Answer to Question #104559 in Differential Equations for mm

Question

The respiratory flow of air in the lungs is affected due to air pollution. If you have to model
respiratory flow write four essentials for the model.

Answer 1

Four Factors Affecting Air Flow

Airway Caliber

• laminar flow () =  pressure (P) / resistance (R)
• slope of line = 1/R = conductance
• resistance (R) to laminar flow  1/radius⁴
•  airway caliber (secretions, bronchoconstriction): < R and <  P

Air-Flow Profile

• laminar flow (<) increases linearly with < driving pressure
• non-laminar flow (<) increases curvilinearly with < driving pressure
• R_{non-laminar flow} is effectively greater than R_{laminar flow} due to turbulence
• for any given < P, <_non-laminar < <_laminar
• or any given <, <P_non-laminar > < P_laminar

Airway Generation

• Airway Generationin general, regional airway resistance decreases as a function of airway generation
• in specific, the highest regional resistance is at generation 4
• medium sized bronchi of short length and frequent branchings highly non-laminar air flow with extreme turbulence

Lung Volume 

• Lung Volumetotal airway resistance = summation of serial regional resistances
• R_total decreases hyperbolically with increases in lung volume
• conductance_total increases linearly with increases in lung volume (dashed line)
• increases in lung volume cause increases in radius due to tethering of the airways
• R_total can be partitioned into two components
• R_peripheral : low resistance (laminar & diffusive zones)
• R_central : high resistance (turbulent flow zone)
• R_central >>> R_peripheral (50% of resistance in nasal passages alone)

More information:

https://www.meddean.luc.edu/lumen/MedEd/medicine/pulmonar/physio/pf2.htm