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KINETIC PARAMETER ESTIMATION FOR DEGRADATION OF
ANTHOCYANINS IN GRAPE POMACE

presented by
Dharmendra Kumar Mishra

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KINETIC PARAMETER ESTIMATION FOR DEGRADATION OF
ANTHOCYANINS IN GRAPE POMACE

By

Dharmendra Kumar Mishra

A THESIS

Submitted to
Michigan State University
in partial fulfillment of requirements
for the degree of

MASTER OF SCIENCE
Department of Biosystems and Agricultural Engineering

2008

ABSTRACT

KINETIC PARAMETER ESTIMATION FOR DEGRADATION OF
ANTHOCYANINS IN GRAPE POMACE

By
Dharmendra Kumar Mishra

Anthocyanins are degraded by heat, especially at temperatures
greater than 70°C. Thermal and kinetic parameters were estimated for the
degradation of anthocyanins in grape pomace, considered a winery waste that
has a potential use as a food ingredient. Nonisothermal experiments were
performed, and thermal and kinetic parameters were estimated, using nonlinear
regression techniques, for the degradation of anthocyanins in grape pomace at
moisture contents of 17, 34, and 42% (wb). Grape pomace was heated in a retort
for 8-25 min, at the retort temperature of 126.7 °C in 202 x 214 steel cans.
Anthocyanin retention in retorted samples was measured using HPLC. The

activation energy Ea, rate of reaction k11o°c, and the moisture parameter b were

estimated as 75.34 leg mol, 0.058 min'1 and 1.87 (MCwb)‘1. Asymptotic
confidence intervals for k11o°c and E, were (0.055, 0.067) and (32697.9),
respectively. Bootstrap 95% confidence interval for k11o°c and Ea were (0.055,
0.066) and (50.9, 100.82) respectively. Prediction bands on the predicted Y
(retentions) were computed using the asymptotic and the bootstrap approach.
Bootstrap prediction bands were smaller than asymptotic prediction bands. Joint
confidence region for thermal parameters were computed using an elliptical

approximation and an iterative method.

DEDICATION

To my parents, Ras Bihari Mishra and Sabita Mishra, for their selfless sacrifice
and for believing in me and providing all the assistance I needed at all times, to
my elder sister Usha Pandey and to my elder brothers Binod Mishra, Ashok
Mishra and Ravindra Mishra for their love and affection and to the younger
generation. To Balram Singh who taught me the concept of belief.

iii

ACKNOWLEDGEMENTS

I would like to express my utmost gratitude to my advisor, Dr. Kirk Dolan, for all
his consistent support and guidance throughout this research period. Dr. Dolan’s
high motivation and expectations inspired me to achieve beyond my capabilities.
Under his mentorship I gained exposure to numerous problem-solving
techniques not only in academics but also in other areas. I would like to thank my
committee members Dr. Maurice Bennink, Dr. Bradley Marks and Dr. Lijian Yang
for their valuable time and effort in the completion of this work and were the

source of invaluable advice through our engaging discussions.

I am also grateful to the faculty and staff of Biosystems Engineering as well as
Food Science, MSU. I am also thankful to all my friends and fellow graduate
students who have provided me the wonderful friendly atmosphere throughout
my Masters program and thanks to Dr. Sanghyup Jeyong, for providing me
timely assistance. Special thanks to my lab mates at room 129 in Food Science

Trout Building for their love and encouragement all the time.

Finally, I would also like to thank my parents, as they are the inspiration for

making me what I am today.

iv

TABLE OF CONTENTS

List of Tables ....................................................................................... vii
List of Figures ..................................................................................... viii
Chapter 1
Introduction
1.1 Structure of this Thesis .......................................................... 2
1.2 Background lnfomnation on Anthocyanins .................................. 3
1.3 Structure of Anthocyanins ....................................................... 5
1.4 Stability of Anthocyanins ......................................................... 6
1.5 Extraction of Anthocyanins and High-Performance
Liquid Chromatography ........................................................... 7
1.6 Experimental Design .............................................................. 8
1.7 References .......................................................................... 9
Chapter 2
Confidence Intervals for Modeling Anthocyanin Retention in Grape Pomace
during Nonisothermal Heating
2.1 Introduction .......................................................................... 12
2.2 Mathematical Model and Simulation .......................................... 17
2.2.1 Thermal Parameter Estimation ..................................... 17
2.2.2 Kinetic Parameter Estimation ....................................... 19
2.2.3 Sum of Squares of Errors ........................................... 20
2.2.4 Confidence Intervals ................................................... 21
2.2.5 Standard Error and Correlation Coefficient ...................... 21
2.3 Methods and Materials ........................................................... 23
2.3.1 Sealing and Retorting of Grape Pomace ......................... 23
2.3.2 Extraction of Anthocyanins from Grape Pomace ............... 24
2.3.3 Anthocyanins measurement ......................................... 24
2.3.3.1 Separation of Anthocyanins and
Polyphenolics ................................................ 24
2.3.3.2 HPLC System ................................................ 25
2.3.3.3 Anthocyanidins Separation ............................... 25
2.4 Results ................................................................................ 26
2.4.1 Thermal Parameter Estimation ..................................... 27
2.4.2 Kinetic Parameter Estimation ....................................... 29
2.4.3 Plot of Sum of Squares ............................................... 32
2.5 Conclusions ......................................................................... 33
2.6 Nomenclature ....................................................................... 35
2.7 References .......................................................................... 37

CHAPTER 3

Multi-parameter Estimation and Parameter Confidence Regions for Degradation
of Anthocyanins in Grape Pomace

3.1 Introduction .......................................................................... 42
3.2 Mathematical Model ............................................................... 44
3.2.1 Parameter estimation using nonlinear regression .............. 45
3.2.1.1 Moisture content model ................................... 45

3.2.1.2 Confidence Intervals ....................................... 43

3.2.1.3 Standard Error and Correlation Coefficient ........... 43

3.2.1.4 Confidence region .......................................... 49

3.3 Methods and Materials ........................................................... 51
3.3.1 Thermal treatment and degradation of anthocyanins ......... 51

3.4 Results ................................................................................ 53
3.5 Conclusion ........................................................................... 53
3.6 nomenclatures ...................................................................... 55
3.7 References .......................................................................... 57

CHAPTER 4

Bootstrap confidence interval for the kinetic parameters for degradation of
anthocyanins in grape pomace

4.1 Introduction .......................................................................... 71
4.2 Mathematical Model and Statistical Methods ............................... 73
4.2.1 Kinetic Parameter Estimation ....................................... 73

4.2.2 Overview of Bootstrap Method ...................................... 74

4.2.3 Application of Bootstrap to Kinetic Model ........................ 75

4.2.4 Bootstrap Confidence Interval on Parameters .................. 77

4.2.5 Bootstrap Confidence Interval on Predicted Y .................. 77

4.3 Methods and Materials ............................................................ 73
4.3.1 Experimentation ......................................................... 78

4.4 Results ................................................................................ 79
4.4.1 Kinetic Parameter Estimation ....................................... 30

4.4.2 Bootstrap Confidence Interval ...................................... 31

4.5 Conclusions ......................................................................... 85
4.6 Nomenclatures ...................................................................... 86
4.7 References ........................................................................... 33
CONCLUSIONS .................................................................................. 90

vi

LIST OF TABLES
Table 1.1: Effect of R group on flavylium cation to produce different
anthocyanidins ...................................................................................... 5
Table 1.2: Experimental Design ................................................................ 5
Table 2.1: Heating time and measured anthocyanin retention for grape pomace
at 42% (wb) moisture content at 126.7 °C retort temperature for 33 heated

cans .................................................................................................. 23

Table 2.2: Thermal property parameters for quadratic model for grape pomace at
42% (wb) moisture content ..................................................................... 29

Table 2.3: Degradation Kinetic parameters for anthocyanin degradation in grape
pomace at 42% (wb) moisture content ...................................................... 29

Table 3.1: Heating time and measured anthocyanin retention for grape pomace
at 17, 34 and 42% (wb) moisture content at 126.7 °C retort temperature .......... 53

Table 3.2: Kinetic parameters for anthocyanin degradation in grape pomace at
17, 34 and 42% (wb) moisture content ...................................................... 55

Table 4.1: Retention (%0 )value of anthocyanins for grape pomace at 42%

MC(wb) as measured from HPLC ............................................................ 79
Table 4.2: Kinetic parameters for anthocyanin degradation in grape pomace at
42% (wb) moisture content ..................................................................... 81
Table 4.3 Bootstrap confidence interval at 95% on E8 and k, ......................... 81

vii

LIST OF FIGURES

Figure 1.1: The anthocyanin ground structure, flavylium
(2-phenylchromenylium) ......................................................................... 5

Figure 2.1: HPLC chromatogram for the raw grape pomace. Peak identification 1,
delphinidin; 2, cyanidin; 3, petunidin; 4, peonidin; 5, malvidin ........................ 26

Figure 2.2: HPLC chromatogram for the retorted grape pomace at 126.7 00 for
14 minutes. Peak identification 1, delphinidin; 2, cyanidin; 3, petunidin; 4,
peonidin; 5, malvidin ............................................................................. 26

Figure 2.3: Example plot of observed and predicted center temperature profiles
from Comsol (triplicate runs) in canned grape pomace ................................ 27

Figure 2.4: Mass average retention of anthocyanins in grape pomace heated in

202 x 214 cans at retort temperature of 126.7 0C ....................................... 30
Figure 2.5: Residual plot of the mass average retention of anthocyanins for cans
heated at retort temperature of 126.7 OC ................................................... 31
Figure 2.6 3-D Surface plot of Sum of Squares (SS) .................................... 33

Figure 3.1: 95% asymptotic confidence band and 95% asymptotic prediction
band for mass average retention of anthocyanins in grape pomace at 42%
moisture content (wb) heated in 202 x 214 cans at retort temperature of 126.7

0C ..................................................................................................... 57

Figure 3.2: 95% asymptotic confidence band and 95% asymptotic prediction
band for mass average retention of anthocyanins in grape pomace at 17%
moisture content (wb) heated in 202 x 214 cans at retort temperature of 126.7

OC ..................................................................................................... 58

Figure 3.3: 95% asymptotic confidence band and 95% asymptotic prediction
band for mass average retention of anthocyanins in grape pomace at 34%
moisture content (wb) heated in 202 x 214 cans at retort temperature of 126.7
00 ..................................................................................................... 59

Figure 3.4: 95% joint confidence region using (1) equation (9) and (2) Motulsky
method for mass average retention of anthocyanins in grape pomace 42%

moisture content (wb) with parameters having correlation coefficient
of —0.5 ............................................................................................... 60

Figure 3.5: 3-D Surface plot of Sum of Squares (SS) ................................... 62

viii

Figure 3.6: 3-D Surface plot of Sum of Squares (SS) for Welt’s Data (Welt,
1997) ................................................................................................. 62
Figure 3.7: Residual plot of the mass average Retention of anthocyanins for
Grape pomace at 17, 34 and 42% moisture content (wb) heated at retort

temperature of 126.7 00 ........................................................................ 63

Figure 4.1: 95% bootstrap confidence band, 95% bootstrap prediction band, 95%
asymptotic confidence band and 95% asymptotic prediction band for mass
average retention of anthocyanins in grape pomace heated in 202 x 214 cans at

retort temperature of 126.7 0C ................................................................ 82

Figure 4.2 3-D plot of the bivariate normal distribution and 90 & 95% contours of
the confidence level .............................................................................. 83

Figure 4.3 scatter plot of all the bootstrap estimated parameters and confidence
regions at 90 & 95% confidence level (1,000 simulated points) ...................... 84

ix

Chapter 1

Introduction

1. Introduction

Degradation of the nutraceutical compounds can happen during thermal
treatment of the product. For the food to be nutritious and retain the value after
processing, one must ensure that the degradation of these compounds is
minimal during processing. Special case of anthocyanins in low-moisture and
high temperature processed foods, such as grape pomace, has been
investigated in this study. Kinetic parameters involved in the degradation model
were estimated using the non-linear method of least squares for the non-
isothermal heating of grape pomace. Confidence intervals, prediction intervals,
joint confidence regions and bootstrap confidence and prediction intervals are

discussed in details in subsequent chapters.

1.1 Structure of this Thesis

This work has been divided into three chapters. Each chapter covers a
different aspect of the kinetic parameter estimation of the anthocyanins
degradation in grape pomace, which is a low- and intermediate-moisture food
processed at higher temperature. The three main parts are 1) nonlinear
estimation of the two thermal kinetic degradation parameters; 2) joint confidence
regions for the two thermal parameters, and multi-parameter parameter
estimation when a moisture parameter is added; and 3) bootstrap method for
parameter estimation, which is a randomized resampling of the original data to

obtain better estimates of the error distribution.

Chapter 1 covers the experimental method used to measure the
anthocyanin retention for different time—temperature treatments in a steam retort.
It also covers the HPLC analysis, estimation of therrnophysical properties and
kinetic parameter estimation using the nonlinear regression technique and the
confidence interval of the parameters and on predicted Y (retentions).

Chapter 2 covers the multi-parameter model and estimation of the kinetic
parameters, such as estimation of parameters at different moisture level of the
grape pomace. It also covers the parameter joint confidence region and the sum
of square plots to evaluate the ease or difficulty in convergence of the
parameters in nonlinear regression.

Chapter 3 is about the bootstrap method to estimate the accurate
confidence interval on the kinetic parameters for the degradation of anthocyanins
in grape pomace. It also shows the method to calculate the bootstrap confidence
interval band and the prediction band on the predicted Y, which provides useful

information about the retention of the anthocyanins.

1.2 Background lnforrnation on Anthocyanins

Diet and nutrition are increasingly linked with disease prevention and
treatment. There has been a great interest in the nutraceuticals in food or as an
additive to the food. Grape pomace, which is leftover after the wine making
process, is a good source of anthocyanins and hence can be used as an
ingredient in food industry. Nutraceutical compounds, such as anthocyanins, are

food components known for their health promoting, disease preventing or

medicinal properties. Nutraceuticals not only can act as bright natural colorants
(Alexandra Pazmino-Duran and others 2001) but also have potential health
benefits, such as antioxidant and anti-inflammatory properties (Wang and others
1999). Anthocyanins have beneficial action against the vascular diseases and
contribute towards the reduction of age-related deficits in neurological

impairments (Youdim and others 2002).

