L02 Respiratory Physiology 1 Overview of the physics of the respiratory system

Overview

This lecture introduces respiration as a five-step process linking the atmosphere, the lungs, the blood and the tissues, and works through the physics that drives it: the partial-pressure gradients that govern gas movement, the mechanics of ventilation and dead space, the pressure changes that drive airflow in and out of the lungs, and the mechanisms by which O2 and CO2 diffuse across membranes and are carried in blood. It closes with the basic architecture of the neural control system that regulates breathing.

The Five Steps of Respiration

Respiration is the exchange of O2 and CO2 between the environment and the tissues. It comprises:

• exchange of O2 and CO2 between the atmosphere and blood flowing through the lungs
• transport of O2 and CO2 between tissues and lungs by the circulating blood
• O2 consumption and CO2 production in the tissues

This is broken down into five steps:

1. Ventilation: moving air in and out of the lungs to supply O2 to, and remove CO2 from, the alveoli. A process of bulk flow.
2. Gas exchange (alveoli): O2 and CO2 move across the alveolar membrane down their partial pressure gradients. A process of diffusion.
3. Gas transport: blood leaves the lungs high in O2 and low in CO2 and is pumped around the body to the cells. A process of bulk flow.
4. Gas exchange (tissues): at the capillary-cell interface, O2 and CO2 exchange down their partial pressure gradients. A process of diffusion.
5. Cellular respiration: cells use the O2 and produce CO2.

The summary diagram used throughout the lecture maps these onto the circulation: an “external respiration” stage (ventilation and alveolar gas exchange), a “transport” stage (pulmonary and systemic circulation), an “internal respiration” stage (tissue gas exchange and cellular respiration), and a “regulation of breathing” stage (respiratory control centres in the brain, receiving input from O2, CO2 and pH sensors and sending motor output to the respiratory muscles).

Symbols and Units

General variables: V (gas volume), $\dot{V}$ (gas volume per unit time), P (gas pressure), F (fractional concentration in dry gas), $\dot{Q}$ (blood volume flow), C (content in blood), f (respiratory frequency, breaths per unit time), R (respiratory exchange ratio, volume CO2/volume O2), D (diffusing capacity).

Gas-phase subscripts: I (inspired), E (expired), A (alveolar), T (tidal), D (dead-space), B (barometric). Blood-phase subscripts: a (arterial), v (venous), c (capillary).

Notation: a bar over a symbol denotes a mean value, a dot denotes a time derivative, an apostrophe after a symbol denotes an “end” value. STPD = standard temperature, pressure, dry (0°C, 760 mmHg); BTPS = body temperature, pressure, saturated with water vapour; ATPS = ambient temperature, pressure, saturated with water vapour.

Lung volumes and flows: VT (tidal volume), FRC (functional residual capacity), ERV (expiratory reserve volume), RV (residual volume), IC (inspiratory capacity), IRV (inspiratory reserve volume), TLC (total lung capacity), VC (vital capacity), Raw (airway resistance), C (compliance), VD (dead-space gas volume), VA (alveolar gas volume), ${\dot{V}}_I$/${\dot{V}}_E$ (inspired/expired ventilation per minute), ${\dot{V}}_S$ (shunt flow), ${\dot{V}}_A$ (alveolar ventilation per minute), ${\dot{V}}_{O_2}$ (O2 uptake per minute), ${\dot{V}}_{C{O}_2}$ (CO2 elimination per minute), DLO2/DLCO (diffusing capacity for O2/carbon monoxide).

Pressures and contents: PB (atmospheric pressure), Palv (alveolar pressure), Ppl (pleural pressure), PO2/PCO2/PN2 (partial pressures), PaO2/PaCO2 (arterial), PAO2/PACO2 (alveolar), PAH2O (alveolar water vapour pressure), CaO2/C$\bar{v}$O2 (O2 content of arterial/mixed venous blood), SO2/SaO2 (haemoglobin O2 saturation, overall/arterial).

Partial Pressures and Dalton’s Law

Dalton’s Law of partial pressures: $P_{gas}=F_{gas}\times P_{Total}$, where $F_{gas}$ = %gas / 100.

Dry atmospheric composition: O2 20.93%, CO2 0.03%, N2 79.04%. At sea level (PB = 760 mmHg):

• $P{O}_2=0.2093\times 760=159mmHg$
• $PC{O}_2=0.0003\times 760=0.23mmHg$
• $P{N}_2=0.7904\times 760=601mmHg$

Once air is inhaled, water vapour (pressure 47 mmHg at body temperature) dilutes the other gases, so tracheal PO2 is lower than atmospheric PO2:
$PI{O}_2=FI{O}_2\times (P_B-47)=0.2093\times (760-47)=149mmHg$

At the summit of Mt Everest (PB = 253 mmHg): $PI{O}_2=0.2093\times (253-47)=43mmHg$, illustrating how a fall in barometric pressure at altitude sharply reduces the inspired O2 pressure.

