This is a summary of simple bedside rules to help interpret blood gases, as well as a synopsis of the equations CICM fellowship candidates are expected to remember.
The Alveolar Gas Equation
A detailed explanation of the alveolar gas equation occurs elsewhere.
PAO2 = (FiO2 × (760 - 47)) - (PaCO2 × 1.25)
Or, at room air:
PAO2 = (149 - (PaCO2 x 1.25)
Thus, the patient with a relatively normal PaCO2 (say, 40) :
PAO2 = (149 - 50)
So, a normal person should have a PaO2 of around 99 mmHg.
We take a range of 75-100.
Or, for a patient with normal PaCO2 and an increased FiO2:
PAO2 = (FiO2 x 713) - 50
The A-a gradient:
The A-a gradient and all the other tension-based indices of oxygenation are discussed elsewhere.
A-a gradient = [PAO2 - PaO2]
i.e. alveolar concentration minus arterial concentration.
The normal A-a gradient in a healthy young person should be aroung 5-10mmHg.
It changes with age.
Age-adjusted A-a gradient = (age / 4) + 4
Thus, an 80 yr old should have an A-a gradient of around 24.
Changes in pH due to acute respiratory acid-base disturbance: a crude calculation
For every 10 mmHg increase in PaCO2, the pH will decrease by 0.08
In other words, pH = 7.40 - ((PaCO2 - 40) × 0.008))
This relationship tends to overestimate the pH change. the reason is its failure to account for the increase in bicarbonate as a result of increasing CO2.
Changes in pH due to chronic respiratory acid-base disturbance
pH = 7.40 - ((PaCO2-40) x 0.003))
Thus, if the CO2 is chronically elevated at 50, one should expect the pH to drop from 7.40 to 7.37. Again, the change in bicarbonate due to dissolved CO2 is unaccounted for. The "0.003" multiplier accounts only for the renal compensation mechanisms.
Changes in pH due to acute respiratory acid-base disturbance: the Hendeson Equation
This equation is a more accurate way of calculating what the pH should be for any given PaCO2 and HCO3- combination:
Note that this [H+] result is in nanomoles; so before calculating pH from it, one must convert it into moles first. Thus: pH = -log10((24 × PaCO2 / HCO3-) × 10-8)
For every 10 mmHg increase in PaCO2, the pH will decrease by 0.08
pH = -log10((24 × PaCO2 / HCO3-) × 10-8)
The HCO3- used for this equation should ideally be the "total bicarbonate" as measured by the enzymatic method, in an autoanalyser. If such a value is not available, one may estimate the "expected" bicarbonate value from the Boston Rules. The various merits and demerits of the Boston and Copenhagen acid-base compensation rules are discussed elsewhere.
(Na+ + K+) - (Cl- + HCO3-)
The normal anion gap is about 12.
Correction of the anion gap for albumin
It changes with changes in albumin concentration; for every 4g/L of albumin below 40 the normal anion gap value should decrease by 1mmol. The anion gap corrected for a given albumin level (reported as Agc) can be calculated in the following manner:
Agc = 0.25 × (albumin in g/L)
Thus for an albumin of 40 the normal AG is 12, but at an albumin level of 20 the AG is 7.
The precise correction factor for albumin, and whether one needs to correct for phosphate, is a matter of some debate. If one were to correct for phosphate, the Agc equation would look like this:
Agc = 0.25 × (albumin in g/L) + 1.5 × (phosphate in mmol/L)
Delta ratio = (change in anion gap) / (change in bicarbonate)
The normal anion gap is assumed to be 12, and the normal HCO3 is assumed to be 24.
A delta ratio of less than 0.4 suggests that none of the change in bicarbonate can be explained by the change in anion gap, and thus a normal anion gap acidosis prevails.
A delta ratio of 0.4-0.8 suggests that a mixed high and normal anion gap acidosis exists.
A delta ratio of 0.8-1.0 suggests that the disorder is purely due to a high anion gap (i.e. the change in bicarbonate is matched by a change in anion gap)
A delta ratio of 1.0-2.0 suggests that a high anion gap metabolic acidosis exists (i.e. the change in anion gap is somewhat greater than the change in bicarbonate)
A delta ratio of over 2.0 suggests that together with a high anion gap acidosis, a metabolic alkalosis is also present (i.e. despite the change in anion gap, the bicarbonate has barely shifted from the normal value)
The osmolal gap is the difference between measured osmolality and calculated osmolality. It alerts one to the presence of unexpected osmoles, which might represent something hideously toxic.
Osmolar gap = measured osmolality - calculated osmolality
Calculated osmolality (Osm) = (Na+ × 2 + urea + glucose)
A normal value being ~ 10 mOsm/Kg
This is the "stripped down" equation which most people remember with relative ease.
However, turns out it is fairly inaccurate.
To complicate an already complicated subject, Oh's Manual presents us with another equation (by Bhagat et al, from 1984) which is much more acurate:
Osm = (1.89 × Na+ ) + (1.38 × K+ ) + ( 1.03 × urea ) + (1.08 × glucose) + 7.45
The Boston Rules of acid-base compensation
The various merits and demerits of the Boston and Copenhagen acid-base compensation rules are discussed elsewhere.
Acute Respiratory Acidosis
For every 10 mmHg increase in PaCO2, the HCO3- will rise by 1 mmol/L
In other words, expected HCO3 = 24 + ((PaCO2-40) / 10)
Chronic Respiratory Acidosis
For every 10 mmHg increase in PaCO2, the HCO3- will rise by 4 mmol/L
In other words, expected HCO3 = 24 + (4 × (PaCO2-40) / 10)
Acute Respiratory Alkalosis
For every 10 mmHg decrease in PaCO2, the HCO3- will fall by 2 mmol/L
In other words, expected HCO3 = 24 + (2 ×(PaCO2-40) / 10)
Chronic Respiratory Alkalosis
For every 10 mmHg decrease in PaCO2, the HCO3- will fall by 5 mmol/L
In other words, expected HCO3 = 24 + (5 ×(PaCO2-40) / 10)
For complete compensation, expected PaCO2 = (1.5 × HCO3-) + 8
This rule is also known as Winter's Rule. An error magin of +/- 2mmHg is tolerated.
For complete compensation, expected PaCO2 = (0.7 × HCO3-) + 20
An error magin of +/- 5mmHg is tolerated.
The Copenhagen Rules of acid-base compensation
Acute Respiratory Acidosis or Alkalosis
An acute change in PaCO2 will not change the Standard Base Excess.
So, expected SBE = 0... in other words, if there is any change in SBE then it cannot be due to acute respiratory acid-base disturbances - it must be of metabolic origin.
Working backwards, expected CO2 = 40 + (0 × SBE)
Chronic Respiratory Acidosis or Alkalosis
Expected change in SBE = 0.4 times the change in PaCO2
In other words, expected SBE = 0.4 × (40 - PaCO2)
Working backwards, expected CO2 = 40 + (0.4 × SBE)
Compensatory change in PaCO2 will be proportional to the SBE.
In other words, expected CO2 = 40 + (1.0 × SBE)
Compensatory change in PaCO2 will be proportional to 0.6 times the SBE.
In other words, expected CO2 = 40 + (0.6 × SBE)