Bootstrap Confidence Intervals for the Kinetic Parameters of Degradation of Anthocyanins in Grape Pomace

Because of the growing interest in nutraceuticals and their health benefits, it is important to develop tools for modeling degradation of nutraceuticals in low-moistureand high-temperature-heated foods. The objective of this study was to estimate the kinetic parameters for the degradation of anthocyanins in grape pomace and to calculate the bootstrap confidence interval (CI), which is a more realistic estimate of the true CI than the commonly used asymptotic CI. Thermal and kinetic parameters for unsteady-state conductionheated foods (grape pomace) were estimated separately using an inverse problem technique. Rate constant (kr) and activation energy (Ea) for the degradation of anthocyanins in grape pomace were estimated, and the 95% bootstrap CIs were calculated and compared with the 95% asymptotic CIs. Grape pomace at 42% moisture content (wet basis) in steel cans (radius 0.027 m, and height 0.073 m) was heated in a steam retort at 126.7C. Anthocyanin retention was measured by high-performance liquid chromatography. The retention values were used to estimate kinetic parameters, which were k113.9C = 0.0606/min and Ea = 65.32 kJ/mol. Asymptotic CIs for k113.9C and Ea were 0.052 and 0.068, and 23.3 and 102.7, respectively. Bootstrap 95% CIs for k113.9C and Ea were 0.053 and 0.066, and 49.08 and 104.9, respectively. Bootstrap confidence band and bootstrap prediction band (PB) for anthocyanin retention were smaller than asymptotic confidence and PBs, respectively. 4 Corresponding author. TEL: +(517) 355-8474, Ext. 119; FAX: +(517) 353-8963; EMAIL: dolank@ msu.edu Journal of Food Process Engineering •• (2009) ••–••. All Rights Reserved. © 2009 Wiley Periodicals, Inc. DOI: 10.1111/j.1745-4530.2009.00425.x 1 The smaller width of the bootstrap bands, which are considered more accurate than asymptotic bands, allows more accurate process design and cost-savings, potentially leading to higher-quality nutraceutical products. PRACTICAL APPLICATIONS Thermal and kinetic parameters for unsteady-state conduction-heated foods (grape pomace) were estimated separately using nonlinear regression techniques. This non-isothermal method of estimating thermal and kinetic parameters is fast, convenient and more accurate than the isothermal method. Also, for certain application such as low-moisture solids at high temperatures, isothermal experiments are not feasible. There is much more information gained from the type of plot presented here than from the typical plot with only one fitted line showing the mean values. The smaller width of the bootstrap bands, which are considered more accurate than asymptotic bands, allows more accurate process design and cost-savings, potentially leading to higherquality nutraceutical products.