QUANTIFYING WATER EFFECTS ON THERMAL INACTIVATION OF SALMONELLA IN
LOW-MOISTURE FOODS
By
Francisco Javier GarcĂŠs-Vega

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Biosystems Engineering - Doctor of Philosophy
2017

ABSTRACT
QUANTIFYING WATER EFFECTS ON THERMAL INACTIVATION OF SALMONELLA
IN LOW-MOISTURE FOODS
By
Francisco Javier GarcĂŠs-Vega
Thermal processing is the most used technology to control pathogens in the food supply.
However, thermal processing of low-moisture foods (LMF) faces challenges, given the enhanced
thermal resistance of Salmonella.
Product water is recognized as a controlling factor in thermal inactivation of Salmonella
in/on LMF, such as almonds. Water activity (aw) describes the state of water; however, aw is
temperature dependent and characterized by hysteresis between sorption states. Moisture content
(%MC) describes the amount of water in a product; it is not temperature dependent, and might be
a more convenient metric than aw to account for water in thermal inactivation processes.
Food products, and microorganisms in/on those products, are influenced by process
conditions involving heat and mass transfer phenomenon. Process temperature and humidity
typically are significant factors in these inactivation systems. The effect of process humidity was
recently quantified and reported, but information about the effect of process air velocity on
microbial inactivation processes for LMF is very limited.
The goal of this study was to improve the understanding of the role of water in thermal
inactivation of bacteria in LMF. The specific objectives were to: (1) evaluate the relationships of
two water metrics with thermal resistance of Salmonella on LMF; (2) describe and quantify the
interactive effects between product water, process humidity, and air velocity on the thermal
resistance of Salmonella on LMF, and (3) propose and evaluate a model to describe the effects of
air velocity, aw, and/or %MC on the thermal resistance of Salmonella on LMF.

Inoculated almonds were equilibrated to two moisture (%MC) levels but the same aw, and
two aw levels but the same %MC. Equilibrated products were vacuum packaged and thermally
treated in a water bath at 80°C. Survivors were recovered and enumerated, the resulting
inactivation curves were used to fit the log-linear inactivation model, and the inactivation kinetics
were compared. D-values ranged from 15.7 to 18.0 min, and the RMSE was 0.25 to 0.69 log
CFU/g. No differentiated effect attributable preferentially to aw or %MC was seen in the
inactivation kinetics (P > 0.05), likely because of the variability of the parameters. However, there
are other effects of the two water metrics that should be further studied.
To assess the effect of process condition, inoculated almonds were equilibrated at 25 and
65% RH. After equilibration, samples at each moisture content were treated in a laboratory-scale
convection oven at four different conditions (121°C, 2 air velocities, and 2 humidities (~3 and 30%
moisture by volume)), for 7 durations in triplicate. Survivors were recovered and enumerated. The
resulting 24 inactivation curves were used to globally estimate the parameters of six inactivation
models. A model incorporating temperature, process humidity, and air velocity performed best,
with a RMSE of 0.51 log N/N0.
The separate effects of aw and %MC on the inactivation kinetics of Salmonella in LMF
remain inconclusive. Further analysis is needed to identify which metric is best for modeling and
validating thermal inactivation processes. However, the effect of air velocity was significant,
indicating a velocity effect independent of the influence on heating rate, due to the relative impact
of product and process moisture on bacterial inactivation. Validation studies with other products
will be important to further test the magnitude of the impact of aw, %MC, and air velocity on
thermal inactivation processes for low-moisture foods.

Copyright by
FRANCISCO JAVIER GARCÉS-VEGA
2017

ACKNOWLEDGMENTS

This dissertation is the result of almost 5 years of learning, enjoying, suffering, struggling,
growing, and many other things. The number of people that one way or another have been part of
this is too long to be listed here; not only for how many you are, but because I will certainly forget
someone. Anyway, I will take the risk to list a few, that I think deserve the public acknowledgment.
First and for most, my family; especially my parents and siblings for their unconditional
support, encouragement and advice.
Dr. Marks, I never imagine having such a wonderful advisor. I have learned more than
what I ever imagine from you; not only scientifically and professionally, but also as a person. Your
support and encouragement in the most difficult moments was decisive to reach this point.
Dr. Dolan, Dr. Mitchel, and Dr. Ryser; your guidance and support as advising committee
was extraordinary. As well as your flexibility to meet in extraordinary short notice to get things
done.
Bernadette; I am sorry, I cannot call you Dr. Klotz, for introducing me to predictive food
microbiology, pushing me to go above and beyond, and helping me to realize that sometimes crazy
dreams come true.
Kaitlyn, you deserve a couple of lines for yourself, your support, especially in the darkest
moments, was more than what I can ever ask from a friend. I cannot tell how many beers and talks
we have in this 3 years but all of them, the good ones and the not so good ones, allow me to
discover an amazing person. I wish you the brightest future as a scientist (the Ph.D. is hard, but
you will nail it) and as a person. My gratitude to you is beyond what I can write in a few sentences.
Our lab-work hours are even!

