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Kinetics of Cholesterol Oxidation in Model Systems and Foods: Current Status
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Transcript of Kinetics of Cholesterol Oxidation in Model Systems and Foods: Current Status
REVIEW ARTICLE
Kinetics of Cholesterol Oxidation in Model Systems and Foods:Current Status
Ilce Gabriela Medina-Meza • Carlo Barnaba
Received: 20 February 2013 / Accepted: 8 June 2013 / Published online: 19 June 2013
� Springer Science+Business Media New York 2013
Abstract In the last decades, cholesterol oxidation
products (COPs) have been one of the most intense topics
in food science because of their biological and pathological
effects on human health. The formation of COPs during
food processing is a thermodynamically governed phe-
nomenon and, as for all chemical and biochemical reac-
tions, this formation can be controlled through a kinetic
monitoring of oxidative trends, in a manner similar to lipid
oxidation. The use of kinetics modeling as a powerful
predictive tool has increased recently, although its appli-
cation in lipid oxidation and cholesterol is poor. Despite
the abundance of data on the subject, as evidenced by the
presence of numerous reviews about the content of COPs
in different foods, contributions to the kinetic modeling are
isolated. Moreover, the application of this mathematical
approach often demonstrates numerous errors in method-
ology. This paper summarizes the scientific advances in
kinetic modeling of thermo- and photo-induced oxidation
of cholesterol. We briefly describe the reaction mecha-
nisms of both degradative pathways, with particular
attention to involucrate variables. Then, state of the art of
mechanistic models that are proposed is discussed in detail.
This analysis shows that it is necessary to broaden and
deepen the kinetic study of cholesterol oxidative phenom-
enon from a mechanistic perspective with a more specific
application of kinetic principles. The development of
effective predictive models may help to monitor COPs
during processing of the food and thus prevent their
accumulation in the final products.
Keywords Cholesterol oxidation � Kinetic models �Oxysterols � Lipid oxidation � Model system
Introduction
Cholesterol (5a-cholesten-3b-ol, Fig. 1) is an essential
biochemical compound in mammalian cells, representing
the most prominent lipid in eukaryotic cells. It is involved
in numerous body function tasks, ranging from the syn-
thesis of bile acids and hormones, to its different roles in
cellular membrane function [29]. Cholesterol is insoluble
in blood, and its effect in biological systems is determined
by the type and nature of lipoprotein complexes that carry
it through the bloodstream [60]. This molecule can be
synthesized de novo or obtained by diet, but it is also
widely distributed in foods of animal origin [31].
As with other lipid molecules, cholesterol is susceptible
to oxidation to form cholesterol oxidation products (COPs)
or oxysterols by heating [32, 45, 66], illumination [6, 46]
and enzymatic activity [3]. COPs are the derivatives of
cholesterol that contain a second oxygen atom as part of a
carbonyl, hydroxyl, ketone or epoxide group on the sterol
nucleus and/or a hydroxyl group on the side chain of the
molecule. Oxysterols usually occur at low levels, accom-
panied by a high concentration of the parent cholesterol.
Accumulation of oxysterols in the body can occur in sev-
eral different ways, the major ones being dietary intake and
internal chemical and enzymatic oxidation [54]. Oxysterols
are present in various foodstuffs, notably cholesterol-rich
I. G. Medina-Meza (&)
Center for Nonthermal Processing of Food, Washington State
University, Pullman, WA 99164-6120, USA
e-mail: [email protected]
C. Barnaba
Departamento de Procesos Tecnologicos e Industriales, Instituto
Tecnologico y de Estudios Superiores de Occidente (ITESO),
Periferico Sur Manuel Gomez Morın 8585, 45604 Tlaquepaque,
Jalisco, Mexico
123
Food Eng Rev (2013) 5:171–184
DOI 10.1007/s12393-013-9069-0
foods such as dairy products, milk, eggs, dried egg powder,
meat products, and dried or stored fish [31, 55].
These compounds have been shown to exert several
in vitro and in vivo biochemical activities of both physio-
logic and pathologic relevance [52, 54], which are medi-
ated by their biophysical effects on membranes and/or
stereospecific interactions with proteins [32]. COPs are
implicated in several pathophysiological mechanisms,
including atherosclerosis, lung disease, liver disease, car-
cinogenesis and neurodegeneration [3].
Due to the high pathological impact of these molecules
and the necessity to control their content and formation in
food processing, the mechanisms and kinetics of the for-
mation of COPs are of crucial importance. One of the
major objectives of food engineering is to develop pre-
dictive models that allow knowledge and control of the
variables that affect the production of certain compounds
harmful to the consumer [62]. Mathematical modeling is a
tool that allows the synthesis of data from one or many
experiments into an integrated system from which quanti-
tative changes in many components may be calculated. In
any mathematical model, the endpoint selected for shelf
life is critical. Most of the time, this endpoint is arbitrarily
selected, whereas it should be based on consumer accept-
ability. Moreover, it is a necessary tool for preventing its
effects on food. Generally, the equations used to model the
mechanisms of reactions allow us to obtain information
about kinetic factors such as constant rates and activation
energy necessary to degradation [18]. Many parameters
need to be considered during modeling, such as loss of the
inducer, use of antioxidants, auto-oxidation and hydroper-
oxides reduction. Consequently, the use of simulation
programs permits evaluation if the proposal model is in
agreement with the experimental data.
In the last few years, thorough reviews have covered
selected aspects of the formation of oxysterols and their
presence in foods [8, 31, 32, 59]; however, these reviews
do not provide a comprehensive analysis of the kinetic
models proposed in the formation of these compounds. In
this work, we have reviewed the effect different mecha-
nistic and empirical mathematical models used to describe
thermo-oxidation and photo-oxidation of cholesterol in
food and model systems. Particular attention has been paid
to the mechanisms involved and the effect of process
variables (presence/absence of antioxidant, temperature,
light source) in the formation of COPs, and how these
variables were included in the different predictive models
proposed.
