Pressure, Flow, Resistance, Compliance, and Elastance

An arterial pressure can rise without a useful increase in blood flow. Airway pressure can rise because the airways have narrowed or because the respiratory system has become harder to inflate. The measurement alone does not identify the mechanism.

Pressure, flow, resistance, compliance, and elastance describe different parts of the same mechanical system. Understanding their relationships helps explain what a bedside measurement means and what an intervention is likely to change.

2.1 Pressure: A Measurement Requires a Reference

Pressure is force distributed over an area. In clinical practice, pressure is usually reported relative to a reference. An arterial transducer is zeroed to atmospheric pressure. A ventilator also generally displays airway pressure relative to the atmosphere.

A pressure of zero on these instruments therefore does not mean that no pressure exists. It means that the measured pressure equals the chosen reference pressure.

The height of the fluid column between the patient and transducer also changes the reading. Fluid above the transducer exerts pressure because of its weight. Moving the transducer below the intended reference level therefore adds pressure to the measurement. Moving it above that level reduces the reading. Zeroing establishes the atmospheric reference. Leveling places the transducer at the height for which the pressure is being reported. Both steps are necessary.

Pressure differences used in a calculation must have compatible reference levels. Subtracting two pressures referenced to different heights can introduce a hydrostatic error. The clinically appropriate level depends on the organ and the purpose of measurement. A pressure referenced to the right atrium does not automatically describe arterial pressure at the brain when the head is elevated.

Units also matter. Vascular pressures are commonly expressed in millimeters of mercury, abbreviated mm Hg. Respiratory pressures are commonly expressed in centimeters of water, written cm H₂O. One mm Hg is approximately 1.36 cm H₂O. Values should be converted before pressures in different units are compared or subtracted.

Before interpreting a pressure, establish its reference, measurement location, and units. A precise display cannot compensate for an incorrect setup.

2.2 Flow Depends on a Pressure Difference

Flow is the volume passing a point per unit time. Cardiac output is blood flow through the systemic circulation. It is usually expressed in liters per minute. Respiratory flow is commonly expressed in liters per second or liters per minute.

For a simple resistance model, the relationship is:

Here, Q is flow. The symbol Δ means a difference, so ΔP is upstream pressure minus downstream pressure. R is the resistance of the pathway. For a given resistance, a larger pressure difference produces more flow. For a given pressure difference, higher resistance reduces flow. This simple equation describes steady flow through a defined pathway. Pulsatility, gravity, and vessel collapse may require additional terms or a different model.

An upstream pressure alone cannot specify flow. The downstream pressure and the properties of the pathway also matter. If both ends of a rigid tube are raised to the same pressure, there is no pressure difference to drive flow through it.

For the systemic circulation, a common mean-pressure approximation is:

Right atrial pressure is often estimated by central venous pressure. In this simplified model, the difference between arterial and right atrial pressure drives systemic flow. This global relationship does not establish the perfusion pressure of every individual organ.

Venous return depends on a pressure difference too. Blood in the systemic venous reservoirs must flow toward the right atrium. If right atrial pressure rises while the upstream pressure and resistance remain unchanged, that pressure difference narrows and venous return falls. Guyton and colleagues examined this relationship experimentally. Their work helped explain why arterial pressure alone cannot describe the return of blood to the heart. 1

Increasing arterial pressure does not guarantee improved tissue perfusion. LeDoux and colleagues studied ten patients with septic shock. Raising mean arterial pressure from 65 to 85 mm Hg with norepinephrine did not significantly improve the measured indices of regional perfusion. This was a small physiological study. It does not establish an optimal pressure target for every patient, but it demonstrates that pressure and perfusion can respond differently. 2

2.3 Resistance: The Opposition to Flow

Resistance describes the pressure difference required to produce a given flow. Rearranging the pressure–flow equation gives:

If a larger pressure difference is required to maintain the same flow, resistance has increased. If flow increases while the pressure difference remains unchanged, calculated resistance has decreased.

Laminar flow means that fluid moves in orderly layers. For steady laminar flow through a long, straight, rigid circular tube, the Poiseuille relationship is:

The symbol η, pronounced eta, represents viscosity. A more viscous fluid requires a greater pressure difference to maintain the same flow. L is tube length, and r is internal radius. A longer tube creates more resistance. Radius appears to the fourth power in the denominator, which makes its effect much larger.