iv

The lab team, guys you are close to 20…, your help is invaluable; especially Mike and
Nicole as lab managers dealing with the smallest details and logistics; even when things just do
not work.
Fellow graduate students in the lab, Dani, Ian, Quincy, Pichamon, Nurul, and Beatriz, I just
have words of thanksgiving for your support, many times in ways that where completely
unexpected.
To my friends, here in Michigan, back in Colombia, and around the world. Thank you for
being there, for making me part of your families away from home, for letting me share wonderful
moments, for sharing the joy, and the sadness…
To the Colciencias-Fullbright agreement, call 529 of 2011 for the economic support and,
USDA-NIFA grant 2015-68003-23415, for the economic support of the experiments.

v

TABLE OF CONTENTS

LIST OF TABLES ....................................................................................................................... viii
LIST OF FIGURES ........................................................................................................................ x
1

INTRODUCTION ........................................................................................................ 1
1.1
The Low-Moisture Food Safety Challenge................................................. 1
1.2
The Knowledge Gap ................................................................................... 3
1.3
Hypotheses .................................................................................................. 4
1.4
General Goal ............................................................................................... 4
1.5
Specific Objectives ..................................................................................... 4

2

LITERATURE REVIEW ............................................................................................. 6
2.1
Salmonella in Low-Moisture Foods............................................................ 6
2.2
Water Metrics.............................................................................................. 8
2.3
Predictive Inactivation Models ................................................................. 10
2.3.1 Primary models .............................................................................................. 10
2.3.2 Secondary models .......................................................................................... 11
2.3.2.1 Optimization of reference conditions. .................................................... 13
2.3.2.2 Are traditional parameters truly constant? ............................................. 13
2.3.2.3 Secondary models involving water ........................................................ 14
2.3.3 Model performance and selection .................................................................. 18
2.4
Summary ................................................................................................... 20

3

MATERIALS AND METHODS ............................................................................... 22
3.1
Product ...................................................................................................... 22
3.2
Bacteria and Inoculum Preparation ........................................................... 22
3.3
Isothermal Experiments (Study 1) ............................................................ 23
3.3.1 Inoculation ..................................................................................................... 24
3.3.2 Equilibration .................................................................................................. 24
3.3.3 Isothermal treatment ...................................................................................... 26
3.3.4 Enumeration of survivors............................................................................... 27
3.3.5 Data analysis .................................................................................................. 28
3.3.5.1 Model fitting and comparison ................................................................ 28
3.3.5.2 Analysis of other secondary data sets .................................................... 28
3.4
Non-Isothermal Experiments (Study 2) .................................................... 29
3.4.1 Inoculation ..................................................................................................... 30
3.4.2 Equilibration .................................................................................................. 30
3.4.3 Thermal treatment .......................................................................................... 30
3.4.3.1 Air velocity estimation ........................................................................... 30
3.4.3.2 Heat treatment and experimental design ................................................ 32
3.4.4 Enumeration of survivors............................................................................... 33
3.4.5 Model parameter estimation and evaluation .................................................. 33
3.4.5.1 Models and model fitting ....................................................................... 33

vi

3.4.5.2 Input data ................................................................................................ 35
3.4.5.3 Model performance and selection .......................................................... 36
4
RELATIONSHIPS OF WATER ACTIVITY AND MOISTURE CONTENT TO
THE INACTIVATION KINETICS OF SALMONELLA IN LOW-MOISTURE FOODS ........ 38
4.1
Sample Characteristics .............................................................................. 38
4.2
Inactivation Results ................................................................................... 40
4.3
Analysis of Data from Other Studies ........................................................ 42
5
MODELING TEMPERATURE, MOISTURE, AND AIR VELOCITY EFFECTS
ON SALMONELLA INACTIVATION DURING DYNAMIC THERMAL PROCESSES OF
LOW-MOISTURE FOODS.......................................................................................................... 45
5.1
Sample Equilibration ................................................................................ 45
5.2
Air Velocity Estimation ............................................................................ 46
5.3
Changes in Product Temperature, Water Activity and Product Moisture
Content during Processing ........................................................................ 48
5.4
Microbial Inactivation Curves .................................................................. 52
5.5
Parameter Estimation - Model Fitting....................................................... 54
6

