Mathematical equivalent of metabolic alkalosis part of the Goldberg acid-base map.

To the Editor:—Metabolic alkalemia is the most common acid–base disturbance among patients in the hospital. Because the disorder is associated with high mortality and morbidity, its prompt diagnosis and treatment is feasible. The expected physiologic compensation for a primary increase in serum bicarbonate concentration ([HCO3 ]), i.e., metabolic alkalosis, is hypoventilation that increases partial pressure of arterial carbon dioxide (PaCO2; hypercapnia). This compensatory process returns the elevated blood pH back to normal, however, metabolic alkalosis is less predictably compensated than other simple acid–base disorders. In 1973, Goldberg et al., based on the Henderson Hasselbalch equation, developed an acid–base map, describing the expected levels of the arterial blood pH, [HCO3 ], and PCO2 in different acid–base disturbances. For bedside application, however, a simple equation that describes the metabolic alkalosis portion of the Goldberg map would facilitate rapid interpretation of whether an individual set of arterial blood gases was consistent with a compensated metabolic alkalosis. To develop an equation that describes the expected compensatory increase in PaCO2 in response to a primary increase in serum [HCO3 ], using a digitizer (CalComp 9500; full size), the minimum and maximum expected PaCO2 values associated with serum [HCO3 ], ranging from 27 mEq/l to 51 mEq/l were identified. Because compensatory hypoventilation rarely results in a PaCO2 exceeding 55 mmHg, 2 values more than 55 mmHg were assumed to be equal to 55 mmHg. Using the principle of least squares, it was found that the area outlined by two parallel lines containing these data points was defined by the equation (r 5 0.97, P , 0.0001) expected PaCO2 5 0.54[HCO3 ] 1 27.84 6 4.17. This equation is mathematically equivalent to the graphical presentation of the metabolic alkalosis portion of the Goldberg map. Because of the wide confidence interval, for more convenient use at the bedside, the equation can be simplified as follows: