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# (p. 335) Respiratory system compliance and resistance in the critically ill

Respiratory system compliance and resistance in the critically ill
Chapter:
Respiratory system compliance and resistance in the critically ill
DOI:
10.1093/med/9780199600830.003.0074
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date: 21 January 2022

## Key points

• Correct understanding of the relationship between pressure, volume, and flow is a basic requirement for correctly setting a ventilator.

• The lungs and chest wall both participate to global respiratory mechanics. In some situations, such as obesity or ARDS, the chest wall could explain a large part of the low compliance of the respiratory system.

• Resistance represents the ratio between the pressure dissipated by the friction of gas and the mean gas flow.

• Compliance denotes the capacity of the pulmonary system to expand and is calculated as ratio between volume and pressure.

• Intrinsic positive end expiratory pressure (PEEP) can be present with short expiratory time, high respiratory rate, or expiratory flow limitation in airway obstructive disease.

## Introduction

Acute respiratory failure is a common situation in patients admitted to intensive care units (ICU) and, in the most severe forms, mechanical ventilation (MV) is a life-saving support. MV can also be harmful and lead to ventilation-associated lung injury (VALI) [1]‌. VALI occurs mainly when pressures (barotrauma) and volumes (volutrauma) are not adapted to the specific respiratory conditions of the patient, which can be assessed by measurement of respiratory mechanics.

Impairment in pulmonary function is, in general, accompanied by changes in respiratory mechanics, especially during acute exacerbations of chronic obstructive pulmonary disease (COPD), asthma, or the acute respiratory distress syndrome (ARDS), situations that are associated with large changes in resistance (R) and compliance (C) of the respiratory system. An assessment of the respiratory mechanics is therefore necessary for correctly adapting the ventilatory settings. Monitoring the magnitude of these changes with time is also important because of their direct relationship with severity of disease. It can help defining prognosis and response to treatment [2,3].

In order to ventilate the patient appropriately, clinicians need to understand the relationship between pressure (P), volume (V), and flow ($V ˙$). To appreciate the risks associated with MV, one also needs to understand the partition between lungs and chest wall in terms of respiratory mechanics.

## Equation of motion of the respiratory system

To move air in and out the thorax, energy must be dissipated mostly against elastic (FEL) and resistive (FR) forces. A simple equation of motion describes the forces in the respiratory system (FRS):

$Display mathematics$
[eqn 1]

Any pressure applied is either stored as elastic pressure (PEL) or dissipated as resistive pressure (PRES). In some circumstances, another force can participate, the inertial force (FIN). Inertia can usually be neglected in the respiratory system, with rare exceptions such as coughing or high-frequency ventilation.

Elastance (E) relates P to V, and resistance relates P to ($V ˙$), so the equation of motion can be modified to explain how the pressure at the airway opening (PAW) can be partitioned into a resistive and an elastic pressure component:

$Display mathematics$
[eqn 2]

where (t) is a given time, P0 is the starting pressure in the respiratory system, and P0 represents the total positive end expiratory pressure (PEEPT).

## Methods of measurement

In passively mechanically-ventilated patients, it is easier to measure pulmonary mechanics during constant flow, volume-controlled ventilation (VCV) than during pressure-controlled ventilation (PCV). In an actively-breathing patient under MV, the total pressure is the sum of PAW and of the muscular pressure. Because the patient’s spontaneous breathing activity is usually not directly monitored, this greatly limits the ability to make these measurements at the bedside.

One simple, but essential manoeuvre involves stopping flow by occlusion at the end of the insufflation phase, allowing measurement of the plateau pressure (PPLAT), which represents the alveolar pressure at end-inspiration (PALV), as shown on Fig. 74.1.

Fig. 74.1 Ventilator screen image representing changes in airway pressure (PAW), flow, volume, and oesophageal pressure (PES) versus time; PPEAK inspiratory peak pressure, PPLAT plateau airway pressure, PPLAT(ES) plateau oesophageal pressure, P0 total PEEP at the airway pressure waveform, P0* total PEEP at the oesophageal pressure waveform, VT tidal volume.