CONCLUSIONS ........................................................................................................ 63

7

FUTURE WORK AND RECOMMENDATIONS .................................................... 65

APPENDICES .............................................................................................................................. 68
Survival plate counts for the isothermal experiments .............................. 69
Example almond surface histories from the isothermal experiments ...... 71
Analysis of covariance effect of water metrics ........................................ 72
Secondary data for analysis of aw and %MC on D-values....................... 73
Air velocity calculations........................................................................... 74
Microbial populations, almond aw (measured at room temperature), and
%MC from the air velocity experiments ................................................... 75
Temperature profiles ................................................................................ 80
Reference conditions optimization .......................................................... 82
Scaled sensitivity coefficients ................................................................... 84
Estimated parameters of other models tested ............................................ 86
MatLabÂŽ Code ........................................................................................ 88
REFERENCES ............................................................................................................................. 91

vii

LIST OF TABLES

Table 1: Salmonella recalls from January to April 1st 2017 related to LMF (U.S. Food and Drug
Administration, 2017). .................................................................................................................... 2
Table 2: Characteristics of the aluminum almond. ....................................................................... 32
Table 3: Non-isothermal treatments experimental design. ........................................................... 33
Table 4: Models acronyms and parameters to be estimated for each of the models. ................... 35
Table 5: Chambers and product characteristics for the isothermal experiments. Mean Âą standard
deviation (n = 3). ........................................................................................................................... 39
Table 6: Model fitting summary for the log-linear and Weibull models based on three
independent replicates. Estimated parameters, relative error of the parameters and RMSE of the
model............................................................................................................................................. 40
Table 7: Correlation coefficients of log(D80°C) vs. aw and %MC of some representative
low-moisture foods. ...................................................................................................................... 43
Table 8: Summary of equilibrium conditions (mean Âą standard deviation) ................................. 45
Table 9: Estimated slopes and convective heat transfer coefficient (h) for the operational set
points tested. ................................................................................................................................. 47
Table 10: Estimated values, relative standard error (RSE) and P-values for the DLM model
parameters. .................................................................................................................................... 54
Table 11: Estimated values, relative standard error (RSE) and P-values for the DLMV model
parameters. .................................................................................................................................... 58
Table 12: Estimated values, relative standard error (RSE) and P-values for the DLMCM2 model
parameters. .................................................................................................................................... 60
Table 13: AICc comparison for the DLMCM and DLMCM2 models using %MC and aw as the
metric of water in the product. ...................................................................................................... 61
Table 14: Estimated values, relative standard error (RSE) and P-values for the DLMCM2V
model parameters .......................................................................................................................... 61
Table 15: Inactivation data of the isothermal experiments. .......................................................... 69
Table 16: ANOVA table of the analysis of covariance. ............................................................... 72
Table 17: Coefficients estimates of the analysis of covariance. ................................................... 72

viii

Table 18: Data from other products; dates (Buchholz et al., 2016), wheat flour (Smith, 2014), and
almonds (Limcharoenchat, 2017). ................................................................................................ 73
Table 19: Thermal properties used in the air velocity estimation. ................................................ 74
Table 20: Air velocity estimation results and intermediate calculations. ..................................... 74
Table 21: Inactivation data and grouping variables from the non-isothermal experiments. ........ 75
Table 22: Summary of temperature profiles of the non-isothermal experiments. ........................ 80
Table 23: Estimated parameter for the DMLC model eqn [15]. ................................................... 86
Table 24: Estimated parameters of the DLMMC model eqn [16]. ............................................... 87

