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Airway resistance quantifies the pressure difference needed to drive a specified volumetric flow rate through the conducting airways. For a steady linear relation with flow $Q$ positive toward the alveoli,The units are pressure divided by volume per time, for example $\mathrm{cm}{\mathrm{H}}_2\mathrm{O}\mathrm{s}{\mathrm{L}}^{-1}$. A stipulated pressure drop of 1 cm water at $Q=0.5\mathrm{L}{\mathrm{s}}^{-1}$ gives $R_{\mathrm{aw}}=2$ in those units. The pressure references matter: mouth-to-alveolar pressure concerns the flow path, whereas transpulmonary pressure also describes elastic loading of the lung.

An instructive idealization is the Hagen-Poiseuille equation. For a rigid cylindrical tube carrying steady laminar flow of a fluid with dynamic viscosity $\mu$,Reducing its radius to 80% while holding length and dynamic viscosity fixed multiplies resistance by $1/0.8^4\approx 2.44$. Real airways form a branching, deformable network and need not carry fully developed laminar flow. The tube equation explains a sensitivity, not a universal law for every lung measurement.

Network structure also matters. For $m$ identical linear branches in parallel, pressure drop is shared and their volumetric flow rates add, giving $R_{\mathrm{eq}}=R/m$. Many narrow distal branches can therefore have a very different combined resistance from one isolated narrow tube. Radius alone is insufficient without the arrangement and number of pathways.

Secant versus differential airway resistance distinguishes two values when the relation is nonlinear. For an original model $\Delta P=aQ+bQ|Q|$, the finite ratio is $\Delta P/Q=a+b|Q|$, while its local slope is $d\Delta P/dQ=a+2b|Q|$ away from zero. Report the operating flow and which definition is used.

A 1959 primary study combined mouth pressure with an intra-esophageal balloon and a differential pressure transducer to investigate resistance and compliance.^[ref] The mouth-to-esophageal difference is not a pure airway pressure drop: its elastic component must be separated. Simultaneous pressure, volume and flow information is what makes this mechanical distinction experimentally accessible.

Chest-wall compliance is the volume response of the passive chest wall to pressure across it. For a local static relation,It differs from lung compliance, which uses the pressure difference between the alveolar gas and pleural surroundings. Active respiratory-muscle effort must be distinguished from passive elastic recoil when defining the chest-wall relation.

The chest-wall relaxation volume is the passive volume at which its recoil pressure is zero. Below that volume, outward recoil corresponds to negative $P_W$ in this convention; above it, inward recoil corresponds to positive $P_W$. Negative recoil pressure is compatible with a positive slope $d{P}_W/dV$ and positive compliance. OpenStax describes chest-wall elasticity opposing the inward pull of the lungs.^[ref]

An original linear illustration makes the signs explicit. Over a chosen volume range, supposewith volume in litres and pressures in centimetres of water. Both components have compliance $0.20\mathrm{L}(\mathrm{cm}{\mathrm{H}}_2\mathrm{O}{)}^{-1}$. At $V=2.5$ L, lung recoil is $+7.5$ and chest-wall recoil is $-7.5$ cm water, so their sum is zero. At $V=3.0$ L, the sum is $10-5=5$ cm water. The same shared half-litre change requires a five-centimetre-water increment even though both component slopes are positive. These are toy relations, not measured normal curves.

Adding pressure drops givesThe combined compliance in the example is $0.10\mathrm{L}(\mathrm{cm}{\mathrm{H}}_2\mathrm{O}{)}^{-1}$. Treating that total as lung compliance alone assigns the chest-wall contribution to the wrong structure.

Pressure partition requires more information than a total volume and airway-pressure measurement. A primary lung-mechanics study's use of an esophageal balloon and differential pressure measurement illustrates the experimental effort to constrain an internal pressure reference.^[ref] Its relationship to pleural pressure, posture and muscle activity must be accounted for rather than assumed away.

A useful mechanical comparison states whether the wall is passive, which pressure zero is used and whether local or interval compliance is reported. Chest movement, total respiratory-system stiffness and the chest wall's own elastic slope answer distinct questions.

