46 Respiratory System Mechanics and Respiratory Muscle Function

Classic respiratory mechanics are based on Newtonian physics, as expressed in the equation of motion. The respiratory system model is derived from an elementary monodimensional system, as depicted by a block with an attached spring, acted on by a unidirectional force (Figure 46-1, *A*).^{1,}^{2} Upon application of force, the response of the system can be characterized in terms of displacement, velocity, and acceleration of a block with a mass of M. The balance of forces acting on the block can be expressed as follows:

Figure 46-1 Mechanical analogs of the equation of motion. **A,** System with unidirectional motion. **B,** Three-dimensional system.

*(From Rodarte JR, Rehder K. Dynamics of respiration. In: Macklem PT, Mead J, editors.* Handbook of Physiology*. Baltimore: Williams & Wilkins; 1986:131-144.)*

where the total force applied to the system (F_{appl}) at a given time (t) is equal to the sum of the elastic (F_{el}), resistive (F_{res}), and inertial (F_{in}) forces.

The equation of motion for a three-dimensional pneumatic system may be written as:

where *P _{(t)}* is the pressure exerted on the system at a given time;

*E*is the elastance (the reciprocal of compliance, i.e., 1/C), which relates pressure to volume (V), and

*R*is the resistance constant, relating pressure to flow. The third term of the equation describes the pressure required to accelerate tissue and gas in the airway, which is an important factor under certain circumstances such as coughing or high-frequency oscillatory ventilation. The inertance constant (I) relates pressure to linear acceleration (). However, the third term is usually omitted in this model of the respiratory system, because inertive forces are negligible during quiet breathing and most forms of mechanical ventilation.

^{3}Thus, in most applications, the respiratory system derivative of the equation of motion considers only the elastic and flow-resistive elements that oppose an applied pressure at time (t):

which may also be expressed as:

In this model, any force applied to the respiratory system is either stored as elastic energy or dissipated as resistive energy. Figure 46-1, *B* shows a three-dimensional model of the respiratory system as it relates to the equation of motion.

# Static Behavior of the Respiratory System

An esophageal balloon catheter can be used to approximate pleural pressure, keeping in mind that pleural pressure is nonuniform and that topographic gradients in pleural pressure vary with posture.^{4} In the recumbent posture, there is no site in the esophagus at which local pressure approximates average lung surface pressure (i.e., average pleural pressure). However, at least in normal lungs, the average change in surface or pleural pressure can be inferred using esophageal manometry.

By assuming that P_{bs} is considered to be zero:

The static respiratory system pressure-volume (P-V) curve is often measured in intubated, mechanically ventilated patients to make inferences about the mechanical properties of the lungs. Although the utility of P-V measurements in clinical decision making remains to be established, the determinants of the P-V relationship should nevertheless be understood. The P-V curve is generated by inflating and deflating the relaxed respiratory system in a stepwise fashion between residual volume and total lung capacity. The airway occlusion pressure at each volume defines the corresponding elastic recoil pressures of the lungs and chest wall. Because the inflation and deflation relationships differ from each other, the resulting curve is often referred to as a *P-V loop*. The respiratory system P-V loop is the summation of individual lung and chest wall P-V loops, termed a *Rahn diagram* (Figure 46-2). Because during normal tidal volume breathing (30% to 70% vital capacity), the relationship between elastic pressure and volume is essentially linear, the system’s elastic properties can be defined by a constant, namely *elastance.* The term *compliance* is more frequently used and is simply the inverse of elastance, defined as the change in volume per unit change in applied pressure. Static respiratory system compliance can be determined by the slope of the P-V curve. In the quiet breathing range, the normal respiratory system elastance averages 8 to10 cm H_{2}O/L, corresponding to a static respiratory system compliance of 0.12 to 0.1 L/cm H_{2}O.

Figure 46-2 Pressure-volume (P-V) loop (Rahn diagram) of the respiratory system (rs), and summation of individual chest wall (W) and lung (L) loops. During normal tidal volume breathing (30%–70% vital capacity), the relationship between elastic pressure and volume is essentially linear. VC, vital capacity.

