L11 Respiratory Physiology 4 Gas exchange

Overview

This lecture covers how ventilation is generated and what limits it (work of breathing), then how gas exchange across the alveolar membrane is described quantitatively: deriving the alveolar gas equation to calculate PAO2, and using the calculated PAO2 alongside a measured arterial PaO2 (A-a gradient) to distinguish hypoventilation from a true gas-exchange problem as the cause of hypoxia.

Work of breathing

Ventilation needs pressure gradients between alveoli and atmosphere, produced by the respiratory system expanding and returning to its resting volume. Two things must be overcome to achieve this, together termed the Work of Breathing (WOB):

1. Elastic recoil of the lung (and chest wall)
2. Airways resistance (friction)

Elastic recoil / compliance

• Lung compliance (CL): a measure of the elastic “stiffness” of the lung.
• CL varies with:
  • Lung volume - harder to stretch as the lung is already stretched
  • Disease - fibrosis or loss of elastic tissue
  • Age - lungs become more compliant, but the chest wall stiffens and respiratory muscles weaken, so vital capacity (VC) decreases
  • Alveolar surface tension - governed by surfactant

Airways resistance

• Airflow is mainly laminar during quiet breathing.
• Governed by Poiseuille’s Law: $R=8\eta l/\pi r^4$ (η = viscosity, l = length, r = radius).
• Resistance is inversely proportional to $r^4$: halving the radius increases resistance 16-fold.
• The main site of airway resistance is the bronchi.
• Bronchoconstriction: vagal parasympathetic activity (a reflex from irritant and cough receptors in the airways); local chemical mediators (histamine, leukotrienes).
• Bronchodilation: activation of B2-adrenoceptors, via circulating adrenaline or administered sympathomimetics (e.g. isoprenaline, salbutamol).

Dynamic compression of airways

• Some airways are highly collapsible. Increased intrathoracic pressure compresses them from outside, raising airway resistance and limiting airflow.
• Limits airflow in normal subjects during a forced expiration.
• Exaggerated when lung elastic tissue is lost (e.g. emphysema): reduced elastic recoil and loss of radial traction let airways collapse even without forced expiration, so flow limitation can occur even during normal expiration and at relatively low expiratory flow rates, reducing exercise ability.
• Purse-lipped breathing counteracts this by maintaining airway pressure, which “splints” the airway open.

Two clinical photographs appear here (elderly patients using nasal-cannula oxygen) with no caption, slide title or accompanying text, so the transcript cannot state what specific teaching point they illustrate.

Work of breathing overall

• Adequate WOB is needed to achieve sufficient alveolar ventilation (VA); hypoventilation reflects a problem with work of breathing.
• Restrictive lung disease: increased work from decreased lung compliance (“stiff lungs”).
• Obstructive lung disease: increased work from increased airway resistance (“narrow pipes”).
• Pulmonary oedema: increased work from decreased lung compliance (“stiff lungs”).
• In a hypoventilating patient (raised PCO2), the cause may be:
  • Work of breathing too high - decreased compliance, increased airway resistance
  • Inability to do the work - fatigue/muscle weakness, depressed central control (e.g. opiates)
  • Not doing enough work - behavioural (e.g. sleep), panic attack

Gas exchange across the alveolar membrane

• Scheme of O2 transfer, atmosphere to tissues: PO2 starts near 160mmHg in the atmosphere, falls to ~150mmHg as inspired air, drops sharply during ventilation to ~100mmHg alveolar PO2 (PAO2), stays broadly similar through gas exchange to ~95mmHg arterial PO2 (PaO2), then drops sharply again to ~40-47mmHg at the tissues. Ventilation causes the large atmosphere-to-alveolar drop; gas exchange (diffusion) causes only a small alveolar-to-arterial drop; a further large drop occurs at the tissues.
• Typical resting demand: O2 consumption $\dot{V}{O}_2$ = 250-300 ml/min, CO2 production $\dot{V}C{O}_2$ = 200-250 ml/min; these amounts must be exchanged across the alveolar membrane for homeostasis, and more in exercise.
• Respiratory exchange ratio $R=\dot{V}C{O}_2/\dot{V}{O}_2$; commonly ~0.8 (diet-dependent), e.g. 200/250 = 0.8.
• Diffusion occurs across a large, thin alveolar surface area, driven by pressure gradients between alveoli and pulmonary capillary blood.
• PAO2 and PACO2 set the alveolar “end” of this diffusion gradient. They are determined by: composition of inspired air, alveolar ventilation, O2 consumption or CO2 production, and how well alveolar ventilation is matched to pulmonary capillary blood flow.