Most kinetic research in food is conducted on high moisture foods (for
example, meats, fruit juice, vegetables and dairy products) at constant
temperatures, usually at less than 100°C. Experimental procedures and basic
statistical analyses for these products are well established for first order
reactions. The 2-step procedure includes plotting the logarithm of concentration
versus time at different constant temperatures. The rate constants will be the
negative of the slopes. Then plotting the logarithm of the rate constant vs. the
reciprocal of temperature will give the activation energy (Ea) from the slope.
However, this method is not suitable for low-moisture and high-temperature
processed foods because constant temperature can’t be attained. There is lack
of experimental procedure and statistical analysis of kinetic parameters for
components in low moisture and high temperature processed foods such as

pastries, breads, baked goods and extruded snacks.

1.3 Structure of Anthocyanins

There are several anthocyanins known to exist (Clifford 2000), and the
molecule consists of three parts: the aglycone base on the flavylium nucleus, a
group of sugars and a group of acyl acids. The difference among various
anthocyanins are: the number of hydroxyl groups, the nature and number of
sugars attached to the molecule and position where it is attached, and the
number and nature of the acids attached to the sugars attached in the molecule
(Mazza and Brouillard 1987). As the number of hydroxyl groups increases, the
intensity of blue color increases, and as the number of methoxy group increases,

the intensity of redness increases.

 

Figure 1.1: The anthocyanin ground structure, flavylium (2-phenylchromenylium)

(Wikipedia, 2007)

Table 1.1: Effect of R group on flavylium cation to produce different
anthocyanidins (Wikipedia, 2007)

. R -w hm.-.“ _—W~.—W‘ m

:x.....‘.;..... R1 R." R R R. ” ' R. ”" i R. " I
’ Aurantinidin -H -OH -H -OH -OH -OH -OH
Cyanidin -OH -OH -H -OH -OH -H -OH
Delphinidin -OH -OH -OH -OH -OH -H -OH
Europinidin -OCH3 -Ol-l -OH -OH OCH; -H -OH
Luteolinidin -OH -OH -H -H -OH -H -OH
Pelargonidin -H -OH -H -OH -OH -H -OH
Malvidin -OCH3 -OH -OCH3 -OH -OH -H -OH
Peonidin -OCH3 -OH -H -OH -OH -H -OH

Petunidin -OH -OH -OCH3 -OH -OH -H -OH

Rosinidin -OCH3 -OH -H -OH -OH -H -OCH3;

1.4 Stability of Anthocyanins

The pH is the most important factor affecting color stabilization (Mazza,
1987). Structure of anthocyanins exists in four forms (Brouillard, 1982) in
equilibrium: the blue quinoidal base A, the red flavylium cation AH+, the colorless
pseudobase B and colorless chalcone C.

Cation AH+ yields the quinoidal base A through the loss of a proton.
Addition of water to the cation AH+ yields the pseudobase B, and this exists in
tautomeric equilibrium with chalcone C. Quinoidal and carbinol pseuodobase are
unstable. The cation AH+ is the most important form in terms of color and exists
in pH below 4. Hence, acidic media are most favorable for the colored

anthocyanins.

Figure 1.2: Predominant structural forms of anthocyanins present at different pH
levels (Brouillard and Delaporte, 1977)

 

Malvidin 3-Glucoside (250 C; 0.2 M ionic strength)
(Brouillard and Delaporte,1977)

R R
,OH 00H
+H+ "
\ OGI / OGI
0H 0H

A‘ Quinoidal base (blue) AH‘: Flawlium cation( red )
R

+H20
-H+
/ 00:
0H

C: Chalcone (colourless) D: Carblnol pseudo-base (colourless)

 

 

 

 

1.5 Extraction of Anthocyanins and High-Performance Liquid
Chromatography

The total extraction of anthocyanins from grape skins has been obtained
optimally by superheated liquid extraction using 1:1 (v/v) ethanol-water acidified
with 0.8% (v/v) HCL, 120 °C, 30 min, 1.2 ml/min and 80 bar (Luque-Rodriguez
and others 2007). Acidified 60% methanol extracts good levels of total
anthocyanins from red grape skin using the pressurized liquid extraction (Ju and
Howard, 2003). Extraction of anthocyanins from grape pomace was performed,
and it was found that the elution with acidified methanol was higher as compared

to ethanol and 2-propanol (Kammerer and others 2005). High Performance

Liquid Chromatography (HPLC) with the diode array detector is the most widely
used method for the identification and quantification of anthocyanins. However,
the quantification of individual anthocyanidins is a challenge, as there are only
few anthocyanin standards available commercially. There are several procedures
adopted for the extraction of anthocyanins using extraction solvents for the HPLC
analysis. Acid hydrolysis of the anthocyanins simplifies its profile, and it can be
separated into five different anthocyanidin aglycones (Zhang and others 2004).
These anthocyanidins can be easily detected and quantified, as the standards
are commercially available.

1.6 Experimental Design

Table 1.2: Experimental Design

 

 

Moistg/rs Sgntent Heating time (minute)
42 8 10 12 15 16 17 19 21 23 25
34 15
17 15 16

 

 

 

 

Grape pomace with moisture content of 42%, 34% and 17% were heated
from 8 min to 25 min in steel cans in a steam retort. The 42% moisture content
experiments were used for the estimation of rate constant and activation energy,
whereas all the moisture content data was used for the estimation of one more
parameter i.e. moisture parameter (b). Oxygen radical antioxidant capacity
(ORAC) was also measured for the heating time of 58 min and is reported in

appendix A.

1.7 References

Alexandra Pazmino-Duran E, Monica Giusti M, Wrolstad RE & Gloria MBA. 2001.

Anthocyanins from Oxalis triangularis as potential food colorants. Food
Chemistry 75(2):21 1-216.

Brouillard R. 1982. Chemical structure of anthocyanins. In: Markakis, P., editor).
Anthocyanins as Food Colors. New York: Academic Press Inc. . p. 1-38.

Brouillard R & Delaporte B. 1977. Chemistry of anthocyanin pigments. 2. Kinetic
and thermodynamic study of proton transfer, hydration, and tautomeric
reactions of malvidin 3-glucoside. J. Am. Chem. Soc. 99(26):8461-8468.

Ju ZY & Howard LR. 2003. Effects of Solvent and Temperature on Pressurized
Liquid Extraction of Anthocyanins and Total Phenolics from Dried Red
Grape Skin. J. Agric. Food Chem. 51(18):5207—5213.

Kammerer D, Gajdos Kljusuric J, Carle R & Schieber A. 2005. Recovery of
anthocyanins from grape pomace extracts (Vitis vinifera L. cv. Cabernet
Mitos) using a polymeric adsorber resin. European Food Research and
Technology 220(3):431-437.

Luque-Rodriguez JM, Luque de Castro MD & Perez-Juan P. 2007. Dynamic
superheated liquid extraction of anthocyanins and other phenolics from
red grape skins of winemaking residues. Bioresource Technology
98(14):2705-2713.

Mazza GaRB. 1987. Colour stability and structural transformations of cyanidin
3,5-diglucoside and four 3-deoxyanthocyanins in aqueous solutions.
Journal of Agricultural and Food Chemistryz422-426.

Wang H, Nair MG, Strasburg GM, Chang YC, Booren AM, Gray Jl & DeWitt DL.
1999. Antioxidant and Antiinfiammatory Activities of Anthocyanins and
Their Aglycon, Cyanidin, from Tart Cherries. J. Nat. Prod. 62(2):294-296.

Wikipedia. 2007. Anthocyanin. http:/Ien.wikipedia.orglwiki/Anthocy§r_lig.

Youdim KA, McDonald J, Kalt W & Joseph JA. 2002. Potential role of dietary
flavonoids in reducing microvascular endothelium vulnerability to oxidative

and inflammatory insults. The Journal of Nutritional Biochemistry
13(5):282-288.

Zhang Z, Kou X, Fugal K & McLaughlin J. 2004. Comparison of HPLC Methods
for Determination of Anthocyanins and Anthocyanidins in Bilberry Extracts.
J. Agric. Food Chem. 52(4):688-691.

CHAPTER 2

Mishra, D.K, Dolan, K.D., Yang L. 2008. Confidence intervals for modeling
anthocyanin retention in grape pomace during nonisotherrnal heating. J. Food
Sci. 73(1):E9-E15.

10

Abstract

Degradation of nutraceuticals in Iow- and intermediate-moisture foods
heated at high temperature (>100°C) is difficult to model because of the
nonisothermal condition. Isothermal experiments above 100°C are difficult to
design, because they require high pressure and small sample size in sealed
containers. Therefore, a non-isotherrnal method was developed to estimate the
thermal degradation kinetic parameters of nutraceuticals, and determine the
confidence intervals for the parameters and the predicted Y (concentration).
Grape pomace at 42% moisture content (wb) was heated in sealed 202 x 214
steel cans in a steam retort at 126.7 °C for > 30 min. Can center temperature
was measured by thermocouple and predicted using Comsol software. Thermal
conductivity (k) and specific heat (Cp) were estimated as quadratic functions of
temperature using Comsol® and nonlinear regression. The k and CI) functions
were then used to predict temperature inside the grape pomace during retorting.
Similar heating experiments were run at different time-temperature treatments
from 8 to 25 min for kinetic parameter estimation. Anthocyanin concentration in
the grape pomace was measured using HPLC. Degradation rate constant
(k11o°c) and activation energy (5,.) were estimated using nonlinear regression.
The therrnophysical properties estimates at 100°C were k = 0.501 W/m°C, CD =
3600. J/kg°C and the kinetic parameters were k11o°c = 0.0607 min'1 and Ea=65.32
kJ/mol. The 95% confidence intervals for the parameters, and the confidence
bands and prediction bands for anthocyanin retention were plotted. These

methods are useful for thermal processing design for nutraceutical products.

11

2.1 Introduction

Diet and nutrition are increasingly linked with disease prevention and
treatment. Nutraceutical compounds, such as anthocyanins, are food
components known for their health promoting, disease preventing or medicinal
properties. Nutraceuticals not only can act as bright natural colorants (Alexandra
Pazmino-Duran and others 2001) but also have potential health benefits, such as
antioxidant and anti-inflammatory properties (Wang and others 1999).
Anthocyanins have beneficial action against vascular diseases and contribute
towards the reduction of age-related deficits in neurological impairments (Youdim
and others 2002). Grape pomace is a rich source of anthocyanins. It is the solid
part of the fresh grapes, and consists of skins and the seeds. Grape pomace, a
waste product from the winemaking process, is used for composting or cattle

feed or may end up in landfills.

Many solid foods could be enriched with anthocyanins, such as extruded
foods, baked goods, cereals, etc. However, anthocyanins are unstable at high
temperatures. Food processing usually involves the use of heat and other
physical methods, which may destroy these beneficial compounds. It is therefore
important to study the effect of such processing on the nutritional quality of
pomace. Developing mathematical models that take into account the important
process variables (T, pH, time) that influence thermal degradation of

therrnosensible compounds will be a useful tool for process design.

12

Anthocyanins are sensitive to temperature, especially above 70° C
(Markakis and others 1957). Anthocyanin obtained from concord grape was
processed, and it was found that the pigment loss, analyzed using
spectrophotometry, was 32% at 77 °C, 53% at 99 °C and 87% at 121 °C (Sastry,
1953). Thermal degradation of anthocyanins was also studied for concord grapes
(Calvi and Francis, 1978). Degradation of anthocyanins was reported while
processing blueberries into juice and concentrate and it was found that different
classes have varying susceptibility to degradation with different unit operations
(Skrede G, 2000). The rate of degradation of anthocyanins is time and
temperature dependent. Temperature dependence of the degradation of
anthocyanins has been shown to follow first-order kinetics (Cemeroglu and
others 1994); (Kirca and Cemeroglu, 2003) and can be modeled using the
Arrhenius relationship (Ahmed and others 2004). The degradation kinetics of
anthocyanins in blood orange juice was studied (Kirca and Cemeroglu, 2003)
and the activation energies for solid content of 11.2 to 69 °Brix were found to be
73.2 to 89.5 kJ/mol.

Although many studies have determined the thermal degradation kinetics of
anthocyanins in solution, very few studies have investigated anthocyanin
degradation in solids. Extrusion of corn meal (extruder die temperature 130°C)
with grape juice concentrate and blueberry concentrate showed up to 74%
anthocyanin degradation in the extruded cereal (Camire and others 2002).
Extrusion of corn meal with dehydrated fruit powder (blueberry, cranberry,

Concord grape and raspberry) in proportions of 84.3, 14.3, 0.4 and 1.0%

13

(cooking temperature up to 130 °C) showed up to 90% decrease of anthocyanins
for all dehydrated fruits used except raspberry (Camire and others 2007).
Although degradation of anthocyanins was reported, kinetic parameters were not

estimated.

Estimation of the parameters for an isothermal process, such as kinetic
parameters for anthocyanin degradation in juices and concentrates, is
mathematically straightforward. Anthocyanins have been found to follow the first-
order reaction kinetics (Cemeroglu et al., 1994); (Kirca and Cemeroglu, 2003)
and can be modeled using the Arrhenius relationship (Ahmed et al., 2004):

152.9 - 3.)

k = kre R T Tr (1)

For isothermal processes, taking the logarithm of both sides of Eq. (1)
simplifies the problem. However, thermal processing of solid foods is not
isothermal, but instead shows time-varying temperature. Therefore, in kinetic
modeling for non-isothermal processes, the exponential term has the time-

temperature history as an integral and hence requires nonlinear regression

techniques (Dolan and others 2007).

Experimental procedure for the kinetics in high moisture content foods (for
example, meats, fruit juice, vegetables and dairy products) is well established.
The 2-step procedure for kinetics in these foods includes plotting the logarithm of

concentration versus time at different constant temperatures. The negative of the

14

slope of this line is the degradation rate constant. Then plotting the logarithm of
the degradation rate constant vs. the reciprocal of temperature will give the
activation energy (Ea) from the slope. However, this method is not suitable for
low- and intermediate-moisture and high-temperature processed foods because
constant temperature cannot be attained. There is lack of experimental
procedure and statistical analysis of kinetic parameters for components in low
moisture and high temperature processed foods such as pastries, breads, baked

goods and extruded snacks.

