F3c Pulmonary resistance

Turbulence significantly increases opposition to flow.

In turbulent conditions, \(\dot{V} \propto \sqrt{\Delta P}\)

Reynold's Number is the ratio of a fluid's inertia and viscosity. Turbulence occurs when this quantity is >2000. In a pipe of fixed diameter,

$$Re = \frac{\rho V D}{\mu}$$

where \(\rho\) is density, V is fluid velocity, D is pipe diameter, and \(\mu\) is viscosity.

Confusingly, decreasing diameter would appear to decrease the Reynold's number. But, for a fixed gas flow Q, we have

$$Q = V \cdot \pi \left( \frac{D}{2} \right)^2$$

$$Q = V \cdot \pi \frac{D^2}{4}$$

$$V = \frac{4Q}{\pi D^2}$$

and therefore

$$Re = \frac{\rho 4Q D}{\mu \pi D^2}$$

$$Re = \frac{\rho 4Q}{\mu \pi D}$$

So, if gas flow (minute ventilation) is held constant, then a smaller diameter increases turbulence.

In laminar conditions, \(\dot{V} \propto \Delta P\), or \(\dot{V} = \frac{\Delta P}{R}\)

Resistance to laminar flow is given by the Hagen-Poiseuille equation.

$$R = \frac{8 l \mu}{\pi r ^ 4}$$

Where l is the pipe length, \(\mu\) is the viscosity, and r is the pipe radius.

Lung volume decreases resistance by expanding the airways through radial tension from the elastic tissues.

Airway radius is the most important, and is affected by:

1. Bronchiolar muscle thickness (hypertrophied in asthma)
2. Bronchiolar muscle tone (\(\uparrow\) \(H_1\), \(M_3\), bronchospasm; \(\downarrow\) \(\beta_2\)
3. Mucus and secretions
4. Airway oedema
5. Compression or obstruction (extrinsic, gas trapping, forced expiration, ETT kinked).

Airway length is increased by circuit components e.g. increased by ETT, decreased by tracheostomy

Gas velocity (\(\therefore\) turbulence) is increased by a short inspiratory time or high respiratory rate.

Gas density (\(\therefore\) turbulence) can be reduced by heliox.

Resistance is much higher in infants.