Equation of Motion Part 2: Application

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Aman Thind
Aman Thind

"Aman is a critical care medicine fellow at the Cleveland Clinic. Interests: Cardiopulmonary physiology, shock, mechanical ventilation, and ARDS. Music genres: Blues, Rock, and Heavy metal".

The Pre-brief

In the last segment, we introduced the concept of the equation of motion. To recap, the ventilatory load can be divided into two categories:

  • Elastic (static) load: a function of elastance and volume
  • Resistive (dynamic) load: a function of resistance and flow

Elastance and resistance are the two basic mechanical properties that can be assessed subjectively and objectively in patients receiving mechanical ventilation. A good subjective analysis can be performed without touching the ventilator. Pressure-time and flow-time scalars in a passively ventilated patient often provide a good insight into whether the predominant load is resistive or elastic. However, this analysis becomes difficult in the presence of significant respiratory muscle activity (Pmus). 

Waveform interpretation is a skill similar to EKG analysis and requires experience and practice.

The easiest way to objectively assess elastance and resistance is to temporarily switch to volume-control (VC) mode with constant flow pattern (square waveform) and a short post-inspiratory pause. As we discussed in the previous post, the inspiratory flow should be constant if the equation of motion has to be applied over steady state. If the patient is actively breathing, the respiratory rate can be set high to sneak in some fully assisted breaths (with zero Pmus). It is highly instructive to analyze the idealized waveform of this mode (figure 1) – 

Figure 1

At the end of inspiratory flow time, the pressure measured at the airway opening (Paw or Pao) is due to a combination of elastic and resistive load. This is designated as the peak inspiratory pressure (PIP). A brief post-inspiratory pause closes the inhalation valve while the exhalation valve remains closed. This results in a state of zero flow. Remember that when flow is zero, the resistive load would be zero. Hence, the Paw at this time is purely due to the elastic recoil of the respiratory system (lungs + chest wall). This is referred to as the plateau pressure (Pplat).

Calculation of elastance/compliance

Elastance of the respiratory system (ERS) is calculated as follows:

ERS = (Pplat – PEEP)/tidal volume

Compliance is the inverse of elastance

CRS = tidal volume/(Pplat – total PEEP)

It is important to note that it’s the total PEEP (set PEEP + auto-PEEP, if any) that should be used for this calculation. Accurate estimation of autoPEEP requires a dedicated, long expiratory pause (longer the better but at least 2-3 seconds).

How to measure Pplat correctly:

To maximize the clinical relevance of the measured Pplat, the duration of post inspiratory pause should be short (<=0.5 seconds). A longer inspiratory pause will cause a gradual decline in the measured Paw. This occurs due to the following reasons:[1]

  1. Practically speaking, perhaps the most common reason is the presence of micro leaks (e.g. from the endotracheal cuff).
  2. Redistribution of air between lung units (pendelluft)
  3. Slow tidal recruitment
  4. Viscoelastic nature of the lung causing ‘stress relaxation’

Due to the special clinical importance of Paw after a short inspiratory pause, it is sometimes given a special designation in literature: Pz (pressure at zero flow) or P1 – to contrast it with the traditional measure of Pplat after a long pause.

In mechanically ventilated patients, a compliance of >50 mL/cmH2O (>0.05 L/cmH2O) is considered acceptable.

Calculation of resistance:

A few theoretical considerations of measuring resistance.

  1. Expiratory resistance is normally higher than inspiratory resistance. However, this difference is accentuated in patients with expiratory flow limitation (e.g. COPD, asthma). Both inspiratory and expiratory resistances have a unique clinical significance. For estimating inspiratory load, it is the inspiratory resistance we are interested in. For assessing the tendency for expiratory flow limitation, the value of expiratory resistance is useful.
  2. Inspiratory resistance varies with the flow, especially in patients with small airway disease. E.g.: In patients with asthma, the inspiratory flow gets more turbulent at higher levels, thereby leading to a higher value of resistance for the same airway anatomy.[2]

Inspiratory resistance can be calculated as follows:

RI = (PIP – Pplat)/(constant) flow

The standard units of resistance are cmH2O/L/s. Hence, the flow has to be converted from L/min to L/sec for this calculation. The easiest way to do this is to set the flow at 60 L/min, which translates to 1 L/sec. Then the resistance is simply (PIP – Pplat)/1 = PIP – Pplat. While trending resistance, setting the flow at 60 L/min every time also avoids the possibility of the value being affected by a change in flow.