Some researchers have proposed small samples, such as 13.5-mm
diameter test tubes (Dolan and Steffe, 1989) with gelatinized starch solutions,
and the use of transient heat-transfer theory to predict the temperature within the
sample. (Rob van den Hout, 1999) used 2-mm thick containers for isothermal
heating of soy flour so that temperature variation over the thickness could be

neglected.

Several non-isothermal methods to estimate kinetic degradation parameters
have been reported. The method of Paired Equivalent Isothermal Exposures
(PEIE) was applied to microbial survival data from retort experiments of canned

pea puree (Welt, 1997). PEIE was used to estimate the Arrhenius parameters.

The kinetic model for thiamine destruction in pea puree (Nasri and others

1993) was developed using nonlinear regression for the parameter estimation

15

and the jackknlfe method for the estimation of the experimental error. However,
in their study the confidence interval of the parameters and the confidence
interval for predicted Y (microbial retention) was not reported.

In summary, no standard method was found in the literature, for the
dynamic kinetic parameter estimation of low- and intermediate-moisture foods.
There is a lack of nonlinear regression techniques for analysis of unsteady-state
conduction-heated foods. In the context of non-isothermal processing, the
objective of this study was to establish an experimental procedure and
mathematical and statistical analysis to (1) estimate kinetic parameters for
thermal degradation of nutraceuticals, and (2) to provide confidence and
prediction bands for the nutrient retention in low- and intermediate-moisture

processed foods, using anthocyanins in grape pomace as a model nutraceutical.

16

2.2 Mathematical Model and Simulation

2.2.1 Thermal Parameter Estimation

A finite element method was used to solve the heat transfer equations and
to predict the center temperature of the can. Finite element approximates a PDE
with finite number of unknown parameters based on the geometry. Actual
dimensions of the can (radius 0.027m, and height 0.073m) were used to create
the finite cylinder geometry in CAD provided in Comsol. The retort time-varying
convective boundary condition (approximately 5-min come-up time, then constant
retort temperature (126.7 0C)) with constant h was used on all surfaces. A
second-order polynomial was used to model thermal conductivity and specific
heat of grape pomace as a function of temperature (Kenneth J. Valentas, 1997),

where T was in Centigrade:

k(T) = a + bT + cT2 (2)
CP(T) = a' + b'T + c'T2 (3)

Comsol is a finite commercial finite-element software package that uses
Delaunay algorithm to create Mesh elements. Mesh parameters determine the
element size and element distribution. Comsol mesh parameters used in this
study were:

Maximum element size scaling factor: this is the scaling factor for maximum

allowed element size.

17

Element growth rate: determines the maximum growth rate of element from
a region with smaller elements to a region with larger elements.

Mesh curvature factor: determines the size of an element near the
boundary depending on the curvature of the geometry.

Mesh curvature cut off: a positive number that prevents formation of many

elements around small curvature of the geometry.

Moreover, the mesh parameters determine the accuracy of the result and
the computation time. Smaller mesh size might provide better estimates, but it
may increase the computation time significantly. Hence, depending on the
problem and the geometry, mesh size can be optimized to reduce the
computation time and to get better estimates of the parameters. The values of
maximum element size scaling factor, element growth rate, mesh curvature
factor and mesh curvature cutoff in the present study were 1.5, 1.5, 0.5, 0.02,
respectively.

Initial guesses of the six parameters (a, b, c, a', b' and c’) were fed into
Matlab. The time step was 30 sec and cooling temperatures were calculated until
the center temperature of can was below 80 °C. Initial values of k and CI) were
computed by Matlab and fed into Comsol to predict the center temperature of the
can. Sum of squares ($80) of predicted and measured can temperature were
minimized by nonlinear regression (nlinfit in Matlab) to obtain the final estimates
of the parameters. Thermal diffusivity was calculated using the following

equafion:

18

_ MT)
am _ p CPU") (4)

2.2.2 Kinetic Parameter Estimation

Predicted mass average concentration of anthocyanins was calculated per

the following equation:

 

0 I

7‘ drdz (5)

fl C0] =2 e
pred 5

Variables r and 2 were normalized, so the limits for the r and z integral were from

 

 

O to 1.

The estimates of the therrnophysical properties were used in Comsol to
compute T(r, z, t,) for the can dimension based on a(T), Ti, and Too, Due to the
symmetry of the can, nine points in 1/8“1 of the can were chosen. Gauss
integration was preferred over the trapezoidal method for the spatial integral, as
Gauss provides more accuracy with minimum number of nodes. Nodes were
chosen at 3 r, and 3 2 locations, giving the total of 9 points as shown in appendix

C. Therefore, the numerical solution to Eq. (5) was

19

509.22%
,. Co

3 3
E ZZZexp[_ r18(njazy'atn J] 7'17“in (6)
pred 1:1 1:]

where the time-temperature history, ,6 is the time integral in Eq. (5)

Because Gauss integration is not convenient when integral limits change, the
trapezoidal method (trapz in matlab) was used for the integration of the time-

temperature history (Dolan and others 2007):

 

 

N‘lAt -E 1 1 —E 1 1

, ,t s — 8 —— + 8 ——

N” ) ":02 ”1’ R, T(r,z,tn+l) , exP R, [T(r,z,t,,) T.)
(7)

2.2.3 Sum of Squares of Errors
Sum of Squares was minimized by nonlinear regression to obtain the

estimated values of k, and Ea.

888:. (%.)....-(%.l,... <8

20

2.2.4 Confidence Intervals

To compute asymptotic confidence/predicted intervals, two commands in
Matlab® were used, which are:

for parameters: nlparci(beta, residuals, Jacobian)

for predicted Y value: nlpredci(model, x, beta, residuals, Jacobian,

simultaneousoption, predictionoption)

nlparci(beta,resid,J) returns the 95% asymptotic confidence interval CI on
the nonlinear least squares parameter estimates “beta”. 95% asymptotic
confidence intervals for the two parameters were calculated using nlparci, and
the 95% asymptotic prediction interval was calculated for the predicted Y using
nlpredci. Asymptotic prediction intervals (95%) were calculated by (Montgomery,

2006)

 

prediction width, = J(confidence widthi)2 + (ta, * RMSE)2 (9)

/ 2,n— p

For researchers without access to Matlab, all of these confidence and
prediction intervals can be computed in Excel using equations found in standard

statistical texts (Seber, 1989).

2.2.5 Standard Error and Correlation Coefficient
Variance-covariance matrix gives the information about the standard error

0“,. of parameters (Van Boekel, 1996). a',- is the square root of the corresponding

diagonal of the symmetric parameter

21

2
T -1 0' kr JkrEa
cov(a) = (X X) (MSE) = 2 (10)

GkrEa 0' Ea

where, X is the Jacobian

/ ar, 61/, I
6k, 615,,
air, an

\ ak, 6E, )

The correlation coefficient Pkr Ea = 0' kr Ea / (Okra-Ea) varies from -1.0 to 1.0.

 

 

(11)

 

 

 

 

The parameter estimation process with higher values oflpkrEalindicate more

difficulty in the estimation process.

22

2.3 Methods and Materials

2.3.1 Sealing and Retorting of Grape Pomace

Concord grape pomace was obtained from St. Julian Winery in Paw Paw,
MI and stored at -15°C for lab analysis. Grape pomace was thawed at room
temperature and kept ready to fill in cans. Steel cans (radius 0.027m, and height
0.073m)were filled with the grape pomace. Density of grape pomace in each can
was approximately 640 kg/m3 at 42% (wb) moisture content and sealed under
vacuum (20 mm Hg) (Dixie Seamer, Athens, Georgia). Cans were fitted with
needle thermocouples (Ecklund-Harrison Technologies Inc., Fort Myers, Florida)
at the geometric center of the can to obtain the center temperature to be used
later for thermophysical properties parameter estimation. Uniform initial
temperature of the product in each can was recorded. These cans were
processed in a rotary steam retort (FMC Steritort Laboratory Sterilizer) in
triplicates. Retort steam temperature was 126.7°C. Cans were not rotated and
were placed stationary on the bottom of the retort throughout heating. For
thermal parameter estimation, heating time >30 min was used for 6 cans with two
replicates. Processing time for kinetic parameter estimation was selected based
on the degradation of the anthocyanins. Three replicates each for 11 times
ranging from 8-25 min were used for estimating kinetic parameters. Two
thermocouples were fixed in the retort to record the retort steam temperature
during processing. Cans were cooled, such that the center temperature was not

more than 40 °C, with water at 25 °C in retort. The grape pomace from each can

23

was then removed and mixed for 40 s in a mixer/blender (Cuisinart® Mini Prep
plus, East Windsor, NJ) to achieve uniform sampling (coefficient of variance <

10%). The samples were then kept in plastic bags at —12°C for further analysis.

2.3.2 Extraction of Anthocyanins from Grape Pomace

Grape pomace (15g) was mixed with solution containing 2 N HCL (50 ml of
methanol + 33 ml of water + 17 ml of 37% HCL) and sonicated for 20 min and
then filtered through the vaccum filter using No. 4 whatman filter paper (Zhang
and others 2004). The filtrate was evaporated in a rotary evaporator at 35°C and
the retained anthocyanins in the flask were diluted with 25 ml of water and kept

for HPLC analysis.

2.3.3 Anthocyanins measurement

Anthocyanins were extracted, and the values were measured in the

laboratory using the HPLC method. E, observed mass-average concentration of

anthocyanins in each can was measured. Observed retention was computed as

(% J . E was computed as the total area under the peaks for all
0 obs

anthocyanidins.

2.3.3.1 Separation of Anthocyanins and Polyphenolics
Extracted anthocyanins solution (1 ml) was mixed with 0.25 ml of 12.1 N
HCL and 0.25 ml of water (Skrede G, 2000) in a screw-cap test tube and heated

for 30 min in a boiling water bath. The hydrolysate was cooled in an ice bath and

24

then centrifuged at 2500 rpm for 10 min. The centrifuged hydrolysate was applied
to C—18 Sep-Pak cartridge which was previously activated with 5 ml ethyl
acetate, 5 ml acidified (0.01% HCI) methanol, and 5 ml acidified (0.01% HCL)
water respectively. The absorbed sample in the cartridge was then washed with
5 ml of acidified (0.01% HCL) water. Polyphenolics were eluted using ethyl
acetate (5 ml). Anthocyanins were recovered from the cartridge using acidified
(0.01% HCL) methanol, and the resulting solution was evaporated to near
dryness in a Heidolph Laborota 4002 rotary evaporator at 35°C. The final

concentrate was taken up in 1 ml of acidified methanol.

2.3.3.2 HPLC system

Waters Breeze software 3.30 (Waters Corp., Milford, Mass., USA) software
was used along with Waters 2487 dual wavelength absorption detector, 1525
binary HPLC pump and a 717 plus autosampler. Samples were filtered through
25 mm nylon 0.2 urn filters and injected through the autosampler, and peaks

were identified according to their absorbances at 520 nm.

2.3.3.3 Anthocyanidins Separation

Anthocyanidins were separated using Agilent Eclipse XDB C-18 column (5
pm) 4.6 x 250 mm id. Solvent A was 100% acetonitrile, and Solvent B was a
mixture of 1% phosphoric acid, 10% acetic acid and 5% acetonitrile (v:v:v) in

water. Linear gradient from O to 30% A was used for 30 min.

25

2.4 Results

The HPLC chromatograms for raw grape pomace and for grape pomace
retorted 14 min at 126.7°C are shown in Figs. 2.1 and 2.2, respectively. The
separation was very clear, and individual anthocyanidins were identified well. The
degradation of the anthocyanins can be seen in Fig. 2.2; the peaks in the
chromatogram are lower for the retorted grape pomace than for the raw grape

pomace.

AU
0.04 . 2

 

0.03 , 1
0.02 3 5

0.01 ,« L 4
0.00 ‘ A A $2 _ L A M -

YrTIIITfrTYrTTT'WVV‘Trvrlt Yr I1r11r11YTr1—I‘VITVV1TV‘It’rr'

2 4 6 8 10 12 I4 16 18 20 22 24 26 28 30
Minutes

 

 

 

 

Figure 2.1: HPLC chromatogram for the raw grape pomace. Peak identification 1,
delphinidin; 2, cyanidin; 3, petunidin; 4, peonidin; 5, malvidin.

 

 

 

 

AU
0.04,
0.03. 2
0,02. 1 5
3 4
0.018 L h M
0.00 .r......r.:,.rfifz..-“.nr,:.tr‘:".‘.jT.A....T...Tr....H...
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
Minutes

Figure 2.2: HPLC chromatogram for the retorted grape pomace at 126.7 CC for
14 minutes. Peak identification 1, delphinidin; 2, cyanidin; 3, petunidin; 4,
peonidin; 5, malvidin.

26

Table 2.1 shows the anthocyanin retention ratios for the 42 samples. The
anthocyanin content of the raw grape pomace was, (70 = 104.7 mg /ml based
on the standard anthoyanin (Pelargonidin). The repeatability of the HPLC assay
was within 4% of the anthocyanin concentration.

2.4.1 Thermal Parameter Estimation
Figure 2.3 shows the observed temperature (provided in appendix D) vs.

the predicted temperature (Comsol). The root mean square error was 135°C.

.s
.5
O

.5
N
O

'1'.
.‘CU
ggggg
vvvv
......
|||||||||
n.
t"
0“.
.s
I
o"
.1
.r

.I

I
o
a
I
o
o
l
v
o
o
o
u
o
a
a
n
’
o
n
o
a

e
e
\
o
I
‘0
\

 

 

 

 

Center temperature of can °C
0)
O

 

 

. observed
60* .8; —predicted
40 i "-95% asymptotic confidence band
.................................................. 95% asymptotic prediction band
i - ‘1' ........... 1 1 1 1 1
20° 5 10 15 2o 25 30

Heating time (min) at 126.7°C

Figure 2.3: Example plot of observed and predicted center temperature profiles
from Comsol (triplicate runs) in canned grape pomace

For 42% moisture (wb) grape pomace, the thermal conductivity (k) and

specific heat (Cp) were estimated as given in Table 2.2. For example, the values

calculated at 100°C are, k = 0.501 W/m°C, Cp = 3600. Jlkg°C and Thermal

Diffusivity = 2.007 x 10-7 m2 Is.

