Sample · ANZCA
Hypoxaemia in recovery: the alveolar gas equation, A-a gradient and the five mechanisms
Applied physiology · 3 parts · 10 marks. Decide what you would write, then compare with the rubric and model answer. In the app you write it under time and it comes back marked.
A 70-year-old man is in the post-anaesthesia care unit (PACU) 40 minutes after an open right hemicolectomy under general anaesthesia. He received 15 mg of intravenous morphine in divided doses during and after the case. He is drowsy but rousable. His oxygen mask has fallen off and his peripheral oxygen saturation (SpO2) is 88%.
An arterial blood gas taken while breathing room air at sea level (barometric pressure 760 mmHg) shows:
- pH 7.31
- arterial partial pressure of oxygen (PaO2) 55 mmHg
- arterial partial pressure of carbon dioxide (PaCO2) 50 mmHg
- bicarbonate 25 mmol/L
Assume a respiratory quotient of 0.8 and saturated water vapour pressure of 47 mmHg.
(a) Calculate his alveolar partial pressure of oxygen and his alveolar-arterial (A-a) oxygen gradient, showing your working, and state whether the gradient is normal for his age. 3 marks
Show the rubric and model answer
- States the alveolar gas equation: PAO2 = FiO2 x (PB - PH2O) - PaCO2 / RQ (1)
- Correct substitution and result: 0.21 x (760 - 47) - 50 / 0.8 = 149.7 - 62.5 = about 87 mmHg (1)
- A-a gradient = 87 - 55 = about 32 mmHg; raised (expected upper limit roughly age/4 + 4, about 22 mmHg at 70) (1)
- Concludes hypoventilation alone does not explain the hypoxaemia; a second mechanism (ventilation-perfusion mismatch or shunt) is present (1)
Alveolar gas equation (simplified): PAO2 = FiO2 x (PB - PH2O) - PaCO2 / RQ
PAO2 = 0.21 x (760 - 47) - 50 / 0.8
= 0.21 x 713 - 62.5
= 149.7 - 62.5
= about 87 mmHg
A-a gradient = PAO2 - PaO2 = 87 - 55 = about 32 mmHg.
A normal A-a gradient on room air rises with age; a common estimate of the upper limit is (age / 4) + 4, about 22 mmHg at 70 years. His gradient is raised.
Interpretation: the raised PaCO2 shows hypoventilation (opioid-induced), but hypoventilation alone would leave a normal gradient. A raised gradient means there is also ventilation-perfusion mismatch or shunt, most likely atelectasis after upper abdominal surgery.
(b) List the five physiological causes of arterial hypoxaemia and, for each, state how it affects the A-a gradient and the response to supplemental oxygen. 4 marks
Show the rubric and model answer
- Low inspired oxygen (altitude, hypoxic gas mixture): normal gradient, corrects with oxygen (0.75)
- Hypoventilation: normal gradient, raised PaCO2, corrects readily with modest oxygen (but CO2 still rises) (0.75)
- Diffusion limitation: raised gradient (especially on exercise or low mixed venous oxygen), corrects with oxygen (0.75)
- Ventilation-perfusion mismatch (low V/Q units): raised gradient, corrects well with oxygen (1)
- True shunt (V/Q = 0): raised gradient, poor response to oxygen; minimal rise in PaO2 once shunt fraction exceeds about 30% (1)
| Cause | A-a gradient | Response to oxygen |
|---|---|---|
| Low inspired oxygen (altitude, hypoxic mixture) | Normal | Corrects |
| Hypoventilation (opioids, residual block) | Normal, PaCO2 raised | Corrects with modest FiO2, but does not treat the hypercapnia |
| Diffusion limitation (interstitial lung disease) | Raised | Corrects |
| Ventilation-perfusion mismatch (low V/Q units: atelectasis, secretions, chronic obstructive pulmonary disease) | Raised | Corrects well, because raising alveolar oxygen in poorly ventilated units saturates their blood |
| True shunt (V/Q = 0: collapsed or consolidated lung, intracardiac right-to-left shunt) | Raised | Poor; little rise in PaO2 once shunt exceeds about 30% |
Low mixed venous oxygen content (low cardiac output, high oxygen consumption) is not a cause on its own but worsens hypoxaemia from shunt or V/Q mismatch.
(c) Explain why supplemental oxygen corrects ventilation-perfusion mismatch but has little effect on a large true shunt. 3 marks
Show the rubric and model answer
- In low V/Q units some ventilation reaches the alveolus, so raising FiO2 raises alveolar PO2 and saturates the end-capillary blood (1)
- Shunted blood never meets alveolar gas, so it leaves with mixed venous content regardless of FiO2 (1)
- Blood from normal units is already near fully saturated (flat upper part of the oxyhaemoglobin dissociation curve); extra oxygen adds only dissolved oxygen (0.003 mL/dL per mmHg), too little to offset the desaturated shunt blood (1)
- Iso-shunt diagram concept: at shunt fractions above about 30%, increasing FiO2 from 0.5 to 1.0 raises PaO2 very little; management is to reduce the shunt (recruitment, PEEP) (1)
Ventilation-perfusion mismatch: low V/Q units receive some fresh gas. Raising the inspired oxygen raises the alveolar PO2 in those units over a few minutes, and their end-capillary blood becomes fully saturated. The mixed arterial content therefore normalises.
True shunt: blood passing collapsed alveoli or a right-to-left connection never meets alveolar gas, so it joins the arterial stream at mixed venous oxygen content, whatever the FiO2.
The blood from normal units cannot compensate. It is already on the flat upper part of the oxyhaemoglobin dissociation curve, close to 100% saturated, so raising FiO2 only adds dissolved oxygen (0.003 mL/dL per mmHg of PO2). That small extra content cannot offset the desaturated shunt blood. On the iso-shunt diagram, once the shunt fraction is above about 30% the PaO2 barely rises even at FiO2 1.0.
For this patient: give oxygen and treat the hypoventilation (stimulate, review opioid, consider titrated naloxone), then reduce the shunt with sitting up, deep breathing, analgesia that allows coughing and, if needed, continuous positive airway pressure.
Where candidates lose marks here
- Forgetting to subtract water vapour pressure or to divide PaCO2 by the respiratory quotient, giving a wrong PAO2.
- Calling the gradient normal without stating a reference range for age, or not drawing the conclusion that hypoventilation is not the whole story.
- Listing "low cardiac output" or "anaemia" as one of the five causes of a low PaO2 (anaemia lowers content, not PaO2).
- Explaining shunt without mentioning the shape of the oxyhaemoglobin dissociation curve: this is the integration examiners look for.
- Writing physiology with no link back to the patient in recovery (Primary examiners penalise failure to apply the science to anaesthesia).
Original content written for Fellowship Ready, for exam preparation only, not clinical advice. Not affiliated with the Australian and New Zealand College of Anaesthetists (ANZCA).