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A Mathematical Model to Describe Fat Oxidation Kinetics during Graded Exercise


Medicine & Science in Sports & Exercise: August 2009 - Volume 41 - Issue 8 - p 1615-1625
doi: 10.1249/MSS.0b013e31819e2f91
Basic Sciences

Purpose: The purpose of this study was to develop a mathematical model (sine model, SIN) to describe fat oxidation kinetics as a function of the relative exercise intensity [% of maximal oxygen uptake (%V˙O2max)] during graded exercise and to determine the exercise intensity (Fatmax) that elicits maximal fat oxidation (MFO) and the intensity at which the fat oxidation becomes negligible (Fatmin). This model included three independent variables (dilatation, symmetry, and translation) that incorporated primary expected modulations of the curve because of training level or body composition.

Methods: Thirty-two healthy volunteers (17 women and 15 men) performed a graded exercise test on a cycle ergometer, with 3-min stages and 20-W increments. Substrate oxidation rates were determined using indirect calorimetry. SIN was compared with measured values (MV) and with other methods currently used [i.e., the RER method (MRER) and third polynomial curves (P3)].

Results: There was no significant difference in the fitting accuracy between SIN and P3 (P = 0.157), whereas MRER was less precise than SIN (P < 0.001). Fatmax (44 ± 10% V˙O2max) and MFO (0.37 ± 0.16 g·min−1) determined using SIN were significantly correlated with MV, P3, and MRER (P < 0.001). The variable of dilatation was correlated with Fatmax, Fatmin, and MFO (r = 0.79, r = 0.67, and r = 0.60, respectively, P < 0.001).

Conclusions: The SIN model presents the same precision as other methods currently used in the determination of Fatmax and MFO but in addition allows calculation of Fatmin. Moreover, the three independent variables are directly related to the main expected modulations of the fat oxidation curve. SIN, therefore, seems to be an appropriate tool in analyzing fat oxidation kinetics obtained during graded exercise.

1Institute of Sport Sciences and Physical Education, University of Lausanne, Lausanne, SWITZERLAND; and 2School of Medical Sciences, Faculty of Health Sciences, University of KwaZulu-Natal, SOUTH AFRICA

Address for correspondence: Xavier Chenevière, Institute of Sport Sciences and Physical Education, University of Lausanne, Bâtiment de Vidy, 1015 Lausanne, Switzerland; E-mail:

Submitted for publication May 2008.

Accepted for publication January 2009.

© 2009 American College of Sports Medicine