3.1 Respiratory Mechanics, Lung Volumes, and Work of Breathing

3.1 Respiratory Mechanics, Lung Volumes, and Work of Breathing

Mastery of respiratory mechanics is essential for managing positive pressure ventilation, predicting perioperative gas exchange failure, and preventing ventilator-induced lung injury (VILI). This section examines lung volumes, compliance, airway resistance, and surfactant biophysics.

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1. Static and Dynamic Lung Volumes and Capacities

Lung volumes are partitioned into four discrete primary volumes and four composite capacities (combinations of two or more primary volumes). Standard physiological values apply to a healthy $70\text{ kg}$ adult male.

                  [ TOTAL LUNG CAPACITY (TLC ~6.0 L) ]
  +-------------------------------------------------------------------+
  |  Inspiratory Reserve Volume (IRV ~3.0 L)                         |
  |                                                                   |
  +---------------------------------+---------------------------------+
  |  Tidal Volume (TV ~0.5 L)       |  Inspiratory Capacity           |
  +---------------------------------+  (IC = TV + IRV ~3.5 L)         |
  |  Expiratory Reserve Vol (~1.1 L)|                                 |
  +---------------------------------+---------------------------------+
  |  Residual Volume (RV ~1.2 L)    |  Functional Residual Capacity   |
  |  (Cannot be exhaled)            |  (FRC = ERV + RV ~2.4 L)         |
  +---------------------------------+---------------------------------+
  [ VITAL CAPACITY (VC = IRV + TV + ERV ~4.6 L) ]

Primary Lung Volumes

• Tidal Volume ($V_T$ or TV): Volume of gas inspired or expired during quiet, normal breathing ($500\text{ mL}$ or $6-8\text{ mL/kg}$ ideal body weight).
• Inspiratory Reserve Volume (IRV): Maximal additional volume of gas inspired from the end of a normal tidal inspiration (approximately $2.5-3.0\text{ L}$).
• Expiratory Reserve Volume (ERV): Maximal volume of gas that can be actively exhaled after the end of a resting tidal expiration (approximately $1.0-1.2\text{ L}$).
• Residual Volume (RV): Volume of gas remaining in the lungs after a maximal forced expiration (approximately $1.2\text{ L}$ or $15-20\text{ mL/kg}$). RV is determined by the balance between expiratory muscle effort and dynamic airway compression/chest wall rigidity.

Composite Lung Capacities

• Functional Residual Capacity (FRC): Gas volume remaining in the lungs at the end of a passive tidal expiration ($FRC = ERV + RV \approx 2.4\text{ L}$ or $\approx 30\text{ mL/kg}$). At FRC, the inward elastic recoil of the lungs exactly balances the outward elastic recoil of the chest wall (the resting equilibrium position of the respiratory system).
• Inspiratory Capacity (IC): Maximal volume inspired from the resting end-expiratory level ($IC = V_T + IRV \approx 3.5\text{ L}$).
• Vital Capacity (VC): Maximal volume of gas exhaled after a maximal inspiration ($VC = IRV + V_T + ERV \approx 4.5-4.8\text{ L}$ or $60-70\text{ mL/kg}$).
• Total Lung Capacity (TLC): Total volume of gas contained in the lungs at maximal inspiration ($TLC = VC + RV \approx 6.0\text{ L}$). Determined by the balance between inspiratory muscle force and the inward recoil of the lung and chest wall.

Measurement Principles and Limitations of Spirometry

Spirometry records the movement of gas into and out of the lungs over time. Consequently, spirometry can measure only mobilizable gas volumes ($V_T$, IRV, ERV, IC, and VC).

Critical Examination Distinction: Spirometry cannot measure any volume or capacity that contains the Residual Volume ($RV$, $FRC$, and $TLC$). To measure these absolute thoracic volumes, three specialized techniques are utilized:

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2. Functional Residual Capacity (FRC) and Closing Capacity (CC)

The Physiology of FRC

At FRC, the respiratory system is in static equilibrium: alveolar pressure ($P_A$) is zero relative to atmospheric pressure, and the outward spring of the thoracic cage matches the inward collapse tendency of the alveolar elastic fibers. Under normal conditions, intrapleural pressure ($P_{pl}$) at FRC is negative, averaging $\approx -5\text{ cmH}_2\text{O}$.

