Ventilation, Perfusion and Gas Exchange

A resting adult moves roughly 6 litres of air and 5 litres of blood through the lungs every minute, and neither number tells you what the blood leaves with. What settles that is whether air and blood arrive at the same places in the same proportion. Gas exchange and breathing gave partial pressure, Fick’s law and minute against alveolar ventilation; lung mechanics and surfactant gave the pressures that move the air. Here you put numbers on the matching.

Not every breath reaches blood

Dead space is lung that is ventilated and not perfused: air arrives, no flowing blood meets it, and the gas comes back out unchanged. Christian Bohr (1855 to 1911) described it in 1891 as the part of the tidal volume that does not undergo gas exchange.

His argument is mass balance. All the carbon dioxide in an expired breath came from units that exchanged, and dead-space gas contributes none, so mixed expired partial pressure is a dilution of the alveolar one:

VD/VT = (PACO2 - PECO2) / PACO2

The problem is PACO2, the mean alveolar partial pressure, which no sample gives you. In 1938 Enghoff proposed replacing it with arterial PCO2, which a blood sample does give:

VD/VT = (PaCO2 - PECO2) / PaCO2

That substitution assumes arterial PCO2 equals mean alveolar PCO2. It fails when blood reaches the left side of the circulation without being ventilated, because that blood raises PaCO2 above PACO2 and inflates the computed fraction. What you get is physiologic dead space, which includes alveolar units ventilated far more than they are perfused. Fowler’s single-breath nitrogen method, which reads where expired nitrogen concentration changes as airway gas washes out, measures something closer to the anatomic dead space of the conducting airways; the two are not interchangeable. In healthy people the physiologic fraction is 0.20 to 0.40 of the tidal volume by the inert-gas method.

A raised physiologic dead space is easy to misread. Across the conditions one 2015 review surveyed, the main mechanism was a wider spread of ventilation-perfusion ratios rather than large regions of alveoli with no blood flow. Nor does wasted ventilation usually raise arterial PCO2: the controller defends it (control of breathing), so the cost appears as more work of breathing.

Alveolar PO2 is calculated, not measured

No sample of alveolar gas serves as the mean, so alveolar PO2 is computed. Oxygen is removed from inspired gas and carbon dioxide added, in the ratio R, the respiratory quotient (carbon dioxide produced per oxygen consumed, about 0.8 at steady state on a mixed diet). Inspired gas is humidified to 47 mmHg of water vapour at 37 C, so that pressure comes off barometric pressure first:

PAO2 = FiO2 x (PB - PH2O) - PaCO2 / R

Each term carries an assumption: a steady state, a value for R assumed rather than measured, an inspired oxygen fraction near that of air, and arterial PCO2 standing in for alveolar PCO2. At sea level on air, with PB 760 mmHg and arterial PCO2 40 mmHg, it returns about 100 mmHg. Comparing arterial blood with a calculated “ideal” alveolar value goes back to Riley and Cournand’s 1949 analysis.

Alveolar ventilation VA 4.2 L per min (4.2 in the lesson’s worked problem; range made up) Inspired O₂ fraction FiO₂ 0.21 (0.21 is air; the lesson works 0.30 in step 7; range made up) Respiratory quotient R 0.80 (about 0.8 at steady state on a mixed diet; range made up) Measured arterial PO₂ PaO₂ 92 mmHg (92 in the worked problem; range made up)

Arterial PCO₂, 0.863 × VCO₂ ÷ VA

0.863 × 195 ÷ 4.2 = 40 mmHg

Inspired PO₂ once humidified, FiO₂ × (PB − 47)

0.21 × 713 = 149.7 mmHg

Alveolar PO₂, inspired − PaCO₂ ÷ R

149.7 − 50.0 = 99.7 mmHg

A-a difference, PAO₂ − PaO₂

99.7 − 92 = 7.7 mmHg

PaO₂ that would keep the difference at the worked problem’s 7.7 mmHg (lesson step 7)

92.0 mmHg

In a young adult the A-a difference is under about 10 mmHg and it rises with age; it is a difference, not a diffusion gradient.