27

Table 2.1: Heating time and measured anthocyanin retention for grape pomace
at 42% (wb) moisture content at 126.7 °C retort temperature for 33 heated cans

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample number Heatifltime Quin.) Retention of anthocyanins
1 0 1.117
2 0 0.855
3 0 0.855
4 0 0.883
5 0 1.029
6 0 0.984
7 0 1.007
8 0 1.110
9 0 1.159
10 8 0.837
11 8 0.733
12 8 0.804
13 10 0.688
14 10 0.684
15 10 0.686
16 12 0.698
17 12 0.744
18 12 0.714
19 14 0.565
20 14 0.515
21 14 0.409
22 15 0.498
23 15 0.507
24 15 0.599
25 16 0.341
26 16 ' 0.285
27 16 0.433
28 17 0.301
29 17 0.309
30 17 0.305
31 19 0.212
32 19 0.241
33 19 0.227
34 21 0.234
35 21 0.188
36 21 0.249
37 23 0.218
38 23 0.222
39 23 0.213
40 25 0.170
41 25 0.155
42 25 0.145

 

 

 

 

 

28

Table 2.2: Thermal property parameters for quadratic model for grape pomace at
42% (wb) moisture content

 

 

 

 

 

 

 

 

Parameter I13:rameter 2:rameter 3rd parameter ZMSE
p temperature
k
$232345 3 = 0.32717 b= 0.00174 c = -3.786e-008
W/m °C) Eq. 2 1.35 00
013
(Specific heat, a' = 2865.2 b' = 09434 c’ = 0.08316
J/kg °C) Eq. 3

 

 

2.4.2 Kinetic Parameter Estimation

The kinetic parameters for the anthocyanin degradation obtained from the

nonlinear regression technique are shown in Table 2.3:

Table 2.3: Degradation Kinetic parameters for anthocyanin degradation in grape
pomace at 42% (wb) moisture content

 

 

 

 

 

 

pkrEa .
No of Parameter Standard Correlation gfidagrycrgptotic RMSE
. ' t C
Parameter Data Estimates Error criefimen interval (A0)
temperature)
0 0.0606
"1 10 C min-1 0.003 (0.055. 0.067)
-0.12
42 T =110°C 0.084
Ea 65.32 ’
kJ/g mol 16.15 (32.7, 97.9)

 

 

 

 

 

 

 

Figure 4 shows the 95% asymptotic confidence band and 95% prediction

band for mass average retention of anthocyanins. The correlation coefficient is —

29

 

0.12. The confidence band (CB) is the region where 95% of the regression lines
are expected to be, so it is not uncommon for large number of data observations
to fall outside this region. The prediction band (PB) is the region where 95% of
the data are expected to be. If more data were collected, we expect ~5% of all

the data would fall outside the PB.

 

 

 

    

 

1_4. 0 observed
12 ..... —predicted
ii -. "-95% asymptotic confidence band
1‘ ' --------- 95% prediction band

.,::