If radius falls to half its original value, r⁴ falls to one-sixteenth of its original value. Resistance therefore rises sixteenfold when the other terms remain constant. At an unchanged pressure difference, flow falls to one-sixteenth of the original flow.

This relationship explains why narrowing a lumen can greatly reduce flow. A short, wide intravenous catheter offers less resistance than a long, narrow catheter under otherwise comparable conditions. The entire infusion pathway still matters: a narrow connector or extension can limit the flow even when the catheter itself is wide.

The exact relationship is less reliable in biological systems. Blood vessels change diameter and are arranged in branching networks. The effective viscosity of blood can change with vessel size and flow conditions. Airflow through a narrowed airway or an endotracheal tube can become turbulent, with irregular motion and eddies. When this occurs, the pressure required for flow may rise more steeply than a linear resistance model predicts.

Calculated systemic vascular resistance is therefore a summary of the circulation at the time of measurement. It is not a direct measurement of arteriolar diameter or sympathetic activity. Errors in cardiac output, arterial pressure, or central venous pressure also affect the calculated result.

Dividing a pressure difference in mm Hg by flow in L/min gives resistance in mm Hg·min/L. This unit is also called a Wood unit. Multiplying the result by 80 converts it to dyn·s·cm⁻⁵.

For an illustrative pressure difference of 60 mm Hg and flow of 5 L/min, first divide pressure by flow:

60 ÷ 5 = 12 Wood units

Then convert the units:

12 × 80 = 960 dyn·s·cm⁻⁵

These are two ways of expressing the same resistance.

2.4 Pathways in Series and Parallel

The arrangement of flow pathways changes their combined resistance.

In a series arrangement, flow passes through one segment and then another. At steady state, the same flow passes through each segment. The pressure falls across each resistance, and the resistances add:

A catheter, connector, and extension tubing form a series pathway. A narrow component can substantially limit flow through the entire assembly. Increasing the diameter of one component may produce little benefit if another component remains the main source of resistance.

In a parallel arrangement, flow divides between branches. In the ideal model, each branch connects the same upstream and downstream pressures. The branches therefore share a pressure difference, but the flow through each depends on its resistance:

Adding an open parallel pathway gives fluid another route between the same pressures. More total flow can then pass without increasing the pressure difference, so total resistance falls. With two identical branches, each carries the flow that one branch would carry alone. Their combined flow doubles, and their combined resistance is half that of either branch.

The systemic organs form a largely parallel circulation. Each organ receives part of the total cardiac output. Constriction of an organ’s resistance vessels can reduce its share of that flow, while dilation can increase it, depending on the accompanying pressure changes. Total cardiac output can remain satisfactory even when one organ receives too little blood.

Local autoregulation further modifies these relationships. An organ may change its vascular resistance to maintain flow over a range of perfusion pressures. Consequently, a fixed-resistance calculation illustrates a mechanical relationship, but it may not predict the intact organ’s response to a pressure change.

2.5 Pressure Along a Pathway and Pressure Across a Wall

Two pressure differences must be distinguished. The pressure difference along a pathway helps drive flow. The pressure difference across its wall helps determine distension.

Transmural pressure is the pressure inside a structure minus the pressure surrounding it.

Consider an illustrative central venous pressure of 15 mm Hg and a surrounding pressure of 5 mm Hg. Subtract the pressure outside from the pressure inside:

15 − 5 = 10 mm Hg of transmural pressure

Now let surrounding pressure rise to 12 mm Hg while central venous pressure remains 15 mm Hg:

15 − 12 = 3 mm Hg of transmural pressure

The monitor shows the same central venous pressure in both situations, but the pressure available to distend the chamber is much lower in the second. These calculations assume that surrounding pressure is known; it is not routinely measured with this precision.

This distinction helps explain why a high measured filling pressure does not necessarily indicate a large distending pressure. Positive intrathoracic pressure can raise the measured pressure within the right atrium. The resulting change in cardiac filling depends on pressure outside the chamber as well as inside it.

