Section H

Table of Contents

Note: This section is from The House Officer's Survival Guide: Rules, Laws, Lists and Other Medical Musings, by Lawrence Martin, M.D. It is written for doctors in training, but will also be of interest to medical students, nurses who work in critical care areas, and respiratory therapists. Unlike other sections of "Survival Guide", Hardcore will not be of much interest to the general public. Please address any feedback to


If you believe that simple equations can be important for patient care, then this section is for you. Listed below are what I consider the Four Most Important Equations in Clinical Practice. A more detailed paper on this same subject is also posted on the Mt. Sinai site. It is called -- what else? -- The Four Most Important Equations in Clinical Practice

1. The PaCO2 equation

PaCO2 = CO2 produced by metabolism (ml/min) x k/alveolar ventilation (L/min)


alveolar ventilation = minute ventilation minus dead space ventilation

k = 0.863.

REASON IMPORTANT: This equation explains why one cannot assess PaCO2 clinically, i.e., with only bedside observations such as respiratory rate, depth of breathing, level of discomfort, breath sounds, etc. There are no clinical variables in this equation. For example, a patient with fast and/or deep breathing can still be retaining CO2 if most of the air goes to dead space (either because of shallow tidal volumes or ventilation-perfusion mismatch). Since there is nothing clinical in this equation, one cannot use clinical criteria to assess PaCO2 (i.e., adequacy of alveolar ventilation). A patient may appear to be "hyper-ventilating" but in fact be hypoventilating, i.e., have a high PaCO2.

2. The alveolar gas equation

PAO2 = FIO2 (B.P. - 47) - 1.2 PaCO2


PAO2 = alveolar PO2

FIO2 = fraction of inspired oxygen

B.P. = barometric pressure

47 = water vapor pressure in airway in mm Hg

Alveolar-arterial PO2 difference [A-a gradient] =

calculated PAO2 - measured PaO2

REASON IMPORTANT: You need the calculated PAO2 to know if arterial PO2 (PaO2) is abnormal or not. Specifically, the variables in this equation (B.P., FIO2 and PaCO2) must be known to properly interpret any PaO2 value. Is a PaO 2 of 28 mm Hg normal? (Yes, if breathing mountain air at the summit of Mt. Everest, where B.P. is only 253 mm Hg). Is a PaO2 of 100 mm Hg abnormal? (Yes, if the patient is breathing 100% oxygen). Does a PaO2 of 50 mm Hg indicate a problem of ventilation-perfusion mismatch? (Yes, if the A-a gradient is increased; no, if the A-a gradient is normal, in which case the low PaO2 may be solely from elevated PaCO2).

3. The Henderson Hasselbalch equation

pH = pK + log HCO3/.03(PaCO2)

REASON IMPORTANT: Helps diagnose presence and type of acid-base disorder, and the body's compensation for it. The abbreviated version is adequate in most clinical situations. Equation shows there are only four primary acid-base disorders: two where the first change is in HCO3- (metabolic alkalosis and acidosis) and two where the first change is PaCO2 (respiratory alkalosis and acidosis).

4. The arterial oxygen content (CaO2 ) equation

CaO2 content = amount O2 bound to hgb + amt.O2 dissolved

= (1.34 x hgb x SaO2) + (.003 x PaO2)


O2 content = ml O2 /100 ml blood

1.34 = ml O2 that can maximally bind to a gram of hgb

hgb = hemoglobin content, in grams/dl

SaO2 = saturation of hemoglobin with oxygen in arterial blood

.003 = ml O2 that can dissolve in plasma per mm Hg PaO2 per 100 ml blood

REASON IMPORTANT: Incorporates factors for adequate arterial oxygen content, most important of which is hemoglobin; over 97% of arterial oxygen content is normally carried by hgb. Note that oxygen content is the only readily available value that directly reflects the number of oxygen molecules in the blood. In assessing degree of hypoxemia (as opposed to the cause), CaO2 is more useful than either PaO2 or SaO2. A patient can be profoundly hypoxemic with a normal PaO2 (for example, from severe anemia or carbon monoxide intoxication) or with a normal SaO2 (from severe anemia).

5. And the fifth most important equation?

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