Respiratory physiology
Introduced| English | Meaning |
|---|---|
| alveolar gas equation | The formula PAO₂ = FiO₂(Patm − PH₂O) − PaCO₂/R for alveolar oxygen pressure. |
| A–a gradient | The difference between alveolar and arterial oxygen pressure; it widens with gas-exchange disease. |
| oxygen dissociation curve/ˈɒksɪdʒn dɪˌsəʊsɪˈeɪʃn kɜːv/ | A graph showing how haemoglobin's percentage saturation with oxygen varies with oxygen partial pressure. |
Physics you can do at the bedside
- Gas exchange is applied physics with clinical arithmetic: one equation for alveolar gas, one curve for oxygen carriage.
- With them, every low-oxygen patient falls into "lung problem" or "not a lung problem".
The alveolar gas equation
- The alveolar gas equation 肺泡气方程 says how much O₂ the alveolus holds:
- At sea level $P_{IO_2} = 0.21 \times (760 - 47) = 150$ mmHg. With $P_{ACO_2} = 40$ and $R = 0.8$: $P_{AO_2} = 150 - 50 = 100$ mmHg.
At sea level a patient's alveolar $P_{CO_2}$ is 60 mmHg. With R = 0.8, what is the alveolar $P_{O_2}$, in mmHg?
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150 − 60/0.8 = 150 − 75 = 75 mmHg.
The A–a gradient
- The alveolus holds 100 mmHg, but arterial blood usually shows a little less. The difference is the A–a gradient 肺泡-动脉梯度, normally 5–15 mmHg (higher with age).
- Shunt, mismatched ventilation and blood flow, and thickened walls widen it. Hypoventilation and high altitude lower the O₂ but leave the gradient normal.
Which cause of low arterial O₂ leaves the A–a gradient normal?
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In hypoventilation the alveolus itself holds less O₂, but what it holds still reaches the blood normally.
The oxygen dissociation curve
- The oxygen dissociation curve 氧解离曲线 is sigmoid, with $P_{50} = 26.6$ mmHg (half saturated).
- Acid, CO₂, heat and 2,3-BPG shift it right, so working tissue gets more O₂.
Which change shifts the oxygen dissociation curve to the left?
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Acid, CO₂, heat and 2,3-BPG shift it right (easier unloading); cooling shifts it left (tighter binding).
Worked example: the opioid overdose
- (Fictional case) Breathing slows and $P_{ACO_2}$ rises to 80 mmHg: $P_{AO_2} = 150 - 80/0.8 = 50$ mmHg.
- Low O₂ with a normal A–a gradient: the lungs are fine, the breathing drive is not. The treatment follows: support the breathing.
Put the steps of working out an A–a gradient in order.
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Three subtractions sort the causes of low O₂ into lung and not-lung.
In the overdose example the alveolar $P_{O_2}$ is 50 mmHg and the arterial $P_{O_2}$ is 44 mmHg. What is the A–a gradient, in mmHg?
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50 − 44 = 6 mmHg, within the normal range: the problem is the breathing drive, not the lungs.
Worked example: saturation is not content
- In the lungs ($P_{O_2} \approx 100$ mmHg) Hb is 97–98% saturated; in resting tissue (40 mmHg) about 75%. The steep middle of the curve releases about a quarter of the O₂ on each pass.
- Anaemia lowers the O₂ content at the same saturation, so a pulse oximeter reads normal in severe anaemia: it measures binding, not carriage.
A normal pulse-oximeter reading means the blood is carrying a normal amount of O₂.
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The oximeter measures the fraction of Hb that is bound. With little Hb (anaemia), saturation can be normal while content is low.
Three common slips
- Assuming R = 1. It is about 0.8; with R = 1 the alveolar O₂ comes out 10 mmHg too high.
- Forgetting water vapour. Subtract 47 mmHg: the inspired value is 150 mmHg, not 160.
- Cyanosis as an O₂ reading. It needs about 5 g/dL of deoxygenated Hb, so it hides in anaemia and shows early in polycythaemia.
Recap
- $P_{AO_2} = 150 - P_{ACO_2}/0.8$ at sea level.
- The A–a gradient separates lung causes (shunt, mismatch, thick walls) from hypoventilation and altitude.
- $P_{50} = 26.6$ mmHg, shifted right by acid, CO₂, heat and 2,3-BPG; saturation is not content.