In this sketch: steady state, near room air, at sea level; no shunt, no ventilation-perfusion spread, no diffusion limitation and no oxygen dissociation curve are modelled. Arterial PCO₂ stands in for alveolar PCO₂, as the lesson’s equation assumes, and is rounded to a whole mmHg as the worked problem does. Held fixed and illustrative: carbon dioxide output VCO₂ 195 mL per min (the worked problem’s made-up value for a healthy young adult at rest, supine), barometric pressure 760 mmHg, water vapour pressure 47 mmHg at 37 °C. R is assumed rather than measured, and is set here by hand independently of VCO₂. The slider ranges, including FiO₂ from 0.21 to 0.30, R from 0.70 to 1.00 and PaO₂ from 40 to 150 mmHg, are made up for the sketch. VA is set by hand; the sketch does not model the controller that, the lesson says, defends arterial PCO₂. PaO₂ is typed in, not calculated. The simplified equation omits a small correction that grows with PaCO₂ and with FiO₂, so treat values as good to a few mmHg.

Alveolar PO₂ is calculated from what is breathed in, FiO₂ × (PB − 47), less the carbon dioxide term PaCO₂ ÷ R, and PaCO₂ falls as alveolar ventilation rises; the A-a difference is that calculated value minus the arterial PO₂ from a blood sample.

Partial pressure is not content. Dalton’s law gives each gas its share of the total pressure; Henry’s law says how much dissolves at that pressure. About 0.003 mL of oxygen dissolves per dL of blood per mmHg, so 100 mmHg dissolves only 0.3 mL per dL, which is why nearly all of it rides on hemoglobin (oxygen transport, with protein binding and allostery for the sigmoid curve). Carbon dioxide is roughly twenty times more soluble, and moves its load on a few mmHg.

Each unit’s gas is set by its own ratio

A lung unit’s gas composition is set mainly by one quantity, its ventilation divided by its perfusion, for a given inspired gas and mixed venous blood. At a ratio of zero the unit is a shunt, perfused and not ventilated, and its blood leaves with the oxygen content it arrived with; at an infinite ratio it is dead space. Below a ratio of about 0.1 a unit’s PO2 sits very close to mixed venous PO2, that of venous blood from the whole body after mixing, sampled in the pulmonary artery (cardiac output and venous return).

Real lungs hold a spread of ratios, which is what Wagner, Saltzman and West’s inert-gas method recovers. In four young semirecumbent normal subjects, 95.5 percent of both blood flow and ventilation lay between ratios of 0.3 and 2.1, with no shunt on air. Reference values for healthy people by the same method put the mean of the blood-flow distribution at 0.80 to 1.00 and shunt below 1 percent of cardiac output. Textbooks quote a single whole-lung ratio of about 0.8, total alveolar ventilation over total blood flow. That is not the same quantity as the mean of a measured distribution.

A spread lowers arterial PO2 by itself, even when every unit equilibrates with its own alveolar gas, because the two averages are taken differently. Expired alveolar gas is weighted by ventilation, so well-ventilated units dominate it; arterial blood is weighted by blood flow, so poorly ventilated units count for more in it than they do in expired gas. Blood from different units then mixes by oxygen content rather than partial pressure, and the dissociation curve is flat at the top: a high-ratio unit adds almost nothing per dL, a low-ratio unit subtracts a great deal. The result is an alveolar-arterial oxygen difference even with no diffusion limitation anywhere.

In the upright human lung both ventilation and perfusion per unit volume are greater at the base than at the apex, and perfusion changes more steeply, so the ratio is higher at the apex. West, Dollery and Naimark’s zones, from an isolated-lung preparation in which arterial, venous and alveolar pressures could each be set, state a condition for flow rather than mark anatomic bands: where alveolar pressure exceeds capillary pressure flow stops, where arterial exceeds alveolar which exceeds venous it follows the arterial-to-alveolar difference, and where arterial and venous both exceed alveolar it is continuous. How much of the remaining unevenness is gravity is unsettled: in anaesthetized supine and prone dogs under zone 3 conditions, with flow in 1.9 cubic centimetre pieces measured by radiolabeled microspheres, vertical height explained only about 6 and 2 percent of the variability, and Glenny and colleagues concluded in 1991 that neither height nor radial position was the principal determinant there. That leaves upright humans, and zones 1 and 2, open.

Hypoxic lungs constrict their own arteries

In systemic beds, low oxygen dilates arterioles and brings more blood (resistance, compliance and local flow). The pulmonary circulation does the opposite, so flow leaves a poorly ventilated region rather than pooling in it.

