by "Grog" (Alan W. Grogono), Professor Emeritus, Tulane University Department of Anesthesiology

Simple Arithmetic - An Alternative Approximation

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Simple Arithmetic

Non-Visual Learners:

This section is aimed at you. The rest of the site makes extensive use of graphic images. This section focuses on using words and arithmetic as an alternative approach to understanding acid-base balance.


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12 = 0.1 = 6

The Simple Equation.

The non-visual learner should try this simple arithmetic relationship between PCO2, pH, and metabolic acid level (BE). Less accurate than the diagrams it, nevertheless, provides an understanding of the inter-relationships and allows predictions to be made about the degree of metabolic acidosis from a knowledge of the PCO2 and the pH.

PCO2     pH     Met Ac

12   =   0.1   =     6  

mmHg               mEq/L

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A pH change may be due to ....

Explanation.

The equation means that a change of 0.1 in the pH can be caused by either:

  1. A respiratory change (PCO2 change) of 12mmHg, or
  2. A metabolic change (Base Excess change) of 6 mEq/L.
  3. A mixture of the two.

This relationship allows the components to be "added" and "subtracted". For example, a pH of 7.2 (0.2 more "Acid") can be caused by:

  1. a PCO2 of 64 with a BE =   0 mEq/L
  2. a PCO2 of 52 with a BE =  -6 mEq/L
  3. a PCO2 of 40 with a BE = -12 mEq/L
  4. a PCO2 of 32 with a BE = -18 mEq/L

Although this relationship is an approximation, it provides acceptable clinical results in most circumstances; its real value is in granting insight and understanding for those who find diagrams and maps less helpful, i.e., the "non-visual" learner.

Examples

A few examples employing this equation may make these concepts easier to understand:

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Pure (Uncompensated) Respiratory

Acute Respiratory:

1) PCO2 = 52, pH = 7.3.

The PCO2 of 52 (+12) would be expected to cause an acid shift in the pH of 0.1 to pH 7.3. The actual pH (7.3) is as expected, i.e., there is no evidence of any metabolic compensation. Pure (acute) respiratory acidosis occurs with acute respiratory depression or by setting an anesthetic ventilator to deliver a minute ventilation smaller than the patient's normal. It takes a day or two for a patient's kidney to respond and produce the typical partial correction.

2) PCO2 = 28, pH = 7.5.

The PCO2 of 28 (-12) would be expected to cause an alkaline shift in the pH of 0.1 to pH 7.5. The actual pH (7.5) is as expected, i.e., there is no evidence of any metabolic compensation. Pure (acute) respiratory alkalosis occurs in acute hyperventilation or by setting an anesthetic ventilator to deliver a minute ventilation greater than the patient's normal. It takes a day or two for a patient's kidney to respond and produce the typical partial correction.

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Compensated Respiratory

Chronic Respiratory:

1) PCO2 = 64, pH = 7.3.

The PCO2 of 64 (+24) would be expected to cause an acid shift in the pH of 0.2 to pH 7.2. The actual pH (7.3) is about halfway between no compensation (pH = 7.2) and full compensation (pH 7.4). This is characteristic of chronic hypoventilation with compensation about half way back to normal and might be seen in chronic obstructive pulmonary disease. The 0.1 difference between expected and actual pH corresponds to 6 mEq/L of compensatory metabolic alkalosis.

2) PCO2 = 28, pH = 7.45.

The PCO2 of 28 (-12) would be expected to cause an alkaline shift in the pH of 0.1 to pH 7.5. The actual pH (7.45) is about halfway between no compensation (pH = 7.5) and full compensation (pH 7.4). This is characteristic of chronic hyperventilation with compensation about half way back to normal and occurs, for example, at high altitude in response to hypoxia. The 0.05 difference between expected and actual pH corresponds to 3 mEq/L of compensatory metabolic acidosis.

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Compensated Metabolic

Metabolic:

1) PCO2 = 28, pH = 7.3.

The PCO2 of 28 (-12) would be expected to cause an alkaline shift in the pH of 0.1 to pH 7.5. The actual pH is, therefore, more acid than expected by 0.2, equivalent to 12 mEq/L of metabolic acidosis. Because the metabolic change is acid, as is the overall change, it is the underlying problem. Alone it would be expected to cause a pH of 7.2. In fact the pH is half way back towards normal, a typical compensation which might be found in lactic acidosis following tissue ischemia.

2) PCO2 = 52, pH = 7.5.

The PCO2 of 52 (+12) would be expected to cause an acid shift in the pH of 0.1 to pH 7.3. The actual pH is, therefore, more alkaline than expected by 0.2, equivalent to 12 mEq/L of metabolic alkalosis. Because the metabolic change is alkaline, as is the overall change, it is the underlying problem. Alone it would be expected to cause a pH of 7.6. In fact the pH is half way back towards normal, a typical compensation which might be found in vomiting or gastric aspiration.

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Respiratory and Metabolic

Mixed Disturbances:

1) PCO2 = 64, pH = 7.1.

The PCO2 of 64 (+24) would be expected to cause an acid shift in the pH of 0.2 to pH 7.2. The actual pH is, therefore, more acid than expected by 0.1 - equivalent to 6 mEq/L of metabolic acidosis. This represents a combination of metabolic and respiratory acidosis. It might occur following trauma with tissue ischemia and respiratory depression.

2) PCO2 = 28, pH = 7.6.

The PCO2 of 28 (-12) would be expected to cause an alkaline shift in the pH of 0.1 to pH 7.5. The actual pH is, therefore, more alkaline than expected by 0.1 - equivalent to 6 mEq/L of metabolic alkalosis. This represents a combination of metabolic and respiratory alkalosis. It might occur with gastric aspiration and mechanical hyperventilation.


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Acid-Base Tutorial
Alan W. Grogono
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