1‘.
‘0

9
co

‘1
~
~~~~~~~
I
~|
‘

.
5.
‘.
§,~
‘~

.~
a. . .~
a o
\ ~
1‘ ' '~‘

.09
Mk

'~
-
-4
-----------

0

Mass average retention of anthocyanins
o
o:

e
d°

 

l I I I J

5 10 15 20 25
Heating time (min) at 126.7°C

Figure 2.4: Mass average retention of anthocyanins in grape pomace heated in
202 x 214 cans at retort temperature of 126.7 0C

The RMSE (Root Mean Square Error) = 0.084 is ~9% of the total scale of

1.0 (Fig. 4), showing a good fit. The CI for Ea is proportionally larger than the CI

for k11o°c (Table 3), but the size of the CB and PB for nutrient retention is
reasonably small (Fig. 2.4). Processors would be more interested in the PB of the

retention, rather than CI of the parameters. For example, using the lower bound

3O

of the PB in Fig. 4, one can predict that only 2.5% of one lot of cans heated for
10 min at 126.7°C will have retention 550%, while the remaining 97.5% of cans
will have retention >50%.

Residual plots were also plotted to check for the absence of trends or
correlations between the parameters. The residuals are scattered around the
center (Fig. 2.5) and show a nearly normal distribution. This plot confirms a good

fit of the Arrhenius model to the degradation of anthocyanins in grape pomace.

0.2 -

0.15 ’

I
I

I
O
.

0.1

0.05 1' . .

I}. O
O
O

Residuals

—0.05 — '

r

-0.1

 

1 1 1 O
0.4 0.6 0.8 1

-0.15 .
0.2
Predicted Y (Mass Average Retention of Anthocyanins)

0

Figure 2.5: Residual plot of the mass average retention of anthocyanins for cans
heated at retort temperature of 126.7 0C

The activation energy for the anthocyanin degradation obtained from this
study was comparable to the values for anthocyanin degradation in solution
found in the literature. Other researchers reported that the activation energy

ranged from 25.0 kJ/g-mol to 85 kJ/g-mol, and the rate of reaction (k0) ranged

31

from 5.62 x 101° min'1to 3.64 x 1025 min'1 (Cemeroglu et al., 1994; Ahmed et al.,
2004; St. S. Tanchev, 1974). The value of rate of reaction, k0, found in the
present study was 4.9 x 107 min". As expected, the degradation rate kg in the

intermediate—moisture food was lower than the kg in liquids.

Kinetic parameters for the anthocyanin degradation obtained from extrusion
of grape pomace with wheat flour in the ratio 1:3 (Lai, 2003) were comparable
with the parameters estimated in this study. The activation energy was 76.0 kJ/g-
mol (Lai, 2003) versus 65.32 kJ/g-mol in the present study, and the rate of

reaction (keg) was 0.049 min'1 (Lai, 2003), versus 0.011 min'1 in the present study

(converted from Table 3 using Eq. 1). Lai (2003) heated her samples at
atmospheric pressure up to 140°C, allowing the moisture content to decrease
during heating, and then corrected the data. In the present study, heating
occurred at constant pressure and constant moisture. The reasonable
agreement of the estimates between two studies that were conducted with
different methods is a strong indication that the estimates are close to the true

values.

2.4.3 Plot of Sum of Squares

The 3-D surface plots of the sum of squares (fig. 2.6) provide information
about the nature of standard error and confidence intervals, and the relative ease
of convergence of the nonlinear regression routine. Figure 6 shows that the

surface is shallower along the E-axis than along the kmoc axis, causing the

32

standard errors and confidence intervals for E to be proportionately larger than
that for kmoc, consistent with the Cl results in Table 2.2. Better convergence can

be obtained if the curve shows steeper change along the E axis.

.0
o'i
.1

.0
1:.
I

.0
to
.1

 

 

SS (Sum of Squares)
O
N

§-

.....
.....
NNNNNN

    
  
 

. V, ' ‘ 0.07
‘ - 0.065

0.06
0.055

50

   

0 0.05

E "W9 ”mm k110°C [1/min]

Figure 2.6 3-D Surface plot of Sum of Squares (SS)

2.5 Conclusions

The method described in this study will be useful in determining the change
in nutraceuticals concentration and the prediction error for non-isothermal
processes in low-lintermedlate-moisture food during high-temperature
processing, which can be a valuable tool for various food industries engaged in

making functional foods. This paper presents three novel results:

1. Using both Comsol (finite-element) and Matlab (non-linear regression) for

nonlinear regression;

33

2. This method is more powerful because it uses k and Cp as functions of
temperature and takes into account the varying boundary condition

during the lag time;

3. It gives CB and PB for nutrient retention, as well as the CI for the

parameters.

For the processors, the sizes of CB and PB for nutrient retention are more

important than size of CI of the parameters. The parameter estimation is the

intermediate step to obtain the nutrient retention CB and PB.

34

2.6 Nomenclature

a

p

0'
p
a,bandc

a', b’ and c'

OI

Cl

Ea

thermal diffusivity, m2/s
density, kg/m3
standard error

correlation coefficient

thermal conductivity parameters (eq. (2))

specific heat parameters (eq. (3))

mass-average anthocyanins concentration within a can, mg/mL

initial mass-average anthocyanin concentration, mg/mL

Specific heat, J/kg °C

confidence band

confidence interval

activation energy, J/g-mol

convective heat transfer coefficient, W/m2K
thermal conductivity, W/m K

degradation rate constant at reference temperature T,, min‘1
number of points for the trapezoidal rule
number of data

number of parameters

prediction band

dimensionless radius

gas constant (J/g-mole K)

container radius, m

35

RMSE root mean square error, g/g or °C

T temperature (K)

Ti initial temperature, K

Tr reference temperature = 383 K

w Gauss weights

Y mass average retention of anthocyanins, fractional g/g.

z dimensionless axial position, where z = 0 is at the half-height

point of the can

36

2.7 References

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anthocyanin and visual colour of plum puree. European Food Research
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Alexandra Pazmino-Duran E, Monica Giusti M, Wrolstad RE & Gloria MBA. 2001.
Anthocyanins from Oxalis triangularis as potential food colorants. Food
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Calvi JP & Francis FJ. 1978. Stability of concord grape (v. Iabrusca)
anthocyanins in model systems. Journal of Food Science 43(5):1448-
1456.

Camire ME, Chaovanalikit A, Dougherty MP & Briggs J. 2002. Blueberry and
Grape Anthocyanins as Breakfast Cereal Colorants. Journal of Food
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Camire ME, Dougherty MP 81 Briggs JL. 2007. Functionality of fruit powders in
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Cemeroglu B, Velioglu S & Isik S. 1994. Degradation Kinetics of Anthocyanins in
Sour Cherry Juice and Concentrate. Journal of Food Science 59(6):1216-
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Dolan KD 8. Steffe JF. 1989. Back extrusion and simulation of viscosity
development during starch gelatinization. Journal of Food Process
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Dolan KD, Yang L & Trampel CP. 2007. Nonlinear regression technique to
estimate kinetic parameters and confidence intervals in unsteady-state
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Kenneth J. Valentas RPS, Enrique Rotstein. 1997. Handbook of food engineering
practice. CRC press.

Kirca A & Cemeroglu B. 2003. Degradation kinetics of anthocyanins in blood
orange juice and concentrate. Food Chemistry 81(4):583-587.

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Lai KPK. 2003. Modeling thermal and mechanical degradation of anthocyanins in
extrusion processing. MS. Thesis, Department of Biosystems and
Agricultural Engineering. East Lansing: Michigan State University. p. 72-
74.

Markakis P, Livingston GE & Fellers CR. 1957. Quantitative aspects of
strawberry pigment degradation. Journal of Food Science 22(2):117-130.

Montgomery DP, EA; Vining, GG. . 2006. Introduction to linear regression
analysis.,4th edition. ed.: John Wiley & sons, inc.

Nasri H, Simpson R, Bouzas J & Torres JA. 1993. Unsteady-state method to
determine kinetic parameters for heat inactivation of quality factors:
Conduction-heated foods. Journal of Food Engineering 19(3):291-301.

Rob van den Hout GMKvtR. 1999. Modelling of the inactivation kinetics of the
trypsin inhibitors in soy flour. Journal of the Science of Food and
Agriculture 79(1):63-70.

Sastry I, Tischer, rg. 1953. Behavior of the anthocyanin pigments in concord
grapes during heat processing and storage.

Seber GAF, & Wild, C.J. , NY. . 1989. Nonlinear regression. NY.: John Wiley 8
Sons,.

Skrede G WR, Durst RW. 2000. Changes in Anthocyanins and Polyphenolics
During Juice Processing of Highbush Blueberries (Vaccinium corymbosum
L.). . J Food Sci 65(2):357-364.

St. S. Tanchev NY. 1974. Kinetics of Thermal Degradation of the Anthocyanins
Delphinidin-3-rutinoside and Malvidin-3-glucoside. Food / Nahrung
18(8):747-752.

Wang H, Nair MG, Strasburg GM, Chang YC, Booren AM, Gray Jl & DeWitt DL.
1999. Antioxidant and Antiinflammatory Activities of Anthocyanins and
Their Aglycon, Cyanidin, from Tart Cherries. J. Nat. Prod. 62(2):294-296.

Welt BA, Teixeira, A.A., Balaban, M.O., Smerage, G.H., Hintinlang, D.E., &
Smittle, B.J. 1997. Kinetic parameter estimation in conduction heating

38

foods subjected to dynamic thermal treatments. J. Food Sci. 62(3):529-
534,538.

Youdim KA, McDonald J, Kalt W & Joseph JA. 2002. Potential role of dietary
flavonoids in reducing microvascular endothelium vulnerability to oxidative

and inflammatory insults. The Journal of Nutritional Biochemistry
13(5):282-288.

Zhang Z, Kou X, Fugal K & McLaughlin J. 2004. Comparison of HPLC Methods
for Determination of Anthocyanins and Anthocyanidins in Bilberry Extracts.
J. Agric. Food Chem. 52(4):688-691.

39

CHAPTER 3

Multi-parameter Estimation and Parameter Confidence Regions for
Degradation of Anthocyanins in Grape Pomace

4O

 

Abstract

Confidence intervals on parameters and predicted retention values can
help design food processes that would improve food quality and safety. In this
study, several models were used to predict the degradation of nutraceuticals in
low-moisture foods processed at higher temperatures. Grape pomace with
different moisture contents of 17, 34, and 42% (wb) was heated in 202x214 steel
cans in a retort at 126.7°C for times ranging from 8 to 25 minutes. Temperature
in canned grape pomace during conduction heating was predicted by comsol®
using known quadratic models for thermal properties. Anthocyanin retention in
retorted samples was measured using HPLC. Rate constant (k11o°c), activation
energy (E3) and moisture content parameter b , initial anthocyanin concentration
(Co) and reference temperature (T,) were estimated using nonlinear regression in
matlab®. Confidence band and the prediction band were computed for the
predicted Y (anthocyanin degradation). Inference regions and joint confidence
regions for k110°c and E8 were estimated using the iterative methods for all the
models. The activation energy Ea, rate of reaction k110°c and the moisture
parameter b estimated using nonlinear regression, were 75.34 kJ/g mol, 0.058
min'1 and 1.87 (MCwb)'1. The availability of the software and the statistical
packages makes nonlinear regression accessible for all researchers. Other
investigators can consider reporting confidence intervals and confidence regions
using the methods presented, for maximizing use of limited data sets and

improving quality of food.

41

3.1 Introduction

Kinetic models often involve two parameters, such as kr-Ea in arrhenius
model, Dr-z in microbial model and Vmax-Km in the Michaelis-Menten model.
Usually these parameters are estimated using isothermal experiments. The
procedure for estimating parameters from isothermal data is mathematically
straightfonivard and well established. However, the commercial processes are
usually dynamic, i.e. have time-varying temperatures or other variables, such as
time-varying moisture during a drying process. Moreover, many commercial
processes for low-and intermediate-moisture foods have more than 2
parameters, because there are multiple variables, such as time, temperature,
moisture content, shear rate, pH, pressure, etc. Therefore, kinetic analysis based
on isothermal 2-parameter models does not apply to many of these commercial

high-temperature processes for low- and intermediate moisture foods.

Use of high temperature (>100 °C) in food processing can lead to the
degradation of some nutraceuticals. Because low-moisture foods processed at
high temperature are necessarily heated nonisothermally, one must use
nonlinear regression techniques for kinetic analysis. As there are no standard
procedures or solutions available for the nonlinear models it is often difficult to
estimate the parameters. Hence iterative techniques are the only tools to find a
solution. Fitting the nonlinear models has become easier and quicker with the
access and advancement in computer software. However, computing the

confidence intervals can be a challenge in nonlinear models as the behavior of

42

parameter estimates are complex functions of the formulation of the equation, the
parameterization, design of experiment and the residual variance (Watts, 1994).
Modeling nutraceutical degration can save time and money spent on actual
lab experiments. Transformation of the equation to linear form in parameters and
fitting it using linear least squares is not always a valid approach for nonlinear
models. The 2-step isothermal approach usually leads to larger confidence
intervals than the 1-step nonisothermal approach (Wendie L. Claeys, 2001a).
Parameters should be estimated using a nonlinear approach with the original rate
equation if the original rate data have constant variance. Confidence band and
the prediction band for the predicted Y (dependent variable) can be computed
along with the confidence interval of the parameters (Dolan and others 2007),
which can provide important information regarding the safe processing as well as

retaining the quality of food.

Confidence intervals for the parameter should be reported at a certain
probability. For example, confidence interval for activation energy of 150 kJ/mol
having a standard error of s can be reported as 150:1:28 at 95% probability.
Confidence interval associated with the parameter can help determine quality
(nutrient retention) or safety (microbial retention) of the processed food. In
absence of estimates of the confidence intervals, safety factors used to be based
on the industry practices and experience. The extra processing time (safety
factor) implied for the food safety without any scientific basis may have

unfavorable effect on processed food. This may result in over-processing, which

43

leads to degradation in color, texture, flavor and nutritive value (Lenz and Lund,

1977) or under-processing, which is favorable for microbial growth.

Confidence interval for the parameters is narrower if the temperature
dependence is directly attached to the rate equation and the rate equation is
analysed over all the temperature ranges (Boekel, 1996). 90% joint confidence
regions were constructed to estimate the statistical accuracy of the
simultaneously estimated parameters for thermal inactivation of alkaline

phosphatase and lactoperoxidase and for the denaturation of fl-actoglobulin

(Wendie L. Claeys, 2001a). Joint confidence regions were also reported for the
forrnatin kinetics of hydroxymethylfurfural, lactulose and furosine in milk at 90%
confidence (Wendie L. Claeys, 2001b). 90% joint confidence intervals were
reported for the Dr and 2 model for inactivation kinetics of freeze dried a-
amylase from Bacillus amyloliquefaciens (Saraiva and others 1996). Parameter
confidence regions were reported for kinetic parameters for microbial death in
unsteady state conduction heated canned foods and for the thiamine

concentration using a nonlinear regression method (Dolan et al., 2007).

In the context of nonisothermal processing and nonlinear regression there is
need for a standard and user-friendly procedure to (a) simultaneously estimate
more than two kinetic parameters for food processes, (2) estimate error in the

parameters (confidence intervals and confidence regions) and in the measured Y

44

 

(confidence bands and prediction bands), (3) construct joint confidence region for

simultaneously estimated parameters.

3.2 Mathematical Model

3.2.1 Parameter estimation using nonlinear regression