Von Euler and Liljestrand’s 1946 preparation was an anaesthetized cat with the chest opened, ventilated by pump with gas mixtures of chosen composition, with pulmonary arterial pressure recorded. If the lung vessels behaved like systemic ones, hypoxia should have lowered that pressure; if the response ran through nerves, cutting them should have abolished it. Ventilation with 10.5 percent oxygen strongly raised the pressure and pure oxygen lowered it slightly, and the rise survived cutting the vagi and removing the stellate ganglia. They concluded it was due in part to a direct constrictive action of hypoxia on the vessels. Keep that hedge: a pressure is not a resistance unless flow and outflow pressure are known, and whole-lung hypoxia cannot test regional matching.

In outline, hypoxia inhibits an outward potassium current in pulmonary artery smooth muscle, depolarizing the cell and opening voltage-gated calcium channels, one route among several that include mitochondrial reactive oxygen species and calcium sensitization (smooth muscle). The sensor upstream of that step is still described in reviews as hypothesized, with mitochondria the leading candidate. In 2017 Sommer, Weissmann and colleagues reported that isolated ventilated, buffer-perfused lungs from mice lacking the cytochrome c oxidase subunit isoform Cox4i2 showed no acute constriction to hypoxia while constricting normally to potassium chloride, and that chronic hypoxic pulmonary hypertension was not affected, with vascular remodeling only slightly affected. One species, one isoform, buffer rather than blood: the response does little in healthy lungs at rest on air at sea level, and matters when ventilation becomes regionally uneven or at altitude. Release of the same hypoxic constriction is one contributor to the fall in pulmonary vascular resistance as the lungs aerate at birth (pregnancy, birth and lactation).

Six mechanisms, and what the numbers separate

A 2015 review lists six mechanisms that lower arterial PO2: a low inspired oxygen partial pressure, hypoventilation, ventilation-perfusion inequality, diffusion limitation, shunt, and a low mixed venous oxygen content. Inequality and shunt are the most frequent, and three numbers separate most of the six: arterial PCO2, the alveolar-arterial difference, and the response to a higher inspired oxygen fraction.

Worked problem: from breath to blood. Made-up but typical values for a healthy young adult at rest, supine, breathing air at sea level. Tidal volume 500 mL, rate 12 per min, PaCO2 40 mmHg, mixed expired PECO2 28 mmHg, PaO2 92 mmHg, FiO2 0.21, PB 760 mmHg, PH2O 47 mmHg, R 0.8. Assume a steady state and no shunt.

1. Minute ventilation. 500 mL x 12 per min = 6,000 mL per min.
2. Dead-space fraction. (40 - 28) / 40 = 0.30, inside the healthy 0.20 to 0.40, so dead space is 0.30 x 500 = 150 mL.
3. Alveolar ventilation. (500 - 150) x 12 = 4,200 mL per min, or 4.2 L per min.
4. Carbon dioxide output. The alveolar ventilation relation PaCO2 = 0.863 x VCO2 / VA (VCO2 in mL per min at standard temperature and pressure, dry; VA in L per min at body temperature and pressure, saturated; 0.863 carries that conversion) rearranges to VCO2 = 40 x 4.2 / 0.863 = 195 mL per min.
5. Alveolar PO2. 0.21 x (760 - 47) - 40 / 0.8 = 149.7 - 50.0 = 99.7 mmHg.
6. A-a difference. 99.7 - 92 = 7.7 mmHg, under the roughly 10 mmHg expected in a young adult. It rises with age and with inspired oxygen fraction, and it is a difference, not a diffusion gradient.
7. Halve alveolar ventilation to 2.1 L per min at unchanged carbon dioxide output: PaCO2 = 0.863 x 195 / 2.1 = 80 mmHg and PAO2 = 149.7 - 100 = 49.7 mmHg, so with the difference still 7.7 mmHg, PaO2 is 42 mmHg. Low PO2, high PCO2, normal difference: hypoventilation, since mismatch, shunt and diffusion limitation all widen the difference. At FiO2 0.30, PAO2 = 0.30 x 713 - 100 = 113.9 mmHg and PaO2 rises to about 106 mmHg while PaCO2 stays at 80 mmHg. These use the simplified equation. The full form subtracts PaCO2 x [FiO2 + (1 - FiO2)/R], which at R 0.8 adds FiO2 x PaCO2 x (1 - R)/R: about 4 mmHg on air at a PaCO2 of 80 mmHg (2 mmHg at 40), and about 6 mmHg at FiO2 0.30 with PaCO2 80 mmHg.
8. A contrast. PaO2 55 mmHg with PaCO2 40 mmHg gives a difference of 99.7 - 55 = 44.7 mmHg. Hypoventilation alone cannot produce that.
9. Shunt arithmetic. Take the illustrative contents from oxygen transport: hemoglobin 15 g per dL, end-capillary content on air 20.00 mL O2 per dL, mixed venous 15.20. If one fifth of the flow bypasses ventilated units, arterial content is 0.80 x 20.00 + 0.20 x 15.20 = 19.04 mL per dL. On pure oxygen, once nitrogen has washed out, the full equation reduces to inspired PO2 minus PaCO2, so PAO2 = 760 - 47 - 40 = 673 mmHg (the simplified form above would give 663 mmHg), and end-capillary content is 1.34 x 15 x 1.00 + 0.003 x 673 = 22.12 mL per dL. Holding mixed venous content at 15.20 (it would rise a little), arterial content becomes 0.80 x 22.12 + 0.20 x 15.20 = 20.74 mL per dL: a gain of 1.70 mL per dL, about 9 percent, for a nearly sevenfold rise in alveolar PO2 (99.7 to 673 mmHg). Recover the fraction: (22.12 - 20.74) / (22.12 - 15.20) = 1.38 / 6.92 = 0.20.