Mechanisms of Cholesterol Oxidation
Auto-oxidation
The formation mechanism of COPs during auto-oxidation
and heat-induced auto-oxidation (also known as thermo-
oxidation or thermal degradation) has been well docu-
mented and illustrated [15, 37, 45, 56]. Auto-oxidation is
an endothermic phenomenon; degradation by auto-oxida-
tion occurs under a variety of circumstances, leading to a
galaxy of products [56]. Cholesterol auto-oxidation occurs
in various model systems, including aqueous emulsion,
micelles, liposomes and monomolecular films spread on
water, and can also occur in the crystalline state [32, 37].
Initially, a series of reactions lead to the formation of
reactive oxygen species (ROS), a group of molecules that
includes oxygen radicals and nonradical derivatives of
oxygen. This auto-catalytic process generates primary
oxidation products followed by further reactions leading to
a high variety of nonvolatile and volatile secondary oxi-
dation products [37]. The ROS are formed enzymatically,
chemically, photochemically and by irradiation of food and
decomposition of hydroperoxides. ROS are also formed by
decomposition and interreaction of ROS.
The oxygen radicals are alkoxy (RO�), hydroxyl (HO�),
hydroperoxy (HOO�), peroxy (ROO�) and superoxide anion
(O��2 ) radicals. Heat accelerates homolysis of hydroperox-
ides and produces peroxy radicals [16]. Nonradical deriv-
atives are hydrogen peroxide (H2O2), ozone (O3) and
singlet oxygen (1O2) [53]. The most reactive ROS is
hydroxyl radical followed by singlet oxygen. Lipid and
1
2
3
4
5
10
19
67
8
9
11 13
12
15
16
17
1820
2122
23
24
25
2627
14
Fig. 1 Chemical structure of cholesterol molecule
172 Food Eng Rev (2013) 5:171–184
123
cholesterol oxidation by ROS produces low-molecular-
weight volatile alcohols, aldehydes and hydrocarbons.
It has been shown that in the absence of other promoters
of oxidation, cholesterol is relatively stable up to temper-
atures below the melting point (148.5 �C) [15, 38, 45], so
the kinetic studies are generally carried out in the presence
of heat sources. In the next paragraphs, we will refer only
to heat-induced auto-oxidation (thermo-oxidation).
Oxidation usually takes place through a radical initiated
chain mechanism [34], involving the following steps:
Initiation RH! R�
R� þ O2 ! RO�2Propagation RO�2 þ RH! RO2Hþ R�
R� þ O2 ! RO�2Branching RO2H! RO� þ �OH
RO� þ OHþ O2 ! ROHþ RO�2�OHþ RHþ O2 ! H2Oþ RO�2
Inhibition InHþ RO�2 ! In� þ RO2H
In a cholesterol molecule, the reaction can be divided into
two major routes of C-7 oxidation and epoxidation (Fig. 2).
The first free radicals that are formed seem to be located in
positions C-7 and C-25, giving 7ab-hydroperoxycholesterol
(7ab-OOH) and 25-hydroperoxycholesterol (25-OOH). The
7-OOH epimers are the only ones to remain at room
temperature, while 25-OOH usually occurs in dry solid
cholesterol, and to a lesser extent in dispersion or solutions
[45]. During heating, 7-OOH epimers can be reduced and
give rise to the corresponding hydroxyl derivatives:
cholesterol-5-en-3b,7a-diol (7a-OH) and cholesterol-5-en-
3b,7b-diol (7b-OH). The formation of epoxy derivatives
occurs by bimolecular reaction mechanism. In fact, 5,6a-
epoxy-5a-cholestan-3b-ol (5a-epoxy) and 5,6a-epoxy-5b-
cholestan-3b-ol (5b-epoxy) are formed by the interaction of
a hydroperoxy radical and cholesterol [26].
Depending on the intensity and time of exposition, choles-
terol and its oxidation products can generate other oxygenated
compounds. Dehydration of 7-OOH and dehydrogenation of
7-OH lead to the formation of 3b-hydroxycholesten-5-en-7-
one (7-keto), as reported by Chien et al. [15].
The formation of COPs in positions other than C-7
during thermo-oxidation has been poorly addressed, espe-
cially the cholest-5-en-3b,4b-diol (4b-OH) and 3b-hydro-
xycholest-4-en-6-one (6-keto) [45]. According to Maerker
and Jones [43], the 3b-hydroxy function of cholesterol
could be oxidized to a 3-keto function, and the 5,6 double
bond could move to the 4,5 position, in conjugation with
the carbonyl group.
The hydration of epoxides in acid is initiated by pro-
tonation of the ring oxygen and is followed by an approach
of a nucleophile, in this case water, at the more highly
branched carbon from the opposite to that of the protonated
oxygen. In the a-epoxide, the rear side of C-5 is sterically
hindered by the angular methyl C-19, and nucleophilic
attack occurs not at C-5, but, reluctantly, at C-6, resulting
in the 5a-cholesta-3b,5,6b-triol (triol).
Oxidative attack at tertiary C-20 and C-25 positions
generates monohydroperoxides 20-OOH and 25-OOH and
their corresponding decomposition products [45], which
are mainly hydroxyl derivatives in position 20 (cholest-5-
en-3b,20a-diol, 20-OH) and 25 (cholest-5-en-3b,25-diol,
25-OH). These last are more stable and can remain for
6 months during continuous heating at 100 �C [58]. The
C-25 radical may form directly from cholesterol by a pri-
mary hydrogen abstraction reaction similar to that reported
at C-7, but it could also be formed by a radical transfer
reaction involving a radical already formed by reaction
with cholesterol [57]. Furthermore, the authors of this
paper found that the formation of 25-OH is strongly
dependent on the physical state of the sample. In anhydrous
cholesterol, the exposition of the aliphatic chain is favored,
resulting in a higher production of 25-OH [45].