The parameters involved in the Arrhenius equation were estimated using
Matlab in combination with Comsol using the following command;
[beta, residual, Jacobian] = nlinfit(X, y, @fun, betaO)

‘fun’ is a function that accept X as input variable and it is of the form;

yhat = fun(beta,X)

In this study ‘fun’ is a function that computes temperature inside the can.

The command ‘nlinfit’ in matlab® returns the estimated parameters, the residuals

and the Jacobian using the least squares, which minimized the following

equafion:

SS = 2100,”),- —(Yp,.ed )1]2 a)
l

45

3.2.1.1 Moisture content model

The degradation of anthocyanins at different temperatures can be

modeled as first-order reaction kinetics (Ahmed and others 2004; Cemeroglu and

others 1994),

E = -kC, (2)

dt

The quantification of the effect of temperature on the reaction rate can be well

expressed by the Arrhenius model,

£4.93]
_ R T Tr
k — kre (3)

under dynamic temperature conditions the degradation of anthocyanins can be

expressed by,

 

t 'Ea{ 1 _i]
_er e R (T(r,z,t) T, dt

(C J = 2 e O I” drdZ (4)
0 pred

46

If moisture content of the product is included as a variable, assuming an
exponential effect and no moisture difference at different locations within the can,

the equation becomes,

 

45: 1 _ -1. -
k t [ R (T(r,;t) T] + b(MC(t) MC,)]dt

z: ‘ _
{/0} -2 e rdrdz
" pred

JJ

 

 

(5)
For the case where the can is sealed, moisture content does not change with

time and can be moved out of the time integral:

 

t -E€1{ 1 -i]
d

- _k eb(MC -MCr)J e R (T(r,z,t) T,

r t
C _ 0
(A0) —2 e rdrdz

pred

 

 

(6)

and the parameters kr, E8 and b were estimated simultaneously using the

nonlinear regression method. Residual plots were also checked for the absence

of trends or correlations.

47

3.2.1.2 Confidence Intervals
Asymptotic confidence intervals on the parameter estimates and predicted

Y (anthocyanin retention) were calculated using the two commands in Matlab,
for parameters: nlparci(beta, residual, Jacobian, a)

The command ‘nlparci(beta,resid,J,alpha)’ returns the confidence interval on the
nonlinear least squares parameter estimates beta at the level of confidence
determined by alpha. 95% confidence intervals for each parameter were

calculated using nlparci.
for predicted Y value: nlpredci(fun, x, beta, residual, Jacobian, ct, 'simopt')

3.2.1.3 Standard Error and Correlation Coefficient

Information about the Standard error a". of parameters was obtained from
the variance-covariance matrix (Boekel, 1996). The square root of the
corresponding diagonal of the symmetrical variance-covariance matrix provides
the information about 0,. of the corresponding parameter.
7

2
0 k, Ukrga 01¢er

cov(a) = (X TX )'1 (MSE) = akrEa 025a 0571b (7)

 

 

2
\ Gkrb UEab 0 b)

48

where, X is the Jacobian

(8)

 

 

 

 

The correlation coefficient ,0)!- =0',-j/(0',-0'j) varies from -1.0 to 1.0.

Higher values of [p lindicates more difficulty in the parameter estimation

process in nonlinear regression method.

3.2.1.4 Confidence region
The confidence region is a set of values for the two parameters.
Approximate inference regions for the estimated parameters using the nonlinear

regression were drawn per the following equation (Bates, 1988),
(e - 61W. (9 - 6) s ps2F(p.N —.ma) (9)

where, the derivative matrix V = QR, and it is calculated at 0.
The boundary of the inference region as mentioned above is

49

 

{0: 6+ JPs2F(P,N—P;a) R," d ||d|| =1} (10)

This equation will provide an ellipsoid, which is an approximation of the true
contour, and is used for computational efficiency, compared to the iterative
method below.

For better accuracy, joint confidence regions were also plotted using the
method of (Motulsky, 2004). This was done by obtaining the sum of squares of
errors less than or equal to a constant value determined by the following

equafion,

 

P
SSaIl— fixed = SSbest— fit (F n _ P +1) (11)

The contour of the joint confidence region was computed using the

program in Matlab as follows: fix one of the parameters equals to best-fit value

and allow the other parameter to vary until SS 9: SSaufued, As the contour is oval

shaped, there will be two values of the second parameter, one on each side of
the oval and these two values are computed till they are almost equal (1 - 5% of
each other). Then fix the parameter 1 at slightly lower value (~95% of the best-fit
value) and again find the two values of the parameter 2. This routine completes
the lower half of the contour. The upper half is computed in the same manner but

using the increasing values of the fixed parameter.

50

For multi-parameter models, plotting the joint confidence regions is not possible
(Bates, 1988). Hence, making pairs of the parameters while holding the other

parameters constant will result in plots of the joint confidence regions.

3.3 Methods and Materials

3.3.1 Thermal treatment and degradation of anthocyanins

Retort simulation, extraction of anthocyanins and high performance liquid
chromatography (HPLC) was adopted from (Mishra and others 2008). Briefly,
grape pomace having moisture content of 42, 34 and 17% (wet basis) was
separately heated in a steam retort at 126.7 °C for time ranging from 8 to 25
minutes. These heating experiments were done in triplicate. After heating, the
grape pomace in each can was mixed for 40 seconds in a food grinder
(Cuisinart® Mini Prep plus) to ensure sufficient mixing for uniform sampling from
each can. Preliminary HPLC experiments showed that mixing for this time gave
coefficient of variance for anthocyanin content at different locations in one can of
< 10%. Retorted samples were then extracted for anthocyanins using the
extraction solvent (Mishra et al., 2008) and then the solution was kept for further
analysis. HPLC with a dual wavelength detector system was used to detect the

individual anthocyanidin peaks. Anthocyanin concentration (,ug/ml) was

51

computed by comparing the area under the all the five peaks (delphinidin,
cyanidin, petunidin, peonidin, malvidin)

to the standard curve of Pelargonidin. Anthocyanidin reference standards
delphinidin chloride, cyanidin chloride, peonidin chloride and malvidin chloride
were purchased from Sigma-Aldrich (St. Louis, MO, USA); petunidin chloride was

purchased from Extrasynthese (Genay Cedex, France)

Anthocyanidin standard curves were prepared by dissolving delphinidin
chloride in methanol; cyanidin chloride was dissolved in 5% hydrochloric acid in
80% ethanol; malvidin chloride was dissolved in 95% ethanol; and petunidin
chloride was dissolved in methanol acidified with 0.1% hydrochloric acid. All
samples were dissolved at 1 mg / mL solvent. Appropriate dilutions were then
made using the solvent recommended to generate a standard curve. The
retention value of the anthocyanin was then calculated by dividing each

concentration by the mean of the raw grape pomace anthocyanin contents.

52

3.4 Results
The anthocyanins retention for the grape pomace at different moisture

content as measured using HPLC was as follows (Table 3.1);

Table 3.1: Heating time and measured anthocyanin retention for grape pomace
at 17, 34 and 42% (wb) moisture content at 126.7 °C retort temperature.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample number Heating time (min.) Retention of anthocyanins MC(wb)
1 0 1.117 0.42
2 0 0.855 0.42
3 0 0.855 0.42
4 0 0.883 0.42
5 0 1.029 0.42
6 0 0.984 0.17
7 0 1.007 0.17
8 0 1.110 0.34
9 0 1.159 0.34
10 8 0.837 0.42
11 8 0.733 0.42
12 8 0.804 0.42
13 10 0.688 0.42
14 10 0.684 0.42
15 10 0.686 0.42
16 12 0.698 0.42
17 12 0.744 0.42
18 12 0.714 0.42

 

 

 

 

 

 

53

 

 

Table 3.1 Con’t

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample number Heating time (min.) Retention of anthocyanins MC(wb)
19 14 0.565 0.42
20 14 0.515 0.42
21 14 0.409 0.42
22 15 0.498 0.42
23 15 0.507 0.42
24 15 0.599 0.42
25 15 0.847 0.17
26 15 0.788 0.17
27 15 0.720 0.17
28 15 0.603 0.17
29 15 0.521 0.17
30 15 0.560 0.17
31 15 0.753 0.34
32 15 0.587 0.34
33 15 0.821 0.34
34 15 0.450 0.34
35 15 0.429 0.34
36 15 0.587 0.34
37 16 0.341 0.42
38 16 0.285 0.42
39 16 0.433 0.42
40 16 0.467 0.17
41 16 0.316 0.17
42 16 0.463 0.17

 

 

 

 

54

 

Table 3.1 Con’t

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample number Heating time (min.) Retention of anthocyanins MC(wb)
43 17 0.301 0.42
44 17 0.309 0.42
45 17 0.305 0.42
46 19 0.212 0.42
47 19 0.241 0.42
48 19 0.227 0.42
49 21 0.234 0.42
50 21 0.188 0.42
51 21 0.249 0.42
52 23 0.218 0.42
53 23 0.222 0.42
54 23 0.213 0.42
55 25 0.170 0.42
56 25 0.155 0.42
57 25 0.145 0.42

 

 

 

 

 

 

The estimated kinetic parameters for the anthocyanin degradation
obtained from the nonlinear regression technique are provided in Table 3.2. The
root mean square error was found to be 0.109, which is ~11% of the total scale
showing good fit as shown in fig. 3.1. The correlation coefficient among the
parameters is shown in table 3.2. As processors would be more interested in the
PB, a plot of PB was plotted along with the predicted Y and Cl on the predicted Y
(fig 3.1).

55

Table 3.2: Kinetic parameters for anthocyanin degradation in grape pomace at

17, 34 and 42% (wb) moisture content

 

 

 

 

 

 

 

 

 

95%
Correlation
No. asymptotic
Parameter Standard coefficient
Parameter of confidence RMSE
Estimates Error (ref.
Data interval
temperature)
k11OOC 0053 min-1 pk E =-0.5
0.0043 ' a (0.049,0.066)
pb Ea =0.029
57 .. 0.109
Ea 75.34 pknb ' 0'43
kJ/ l 2 . _ o 22.1, 128.5
9 "‘0 6 5 Tr -110 c ( l
B 1.87 (min.)“ 0.57 (0.71, 3.02)

 

 

 

 

 

 

 

56

 

 

0 observed
,,,,,,,, . —predicted
,,,,,,,, ---~-95% asymptotic confidence band
......... 95% asymptotic prediction band

.5
a.

...........
1:.

A

‘11.
-t..
.....
ti.

 

 

  

.u u up i- -,-._ -_-_

 

;
I
”I
r
'0
‘r
.......
'00.
'n
n
h

I!

v
.............

'''''
'1
1
l
I.“

I

‘. 'I

..........
'1

a"
'1.

’h.

r
'0
I
P
'r
'7
'0
'r
'I
I.
'o
0,,
‘1
n,
”I

C.’

..,l
i.
"1-
I)
.1
'-
1,,

o
I
n"

- ..........

Mass Average Retention of Anthocyanins
o o o o
N is 0) co

5
ON

 

1 L L 1

5 10 15 20 25
heating time (min) at 126.7°C
Figure 3.1: 95% asymptotic confidence band and 95% asymptotic prediction

band for mass average retention of anthocyanins in grape pomace at 42%
moisture content (wb) heated in 202 x 214 cans at retort temperature of 126.7

°C.

To check for the absence of trends or correlations between the parameters,
a residual plot was constructed. The residuals followed a normal distribution and
were found to be scattered around the center (Fig. 3.7) This plot shows a good fit
of the modified Arrhenius model to accommodate the change in moisture content

to the degradation of anthocyanins in grape pomace.

57

 

.L
O)

    
  
 
 
 
 

I observed
—predicted
----95% asymptotic confidence band

.3
.p

..........

'11.
'1.-
.....
1

 

 

.1.
N

 

......
-----
-1.
I
"11
t...
1:
""""""""
‘‘‘‘‘‘
., ‘1
'1
,,,,,,
.......

""""
”.1
..........
'I I.
1...
t._.

H .....
I
‘l-.
.,

—h

..........
.....

A. .- - '— ~ '11- .Illli;"

. , .

.T ‘0- ‘ ~ .- - .....
Q ~ . q

I-
... a‘,
~‘-,_. ""C—,
‘h_ “Ht.

.0
00

-~
-- .
~~‘. --"1.
.‘ .~L
‘u- ~“-
0. ~ - b
.
‘1

 

 

Mass Average Retention of Anthocyanins

11111111111111111111111111111111
------------------------ A l
..........................
it. ............................
.,-,...i:1.111,..11- i'llI'ltlI'A’I

heating time (min) at 126.7°C

Figure 3.2: 95% asymptotic confidence band and 95% asymptotic prediction
band for mass average retention of anthocyanins in grape pomace at 17%
moisture content (wb) heated in 202 x 214 cans at retort temperature of 126.7

°C.

58

.3
O)

 

a observed
—predicted
...... _ IIIIIIIII "-95% asymptotic confidence band
--------------------- 95% asymptotic prediction band

.3
h.

 

 

—L

 

..
11111
......
1‘1; ......
,,,,,,

 

.0
A
-

.....
1
I‘ IIIIIII
’li-

.......

Mass Average Retention of Anthocyanins

 

111111
I-
llllll
......
'111
1..

 

heating time (min) at 126.7°C

Figure 3.3: 95% asymptotic confidence band and 95% asymptotic prediction
band for mass average retention of anthocyanins in grape pomace at 34%
moisture content (wb) heated in 202 x 214 cans at retort temperature of 126.7

0C.

Kinetic parameters for the anthocyanin degradation obtained from this study
are comparable to the values for anthocyanin degradation in extruded flour mixed
with grape pomace (Lai, 2003): The activation energy was 76.0 kJ/g-mol, the rate

of reaction (keg) was 0.049 min‘1 and the value of b was 5.28 MCwb'1whereas in

this study the value of activation energy was found to be 75.34 kJ/g-mol, rate of
reaction keg was 0.011 min‘1 and the value of b was 1.87 MCwb". As expected,
the degradation rate R30 and the activation energy in the intermediate-moisture

food was nearly same in both the studies.

59

95% joint confidence region was plotted as an ellipse in Figure 3.4.
Moreover, the true 95% joint confidence region was also plotted on the same plot
using the Motulsky method (Motulsky, 2004). The sum of squares around the
contour was also calculated in both the cases and it was found that the SS was
constant along the contour in case of Motulsky while the SS was not constant
along the approximate elliptical contour, which shows that approximate CRs may

have significant errors.

0.08

1

0.075

T

 

 

 

0.0% i 1 ‘

100 120 140 160 130

0 40 60 80
E [kJ/(g mol)]

Figure 3.4: 95% joint confidence region using (1) equation (9) and (2) Motulsky
method for mass average retention of anthocyanins in grape pomace 42%
moisture content (wb) with parameters having correlation coefficient of -0.5.

The 3-D plot of sum of squares was constructed using Matlab for the kinetic
parameters E, and km for the grape pomace at 42% moisture content (wb).

These plots provide information about the nature of standard error and

confidence intervals, and the relative ease of convergence of the nonlinear

60

regression. Fig. 3.5 shows that the surface is shallower along the E-axis than
along the kiiooc axis, causing the standard errors and confidence intervals for E,
to be proportionately larger than that for kmoc, consistent with the CI results in
Table3.4. Better convergence can be obtained if the curve shows steeper
change along the Ea axis. This plot was compared with the SS plot constructed
for Welt’s data for microbial death of Bacillus stearothennophilus (Welt, 1997).
Fig. 3.7 shows a good convergence on both the parameters E, as well as km.
Because there is a steeper surface down towards the minimum 88, this visual
check shows that the microbial death data of Welt et al. fit the Arrhenius model
(equ. 3) better than our anthocyanin degradation data. The shallower surface
might be improved by collecting more data at different moisture content and at
different times. Welt et al.’s confidence intervals for E were proportionately
smaller than ours, a result that could be deduced by examining these SS surface

plots.

61

.0
or
1

.0
A
I

.0
00
1.

 

o
N
11

SS (Sum of Squares)
8.

    
  
 

0.07
0.065

50 i 0.06

   

0.055
k1 10°C [1/min]

E [kJ/(g mol)]

Figure 3.5: 3-D Surface plot of Sum of Squares (SS)

48

.0
0)
.1

.0
N
/

 

1

SS (Sum of Squares)
O
N
01

5

      

h 0.04
0.035

  

300

 

1' 0.03

250 0.025
E IkJ/(g mol)] k110C [1/min]

Figure 3.6: 3-D Surface plot of Sum of Squares (SS) for Welt’s Data (Welt, 1997)

62

0.3

 

 

 

0.2 i

0.1- ' :o '
to o ”
- ° : - r . :
g 0 ‘ . ' e
32 , . °
£00 1 ' ‘ v . 1 . .

-o.2~

-o.3~

‘0'40 0.4 0.6 0.8 1

0.2
Predicted Y (Mass Average Retention of Anthocyanins)

Figure 3.7: Residual plot of the mass average Retention of anthocyanins for
Grape pomace at 17, 34 and 42% moisture content (wb) heated at retort

temperature of 126.7 00

3.5 Conclusion

The multi parameter approach to model nutraceutical degradation is a good
method, as it incorporates the challenges faced in the processing industry, such
as the simultaneous effect of temperature and moisture content, and potentially
could describe the effect of other factors such as pH, pressure and viscosity.
Confidence intervals and the joint confidence regions provide useful information
about the nature of the parameters and their correlation. The net effect of these
parameters is shown by plotting confidence bands (for the regression line) and

prediction bands (for individual data). This paper shows a novel method to

63

estimate the parameters using nonlinear method for low-and intermediate-
moisture food processed at high-temperature. Determining the confidence