ix

LIST OF FIGURES

Figure 1: Effect of aw on ZT for wheat flour (×) (Smith, 2014), peanut butter (◊), and low-fat
peanut butter (□) (He et al., 2013). - - best-fit lines plotted for reference only. ........................... 14
Figure 2: Example of the discontinuity of ZT vs. aw. A) low-fat peanut butter (Garces-Vega &
Marks, 2015), data from He et al., (2013) B) wheat flour (Garces-Vega & Marks, 2015), data
from (Smith, 2014) . - - best-fit lines and shadow zones showed as reference only. ................... 17
Figure 3: Flow diagram for isothermal experiment. ..................................................................... 24
Figure 4: Moisture equilibration states (a, b, and c) for the various samples subsequently
subjected to isothermal inactivation treatments. ........................................................................... 25
Figure 5: Instrumented almond. .................................................................................................... 27
Figure 6: Flow diagram for non-isothermal experiments. ............................................................ 29
Figure 7: Simulated profiles for temperature, dew point (Increasing and decreasing) and %MC.
....................................................................................................................................................... 37
Figure 8: Product condition at processing time. Adsorption 45% RH (◊), desorption 45% RH (○),
and adsorption 52% RH (□). The error bars represent the 95% confidence interval of the
measured aw and %MC. ................................................................................................................ 39
Figure 9: Thermal inactivation results. Log reductions (○), log-linear predicted inactivation (˗),
95% confidence interval (- -). A: Adsorption at 45 %RH, B: Desorption at 45 %RH, and C:
Adsorption at 52 %RH. ................................................................................................................. 41
Figure 10: Relationship of log(D80°C) with aw and %MC. ○ Almonds (Limcharoenchat, 2017), □
wheat flour (Smith, 2014), and ◊ dates (Buchholz et al., 2016), dotted lines (- -) are plotted for
reference only................................................................................................................................ 43
Figure 11: Dimensionless temperature profiles ............................................................................ 47
Figure 12: Examples of temperature profiles. A, high-velocity low-humidity (hV), B,
high-velocity high-humidity (HV), C, low-velocity low-humidity (hv), and D, low-velocity
high-humidity (Hv). ...................................................................................................................... 49
Figure 13: Moisture content histories. The letters corresponds to the process humidity (H = high
(30% Mv, h = low < 3% Mv), and the air velocity (V = high, v =low). ....................................... 49
Figure 14: Water activity histories. The letters corresponds to the process humidity (H = high
(30% Mv, h = low < 3% Mv), and the air velocity (V = high, v =low). ....................................... 50

x

Figure 15: Observed inactivation curves. Individual plots are coded as follow: process humidity
(H = high, h = low), for air velocity (V = high, v = low), 25 and 65 for %RH of equilibration
respectively. .................................................................................................................................. 53
Figure 16: SSC for the DLM model with decreasing (left) and increasing (right) dew point. ..... 55
Figure 17: Observed vs. fitted log CFU/g for the DLM model by %Mv, air velocity, and initial
water content in the product. (○) High level, (+) low level. ......................................................... 56
Figure 18: Observed vs. fitted log(N/N0) for the DLMV model by %Mv, air velocity, and initial
water content in the product. (○) High level, (+) low level. ......................................................... 58
Figure 19: Example almond surface temperature histories from the isothermal experiments. .... 71
Figure 20: Optimization contour plots for the DLM model. ........................................................ 82
Figure 21: SSC for the DLMV model........................................................................................... 84
Figure 22: SSC for DLMCM2V model. ....................................................................................... 85

xi

1

INTRODUCTION

Thermal inactivation of microorganisms is an important tool to ensure the microbial safety
of the food supply. In such processes, the interactions among the microorganism, product, and
process dictate the food safety outcome of the process. Sometimes, these interactions are ignored,
either by looking at a process with a “black box” approach (i.e., neglecting fundamental or firstprinciple interactions), or by underestimating the potential effects of complex (i.e., hard to measure
and/or highly variable) factors on the outcomes. New challenges in food processing, such as
process validation (U.S. Food and Drug Administration, 2014), and demands for natural or
minimally-processed products, are pushing the boundaries of what is known and what can be done
to fulfil the legal, commercial, and societal expectations to provide safe foods.
1.1

The Low-Moisture Food Safety Challenge
The inactivation of microorganisms, particularly pathogens, in low-moisture foods (LMF)

was not a major concern until recent years. These products (e.g., nut products, powdered milk,
chocolate, dried fruits, flour) were typically considered “safe” because microbial growth was
suppressed, and other deteriorative reactions (i.e., crystallization, desiccation, lipid oxidation, etc.)
were more relevant as indicators of quality loss and spoilage. Recently, evidence has been
accumulating showing that microorganisms, including pathogens (e.g., Salmonella, Listeria,
Cronobacter sakazakii), can survive in LMF, and eventually lead to illness when these products
are consumed (Beuchat et al., 2013; Lambertini, Danyluk, Schaffner, Winter, & Harris, 2012; Van
Doren, Neil, et al., 2013a).
Salmonella is the primary pathogen linked to LMF. Numerous salmonellosis outbreaks
(e.g., pistachios (CDC, 2016), nut butter (CDC, 2014)), and several recalls (e.g., nut products (U.S.
Food and Drug Administration, 2010a, 2010c), seeds, sunflower kernels, pepper (U.S. Food and
Drug Administration, 2010b)), are evidence of this emerging food safety challenge (Table 1). The
1

outbreaks impact both public health and economics. The economic impact of most recalls and
outbreaks is unknown; however, the economic impact, on business alone, of several earlier recalls
of LMF from 2007 and 2009 was estimated at US$133 and US$70 million respectively (Hussain
& Dawson, 2013).