Usually, P, V and $V ˙$are directly measured by the ventilator; V is calculated as the integral of inspiratory flow tracing over time. There are several technological limitations with the calculation of V [4]‌.

## Resistance and flow

### Definition

Resistance (R) represents the ratio between the pressure dissipated and the mean gas flow ($V ˙$). The resistance of the respiratory system (RRS) is a purely dynamic force caused by the movement of molecules and the friction between them, and against the tracheobronchial tree and the endotracheal tube (ETT), and, to a smaller extent, to the resistance to parenchyma deformation.

### Measurement

In a situation of constant flow, RRS can be calculated as:

$Display mathematics$
[eqn 3]

Because flow is constant, one can approximate that this value of RRS is constant during the whole insufflation. Such an assumption cannot be made if ($V ˙$) is not constant during insufflation, such as during PCV. The resistive pressure (PRES) reflects the energy lost to overcome FR, which is usually mainly situated in the upper or proximal airways, including the ETT. As a consequence, PRES disappears before reaching the deep lung and is not present in alveoli.

PRES gives insight about the conducting airways and tells the clinician which part of PAW is not transmitted to the alveoli and does not contribute to a risk of VALI. PRES is, by definition, dependent on flow. RRS can also increase with flow when it changes from laminar to partially or fully turbulent. The pressure and flow relationship is curvilinear as it is the case in endotracheal tubes [5]‌. In other words, small changes in flow can induce large changes in PRES.

There are many other methods to calculate resistance, but the end-inspiratory occlusion method described here is the simplest.

### Flow

In the lung, flow can change from purely laminar with little friction, to fully turbulent with instabilities, large frictional forces and high pressure dissipation. In ETT and in upper airways flow is mostly turbulent, whereas laminar flow predominates in the more distant and small airways.

According to Hagen–Poiseuille’s Law during laminar flow, R is directly related to airway length (L), gas viscosity (η‎) and inversely proportional to tube radius to the fourth power:

$Display mathematics$
[eqn 4]

where Π‎ is a mathematical constant.

### Clinical implications

To avoid excessive FR and, subsequently energy loss, an adequately-sized ETT is important. In severe obstructive lung disease a mixture of helium and oxygen has a decreased density, reducing the resistance of the airway [6]‌. In a healthy individual adult under MV using a square flow set at 60 L/min (or 1 L/sec), RRS is usually less than 10 cmH2O/L/sec and rarely exceeds 15 cmH2O/L/sec. During acute exacerbation of COPD or asthma, RRS can increase up to 20 cmH2O/L/sec or 40 cmH2O/L/sec in the most severe forms of bronchospasm. During MV, a sudden augmentation in PPEAK without an increase in PPLAT indicates an abrupt increase in PRES and in RRS; the most common reasons like tube kinking, mucus clotting in the airway or bronchospasm can be readily identified and treated after visualizing the increase of PRES on the PAW curve.

Resistance is a dynamic force, acting only when flow is present. During constant flow VCV the same amount of PRES is present during the whole insufflation. During PCV, the major part of PRES is dissipated at the beginning of the breath due to the decelerating flow pattern. Because flow is decelerating, PRES progressively decreases along insufflation and PPEAK becomes close to PPLAT. PPEAK equals PPLAT only when flow has reached zero at the end of insufflation. So in many instances, PPEAK during PCV remains higher than the true PPLAT.

### Flow–volume curves

The effects of airway resistance can be visualized on dynamic flow–volume curves (during inspiration and expiration). Analysis of this curve may be useful for identifying different clinical situations (Fig. 74.2) [7]‌.

Fig. 74.2 Flow volume curves in different situations. (a) Normal patient; (b) COPD patient with dynamic hyperinflation and auto-PEEP, and after bronchodilator treatment; (c) sudden interruption of exhalation flow representing an important gas leak from the patient (bronchopleural fistulae) or from the ventilator circuit; (d) a saw-tooth pattern is observed in both inspiratory and expiratory limbs and indicate presence of secretions in the airways.