Surrounding pressure can also compress a vessel and limit flow. Consider a collapsible pulmonary vessel exposed to alveolar pressure. If alveolar pressure exceeds venous pressure, the vessel can narrow. Flow then depends more on the difference between arterial and alveolar pressure than on the difference between arterial and venous pressure. Lowering venous pressure further may produce little additional flow. West, Dollery, and Naimark demonstrated these relationships in an isolated lung preparation. Their experiments underpin the model of pulmonary vascular zones. 3

Venous pressure also affects perfusion when vessels remain open. Raising an organ’s venous pressure narrows the pressure difference between its arterial inflow and venous outflow. Flow can fall even if arterial pressure stays unchanged. Mullens and colleagues found that venous congestion was associated with worsening renal function in advanced decompensated heart failure. This observational result supports assessing venous pressure, but it does not establish a central venous pressure target that prevents kidney injury. 4

2.6 Compliance: The Volume Change Produced by Pressure

Compliance describes how much volume changes for a given change in distending pressure.

A highly compliant structure accepts a relatively large increase in volume with a small increase in pressure. A poorly compliant structure requires a larger pressure increase for the same volume change.

A structure’s current volume does not establish its compliance. Volume describes how much it contains at that moment. Capacity refers to the volume it can hold under specified conditions. Compliance describes how much more volume enters for each increase in distending pressure. A large, already distended chamber may accept little additional blood before its pressure rises sharply.

Pressure–volume relationships are often curved rather than straight. The same pressure increase may produce a large volume change in one part of the curve and a small change in another. A compliance calculated between two measurements is an average over that range. It may not describe what happens at much lower or higher volumes.

Veins illustrate the importance of this behavior. They can accommodate changes in blood volume with relatively small pressure changes over part of their operating range. Changes in venous tone also alter the relationship between volume and pressure. A venous pressure cannot therefore be interpreted as a direct measure of total blood volume.

For a passive patient during mechanical ventilation, static respiratory system compliance is commonly estimated as:

PEEP means positive end-expiratory pressure. Total PEEP includes both externally applied PEEP and intrinsic PEEP. Plateau pressure is assessed during an end-inspiratory pause, when flow has stopped. Total PEEP is assessed under appropriate passive, no-flow conditions at end expiration.

For an illustrative tidal volume of 420 mL, plateau pressure of 24 cm H₂O, and total PEEP of 10 cm H₂O, first calculate the pressure increase used to deliver the breath:

24 − 10 = 14 cm H₂O

Then divide the delivered volume by that pressure increase:

420 ÷ 14 = 30 mL/cm H₂O

Over this breath, each 1 cm H₂O increase in pressure corresponds to an average volume increase of 30 mL. This describes the combined lung and chest wall response.

This calculation assumes that the patient is not generating respiratory muscle pressure and that the measurements are valid. Significant leaks, incomplete pressure equilibration, or persistent effort can make the result misleading.

2.7 Elastance: The Pressure Required to Change Volume

Elastance describes how much pressure must change to produce a given volume change. It expresses stiffness and is the reciprocal of compliance when both describe the same pressure–volume relationship.

Keep the volume unit consistent before taking the reciprocal. A compliance of 30 mL/cm H₂O equals 0.030 L/cm H₂O. The corresponding elastance is:

1 ÷ 0.030 ≈ 33.3 cm H₂O/L

This is the same pressure–volume relationship expressed as pressure per unit volume instead of volume per unit pressure. It does not imply that delivering an entire liter would be safe or that the relationship would remain linear over that volume.

Inflating the respiratory system expands both the lung and the chest wall. In a simplified passive model, both undergo the same volume change. Part of the applied pressure distends the lung, and part expands the chest wall. Because these pressure requirements add, their elastances also add:

Their compliances therefore do not simply add.

A high respiratory system elastance does not establish that the lung alone is stiff. Obesity, abdominal distension, or other changes affecting the chest wall can contribute. The pressure needed to expand the chest wall is part of the measured airway pressure.

Gattinoni and colleagues studied patients with pulmonary and extrapulmonary causes of acute respiratory distress syndrome. Similar overall respiratory mechanics concealed different contributions from the lung and chest wall. This small physiological study illustrates why total respiratory system mechanics cannot be assumed to represent lung mechanics alone. It does not justify assigning an individual patient’s mechanics solely from the cause of ARDS. 5

The pressure that distends the lung is transpulmonary pressure: alveolar pressure minus pleural pressure. At the same alveolar pressure, a higher pleural pressure leaves less pressure to distend the lung. Airway plateau pressure can approximate alveolar pressure when flow has stopped and pressures have equilibrated. It does not measure pleural pressure. Separating lung and chest wall contributions therefore requires additional assessment.