          [ CHEST WALL ]                 [ LUNG TISSUE ]
       Outward Elastic Recoil         Inward Elastic Recoil
               <===                            ===>
                 \                              /
                  \-- Intrapleural Space (~ -5 cmH2O) -/
                                    |
                         [ FRC Equilibrium Point ]

FRC functions as an essential oxygen buffer. Because pulmonary capillary blood flow is continuous across the entire cardiac cycle, alveolar oxygen stored in the FRC sustains systemic arterial oxygenation during the expiratory pause and prevents arterial desaturation during periods of transient apnea (e.g. tracheal intubation).

Factors Reducing FRC

1. Body Position: Moving from the upright to the supine position shifts the abdominal viscera cephalad against the diaphragm, reducing FRC by $0.5\text{ to }1.0\text{ L}$ (a $\approx 25-30\%$ reduction, primarily at the expense of ERV).
2. General Anaesthesia: Induction of general anaesthesia (whether via volatile or intravenous agents) eliminates diaphragmatic and intercostal muscle tone. Within minutes of induction, the diaphragm shifts cephalad by $\approx 2\text{ cm}$, reducing FRC by an additional $15\%\text{ to }20\%$ (roughly $400-500\text{ mL}$ in adults), regardless of whether spontaneous or mechanical ventilation is used.
3. Body Mass Index: In obesity, excess adipose tissue on the chest wall and abdomen decreases chest wall compliance, markedly reducing ERV and FRC.
4. Pregnancy: By the third trimester, the gravid uterus elevates the diaphragm, reducing FRC by $20-25\%$ while metabolic oxygen consumption increases by $30-40\%$, accelerating hypoxemic desaturation during induction.
5. Surgical Interventions: Steep Trendelenburg positioning, peritoneal insufflation with $\text{CO}_2$ (laparoscopic pneumoperitoneum), and upper abdominal surgical packs/retractors directly displace the diaphragm cephalad, precipitating severe FRC loss.

Closing Volume (CV) and Closing Capacity (CC)

Small peripheral conducting airways (diameter $<1\text{ mm}$) lack cartilaginous support and depend entirely on radial traction exerted by surrounding alveolar elastic tissue to maintain patency. During forced exhalation, intrapleural pressure becomes positive, compressing peripheral airways.

• Closing Volume (CV): The volume of gas exhaled between the onset of small airway closure in dependent lung bases and the end of a maximal expiration.
• Closing Capacity (CC): The absolute volume of gas in the lungs at which airway closure begins: $CC = CV + RV$.

Closing Capacity versus FRC Relationships:

• Erect Young Adult: $FRC \gg CC$. Airway closure occurs only near the very end of maximal expiration.
• Supine at Age $\approx 44$ Years: Due to age-dependent loss of lung elastic recoil and the gravity-dependent cephalad diaphragmatic shift, CC equals FRC in the supine position.
• Erect at Age $\approx 65$ Years: CC equals FRC in the upright position.
• Under Anaesthesia: When FRC falls below CC ($FRC < CC$), small dependent airways close during normal tidal breathing. Alveolar gas distal to collapsed airways is absorbed into the pulmonary circulation, causing compression and absorption atelectasis, intrapulmonary shunt, and arterial hypoxemia.

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3. Compliance and Elastance of the Respiratory System

Definitions and Physical Principles

• Elastance ($E$): The measure of the elastic resistance to deformation, defined as change in pressure per unit change in volume: $E = \frac{\Delta P}{\Delta V}$.
• Compliance ($C$): The measure of distensibility, defined as the volume change per unit change in distending pressure: $C = \frac{\Delta V}{\Delta P} = \frac{1}{E}$.

The total respiratory system consists of two elastic structures arranged in series: the lungs and the chest wall. Because pressures are additive ($P_{\text{total}} = P_{\text{lung}} + P_{\text{chest}}$), their elastances add directly, and their compliances add as reciprocals:

$\frac{1}{C_{\text{total}}} = \frac{1}{C_{\text{lung}}} + \frac{1}{C_{\text{chest}}}$

In a conscious, healthy adult: $C_{\text{lung}} \approx 200\text{ mL/cmH}_2\text{O}$ and $C_{\text{chest}} \approx 200\text{ mL/cmH}_2\text{O}$. Therefore:

$\frac{1}{C_{\text{total}}} = \frac{1}{200} + \frac{1}{200} = \frac{2}{200} \implies C_{\text{total}} \approx 100\text{ mL/cmH}_2\text{O}$

Under general anaesthesia and endotracheal intubation, normal static respiratory system compliance declines to approximately $50-70\text{ mL/cmH}_2\text{O}$.

