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To this point, models of static lung and chest wall compliance have been used to estimate resistances to ventilation that are generated by surface and tissue recoil of lung tissue, and by thoracic musculoskeletal elements. However, additional resistance to ventilation also occurs in the airways during flow, only to disappear under no-flow conditions such as FRC. Such dynamic airway resistance is nevertheless a powerful determinant of the pattern, energetic cost, and overall efficiency of ventilation. Thus, dynamic airway compliance measurements are made to directly determine in-line resistances due to the airways. Such measurements have shown that most dynamic airway resistance resides in the upper airways (generations 1-7) because their flow rates tend to be high, their end-to-end pressure changes are large, and their aggregate cross-sectional areas are small. By the same argument, the smaller peripheral airways usually contribute less resistance despite having smaller individual diameters, due to their shorter lengths and their exponentially larger cross-sectional areas (Fig. 6.4).
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To appreciate the role that airway dimensions play in creating resistance to ventilation and thereby add to the work of breathing, recall Ohm’s law:
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where I = current, ΔV = voltage potential, and R = resistance
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In airways and other tubes, this becomes a generalized flux equation:
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where ΔP = pressure differential, either end-to-end or end-to-side, and
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R = resistance due to airway dimensions and gas viscosity, and thus:
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where r = airway radius, η = viscosity, and l = airway segment length
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Substituting terms gives the well-known Poiseuille equation:
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Air flow = (ΔP · π · r4)/(8 · η · l)
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Considering the dependence of resistance on radius to the fourth power, the importance of even a small change in airway radius is apparent. It will be shown in later chapters that many respiratory diseases pivot on this aspect of airway resistance, versus a lesser dependence on airway length or viscosity.
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Applying the Poiseuille equation to human ventilation presumes an idealized laminar flow pattern, but evidence is not persuasive as to how often and how distally such flow exists in the airways (Fig. 6.5). Most bronchial airways are too wide, too frequently bifurcated, or too short before branching to promote consistent laminar flow. Rather, it seems likely transitional flow patterns predominate at rest, that deteriorate to turbulent patterns during exercise and other events associated with hyperventilation.
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Clinically, airway resistance is calculated using the pressure gradient from trachea to alveolus divided by flow rate; the subject’s tracheal pressure and flow rate are estimated at the mouth by anemometer, and alveolar pressure by esophageal transducer or plethysmography (Chap. 16). When the in vivo volume/pressure changes are plotted for such a dynamic compliance maneuver, the area between the inflation and deflation curves representing hysteresis is larger than for excised lungs of the same size (see Fig. 5.2). Most importantly, this increased area represents additional nonrecoverable work during both inflation and deflation to overcome airway resistance.
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In summary, the total work of breathing in a healthy adult can be partitioned into energy that must be applied to overcome:
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Static lung resistance caused by tissue elasticity and surface tension forces that must be overcome regardless of dynamic resistance, normally 65%-70% but higher when pathologies involving surfactant or the respiratory parenchyma are present;
Dynamic airway resistance that exists only when gas is moving, normally 25%-30% and mostly in the upper 10 generations, but much higher in patients with obstructive disorders; and
Tissue viscous drag due to physical abrasion and friction between pleural surfaces of the lung and chest, normally 5% but can become fatally high if adhesions, congenital anomalies, or effusions are present.