Table 1: Salmonella recalls from January to April 1st 2017 related to LMF (U.S. Food and Drug
Administration, 2017).
Date
04/02/2017
03/20/2017

Product
Chili Kit
Dog Treat-Pig Ears

Company
Conagra Brands, Inc.
EuroCan Manufacturing

01/20/2017

CandyTrays

Nama Hy-Vee, Inc.

01/11/2017

Southwest Chipotle
Seasoning

Tupperwear U.S., Inc.

01/09/2017

Chocolate coated candy

Palmer Candy Company

01/04/2017

Cappuccino Snack Mix

Dutch Valley Food
Distributors, Inc.

Other Details
3 lots
1 lot
Products produced
between Oct. 20 and
Dec. 09, 2016.
Distributed nationwide.
1 lot
Distributed nationwide
Products produced
between October 20,
2016 and December 9,
2016
1 lot
Distributed in 22 states

Salmonella exhibits increased thermal resistance in LMF exposed to heat treatments (e.g.,
Archer, Jervis, Bird, & Gaze, 1998; Hsieh, Acott, Elizondo, & Labuza, 1975; Syamaladevi et al.,
2016), and can persist for months or years (Beuchat et al., 2013). Both of these characteristics
make Salmonella the primary microbial pathogen of concern in LMF processes.
Within the framework of the Food Safety Modernization Act (FSMA) Preventive Controls
Rules (U.S. Food and Drug Administration, 2014), processors of LMF are required to scientifically
validate, that their microbial reduction process will deliver the targeted reduction for the pathogen
of concern. Predictive microbiology tools are helpful in validating and analyzing the reliability of

2

such processes. However, reliable and robust models are needed that describe the process and
properly account for the relevant variables.
1.2

The Knowledge Gap
Water activity (aw) is a useful and common metric to account for the state of water in foods.

It is commonly used to predict and understand product shelf-life, stability (i.e., agglomeration,
compaction, etc. (G. F. GutiĂŠrrez-LĂłpez et al., 2015)), and, from the microbiology point of view,
the boundary for growth of microorganisms (i.e., 0.80 minimum for bacteria, 0.675 minimum for
yeast and molds (Lopez-Malo & Alzamora, 2015)). Some models describing the reduction of
Salmonella in LMF include process temperature, water in the product, and in some cases humidity
in the process (See Section 2.3.2.3). However, those that account for water in the product are,
almost exclusively, based on aw, and assume iso-moisture conditions (i.e., constant aw or moisture
content (%MC)) that do not reflect the true dynamic characteristics of some laboratory experiments
and most industrial processes. Also, aw is characterized by hysteresis between sorption states,
which is almost always ignored; however, in low-aw products, hysteresis can be up to 1% MC or
larger, and could have potential effects on the microbial inactivation response. Water activity is
also a function of temperature, meaning that the value measured at room temperature (i.e., the way
it is commonly measured) is different from the value at the actual process temperature, which is
usually higher (Syamaladevi, Tang, et al., 2016).
Thermal inactivation involves dynamic and coupled heat and mass transfer phenomena that
are rarely linked to bacterial reduction. Temperature is not only one of the driving forces of the
inactivation process (i.e., mainly through protein denaturation), but it also affects mass transfer
(i.e., mainly water removal), which potentially affects the heat resistance of bacteria (Garces-Vega
& Marks, 2015; Lievense, Verbeek, Noomen, & van’t Riet, 1994; Syamaladevi et al., 2015;
Valdramidis et al., 2005). Air velocity, which is most often ignored in thermal inactivation studies,
3

could play a critical role in thermal inactivation of pathogens in LMF since the air is carrying heat
to the product. Also, air velocity and humidity are relevant factors in the water dynamics between
the product and process, which impact inactivation by affecting the heat transfer, mass transfer,
and thermal resistance of microorganisms. The magnitude of the effect of air velocity on the
inactivation of pathogens remains unknown, or completely unreported.
Enhanced understanding of the role of water, and novel approaches to quantify process
humidity, air velocity, and product water effects are necessary to achieve accurate, reliable, and
more robust solutions for modeling microbial inactivation in LMF pasteurization systems, and to
fulfil the legal and commercial expectations to produce microbiologically safe foods.
1.3