O2 cascade: PO2 falls in a series of steps from atmosphere to mitochondria: roughly 160 mmHg in the atmosphere, about 150 mmHg once humidified in the trachea, around 100 mmHg in alveolar gas/capillary/arterial blood (where the three run roughly level), and down to about 50 mmHg at the tissues.

Typical values (PB = 760 mmHg): PO2 159 mmHg, PIO2 149 mmHg, $P_A{O}_2$ 100 mmHg (= $PI{O}_2-PAC{O}_2/0.8$), PaO2 95 mmHg, PvO2 40 mmHg, PACO2 40 mmHg, PaCO2 40 mmHg, PvCO2 46 mmHg.

The slide intended to show "Partial Pressures of Gases in Inspired Air and Alveolar Air" (referencing textbook fig. 16.20) was never completed: the source only shows an arrow from "Inspired air" to an empty "Alveolar air" outline and the placeholder text "Insert fig. 16.20", with a stray, unlabelled value "0.23" and no figure content.

Ventilation and Dead Space

Pulmonary (total) ventilation: ${\dot{V}}_E=f\times V_T$.

Not all inspired air reaches the alveoli: fresh air mixes with air already in the anatomical dead space. Alveolar ventilation is therefore lower than pulmonary ventilation:
${\dot{V}}_A=f\times (V_T-D)$
where f = frequency (breaths/min), VT = tidal volume, D = dead space.

Worked example: VT = 0.5 L, f = 20 breaths/min, anatomic dead space = 0.15 L.

• Pulmonary ventilation: ${\dot{V}}_E=20\times 0.5=10L/min$
• Alveolar ventilation: ${\dot{V}}_A=20\times 0.35=7L/min$

Effect of breathing pattern on alveolar ventilation (dead space assumed 150 mL, total ventilation held constant at 6000 mL/min):

Pattern	VT (mL)	Rate (breaths/min)	Fresh air to alveoli per breath (mL)	Alveolar ventilation (mL/min)
Normal	500	12	350	4200
Rapid, shallow	300	20	150	3000
Slow, deep	750	8	600	4800

Slow, deep breathing increases alveolar ventilation; rapid, shallow breathing decreases it, even though total (pulmonary) ventilation is unchanged, because dead space is a fixed volume per breath: more breaths per minute wastes proportionally more of each breath on dead space, while fewer, larger breaths deliver proportionally more fresh air to the alveoli.

The transcript flags a discrepancy in this table: one source page gives the alveolar ventilation column filled in as above, while a handout reproduction of the same slide shows this column blank/grey instead. The values above are as given by the filled-in source.

Typical resting volumes and flows: tidal volume 500 mL, anatomic dead space 150 mL, total ventilation 6000 mL/min, frequency 12/min, alveolar ventilation 4200 mL/min, pulmonary blood flow 5000 mL/min.

Mechanics of Breathing

Primary principle of ventilation: air moves from an area of high pressure to an area of low pressure. During inspiration, barometric (atmospheric) pressure is higher than alveolar pressure, so air flows in; during expiration, alveolar pressure is higher than barometric pressure, so air flows out.

The causal chain is: volume changes, then pressure changes, then gas flow and pressure equalisation.

Sequence producing inspiration:

1. Contraction of the diaphragm, relaxation of the expiratory muscles, and contraction of the chest-elevating muscles (sternocleidomastoid, pectoralis minor, external intercostals).
2. This increases the vertical diameter of the thorax (diaphragm) and its anteroposterior and transverse dimensions (rib cage muscles).
3. Intrapleural (intrathoracic) pressure falls, aided by cohesion between the visceral and parietal pleurae and by the compliance of the thorax and lungs.
4. The lungs expand.
5. Alveolar pressure falls.
6. A pressure gradient from atmosphere to alveoli is established.
7. Air flows in: inspiration.

Diffusion and Fick’s Law

Fick’s Law of Diffusion explains gas exchange across the alveolar membrane:
$F=\frac{A}{T}D(P_1-P_2)$
where A = surface area, T = membrane thickness, D = a diffusion constant, and $P_1-P_2$ = the partial pressure difference across the membrane.

The blood-gas barrier in the lung has an enormous surface area and is only about 0.3 µm thick in many places, both of which maximise the rate of diffusion (F).

Gas transfer capacity can be impaired by:

1. Thickening of the alveolar membrane (increases T), e.g. pulmonary fibrosis.
2. Reduction in surface area (decreases A), e.g. emphysema, where destruction of alveoli reduces the surface area available for exchange.