Static vs Dynamic Compliance

  Pressure
     ^
     |         /\ Peak Inspiratory Pressure (Ppeak)
     |        /  \________________
     |       /    |              | Plateau Pressure (Pplat)
     |      /     | Dynamic      |
     |     /      | Compliance   | Static Compliance
     |    /       | Component    | Component
     |   /        | (Flow-dep.)  | (Elastic recoil only)
     |  /         |              |
     +---------------------------------> Time
       [ Flow > 0 ]   [ End-Inspiratory Pause (Flow = 0) ]

1. Static Compliance ($C_{\text{stat}}$): Assessed when gas flow is zero during an end-inspiratory hold (pause). Because flow velocity is zero, no pressure is dissipated to overcome airway resistance. It reflects purely elastic properties of the lung and chest wall: $C_{\text{stat}} = \frac{V_T}{P_{\text{plat}} - \text{PEEP}}$ Normal in ventilated adults: $60-100\text{ mL/cmH}_2\text{O}$.

2. Dynamic Compliance ($C_{\text{dyn}}$): Calculated from the peak inspiratory pressure during active gas delivery. It reflects both the elastic recoil of the system and the frictional resistance opposed to gas movement through conducting airways and the endotracheal tube: $C_{\text{dyn}} = \frac{V_T}{P_{\text{peak}} - \text{PEEP}}$ Normal in ventilated adults: $40-70\text{ mL/cmH}_2\text{O}$.

Clinical Interpretation of Airway Pressures

Driving Pressure Clinical Pearl: Keeping the driving pressure ($\Delta P = P_{\text{plat}} - \text{PEEP}$) below $14-15\text{ cmH}_2\text{O}$ significantly reduces barotrauma, volutrauma, and mortality in acute respiratory distress syndrome (ARDS).

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4. Airway Resistance and Flow Dynamics

Airway Resistance ($R_{\text{aw}}$)

Airway resistance represents the pressure gradient required to drive gas flow through the tracheobronchial tree:

$R_{\text{aw}} = \frac{\Delta P}{\dot{V}} = \frac{P_{\text{peak}} - P_{\text{plat}}}{\dot{V}}$

In a conscious, healthy adult, normal total airway resistance is $1.0-2.5\text{ cmH}_2\text{O}/(\text{L/s})$. In an intubated patient on mechanical ventilation, normal values range between $5.0\text{ and }10.0\text{ cmH}_2\text{O}/(\text{L/s})$, with the endotracheal tube accounting for up to $50\%$ of the total resistance.

Anatomical Distribution of Resistance: Generations 4 to 8 (medium-sized bronchi with internal diameters of $2-5\text{ mm}$) account for the highest individual proportion of airway resistance. While individual terminal bronchioles have tiny radii, their parallel bifurcations generate an exponential increase in total cross-sectional surface area, rendering the terminal "silent zone" responsible for $<20\%$ of total airway resistance.

Laminar vs Turbulent Flow and Reynolds Number

1. Laminar Flow (Hagen-Poiseuille Law): Flow occurs in concentric streamlines with parabolic velocity profiles. Governed by: $\dot{V} = \frac{\pi \cdot \Delta P \cdot r^4}{8 \cdot \eta \cdot l} \implies R = \frac{8 \cdot \eta \cdot l}{\pi \cdot r^4}$ Resistance is inversely proportional to the fourth power of the radius ($r^4$) and depends on gas viscosity ($\eta$), independent of gas density ($\rho$). A $50\%$ reduction in airway radius increases resistance 16-fold.
2. Turbulent Flow: Streamlines break down into chaotic vortices. Pressure drop is proportional to the square of flow velocity ($\Delta P \propto \dot{V}^2$) and depends directly on gas density ($\rho$), independent of viscosity.
3. Reynolds Number ($Re$): Dimensionless number predicting the transition from laminar to turbulent flow: $Re = \frac{2 \cdot r \cdot v \cdot \rho}{\eta}$ Where $r$ is airway radius, $v$ is linear flow velocity, $\rho$ is gas density, and $\eta$ is dynamic viscosity.
   • $Re < 2000$: Flow is predominantly laminar.
   • $Re > 2000$: Flow becomes turbulent.

Clinical Application (Heliox): In severe upper airway obstruction (croup, subglottic stenosis, tracheal tumors), flow in the large conducting airways is turbulent. Helium is substantially less dense than nitrogen (density of $80:20$ Heliox is one-third that of air), decreasing $Re$, restoring laminar flow kinetics, and dramatically reducing the resistive work of breathing.

