Trekker at 3,800 m: Alveolar Oxygen, the Right-Shifted Curve and a Daylight-Only Helicopter
A 32-year-old trekker is brought to a health post at 3,800 m in Manang with breathlessness at rest and a dry cough that began the previous night. Barometric pressure there is about 480 mmHg and alveolar water vapour pressure at 37 °C is 47 mmHg. Arterial blood: PaO₂ 52 mmHg, PaCO₂ 30 mmHg, pH 7.48, haemoglobin 15.5 g/dL, arterial oxygen saturation 82% by co-oximetry. Two weeks earlier at sea level his saturation was 98%. His 2,3-bisphosphoglycerate is now raised, shifting his oxygen dissociation curve so that P50 has moved from 26.6 to about 30 mmHg. He is afebrile, but chest auscultation reveals crackles at the right base and the radiograph shows patchy shadowing. The health post has a portable oxygen concentrator, acetazolamide tablets, and a helicopter that can fly only in daylight; it is 3 p.m.
1. Using the alveolar gas equation, calculate the alveolar PO₂ and the alveolar–arterial gradient. What does the size of that gradient tell you about why he is hypoxaemic, and what does it predict about his response to supplemental oxygen?
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Inspired oxygen: PIO₂ = FiO₂ × (Pb − 47) = 0.21 × (480 − 47) = 0.21 × 433 = 90.9 mmHg.
Alveolar oxygen: PAO₂ = PIO₂ − PaCO₂/R = 90.9 − 30/0.8 = 90.9 − 37.5 = 53.4 mmHg.
A–a gradient: 53.4 − 52 = ≈1.4 mmHg (normal is well under 15–20 mmHg in a young adult).
Judgement. The hypoxaemia is almost entirely explained by the low barometric pressure - hypobaric hypoxia - not by a large shunt or gross V/Q mismatch, even though the radiograph is abnormal. A near-normal gradient despite patchy shadowing means the lesion is not yet producing a big shunt fraction.
Prediction for oxygen. Because the gradient is small, a modest rise in FiO₂ translates into a large rise in alveolar and arterial PO₂: at FiO₂ 0.28, PAO₂ = 0.28 × 433 − 37.5 = 121.2 − 37.5 = 83.7 mmHg, so PaO₂ would be roughly 82 mmHg. This is the key judgement - at altitude, low-flow oxygen is disproportionately effective, and it can be used to buy time rather than being held back as a last resort.
2. Calculate his arterial oxygen content now and at sea level using CaO₂ = 1.34 × Hb × SaO₂ + 0.003 × PaO₂. Then judge whether the rise in 2,3-BPG is helping or harming him, taking the pH into account.
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At altitude: CaO₂ = 1.34 × 15.5 × 0.82 + 0.003 × 52 = 17.03 + 0.16 = 17.2 mL/dL. At sea level: CaO₂ = 1.34 × 15.5 × 0.98 + 0.003 × 98 ≈ 20.36 + 0.29 = 20.6 mL/dL. So he has lost about 3.4 mL/dL of carriage, roughly a sixth - comparable to losing 1.5–2 g/dL of haemoglobin.
Is the right shift good or bad? A rise in P50 from 26.6 to 30 mmHg reduces saturation at any given PaO₂, so it lowers his arterial saturation slightly at the lung - at PaO₂ 52 mmHg he sits on the steep part of the curve, so the penalty is real but modest. At tissue PO₂ (say 25–30 mmHg) the same shift releases substantially more oxygen. Net effect: adaptive, because the limiting factor at altitude is tissue unloading, not loading.
But note the counter-force: his pH is 7.48. The Bohr effect of alkalosis shifts the curve back to the left, partly cancelling the 2,3-BPG effect - helpful in the lung, unhelpful in tissue. The practical consequence is that SaO₂ read off the monitor understates his true problem less than it seems: he is on the steep portion, so small rises in PaO₂ (oxygen therapy) produce large rises in saturation.
3. Rank descent, oxygen and acetazolamide for this patient, given that the helicopter can only fly in daylight and it is 3 p.m. Justify the ranking on mechanism and on the constraints.
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Oxygen - start now, first. Mechanism: raises PIO₂ directly, and with an A–a gradient of only 1.4 mmHg the response is near-linear in FiO₂. It is available on site, acts in minutes, and is the only intervention that immediately corrects the arterial content.
Descent - definitive, do not wait for the helicopter. Mechanism: restoring barometric pressure reverses the whole cascade. A descent of 500–1000 m is usually enough to improve symptoms substantially, and walking down is feasible with support. Given a 3 p.m. start and an unknown weather window, treating the helicopter as the plan is the error: cloud can close the valley and he can deteriorate overnight. Descend on foot unless he is too unstable to move.
Acetazolamide - useful adjunct, not rescue. Mechanism: carbonic anhydrase inhibition causes a bicarbonate diuresis, producing a mild metabolic acidosis that drives ventilation and speeds acclimatisation; it also reduces periodic breathing. It does not treat established high-altitude pulmonary oedema and will not raise PaO₂ acutely. It is worth giving while arranging evacuation, but it cannot substitute for oxygen or descent.
Judgement. Oxygen + acetazolamide + immediate descent, with the helicopter as an evacuation backup. The correct ordering follows mechanism (oxygen works fastest), then durability (descent is curative), then logistics (daylight limits the aircraft, not the decision to move).