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Respiratory system · ventilation and gas exchange

Lungs — 20,000 breaths a day

We usually breathe 12–20 times a minute — about 20,000 times a day, mostly without giving it a thought. See how the diaphragm draws air in, how the airways branch as many as 23 times, how oxygen crosses a barrier about 200 times thinner than a sheet of paper, and what actually makes us take a breath.

An educational page — not a substitute for medical advice. The values shown are typical for a healthy adult; in reality they depend on height, sex, age and fitness. The models are simplified.

Modes: Q W E R T · other keys in the “Keys” box below

The lungs have no muscles of their own. When you inhale, the diaphragm contracts (it flattens and moves down) and the external intercostal muscles lift the ribs. The chest gets bigger, and the lungs — “stuck” to it by a thin film of fluid in the pleural cavity — stretch along with it. Pressure in the alveoli drops below atmospheric pressure, and air flows in by itself. Exhaling at rest is passive: the muscles relax and the elastic lungs shrink back like a stretched rubber band. On the right is the same mechanism in the classic bell-jar model — grab the rubber membrane and pull it down.

Grab the membrane handle (or the diaphragm) and pull it down: the volume of the jar grows, the pressure inside drops (Boyle’s law), and the balloons inflate by themselves.

Inhaling — muscle work

The diaphragm does most of the work in quiet breathing. In deep breathing, accessory muscles (e.g. the sternocleidomastoid and scalenes) help by lifting the sternum and upper ribs.

Exhaling — elasticity

At rest, exhaling takes no muscle work. During exercise, coughing or blowing, the internal intercostal muscles and the abdominal muscles join in.

Boyle’s law

At constant temperature p · V = const: as lung volume grows, the pressure of the gas inside falls. A difference of about 1 cmH₂O — roughly 0.1% of atmospheric pressure — is enough to draw in about half a liter of air at rest.

How does it work?

The respiratory system consists of the airways (nose, throat, larynx, trachea, bronchi) and the lungs. The right lung has three lobes, the left has two. Air is warmed, humidified and cleaned in the conducting airways, and gas exchange happens only in the hundreds of millions of alveoli, wrapped in a network of capillaries.

Ventilation

Inhaling is active (diaphragm, external intercostal muscles); quiet exhaling is passive. At rest, the pressure in the alveoli changes by only about ±1 cmH₂O, while the pleural cavity stays at negative pressure: about −5 cmH₂O at the end of an exhale and about −7 to −8 cmH₂O at the peak of an inhale.

p1V1 = p2V2Boyle–Mariotte law (constant temperature): larger volume → lower pressure
V̇A = (VT − VD) · falveolar ventilation; e.g. (500 − 150) mL · 12/min = 4.2 L/min

Alveoli and surfactant

P = 2TrLaplace’s law for a spherical alveolus; surfactant lowers the surface tension T — the more strongly, the more the alveolus is compressed

Gas exchange

V̇gas ∝ A · D · (p1 − p2)dFick’s law: A — area, d — barrier thickness, D — diffusion constant of the gas (CO₂ diffuses about 20 times more easily than O₂)
pIO₂ = 0.21 · (patm − 47 mmHg)    pAO₂ ≈ pIO₂ − pACO₂0.847 mmHg is the water vapor pressure at 37 °C; the second formula is a simplified alveolar gas equation. At sea level: 0.21 · 713 ≈ 149 mmHg and 149 − 40/0.8 ≈ 99 mmHg. On Everest (about 253 mmHg): about 43 mmHg in the inhaled air.

Control

The respiratory center in the medulla oblongata sets the rhythm, and the chemoreceptors fine-tune it so that CO₂ in arterial blood stays at about 40 mmHg. That’s why we breathe mainly to get rid of CO₂ — oxygen usually comes along “for free” in plenty.

Simplifications: lung mechanics is a model with a single compliance (about 200 mL/cmH₂O) and a single airway resistance; the bell jar and the chest share the same controls. Pressure at altitude is computed with a barometric formula fitted to measurements in high mountains (J. B. West), and alveolar CO₂ in an acclimatized climber comes from an approximate table. The hemoglobin oxygen-binding curve is the Hill equation. We model surfactant as a surface tension that decreases with the square of the radius. The breath-hold curves are illustrative, not exact physiology.

See also

Did you know…?

  • The right lung has three lobes, while the left has only two and a distinct notch — the left side needs room for the heart.
  • With every breath out we lose water vapor — usually a few hundred milliliters of water a day (about 300–400 mL, more during exercise and in dry, cold air). That’s why you can “see your breath” in winter.
  • Healthy lung tissue floats on water, because some air always stays in the alveoli. Even after the deepest exhale, about 1.2 liters remain in the lungs (the residual volume).

Challenges

  • Inflate the balloons in the bell jar“How we breathe” mode: pull the membrane hard enough that at least 900 mL of air flows into the balloons.
  • Count the bronchial generations down to the alveoli“Bronchial tree” mode: go all the way down from the trachea to the alveolar sacs (generation 23).
  • Climb Mount Everest“Gas exchange” mode: set the altitude of the summit (8,849 m) and see how oxygen exchange drops.
  • Measure your vital capacity“Spirometer” mode: the deepest breath in and a full breath out — a result of at least 4,400 mL.
  • Beat Laplace’s law with surfactant“Bronchial tree” mode: connect two alveoli of clearly different sizes so that neither collapses and their sizes even out.

Keys

  • Q W E R T — switch modes
  • How we breathe: P pause breathing, O puncture / seal the pleura, ↑ ↓ membrane (when the drawing has focus)
  • Bronchial tree: + − generation (also ← → on the drawing), U spread out the alveoli
  • Gas exchange: 1–5 altitude: sea level, Rysy (Poland’s highest peak), La Paz, Mont Blanc, Everest
  • Spirometer: hold Space or ↑ — inhale, ↓ — forced exhale
  • What controls breathing: B hold your breath / breathe
  • Esc — pauses / resumes the current mode’s animation (in the spirometer it also releases the buttons)