Methods for food shelf life determination and prediction - Oxidation in Foods and Beverages and Antioxidant Applications - page 205

oxidative reactions, fitting data with these models may be precluded and other
models have to be found. For instance, the evolution of peroxide index is a case
in point. As is well known, peroxide values as a function of storage time follow
typical bell-shaped curves. After the induction period, during which no
significant changes of peroxide value are observed, the progressive increase
of peroxide value occurs until a maximum is reached, indicating that the
oxidative reactions approaches the termination step. Traditionally, the kinetics
of peroxide formation and decomposition has been modelled by separately
considering each reaction step. The assumption is that all the intermediate
reactions follow fixed order reaction kinetics, each having its characteristic
apparent rate constant.
It should be noted that, depending on the environmental and compositional
factors, the induction period could be negligible or even very long. In the latter
case the estimation of the lag time (lag) may be critical for the final product
dating. For this reason, the lag time should be carefully estimated and included
in the shelf life equation as shown in the following example referred to a zero
order kinetic:
SL I ox ÿ I ox 0
k

lag T const 9:3

The second approach is to consider the entire evolution of the peroxide value
during the overall product life. In this case, the fundamental kinetic concepts are
skipped and empirical mathematical model can be achieved by best fitting the
peroxide value curves. Different mathematical models have been applied. For
instance, Aragao et al. (2009) proposed a phenomenological mathematical
model, comprising a decay factor superimposed on an accumulation term, to
describe peroxide changes during lipid oxidation. Additional models (i.e.,
sigmoidal model, Weibull distribution function, logistic model) are also
frequently used ( È zilgen and È zilgen, 1990; Cunha et al., 1998; Corradini
and Peleg, 2007; Calligaris et al., 2008; Imai et al., 2008; Odriozola-Serrano et
al., 2009).
As an example, equation 9.4 shows the mathematical model, obtained by best
fitting approach, applied to describe peroxide value (PV) changes as a function
of storage time:
PV PV 0 PV max ÿPV 0
1e

9:4

4k max ÿt
PV max ÿPV 0 2

where PV 0 is the initial peroxide value, PV max is the peroxide value at the
maximum of the curve, is the lag phase defined as the crossing point between
the tangent through the inflection and k max is the maximum reaction rate. By
solving equation 9.4 as a function of time, a shelf life prediction model can be
built up:
SL ÿ PV max ÿPV 0
4k max

PV max ÿPV lim
PV lim ÿPV 0

PV max ÿPV 0
4k max

ln 2 9:5