Table of Contents
ISRN Pulmonology
Volume 2012, Article ID 305176, 13 pages
http://dx.doi.org/10.5402/2012/305176
Research Article

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

1Institute for Social and Preventive Medicine, University of Berne, 3010 Berne, Switzerland
2Children's Hospital Basel, University of Basel, 4056 Basel, Switzerland
3Department of Pediatric, Cantonal Hospital Fribourg, 1708 Fribourg, Switzerland
4Department of Biomedical Engineering, Technion-Israel Institute of Technology, 32000 Haifa, Israel

Received 30 November 2011; Accepted 10 January 2012

Academic Editor: M. Tatar

Copyright © 2012 Ben Spycher et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Maximal expiratory flow-volume (MEFV) curves of pediatric patients are investigated using differentiation schemes and by computing their second derivative, 𝑑2̇𝑉/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 of 𝑑2̇𝑉/𝑑𝑉2 such that the descending MEFV limb may be captured by a quadratic function. Based on simple expiratory flow modeling, we show that 𝑑2̇𝑉/𝑑𝑉2, and alternatively the local geometrical curvature πœ…(𝑉), yield a measure of the relative degree of flow obstruction. In view of future clinical applications, we make use of an β€œaverage curvature index”, to assist clinician’s assessment of asthma severity, by quantifying curvature and summarizing global information in MEFV curves.