Chest-wall relaxation volume is the volume at which the passive chest wall has zero elastic recoil pressure. With pressure across the wall defined as $P_W=P_{\mathrm{pleural}}-P_{\mathrm{body}\mathrm{surface}}$, write that volume as $V_{W,0}$, so $P_W(V_{W,0})=0$. Below it, the wall tends to expand; above it, the wall tends to recoil inward. The zero of pressure and the slope defining chest-wall compliance are different features of the pressure-volume curve.

The coupled lung and chest wall generally settle at another volume. Their elastic pressures add:In a passive, open-airway equilibrium, total recoil is zero even though the individual pressures need not vanish. This balance underlies the relaxed end-expiratory volume, or functional residual capacity, in the ideal passive setting. OpenStax describes the opposed lung and chest-wall recoil and defines the volume remaining after normal expiration.^[ref]

An original linear model makes partitioning passive recoil equilibrium explicit:For positive compliances, the coupled equilibrium lies between the two component zero-recoil volumes. Choose $V_{L,0}=1$ L, $V_{W,0}=4$ L and $C_L=C_W=0.20\mathrm{L}(\mathrm{cm}{\mathrm{H}}_2\mathrm{O}{)}^{-1}$. Then $V_{\ast }=2.5$ L, with lung pressure $+7.5$ and wall pressure $-7.5$ cm water. Calling 2.5 L the chest-wall relaxation volume would confuse zero total pressure with zero wall pressure.

Changing the wall's slope can move the coupled equilibrium without moving its own zero. In the same model, increasing $C_W$ to 0.40 while holding everything else fixed gives $V_{\ast }=2.0$ L; $V_{W,0}$ remains 4 L. The more compliant wall supplies a smaller outward pressure at a given volume below its zero. These numbers explain a mechanical distinction rather than state normal human volumes.

A measurement must therefore distinguish passive wall recoil, total respiratory-system recoil and active respiratory-muscle pressure. The relationship between esophageal-balloon pressure and pleural pressure also needs experimental justification when partitioning these components.^[ref] Posture and muscle activity belong to the stated measurement conditions; a measured end-expiratory volume need not equal a purely passive equilibrium.

Lung compliance measures how much lung volume changes for a change in distending pressure. For a static pressure-volume relation, the local value isThe relevant pressure is transpulmonary pressure, not alveolar pressure or airway-opening pressure alone. The pleural pressure reference separates the lung's elastic behaviour from that of the surrounding chest wall.

OpenStax connects lung expansion to pressure changes, elastic recoil and pulmonary surfactant, which modifies surface-tension effects.^[ref] A compliant lung needs a smaller pressure increment for the same small volume increment, but that statement alone does not describe recoil, airway patency or overall respiratory function.

A finite pressure-volume ratio is a secant slope, while $dV/d{P}_L$ is a local slope. In an original nonlinear example, set $x=V-V_0$ and $P_L-P_{L,0}=5x+5x^3$ when volume is measured in litres and pressure in centimetres of water. Local compliance is $1/(5+15x^2)$. It falls from $0.20$ at $x=0$ to $0.05\mathrm{L}(\mathrm{cm}{\mathrm{H}}_2\mathrm{O}{)}^{-1}$ at $x=1$ L. Across that entire one-litre interval, however, the secant compliance is $1/10=0.10$ in the same units. These are constructed values, not clinical reference ranges.

Static versus dynamic lung compliance distinguishes elastic behaviour from measurements during airflow. A simplified lumped dynamic model adds an airway resistance term proportional to volume-flow rate: pressure depends on both $V$ and $R\dot{V}$. A pressure ratio obtained while air is moving can therefore differ from the static elastic slope. Inflation history and hysteresis also require the direction and volume interval to be specified.

In a 1959 primary study, researchers used an intra-esophageal balloon connected to a differential pressure transducer, with a mouthpiece pressure connection, to obtain pressure differences relevant to lung mechanics.^[ref] Such a surrogate pressure measurement has its own positioning and calibration assumptions. Spirometry supplies volume information; volume measurement alone does not establish lung compliance.

Report the pressure references, volume range, flow conditions and measurement history alongside a compliance value. A single number is a property of the specified experiment and state, not an invariant description of every breath.