interval on parameters for the change in nutraceuticals concentration for non-
isothermal heating will be a valuable tool for researchers and various food
industries designing functional foods processes. By obtaining more information
from limited data sets, these methods can help reduce experimental effort and
cost, both major concerns for academia and industry. For researchers without
access to Matlab, all statistical calculations can be done in Excel. For
researchers without a Comsol or similar software, temperatures during
conduction heat transfer can be approximated using the analytical solution with

Excel (Dolan, 2007).

3.6 nomenclatures

(VG ) anthocyanin retention, where 0 s(% )3 1)
0 0

 

CO initial mass-average anthocyanins concentration
0' standard error

p number of parameters

,0 correlation coefficient

Ea activation energy, J/g-mol

Kk rate constant min'1

K thermal conductivity, W/m K

k, rate constant at reference temperature T,, min'1
0 mass-average anthocyanins concentration

n number of data

R gas constant (J/g-mole K)

r dimensionless radius

R container radius, m

RMSE root mean-square error = J20; —Y,)2 /(n— p)

T temperature (K)

7'; initial temperature, K

T, reference temperature, K

2 dimensionless axial position

SS sum of squares

65

SSbest-fit

SSaIl-fixed

minimum sum-of-squares of errors, i.e. sum-of-squares when
nonlinear regression fits the curve

target value for sum-of—squares to compute parameter joint
confidence regions

number of parameters

parameter estimates

critical value of the F distribution for a given confidence level and
degrees of freedom. For example, in Excel, finv(95%
confidence, n, n-p) = finv(0.05,2,28) = 3.34. In matlab, the

identical expression is finv(0.95,2,28) = 3.34.

66

3.7 References

Ahmed J, Shivhare US & Raghavan GSV. 2004. Thermal degradation kinetics of
anthocyanin and visual colour of plum puree. European Food Research
and Technology 218(6):525-528.

Bates DM, 8. Watts, D.G. . 1988. Nonlinear regression analysis and its
applications. New York: Wiley.

Boekel MAJS. 1996. Statistical Aspects of Kinetic Modeling for Food Science
Problems. Journal of Food Science 61(3):477-486.

Cemeroglu B, Velioglu S & Isik S. 1994. Degradation Kinetics of Anthocyanins in
Sour Cherry Juice and Concentrate. Journal of Food Science 59(6):1216-
1218.

Dolan KD, Yang L & Trampel CP. 2007. Nonlinear regression technique to
estimate kinetic parameters and confidence intervals in unsteady-state
conduction-heated foods. Journal of Food Engineering 80(2):581-593.

Lai KPK. 2003. Modeling thermal and mechanical degradation of anthocyanins in
extrusion processing. Department of Agricultural Engineering. East
Lansing: Michigan State University. p. 72-74.

Lenz MK & Lund DB. 1977. The lethality-fourier number method: confidence
intervals for calculated lethality and mass-average retention of conduction-
heating, canned foods. Journal of Food Science 42(4):1002-1007.

Mishra DK, Dolan KD & Yang L. 2008. Confidence Intervals for Modeling
Anthocyanin Retention in Grape Pomace during Nonisothermal Heating.
Journal of Food Science 73(1):E9-E15.

Motulsky HJ, & Christopoulos, A. . 2004. Fitting models to biological data using
linear and nonlinear regression. A practical guide to curve fitting. New
York Oxford University Press.

Saraiva J, Oliveira JC, Hendrickx M, Oliveira FAR & Tobback P. 1996. Analysis
of the Inactivation Kinetics of Freeze-dried alpha-Amylase from Bacillus

67

amyloliquefaciens at Different Moisture Contents. Lebensmittel-
Wissenschaft und-Technologie 29:260-266.

Watts DG. 1994. Estimating parameters in nonlinear rate equation. The
Canadian journal of chemical engineering 72.

Welt BA, Teixeira, A.A., Balaban, M.O., Smerage, G.H., Hintinlang, DE, 81
Smittle, B.J. 1997. Kinetic parameter estimation in conduction heating
foods subjected to dynamic thermal treatments. J. Food Sci. 62(3):529-
534,538.

Wendie L. Claeys LRL, Ann M. Van Loey and Marc E. Hendrickx 2001a.
Inactivation kinetics of alkaline phosphatase and lactoperoxidase, and
denaturation kinetics of [beta]-Iactoglobulin in raw milk under isothermal
and dynamic temperature conditions. Journal of Dairy Research 68 95-
107.

Wendie L. Claeys LRL, Marc E. Hendrickx 2001b. Formation kinetics of
hydroxymethylfurfural, lactulose and furosine in milk heated under

isothermal and non-isothermal conditions. Journal of Dairy Research
68:287-301.

68

CHAPTER 4

Bootstrap confidence interval'for the kinetic parameters for degradation of

anthocyanins in grape pomace

69

Abstract

Due to the growing interest in nutraceuticals and their health benefits, it is
important to develop tools for modeling degradation of nutraceuticals in low-
moisture and high temperature heated foods. The objective of this study was to
estimate the thermal and kinetic parameters for the degradation of anthocyanins
in grape pomace and to calculate the bootstrap confidence interval. Thermal and
kinetic parameters for unsteady-state conduction-heated foods (grape pomace)
were estimated using nonlinear regression techniques. Rate constant (k11o°c) and
activation energy (5,.) for the degradation of anthocyanins in grape pomace were
estimated and bootstrap confidence intervals were calculated and compared to
the 95% asymptotic confidence intervals. Grape pomace at 42% moisture
content (wb) was heated in a steam retort at 126.7 °C in steel cans (radius
0.027m, and height 0.073m). Anthocyanin degradation was measured by high
performance liquid chromatography. The degradation values were used to
estimate kinetic parameters, which were k110°c =0.06 min'1 and Ea=65.3 kJ/mol.
Asymptotic confidence intervals for k11o°c and Ea were (0.055, 0.067) and (32.6,
97.9), respectively. Bootstrap 95% confidence intervals for k11o°c and E8 were
(0.055, 0.066) and (50.9, 100.82), respectively. Bootstrap confidence band and
prediction bands for anthocyanin retention were smaller than asymptotic
confidence and prediction bands, respectively. 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.

70

4.1 Introduction

Estimation of parameters for isothermal processes, such as degradation of
nutraceutical compounds in foods with high moisture content, is well established.
Isothermal experiments can be performed with high-moisture food samples as
the temperature gradient is very small and isothermal heating has very short lag
times. The rate of reaction and the activation energy for the degradation of
nutraceuticals can be computed by taking logarithm of the well-known Arrhenius
equation as the process follows first-order reaction kinetics. Conducting
isothermal experiments for the low- and intermediate-moisture foods is
challenging because of the large temperature gradients within the sample and
long lag times. Hence, nonisothermal experimentation is required for the low
moisture foods like extruded products, breads, jam and jelly and vegetable
pastes. For nonisothermal processes, kinetic parameters can be estimated by
nonlinear regression methods using the least square methods.

Statistical method is important tool to estimate the accuracy of estimated
parameter. However, it is not widely used in modeling for nutraceutical retention.
Some researchers have proposed methods to calculate the asymptotic
confidence interval and the joint confidence region to get good estimates of the
error and correlation on estimated parameters (Dolan and others 2007; Bates,
1988; Wendie L. Claeys, 2001). The Jackknife method for the estimation of the
experimental error on parameters was used for the kinetic model for thiamine
destruction in pea puree (Nasri and others 1993). However, confidence intervals

on predicted Y (microbial retention) and confidence intervals of the parameters

71

were not reported. Monte Carlo method was used to estimates the confidence
intervals for mass average retention of conduction-heated canned foods (Lenz
and Lund, 1977), but the confidence intervals on predicted Y were not reported.
novel method has been proposed (Dolan et al., 2007) to calculate the confidence
and prediction band on the predicted Y. In the literature surveyed, there were
very few confidence intervals reported for parameters and none for predicted Y,
which is the most important variable for processors.

Some researchers have applied the method of bootstrapping to get the
confidnce intervals on the estimated parameters. However, no study showed
computation of confidence intervals using bootstrap for degradation of
nutracuticals in food materials. The purpose of this study is to provide a tool to
the future researchers who can apply this method to report the confidence
intervls on the parameters thereby providing safety and quality to the processed
food. In the context of providing realistic estimate of error on the parameters
involed in nonisothermal processing, the objectives of this study were to (1)
compute bootstrap confidence intervals of kinetic parameters, (2) compute
bootstrap confidence bands and bootstrap, (3) prediction bands for predicted
anthocyanin retention, (4) compare bootstrap confidence and prediction values to

their asymptotic counterparts.

72

4.2 Mathematical Model and Statistical Methods
4.2.1 Kinetic Parameter Estimation

A detailed discussion about the nonlinear regression technique can be
found in (Mishra and others 2008). The parameter estimation process is
described briefly in this paper. Thermal degradation of anthocyanins has been
shown to follow first-order reaction kinetics (Ahmed and others 2004; Cemeroglu

and others 1994),

dC
— = -kC 1
dt ( )

The reaction rate can be quantified by the Arrhenius model;

5(22)
k ___ k R T T,
re (2)

 

Under dynamic temperature conditions, retention of anthocyanins can be

expressed by,

 

t 'Ea{ 1 _L]
(C j =2 e 0 r dr dz
0 pred

.l J (3)

 

 

73

where variables r and 2 were normalized; hence, the limits of both integrals were

from 0 to 1. The kinetic parameters E, and kr were estimated using matlab® in

combination with comsol® using the following command.
[beta, r, J] = nlinfit(X, y, @fun, betaO)

The command ‘nlinfit' in matlab® returns the estimated parameters (beta), the
residuals (r) and the Jacobian (J) using the least squares, which minimized the

following equation to get the best sum of squares for the estimated parameters.

SS = Z [(Yobs )i _ (Ypred )1" ]2
.- (4)

Parameters kr and E8 were estimated simultaneously using the nonlinear
regression method. Residual plots were also checked for the absence of trends

or correlations.

4.2.2 Overview of Bootstrap Method

The bootstrap method was found to be a better tool than the jackknife
method, which was proved to be a linear approximation of the bootstrap method
(Efron, 1979). If the distribution from which the samples are drawn is known and
if the function is sufficiently tractable, the standard errors and hence the

confidence intervals (Cls) can be constructed (Felsenstein, 1985). Bootstrap

74

procedure is most useful when the distribution of the sample is not known. When
Cls for the parameters or retention are reported, typically they are asymptotic,
because these are computationally efficient. Monte Carlo methods such as
bootstrap, are known to produce more realistic Cls. Now that software is
available for all most researchers, we can take advantage of these powerful
statistical techniques to improve quality and safety of foods.

Bootstrap method, as it was found in the literature, follows the following
procedure:

Step 1: For the data points 3:1,a:2,...,a:n, an estimate of parameter tcan

be obtained using a method T of statistical estimation (Felsenstein, 1985),

t = T(ccl,:1:2,...,a:n)

for example, T can be nlinfit in Matlab which is based on gauss-newton
method of nonlinear regression.

Step 2: The bootstrap method allows resampling of the data to construct a
fictional set of data. Each of these data sets is constructed by sampling n points

with replacement from the 23,, data. These fictional data sets consist of
231*,cl:2*,...,:cn* points, where each :13; is drawn at random from the original

data set. Then, t is again estimated for the new data set as,

till _ T III at: *
_ ($1 1$21H°1$n )

75

Step 3: The sampling process i.e. step 2 is repeated many times to get a
set of values of the estimated t“. The distribution of this estimate approximates
the distribution of the actual estimate t.

Step 4: Confidence limit on the parameter is calculated based on the upper

or lower percentiles of the observed 15" values.

4.2.3 Application of Bootstrap to Kinetic Model
For 42 retention values of anthocyanins, predicted Y and time-temperature

(tT) history i.e. 111,7], Y2t2T2,...,Y42t42Z,2 were used to get an estimate of E, and k,;

[Eaikr] ___ n1infit<ntlTl1Y2t2T21°881Y42t42T4‘2) (5)

Fictional data set was constructed by random sampling with replacement to
get(thl‘Tf,Y2*t2*T2*,...,Y42*t42*fl‘42*). As the sampling was with replacement,
there were chances that one data point occurred more than once, and that one

data point did not occur at all. These new data sets were used to estimate the

new set of parameters,

[EMS] = nlinfit(Yi*ti*fli*.Ye*ti*7‘2*.....Y.-i*te*T.2*) (6)

Random sampling process was repeated many times to get a set of values

of the estimated [ Edi , k: ] .

76

4.2.4 Bootstrap Confidence Interval on Parameters

The confidence limit on parameter was calculated based on the upper and

lower 95 percentiles of the observed [Ea*,k,.*] values. For example, the

confidence interval on E21 for the 100.(1—a) percentile can be obtained by,

010 ’

(E Eaup) = [t,‘(%),12~;(‘“%)] (7)

4.2.5 Bootstrap Confidence Interval on Predicted Y
The bootstrap confidence band on predicted Y was calculated using
“nlpredci” in Matlab and bootstrap prediction band was calculated using the

equation (Montgomery, 2006),

 

prediction width, = J(confidence widthi)2 + (1,, ,2” * RMSE)2 (8)

77

4.3 Methods and Materials

4.3.1 Experimentation

Analytical method to determine the anthocyanin content was adopted from
(Mishra et al., 2008).ln short, grape pomace (42% moisture content (wb)) was
retorted in steel cans (radius 0.027m, and height 0.073m) in a rotary steam retort
at 126.7 °C. The time was varied from 8 to 25 minutes to get the different level of
degradation of anthocyanins in grape pomace. Extraction solvent (50 ml of
methanol + 33 ml of water + 17 ml of 37% HCL) was used to extract the
anthocyanins from the raw and retorted grape pomace. The quantification of
anthocyanins was done by hydrolyzing the anthocyanins to anthocyanidins and
was injected in HPLC (High performance Liquid Chromatography) system and
the dual wavelength detector read the absorbance reading. The area under the
peaks of chromatograms was used to calculate the anthocyanin content in the

raw and retorted samples.

78

4.4 Results

Data used in this study was adopted from (Mishra et al., 2008). The

heating time and retention of anthocyanins are provided in table 4.1.

Table 4.1: Retention (%0 )value of anthocyanins for grape pomace at 42%
MC(wb) as measured from HPLC

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample Heating time Retention of
number (min.) anthocyanins

1 0 1.117
2 0 0.855
3 0 0.855
4 0 0.883
5 0 1.029
6 0 0.984
7 0 1.007
8 0 1.110
9 0 1.159
10 8 0.837
1 1 8 0.733
12 8 0.804
13 10 0.688
14 10 0.684
15 10 0.686
16 12 0.698
17 12 0.744
18 12 0.714
19 14 0.565
20 14 0.515
21 14 0.409
22 15 0.498
23 15 0.507
24 15 0.599
25 16 0.341
26 16 0.285
27 16 0.433
28 17 0.301
29 17 0.309
30 17 0.305
31 19 0.212

 

 

 

 

79

Table 4.1 Con’t

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample Heating time Retention of
number (min.L anthocyanins

32 19 0.241

33 19 0.227

34 21 0.234

35 21 0.188

36 21 0.249

37 23 0.218

38 23 0.222

39 23 0.213

40 25 0.170

41 25 0.155

42 25 0.145

 

4.4.1 Kinetic Parameter Estimation

Kinetic parameters (table 4.2) from the nonlinear regression routine were
obtained using the least square method. There were 42 data points, and the
repeated converged value of the rate of reaction was 0.0606 min", whereas the

activation energy was found to be 65.32 kJ/gmol. Correlation coefficient plots. was

—0.12. The root mean squared error was 0.084, which is approximately 9% of the
total scale of 1.0, shows a good fit. 95% bootstrap confidence interval for km°c
was very close to the 95% asymptotic confidence interval but the bootstrap

confidence interval on E8 was tighter than the asymptotic confidence interval for

95% confidenc.

80

 

