THE FOUR MOST IMPORTANT EQUATIONS IN CLINICAL PRACTICE

Four equations are taught briefly in medical school but are grossly under-emphasized 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:

1. PCO₂ equation
2. Henderson-Hasselbalch equation
3. Alveolar Gas equation, and
4. 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 acid-base balance. For example, variables in the PCO₂ equation, and not any bedside observations, define the common terms hyperventilation and hypoventilation and explain why a dyspneic, tachypneic patient may be retaining CO₂. Ignorance of this and other relationships expressed in the four equations is reflected in some common diagnostic and therapeutic mistakes.

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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 organ-specific 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.

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TABLE I: THE FOUR MOST IMPORTANT EQUATIONS
IN CLINICAL PRACTICE

Equation Title	Complete Equation	Abbreviation Sufficient for Most Clinical Applications
1. PCO 2 equation	PACO2=VCO2 x 0.863 / VA where VA=VE-VD	PaCO2 ~ VCO2 / VA
2. Henderson- Hasselbalch equation	pH=pK + log HCO3- / 0.03(PaCO2)	pH ~ HCO3- / PaCO2
3. Alveolar gas equation	PAO2=FIO2(PB-PH2o)-PACO2[FIO2 + (1-FIO2) / R]	PAO2=FIO2(PB-47)-1.2(PaCO2)
4. Oxygen content equation	CaO2=(SaO2 x Hb x 1.34) + .003(PaO2) where: 1.34=ml O2/gram Hb .003=ml O2/mm Hg PaO2/dl Hb=content in grams/dl	CaO2=SaO2 x 1.34 x Hb

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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. Non-intensivists 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.

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