Respiratory mechanics: compliance, resistance and the work of breathing

Why this matters to the anaesthetist

Anaesthesia is a mechanical experiment performed on the lung in real time. The supine position, loss of respiratory muscle tone, the cephalad shift of the diaphragm and the endotracheal tube all change compliance and resistance within minutes of induction, and the ventilator settings the anaesthetist chooses (tidal volume, inspiratory flow, inspiratory-to-expiratory ratio, PEEP) are direct mechanical interventions on these same variables [5][6]. A rising peak airway pressure, a falling tidal volume on pressure control, or failure to oxygenate are all problems of respiratory mechanics, and every protective-ventilation strategy (low tidal volume, recruitment, PEEP, permissive hypercapnia) is derived from the pressure-volume curve and the time constant [3][7].

The respiratory pump and the two loads

Air moves because the inspiratory muscles, chiefly the diaphragm, expand the thoracic cage so that alveolar pressure falls below atmospheric and gas flows inward; expiration at rest is passive, driven by the stored elastic recoil of the lung and chest wall. The pressure developed by the muscles is spent doing work against two mechanical loads: [1]

• an elastic load — the recoil of the lung tissue and the chest wall, described by compliance; and
• a resistive load — the friction of moving gas through the airways (and, when intubated, through the breathing circuit and tube) [1].

The total pressure applied to the respiratory system is therefore the sum of an elastic term and a resistive term: transrespiratory pressure equals elastic pressure plus resistive pressure, where elastic pressure equals volume divided by compliance and resistive pressure equals flow times resistance. This single relationship is the whole of respiratory mechanics, and every ventilator waveform can be read from it. [1]

[1]

Compliance and elastance

Definition and the series rule

Compliance is the change in volume produced by a unit change in pressure, C equals delta V over delta P, measured in mL per cmH2O. Elastance is its inverse, the pressure generated per unit volume, and is the property that returns the lung to its resting state. The lung, the chest wall and the total respiratory system each have a compliance, and because the lung and chest wall are coupled in series the total compliance is LESS than either component alone: [1]

1 over C-total equals 1 over C-lung plus 1 over C-chest wall. [1]

With lung compliance about 200 and chest wall compliance about 200 mL per cmH2O, the total is about 100 mL per cmH2O [5]. The two springs behave like electrical capacitances in series: the softer the combination, the larger the volume change for a given pressure.

Static and dynamic compliance

Static compliance is measured under conditions of no flow, with the airway occluded long enough for flow and resistive pressure to decay to zero; it reflects pure elastic recoil and so depends only on tissue and surface-tension properties. Dynamic compliance is measured during spontaneous or mechanical ventilation, as tidal volume divided by the difference between end-inspiratory and end-expiratory plateau pressures (peak minus PEEP when there is no pause); because it is measured during flow it incorporates any pressure lost to resistance [1].

The two diverge when resistance rises or when flow does not equilibrate within the breath: [1]

• Dynamic compliance falls BELOW static compliance when airway resistance is high (the resistive pressure drop is counted in the denominator), and it falls further still in disease because some lung units with long time constants never finish filling or emptying within the breath, so-called frequency dependence of compliance.
• In the intubated patient, static (or plateau) compliance is the bedside number that tracks the lung: tidal volume divided by (plateau pressure minus total PEEP). A falling static compliance warns of a stiffening lung from atelectasis, oedema, ARDS or overdistension. [1]

The pressure-volume curve

Plotting lung (or respiratory-system) volume against the distending transpulmonary pressure traces a characteristic sigmoid, not a straight line [5]:

• at low volumes the curve is flat — compliance is low because small airways and alveoli are closed and must be recruited (the opening pressure must be overcome);
• in the mid-volume range, around functional residual capacity, the curve is steepest — compliance is maximal and ventilation is cheapest; and
• at high volumes the curve flattens again — compliance falls as collagen and elastin reach their elastic limit and the lung is overdistended. [1]

FRC is the operating point at which the inward recoil of the lung exactly balances the outward recoil of the chest wall; it sits on the steep, compliant part of the curve. This is the mechanical reason why ventilation should be kept in the mid-range: breathing (or ventilating) at low volumes invites atelectasis and gas-trapping, while large tidal volumes at high volumes cause overdistension, volutrauma and a fall in compliance. The protective-ventilation strategy — a low tidal volume of about 6 mL per kg predicted body weight with enough PEEP to hold the lung above the lower inflection — is a direct application of staying on the compliant middle of the curve [7].