Photo-oxidation
Cholesterol is known to be as susceptible to peroxidative
modification as other unsaturated lipids when exposed to
exciting light of suitable wavelength and molecular oxygen
[25]; however, the kinetics of cholesterol photo-oxidation
has not been sufficiently studied [46]. Chemical studies on
model systems have led to rapid advances in the under-
standing of a number of different photo-oxidation pathways
that can occur.
As discussed above for auto-oxidation (see ‘‘Auto-oxi-
dation’’ section), photo-oxidation processes can be initiated
by ROS. Among physical agents, near ultraviolet (UVA,
340–400 nm) and visible (400–700 nm) radiations are of
special interest in photo-induced oxidation. These, together
with appropriate photoexcitable compounds (sensitizers)
and ground state molecular oxygen (3O2) produce oxidative
injury through photodynamic action [21, 24].
Oxygen has two metastable molecular state excitements;
in the presence of light, 1O2 is typically generated by
energy transfer from a sensitizer in the relatively long-lived
triplet excited state (3S) to ground molecular state oxygen
(3O2). 1O2, wherein having high energy of 93.6 kJ above
the ground state triplet oxygen [24], reacts with lipids at a
higher rate than triplet oxygen. Since 1O2 is electrophilic
due to a completely vacant p2p orbital [25], it directly
reacts with high-electron-density double bonds via
6-membered ring without lipid radical formation [16]. The
lifetime of 1O2 is from 50 to 700 ls, depending on the
solvent systems of foods. The reaction temperature has
little effect on the oxidation rate of this nonradical
Food Eng Rev (2013) 5:171–184 173
123
derivative with foods due to the low activation of 0–6 kcal/
mol [20].
The major pathway for 1O2 formation in food is pho-
tosensitization [16], which can be initiated in the presence
of sensitizers. These last are pigments such as porphyrins,
carotenoids and chlorophyll, and dyes such as methylene
blue, eosin and curcumin [17], which can absorb energy
such as radiation and transfer it to the triplet oxygen, which
is less active than singlet oxygen. Riboflavin also acts as a
sensitizer [16]. Excited singlet state sensitizers return to
ground state via emission of light, internal conversion or
intersystem crossing. Fluorescence or heat is produced
from the excited singlet sensitizer by light emission or
internal conversion, respectively.
There are two different mechanisms of photoreaction
(Type I and Type II), one in which the primary interaction
of the triplet sensitizer is with oxygen, and the other in
which the interaction is with the substrate. The efficiency
of each path depends on the relative concentrations of
oxygen and substrate, the rates of reaction of sensitizer
triplet with substrate and with oxygen and the rate of triplet
decay [21].
Type I photoperoxidation is similar to ordinary lipid
auto-oxidation, with the exception of the mechanism of
primary oxidant generation. The excited triplet sensitizer
can interact directly with a substrate such as phenol or lipid
compounds by donating an electron or accepting hydrogen,
resulting in the production of free radicals. After initiation
of the free radicals (R�), the radical compound may react
with triplet oxygen via the free radical oxidation mecha-
nism [22]. The initiation of radical formation in the food
molecule will be at the site most liable for the loss of a
hydrogen atom. Each of these reactions pathways may give
rise to a large number of primary and secondary oxidation
Fig. 2 The formation pathways of some COPs during thermo-oxidation. The boxes indicate the kinetic routes studied by Chien et al. [15] and
Medina-Meza et al. [45]
174 Food Eng Rev (2013) 5:171–184
123
products. The excitation energy of the triplet sensitizer can
be transferred to triplet oxygen to produce singlet oxygen,
and the excited triplet sensitizer then returns to its ground
state (Type II) [16]. The rate of these two types of pro-
cesses depends on kind of sensitizers and substrates, con-
centrations of substrate and oxygen in the reaction
environments [10]. Type II photoperoxidation is consider-
ably less complex mechanistically than Type I; in general,
there are fewer products [25]. Both mechanisms are sum-
marized in Fig. 3.
Light promotes oxidation in lipids and steroids, such
cholesterol, especially in the presence of photosensitizers.
Medina-Meza et al. [46] reported that the mechanism of
cholesterol photo-oxidation presents both processes: Type
II photo-reaction may be divided into two major routes, the
C-6 oxidation and epoxidation, while in Type I it can be
observed two major pathways, the C-7 and the side-chain
oxidation (Fig. 4). The most reactive group of the choles-
terol side chain is the ternary carbon C-25. Thus, the for-
mation of alcohols in position C-20, C-24, C-25 and C-26
can occur via a direct free radicals reaction without any
intermediate forms being generated [56].
Cholesterol photo-oxidation begins with a sensitizer
absorbing energy from light and transferring it to triplet
oxygen to form singlet oxygen. Then, singlet oxygen reacts
with C-5,6 double bond, producing hydroperoxides
(OOH�), resulting the formation of 5-OOH and 6-OOH
[23]. It is well known that an allylic rearrangement of
5-OOH to epimeric 7ab-OOH [56] is more stable. Next,
hydroperoxides are reduced to diols, continuing the chain
reaction of free radical resulting in the 7-keto and other
species, such as epimeric 5,6ab-epoxides. However, other
mechanisms may also be operating in relation to further
oxidations of epimeric 7ab-OH in order to account for the
rather specific accumulation of 7-keto. The reaction rate of
cholesterol with singlet oxygen is 2.5 9 108 M-1 s-1 [33].