*(From Agostoni E, Hyatt RE. Static behavior of the respiratory system. In: Fishman AP, editor.* Handbook of Physiology*. Baltimore: Williams & Wilkins; 1986:113-130.)*

Figure 46-2 shows the P-V curves of the respiratory system’s component structures, the lung and chest wall. At high lung volumes, the total respiratory system compliance is reduced (the P-V curve is concave to the pressure axis), primarily because the lung reaches total capacity, its structural limit. In contrast, the P-V curve of the chest wall remains linear at high volumes (i.e., the chest wall offers much less resistance to further lung expansion).

At low lung volumes, a decrease in chest wall compliance is the major contributor to low respiratory system compliance. At relaxation volume (functional residual capacity), the inward recoil of the lung is equal to the outward recoil of the chest wall, so that alveolar pressure is atmospheric. At a volume of 60% of vital capacity, the chest wall reaches a “resting” position, that is, it exerts no force on the lungs, and the pleural pressure is atmospheric. In the normal tidal breathing range, the slopes of the lung and chest wall P-V curves are similar (i.e., lung and chest wall contribute about equally to overall respiratory system compliance). Figure 46-3 shows the volume dependence of the inwardly and outwardly directed forces of the respiratory system during inflation.^{4}

Figure 46-3 Static pressure-volume curves of the chest wall (P_{w}), lungs (P_{L}), and respiratory system (P_{rs}). Drawings of the thorax *(left to right)* at residual volume, functional residual capacity, resting position (no force exerted by the chest wall), and total lung capacity. Arrows indicate direction of elastic recoil. VC, vital capacity.

*(From Agostoni E, Hyatt RE. Static behavior of the respiratory system. In: Fishman AP, editor.* Handbook of Physiology*. Baltimore: Williams & Wilkins; 1986:113-130.)*

Surface forces (i.e., surface tension) are generated because liquid molecules in contact with air attempt to conserve energy by decreasing the area available for interaction. In the lung, the resulting force acts parallel to the alveolar septa and balances a helical fiber network that supports alveolar ducts and forms alveolar entrance rings.^{6}

As demonstrated in Figure 46-4, the elimination of surface tension has two important consequences on lung mechanics^{7}:

Figure 46-4 Plot of airway–atmospheric pressure gradient for an isolated lung inflated with air *(purple line)* and saline *(red line)*. Reduction in surface tension in the saline-filled lung results in increased compliance.

*(From Taylor A, Rehder K, Hyatt R, et al. Mechanics of breathing: static. In: Taylor AE, editor.* Clinical Respiratory Physiology*. Philadelphia: Saunders; 1989:89-105.)*

In the normal lung, hysteresis is caused by volume- and time-dependent changes in the molecular composition and hence the biophysical properties of surfactant. *Surfactant* is a protein-enriched lipid film that coats air-liquid interfaces in distal lung units and lowers surface tension. *Hysteresis* implies that energy added to the system during inflation is not fully recovered during deflation. The hysteretic loss of energy does not scale with frequency and flow the way a Newtonian viscous resistance does, underscoring one of the many limitations of linear resistance-compliance circuits in modeling lung mechanics.^{8} Whereas interfacial phenomena are the primary source of hysteresis in the normal lung, alveolar recruitment and derecruitment are important sources of hysteresis in disease.

Applied to the lung, this means that changes in alveolar dimensions at low lung volumes would promote alveolar collapse were it not for surfactant’s surface tension–lowering properties. A surfactant-depleted lung exhibits alveolar instability and collapse in the tidal breathing range. In normal pigs, high-tidal-volume ventilation does not alter alveolar mechanics in the normal lung; however, in the surfactant-deactivated lung, it causes alveolar overdistension and exacerbates alveolar instability.^{9} Figure 46-5 shows a pressure-volume loop of a normal lung and a surfactant-depleted lung. As a consequence of surfactant depletion, larger than normal transpulmonary pressures are required to keep the surfactant-depleted lung inflated.

Figure 46-5 Pressure-volume loop of a normal lung *(solid line)* and a surfactant-depleted lung *(dashed line)*. Larger than normal transpulmonary pressures are required to keep the surfactant-depleted lung inflated. TLC, total lung capacity.