The specific compliance

Because a large lung holds more volume at a given pressure than a small one, raw compliance is not comparable between subjects of different size. Specific compliance normalises for lung size by dividing compliance by the FRC (specific compliance equals compliance divided by FRC). The specific compliance is similar across mammalian species and across adults of different size, which confirms that most of the variation in measured compliance is a matter of lung size rather than tissue stiffness. It falls, however, in diseases that stiffen the tissue itself (fibrosis, ARDS, pulmonary oedema) even after correcting for lung volume. [1]

Hysteresis, surface tension and surfactant

Hysteresis

The inflation and deflation limbs of the pressure-volume curve do not lie on top of each other: for any given pressure the lung holds more volume during deflation than during inflation. This separation is hysteresis, and it has two causes: [1]

• surface tension at the air-liquid interface of the alveolar lining fluid, which is higher (and so compliance lower) during inflation, when the surface is being expanded and surfactant molecules are spread thinly; and
• recruitment of previously collapsed alveoli during inflation, which requires a higher opening pressure than is needed to hold them open once recruited. [1]

The practical consequence is that the lung volume at a given pressure depends on the volume history: a lung recruited by a sigh or a sustained inflation stays open at a lower pressure than was needed to open it. This is the mechanical basis of recruitment manoeuvres and of PEEP — PEEP does not recruit lung so much as it holds recruited lung open once the opening pressure has been applied [3][6].

Laplace law and surfactant

The alveolus behaves as a tiny sphere, and the pressure tending to collapse a sphere is given by the Laplace law: collapsing pressure equals two times surface tension divided by radius. Small alveoli (small radius) would therefore generate a higher collapsing pressure than large ones and would empty into them, so the lung would be unstable — every alveolus collapsing into its neighbour [4].

Pulmonary surfactant prevents this. It is a phospholipid mixture (chiefly dipalmitoylphosphatidylcholine, with surfactant proteins A to D) secreted by the type II pneumocytes of the alveolar epithelium. Surfacing the air-liquid interface, surfactant lowers surface tension; crucially, it lowers it MORE as the alveolus shrinks, because the molecules crowd together as the surface area falls. The result is that a small alveolus ends up with a lower surface tension and therefore a lower collapsing pressure than a large one, so alveoli of different sizes are stable side by side. Surfactant has four exam-critical effects: [1]

1. it raises compliance by lowering surface tension, reducing the work of inflation;
2. it prevents atelectasis at end-expiration by stabilising small alveoli;
3. it keeps the alveoli dry by lowering the inward pressure that would pull fluid across the capillary into the alveolar space; and
4. it participates in lung host defence (the surfactant proteins A and D are collectins). [1]

Loss or inactivation of surfactant stiffens and collapses the lung: the classic example is the preterm neonate whose immature type II cells have not yet begun surfactant production, producing the respiratory distress syndrome (Avery and Mead showed that the lungs of infants who died of hyaline membrane disease had a high surface tension) [4]. Surfactant is also depleted and inactivated in ARDS, pulmonary oedema, and after pulmonary aspiration, contributing to the stiff, atelectatic lung of these conditions.

Airway resistance

Definition and normal value

Airway resistance (Raw) is the pressure drop across the airways per unit of flow: Raw equals the change in pressure divided by the change in flow, in cmH2O per L per s. In a healthy adult breathing quietly through the nose it is about 1 to 2 cmH2O per L per s; mouth breathing roughly halves it, because the nose is the single largest resistor during spontaneous respiration. Under general anaesthesia the endotracheal tube adds a fixed high-resistance segment, so the total resistance of the intubated airway is several times the native value. [1]

Laminar flow and Poiseuille law

When gas flows slowly along a straight tube as a series of concentric streamlines, with the parabolic velocity profile fastest at the centre, the flow is laminar. The pressure difference driving laminar flow is given by the Poiseuille (Hagen-Poiseuille) law: [1]

delta P equals eight times viscosity times length times flow, divided by pi times radius to the fourth power. [1]

Equivalently, resistance equals eight times viscosity times length divided by pi times radius to the fourth power. Two points are exam-critical: [1]

• resistance is proportional to radius to the fourth power (through the inverse), so halving the radius multiplies resistance sixteenfold and reduces it by a third only if radius increases by ten per cent; and
• laminar resistance depends on viscosity (not density) and on tube length. [1]

This is the mechanical reason why bronchospasm, mucosal oedema, secretions and a small endotracheal tube so sharply raise the work of breathing: the radius term dominates everything else [2].