Step 9 shows that shunted blood still holds arterial oxygen content down on pure oxygen. The percentage gain is small mostly because hemoglobin is nearly saturated either way, so compare arterial PO2 against what no shunt would predict. A low-ratio unit is still ventilated, so filling it with oxygen usually saturates its blood, though at very low ratios the correction is incomplete and high oxygen can collapse the unit by absorption atelectasis; an unventilated unit never sees the gas, and its blood dilutes whatever the rest achieves.

Now predict directions. Suppose some units’ airways narrow so their ventilation falls while perfusion continues, and others lose capillaries so perfusion falls while ventilation continues. The low-ratio units pull arterial PO2 down and widen the A-a difference; the high-ratio units add wasted ventilation, so dead-space fraction rises. Arterial PCO2 often stays near normal, because the controller raises total ventilation to defend it at the price of more work of breathing. Blunt the hypoxic constriction and flow returns to the poorly ventilated units, so arterial PO2 falls further.

Diffusion limitation is the mechanism these numbers do not reach. A red cell spends about 0.75 s in a pulmonary capillary at rest and roughly 0.25 s suffices for equilibration, so oxygen transfer in healthy lungs at rest is limited by blood flow rather than by the barrier, though oxygen can become diffusion limited when transit is shortened; carbon monoxide, whose partial pressure in blood stays near zero, is the diffusion-limited case. In healthy people, signs of diffusion limitation are reported mainly in heavy exercise (exercise physiology). What arterial PCO2 does to pH belongs to acid-base balance.

Design problem

A whole-animal pressure record like the 1946 cat experiment leaves three gaps: a pressure rise can come from higher flow rather than higher resistance, whole-lung hypoxia cannot show redistribution between regions, and the sensor is untouched. Design a short series that closes each gap.

One way to do it

Use an isolated lung, ventilated by pump and perfused at constant flow with a set outflow pressure. Then resistance = (inflow pressure - outflow pressure) / flow, so a pressure rise can only be a resistance rise, and nerves and hormones left with the rest of the animal.

Alternate normoxic and hypoxic ventilation. Expect a rise within seconds and an early peak within minutes, with a later sustained phase if hypoxia continues, reversing on reoxygenation, with time controls against drift and potassium chloride as a contraction control.

For redistribution, ventilate one lobe with the hypoxic mixture and the rest with air at constant total flow, and measure each region’s share with flow probes or radiolabeled microspheres. Matching predicts flow shifting away from the hypoxic lobe, raising its ratio.

For the sensor, repeat on lungs from animals lacking a candidate protein, as in the Cox4i2 work: no hypoxic rise, a normal potassium chloride response.

Limits: one species; buffer instead of blood and no extrinsic nerves; constant-flow perfusion is itself unphysiological; and an acute response says nothing about weeks of hypoxia.