Mathematical Behavior of MEFV Curves in Childhood Asthma and the Role of Curvature in Quantifying Flow Obstruction

Figure 4

Stability analysis of the second derivative, 𝑑²𝑉̇/𝑑𝑉², of the MEFV curve. Curves illustrate the function ⟨(𝑑²𝑉̇/𝑑𝑉²)_𝑖⟩ (4) over the interval running from 𝑖=0, at IP, to 𝑖_max at 𝑉_max, for various patients. Horizontal lines correspond to values 𝑑²𝑉̇/𝑑𝑉²=2𝑎 obtained from the quadratic fit of (3). For brevity and clearness, a restricted number of patient plots from Figure 1 are presented: (-) first row, second column; (--) second row, first column; (-·-) third row, first column.