Lung compliance

Key takeaways

Lung compliance belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Lung compliance to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Lung compliance from memory before moving on to harder problems.

Reference excerpt

Lung compliance, or pulmonary compliance, is a measure of the lung's ability to stretch and expand (distensibility of elastic tissue). In clinical practice it is separated into two different measurements, static compliance and dynamic compliance. Static lung compliance is the change in volume for any given applied pressure. Dynamic lung compliance is the compliance of the lung at any given time during actual movement of air. Low compliance indicates a stiff lung (one with high elastic recoil) and can be thought of as a thick balloon – this is the case often seen in fibrosis. High compliance indicates a pliable lung (one with low elastic recoil) and can be thought of as a grocery bag – this is the case often seen in emphysema. Compliance is highest at moderate lung volumes, and much lower at volumes which are very low or very high. The compliance of the lungs demonstrate lung hysteresis; that is, the compliance is different on inspiration and expiration for identical volume.

Calculation Pulmonary compliance is calculated using the following equation, where ΔV is the change in volume, and ΔP is the change in pleural pressure:

C o m p l i a n c e = Δ V Δ P {\displaystyle Compliance={\frac {\Delta V}{\Delta P}}}

For example, if a patient inhales 500 mL of air from a spirometer with an intrapleural pressure before inspiration of −5 cm H2O and −10 cm H2O at the end of inspiration. Then:

C o m p l i a n c e = Δ V Δ P = .5 L − 5 cm H 2 O − ( − 10 cm H 2 O ) = .5 L 5 cm H 2 O = 0.1 L × cm H 2 O − 1 {\displaystyle Compliance={\frac {\Delta V}{\Delta P}}={\frac {.5\;{\ce {L}}}{-5\;{\ce {cm\,H2O}}-(-10\;{\ce {cm\,H2O}})}}={\frac {.5\;{\ce {L}}}{5\;{\ce {cm\,H2O}}}}=0.1\;{\ce {L}}\;\times \;{\ce {cm\,H2O^{-1}}}}

Static compliance (Cstat) Static compliance represents pulmonary compliance during periods without gas flow, such as during an inspiratory pause. It can be calculated with the formula:

C s t a t = V T P p l a t − P E E P {\displaystyle C_{stat}={\frac {V_{T}}{P_{plat}-\mathrm {PEEP} }}}

where

VT = tidal volume; Pplat = plateau pressure; PEEP = positive end-expiratory pressure. Pplat is measured at the end of inhalation and prior to exhalation by using an inspiratory hold maneuver. During this maneuver, airflow is transiently (~0.5 sec) discontinued, which eliminates the effects of airway resistance. Pplat is never bigger than PIP and is typically <10 cm H2O lower than PIP when airway resistance is not elevated.

Dynamic compliance (Cdyn) Dynamic compliance represents pulmonary compliance during periods of gas flow, such as during active inspiration. Dynamic compliance is always lesser than or equal to static lung compliance because PIP − PEEP is always greater than Pplat − PEEP. It can be calculated using the following equation,

C d y n = V T P I P − P E E P {\displaystyle C_{dyn}={\frac {V_{T}}{\mathrm {PIP-PEEP} }}}

where

Cdyn = Dynamic compliance; VT = tidal volume; PIP = Peak inspiratory pressure (the maximum pressure during inspiration); PEEP = Positive End Expiratory Pressure: Alterations in airway resistance, lung compliance and chest wall compliance influence Cdyn.

Dimensionality and physical analogues The dimensions of compliance in respiratory physiology are inconsistent with the dimensions of compliance in physics-based applications. In physiology,

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Lung compliance

Start with the simplest possible case. Write down what Lung compliance claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Lung compliance before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Lung compliance ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Lung compliance

In research: Lung compliance appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Lung compliance in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Lung compliance is common in secondary-school and first-year university syllabi. It links to neighbouring topics Mathematics in medicine, Respiratory physiology, Respiratory therapy, so understanding it makes those chapters shorter.
In everyday life: Look for Lung compliance outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Lung compliance in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Lung compliance means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Lung compliance out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Lung compliance in simple terms?

Lung compliance, or pulmonary compliance, is a measure of the lung's ability to stretch and expand (distensibility of elastic tissue). In clinical practice it is separated into two different measurements, static compliance and dynamic compliance.

Why does Lung compliance matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Lung compliance?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Lung compliance.