The hydration of epoxides in acid is initiated by pro-
tonation of the ring oxygen and followed by the approach
of a nucleophile. In the 5,6a-epoxide, the rear of C-5 is
sterically hindered by the angular methyl C-19, and
nucleophilic attack occurs not at C-5, but at C-6, resulting
in the formation of triol, which results in one hydroxyl
group being sterically hindered [45]. Isomers 6ab-OOH
give 5a-cholestan-3,6-dione (3,6 dione) and 4-cholestan-
3,6-dione, as results of dehydration via free radicals and/or
pyrolysis, having as intermediate product 3b-hydro-
xycholest-4-en-6-one.
It is known that in the A-ring, 3b-hydroxy function is
oxidized to a 3-keto function, and the 5,6-double bond may
move to the 4,5 position, in conjugation with the carbonyl
group; this process is promoted by the crystalline state of
cholesterol, probably due to the rigidity conferred by the
physical state [43, 46].
It is important to point out that the light source is of
great importance in the dynamics of photosensitization.
Most studies reported in the literature consider sources of
fluorescent light, with emission characteristics in the visi-
ble spectrum [5, 6, 14, 30, 40, 46]. The use of this type of
lamp simulates the situation present in retail shops [6].
COPs can also be formed in aqueous systems when cho-
lesterol is exposed to ionizing radiation. The products are
similar to those formed by auto-oxidation, but in different
relative amounts [35]. Maerker and Jones [42] reported that
cholesterol in aqueous environments exposed to gamma
radiation leads to generation of COPs in ratios different
than those produced by auto-oxidation. They stated that
7-keto and the isomeric 5,6-epoxides are the principal
products.
Kinetic Modeling of Cholesterol Oxidation in Model
and Food Systems
Despite the scientific impact of chemical kinetics in food
technology and engineering as a powerful predictive tool
against certain compounds (whether harmful or healthy),
its application in the oxidative processes is still poor.
Kinetic studies are important, since empirical and semi-
empirical rate expressions based on those studies are
obtained, which can then be used for predictive purposes to
Fig. 3 Scheme showing photo-
induced oxidation by Type I or
Type II chemistry (adapted from
[23])
Food Eng Rev (2013) 5:171–184 175
123
Fig. 4 Cholesterol oxidation products (COPs) generated via Type I and Type II photochemistry (adapted from [46])
176 Food Eng Rev (2013) 5:171–184
123
analyze a system’s dynamic behavior or to design chemical
reactors. As a result of the kinetic study, the authors have
composed a scheme of the mechanism of the process, as
well as analyzing it and comparing it with experimental
data in the literature, finding that there is a need for new
testing experiments, and if necessary supplementation of
the scheme and repeated checking [18]. The rate constants
can be calculated in different ways, such as empirically,
mechanistically and by performing molecular and quantum
level calculations.
There is a great deal of literature on the kinetics of
oxidation in oils and fats [7, 10, 49] as well as pigments
[20, 28], although the primary source of information refers
to works published a few decades ago [34]. The difficulty
lies in understanding the cascade of reactions and in the
limitations associated with the different methods of
assessing the degree of oxidation [7]. The study of complex
chemical reactions, such as lipid oxidation has shown that
most of those reactions are a composite of elementary steps
that involve very reactive intermediate species, known as
radicals. Generally, chemical kinetic studies in food sci-
ence do not use a macroscopic deterministic approach,
coupling differential equations (rate equations) and solving
them, sometimes analytically, but often by numerical
methods because of their complicated forms. This method
is based on the identification and quantification of each
species, which usually is not viable. Furthermore, in the
case of lipid oxidation, many intermediate products have a
limited half-life and are difficult to isolate. So, an alter-
native heuristic approach is usually used, defining a system
of few equations that represent the main reactions involved
during oxidation, or more frequently considering each
oxidative pattern as independent [34]. In this last case, the
food engineer’s goal is to find an empirical nth order rate
expression since such a form can often match the data
reasonably well within the experimental accuracy and is
easier to use than the complex rate form. Table 1 sum-
marizes the rate laws for zero, first and second order in
their differential and integrated forms.
In the next section, we will discuss the kinetic models
(empirical and mechanistic) proposed for the oxidation of
cholesterol in model systems, namely those in which the
cholesterol is alone, or combined with inhibitors/activators
of known nature. Then, we discuss the application of these
models in real systems, with a focus on their predictive
efficacy.
Thermo-oxidation
Kinetic Modeling in Thermo-oxidation of Cholesterol
The first proposals of a rigorous mathematical model of
cholesterol thermo-oxidation were conducted by Chien’s
group [11–13, 15]. Previously, Yan and White [65] studied
the kinetics of cholesterol oxidation during the heating of
lard and found that the reactions for the formation of 7-OH,
7-keto and 5,6-epoxy fit the first order. In contrast, in
another study, Park and Addis [51] reported that the reac-
tion for the formation of 7-keto during heating fits the zero
order. These two works will be discussed in full in
‘‘Applications in food systems’’ section. In 1996, Park et al.
[50] predicted chemical stability of 7-keto during hot
saponification at 45, 55, 65 and 75 �C using the Arrhenius
equation. Chemical reaction of 7-keto was described by a
pseudo-first-order reaction, because base reagent was in
excess. The rate equation for a first-order reaction is:
log½7� keto�½7� keto�0
¼ � k
2:303t
where [7-keto]0 is the initial concentration of 7-keto. The
study confirmed that higher temperature and prolonged
exposure promoted higher degradation of 7-keto. The cal-
culated activation energy for the reaction was about
113 kJ/mol.
Chien et al. [15] developed a mathematical model in
order to describe kinetic degradation of thermo-oxidized
cholesterol. Their model system consists of a microfilm
deposited on the inner surface of a flask; the authors did not
investigate the crystalline characteristics of sample
obtained, which could markedly influence oxidative pat-
terns, as speculated by Smith one decade before [56]. Due
to the complexity of COPs formation, they selected only
four major COPs (7-OOH, 7-OH, 7-keto and 5,6-epoxy),
dividing the reaction into two principal routes, C-7 oxi-
dation and epoxidation, considering these last as irrevers-
ible reactions. Another assumption made by the authors is
that oxygen concentration could be considered constant
and so can be despise in numerical analysis.
