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

摘要

Maximal expiratory flow-volume (MEFV) curves of pediatric patients are investigated using differentiation schemes and by computing their second derivative,d2V˙/dV2. Results show that spirometric tracings illustrate a characteristic well-defined behavior, where two distinct regions of the MEFV curve may be identified: (1) a concave profile during the initial expiratory maneuver, and (2) a convex profile over the greater lower region of the descending phase of the MEFV curve; this latter region is characterized by an approximately constant positive value ofd2V˙/dV2such that the descending MEFV limb may be captured by a quadratic function. Based on simple expiratory flow modeling, we show thatd2V˙/dV2, and alternatively the local geometrical curvatureκ(V), yield a measure of the relative degree of flow obstruction. In view of future clinical applications, we make use of an “average curvature index”, to assist clinician’s assessment of asthma severity, by quantifying curvature and summarizing global information in MEFV curves.