What is respiratory resistance?
  • Respiratory system resistance is mainly a combination of resistance to gas flow in the airways and resistance to deformation of tissues of both the lung and chest wall.
  • Its reciprocal is conductance. Normally, specific airway conductance is used, which is conductance expressed per unit of lung volume. Conductance is "the instantaneous rate of gas flow in the airway per unit of pressure difference"
What are the contributing factors of total respiratory resistance?

Respiratory resistance is a combination of multiple factors, which contribute unequally and which have different importance at different points in the respiratory tract and under different flow conditions:

  • Resistance from deformation of the tissues (important at all flow rates)
    • Tissue resistance from lung parenchyma (~70%)
    • Tissue resistance from chest wall (~30% )
  • Inertance of air and thoracic tissues (important at high respiratory rates) 
  • Compression of intrathoracic gas (important mainly with high respiratory pressures)
  • Resistance from air flow friction, which in turn depends on
    • Reynolds number, which depends on
      • Airway diameter (increases with lung volume)
      • Airway length (increases with lung volume)
      • Flow rate
      • Gas density
      • Gas viscosity
    • Proportion of turbulent flow (at high flow, upper airways)
    • Proportion of laminar flow (low flow rates and in the lower airways)

This is expressed in Rohrer's equation, after Rohrer (1915):

Rohrer's equation

where

  • Rrs is the resistance of the respiratory system,
  • Rt is the resistance from deformation of the lungs and chest wall,
  • K1 is an empirical constant representing gas viscosity 
  • K2 is an empirical constant representing gas density and airway geometry, and
  •  is the flow as volume per unit time
Where in the respiratory tract is the airway resistance greatest?
  • At the "transition point", which is  somewhere in the 5th-8th generation of bronchi.
  • As airways get narrower one might expect the resistance to increase but because their total crossectional area becomes exponentially greater the flow in them slows down to the point where all the airways distal to Generation 10 contribute less than 16% to the total airway resistance.
What is Reynold's number?
  • Reynold's number is defined as the "the ratio of inertial forces to viscous forces" in fluid dynamics, or the ratio of gas density to gas viscosity. It is described by the equation,
    Reynolds%20number%20equation%201.jpg
    where
    • V is the velocity of the gas flow,
    • D is the diameter of the tube, 
    • ρ is the gas density, and
    • μ is the gas viscosity.
  • This number describes whether the flow will be turbulent or laminar 
  • Numbers under 2000: flow is mainly laminar
  • Numbers 2000-4000: flow is "transitional", laminar turning to turbulent
  • Numbers >4000: flow is mainly turbulent.
What is the relationship between flow and pressure in laminar flow?
  • Flow is proportional to driving pressure
    pressure-flow relationship for laminar flow 
  • Resistance is described by the classical Hagen-Poiseuille equation:
    ​​
    Hagen-Poiseuille equation
    which means that airway characteristics (eg. length and radius) are the most important determinants of resistance, followed by the viscosity of the gas. 
  • A maximum flow rate exists; beyond which various eddies and vortices develop, making the flow becomes turbulent. The smaller the calibre of the airway, the lower the flow rate required to produce this effect. 
  • The volume of gas moving through the tube is smaller than the volume of the tube. This is because gas which is in contact with the walls is essentially motionless
  • Viscosity is the most important gas property which influences the resistance to laminar flow.
  • A minimum length of unbranched tube is required for laminar flow to be established;  the term to describe this is "entrance length" and it depends on the diameter of the tube and the Reynolds number of the gas. For an 8mm tube (eg. a secondary bronchus), the entrance length is about 21cm (Olson et al, 1970), i.e. in the vast majority of circumstances there is not enough airway length to establish laminar flow.
What is the relationship between flow and pressure in turbulent flow?
  • Flow is proportional to the square root of driving pressure. In other words, as the pressure gradient increases, flow increases less (i.e. the relationship is not linear): 
    pressure-flow relationship for turbulent flow
  • Resistance increases in proportion to flow rate, and cannot be described using the traditional Hagen-Poiseuille equation. In fact, because of that, you should't even use traditional units to measure it. It is usually represented in terms of a pressure gradient:

    Pressure gradient = K(flow)n

    where
    • K  is an empirical constant which, for the human respiratory tract, appears to be 0.24 ( when the pressure gradient is expressed in kPa), and
    • n is an exponent which is 1.0 for a purely laminar flow and 2.0 for a purely turbulent flow. According to the ancient Handbook of Physiology, empirical measurements suggest that for the human respiratory tract,  n=1.3 
  • The volume of gas moving through the tube is proportional to the volume of the tube, i.e. the "front" of the flowing gas is square rather than conical as in laminar flow.
  • Density is the most important determinant of whether or not flow will be turbulent, all other things being equal. This is where helium becomes useful, i.e. by decreasing the density of the inspired gas mixture helium improves the likelihood of laminar flow occurring in narrowed airways, and this decreases the resistance to flow.

References

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