Respiratory physiology
Введено| English | Значение |
|---|---|
| alveolar gas equation | alveolar gas equation |
| A–a gradient | A–a gradient |
| 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?
Сложность 2/5 · 140 монет + небольшой бонус за первое завершение сегодня
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?
Сложность 1/5 · 100 монет + небольшой бонус за первое завершение сегодня
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?
Сложность 1/5 · 100 монет + небольшой бонус за первое завершение сегодня
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.
Сложность 3/5 · 200 монет + небольшой бонус за первое завершение сегодня
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?
Сложность 2/5 · 140 монет + небольшой бонус за первое завершение сегодня
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.
Сложность 1/5 · 100 монет + небольшой бонус за первое завершение сегодня
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.