Turbulent flow and the Reynolds number

At higher velocities, at branch points and in large-diameter airways, the streamlines break down and gas moves as eddies. Turbulent flow is not described by Poiseuille law: the pressure drop is proportional to flow squared (not flow), so doubling flow quadruples the driving pressure, and the resistance depends on gas density (not viscosity). The transition from laminar to turbulent flow is predicted by the dimensionless Reynolds number: [1]

Re equals density times velocity times diameter, divided by viscosity. [1]

Flow becomes turbulent when the Reynolds number exceeds about 2000. Turbulence is promoted by high gas density (the heavy volatile agents and nitrous oxide raise it slightly), high velocity (high inspiratory flow), large tube or airway diameter, and branching or irregularity of the wall. It is reduced by using a gas of low density (helium-oxygen mixtures, heliox, lower the density and so reduce turbulent resistance in upper-airway obstruction). [1]

The transition through the bronchial tree

The character of flow changes as gas moves down the airway tree: [1]

• the nose, pharynx and larynx are short, large-diameter, irregular and branching — flow here is largely turbulent;
• the large and medium bronchi (down to about generation 8) carry fast flow through branching tubes — flow is transitional (mixed, with a turbulent core and laminar edges); and
• the small airways (generations beyond about 8, less than 2 mm diameter) carry very slow flow through an enormous total cross-section — flow here is almost wholly laminar [2].

The site of airway resistance

A common and dangerous misconception is that because the small airways are narrow they must be the main site of resistance. They are not. Macklem and Mead, using a retrograde catheter wedged in the peripheral airways, showed that in the healthy lung most resistance lies in the medium-sized bronchi (generations 2 to 8), and that the small airways (the so-called silent zone, less than 2 mm) contribute only about 10 to 20 per cent of total resistance [2].

The reason is geometry. Although each small airway is narrow, there are enormous numbers of them arranged in parallel, and the total cross-sectional area of the airway tree rises steeply toward the periphery (from a few cm squared at the trachea to thousands of cm squared at the level of the respiratory bronchioles). The summed cross-sectional area is so large that the collective resistance of the small airways is small. This is the same principle by which adding resistances in parallel lowers their combined resistance. The clinical corollary is the silent zone: small-airway disease (early COPD, bronchiolitis) can destroy much of the peripheral airway bed before total airway resistance or spirometry becomes abnormal, which is why the forced expiratory flow at 25 to 75 per cent of vital capacity is a sensitive but non-specific early marker. [1]

The time constant

Definition and the 95 per cent rule

A lung unit does not fill or empty instantly; it does so exponentially, with a rate set by its resistance and its compliance. The time constant tau is their product: [1]

tau equals resistance times compliance (tau equals R times C). [1]

With normal airway resistance of about 2 cmH2O per L per s and lung compliance of about 0.1 L per cmH2O (100 mL per cmH2O), the normal time constant is about 0.2 to 0.3 s. Because filling is exponential, one time constant gives 63 per cent of a volume change, two give 86 per cent, and three time constants give 95 per cent; five are needed for near-complete (99 per cent) equilibration [1].

Clinical relevance — air trapping

The time constant matters whenever the breath is too short for equilibration: [1]

• in obstructive disease (asthma, COPD) the airway resistance rises and the time constant lengthens, so the lung needs a longer expiration to empty; if the respiratory rate is high and the expiratory time is short, expiration is interrupted before the lung reaches its resting volume, and the next breath begins from a higher volume. Gas is trapped, intrinsic PEEP (auto-PEEP, PEEPi) builds up, the lung hyperinflates, and the work of breathing rises (the patient must generate a higher elastic recoil to exhale, and the hyperinflated chest pushes the diaphragm flat so the muscle works at a mechanical disadvantage).
• in a lung with uneven time constants (regional differences in resistance or compliance, as in COPD, ARDS or pneumonia) some units fill and empty fast and others slowly, so the distribution of ventilation becomes non-uniform and gas exchange worsens — the basis of the frequency dependence of dynamic compliance. [1]

The mechanical remedy is to lengthen expiration: a slower respiratory rate, a lower inspiratory-to-expiratory ratio (typically 1 to 3 or 1 to 4 in obstructive disease), and sometimes a smaller tidal volume, so that expiration has time to complete [1].