The results presented by Chien et al. [15] show that
cholesterol oxidation can be initiated by a second-order
reaction, and the first-order reactions follow afterward
(propagation). It is understood that the authors consider the
reactions as elementary, though they were not. For ele-
mentary reactions, the one-to-one correspondence exists
between order and molecularity of reaction. Unimolecular
reactions are first order; bimolecular are second order, etc.
Table 1 Summary of basic rate laws
Order Differential rate law Integrated rate law
0 dCi
dt¼ k Ci ¼ �kt þ C0
1 dCi
dt¼ kCi ln Ci ¼ �kt þ ln C0
1 dCi
dt¼ kCi Ci ¼ C0e�kt
2 dCi
dt¼ kC2
i1Ci¼ 1
C0þ kt
Food Eng Rev (2013) 5:171–184 177
123
[18, 34]. The system of differential equations that describe
the overall oxidative system considered is as follows:
d½Chol�dt
¼ �k1½Chol�½7� OOH� � k5½Chol� ð1Þ
d½7� OOH�dt
¼ k1½Chol�½7� OOH� ð2Þ
d½7� OH�dt
¼ k2½7� OOH� � k3½7� OH� ð3Þ
d½5; 6� epoxy�dt
¼ �k4½Chol� ð4Þ
d½7� keto�dt
¼ k3½7� OOH� þ k0
3½7� OH� ð5Þ
Equation 2 could be reduced to the logistic equation
proposed by Ozilgen and Ozilgen [49] to describe lipid
oxidation:
½7� OOH� ¼ ½Chol�ek1t
½Chol�½7�OOH�max
ð1� ek1tÞð6Þ
where [7-OOH]max is the maximum attainable value of
concentration at the end of the cholesterol oxidation pro-
cess for 7-OOH, k1 is the reaction rate constant (h-1) and t
is the time. Equations 1, 3–5 were integrated and resolved
by numerical analysis. If [7-OOH] � [7-OOH]max. The
equation can be rewritten as ½7� OOH� ¼ ½Chol�ek1t,
which is a first-order rate equation. Chien and coworkers
reported good correlation between experimental and theo-
retical data (R2 [ 0.80), especially for cholesterol degra-
dation and C-7 route.
Nonetheless, Chien’s approach seems to be incomplete,
considering that at least eight/ten different compounds are
found in considerable amounts during cholesterol degra-
dation in experimental conditions [45, 56], including both
7ab-OH and 5,6ab-epoxy isomers, as well as side-chain
oxysterols (20-OH, 25-OH). It is well known that during
auto-oxidation, the quasi-axial 7b-OH is produced more
abundantly than the quasi-equatorial a-isomer, due to steric
effect [41]. Both are transformed in 7-keto at different rates
[47]. Furthermore, after the C-7 position, ternary carbon
C-25 is the most susceptible to radical attack, followed by
C-20, giving their respective hydroperoxides 25-OOH and
20-OOH. These may be subject to a further degradation to
give 25-OH and 20-OH, respectively, which are currently
found in a great amount of animal products [31], as well as
dairy foods [59].
Medina-Meza et al. [45] studied thermo-oxidation of
cholesterol at 150 �C using a model system that consisted
of a thin crystalline microfilm deposited on a flask. The
hypothesis underlying the study was that the physical state
of cholesterol would markedly affect the oxidative pattern.
The cholesterol was re-crystallized in order to obtain
anhydrous crystals, as described by Loomis et al. [38]. The
authors observed that the solid state limited the mass
transference, with a lower diffusion of radical species and
availability of substrate. As a result, the kinetic profile was
deceleratory in the case of primary oxidation products
(hydroperoxides) during the initiation phase (0–60 min). In
the propagation phase, a rapid decrease in hydroperoxides
content was followed by the formation of different COPs.
Nine COPs were present at the end of the heat treatment:
7a-OH, 7b-OH, 5,6a-epoxy, 5,6b-epoxy, triol, 7-keto,
25-OH, as well as 4b-OH and 6-keto; these last two scar-
cely found in large amount in previous studies.
Barriuso et al. [1] recently realized a heat-induced oxi-
dative kinetic study of different steroids, among other
cholesterol. Similar to Chien’s work, they focused on 7ab-
OH and 5,6ab-epoxy epimers, 7-keto and triol. Although
expressed in the text, they did not propose a kinetic model,
but used nonlinear regression to fit experimental data,
considering each molecular formation as independent. The
rate constants thus obtained were not very indicative and
cannot be related to the reactions present during the oxi-
dative phenomenon. They used inverse, logarithmic and
exponential equation, obtaining good correlation between
data; even so the fitting parameters have no physical or
chemical significance.
As mentioned above, those models consider oxygen as
reactant in excess, thereby simplifying the kinetic system.
It is essential to mention that an effective model should
consider the concentration of oxygen as a key variable, as
well as the setup proposed by Bimberg [7]. This author
develops an oxidative model for fats, in which the oxida-
tion is characterized by the classic three stages (see ‘‘Auto-
oxidation’’ section), whereas the intake of oxygen is not
constant over time. Incidentally, the approach developed
by Bimberg, despite considerable interest, had no sub-
sequent applications.
Effects of Antioxidants in the Kinetics
One of the most effective methods to control lipid oxidation
is the incorporation of antioxidants [36, 44]. Antioxidants
work by a variety of different methods, including control of
oxidation substrates (for example, oxygen and lipids), con-
trol of pro-oxidants (for example, reactive oxygen species
and pro-oxidant metals) and inactivation of free radicals.