Ole Storstein is first author of a 1959 experimental study separating airway resistance from lung compliance. The investigators recorded mouth-to-esophageal pressure differences, breathing volume and airflow to analyze the mechanical behavior of respiration.^[ref]

The apparatus used an intra-esophageal balloon, a differential pressure transducer and a pneumotachograph with volume integration. The paper selected corresponding points of no mouth airflow for its compliance calculation and used paired observations during inflation and deflation to estimate resistance.^[ref] Simultaneous signals matter because a pressure observed during flow includes a different mechanical contribution from pressure observed after that flow term vanishes.

For an original one-compartment model with a chosen zero-volume baseline, writewhere $C$ is lung compliance and $R$ is airway resistance. This neglects inertial and regional effects. At stipulated $C=0.10\mathrm{L}/(\mathrm{cm}{\mathrm{H}}_2\mathrm{O})$, $V=0.40$ L, $R=5\mathrm{cm}{\mathrm{H}}_2\mathrm{O}s/L$ and $\dot{V}=0.20$ L/s, the elastic contribution is 4 and the resistive contribution is 1 cm of water. Total modeled pressure is 5 cm of water.

Dividing volume by that total would give $0.08\mathrm{L}/(\mathrm{cm}{\mathrm{H}}_2\mathrm{O})$, below the chosen compliance. At the same modeled volume and zero flow, pressure becomes 4 cm of water and the ratio recovers 0.10. A time point and the definition of the pressure difference are therefore part of the observable, rather than optional details.

The primary paper explicitly notes the limitation of treating a nonuniform mechanical system as uniform.^[ref] Zero net airflow at the mouth need not establish that every region has identical local behavior. Storstein's documented contribution combines apparatus, simultaneous observations and a stated mechanical interpretation, rather than equating one pressure/volume ratio with every aspect of lung function.

Partitioning passive recoil equilibrium separates the elastic pressure contributions of the lung and chest wall at a shared volume. With transpulmonary pressure $P_L=P_{\mathrm{alv}}-P_{\mathrm{pl}}$ and wall pressure $P_W=P_{\mathrm{pl}}-P_{\mathrm{surface}}$,At a passive, open-airway equilibrium the total is zero, but the lung and wall contributions can be equal and opposite rather than individually zero. Their pressure references determine what is being added.^[ref]

The component-elastance ambiguity in total recoil measurements persists away from equilibrium. An original linear family writeswhere $E>0$ is total stiffness and $0<\lambda <1$. Every choice of $p_0$ and $\lambda$ produces the identical total curve $P_{\mathrm{rs}}=E(V-V_{\ast })$. Measuring that total curve alone cannot identify either the baseline pressure partition or the component slopes.

For stipulated $E=10\mathrm{cm}{\mathrm{H}}_2\mathrm{O}{\mathrm{L}}^{-1}$, $V_{\ast }=2.5$ L and $p_0=7.5$ cm water, choosing $\lambda =0.5$ gives equal component slopes of 5. Choosing $\lambda =0.8$ gives slopes 8 and 2. At equilibrium both cases even have the same component pressures, $+7.5$ and $-7.5$. After a 0.5 L increase, the pressure increments are either 2.5 plus 2.5 or 4 plus 1 cm water. Both totals equal 5 cm water.

The respective lung compliances are 0.20 and $0.125\mathrm{L}(\mathrm{cm}{\mathrm{H}}_2\mathrm{O}{)}^{-1}$, while the chest-wall compliances are 0.20 and 0.50. The combined compliance is 0.10 in either case. Thus one equilibrium internal-pressure reading, in addition to the total curve, still does not determine both component slopes.

A measurement series with a justified pleural pressure estimate supplies the missing partition across volume. The 1959 primary study used an intra-esophageal balloon, a mouthpiece connection and differential pressure recording to obtain such internal mechanical information.^[ref] The estimate's positioning and relation to pleural pressure require validation. Passive conditions matter as well: respiratory-muscle pressure would add another contribution to an equation intended to describe elastic recoil alone.

Secant versus differential airway resistance distinguishes a finite pressure-to-flow ratio from the local slope of a pressure-flow relation. If $Q$ is volumetric flow rate and $\Delta P$ the corresponding airway pressure difference, defineThe secant joins the origin to the operating point. The differential value describes a sufficiently small change about that operating point. Both have units of pressure divided by flow, but they agree at every flow only for a linear relation through the origin.