Alveolar gas equation

• $PA{O}_2=PI{O}_2-V{O}_2/VA$
• $PAC{O}_2=PIC{O}_2+VC{O}_2/VA$
• Rearranging the CO2 relationship: $VA=(VC{O}_2/PAC{O}_2)\times 863$ (the factor 863 corrects for pressure/volume units). Assuming resting $VC{O}_2$ = 200 ml/min: $VA=(200/PAC{O}_2)\times 863$ ml/min. Since $PAC{O}_2\approx PaC{O}_2$, this lets alveolar ventilation be calculated from an arterial blood gas. There is an inverse relationship between VA and PACO2.
• Combining the two equations gives the Alveolar Gas Equation: $PA{O}_2=PI{O}_2-PAC{O}_2/R$.
• Respiratory Quotient (R) / Respiratory Exchange Ratio (RER): $R=\dot{V}C{O}_2/\dot{V}{O}_2$; depends on diet, ~0.8 on a mixed diet.

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• Practical form, assuming R = 0.8 and $PAC{O}_2\approx PaC{O}_2$: $PA{O}_2=PI{O}_2-PaC{O}_2/0.8$.
  • Breathing room air, $PI{O}_2$ = 150mmHg: $PA{O}_2=150-PaC{O}_2/0.8$.
  • Not breathing room air, calculate $PI{O}_2$ first: $PA{O}_2=FI{O}_2(PB-47)-PaC{O}_2/0.8$.
• Worked example: room air, $PB$ = 760mmHg ($PI{O}_2$ = 150), $PaC{O}_2$ = 40mmHg, R = 0.8: $PA{O}_2=150-40/0.8=150-50=100$ mmHg (normal).

A-a gradient

Calculating PAO2 (via the alveolar gas equation) and measuring PaO2 (via an arterial blood gas, ABG) lets you identify a difference between them - the A-a gradient ($\Delta A-a$) - which indicates a problem with gas exchange.

An unlabelled photograph of an arterial blood sample being drawn (radial puncture site) appears between the two A-a gradient formula slides. It carries no caption or slide text; its interpretation as illustrating an ABG draw is inferred from the image content and its position between the A-a gradient slides, not stated on the slide itself.

• $A-agradient=PA{O}_2(calculated)-Pa{O}_2$. The $PaC{O}_2$ used in the $PA{O}_2$ calculation comes from the ABG result.
• Normal A-a gradient: <10mmHg. An increased ΔA-a indicates decreased gas exchange.
• Worked clinical example - hypoxic patient breathing room air ($FI{O}_2$ 0.21): $Pa{O}_2$ 68mmHg (normal >90), $PaC{O}_2$ 60mmHg (normal 40), pH 7.20 (normal 7.40).
  • Question: is the hypoxia due to impaired gas exchange, hypoventilation, or both?
  • Ventilatory status: $PaC{O}_2$ = 60mmHg indicates hypoventilation.
  • Gas exchange: $PA{O}_2=150-60/0.8=150-75=75$mmHg. $A-a=75-68=7$mmHg (normal, <10).
  • Conclusion: ΔA-a is normal, so there is no gas-exchange problem (“what gets in, gets across”). The low PaO2 is entirely due to hypoventilation - not enough air is getting in, so less can get across (a work-of-breathing problem).