It is well established that c-tocopherol has a good
inhibitory effect in thermo-induced cholesterol oxidation,
retarding induction period, whereas a and d-tocopherol do
not [61]. Chien et al. [13] extended the proposed kinetic
model by including the antioxidant effect of a secondary
amine, stearylamine on cholesterol heating. Stearylamine
has a protective effect against oxidation of cholesterol,
since it reacts with the epoxy ring formed by the radical
178 Food Eng Rev (2013) 5:171–184
123
attack in a double bond, resulting in a stable amine product.
In this study, the cholesterol was solubilized in oil, and
thermo-oxidative study was carried out at 140 �C. The
results lend themselves to doubts about the effectiveness of
the proposed model, since the residual cholesterol found at
the end of kinetics is quite similar in both tests, although
the protective effect seems to be strong during the first 2 h
of treatment. This consideration is confirmed by the
unsatisfactory coefficient of determination (\0.80) for
most of the oxidative routes. In a subsequent work, Chien’s
group widened the kinetic model to triol (derived from
acidic hydration of isomeric 5,6ab-epoxy), studying the
antioxidant effect of quercetin (0.002 % w/w) on choles-
terol thermo-oxidation [12]. Quercetin has a marked ability
to scavenge highly reactive species such as peroxynitrite
and the hydroxyl radical, which are responsible for the
process of radical oxidation [4, 61]. On this occasion, a
good correlation is shown between theoretical and experi-
mental data. The principal outcomes of quercetin are in the
reduction in rate constants of the free radical chain reaction
of 7-OOH (from 453.5 h-1 to 117.7 h-1) and subsequent
dehydration of the last to form 7-keto (from 155.5 h-1 to
31.0 h-1). However, as in the case of stearylamine, the
effects are significant only for short periods of heat
treatment.
Finally, Yen et al. [66] developed a GC–MS analytical
method to determine COPs and conjugated linoleic acids
(CLAs) in a model system. CLAs are usually found in high
amounts in various meat products, whereas their occurrence
is scarce in vegetable oils and butter [2]. The role played by
CLAs as antioxidants is not clear, and there is still much
uncertainty about their actual scavenger properties [9, 68]. In
their work, they fitted kinetic curves with Chien’s model
(corresponding to a first-order integrated law, as shown in
Table 1), obtaining good correlation values. However, their
results are mathematically inconsistent, because the equa-
tion used by the authors in the kinetic modeling of COPs
refers to an exponential degradation.
Applications in Food Systems
Kinetic modeling is gaining increasing interest in food
science because it provides the possibility of controlling
changes in foods, i.e., to control food quality during pro-
cessing and shelf life [62]. If the development of kinetic
modeling in the thermo-oxidation of pure cholesterol is
limited, it will be even more so in more complex systems,
like foods. A high number of papers have been published
on the quantification of COPs in different food products,
and there are many reviews that regularly update the state
of the art [31, 59, 63]. Nevertheless, the kinetic approach is
rarely used, and even less so the application of mathe-
matical models.
The first attempt was made by Yan and White [65], who
studied the kinetics of cholesterol oxidation during the
heating of lard and found that the reactions for the formation
of 7-OH, 7-keto and 5,6-epoxy fit the first order. An analog
experiment with lard was carried out by Derewiaka et al.
[19], considering the geometry of the product, an essential
factor during any phenomenon of transference of energy, as
this can be a thermo-induced oxidation. Surprisingly, the
authors do not use the valuable information of Yan and White
about the reaction orders, but describe the change in the
dynamics of COPs using a second-degree polynomial.
In contrast, in another study, Park and Addis [49],
studying the thermo-oxidation of tallow at 155 and 190 �C
for 250 and 400 h, respectively, reported that the reaction
for the formation of 7-keto during heating fits the zero
order between certain temperature ranges, while choles-
terol presented an exponential decay behavior. The absence
of COPs at 190 �C leads the authors to hypothesize that at
an extremely elevated temperature, there may either be less
chance for cholesterol oxidation to occur, or more probably
for COPs to break down quickly after formation. The rate
of formations can be inferred from the graphics presented
in the article: for cholesterol degradation 3.2 9 10-3 h-1
and 2.4 9 10-3 h-1, at 155 and 190 �C, respectively,
whereas for 7-keto it is approximately 0.03 h-1 at 155 �C.
It is important to point out that in these early attempts the
authors used mechanistic models that consider each oxi-
dative step separately.
Ohshima et al. [48] studied the decomposition of cho-
lesterol in fish oils, approaching a real food system. This
study is interesting because the authors created a microfilm,
mixing crystalline microcellulose with cholesterol and fish
oil, which was subjected to auto-oxidation for a few weeks.
Despite the fact that the authors did not propose any kinetic
model, an accurate interpretation of their data suggests that
COPs formation (expressly, 7-keto, 7-OH and 5,6-epox-
ides) follows a hyperbolic behavior, similar to that
observed by Medina et al. [45].
Although the kinetic model proposed by Chien et al.
[15] (see ‘‘Kinetic modeling in thermo-oxidation of cho-
lesterol’’ section) could be used to predict the concentration
changes of main COPs during heating, its use was limited
to model system. Still, the literature does not report
applications in foods. In a recent work [67], the authors
prefer to use a simple exponential equation to fit the
experimental data obtained from thermo-oxidation of lard
in the presence/absence of CLAs at 150 and 200 �C.
