THE FOUR MOST IMPORTANT EQUATIONS IN CLINICAL PRACTICE
Lawrence Martin, M.D., FACP, FCCP
Clinical Associate Professor of Medicine
Case Western Reserve University School of Medicine
Cleveland, Ohio
S U M M A R Y
Four equations are taught briefly in medical school but are grossly underemphasized
in importance and are therefore invariably forgotten in later years, when they are most
needed. The reasons why these highly important equations are 'under taught' in medical
school are several:
 a crowded curriculum that must make room for immunology and cell
biology
 the teachers may have little or no clinical experience with respiratory patients,
and therefore can't possibly know how important these equations are in the everyday practice
of medicine
 misguided leadership of curriculum committees that may feel every subject
deserves equal balance, and thus leave it up to the student to 'learn it all' without anyone
guiding them as to what is really important in the care of patients. (For example,
one hour on surfactant may be equally weighted with one hour on gas exchange, which
may be OK for training Ph.D.'s but is misguided for training physicians).
These four equations express relationships that are extremely important
in clinical practice. They are the:
 PCO_{2} equation
 HendersonHasselbalch equation
 Alveolar Gas equation, and
 Oxygen Content equation.
Emphasis should be placed on understanding the simple qualitative
relationships expressed by these equations. Each equation can be
clinically applied in the assessment of abnormal oxygenation,
ventilation, or acidbase balance. For example, variables in the
PCO_{2} equation, and not any bedside observations, define the common
terms hyperventilation and hypoventilation and explain why a dyspneic,
tachypneic patient may be retaining CO_{2}. Ignorance of this and other
relationships expressed in the four equations is reflected in some common
diagnostic and therapeutic mistakes.
INTRODUCTION
There is disparity between the physiology we teach and expect medical students to
learn and the physiology that medical residents and practicing physicians seem to know
and understand. This disparity is perhaps best exemplified by four simple equations
important in understanding cardiopulmonary and renal disorders
(Table I).
These equations are seldom emphasized beyond medical school, yet not appreciating the
physiology behind them can (and often does) lead to clinical errors.
Intensive care units have contributed to the weakening knowledge of physiology among
primary care physicians. Today, the more profound physiologic derangements are usually
managed in ICUs by organspecific specialists; these derangements (e.g., shock,
pulmonary edema, acute ventilatory failure, acute renal failure) are literally outside the care
of most physicians and surgeons. Not all serious physiologic problems are handled in ICUs
however, and the need for understanding basic physiology  in the office, on the general
medical wards  remains paramount.
The four equations in this paper (Table I, below) are important clinically not so much for the
numbers they generate as for their qualitative relationships. All four equations can be
abbreviated to simpler terms that are adequate for most clinical purposes.
TABLE I: THE FOUR MOST IMPORTANT EQUATIONS
IN CLINICAL PRACTICE
Equation Title 
Complete Equation 
Abbreviation Sufficient for
Most Clinical Applications 
1. PCO _{2}
equation 
PACO_{2}=VCO_{2} x 0.863 / VA
where VA=VEVD 
PaCO_{2} ~ VCO_{2} / VA 
2. Henderson
Hasselbalch
equation 
pH=pK + log HCO_{3}^{} / 0.03(PaCO_{2}) 
pH ~ HCO_{3}^{} / PaCO_{2} 
3. Alveolar
gas
equation 
PAO_{2}=FIO_{2}(P_{B}P_{H2o})PACO_{2}[FIO_{2} + (1FIO_{2}) / R] 
PAO_{2}=FIO_{2}(P_{B}47)1.2(PaCO_{2}) 
4. Oxygen
content
equation 
CaO_{2}=(SaO_{2} x Hb x 1.34) +
.003(PaO_{2})
where:
1.34=ml O_{2}/gram Hb
.003=ml O_{2}/mm Hg PaO_{2}/dl
Hb=content in grams/dl 
CaO_{2}=SaO_{2} x 1.34 x Hb 
Obviously other equations besides those in Table 1 can
be important in assessing disordered physiology.
The point is not to belabor equations but to emphasize a few key
relationships often overlooked or misapplied in the daily practice
of medicine. By understanding them we can take better care of our
sickest patients wherever they are encountered. Nonintensivists
should be familiar with these particular equations and their
clinical relevance. They were probably all learned by most
physicians at one time. For physicians in training and practitioners
alike, now is the time to review.
Top of Page 
Table of Contents 
References 
TrueFalse Quiz for Top 4 Paper 
Return to Subject Index
Forward any comments to:
larry.martin@roadrunner.com
Copyright © 19962009 Lawrence Martin, M.D.
