Research Article

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

Figure 2

Corresponding plots of second derivative, 𝑑 2 ̇ 𝑉 / 𝑑 𝑉 2 , versus expired volume, V, for the pediatric patients presented in Figure 1. Coordinates are as shown in the top left corner subplot. Note that all plots illustrate a similar characteristic behavior: (1) an initial monotonically increasing profile where 𝑑 2 ̇ 𝑉 / 𝑑 𝑉 2 < 0 which (2) settles towards a small finite positive steady-state value, with 𝑑 2 ̇ 𝑉 / 𝑑 𝑉 2 > 0 . Several examples illustrate an overshoot before converging towards a steady-state value (e.g. fifth row, second column), while others show a period of oscillation about the x-axis before reaching their steady-state value (e.g. first row, second column). Steady-state values of 𝑑 2 ̇ 𝑉 / 𝑑 𝑉 2 are indicated in each subplot.
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