Table 4.2: Kinetic parameters for anthocyanin degradation in grape pomace at
42% (wb) moisture content

 

 

 

 

 

N o 95% 95%

' Parameter Standard Bootstrap asymptotic

Parameter D: a Estimates Error confidence confidence RMSE
interval interval
0 . __1

km 0 90606 "1'" 0.003 (0.053, 0.066) (0.055, .067)
42 0.084

E3 6532 “/9 m°' 16.15 (49.06, 104.93) (32.7, 97.9)

 

 

 

 

 

 

 

 

4.4.2 Bootstrap Confidence Interval

The bootstrap confidence interval was calculated with random sampling of
the original data set. Table 4.3 shows the confidence intervals at different
number of time of bootstrapping. From these results it was concluded that 1000
bootstrap (Efron, 1987) was sufficient to get the confidence interval on the

parameters.

Table 4.3 Bootstrap confidence interval at 95% on E, and k,

 

 

 

 

 

 

 

 

 

Number of bootstraps Confidence interval Ea Confidence Interval kr

10 (55.16, 82.73) (0.0572, 0.0630)
100 (50.65, 115.92) (0.0522, 0.0652)
200 (50.20, 107.10) (0.0531, 0.0658)
500 (49.89, 106.54) (0.0533, 0.0660)
1000 (49.08, 104.93) (0.0531, 0.0660)
2000 (49.60, 106.28) (0.0533, 0.0658)
5000 (49.31, 106.11) (0.0532, 0.0659)

 

 

 

 

81

Figure 4.1 shows 95% bootstrap confidence band, 95% bootstrap
prediction band, 95% asymptotic confidence band and 95% prediction band for
mass average retention of anthocyanins. Correlation coefficient was —0.12. Many
data fall outside the confidence band, as confidence band (CB) is the region
where 95% of the regression lines are expected to be. The prediction band (PB)
is the region where 95% of the data are expected to be. If more data were

collected, we expect ~5% of all the data would fall outside the PB.

 

 
 
 
 
 
 
 

 

 

 

 
 

 

 

"g 1.5 0 observed
5 —predicted
g ................... . . 95% asymptotic confidence band
5 ._,___.: ----------------------------------------------- 95% asymptotic prediction band
5 1 ___ '7'.","':-.-.---_.. ....... -----95% bootstrap confidence band
“6 N. """"" ¥-'."""'-<-.re. - . --'---95% bootstrap prediction band
‘5 0 5- ' """ ...
a: " . . .
o: . ..__ .
0 “‘1 ~ .
O) ""'------'.‘..'.',.‘
i! 0»
<
8
g _0 5 1 1 J 1 1

' 0 5 10 15 20 25

heating time (min) at 126.7°C

Figure 4.1: 95% bootstrap confidence band, 95% bootstrap prediction band, 95%
asymptotic confidence band and 95% asymptotic prediction band for mass
average retention of anthocyanins in grape pomace heated in 202 x 214 cans at
retort temperature of 126.7 00.

The confidence interval for the bootstrap is tighter in case of E8 whereas it
was nearly same for the k,as it has been shown in table 4.2. Confidence band for

the predicted Y is very small for the bootstrap as compared to the asymptotic (fig.

82

1). Prediction band also shows the same trend for the bootstrap i.e bootstrap

prediction band is much smaller than the asymptotic prediction band.

The normal bivariate distribution (figure 4.2) for the 5000 bootstrap
parameters was plotted as a 3-D plot in Matlab. The contours of the confidence

level of 90 and 95% were constructed out of the plotted distribution.

 

P (probability)

 

   
 

I 150
100

k110C [1/min] 0-04 0

E [kJ/(g mol)]

Figure 4.2 3-D plot of the bivariate normal distribution and 90 & 95% contours of
the confidence level

Plot of 1000 bootstrap estimated parameters is shown in fig. 4.3. Joint
confidence region was plotted on the same plot to compare confidence regions at
90 81 95% confidence level. 90% confidence level has the bigger region as it was

expected, which covers 90% of the bootstrap estimated parameters.

83

 

 

(142.: . .

.0
.h

.0
0.1
°.°

k1 10°c [1lmin]
,0 o
i“ 83

.0
(.0
N
I. .

0.3;» 1'

20 30 40 5o

 

 

 

 

60 7o 80 90 100‘110
E [kJ/(g mol)]

Figure 4.3 scatter plot of all the bootstrap estimated parameters and confidence
regions at 90 & 95% confidence level (1,000 simulated points)

84

4.5 Conclusions

The bootstrap approach to determine the confidence interval on parameters
for the change in nutraceuticals concentration for non-isothermal processes in
Iow-lintermedlate-moisture and high-temperature food during processing will be a
valuable tool for researchers and various food industries engaged in making
functional foods. Bootsrtap confidence interval is more advantageous if no other
method of calculating the confidence interval is present. The bootstrap helps and
shows the asymptoic confidence interval. This study was done with a hope that
future researchers will use these methods to report the error estimates and
confidence intervals, which will help processors to enhance the design of the

processing system to have safe and quality food.

85

4.6 Nomenclatures

a

level of significance
density, kg/m3
standard error

correlation coefficient

mass-average anthocyanins concentration within a can

initial mass-average anthocyanin concentration

Specific heat, J/kg °C

activation energy, J/g-mol

rate constant min'1

thermal conductivity, W/m K

rate constant at reference temperature T,, min“1
number of data

number of parameters
dimensionless radius

gas constant (J/g-mole K)
container radius, in

root mean square error, g/g or °C
Time

t-value from T-test

temperature (K)
initial temperature, K

reference temperature = 383 K

86

Gauss weights

time-temperature history (independent variable)
mass average retention of anthocyanins, fractional g/g.
dimensionless axial position, where z = 0 is at the half-height

point of the can

87

4.7 References

Ahmed J, Shivhare US & Raghavan GSV. 2004. Thermal degradation kinetics of
anthocyanin and visual colour of plum puree. European Food Research
and Technology 218(6):525-528.

Bates DM, 8. Watts, D.G. . 1988. Nonlinear regression analysis and its
applications. New York: Wiley.

Cemeroglu B, Velioglu S & Isik S. 1994. Degradation Kinetics of Anthocyanins in
Sour Cherry Juice and Concentrate. Journal of Food Science 59(6):1216-
1218.

Dolan KD, Yang L & Trampel CP. 2007. Nonlinear regression technique to
estimate kinetic parameters and confidence intervals in unsteady-state
conduction-heated foods. Journal of Food Engineering 80(2):581-593.

Efron B. 1979. Bootstrap Methods: Another Look at the Jackknife. The Annals of
Statistics 7(1):1-26.

Efron B. 1987. Better Bootstrap Confidence Intervals. Journal of the American
Statistical Association 82(397):1 71 -1 85.

Felsenstein J. 1985. Confidence Limits on Phylogenies: An Approach Using the
Bootstrap. Evolution 39(4):783—791.

Lenz MK & Lund DB. 1977. The lethality-fourier number method: confidence
intervals for calculated lethality and mass-average retention of conduction-
heating, canned foods. Journal of Food Science 42(4):1002-1007.

Mishra DK, Dolan KD & Yang L. 2008. Confidence Intervals for Modeling
Anthocyanin Retention in Grape Pomace during Nonisothermal Heating.
Journal of Food Science 73(1):E9-E15.

Montgomery DP, EA; Vining, GG. . 2006. Introduction to linear regression
analysis.,4th edition. ed.: John Wiley & sons, inc.

88

Nasri H, Simpson R, Bouzas J & Torres JA. 1993. Unsteady-state method to
determine kinetic parameters for heat inactivation of quality factors:
Conduction-heated foods. Journal of Food Engineering 19(3):291-301.

Wendie L. Claeys LRL, Marc E. Hendrickx 2001. Formation kinetics of
hydroxymethylfurfural, lactulose and furosine in milk heated under

isothermal and non-isothermal conditions. Journal of Dairy Research
68:287-301.

89

5 Conclusion

Many low- and intermediate moisture foods are processed
nonisothermally at high temperatures that require attention. Based on the
estimated temperature-dependent thermophysical properties, the thermal
conductivity and specific heat of grape pomace increased about 45% and 37%

respectively, from 25°C to 121°C. When heating for 10 min at 126.7 °C,

anthocyanins were degraded up to 32%. The kinetic parameters k, = 0.058 mm“1
and E = 75.34 kJ/g mol were very close to those estimated by Lai (2003), who
used a 1:3 grape pomace: wheat flour mixture and heated the mixture in steel
cells dipped in heated oil. The fact that the estimates in the present study are so
close to Lai’s, who used a different procedure, strengthens the reliability of the
estimates. Although the moisture parameter estimate b = 1.9 MOW);1 was smaller
than Lai’s b = 5.28 (MCwb'1), the trend of the degradation rate kr increasing with
increasing moisture was the same in both studies. Joint confidence region for the
parameters showed a good way to represent the correlation between the two
parameters.

Asymptotic confidence band and prediction band on predicted Y
(anthocyanin retention) gave an approximate estimate of the error on estimated
parameters, whereas bootstrap method provided narrow confidence interval for
parameters, and bootstrap confidence band and prediction band for anthocyanin
retention. Industrial processes for food manufacturing involve many variables that
can be estimated using multiple parameter estimation method. Process design to

improve food quality and ensure safety would be enhanced by knowledge of the

90

actual dynamic kinetic parameters of the desired components, such as
nutraceuticals (quality) or pathogens (safety). Better estimates of the true error
would also reduce experimental effort and cost. The method showed in this study
will be a beneficial tool for future researchers involved in kinetic parameter
estimation of nutraceuticals in Iow- and intermediate-moisture food heated at

high temperatures.

91

Appendix A

 

 

 

 

 

 

 

 

 

 

ORAC Results
Sample number Heating time (min) ORAC pmol TEIgTS
1 0 1648
2 0 1850
3 0 1763
4 58 15.98
5 58 16.02
6 58 16.46
7 58 17.77
8 58 18.90
9 58 1794

 

 

 

 

 

One-way ANOVA

Dependent Variable: ORAC

Sum of
Source DF Squares Mean Square F Value Pr > F
Model 2 6.06586667 3.03293333 5.07 0.0514
Error 6 3.59193333 0.59865556

Corrected Total 8 9.65780000

The p value (p>0.05, at 95% of confidence level) suggests that there is no
significant difference in mean value of ORAC in raw grape pomace and in
retorted grape pomace. Hence, it is concluded that there is no degradation in the
ORAC of grape pomace as a result of heating the canned grape pomace in

retort.

92

Appendix B

Flow chart of overall process

Overview of the process

Retorting at Thermal parameter

Can Sealing 11‘ (1,5,16,11,11,... 11‘ estimation

 

kinetic parameter II HPLC analysis _II Extraction of
esttmatlon antl1ocs- anins

        

93

 

Appendix C

3~point Gauss integration. Figure represents half of the can size.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gauss points normalized from 0 to 1 are;

1. 0.112701665379
2. 0.5
3. 0887298334261

94

Appendix D

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Can Temperature (°C) R°t°"t
Time (sec) Temperature
1 2 3 (°C)
0 24.68 25.53 22.34 39.13
10 24.52 25.56 25.36 39.02
20 24.71 25.61 25.51 39.16
30 24.65 25.79 25.61 39.13
40 24.66 25.61 25.31 38.94
50 24.63 25.65 25.41 39.24
60 24.82 25.74 25.56 40.03
70 24.79 25.69 25.67 42.63
80 24.83 25.83 25.71 45.16
90 24.96 25.86 25.78 48.06
100 24.94 25.95 25.78 50.59
110 24.99 26.16 26.17 53.61
120 25.56 27.19 26.56 74.06
130 25.82 27.29 26.48 80.19
140 25.94 27.22 27.02 84.68
150 25.87 27.25 26.84 87.01
160 25.96 27.15 26.62 89.31
170 26.01 27.06 26.87 90.81
180 26.18 27.24 27.13 92.49
190 26.17 27.17 27.07 93.96
200 26.30 27.23 27.22 95.21
210 26.54 27.29 27.35 96.59
220 26.58 27.49 27.56 98.01
230 26.85 27.80 27.82 99.41
240 26.93 27.73 27.97 100.59
250 27.00 28.02 28.08 101.52
260 27.11 28.13 28.32 102.35
270 27.46 28.19 28.54 103.12
280 27.71 28.41 28.86 103.76
290 27.87 28.53 29.02 104.17
300 27.94 28.88 29.38 104.56
310 28.39 29.02 29.61 105.02
320 28.69 29.27 29.96 105.34
330 29.04 29.64 30.29 107.57
340 29.43 30.02 30.79 109.71
350 29.96 30.42 31.30 11 1.83
360 30.15 30.93 31.73 113.53
370 30.72 31.39 32.31 115.36
380 31.21 31.71 32.81 116.87
390 31.86 32.33 33.46 118.58
400 32.44 32.84 33.99 1 19.98
410 32.92 33.41 34.75 121.54
420 33.72 34.17 35.52 123.06

 

95

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Can Temperature (°C) R910"
Time (sec) Temperature
1 2 3 (°C)

430 34.36 34.91 36.31 124.51
440 35.03 35.46 36.87 125.84
450 35.76 36.19 37.81 127.18
460 36.61 37.08 38.82 128.48
470 37.41 37.60 39.56 127.02
480 38.37 38.41 40.58 125.65
490 39.30 39.44 41.70 125.18
500 40.39 40.45 42.69 127.1 1
510 41.27 41.36 43.68 128.69
520 42.36 42.28 44.83 127.98
530 43.57 43.55 46.30 126.73
540 44.46 44.63 47.08 126.04
550 45.78 45.63 48.49 126.63
560 47.03 47.01 49.82 128.65
570 48.31 48.15 51.08 128.57
580 49.52 49.31 52.31 127.53
590 50.79 50.69 53.64 126.67
600 52.44 52.29 55.21 126.63
610 53.67 53.65 56.44 127.74
620 54.92 55.02 57.68 128.32
630 56.44 56.42 59.09 127.71
640 58.17 58.09 60.72 126.92
650 59.51 59.62 62.11 126.76
660 60.84 60.96 63.33 127.34
670 62.45 62.63 64.72 128.14
680 63.86 64.04 66.03 127.79
690 65.27 65.41 67.31 127.22
700 66.72 66.85 68.58 126.86
710 68.37 68.54 70.08 127.23
720 69.53 69.79 71.14 127.74
730 71.12 71.26 72.51 127.87
740 72.48 72.69 73.76 127.38
750 73.91 74.08 75.06 127.09
760 75.27 75.41 76.21 127.07
770 76.51 76.80 77.42 127.49
780 78.00 78.13 78.69 127.70
790 79.21 79.41 79.81 127.51
800 80.54 80.58 80.91 127.26
810 81.71 81.76 81.92 127.24
820 83.08 83.03 83.17 127.30
830 84.16 84.14 84.17 127.51
840 85.20 85.14 85.07 127.57
850 86.43 86.31 86.16 127.39
860 87.50 87.26 87.13 127.29
870 88.44 88.21 87.95 127.28

 

 

 

 

 

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Can Temperature (°C) Retort
Time (sec) Temperature
1 2 3 (°C)

880 89.44 89.20 88.89 127.36
890 90.56 90.26 89.89 127.52
900 91 .43 90.98 90.71 127.48
910 92.37 91.93 91.56 127.27
920 93.22 92.85 92.37 127.31
930 94.06 93.63 93.18 127.35
940 94.83 94.38 93.91 127.46
950 95.61 95.12 94.64 127.43
960 96.52 95.92 95.48 1 27.33
970 97.15 96.59 96.08 127.32
980 97.82 97.18 96.74 127.32
990 98.71 97.93 97.56 127.37
1000 99.17 98.56 98.08 127.30
1010 99.81 99.12 98.71 127.31
1020 100.48 99.73 99.35 127.28
1030 101.02 100.58 100.12 127.26
1040 101.61 100.88 100.53 127.29
1050 102.25 101.52 101.18 127.28
1060 102.79 101.98 101.78 127.24
1070 103.31 102.32 102.17 127.28
1080 103.76 102.90 102.81 127.22
1090 104.24 103.40 103.29 127.22
1100 104.72 103.88 103.84 127.26
1110 105.14 104.26 104.26 127.26
1120 105.77 104.65 104.92 127.36
1130 105.98 105.09 105.20 127.29
1140 106.49 105.56 105.67 127.26
1150 106.83 105.85 106.11 127.21
1160 107.11 106.22 106.55 127.18
1170 107.55 106.76 107.07 127.29
1180 107.83 106.96 107.31 127.25
1190 108.20 107.25 107.68 127.26
1200 108.67 107.66 108.19 127.26
1210 108.87 107.97 108.46 127.14
1220 109.15 108.27 108.80 127.16
1230 109.48 108.59 109.18 127.25
1240 109.73 109.01 109.47 127.21
1250 110.08 109.19 109.86 127.27
1260 110.41 109.47 110.14 127.16
1270 110.58 109.76 110.48 127.15
1280 110.84 110.08 110.78 127.19
1290 111.19 110.34 111.19 127.25
1300 111.41 110.52 111.42 127.19
1310 111.65 110.82 111.73 127.13
1320 111.87 111.17 111.98 127.11

 

 

 

 

 

97

 

 

Can Temperature (°C)

 

 

Retort

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time (sec) Temperature
1 2 3 (°C)
1330 112.12 111.31 112.33 127.17
1340 112.33 111.72 112.54 127.15
1350 112.58 111.89 112.79 127.17
1360 112.65 112.09 113.07 127.16
1370 112.89 112.34 113.26 127.13
1380 113.15 112.61 113.56 127.15
1390 113.37 112.76 113.78 127.14
1400 113.76 112.79 113.86 127.10
1410 113.72 113.16 114.28 127.16
1420 113.86 113.31 114.46 127.12
1430 114.26 113.41 114.74 127.11
1440 114.17 113.69 114.89 127.10
1450 114.41 113.84 115.11 127.13
1460 114.53 114.14 115.30 127.13
1470 114.80 114.19 115.54 127.21
1480 114.92 114.35 115.63 127.12
1490 114.97 114.54 115.87 127.11
1500 115.20 114.59 116.02 127.06
1510 115.32 114.92 116.21 127.13
1520 115.43 115.09 116.39 127.15
1530 115.54 115.23 116.57 127.01
1540 115.74 115.39 116.67 127.09
1550 115.78 115.52 116.82 127.10
1560 115.97 115.63 116.94 127.07
1570 116.14 115.76 117.04 127.09
1580 116.26 115.88 117.22 127.13
1590 116.37 115.99 117.37 127.13
1600 116.44 116.17 117.47 127.08
1610 116.62 116.30 117.71 127.12
1620 116.66 116.36 117.75 127.07
1630 116.79 116.56 117.95 127.03
1640 116.84 116.63 117.92 127.21
1650 117.03 116.76 118.18 127.07
1660 117.06 116.86 118.23 127.05
1670 117.21 116.98 118.39 127.08
1680 117.21 116.82 118.47 126.89
1690 117.29 116.89 118.53 127.61
1700 117.34 116.99 118.63 127.46
1710 117.48 117.09 118.76 126.96
1720 117.51 117.21 118.82 127.18
1730 117.63 117.34 118.95 126.48
1740 117.70 117.42 119.03 126.31

 

 

 

 

 

98

 

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