Causes of Arterial Hypoxaemia

Five mechanisms of arterial hypoxaemia:

1. Reduced PB or FIO2 (e.g. altitude)
2. Hypoventilation
3. Impaired diffusion
4. Shunt
5. Ventilation-perfusion (V/Q) mismatching

Oxygen Transport in Blood

O2 is carried in blood in two forms:

• Dissolved in plasma: about 0.3 ml O2 per 100 ml blood; PO2 falls from about 100 mmHg (alveolar/arterial) to about 40 mmHg (venous) as O2 is given up to tissues.
• Combined with haemoglobin, in red blood cells: about 20 ml O2 per 100 ml blood, the same PO2 fall from about 100 to 40 mmHg.

O2 forms an easily reversible combination with haemoglobin: $O_2+Hb\leftrightarrow Hb{O}_2$. The maximal amount of O2 that can combine with Hb is the O2 capacity. One gram of Hb binds 1.34 ml O2, and normal blood contains about 150 g Hb per litre, so:
$O_{2}capacity=1.34\times 150=201ml{O}_{2}perlitreblood$

The O2 dissociation curve is sigmoid, plotting %Hb saturation and O2 content against PO2. The total O2 curve closely tracks the O2-combined-with-Hb curve, since dissolved O2 contributes only a small, near-flat component across the range of PO2.

Carbon Dioxide Transport

CO2 leaving a body cell is transported in the blood in three forms:

1. 10% dissolved in plasma.
2. 20% combined with haemoglobin as HbCO2 (carbaminohaemoglobin).
3. 70% as bicarbonate (HCO3−) dissolved in plasma. Inside the red blood cell, CO2 combines with H2O to form H2CO3, which dissociates to HCO3− and H+; the H+ binds Hb (forming HHb), and the HCO3− leaves the cell for the plasma via the Chloride Shift, with Cl− entering the cell to maintain electroneutrality.

Control of Breathing

The control system for breathing has three components:

• Central controller: the pons, medulla, and other parts of the brain.
• Sensors: chemoreceptors, lung and other receptors.
• Effectors: the respiratory muscles.

Sensors and effectors both send signals to the central controller, and the central controller’s output to the effectors feeds back to influence what the sensors subsequently detect, forming a closed feedback loop that regulates breathing (drawing on O2, CO2 and pH sensing, as introduced in the overview diagram).

Self-test

1. State the definition of respiration and list its three components.
2. List the five steps of respiration in order, stating whether each is a process of bulk flow or diffusion.
3. Define pulmonary (total) ventilation and alveolar ventilation, giving the equation for each.
4. A patient has a tidal volume of 0.5 L, a breathing frequency of 20 breaths/min, and an anatomic dead space of 150 mL. Calculate their pulmonary ventilation and alveolar ventilation.
5. Explain why slow, deep breathing produces greater alveolar ventilation than rapid, shallow breathing, even when total (pulmonary) ventilation is the same.
6. State Dalton’s law of partial pressures and use it to calculate the partial pressure of O2 in dry atmospheric air at sea level (PB = 760 mmHg).
7. Explain why the partial pressure of inspired O2 in the trachea (PIO2) is lower than atmospheric PO2, and give the equation used to calculate it.
8. Describe how PO2 changes progressively from atmosphere to mitochondria (the O2 cascade), including the approximate value at each stage.
9. State the primary principle governing airflow during ventilation, and describe how the pressure gradient between the atmosphere and the alveoli reverses between inspiration and expiration.
10. Describe the sequence of events, from respiratory muscle contraction to airflow, that produces inspiration.
11. State Fick’s law of diffusion and explain how alveolar surface area and membrane thickness each affect the rate of gas diffusion.
12. Predict how (a) pulmonary fibrosis and (b) emphysema each impair gas diffusion, referring to the relevant term in Fick’s law.
13. List the five mechanisms of arterial hypoxaemia.
14. Distinguish the two forms in which O2 is carried in blood, including their approximate quantities per 100 ml of blood.
15. Define O2 capacity and calculate it for blood containing 150 g of haemoglobin per litre.
16. List the three forms in which CO2 is transported in the blood, with their approximate percentages, and describe the chloride shift.
17. Describe the three components of the control-of-breathing system and how they form a feedback loop.
18. Trace the pathway of an O2 molecule from atmospheric air to a mitochondrion, and of a CO2 molecule from a mitochondrion back to expired air, naming the mechanism (bulk flow or diffusion) that moves it at each stage.

