L12 Respiratory Physiology 5 Gas exchange 2

Overview

This lecture builds the tools for quantifying gas exchange — the alveolar ventilation equation and the alveolar gas equation — then uses them to define the A-a gradient and work through its three causes (impaired diffusion, shunt, V/Q mismatch) before placing gas exchange within the full five-mechanism scheme of arterial hypoxaemia. A worked clinical example (a hypoxic pneumonia patient) ties the equations to bedside interpretation.

Alveolar ventilation and the alveolar gas equation

Alveolar ventilation equation: $P_{A} C O_{2} = P_{I} C O_{2} + \dot{V} C O_{2} / \dot{V}_{A}$ , rearranged to $\dot{V}_{A} = \dot{V} C O_{2} / P_{A} C O_{2} \times 863$ .
- Assuming resting $\dot{V} C O_{2} = 200$ ml/min: $\dot{V}_{A} = 200/ P_{A} C O_{2} \times 863$ (ml/min).
- The 863 factor corrects for pressure differences and lets volume and pressure values be combined.
- Since $P_{A} C O_{2} \approx P_{a} C O_{2}$ , arterial $C O_{2}$ (from an ABG) can be used to calculate alveolar ventilation.
- $\dot{V}_{A}$ and $P_{A} C O_{2}$ are inversely related.
Alveolar gas equation: $P_{A} O_{2} = P_{I} O_{2} - P_{a} C O_{2} /0.8$ , assuming a respiratory quotient $R = 0.8$ and that alveolar $P C O_{2}$ equals arterial $P C O_{2}$ (from an ABG).
- Breathing room air, $P_{I} O_{2} = 150$ mmHg, so $P_{A} O_{2} = 150 - P_{a} C O_{2} /0.8$ .
- Full form: $P_{A} O_{2} = F_{I} O_{2} (P_{B} - 47) - P_{a} C O_{2} /0.8$ .
Why calculate this: if $P_{A} O_{2}$ is calculated and $P_{a} O_{2}$ is measured (ABG), the A-a gradient can be found: $A-a = P_{A} O_{2} - P_{a} O_{2}$ .
- Normal A-a gradient is <10 mmHg.
- An increased A-a gradient indicates decreased gas exchange.

The O2 transfer pathway and causes of a raised A-a gradient

$P O_{2}$ falls in a stepwise fashion along the O2 transfer pathway (atmosphere -> tissues): ~150 mmHg in the atmosphere/inspired air, drops to ~100 mmHg at alveolar gas ( $P_{A} O_{2}$ ), stays roughly 95-100 mmHg through the pulmonary capillary into arterial blood ( $P_{a} O_{2}$ ), then falls sharply to ~45 mmHg at the tissues. “Gas exchange” is specifically the step between $P_{A} O_{2}$ and $P_{a} O_{2}$ .
Three causes of an increased A-a gradient (a gas exchange problem):
1. Impaired diffusion
2. Shunt
3. Ventilation-perfusion (V/Q) mismatch

Impaired diffusion

Causes: thickening of the diffusion barrier, decreased surface area, exercise, breathing a low $O_{2}$ mix.
The alveolar-capillary diffusion barrier has area $A \approx 100$ m² and thickness $T = 0.2 - 0.5$ μm. Diffusion rate depends on $A$ , $T$ , a diffusion coefficient $D$ (proportional to gas solubility, inversely related to molecular weight), and the partial pressure gradient across the membrane (e.g. $P_{1} - P_{2} = 100 - 40$ mmHg for $O_{2}$ ).
Timing: each erythrocyte spends ~0.75 s in the pulmonary capillaries; equilibration between alveolar gas and capillary blood normally occurs within ~0.25 s, and still occurs even when transit time is reduced (e.g. exercise).
- Because of this reserve, diffusion must be significantly impaired before resting $P_{a} O_{2}$ falls — but problems appear during exercise.
- Diffusion impairment responds well to supplemental $O_{2}$ .
$C O_{2}$ diffusion: equilibrium between alveolar and capillary $P C O_{2}$ also takes ~0.25 s. $C O_{2}$ ‘s diffusion constant is 23x that of $O_{2}$ , so $C O_{2}$ diffusion is rarely impaired.

Shunt

Definition: blood that re-enters the arterial system without passing through ventilated areas of the lung.
Anatomical shunt, e.g. cardiac defects, bronchial artery blood, myocardial blood via Thebesian veins.
Pathological shunt, e.g. pneumonia: alveoli fill with exudate (pus) and are not ventilated, but are still perfused, so the blood passing through is not oxygenated.
Effects of shunt:
1. Shunted blood is essentially venous blood, which dilutes oxygenated arterial blood and reduces $P_{a} O_{2}$ .
2. Shunt increases the A-a gradient.
3. Shunts respond poorly to additional oxygen.