*(From Taylor A, Rehder K, Hyatt R, et al. Mechanics of breathing: static. In: Taylor AE, editor.* Clinical Respiratory Physiology*. Philadelphia: Saunders; 1989:89-105.)*

# Dynamic Behavior of the Respiratory System

According to Ohm’s law, resistance (R) can be calculated by dividing the driving pressure by flow:

Total pulmonary resistance reflects the gas flow–dependent pressure dissipation in the conducting airways (airway resistance) and the frequency-dependent loss of energy associated with parenchymal deformation (tissue resistance). Originally considered only a minor component of total pulmonary resistance, it is now appreciated that the so-called tissue resistance dominates the measurement, at least at low frequencies.^{10} As outlined by Fredberg and Stamenovic,^{8} tissue resistance and tissue hysteretic properties are model-specific descriptors of energy loss, the structural and molecular basis of which remains uncertain.^{11}

These determinants can be captured by *Reynold’s number*, a quantity that represents the ratio of inertial forces to viscous forces.^{12} A low Reynold’s number (<50) corresponds to laminar flow, and a Reynold’s number greater than 2300 is associated with turbulent flow. Accordingly, the low gas velocity in peripheral airways favors laminar flow, and the acceleration associated with the decrease in total cross-sectional area in central airways promotes turbulence.

where Δ*P* is the pressure drop, *L* is the length of pipe, *µ* is the dynamic viscosity, *Q* is the volumetric flow rate, *r* is the radius, and *π* is the mathematical constant (approximately 3.141592654). In contrast, turbulent flow is associated with nonlinear pressure-flow relationships that are gas-density dependent. The density dependence of turbulent flow is occasionally exploited in the medical use of heliox, a low-density helium-oxygen mixture given to patients with central airway lesions or asthma.^{13} However, the available clinical data on inhaled He/O_{2} mixtures are insufficient to prove that this therapy has benefit with respect to outcome variables.^{14}

The flow-dependent shift from laminar to turbulent flow is captured in the *Rohrer* equation:

where *K _{1}* and

*K*are constants that scale frictional pressure dissipation associated with laminar and turbulent flow, respectively.

_{2}A second mechanism of pressure loss during gas flow is related to the *Bernoulli principle*, which describes convective pressure dissipation. That is, as a gas flows from a large cross-sectional area to a smaller area, velocity must increase to maintain flow. This results in energy dissipation and a drop in pressure and correlates to expiratory flow of gas from the bronchioles to the central airways. As mentioned previously, *ohmic resistance* can be computed by dividing resistive pressure by inspiratory flow (see Equation 13).

The respiratory time constant (τ) is the time required for the lung to fill or passively discharge approximately 63% of its contents. It can be determined from the slope of the passive expiratory flow-volume curve (Figure 46-6) or calculated directly by the equation:

Figure 46-6 Flow-volume curve. The expiratory time constant (τ) is equal to the slope of the expiratory limb. flow; V_{RS}, volume of respiratory system.

*(From Loring SH. Mechanics of the lung and chest wall. In: Marini JJ, Slutsky AS, editors.* Physiological Basis of Ventilatory Support. *New York: Marcel Dekker; 1998:177-205.)*

where *τ* is usually measured in seconds because respiratory system resistance (R_{rs}) is expressed in units of pressure × time × volume^{−1}, and respiratory system compliance (C_{rs}) is expressed in units of volume × pressure^{−1}.

The value of τ for a normal respiratory system is approximately 0.3 second.^{3} As can be inferred from the equation, patients with high respiratory system resistance or compliance, such as those with chronic obstructive lung disease (COPD), have correspondingly large τ values.

The added resistance of the artificial tubing in a mechanically ventilated patient may increase τ to 1 second or more. In addition, in patients with even minimally elevated τ values, the expiratory time (depending on the preset inspiratory time in time cycled ventilatory support or from the expiratory threshold in a flow cycled ventilatory mode^{15}) may not be enough to fully empty the lungs during mechanical ventilation. Consequently, the demand for expiratory flow is not met as the lungs near relaxation volume, resulting in dynamic hyperinflation even in healthy lungs at high rates of respiratory frequency.

Another important concept that explains the dynamic behavior of the respiratory system is shown in Figure 46-7. Higher lung volumes (curve A) yield higher expiratory flow rates compared with the flow seen at lower lung volumes (curve C). In a classic set of experiments performed on normal subjects, Fry and Hyatt demonstrated that maximal expiratory flow is determined by lung volume.^{16} They concluded that on the basis of volume-related dynamic airway collapse, expiratory flow plateau cannot be exceeded irrespective of the magnitude of subject effort or applied transpulmonary pressure. Herein lies the value of the forced vital capacity maneuver as a reproducible measure of maximal expiratory flow.