Hypotheses
Considering the situation stated above; two working hypotheses were identified. (1) %MC

is an equivalent or better metric than aw to account for the effects of product water on thermal
inactivation of microorganisms in LMF; and (2) Air velocity has a significant effect on the
inactivation kinetics of microorganisms in LMF, beyond the expected heat transfer effects.
1.4

General Goal
To improve the understanding of the role of water in thermal inactivation of

microorganisms in LMF.
1.5

Specific Objectives
1. To evaluate the relationships of two water metrics (i.e., aw and %MC) with thermal
resistance of Salmonella on LMF.
2. To describe and quantify the interactive effects between product water (aw and/or
%MC), process humidity, and air velocity on the thermal resistance of Salmonella on
LMF.

4

3. To propose and evaluate a model to describe the effects of air velocity, aw, and/or
%MC on the thermal resistance of Salmonella on LMF.

5

2

LITERATURE REVIEW

Low-moisture food (LMF) is a category that clusters a wide range of products including
nuts, cereals, dried fruits, powders, and particulate products. Common characteristics include their
low %MC (i.e., usually < 30% db), and aw, depending of the criteria used, < 0.70 (Gurtler, Doyle,
& Kornacki, 2014) or < 0.85 (FAO & WHO, 2014). Salmonella species are recognized as the
major agents of foodborne illness associated with LMF. In the interest of public health, several
regulations have been developed to minimize the presence of Salmonella in the food supply. This
literature review highlights the connection between Salmonella and LMF, some of the current
practices and limitations of the metrics used to describe water status in this food category, and
finally describes the current state-of-the-art of predictive food microbiology for thermal
inactivation of Salmonella in LMF.
2.1

Salmonella in Low-Moisture Foods
Salmonella was not a major concern in LMF until it was associated with salmonellosis

outbreaks linked to these food category (Isaacs et al., 2005; Van Doren, Neil, et al., 2013b), and,
more recently, as it was recognized that low-moisture ingredients may play a significant role in
propagation of the pathogen (Beuchat et al., 2011; Y. Chen et al., 2009; Zweidel & Stephan, 2012).
The presence of Salmonella in LMF is highly variable and is sporadically found in nuts at low
levels (i.e., < 1 CFU/g (Danyluk et al., 2007; Danyluk, Harris, & Schaffner, 2006; Harris et al.,
2016; Lambertini et al., 2012; Young et al., 2015; Zhang et al., 2017)), while in spices Salmonella
has been found more frequently and at comparatively higher levels (i.e., > 2 CFU/g (Van Doren,
Neil, et al., 2013b; Van Doren, Kleinmeier, Hammack, & Westerman, 2013; Vij, Ailes, Wolyniak,
Angulo, & Klontz, 2006; Zweidel & Stephan, 2012)). Although the sources and routes of
contamination are not completely understood, environmental contamination (i.e., ground
contamination, bird and animal droppings), poor agricultural practices, and insufficient control
6

steps in the industry likely play a major role in the presence of this pathogen in the final product
(Al-Moghazy, Boveri, & Pulvirenti, 2014). Despite its low frequency and levels in nuts,
Salmonella has been associated with the risk of disease (Danyluk et al., 2006; Lambertini et al.,
2012; Young et al., 2015), and specific regulations have been implemented to reduce the incidence
of the pathogen (Agricultural Marketing Service USDA, 2007) in almonds and other nuts (U.S.
Food and Drug Administration Center for Food Safety and Applied Nutrition, 2011).
Salmonella exhibits increased resistance to heat in LMF (Archer et al., 1998; Beuchat et
al., 2011, 2013; Z. Chen et al., 2013; Harris, Uesugi, Abd, & McCarthy, 2012; Krapf &
Gantenbein-Demarchi, 2010; Laroche, Fine, & Gervais, 2005; Sumner, Sandros, Harmon, &
Bernard, 1991), surviving for several minutes at temperatures considered lethal within a few
seconds in high-moisture foods (e.g., 18 s in milk at 60°C (Pearce et al., 2012)). Earlier studies
conducted in liquid media, adjusting aw by concentration of sugars, showed a >100-fold increase
(i.e., from 0.29 to 40.2 min) in the resistance of Salmonella Typhimurium when the aw decreased
from 0.98 to 0.83 (Sumner et al., 1991). Experiments adjusting the aw with glycerol showed similar
results between 55°C and 60°C for multiple microorganisms (Hsieh et al., 1975). Also, inactivation
rates for Salmonella Anatum in pasta dough increased 5-fold at 60°C when the aw decreased from
0.92 to 0.80 (Hsieh, Acott, & Labuza, 1976). That study also reported that thermal resistance
peaked up at aw of 0.8, with small increments in the inactivation rate at aw between 0.8 and 0.6,
similar to what was reported by Hsieh et al., (1975). However, in these studies, the aw of the
products was towards the upper limit of low-aw products (i.e., aw > 0.7); nevertheless showed that
aw has a significant effect on the inactivation response.
Most recent studies done with LMF have shown similar trends, as well as some dependence
on the Salmonella strain (Ma et al., 2009; Mattick et al., 2001). For almond flour a ~3-fold increase