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Worked example: hypoxic pneumonia patient

Breathing room air ( $F i O_{2}$ 0.21): $P_{a} O_{2}$ 60 mmHg (normal >90), $P_{a} C O_{2}$ 52 mmHg (normal 40), pH 7.29 (normal 7.40).
Question: is this hypoxia due to impaired gas exchange, hypoventilation, or both? Ventilatory status is assessed from $P_{a} C O_{2}$ ; gas exchange is assessed from the A-a gradient.
Ventilation: $P C O_{2} = 52 \Rightarrow$ hypoventilating.
Gas exchange: $P_{A} O_{2} = 150 - 52/0.8 = 150 - 65 = 85$ mmHg. A-a $= 85 - 60 = 25$ mmHg (normal <10) $\Rightarrow$ increased, i.e. a gas exchange problem.
Conclusion: hypoxaemia is partly due to hypoventilation (pus-filled lungs are hard to inflate) and partly due to shunt/impaired gas exchange (pus-filled alveoli are perfused but not ventilated).

Ventilation-perfusion (V/Q) mismatch

The $P O_{2}$ of gas in each alveolus (and of the capillary blood leaving it) is set by the ratio of ventilation to perfusion (V/Q) for that alveolus. Any mismatch between ventilation and perfusion alters gas exchange and produces an abnormal A-a gradient — described as “wasted ventilation” or “wasted perfusion.”
Causes of non-uniform ventilation: uneven airway resistance (airway collapse in emphysema, asthma, bronchitis; compression by tumours or oedema) or non-uniform compliance (fibrosis; regional variation in surfactant production; pulmonary congestion/oedema; emphysema; atelectasis; pneumothorax; compression by tumours or cysts).
Causes of non-uniform perfusion: embolisation or thrombosis; compression of pulmonary vessels by high alveolar pressures; tumours; exudates; pneumothorax; destruction or occlusion of pulmonary vessels by disease; pulmonary vascular hypotension; collapse or overexpansion of alveoli.
V/Q mismatch occurs even in normal lungs: both ventilation and perfusion increase from apex to base, but perfusion increases more than ventilation, so a range of V/Q ratios exists across the normal lung (V/Q rises sharply toward the apex).
Any disease altering ventilation and/or perfusion increases V/Q mismatch, impairing overall gas exchange and raising the A-a gradient. V/Q mismatch responds well to supplemental $O_{2}$ : enriching inspired air lets poorly-ventilated (low-V) alveoli still oxygenate their blood, reducing “wasted perfusion.”

Arterial hypoxaemia: the full picture

Arterial hypoxaemia means $O_{2}$ cannot be delivered to cells. It can be caused by five mechanisms:

Reduced barometric pressure ( $P_{B}$ ) or $F i O_{2}$
Hypoventilation
Impaired diffusion
Shunt
Ventilation-perfusion (V/Q) mismatch

Of these, mechanisms 3-5 are specifically “gas exchange problems” — they raise the A-a gradient. Mechanisms 1-2 (reduced $P_{B}$ / $F i O_{2}$ , hypoventilation) do not raise the A-a gradient.

Self-test

Write the alveolar ventilation equation in its rearranged form and state what the 863 factor corrects for.
State the alveolar gas equation for a patient breathing room air, and the two assumptions it relies on.
Define the A-a gradient and state its normal value.
Describe how $P O_{2}$ changes along the O2 transfer pathway from atmosphere to tissues, and identify which step “gas exchange” refers to.
List the three causes of an increased A-a gradient.
What properties of the alveolar-capillary membrane and gas determine the rate of diffusion across it?
List four causes of impaired diffusion.
Explain why impaired diffusion rarely reduces resting $P_{a} O_{2}$ but causes problems during exercise.
Explain why $C O_{2}$ diffusion is rarely impaired even when $O_{2}$ diffusion is.
Define shunt and distinguish an anatomical from a pathological shunt, giving one example of each.
Describe the three effects of shunt on arterial blood gases and its response to supplemental oxygen.
A patient on room air has $P_{a} O_{2}$ 60 mmHg and $P_{a} C O_{2}$ 52 mmHg. Calculate the A-a gradient and use it, together with the $P_{a} C O_{2}$ , to determine whether the hypoxaemia is due to hypoventilation, impaired gas exchange, or both.
Explain how the V/Q ratio of an alveolus determines its $P O_{2}$ , and why V/Q mismatch exists even in normal lungs.
List two causes of non-uniform ventilation and two causes of non-uniform perfusion.
Distinguish impaired diffusion, shunt and V/Q mismatch by their response to supplemental oxygen.
List the five causes of arterial hypoxaemia and state which of them are specifically “gas exchange problems.”