Cholesterol degradation and COPs shows a first-order
kinetic at 150 �C, whereas at 200 �C the authors preferred
a pseudo-second-order equation:
dðCi=CmaxÞdt
¼ kf Cmax 1� Ci
Cmax
� �� �2
ð7Þ
Food Eng Rev (2013) 5:171–184 179
123
where Ci is the COPs concentration at time t, Cmax is the
COPs concentration at the equilibrium, kf is the formation
rate constant and t is the heating time. Equation (8) was
recently introduced for the description of adsorption kinetic
in liquid-phase adsorption systems [64]. The dimensionless
concentration, d(Ci/Cmax)/dt, is proportional to the square
of the residual amount of reactant, 1 - Ci/Cmax. Conse-
quently, the proportional constant kfCmax can be defined as
the second-order rate index [64].
The different kinetic approaches used for thermal cho-
lesterol degradation and single COPs formations are sum-
marized in Table 2.
Photo-oxidation
Kinetic Modeling in Photo-oxidation of Cholesterol
Cholesterol photosensitized oxidation has been studied
both alone and in the presence of pro- or antioxidants.
Considering the scarcity of works about oxidation kinetics,
in this section, we will deal with both situations. In two
similar works, Hu et al. [30] and Chien et al. [14] studied
the protective effect of riboflavin and fatty acid methyl
esters (stearic, linoleic and docosahexaenoic acids) on
cholesterol during illumination; a model system consisting
of an organic solution of cholesterol subjected to exposure
of three 40-W fluorescent tubes was used. The distance
between sample vials and the light source was about
50 cm, and the illumination intensity was 2,000–3,000 lux
at 25 �C for 28 days.
The authors determine the degradation rate constant of
cholesterol using the following equation, representing first-
order degradation:
k ¼ln½Chol�½Chol�0t
ð8Þ
where [Chol] is the concentration of cholesterol after light
exposure, [Chol]0 is the initial concentration of cholesterol
and t is the illumination time (days).
In the first study, Hu et al. determined the rate of deg-
radation of cholesterol (expressed in d-1) in coexistence
Table 2 Kinetic models proposed for thermal oxidation of cholesterol in food and model systems
Oxidation route Kinetic type Model Reference
Cholesterol degradation First order Tallow (155 and 190 �C) Park and Addis [51]
First order Lard (180 �C) Yan and White [65]
First order Lard (100, 150 and 200 �C, CLAs as antioxidant) Yen et al. [67]
First order Solid state, anhydrous (150 �C) Medina-Meza et al. [45]
C-7
7-OOH Second order Solid state (150 �C) Chien et al. [15]
Second order Solution (140 �C, stearylamine as antioxidant) Chien et al. [13]
Second order Solution (150 �C, quercetin as antioxidant) Chien et al. [12]
First order Lard (100, 150 and 200 �C, CLAs as antioxidant) Yen et al. [67]
Deceleratory Solid state, anhydrous (150 �C) Medina-Meza et al. [45]
7a,b-OH First order Lard (180 �C) Yan and White [65]
First order Solid state (150 �C) Chien et al. [15]
First order Lard (150 �C, CLAs as antioxidant) Yen et al. [67]
First order Solid state, anhydrous (150 �C) Medina-Meza et al. [45]
Pseudo-second order Lard (200 �C, CLAs as antioxidant) Yen et al. [67]
7-keto Zero order Tallow (155 �C) Park and Addis [51]
First order Lard (180 �C) Yan and White [65]
First order Solid state (150 �C) Chien et al. [15]
First order Lard (150 �C, CLAs as antioxidant) Yen et al. [67]
Pseudo-second order Lard (200 �C, CLAs as antioxidant) Yen et al. [67]
C-5
5,6ab-epoxy First Lard (180 �C) Yan and White [65]
Second Solid state (150 �C) Chien et al. [15]
Second Solution (140 �C, stearylamine as antioxidant) Chien et al. [13]
Side-chain
25-OH First order Solid state, anhydrous (150 �C) Medina-Meza et al. [45]
180 Food Eng Rev (2013) 5:171–184
123
with stearic acid methyl ester, linoleic acid methyl ester
and docosahexaenoic acid methyl ester, and obtained the
values 0.0322, 0.0152 and 0.0198, respectively, with high
correlation coefficients ([0.9). Regarding the rate of deg-
radation of cholesterol, in the presence of 50 ppm and
100 ppm of riboflavin, the constant values were 0.0655 and
0.0747 d-1, respectively. No degradation rate of riboflavin
was calculated because it was not detected after 1 day of
light exposure.
In the second paper [14], the authors also analyzed the
hydroperoxides formed under the same conditions of
treatment. Cholesterol hydroperoxides were measured in
the first 7 days; after that, both linoleic acid methyl ester
and docosahexaenoic acid methyl ester were completely
degraded. The degradation rate constants for cholesterol in
the presence of stearic methyl acid ester, linoleic acid
methyl ester and docosahexaenoic acid methyl ester were
0.0549, 0.0567 and 0.0512 d-1, respectively, about 3 times
more rapid than cholesterol exposed to treatment in the
absence of the sensitizer (0.0175 d-1). The results are
higher than those found in previous research, showing that
the addition of riboflavin facilitates cholesterol degradation
during light exposure.
Medina-Meza et al. [46] studied photo-oxidation of
crystalline cholesterol, reporting the formation of side-
chain COPs. They formed a thin crystalline film of anhy-
drous cholesterol by slow evaporation of a cholesterol/
chloroform solution, adding a certain amount of hemato-
porphyrin as a sensitizer. The system was illuminated in an
incubator at 25 ± 2 �C for 21 days. The light source was a
lamp with a fluorescent tube of 18 W and 6,500 K, lumi-
nous flux 1,300 Lm and light intensity of 4,300 ± 100 lx.
Among the results achieved, a hyperbolic trend was
observed in hydroperoxides formation, which could be
justified considering the inhibition due to end-to-end
crystalline arrangement that slows peroxidation rate for the
reduced availability of sites susceptible to radical attack.
