Resistance

Explain the relationship between resistance and respiratory gas flow

Describe the factors affecting airway resistance, and its measurement

Resistance (measured in cmH₂O.L^-1.sec^-1) comprises the energy lost as frictional and inertial impedance to gas flow, where energy is lost as heat. Flow is a function of pressure gradient, resistance, and type of flow.

Types of Flow

Flow can be either laminar or turbulent. In laminar conditions flow is proportional to driving pressure, whilst in turbulent conditions flow is proportional to the square root of driving pressure.

Reynolds' Number

Type of flow can be predicted by Reynolds's Number, a dimensionless index where:

$Reynolds' \ Number = {2r.d.v \over \eta}$, where:

• $r$ = Radius
• $d$ = Gas density
• $v$ = Velocity
• $\eta$ = Gas viscosity

A Reynolds' Number of < 2000 is predominantly laminar flow, whilst >4000 is predominantly turbulent.

Laminar Flow

In laminar flow:

• Gas moves in a series of concentric cylinders which slide over one another
  • Gas in the centre moves twice as fast compared to the outside, where it is almost stationary
• Gas appears in cross-section as an advancing cone
  Gas may reach the end of the tube when the volume of flow is less than the volume of the tube.
  • This is the mechanism of alveolar ventilation when tidal volumes are less than anatomical dead space volume

In a straight unbranched tube, flow can be quantified by the Hagen-Poiseuille Equation:
$F = {\Delta P \pi r^4 \over 8l.\eta}$, where:

• $F$ = Flow
• $\Delta P$ = Driving pressure
• $r$ = Radius
• $l$ = Length
• $\eta$ = Viscosity

However, as in laminar conditions flow is proportional to the driving pressure and inversely proportional to resistance, flow can be substituted and the equation solved for resistance:

$Resistance = { 8l. \eta \over \pi r^4}$

This can be used to describe the factors affecting resistance:

• Length
  Fixed constant.
• Viscosity
  Varies with the particular gas mixture being used.
• Radius
  Main determinant. May be divided into:
  • Extraluminal factors
    • Compression:
      • Haemorrhage, tumour, dynamic hyperinflation, atelectasis compressing airways, etc.
    • Lung volume:
      • Airway radius increases when lung volume expands due to radial traction on airways (until dynamic hyperinflation occurs, at which point airways are compressed again)
  • Luminal constriction
    Bronchospasm, bronchoconstriction.
  • Intraluminal obstruction
    Sputum plugging, aspiration.

Note that airway resistance:

• Peaks at the 5^th generation
• Rapidly decreases with each airway division thereafter
  This is due to the total cross-sectional area increasing dramatically.

• Reduces with increasing lung volume, as radial tension distends airways, increasing their cross sectional area

Turbulent Flow

High flow rates and branching of airways disrupt disciplined laminar flow. Turbulent flow is:

• Dominant in the upper airway (where velocity is high)
• Dominant in early-generation airways due to regular branching, changes in diameter, and sharp angles
• Reduces after the 11th generation bronchioles
• Proportional to the square root of the driving pressure
  Therefore, resistance is higher in turbulent flow than in laminar flow.
  • Driving pressure is proportional to gas density, and independent of viscosity

Resistance in turbulent flow is managed by making flow less turbulent:

• Achieved by reducing Reynolds number
  • Helium mixtures reduce gas density
    Of greater benefit in upper airway than lower airway disease.

Transitional Flow

Transitional flow is the change between laminar and turbulent flow. It occurs at branches and angles in the airways, seen in most of the bronchial tree.

References

1. Lumb A. Nunn's Applied Respiratory Physiology. 7th Edition. Elsevier. 2010.