## Elastance (e) and compliance (c)

### Definition

The elastance of the respiratory system (ERS) reflects the capacity of the pulmonary system to return to its resting position and measure the recoil pressure over a given volume. Since E = 1/C, the compliance of the respiratory system (CRS) denotes the capacity of the pulmonary system to expand. Traditionally, CRS has been used to assess the severity of ARDS [8,9].

### Measurement

Compliance (C) can be defined as the change in volume (Δ‎V) per unit of change in applied pressure (Δ‎P):

$Display mathematics$
[eqn 5] When applying an end-inspiratory occlusion or pause, there is no movement of gas (i.e. no resistive pressure) and the elastic properties can be calculated by these static (or quasi-static) measurements. The static compliance of the respiratory system (CSTAT(RS)) can be calculated as:

$Display mathematics$
[eqn 6]

During MV, P0 is the total PEEP, which is the sum of extrinsic positive end expiratory pressure (PEEPE) set on the ventilator and intrinsic PEEP above it (PEEPI or auto-PEEP). The latter can be present during short expiratory times (e.g., inverted I/E ratio ventilation), high respiratory rate with fixed inspiratory time, or in expiratory flow limitation (COPD, asthma, cardiogenic pulmonary oedema, ARDS) where alveoli have prolonged and delayed emptying due to their mechanical characteristics or collapse of the small airways, trapping residual gas inside the alveoli. It can be measured with an occlusion manoeuvre at the end of the expiratory phase under controlled MV (Fig. 74.3). PEEPI and PEEPE must be taken into account when measuring P0 with eqn 2. CRS and the equation of motion should be written as:

Fig. 74.3 The occurrence of intrinsic PEEP can be observed on the screen of the ventilator from a patient with obstructive lung disease. (a) Airway pressure waveform with an expiratory pause showing the existence of PEEPI (or auto-PEEP). (b) Flow curve demonstrating the failure to exhale all gas during the expiratory time and, consequently, formation of gas trapping.

$Display mathematics$
[eqn 7]

$Display mathematics$
[eqn 8]

## Pressure–volume curve

CRS can vary with lung volume. It is analysed over the whole lung volume by plotting static pressure values over a large volume ranges, e.g. from functional residual capacity (FRC) to total lung capacity (TLC), with construction of a pressure–volume (P/V) curve [10,11,12] (Fig. 74.4). The slope of this curve represents the CRS and is not constant over lung volume. The patient must be passive for accurate results, though paralysis is not always mandatory [13].

Fig. 74.4 Pressure–volume curves (P/V) and its hysteresis. (a) P/V curve from a normal patient. (b) P/V curve from an ARDS patient.

FRC, functional residual capacity; TLC, total lung capacity.

The P/V curve of the respiratory system depends on both compliance of the chest wall (CCW) and the lung (CL). The latter depends primarily on the aerated lung volume available to ventilation.

Information from the shape and the different values of the P/V curve can be extrapolated to the clinical condition of a mechanically ventilated patient [11]. The first part of the P/V curve (starting from FRC) in patients with ARDS often has a relatively flat shape with a low CRS due to a collapsed lung. In this phase, a larger change in PAW is necessary to produce a small change in volume. In the second part, part of the lung has been reopened and/or is reopening, and CRS becomes higher with a more linear curve. It indicates a region where the work of breathing is lower. Finally, the upper section of the P/V curve shows a lower CRS reflecting that the lung has been reopened and possibly overdistended [14].

The lower inflection point (LIP) and upper inflection point (UIP) represent a separation of the different parts. Schematically in ARDS, the LIP represents the beginning of substantial recruitment, while the majority of recruitment has already occurred at the UIP. In reality, alveolar recruitment occurs all over the curve [15].

The P/V curve can also be drawn during the expiratory phase of ventilation, better reflecting the closing pressures and more useful when setting PEEP, but being more complex to analyse.

