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Mechanics II

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Respiratory Lecture 10: Mechanics of Breathing II


Topics to be covered:


  1. Dynamic properties of ventilation
    1. Elastic recoil of lungs and chest wall
    2. Resistance to airflow
    3. The three patterns of airflow through tubes
      1. Laminar flow
      2. Turbulent flow
      3. Transitional flow
  2. Factors determining airway resistance
    1. Viscosity
    2. Lung volume
    3. State of contraction of bronchial smooth muscle
  3. Pressure changes during restful breathing
  4. Dynamic compression of airways
  5. Causes of uneven ventilation
  6. Work of breathing


Main objective:

To learn how the fluid properties of air and the structure of the conducting airways affect airflow in the lungs.


Assigned reading: West, Chapter 7, pp 93-120.


Problems: Questions 1-14 on pp 118-120;

Problem Set 10

Mechanics of Breathing II


A. Dynamic Properties of Ventilation


  • Elastic recoil of lung and chest (due to surface tension & tissue elastic recoil)
  • Resistance (R) to air flow is composed of airway resistance* (4/5) and tissue resistance (1/5). See figures 1.5 and 7.14 in West.

* 80% of airway resistance (AWR) is produced by medium sized bronchi, 20% of AWR is produced by small airways with a diameter <2mm.

  • Three patterns of air flow
    • Laminar flow pattern is seen mainly in very small airways.

Pressure/Flow Relationship for Laminar Flow is given by:

Poiseuille’s Law: V = Pπr4/8ηl

η = viscosity ; l = length of tube or vessel

    • Turbulent flow pattern is seen in the trachea and larger airways, especially with higher velocity (e.g., exercise).

Reynold’s number (Re) = 2rvd/η

r = radius

v = velocity

d = density

η = viscosity

If Re >2000, air flow is turbulent

    • Transitional flow pattern (combination of laminar and turbulent) is seen in most medium-sized airways especially at branch points. Medium-sized airways offer the most resistance to air flow.


Flow of air (V) = ∆P/R

∆P = pressure difference between alveoli (or “equal pressure point” in airways during forced expiration) and mouth

∆P down an airway depends on Flow Rate (V) and airflow pattern.

Since R is chiefly AWR, AWR = (Palv - Pmouth) / V

Pressure drop for Laminar Flow, P∝V

Pressure drop for Turbulent Flow, P∝V2


The overall driving pressure is determined by both V and V2:

P = K1V + K2V2

K1 and K2 are constants that take into consideration all the resistances associated with flow.


B. Factors Determining Airway Resistance (AWR)


  • Viscosity (η)
    • Laminar flow areas: R = 8ηl/πr4 (viscosity elevates AWR)
    • Turbulent and Transitional Flow areas: viscosity lowers AWR, density and velocity elevate AWR. Consider the effect of replacing N2 with He.
  • Lung volume (Figs. 4.6 and 7.15 in West)
    • Bronchi are pulled open by radial traction (interdependence) as lung expands to larger volume (AWR decreases due to increased radius).
    • At low lung volumes, small airways at the base of lung close and trap air. These small airways represent the “silent zone” -- contribute little to overall AWR.
    • Considerable small airway disease can be present but remain undetected by usual AWR measurements (Fig. 4) because medium-sized airways contribute the predominate AWR.
    • Patients with ↑ AWR (e.g., emphysema or asthma = obstructive diseases) breathe at large lung volume (top of lung) to minimize AWR and reduce the work of breathing.
  • State of contraction of bronchial smooth muscle
    • Bronchoconstriction:
      • Parasympathetic Nervous System (ACh) - (Efferents of reflexes provoked by irritants)
      • ↓PACO2 in alveoli
        • ↓PACO2 in alveoli produces vasoconstriction
      • Histamine constricts the smooth muscle of alveolar ducts.
    • Bronchodilation:
      • Sympathetic Nervous System:

NE (α1, β1, weak β2)

E (α1, α2, β1, β2)

Isoproterenol (β agonist)

Pressure Changes during Restful Breathing (pp. 105-107 of West)

  • Correlation of pressures to lung volume and airflow rate (fig. 7.13 of West and Fig. 5 of notes).

x. Pressure needed to overcome lung elastic recoil; y. Pressure needed to overcome lung elastic recoil plus AWR

Figure 5. Intrapleural pressure during the breathing cycle. The pressure difference between -5 (start of inspiration) and the broken line (ABC) represents the pressure needed to overcome lung elastic recoil. The additional pressure needed to overcome AWR (and some tissue resistance) is depicted by the hatched area. The actual intrapleural pressure follows the solid line (AB’C). NOTE: the pressure difference between B and B’ is the alveolar pressure at that instant.

D. Dynamic Compression of Large Airways (Figs. 6 and 7)


  • Flow-Volume curves of forced expiration (Fig. 6)
  • Flow rate is limited and effort independent.
  • Compression, not closure, of larger airways
    • Transmural pressure = Pinside - Poutside
      • pressure holding chamber or airway open
  • The maximum flow rate decreases with decreasing lung volume because:
    • The difference between alveolar pressure and intrapleural pressure lessens causing a decreased driving pressure.
    • As the volume decreases, there is less radial traction on the airways causing a progressive increase in AWR.
  • Obstructive (emphysema) and restrictive (fibrosis) diseases cause a characteristic variation of the normal forced expiration flow-volume curve (Fig. 6B).

Figure 6. Flow-volume curves obtained by recording flow rate against volume during a forced expiration from maximum inspiration. The figure shows absolute lung volumes, although these cannot be measured from single expiration. A) A normal flow-volume pattern. B) Comparison of typical obstructive and restrictive diseases to the normal flow-volume curve.

Figure 7. Compression of larger airways during forced expiration. When transmural pressure (pressure difference across the airway) becomes negative (inside – outside), airways will collapse. As the forced expiration continues, the equal pressure point will move inwards (towards the lung) because you are exhaling air and the pressure falls throughout the airways.


    • E. Three Causes of Uneven Ventilation in different lung units at any given vertical level (Review fig. 7.19 in West prior to lecture)
  • ↓ compliance
  • ↑ airway resistance
  • Incomplete diffusion in airways of respiratory zone (enlarged space as in emphysema)

F. Work of Breathing**

  • Work done on lung (= pressure x volume) must overcome the following:
    • Elastic forces: lung recoil (collagen/elastin and surface tension).
      • Static: at FRC, before breathing
      • Dynamic: during breathing (Fig. 8,A2)
    • Viscous forces (Fig 8,A3)
      • 80% due to AWR (especially at medium-sized pulmonary airways)
      • 20% due to tissue resistance (friction)
  • Total work of breathing (lung + chest) (Fig 8,A1)
  • Restful vs. exercise; efficiency

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