Cholesterol degradation was fitted with a first-order expo-
nential decay equation [28, 66], obtaining a good correla-
tion value (R2 [ 0.98) and a kchol = 0.0395 d-1, about half
of the value obtained by Hu et al. [30]. This result could be
attributed to increased activity of hematoporphyrin as a
sensitizer, and to the different conditions of the experiment.
The rates of formation of Type II photoreaction products
(namely 5,6a-epoxy, 5,6b-epoxy, 6-ketostanol and 6-OH)
were lower than Type I ones (7a-OH, 7b-OH and 7-keto).
This result is probably due to the reaction mechanism and
radiolytic stability of these COPs, since susceptibility of
7-keto and 5,6b-epoxi has been found to be dependent on
its microenvironment [43]. To emphasize the importance of
the physical state in the oxidative pattern, the formation
rate and the final concentration of 25-OH (a side-chain
oxysterol) are higher than 7-keto; in particular, the value of
the constant rate is 0.8 9 10-2 d-1 for 25-OH and
0.2 9 10-2 for 7-keto.
Applications in Food Systems
There is some negligence in modeling the kinetics of photo-
oxidative phenomena in foods, and information regarding
cholesterol and COPs is therefore poor. Butter and meat
products are the most studied foods, and a comprehensive
review of the content of COPs in these products can be found
in Cardenia et al. [8]. Luby et al. [39] kinetically analyzed
butter photo-oxidation, since these oxidation products are
detectable only after prolonged exposure to light. They
further investigated the effect of packaging and light source
on oxidative stability [40]. It is interesting that the authors
consider oxidation as a light-induced surface phenomenon,
realizing their food model on this basis. A wide range of
wavelength (276–700 nm) was chosen to prove the effect of
different packaging material (HD and LD polyethylene
films, wax paper and aluminum foil, among others), moni-
toring peroxide value at 1 and 2 weeks of light exposition,
and obtaining a first-order trend in hydroperoxides accu-
mulation. It should be pointed out that an analysis carried out
with a reduced number of progressive sampling points is
insufficient for a correct determination of the kinetic
dynamic.
Storage under artificial light is a strong pro-oxidant agent,
especially for meat products. Boselli and coworkers studied
the formation of COPs in turkey [5] and beef [6] meat, using a
kinetic approach. In their first work, the samples were
exposed to warm-tone and daylight lamps. The first one
emanated red light with low emission in the blue radiation
(3,000 K, 36 W), while the second one was a fluorescent
light (6,000 K, 36 W). The oxysterols concentration in
samples irradiated with the warm-tone lamp was comparable
to that of meat kept in darkness with a similar storage time,
thus being much lower than that of irradiated samples with
the daylight lamp. The different degrees of oxidation
induced by the two types of lamps can be attributed in part to
their energy of radiation, which is higher in the daylight lamp
than in the red fluorescent lamp, because it contains a greater
amount of blue light. However, as in most of the works cited
above, the energy aspects relating to the source of light were
not examined in depth. For instance, Hansen and Skibsted
[27], studying light-induced oxidative changes in a dairy
spread, observed that lipid peroxidation increased with
decreasing wavelength.
Similar experiments were carried out by Boselli et al. [6]
in a subsequent work in cow meat; this time the authors
analyzed kinetic data of cholesterol degradation and total
COPs content by fitting it with a simple linear model:
Ci ¼ kit þ C0 ð9Þ
Food Eng Rev (2013) 5:171–184 181
123
where Ci is the concentration of the considered compound
and C0 is the initial concentration. ki assumes positive or
negative values, depending on whether it is a formation or
degradation of compounds. Equation (9) represents the
integrated law of a zero-order reaction, in which the rate is
independent of the concentration of reactant [18], as shown
in Table 1. The numerical value of the order does not need
to correspond to molecularity [63]; furthermore, in this
case the fit gives no statistically significant results, since
the coefficients of determination (R2) are 0.64 for choles-
terol degradation and 0.40 for total COPs formation. This
result demonstrates the lack of familiarity of many authors
with kinetic modeling and the fact that researchers in food
science have limited themselves to heuristic approaches
[62].
Table 3 reassumes the different kinetic models used for
cholesterol degradation and single COPs formations in
photo-oxidation.
Conclusions
In this paper, we have reviewed the state of the application
of kinetic models in the study of cholesterol oxidation
products. Despite the significance of kinetic modeling in
food engineering as a powerful tool to control/prevent the
formation and accumulation of these important molecules,
there has been little interest in researching this area.
Among the major points that make it difficult to design a
comprehensive model of the phenomenon of cholesterol
oxidation in food systems, we can highlight the following:
• The large number of molecules derived from oxidation
([80), many of which are volatile compounds difficult
to quantify.
• The presence/absence of antioxidants and pro-oxidants
and the interference of other macromolecules (proteins,
carbohydrates, lipids), which can exert a pro- or
antioxidant effect.
• Difficulties inherent in the analytical or numerical
resolution of systems of kinetic equations and the
correct interpretation of the obtained data.
Furthermore, analysis of the current status of the liter-
ature leads us to a future perspective view in which the
kinetic study of oxidative phenomena, and in particular of
cholesterol, will play a greater importance in Food Science
and Engineering. Among the different challenges that we
can mention are:
1. Correct application of the principles of chemical
kinetics, with the use of multiresponse approaches,
facilitated by the availability of more and more
powerful computational tools.
2. In the case of thermo-oxidation, evaluation of response
kinetics at different temperatures, better understanding
of the mechanisms of inhibition of antioxidants, ther-
modynamic considerations and transport phenomena.
3. In the case of photo-oxidation, there is an urgent need
to explore further aspects of transmission quantum
energy in food systems, considering not only the nature
of the source of induction, but also the effect of
inhibitors or activators of other molecules.
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Table 3 Kinetic models proposed for photo-oxidation of cholesterol in food and model systems
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