 46%.
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.
Carbon monoxide by itself does not affect PaO2 but only SaO2 and
O2 content. (Slight reduction in PaO2 on the patient's second visit was
attributed to some basilar atelectasis and resulting V-Q imbalance. The
SaO2 and O2 content on the second visit are shown by an "X" in Figure
3.) Confusion about interpretation of oxygen saturation in the presence
of excess CO is not unusual and even finds its way into peer-review
literature.28
To know the oxygen content one needs to know the hemoglobin
content and the SaO2; both should be measured as part of each arterial
blood gas test. As shown above, a calculated SaO2 may be way off the
mark and can be clinically misleading. This is true even without excess
CO in the blood. One study of over 10000 arterial samples found wide
variation in measured SaO2 for a given PaO2; for example, in the PaO2
range of 56-64 mm Hg the measured SaO2 ranged from 69.7 percent to
99.4 percent. 28
Finally, it should be noted that pulse oximeters are not reliable in
the presence of dyshemoglobins - hemoglobins that cannot bind oxygen.
The two major dyshemoglobins encountered in clinical practice are
carboxyhemoglobin (COHb) and methemoglobin (Methb). Oximeters do
not differentiate hemoglobin bound to carbon monoxide from hemoglobin
bound to oxygen; the machines report the sum of both values as
oxyhemoglobin.30-34
In contrast to blood co-oximeters, which utilize four wavelengths
of light to separate out oxyhemoglobin from reduced hemoglobin,
methemoglobin and carboxyhemoglobin, pulse oximeters utilize only two
wavelengths of light 33-34. As a result, pulse oximeters measure COHb
and part of any MetHb along with oxyhemoglobin, and combine the three
into a single reading, the SpO2. (MetHb absorbs both wavelengths of
light emitted by pulse oximeters, so that SpO2 is not affected as much by
MetHb as for a comparable level of COHb).
Thus a patient with 80% oxyhemoglobin and 15%
carboxyhemoglobin would show a pulse oximetry oxygen saturation
(SpO2) of 95%, a value too high by 15%. For this reason pulse
oximeters should be used cautiously (if at all) when there may be an
elevated carbon monoxide level, for example in patients assessed in an
emergency department. Note that excess carboxyhemoglobin is present in
all cigarette and cigar smokers. A resting SpO2 should be interpreted
cautiously in any outpatient who has smoked within 24 hours. The half-
life of CO breathing ambient air is about 6 hours, so 24 hours after
smoking cessation the CO level should be normal, i.e., less than 2.5%.
If there is concern about the true SaO2, it should be measured on an
arterial blood sample; alternatively, the percent COHb can be measured
on a venous sample, and the value subtracted from the SpO2.
The spectrophotometric technique used by pulse oximeters also
makes their oxygen saturation reading less reliable in the presence of
excess methemoglobin (metHb). MetHb reduces the SpO2 linearly until a
level of about 85%, at which point further increases in metHb do not
cause further lowering of SpO2.35-37 A finding of
unexpectedly low SpO2 (e.g., 91% in a patient with normal cardiorespiratory system who is
receiving nasal oxygen) should make one think of excess methb; in such
cases an arterial blood sample should be obtained for direct measurement
of SaO2 and PaO2.
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