Self-test

1. Define lung compliance and list the factors it varies with.
2. State Poiseuille’s Law for airway resistance and explain what happens to resistance if the airway radius is halved.
3. Distinguish the mechanisms of bronchoconstriction from bronchodilation, giving an example mediator or receptor for each.
4. Describe the mechanism of dynamic compression of airways during forced expiration, and explain why flow limitation can occur at lower flow rates (even during normal expiration) in emphysema.
5. Explain how purse-lipped breathing helps a patient with dynamic airway compression.
6. List the two components of the work of breathing, and give an example lung condition that increases each.
7. A patient is hypoventilating (raised PCO2). List the three broad categories of cause you would consider.
8. Describe how PO2 changes from atmospheric air to the tissues, and identify which step - ventilation or gas exchange - accounts for the larger drop.
9. Give the typical resting values for O2 consumption and CO2 production, and define the respiratory exchange ratio (R).
10. List the four factors that determine PAO2 and PACO2.
11. Starting from $PA{O}_2=PI{O}_2-V{O}_2/VA$ and $PAC{O}_2=PIC{O}_2+VC{O}_2/VA$, state the combined Alveolar Gas Equation.
12. Using the alveolar gas equation, calculate PAO2 for a patient breathing room air (PB 760mmHg) with PaCO2 40mmHg and R 0.8.
13. Define the A-a gradient and state its normal value.
14. A patient breathing room air has PaO2 68mmHg, PaCO2 60mmHg and pH 7.20. Calculate the A-a gradient and use it to determine whether the hypoxia is due to hypoventilation, impaired gas exchange, or both.

Answers

Reveal answers

1. Compliance is a measure of lung “stiffness”/elastic properties. It varies with lung volume (stiffer as more stretched), disease (fibrosis, loss of elastic tissue), age (lungs more compliant but chest wall stiffer and muscles weaker), and alveolar surface tension (surfactant).
2. $R=8\eta l/\pi r^4$ (η = viscosity, l = length, r = radius). Halving the radius increases resistance 16-fold, since R is inversely proportional to $r^4$.
3. Bronchoconstriction: vagal parasympathetic activity (irritant/cough receptor reflex) or local mediators (histamine, leukotrienes). Bronchodilation: B2-adrenoceptor activation via circulating adrenaline or sympathomimetics (isoprenaline, salbutamol).
4. Rising intrathoracic pressure during forced expiration compresses collapsible airways from outside, increasing resistance and limiting flow. In emphysema, loss of elastic tissue and radial traction means airways collapse even without forced expiration, so flow limitation occurs even during normal expiration and at relatively low flow rates.
5. It maintains airway pressure, “splinting” the airway open and preventing dynamic collapse.
6. Elastic recoil/compliance (e.g. restrictive disease, pulmonary oedema - “stiff lungs”) and airways resistance (e.g. obstructive disease - “narrow pipes”).
7. Work of breathing too high (decreased compliance, increased resistance); inability to do the work (fatigue/muscle weakness, depressed central control e.g. opiates); not doing enough work (behavioural, e.g. sleep, panic attack).
8. PO2 falls from ~160mmHg (atmosphere) to ~150mmHg (inspired air), drops sharply to ~100mmHg alveolar PO2 (PAO2) during ventilation, stays similar (~95mmHg, PaO2) through gas exchange, then drops sharply again to ~40-47mmHg at the tissues. Ventilation causes the larger drop (atmosphere to alveolar); gas exchange causes only a small drop.
9. $\dot{V}{O}_2$ = 250-300 ml/min, $\dot{V}C{O}_2$ = 200-250 ml/min. $R=\dot{V}C{O}_2/\dot{V}{O}_2$, commonly ~0.8 on a mixed diet.
10. Composition of inspired air, alveolar ventilation, O2 consumption/CO2 production, and matching of alveolar ventilation to pulmonary capillary blood flow.
11. $PA{O}_2=PI{O}_2-PAC{O}_2/R$.
12. $PA{O}_2=150-40/0.8=150-50=100$mmHg (normal).
13. A-a gradient = PAO2 (calculated) minus PaO2 (measured); normal value is <10mmHg.
14. $PA{O}_2=150-60/0.8=150-75=75$mmHg. A-a = $75-68=7$mmHg (normal). Since ΔA-a is normal, gas exchange is not impaired; the raised PaCO2 (60mmHg) indicates hypoventilation, so the hypoxia is entirely due to hypoventilation (a work-of-breathing problem), not impaired gas exchange.