When analysing a paO2 value on an arterial blood gas we must factor in both the degree of alveolar ventilation and the level of inspired oxygen (the FiO2). This is achieved by calculating the ‘A-a gradient’. It is well worth getting to grips with this topic.

In order to ensure elimination of all CO2 produced during metabolism, centers in the brainstem control the volume of air per unit time entering the alveoli (‘the alveolar ventilation’). This is controlled by altering the depth and rate of respiration. In addition to the elimination of CO2, a normal level of alveolar ventilation maintains the partial pressure of oxygen in the alveoli (the pAO2) at a level well above that required to saturate hemoglobin in the arterial blood.

At a given level of alveolar ventilation the pAO2 is also critically dependent on the level of inspired oxygen in inhaled air. Normally 21%, we can increase this and consequently the pAO2 by adding oxygen to the inhaled air.

Diffusion of oxygen across the alveolar-capillary membrane is not a perfectly efficient process. Due to normal physiological effects, the level (i.e concentration = partial pressure) of oxygen in the arterial blood returning to the left ventricle from the lungs (the paO2) never quite reaches the level of the pAO2. There is a difference, (a ‘gradient’)  between the alveolar (pAO2) and the arterial (paO2) concentration of oxygen. pAO2 – paO2 is termed the A-a gradient. There is a normal range of values for the A-a gradient depending on the subjects age and the level of inspired oxygen. In the presence of disease, the A-a gradient may rise above this normal range. Therefore, if we detect an A-a gradient above the normal expected range on the basis of the patients age we must explain this finding.

How do we calculate the alveolar pAO2?

We can calculate the pAO2 in mmHg from the values recorded on the ABG using the following equation (‘the alveolar gas equation’).

pAO2 = FiO2(atmospheric pressure – vapour pressure in the airways) – paCO2/respiratory quotient

At sea level breathing room air:

pAO2 (mmHg) = 0.21(713) – paCO2(mmHg)/0.8

Note: in this equation FiO2 is expressed as a decimal fraction (21% = 0.21).

Note: If you normally work in kPa (eg UK and Ireland), it is very useful to be able to work in the US units in these calculations. It is simple, mmHg = 7.5 x kPa.

The effects of oxygen therapy

In a patient, we can adjust the FiO2 and, therefore, the pAO2, by mixing oxygen with the inhaled room air. Our patient was receiving 4L of oxygen per minute  (we presume via nasal prongs as this is usually the case for patient comfort). What FiO2 does this generate? You will need to know the relationship between litres of oxygen administered per minute (via nasal prongs) and FiO2. The relationship is shown below (+3 then all +4′)

Oxygen (l/min)                                        FiO2

RA                                                           21%

1l                                                             24% (ie +3%)

2l                                                             28% (ie +4%)

3l                                                             32% (ie +4%)

4l                                                             36% (ie +4%)

5l                                                             40% (ie +4%)

6l                                                             44% (ie +4%) (maximum achievable with nasal canula)

Calculating the A-a gradient in our patient (Course 3 Case 1)

So, in our patient

pAO2 = 0.36(713) – 35/0.8 = 213 mmHg

Therefore, observed A-a gradient = (pAO2 – paO2) = 128 mmHg

Calculation of the predicted A-a gradient in our patient

Predicted A-a gradient is given by:

Age/4 + 4 = 19 mmHg (if breathing room air)

However, the A-a gradient rises stepwise with increases in FiO2 in normal individuals. We need to add 7.5 mmHg to the predicted A-a gradient for every 10% increase in the FiO2.

So, predicted A-a gradient for a 60 year old woman on 4L (36%) O2 should be close to:

(60/4 + 4) + 11 = 30 mmHg

Despite a superficially normal ABG, our patient had a markedly elevated A-a gradient. In effect, this analysis is telling us that in a lady of this age, breathing this concentration of oxygen (FiO2) at this level of alveolar ventilation (paCO2), we should expect a much higher paO2. Something is reducing the level of oxygenation of the blood flowing through the lungs to the left ventricle. In this case that something was probably a pulmonary embolism (or emboli).

The calculations above look onerous but can by carried out by apps available on your mobile telephone. Usually it makes little difference but very occasionally, it makes all the difference.