7

(i.e., from 3 to 8.8 min) in Salmonella thermal resistance from 0.95 to 0.60 aw has been reported
(Villa-Rojas et al., 2013). Also, low-moisture linked outbreak isolates have shown higher thermal
resistance. One strain isolated from a peanut butter outbreak showed 56% and 43% higher
resistance in contrast to a cocktail of other Salmonella strains and clinical isolates from sporadic
cases (Ma et al., 2009). The effect of product characteristics has also been reported. A ~4 min
difference (i.e., 12.2 min vs. 16.1 min) in Salmonella D-values at 93°C was observed between two
different almond cultivars; suggesting that other product characteristics can also play a significant
role in the thermal resistance of Salmonella on LMF (Lee et al., 2006).
Although increased thermal resistance of bacteria in LMF has been widely reported
(Archer et al., 1998; Laroche et al., 2005; Smith & Marks, 2015; Syamaladevi, Tang, et al., 2016),
the mechanisms of resistance are not yet well understood. Some evidence suggests that crossresistance due to osmotic stress, and selective gene expression in some of the pathogenicity islands
(Finn, Condell, McClure, AmĂŠzquita, & Fanning, 2013) could be the main drivers.
2.2

Water Metrics
Various water metrics have been used to account for water in a food product. The most

commonly used are water or moisture content (%MC), which relates the mass of water per mass
of dry matter (i.e., dry basis (db)) or the mass of water per total mass of product (i.e., wet basis),
and is usually presented as a percentage. The second metric is water activity (aw), which is defined
as the ratio of the water vapor pressure of the product at equilibrium over the vapor pressure of
pure water at the same temperature.
Water activity and %MC are closely related in a way that is characteristic for each product
or group of products. That relationship, the moisture isotherm, is typically determined from
simultaneous measurements of aw and %MC in equilibrium at the same temperature. Moisture
isotherms vary slightly between the adsorption (i.e., gaining water) and desorption (i.e., losing
8

water) states, generating hysteresis. In LMF, the differences between the two states can be as large
as 1 g of H2O / 100 g of dry product, and up to ~0.2 aw units (Al-Muhtaseb, McMinn, & Magee,
2002). This characteristic allows the existance of products with the same aw but different %MC,
and with the same %MC but different aw between isotherms. The isotherms have been described
with various models (e.g., Al-Muhtaseb, McMinn, & Magee, (2002)), including several accounting
for temperature (Staudt, Kechinski, et al., 2013; Staudt, Tessaro, Marczak, Soares, & Cardozo,
2013; Syamaladevi et al., 2015). However, the validity of these models is limited to lower
processing temperatures (i.e., < 80°C, and most often < 60°C) because of measuring limitations,
the iso-moisture assumption needed to perform the estimations (i.e., %MC of the product does not
change during heating), and uncertainty in the equilibrium of the product. Most LMF exhibits a
higher aw at elevated temperatures, however, some products exhibit the opposite behavior (e.g.,
peanut butter), likely because of changes in the structure at higher temperatures or other
physicochemical reactions (Syamaladevi, Tadapaneni, et al., 2016).
Detailed descriptions of the effect of temperature on aw can be found in Syamaladevi et al.,
(2015) and Syamaladevi, et al., (2016). In summary, it appears that there are significant productspecific temperature effects on aw; which may be critical for thermal inactivation of bacteria in
LMF. Specifically, the direction (i.e., whether aw increases or decreases with temperature) and
magnitude of the effect are highly variable among products. However, a w effects on thermal
inactivation of bacteria are typically tested by equilibrating samples to the same a w at room
temperature and then heating to the test temperature, which ignores the product-specific changes
in aw due to temperature. Additionally, there are no standard methods for conducting equilibration
tests to determine such isotherms at elevated temperatures, which can be complicated by changes
in the product and uncertainty of the equilibrium at higher temperatures.

