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The mechanics of a forced expiration

By taking a deep breath and then exhaling with maximal force, we apply force to the thoracic cavity and its contents: pleural and alveolar pressure increase to well above barometric pressure, and gas is expelled from the lung. The energy required to overcome resistance to flow translates into a pressure drop. In the simplest case (that of laminar flow) the pressure drop (dP) is proportional to airways resistance (Raw) and flow (V'):

dP = V'·Raw

Going from the alveoli to the mouth, the pressure falls steadily; it is high in the alveoli (Palv), falls steadily within bronchi (Pbr) to the level of mouth pressure and subsequently barometric pressure (Pbar). The pressure outside intrathoracic airways is pleural pressure, the pressure outside extrathoracic airways approximates barometric pressure.

Equal pressure point concept

It follows that during a forced expiration all intrathoracic airways are exposed to a high outside (pleural) pressure, whilst pressure within airways drops from a high level near the alveoli to a low level near the thoracic outlet. The intrathoracic airways can be divided into three sections:

  1. A section nearest the alveoli where bronchial pressure exceeds outside pressure: the pressure difference expands the airways.
  2. A point where intra- and extrabronchial pressures are equal (‘equal pressure point’); the pressure drop from the alveoli at this point equals Palv – Pbr = Palv – Ppl = PL,el.
  3. A section nearest the mouth where bronchial pressure is lower than outside pressure: the airway will be compressed.

Airway compression always occurs first in the trachea. The horseshoe shaped cartilaginous rings have a dorsal membranous part, which easily gives way to pressure. The cartilaginous rings bend in the process, so that a slit-like airway cross-section remains. This narrow airway segment functions as a check valve where the speed of gas molecules is limited to the speed at which a wave can propagate in the airway wall, and no longer governed by the pressure difference from alveoli to mouth. This resembles a waterfall, where the amount of water falling down is similarly independent of height of the waterfall. The creation of an intrathoracic check valve (see literature) is demonstrated in the accompanying animation.

Now see this in action during a forced expiratory vital capacity manoeuvre.

Literature on flow limitation
Einthoven W. Über die Wirkung der bronchial Muskeln, nach einer neuen Methode untersucht, und über Asthma Nervosum. Arch Ges Physiol 1892; 51: 367-445.
Dayman H. The mechanics of airflow in health and in emphysema. J Clin Invest 1951; 30: 1175-1190. Manuscript
Fry DL, Ebert RV, Stead WW, Brown CC. The mechanics of pulmonary ventilation in normal subjects and in patients with emphysema. Am J Med 1954; 16: 80-97. Abstract
Dekker E, Defares JG, Heemstra H. Direct measurements of intrabronchial pressure. Its application to the location of the check-valve mechanism. J Appl Physiol 1958; 13: 35-41.
Hyatt RE, Schilder DP, Fry DL. Relationship between maximum expiratory flow and degree of lung inflation. J Appl Physiol 1958; 13: 331-336. Abstract
Fry DL, Hyatt RE. Pulmonary mechanics: a unified analysis of the relationship between pressure, volume and gas flow in the lungs of normal and diseased human subjects. Am J Med 1960; 29: 672-689. Abstract
Hyatt RE. The interrelationship of pressure, flow and volume during various respiratory maneuvers in normal and emphysematous subjects. Am Rev Respir Dis 1961; 83: 676-683. Abstract
Hyatt RE, Flath RE. Relationship of airflow to pressure during maximal effort in man. J Appl Physiol 1966; 21: 477-482. Abstract
Mead J, Turner JM, Macklem PT, Little JB. Significance of the relationship between lung recoil and maximum expiratory flow. J Appl Physiol 1967; 22: 95-109. Manuscript
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Griffiths DJ. Hydrodynamics of male micturition. I. Theory of steady flow through elastic-walled tubes. Med Biol Eng 1971; 9: 581-588. Abstract
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Dawson SV, Elliott EA. Wave-speed limitation on expiratory flow – a unifying concept. J Appl Physiol 1977; 43: 498-515. Abstract
Hyatt RE, Rodarte IR, Mead J, Wilson TA. Changes in lung mechanics; flow-volume relations. In: PT Macklem & S Permutt (eds), The lung in the transition between health and disease. New York, Dekker, 1979, 73-112.
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Koulouris NG, Hardavella G. Physiological techniques for detecting expiratory flow limitation during tidal breathing. Eur Respir Rev 2011; 20(121): 147-155. Manuscript
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Hedges KL, Tawhai MH. Simulation of forced expiration in a biophysical model, with homogeneous and clustered bronchoconstriction. J Biomech Eng 2016; 138(6): 061008. Abstract
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