2.8 Resistance and Compliance Determine How Quickly Volume Changes

Resistance and compliance also influence the time course of filling and emptying. Their product gives a time constant:

The Greek letter τ, pronounced tau, represents time. When respiratory resistance is expressed in cm H₂O·s/L and compliance in L/cm H₂O, their product is in seconds.

In an ideal passive compartment, volume approaches its final value progressively. The initial change is fastest, and the remaining change becomes smaller with time. With constant resistance and compliance, approximately 63% of the total change occurs within one time constant. About 95% occurs within three. During passive emptying, this means that about 37% of the initial excess volume remains after one time constant and about 5% after three. These percentages describe the model; they do not define a universal expiratory time for patients.

For an illustrative resistance of 10 cm H₂O·s/L and compliance of 0.05 L/cm H₂O, multiply the two values:

10 × 0.05 = 0.5 seconds

One time constant is therefore 0.5 seconds. Three time constants take 3 × 0.5, or 1.5 seconds. In this model, about 95% of the volume change occurs over those 1.5 seconds. Doubling resistance while compliance stays unchanged doubles the time needed for the same fraction of emptying.

An obstructed lung region therefore empties more slowly if the other conditions remain similar. If the next inspiration starts before adequate expiration has occurred, gas can remain trapped. Repeated breaths may increase end-expiratory lung volume and produce intrinsic PEEP.

Real lungs contain regions with different time constants. Airway closure and flow limitation can also make resistance change during expiration. A single calculated time constant cannot capture all of this behavior. The expiratory flow waveform provides useful additional information. Flow that has not returned to zero before the next breath suggests incomplete emptying, although interpretation depends on the ventilator circuit and any leak.

2.9 Separating Resistive and Elastic Pressure During Ventilation

During passive inflation, airway pressure must overcome resistance and expand the respiratory system. A simplified equation of motion expresses these contributions:

Volume change is measured from the end-expiratory baseline. This model assumes a passive patient and treats resistance and elastance as approximately constant. It omits additional effects, including the pressure needed to accelerate gas and the gradual relaxation of tissues after inflation.

While gas moves, part of the airway pressure is needed to overcome resistance. During an inspiratory pause, flow stops, so that pressure difference falls. Pressure then settles toward a plateau. In a passive patient with adequate equilibration, plateau pressure reflects total PEEP plus the pressure needed to keep the respiratory system expanded at the delivered volume.

With constant inspiratory flow, resistance can be estimated as:

This is an estimate of resistance through the measured system, including the artificial airway. It is not a measurement of native airway resistance alone. The timing of pressure measurements and tissue pressure relaxation can affect the estimate.

The difference between plateau pressure and total PEEP is respiratory system driving pressure:

Amato and colleagues reanalyzed data from 3,562 patients in nine ARDS trials. Higher driving pressure was associated with worse survival. Patients had not been randomly assigned to different driving-pressure targets. The analysis therefore identifies an important association, but it does not establish that one threshold is safe for every patient. 6

Randomized evidence also shows that the ventilation strategy can change outcomes in ARDS. In the ARDS Network trial, a strategy using lower tidal volumes and a lower plateau-pressure limit reduced mortality compared with the traditional strategy. Mortality was 31.0% versus 39.8%. Because the trial tested a combined strategy, its benefit cannot be assigned to one pressure variable alone. 7

2.10 Applying the Relationships at the Bedside

Consider an illustrative patient receiving passive volume-controlled ventilation. Tidal volume is 420 mL, and constant inspiratory flow is 0.5 L/s. Peak airway pressure is 34 cm H₂O. Plateau pressure is 24 cm H₂O, and total PEEP is 10 cm H₂O.