Answers

Reveal answers

$\dot{V}_{A} = \dot{V} C O_{2} / P_{A} C O_{2} \times 863$ . The 863 factor corrects for pressure differences and allows volume and pressure values to be combined.

$P_{A} O_{2} = 150 - P_{a} C O_{2} /0.8$ . Assumes $R = 0.8$ and that alveolar $P C O_{2}$ equals arterial $P C O_{2}$ (measured by ABG).

A-a gradient $= P_{A} O_{2} - P_{a} O_{2}$ ; normally <10 mmHg.

$P O_{2}$ falls stepwise: ~150 mmHg in atmosphere/air, drops to ~100 mmHg at alveolar gas ( $P_{A} O_{2}$ ), stays ~95-100 mmHg through the capillary to arterial blood ( $P_{a} O_{2}$ ), then falls sharply to ~45 mmHg at the tissues. “Gas exchange” is the fall between $P_{A} O_{2}$ and $P_{a} O_{2}$ .

Impaired diffusion, shunt, ventilation-perfusion (V/Q) mismatch.

Membrane area (~100 m²) and thickness (0.2-0.5 μm), a diffusion coefficient (proportional to solubility, inversely related to molecular weight), and the partial pressure gradient across the membrane.

Thickening of the diffusion barrier, decreased surface area, exercise, breathing a low $O_{2}$ mix.

Equilibration between alveolar gas and capillary blood normally takes only ~0.25 s of the ~0.75 s an erythrocyte spends in the pulmonary capillary, and still completes even with reduced transit time — so there is a large reserve at rest. Exercise shortens transit time further and increases demand, which can outstrip this reserve.

$C O_{2}$ ’s diffusion constant is 23x that of $O_{2}$ , so equilibration is far less sensitive to barrier changes that would impair $O_{2}$ diffusion.

Shunt is blood that re-enters the arterial system without passing through ventilated lung. Anatomical: e.g. a cardiac defect, bronchial artery blood, myocardial blood via Thebesian veins. Pathological: e.g. pneumonia, where pus-filled alveoli are perfused but not ventilated.

Shunted (venous) blood dilutes oxygenated arterial blood and lowers $P_{a} O_{2}$ ; shunt increases the A-a gradient; shunts respond poorly to supplemental oxygen.

A-a $= (150 - 52/0.8) - 60 = 85 - 60 = 25$ mmHg (normal <10), so there is a gas exchange problem. $P_{a} C O_{2} = 52$ mmHg shows hypoventilation. The hypoxaemia is due to both: hypoventilation (pus-filled lungs are hard to inflate) and impaired gas exchange/shunt (pus-filled alveoli are perfused but not ventilated).

An alveolus’s $P O_{2}$ (and that of the capillary blood leaving it) is set by the ratio of ventilation to perfusion it receives. Even in normal lungs, both ventilation and perfusion increase from apex to base, but perfusion increases more steeply than ventilation, so a range of V/Q ratios exists across the lung.

Non-uniform ventilation: uneven airway resistance (e.g. emphysema, asthma) or non-uniform compliance (e.g. fibrosis, atelectasis). Non-uniform perfusion: embolisation/thrombosis, or compression of vessels by tumours/high alveolar pressure.

Impaired diffusion and V/Q mismatch respond well to supplemental oxygen; shunt responds poorly.

Reduced $P_{B}$ / $F i O_{2}$ , hypoventilation, impaired diffusion, shunt, V/Q mismatch. Impaired diffusion, shunt and V/Q mismatch are the “gas exchange problems” (they raise the A-a gradient); reduced $P_{B}$ / $F i O_{2}$ and hypoventilation do not.

tags	respiratory, physiology, lecture
aliases	L12 Respiratory Physiology 5 Gas exchange 2

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L12 Respiratory Physiology 5 Gas exchange 2

Overview

Alveolar ventilation and the alveolar gas equation

The O2 transfer pathway and causes of a raised A-a gradient

Impaired diffusion

Shunt

Worked example: hypoxic pneumonia patient

Ventilation-perfusion (V/Q) mismatch

Arterial hypoxaemia: the full picture

Self-test

Answers

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