Figure 46-7 *Left*, maximal expiratory flow-volume curve. *Right*, three isovolume pressure-flow curves at different lung volumes (A, B, C). Left side of figure shows an expiratory flow-volume plot for a normal subject, similar to that generated by a forced vital capacity maneuver in the pulmonary function lab. Right side of figure shows three driving pressure-flow curves at progressively smaller lung volumes from A to C. Curves are nonlinear, and each has a driving pressure–dependent and –independent limb separated by the critical driving pressure. Note flow limitation associated with submaximal lung volumes B and C. TLC, total lung capacity.

*(From Hyatt RE. Forced expiration. In: Macklem PT, Mead J, editors.* Handbook of Physiology*. Baltimore: Williams & Wilkins; 1986:295-314.)*

# Assessment of Respiratory System Mechanics in the Intensive Care Unit

Assuming constant flow in a relaxed or paralyzed patient without respiratory muscle contribution, pressure at the ventilator inlet increases linearly with time and volume to a peak. A typical simplified waveform output is demonstrated by Figure 46-8, with a model of the system represented on the right. Pressures are measured at the ventilator inlet or at the airway opening at the level of the “Y” connection. Assuming inflation onset with a constant (square wave) flow, an initial step change in driving pressure is recorded, which precedes alveolar filling and corresponds to resistive pressure related to gas flow in the airways (see Figure 46-8, *dotted arrow*). When making an end-inspiration airway occlusion after a rapid initial step-off in resistive pressure drop (Pmax–P1), there is then a gradual decrease in pressure to a plateau value (P2) (see Figure 46-8, *full thick arrows*). This pressure, usually reached after 3 seconds of end-inspiratory occlusion, indicates the true static end-inspiratory elastic recoil pressure of the total respiratory system (P_{st,rs})^{17}^{–}^{18} and represents the static summation of elastic recoil forces corresponding to the applied tidal volume. During this period, the contribution in reduction in pressure due to volume loss by continuing gas exchange should be negligible.

Figure 46-8 Airway pressure and flow wave patterns during volume-preset mechanical ventilation. After an end-inspiratory airway occlusion, there is an immediate drop in pressure from Pmax to P1, followed by a slow decay to a plateau value (P2) that represents static elastic recoil pressure (Pst,_{rs}) at end-inspiratory lung volume. Increasing inspiratory flow also determines an increase in Pmax to P1; difference due to an increase in “ohmic “airway resistance (R_{min,rs}).

*(Modified from D’Angelo E, Calderini E, Torri G, et al. Respiratory mechanics in anesthetized paralyzed humans: effects of flow, volume, and time.* J Appl Physiol*. 1989;67[6]:2556-64.)*

The initial drop in Pmax, namely P1 divided by the preceding steady flow, provides the so-called ohmic resistances (Rmin,rs). Rmin,rs increases linearly with flow according to the Rohrer equation. The slow decrease of pressure (P1 − P2) divided by the preceding steady flow yields the effective additional resistance (ΔRs) due to the viscoelastic properties of the thoracic tissues and time constant inequalities within the lung and the chest wall (so-called pendelluft).^{19} The sum of Rmin,rs and ΔRs is defined as *Rmax.rs*.^{20} In a mechanically ventilated patient, where endotracheal tube resistance dominates measured total respiratory system resistance, the derived value of respiratory resistance must be interpreted with caution.

where *dP* = change in pressure; *dt* = change in time; and *dV* = change in volume.

where *PEEP* is the set end-expiratory positive pressure and *PEEPi* the intrinsic PEEP (see below).

and the chest wall:

For example, if the elastance of the chest wall is twice that of the lung, then two-thirds of P_{rs} is used to distend the chest wall and only one-third to inflate the lung.^{21} Of note, the chest wall in this context comprises not only the thoracic rib cage but also the abdomen.

Compliance of the respiratory system can be also measured by the super syringe method. This method for static P-V curve recordings has been associated with spurious changes in lung volume because of gas absorption during measurement.^{22} There are also issues related to user interpretation (e.g., difficulties in defining morphologic characteristics of the curve), and interobserver variability is often high.^{23,}^{24} Some have advocated inductive machine learning in an attempt to standardize interpretation.^{25}