Isometric growth: conditions
MEF is the maximum expiratory flow obtained during a forced expiration. What is its magnitude? The volume displaced per unit of time is the product of speed and surface area through which the gas flows. MEF is determined by the maximum flow that can be reached in the compressed airway segment, and is of course proportional to the surface area (A) of the compressed airway segment. The maximum speed of gas in this flow limiting segment is determined by the elastic properties of that segment; we assume that these remain the same during the growth process. (The elastic properties of lung parenchyma also come into play, but the relationship with MEF is complicated and distracts from the flow of reasoning, so let us not consider it here).
If isometry applies, then the radius (r) of airways and alveoli, and the airway length (L), increase proportionately during growth, and r/L is constant. So we have:
- MEF is proportional to A,
- A is proportional to r2
- V is proportional to r3
- hence in the case of isometric growth MEF is proportional to V2/3= V0.67.
We do have to take into account the flow profile: turbulent or laminar. Let us address that now.