Work of breathing

The two components

The work of breathing is the work done by the respiratory muscles (or, during controlled ventilation, by the ventilator) to move a tidal volume against the elastic and resistive loads. It is the integral of pressure with respect to volume, and on a pressure-volume loop it is the area enclosed by the loop. It divides into: [1]

• elastic work (about two thirds, or roughly 65 per cent), stored as potential energy in the stretched lung and chest wall and recovered during passive expiration; and
• resistive work (about one third, or roughly 35 per cent), dissipated as heat by friction in the airways and tissues and not recoverable [1][9].

The optimal frequency

Because the two components respond differently to the pattern of breathing, there is an energetically optimal respiratory frequency. Shallow, rapid breathing (high rate, small tidal volume) minimises the elastic work per minute (less volume stretched per breath) but maximises the resistive work (more flow, more breaths, and a larger dead-space fraction of each breath). Deep, slow breathing (low rate, large tidal volume) minimises the resistive work but maximises the elastic work (more volume stretched per breath). The respiratory controller normally settles on a frequency near the minimum of the total work curve — about 12 to 15 breaths per minute in the resting adult — and disease shifts this optimum: the stiff lung of fibrosis pushes toward a rapid, shallow pattern (to minimise elastic work), whereas the obstructed airway of COPD pushes toward a slow, deep pattern (to minimise resistive work) [1].

The oxygen cost of breathing

The healthy respiratory muscles consume only about 1 to 2 per cent of total body oxygen consumption at rest, but this rises steeply when the work of breathing increases — to 10 per cent or more in exercise, and to a large fraction of cardiac output in respiratory failure, where the fatiguing respiratory muscle may itself become a limiting organ. Increased dead space, a small endotracheal tube, a high-resistance breathing circuit, and bronchospasm all raise this oxygen cost [9].

Factors that move compliance and resistance

Position and anaesthesia

Moving from upright to supine reduces functional residual capacity by about 0.5 to 1 L as the abdominal contents push the diaphragm cephalad; induction of anaesthesia and the onset of muscle paralysis reduce it a further 15 to 20 per cent and shift the pressure-volume curve downward and to the right, lowering compliance [5]. Within minutes of induction, dependent lung develops crest-shaped densities on computed tomography that represent compression atelectasis — a true shunt — and these are reduced or abolished by PEEP [3][6]. In the obese patient the fall is exaggerated: the heavy abdomen splints the diaphragm, FRC may fall below closing capacity, and both respiratory-system and chest-wall elastance rise, which is why the obese anaesthetised patient benefits disproportionately from PEEP and from a head-up or ramped position [7].

PEEP, recruitment and bronchodilators

• PEEP recruits collapsed alveoli back onto the steep, compliant part of the curve, raises FRC above closing capacity, restores surfactant function and so raises compliance — but only up to the point where added pressure begins to overdistend already-open alveoli, after which compliance falls again. PEEP is therefore set on the compliant part of the curve, and the best PEEP is often defined as that which gives the best compliance (or best oxygenation without a rise in dead space).
• Recruitment manoeuvres (a sustained inflation of about 35 to 40 cmH2O for 30 to 40 seconds) apply the opening pressure that PEEP alone cannot, after which PEEP holds the recruited lung open [6].
• Bronchodilators lower airway resistance and so lower the resistive work of breathing and shorten the time constant, easing air trapping in obstructive disease.

The breathing circuit and the endotracheal tube

The anaesthetic machine and breathing circuit add their own resistance in series with the airway, and the endotracheal tube is by far the dominant added resistor. [1]

• The endotracheal tube is a long, narrow, fixed-radius tube: by Poiseuille law its resistance is high and rises steeply as the internal diameter falls (resistance is inversely proportional to radius to the fourth power for laminar flow, and turbulence at high flow makes the rise even steeper). A 6 mm tube has roughly four times the resistance of an 8 mm tube. This matters during pressure-support weaning (a high tube resistance can mimic persistent respiratory failure and may require tube compensation), during spontaneous breathing through the circuit, and in the child, where small absolute changes in tube size cause large changes in resistance.
• The breathing circuit (tubing, connectors, humidifier, filters, valves) adds a smaller but measurable resistance, and an obstructed or waterlogged filter can suddenly raise circuit resistance and peak airway pressure. High-resistance expiratory valves and inadequate continuous flow during spontaneous CPAP can increase the work of breathing many-fold [9].
• During spontaneous ventilation through a circle or Mapleson circuit, the patient must also overcome the resistance of the absorber, the valves and the fresh-gas pathway; this is one reason why pressure-support or assisted modes are used to offload the work of the intubated, spontaneously breathing patient.