An original nonlinear model is $\Delta P=aQ+bQ|Q|$, with $a,b>0$. For nonzero flow,Choose coefficients $a=2$ and $b=4$ when pressure is expressed in centimetres of water and flow in litres per second. At $Q_0=0.5\mathrm{L}{\mathrm{s}}^{-1}$, pressure is 2 cm water, so the secant resistance is 4 and differential resistance is 6 in $\mathrm{cm}{\mathrm{H}}_2\mathrm{O}\mathrm{s}{\mathrm{L}}^{-1}$. At $Q=0.6$, pressure is 2.64 cm water. The tangent predicts an increase $6(0.1)=0.60$ cm water; the exact increase is 0.64. Their difference is the quadratic remainder $b(\Delta Q{)}^2$.

At negative flow the pressure reverses sign in this odd model, but both resistance measures remain positive. At zero flow the ratio needs its limiting definition, which here equals $a$. These are properties of the stipulated curve, not measured airway coefficients.

Operating-point time constants with nonlinear airway resistance use the differential value. Linearizing a flow equation around a fixed operating point gives $\delta P\simeq R_{\mathrm{diff}}\delta Q$. If that flow charges a local elastic compartment of lung compliance $C$, the small-perturbation time constant is $R_{\mathrm{diff}}C$, rather than an arbitrary finite secant ratio multiplied by $C$.

An experiment must identify the pressure drop belonging to the airways. Mouth-to-pleural pressure also contains elastic loading, so its slope is not automatically airway resistance. The pulmonary-function text treats airway resistance and lung compliance separately, and the 1959 study's differential pressure and balloon apparatus illustrates the need for multiple mechanical measurements.^[ref][ref]

Static versus dynamic lung compliance distinguishes an equilibrated elastic pressure-volume relation from a breathing-cycle measurement. Lung compliance uses transpulmonary pressure, the difference between alveolar pressure and pleural pressure. A static local value is $C_{L,\mathrm{stat}}=dV/d{P}_L$ after flow and relevant transients have subsided; a finite interval instead gives $\Delta V/\Delta P_L$ over a stated pressure range.

The timing convention for dynamic measurements must be explicit. Conventional dynamic lung compliance uses volume and transpulmonary-pressure changes between the zero-flow endpoints of a breath. It is not automatically the same quantity as a ratio using peak airway pressure. The respiratory-function treatise distinguishes these definitions.^[ref]

An original one-compartment model isolates flow contamination. Relative to a chosen baseline, let mouth-to-pleural driving pressure satisfyWith stipulated $C_L=0.20\mathrm{L}(\mathrm{cm}{\mathrm{H}}_2\mathrm{O}{)}^{-1}$, $R=5\mathrm{cm}{\mathrm{H}}_2\mathrm{O}\mathrm{s}{\mathrm{L}}^{-1}$, $\Delta V=0.50$ L and $\dot{V}=0.50\mathrm{L}{\mathrm{s}}^{-1}$, the pressure is $2.5+2.5=5$ cm water. Dividing volume by that pressure gives 0.10 rather than the actual elastic compliance 0.20. Setting flow to zero removes the resistive term in this ideal model. This is a demonstration of a flow-contaminated pressure ratio, not a redefinition of the zero-flow dynamic measurement.

Even zero flow at the mouth need not establish full internal equilibration. Unequal filling times in apparent lung compliance can be illustrated with two independent elastic compartments receiving the same imposed pressure step. If their time constants are ${\tau }_i=R_i{C}_i$, thenFor $C_1=C_2=0.10$ in compliance units and ${\tau }_1=0.2$ s, ${\tau }_2=2$ s, the effective response after 0.5 s is about 0.114, whereas its long-time limit is 0.20. The shorter observation captures less filling of the slow compartment. These are constructed passive model values, not clinical reference ranges.

A primary 2022 pilot study compared four static and dynamic calculation methods during passive mechanical ventilation. Its methods distinguish plateau pressure, pressure at zero flow, constant-flow slopes and expiration-derived estimates.^[ref] Those airway-pressure measurements describe the respiratory system, including the chest wall. Separating lung mechanics requires an additional internal pressure reference, such as the esophageal-balloon approach used in the 1959 experiment.^[ref]