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5. Work of Breathing (WOB)

The work performed by the respiratory muscles (or mechanical ventilator) during inspiration is defined as:

$W = \int P \cdot dV$

Work of breathing is visually depicted on a Campbell diagram (plotting transpulmonary pressure against lung volume) and divides into two physical components:

1. Elastic Work ($\approx 65\%$ of total resting work): Work required to overcome the elastic recoil of lung parenchyma, chest wall structures, and alveolar surface tension. Elastic work is stored as potential energy during inspiration and powers passive exhalation.
2. Resistive Work ($\approx 35\%$ of total resting work): Work dissipated as heat to overcome frictional forces:
   • Airway resistance (viscous work of gas flow, $\approx 28\%$)
   • Tissue viscous resistance (deformation of pulmonary and thoracic soft tissues, $\approx 7\%$)

  Work Rate
     ^
     |  \                                   / Total Work Curve
     |   \       Optimum (~12-15 bpm)      /
     |    \               |               /
     |     \              v              /
     |      \___________.....___________/
     |       \                         /   Elastic Work
     |        \                       /    (Increases at low RR/high VT)
     |         \                     /
     |          ---------------------
     |         /                     \     Resistive Work
     |        /                       \    (Increases at high RR/high flow)
     +-----------------------------------------> Respiratory Rate

Optimization of Respiratory Rate

Total work of breathing exhibits a minimum at a normal resting respiratory rate of $12-15\text{ breaths/min}$:

• Restrictive Lung Disease (e.g. pulmonary fibrosis, ARDS): High elastic recoil shifts the work minimum to the right. Patients spontaneously adopt a rapid, shallow breathing pattern to minimize elastic work.
• Obstructive Lung Disease (e.g. severe asthma, COPD): High airway resistance shifts the work minimum to the left. Patients spontaneously adopt a slow, deep breathing pattern to minimize resistive work.

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6. Pulmonary Surfactant Biophysics

Composition and Cellular Origin

Pulmonary surfactant is synthesized, stored in lamellar bodies, and secreted into the alveolar hypophase by Type II alveolar epithelial cells (pneumocytes), which constitute $60\%$ of alveolar epithelial cells but cover only $5-10\%$ of the alveolar surface area.

• Lipids ($90\%$): Primarily dipalmitoylphosphatidylcholine (DPPC), an amphipathic phospholipid with hydrophobic palmitic acid tails directed toward the alveolar air phase and hydrophilic choline heads directed toward the aqueous hypophase.
• Proteins ($10\%$): Four surfactant-associated apoproteins:
  • SP-B and SP-C (Hydrophobic): Essential for spreading and stabilizing the DPPC phospholipid monolayer across the alveolar interface.
  • SP-A and SP-D (Hydrophilic): Collectins involved in innate host immune defense and opsonization of pathogens.

Law of Laplace and Surfactant Function

Alveoli behave mechanically as fluid-lined spherical structures. The transmural collapsing pressure is described by Laplace's Law for a sphere:

$P = \frac{2T}{r}$

Where $P$ is the inward collapsing pressure, $T$ is the surface tension of the liquid lining, and $r$ is the alveolar radius.

  WITHOUT SURFACTANT (Constant Surface Tension T = 50 mN/m):
   Small Alveolus (r = 50 um)             Large Alveolus (r = 100 um)
   P = 2(50) / 50 = 2.0 kPa              P = 2(50) / 100 = 1.0 kPa
              [ High P ] ===================> [ Low P ]
              Small alveolus empties into large alveolus (Atelectasis!)

  WITH SURFACTANT (Variable Surface Tension T proportional to r):
   Small Alveolus (r = 50 um, T = 5 mN/m) Large Alveolus (r = 100 um, T = 10 mN/m)
   P = 2(5) / 50 = 0.2 kPa               P = 2(10) / 100 = 0.2 kPa
              Pressures equalize -> Both alveoli remain stable!

Surfactant Mechanisms:

1. Alveolar Stabilization: Without surfactant, smaller alveoli would have higher internal collapsing pressures than adjacent larger alveoli, causing smaller alveoli to empty into larger ones (Laplace instability). As an alveolus deflates, DPPC molecules become tightly packed, reducing surface tension from $\approx 50\text{ mN/m}$ to near $0-5\text{ mN/m}$. This equalizes pressures across interconnected alveoli of differing diameters.
2. Augmentation of Compliance: By lowering surface tension, surfactant markedly increases lung compliance, drastically reducing the muscular work required for lung expansion.
3. Prevention of Alveolar Edema: Inward collapsing pressure creates a negative hydrostatic vector pulling fluid from the pulmonary capillaries into the alveolar space. By reducing surface tension, surfactant prevents hydrostatic pulmonary edema.