# oxygen pressure at altitude

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This equation computes the oxygen partial pressure at varying altitudes.

# Notes

Oxygen availability and altitude

Although the percentage of oxygen in inspired air is constant at different altitudes, the fall in atmospheric pressure at higher altitude decreases the partial pressure of inspired oxygen and hence the driving pressure for gas exchange in the lungs. An ocean of air is present up to 9-10 000 m, where the troposphere ends and the stratosphere begins. The weight of air above us is responsible for the atmospheric pressure, which is normally about 100 kPa at sea level. This atmospheric pressure is the sum of the partial pressures of the constituent gases, oxygen and nitrogen, and also the partial pressure of water vapour (6.3 kPa at 37C). As oxygen is 21% of dry air, the inspired oxygen pressure is 0.21×(100−6.3)=19.6 kPa at sea level.

Atmospheric pressure and inspired oxygen pressure fall roughly linearly with altitude to be 50% of the sea level value at 5500 m and only 30% of the sea level value at 8900 m (the height of the summit of Everest). A fall in inspired oxygen pressure reduces the driving pressure for gas exchange in the lungs and in turn produces a cascade of effects right down to the level of the mitochondria, the final destination of the oxygen.
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Physiological effects of altitude
Lung

Hypoxic ventilatory response

At sea level carbon dioxide is the main stimulus to ventilation. At altitude hypoxia does increase ventilation, but usually only when the inspired oxygen pressure is reduced to about 13.3 kPa (3000 m altitude). At this inspired oxygen pressure the alveolar oxygen pressure is about 8 kPa, and with further increases in hypoxia ventilation rises exponentially. This hypoxic ventilatory response is mediated by the carotid body, and response varies widely among subjects. Interestingly, however, the ability to tolerate altitude does not seem to relate to the presence of a brisk hypoxic ventilatory response. Some climbers with poor hypoxic ventilatory response do particularly well—for example, Peter Habeler, who in 1978 became (with Rheinhold Messner) the first to climb Everest without oxygen.

Pulmonary circulation

In the systemic circulation hypoxia acts as a vasodilator, but in the pulmonary circulation it is a vasoconstrictor. The purpose of hypoxic pulmonary vasoconstriction is unclear. It may help match ventilation and perfusion within the lung, but in hypoxia of altitude the reflex leads to pulmonary hypertension and is associated with high altitude pulmonary oedema.

Gaseous diffusion

At sea level gaseous diffusion is probably limited by ventilation-perfusion matching in the lung. At high altitude, however, the alveolar-arterial difference for oxygen is higher than would be predicted from the measured ventilation-perfusion inequality. This is because the decreased driving pressure for oxygen from alveolar gas into arterial blood is insufficient to fully oxygenate the blood as it passes through the pulmonary capillaries. This is more evident on exercise as cardiac output increases and blood spends less time at the gas exchanging surface (diffusion limitation).
Heart

The heart works remarkably well at altitude. Initially there is an increase in cardiac output in relation to physical work but later this settles to sea level values. At all times there is increased heart rate and decreased stroke volume for a given level of work, though the maximum obtainable heart rate falls as higher altitudes are reached.
Brain

Hypoxia has progressive effects on the functioning of the central nervous system. Accidents that occur at extreme altitude on Everest and other mountains may be due to poor judgment as a consequence of hypoxic depression of cerebral function. More worrying is that these effects on cerebral function may be permanent. The American Medical Research Expedition to Everest studied its climbers a year after return to sea level and found some enduring abnormalities of cognitive function and ability to perform fast repetitive movements, although most functions tested had returned to pre-expedition values.
Blood

Initially on travelling to altitude haemoglobin concentrations rise through a fall in the plasma volume due to dehydration. Later, hypoxia stimulates production of erythropoietin by the juxtaglomerular apparatus of the kidney so haemoglobin production increases and haemoglobin concentrations may rise to 200 g/l. The increased viscosity of the blood coupled with increased coagulability increases the risk of stroke and venous thromboembolism. Some authors advocate regular venesection in high altitude climbs; others recommend prophylactic aspirin. Neither has been shown scientifically to reduce the incidence of venous or arterial thrombosis.
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Acclimatisation

Adequate acclimatisation is essential for safe travelling in the mountains. The climbers adage is “climb high and sleep low.” Ideally acclimatisation should be progressive. At altitudes above 3000 m individuals should climb no more than 300 m per day with a rest day every third day. Anyone suffering symptoms of acute mountain sickness should stop, and if symptoms do not resolve within 24 hours descend at least 500 m.

There can be a tendency, particularly on commercial expeditions, to push on at a rate that is too fast for weaker members of the group. This is dangerous, and the rate of ascent should be set to that of the slowest members of the party.
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Recognising altitude related illness
Acute mountain sickness

Acute mountain sickness is self limiting and usually affects previously healthy individuals who go too rapidly to altitude. There may be no symptoms for the first 12-24 hours. Thereafter symptoms develop and usually peak on the second or third day. Symptoms include headache, anorexia, insomnia, and breathlessness. The cause of acute mountain sickness is not understood but is clearly related to hypoxia and factors such as effort, air temperature, previous viral respiratory tract infection, and innate susceptibility. The incidence is quite high. Work at Pheriche, Nepal (4343 m) in 1979 found that 43% of trekkers passing through were experiencing symptoms.