The different slopes of the P/V curve between inspiration and expiration generate an area called hysteresis. P/V curve with a large hysteresis could represent a potential for alveolar recruitment, especially at the early stage of ARDS [11].

### Partition of the respiratory system elastance/compliance

The ERS represents the sum of the effects of the lung (EL) and of the chest wall elastance (ECW):

$Display mathematics$
[eqn 9]

Usually, the chest wall has a modest influence and more than 80% of the pressure is generated by the lungs. In several situations (e.g. obesity, highly oedematous patients, large pleural effusions, increased intra-abdominal pressure, ARDS) the differentiation of the sources of elastance is important. If ECW is high compared with EL, then a large part of the elastic pressure will be used to distend the chest wall and much less than the total PAW to expand and distend the lung. Interpretation of the PAW in terms of risk of VALI then differs.

The pleural pressure (PPL) has to be estimated to calculate CCW, and in critical practice this is done using oesophageal catheters with a balloon that measure oesophageal pressure (PES) (Figs 74.1 and 74.5) [16]. PES is a very useful substitute in determining PPL, although there are some controversies about its absolute value. The CCW can be calculated with the following equation:

Fig. 74.5 The main different pressures involved in pulmonary mechanics.

PABD, intra-abdominal pressure; PATM, atmospheric pressure; PALV, alveolar pressure; PAW, airway pressure; PAWO, opening airway pressure; PBS, body surface pressure; PES, oesophageal pressure; PPL, pleural pressure; PPLAT, plateau pressure. Transpulmonary pressure (PL) is the difference between PAW and PES.

$Display mathematics$
[eqn 10]

PPLAT(ES) is the end-inspiratory plateau pressure and P0 the starting pressure both measured on the oesophageal pressure.

Transpulmonary pressure is the difference between PAW and PES = PL. It represents the force really distending the lung parenchyma. Elastance or compliance of the lung can then be easily obtained as:

$Display mathematics$
[eqn 11]

### Clinical implications

The normal CSTAT(RS) in a patient depends first on the size of the lung and, therefore, of the height of the patient (and age for children). Volumes are preferentially expressed in mL/kg of predicted body weight reflecting the height rather than the current weight of the patient [17].

Because compliance has a direct relationship with the lung volume available for ventilation, loss of lung volume (e.g. during atelectasis, pneumonia or pulmonary oedema) will cause a proportional drop in compliance. The concept of ‘baby lung’, introduced in the middle of 1980s showed that, in most ARDS patients, the normally aerated tissue represents only a small proportion of the whole lung, explaining why CSTAT(RS) is low, and CRS is proportional to the size of the ‘baby lung’ (amount of normally aerated tissue) [18]. FRC, representing the amount of lung aerated at end expiration, is much smaller in ARDS patients than in patients with normal lungs [19]. In other words, C and E changes do reflect the amount of aerated lung volume available, which indirectly reflects the severity of the ARDS process in the whole lung. It is an important indication of the volume that can be safely delivered to the remaining lung and the risks of ventilation in terms of VALI.

In mechanically-ventilated adults in the supine position, CSTAT(RS) is frequently lower than in erect healthy subjects, often in a range of 40–70 mL/cmH2O. When it becomes lower than 25 mL/cmH2O, like in severe ARDS patients, the work of breathing can be 4–6-fold increased, and the total energy dissipated becomes much greater.

The specific elastance is the ratio of elastance to FRC. The concept of specific lung elastance reflects the ratio between the transpulmonary pressure (stress) and the change in lung volume relative to its resting volume during respiration (strain). Specific lung elastance was shown to be constant among patients with ARDS and healthy subjects [20], suggesting that the measurement of FRC could be used to evaluate the change in transpulmonary pressure induced by tidal volume. Therefore, monitoring these parameters could potentially be used to better set MV and avoid VALI [3]‌.

## Conclusion

Understanding the relationship between P, V, and $V ˙$ as well as the concepts of R and C makes understanding of ventilation much easier, as well as the interpretation of the changes of pressure and flow traces on the ventilator screen. This knowledge helps the clinician to decide for the best treatment option.

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