First separate the pressure needed for flow from the pressure that remains when flow stops. The peak-to-plateau difference is 34 − 24, or 10 cm H₂O. Divide this by the inspiratory flow:

Estimated resistance = 10 ÷ 0.5 = 20 cm H₂O·s/L

Next subtract total PEEP from plateau pressure:

Driving pressure = 24 − 10 = 14 cm H₂O

Finally, divide tidal volume by driving pressure:

Compliance = 420 ÷ 14 = 30 mL/cm H₂O

Now suppose peak pressure rises to 44 cm H₂O while plateau pressure remains 24 cm H₂O. Tidal volume, inspiratory flow, and total PEEP are unchanged. The peak-to-plateau difference has increased to 44 − 24, or 20 cm H₂O. Estimated resistance is now 20 ÷ 0.5, or 40 cm H₂O·s/L. It has doubled.

Driving pressure and calculated compliance remain unchanged because plateau pressure, total PEEP, and tidal volume have not changed. The extra pressure is required while gas is moving. Assess for secretions, bronchospasm, or a narrowed endotracheal tube or circuit. The pressure pattern identifies increased resistance; the examination must identify its cause.

Return to the original measurements and consider a different change. Peak pressure rises to 44 cm H₂O, and plateau pressure rises to 34 cm H₂O. Tidal volume, flow, and total PEEP remain unchanged. The peak-to-plateau difference is 44 − 34, or 10 cm H₂O. Estimated resistance therefore remains 10 ÷ 0.5, or 20 cm H₂O·s/L.

Driving pressure, however, has risen to 34 − 10, or 24 cm H₂O. Compliance is now 420 ÷ 24, or 17.5 mL/cm H₂O. More pressure is needed to maintain the same volume after flow has stopped. Assess for a change in lung or chest wall mechanics.

Circulatory measurements require the same sequence. For an illustrative mean arterial pressure of 70 mm Hg and right atrial pressure of 10 mm Hg, the pressure difference is 70 − 10, or 60 mm Hg. If cardiac output is 5 L/min, calculated systemic resistance is 60 ÷ 5, or 12 Wood units.

Now raise right atrial pressure to 20 mm Hg while keeping arterial pressure and resistance unchanged in the model. The pressure difference falls to 70 − 20, or 50 mm Hg. Predicted flow is 50 ÷ 12, or approximately 4.2 L/min. Flow falls because the pressure difference has narrowed. The example isolates the effect of downstream pressure; an intact circulation may change its other pressures and resistance at the same time.

These examples show why the direction of a pressure change is insufficient to guide treatment. The interpretation depends on which pressure changed, where it was measured, and how flow or volume changed with it. Identifying the mechanical relationship narrows the explanation. Clinical examination and further measurements then establish the cause.

References

1. Guyton AC, Lindsey AW, Abernathy B, Richardson T. Venous return at various right atrial pressures and the normal venous return curve. American Journal of Physiology. 1957;189(3):609–615. doi:10.1152/ajplegacy.1957.189.3.609.

2. LeDoux D, Astiz ME, Carpati CM, Rackow EC. Effects of perfusion pressure on tissue perfusion in septic shock. Critical Care Medicine. 2000;28(8):2729–2732. doi:10.1097/00003246-200008000-00007.

3. West JB, Dollery CT, Naimark A. Distribution of blood flow in isolated lung; relation to vascular and alveolar pressures. Journal of Applied Physiology. 1964;19(4):713–724. doi:10.1152/jappl.1964.19.4.713.

4. Mullens W, Abrahams Z, Francis GS, et al. Importance of venous congestion for worsening of renal function in advanced decompensated heart failure. Journal of the American College of Cardiology. 2009;53(7):589–596. doi:10.1016/j.jacc.2008.05.068.

5. Gattinoni L, Pelosi P, Suter PM, Pedoto A, Vercesi P, Lissoni A. Acute respiratory distress syndrome caused by pulmonary and extrapulmonary disease. Different syndromes? American Journal of Respiratory and Critical Care Medicine. 1998;158(1):3–11. doi:10.1164/ajrccm.158.1.9708031.

6. Amato MBP, Meade MO, Slutsky AS, et al. Driving pressure and survival in the acute respiratory distress syndrome. New England Journal of Medicine. 2015;372(8):747–755. doi:10.1056/NEJMsa1410639.

7. Acute Respiratory Distress Syndrome Network. Ventilation with lower tidal volumes as compared with traditional tidal volumes for acute lung injury and the acute respiratory distress syndrome. New England Journal of Medicine. 2000;342(18):1301–1308. doi:10.1056/NEJM200005043421801.