Answers

Reveal answers

1. Respiration is the exchange of O2 and CO2 between the environment and the tissues. Its three components are: exchange of O2 and CO2 between atmosphere and blood in the lungs; transport of O2 and CO2 between lungs and tissues by circulating blood; and O2 consumption and CO2 production in the tissues.
2. (1) Ventilation, bulk flow, moves air in/out of the lungs; (2) gas exchange at the alveoli, diffusion, down partial pressure gradients; (3) gas transport in blood, bulk flow, from lungs to tissues; (4) gas exchange at the tissues, diffusion, down partial pressure gradients; (5) cellular respiration, O2 consumed and CO2 produced.
3. Pulmonary ventilation ${\dot{V}}_E=f\times V_T$. Alveolar ventilation ${\dot{V}}_A=f\times (V_T-D)$, where f = frequency, VT = tidal volume, D = dead space; alveolar ventilation excludes the fraction of each breath that only reaches the dead space.
4. Pulmonary ventilation = 20 × 0.5 = 10 L/min. Alveolar ventilation = 20 × (0.5 - 0.15) = 20 × 0.35 = 7 L/min.
5. Dead space volume is fixed per breath. Rapid, shallow breathing takes more breaths to deliver the same total ventilation, so a larger fraction of each minute’s air is wasted ventilating dead space; slow, deep breathing uses fewer, larger breaths, so proportionally more of each breath reaches the alveoli, e.g. in the lecture’s table, 6000 mL/min total ventilation gives 4800 mL/min alveolar ventilation at 8 breaths/min but only 3000 mL/min at 20 breaths/min.
6. Dalton’s law: $P_{gas}=F_{gas}\times P_{Total}$. For O2: $F_{O_2}=0.2093$, so $P{O}_2=0.2093\times 760=159mmHg$.
7. Once air is inhaled it is humidified; water vapour exerts its own pressure (47 mmHg at body temperature), which dilutes the other gases and lowers their partial pressures. $PI{O}_2=FI{O}_2\times (P_B-47)=0.2093\times (760-47)=149mmHg$.
8. PO2 falls in steps along the pathway: about 160 mmHg in the atmosphere, about 150 mmHg in humidified tracheal air, about 100 mmHg in alveolar gas and in capillary/arterial blood (roughly level across these three), and about 50 mmHg at the tissues.
9. Air moves from high pressure to low pressure. During inspiration, barometric pressure exceeds alveolar pressure, so air flows into the lungs; during expiration, alveolar pressure exceeds barometric pressure, so air flows out.
10. Contraction of the diaphragm and chest-elevating muscles (with relaxation of expiratory muscles) increases the thorax’s vertical, anteroposterior and transverse dimensions; intrapleural pressure falls (aided by pleural cohesion and thoracic/lung compliance); the lungs expand; alveolar pressure falls; this establishes a pressure gradient from atmosphere to alveoli; air flows in.
11. Fick’s law: $F=\frac{A}{T}D(P_1-P_2)$. Increasing surface area (A) increases the rate of diffusion; increasing membrane thickness (T) decreases it (F is inversely proportional to T).
12. (a) Pulmonary fibrosis thickens the alveolar membrane, increasing T and so reducing diffusion (F). (b) Emphysema destroys alveoli, reducing the surface area A available for diffusion and so reducing F.
13. Reduced PB or FIO2; hypoventilation; impaired diffusion; shunt; ventilation-perfusion (V/Q) mismatching.
14. O2 is carried dissolved in plasma (about 0.3 ml O2/100 ml blood) and combined with haemoglobin in red blood cells (about 20 ml O2/100 ml blood); the haemoglobin-bound form carries the great majority of blood O2.
15. O2 capacity is the maximal amount of O2 that can combine with haemoglobin. One gram of Hb binds 1.34 ml O2; at 150 g Hb/L, O2 capacity = 1.34 × 150 = 201 ml O2 per litre of blood.
16. CO2 is transported as: 10% dissolved in plasma; 20% bound to haemoglobin as HbCO2 (carbaminohaemoglobin); 70% as bicarbonate (HCO3−) in plasma, formed inside the red blood cell (CO2 + H2O → H2CO3 → HCO3− + H+, with H+ buffered by Hb). The chloride shift is the movement of Cl− into the red blood cell to balance the charge as HCO3− leaves it for the plasma.
17. The central controller (pons, medulla and other brain regions) receives input from sensors (chemoreceptors, lung and other receptors) and sends output to effectors (respiratory muscles); the effectors’ action changes ventilation, which alters what the sensors detect, closing the feedback loop that regulates breathing.
18. O2: bulk flow moves it into the alveoli during ventilation, diffusion moves it across the alveolar membrane into blood down its partial pressure gradient, bulk flow (circulation) carries it to the tissues, diffusion moves it from capillary blood into cells down its partial pressure gradient, and it is consumed in cellular respiration. CO2: produced in cellular respiration, diffusion moves it from cells into capillary blood down its partial pressure gradient, bulk flow (circulation) carries it to the lungs, diffusion moves it across the alveolar membrane into alveolar gas down its partial pressure gradient, and bulk flow (ventilation) carries it out in expired air.