Normal value of inspiratory resistance: A value of <10 cmH2O/L/sec is considered normal. Some consider the range of 10 to 15 cmH2O/L/sec as the grey zone and >15 cmH2O/L/sec is definitely abnormal.

Now that you have a better understanding of elastic and resistive loads, can you predict what would happen to PIP and Pplat with an increase in elastic or resistive load? Can you visualize how that would change the waveform in figure 1? Check figure 2 for the answer.

Figure 2

Going Deeper

Although the calculation of inspiratory resistance always requires switching to VC with constant flow, plateau pressure (and compliance) can be measured in other modes as well. Irrespective of the mode, you can do a post-inspiratory pause to determine Pplat. There are certain nuances of measuring Pplat in pressure support mode, which is elegantly discussed here.[6]

In certain situations, you can estimate Pplat even without doing a manual pause. Remember, Pplat = Paw when inspiratory flow is zero. This is often the case at end-inspiration in VC with decelerating flow pattern (descending ramp); although, not all ventilators drop the flow to zero in this pattern. Also, if the I-time is long enough for the given respiratory mechanics in pressure-control (PC) mode, the inspiratory flow drops to zero at end-inspiration. In both of the aforementioned situations, end-inspiratory pressure (EIP) = Pplat (figure 3).

Figure 3

In PC, ideally EIP should equal PIP (which is set by the user). However, there is a caveat to this as well. In general, ventilators can control flow with absolute precision but they are not very good in controlling pressure. We often see a pressure overshoot at the beginning of the PC breath that drives the PIP higher than the set value. In this case, the PIP value listed on the ventilator cannot be used to determine Pplat (Pplat < PIP). Similarly, EIP is not equal to PIP in VC with decelerating ramp (figure 4).

Figure 4

The Debrief

  • Key formulas: Compliance of the respiratory system (CRS) = tidal volume/(Pplat – total PEEP)
  • Inspiratory resistance (RI) = (PIP – Pplat)/(constant) flow
  • The easiest way to assess both resistance and compliance simultaneously is VC-constant flow.
  • A constant flow pattern (square waveform) is a pre-requisite for the measurement of resistance.
  • A brief post-inspiratory pause (<0.5 seconds) provides the most clinically relevant estimate of plateau pressure.
  • Knowledge of the resistive and elastic loads has important diagnostic and therapeutic implications.


  1. Henderson WR, Chen L, Amato MBP, Brochard LJ. Fifty Years of Research in ARDS. Respiratory Mechanics in Acute Respiratory Distress Syndrome. Am J Respir Crit Care Med. 2017;196(7):822-833.
  2. Prezant DJ, Aldrich TK, Karpel JP, Park SS. Inspiratory flow dynamics during mechanical ventilation in patients with respiratory failure. Am Rev Respir Dis. 1990;142(6 Pt 1):1284-1287.
  3. Vyaire medical iX5™ Ventilator Operator’s Manual. Link: https://intl.vyaire.com/sites/default/files/2020-05/806-00535-i-ix5-4th-edition-op-manual-en_rev01_0.pdf
  4. Akoumianaki E, Kondili E, Georgopoulos D. Proportional-assist ventilation. Eur Respir Soc Monogr. 2012;55:97–115 (New developments in Mechanical Ventilation). DOI: 10.1183/1025448x.10001911
  5. Iotti GA, Braschi A, Brunner JX, et al. Respiratory mechanics by least squares fitting in mechanically ventilated patients: applications during paralysis and during pressure support ventilation. Intensive Care Med. 1995;21(5):406-413.
  6. Can we measure Plateau pressure during pressure support? And what does it indicate? Link: https://coemv.ca/can-we-measure-plateau-pressure-during-pressure-support-and-what-does-it-indicate/


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