A practical rule: a sudden rise in peak airway pressure during controlled ventilation should be separated into a rise in plateau pressure (a compliance problem — stiff lung, overdistension, pneumothorax, abdominal distension) versus a rise in peak with a normal plateau (a resistance problem — kinked tube, bronchospasm, obstructed filter, secretions, circuit obstruction). This single distinction, peak versus plateau, is the bedside expression of compliance versus resistance. [1]

Integration — reading the ventilator

Every ventilator number is a mechanical quantity: [1]

• peak inspiratory pressure reflects resistance plus compliance (it is dominated by the resistive pressure needed to push flow through the tube and airways);
• plateau pressure (measured during an inspiratory pause, with no flow) reflects compliance alone, and is the number that tracks the risk of overdistension (kept below about 30 cmH2O in protective ventilation);
• the difference between peak and plateau is the resistive pressure drop; and
• driving pressure (plateau minus PEEP, the pressure that delivers the tidal volume) normalises compliance for the size of the breath and is a stronger predictor of outcome than tidal volume alone. [1]

Red flags

[1] [1] [1] [1] [1]

References and further reading

• Otis AB, Fenn WO, Rahn H. Mechanics of breathing in man. J Appl Physiol 1950. PMID 15436363.
• Macklem PT, Mead J. Resistance of central and peripheral airways measured by a retrograde catheter. J Appl Physiol 1967. PMID 4960137.
• Avery ME, Mead J. Surface properties in relation to atelectasis and hyaline membrane disease. AMA J Dis Child 1959. PMID 13649082.
• Brismar B, Hedenstierna G, Lundquist H, et al. Pulmonary densities during anesthesia with muscular relaxation — a proposal of atelectasis. Anesthesiology 1985. PMID 3885791.
• Westbrook PR, Stubbs SE, Sessler AD, Rehder K, Hyatt RE. Effects of anesthesia and muscle paralysis on respiratory mechanics in normal man. J Appl Physiol 1973. PMID 4697382.
• Rehder K, Mallow JE, Fibuch EE, Krabill DR, Sessler AD. Effects of isoflurane anesthesia and muscle paralysis on respiratory mechanics in normal man. Anesthesiology 1974. PMID 4429217.
• Pelosi P, Ravagnan I, Giurati G, et al. Positive end-expiratory pressure improves respiratory function in obese but not in normal subjects during anesthesia and paralysis. Anesthesiology 1999. PMID 10551570.
• Hedenstierna G, Edmark L. Effects of anesthesia on the respiratory system. Best Pract Res Clin Anaesthesiol 2015. PMID 26643094.
• Banner MJ, Downs JB, Kirby RR, et al. Effects of expiratory flow resistance on inspiratory work of breathing. Chest 1988. PMID 3280260. [1]

References

1. [1]Otis AB, Fenn WO, Rahn H. Mechanics of breathing in man J Appl Physiol, 1950.PMID 15436363
2. [2]Macklem PT, Mead J. Resistance of central and peripheral airways measured by a retrograde catheter J Appl Physiol, 1967.PMID 4960137
3. [3]Brismar B, Hedenstierna G, Lundquist H, et al. Pulmonary densities during anesthesia with muscular relaxation--a proposal of atelectasis Anesthesiology, 1985.PMID 3885791
4. [4]Avery ME, Mead J. Surface properties in relation to atelectasis and hyaline membrane disease AMA J Dis Child, 1959.PMID 13649082
5. [5]Westbrook PR, Stubbs SE, Sessler AD, Rehder K, Hyatt RE. Effects of anesthesia and muscle paralysis on respiratory mechanics in normal man J Appl Physiol, 1973.PMID 4697382
6. [6]Hedenstierna G, Edmark L. Effects of anesthesia on the respiratory system Best Pract Res Clin Anaesthesiol, 2015.PMID 26643094
7. [7]Pelosi P, Ravagnan I, Giurati G, et al. Positive end-expiratory pressure improves respiratory function in obese but not in normal subjects during anesthesia and paralysis Anesthesiology, 1999.PMID 10551570
8. [8]Rehder K, Mallow JE, Fibuch EE, Krabill DR, Sessler AD. Effects of isoflurane anesthesia and muscle paralysis on respiratory mechanics in normal man Anesthesiology, 1974.PMID 4429217
9. [9]Banner MJ, Downs JB, Kirby RR, et al. Effects of expiratory flow resistance on inspiratory work of breathing Chest, 1988.PMID 3280260