9

From the processing point of view, there are some advantages and disadvantages regarding
the measurement and usefulness of %MC and aw. %MC is independent of temperature; whereas,
aw is temperature-dependent, and there are no reliable means to measure aw at high temperatures
(i.e., > 80°C). In contrast, there are tools capable of measuring %MC during processing, as well
as generally accepted models (e.g., Page’s equation drying curve (Kemp, 2011; Page, 1949)) that
can be used to accurately describe the change in %MC during processing as functions of time and
temperature. Other product characteristics have been correlated with aw (e.g., the boundary for
microbial growth, adhesivity, glass transition temperatures), which makes the final aw a commonly
used process control variable that remains important (G. F. GutiĂŠrrez-LĂłpez et al., 2015).
2.3

Predictive Inactivation Models
Predictive microbiology models describe the response of bacteria to processes and

environmental factors. Traditionally, models describing thermal inactivation of bacteria have
accounted for the effects of temperature during processing. The evolution of modeling capabilities
(i.e., mainly through software, data collection, and analysis, parameter estimation, etc.) allow the
inclusion of new variables and improved model performance, sensitivity, and robustness. This
section, covers the general characteristics of thermal inactivation models, criteria to evaluate
performance and selection of models, and some factors that may affect the inactivation process but
that are rarely considered.
2.3.1 Primary models
The models most commonly used to describe inactivation of microorganism are the loglinear (eqn [1]) and Weibull (eqn [2]) models. The log-linear model often is preferred because of
its simplicity and ease of use. It is the most common predictive inactivation model, and is widely
accepted for the design and control of processes in industry. The Weibull model may be preferred

10

because of its flexibility to account for nonlinearities (e.g., “shoulder” or “tailing”) in inactivation
curves,
𝐿𝑜𝑔(𝑁⁄𝑁0 ) = −𝑡⁄𝐷

[1]

where N/N0 is the survival ratio at time t, and D is the thermal resistance, represented as the decimal
reduction time at constant conditions (time units),
𝐿𝑜𝑔(𝑁⁄𝑁0 ) = −(𝑡⁄𝛿 )𝛽

[2]

where N/N0 is the survival ratio at time t, δ is the inactivation factor (time units), and β is the shape
factor (unitless).
The log-linear model (eqn [1]) has one parameter, the D-value, a measure of the dose of
treatment needed to reduce the population by 90%. For thermal treatments, it is the time necessary
to achieve a 90% reduction of the target organism at a constant temperature. The Weibull model
(eqn [2]) has two parameters: the inactivation factor (δ), which describes the inactivation rate
analogously to the D-value, and the shape factor (β), which describes the form of the inactivation
curve (i.e., β < 1 yields tailing; β = 1 yields a line, and β > 1 yields a shoulder). Therefore, the loglinear model can be considered a special case of the Weibull where β is equal to 1 and δ is equal
to the D-value. Both models are useful in predicting microbial inactivation when treatment
conditions remain constant or close to constant; when treatment conditions change during
processing (e.g., the temperature during heating or cooling), it is necessary to account for such
changes through secondary models.
2.3.2 Secondary models
Secondary models describe the primary model parameter relationships to intrinsic and
extrinsic factors. For example, the most common secondary model for thermal inactivation
processes is for temperature; which was developed nearly a century ago (Bigelow, 1921). Similar

11

approaches have been taken for other variables, such as pH and aw (Gaillard, Leguerinel, & Mafart,
1998), and process humidity (Jeong, Marks, & Orta-Ramirez, 2009), etc.
A traditional secondary model for D-value assumes a log-linear relationship with
temperature (eqn [3]), where ZT is the change in temperature necessary to change the D-value by
90%. Similar approaches can be used to describe δ and β in the Weibull model; however, additional
assumptions are commonly needed to minimize the interaction of the two primary parameters in
the response, and to isolate the effects of external factors.
𝐿𝑜𝑔(𝐷(𝑇)) = 𝑙𝑜𝑔(𝐷𝑟𝑒𝑓 ) −

(𝑇−𝑇𝑟𝑒𝑓 )
𝑍𝑇

[3]

Other approaches also have been tested successfully, such as response surface and
generalize linear model methodologies (Santillana Farakos, Frank, & Schaffner, 2013; Villa-Rojas
et al., 2013). However, these approaches are hard to generalize; and often fail to accurately predict
the microbial response under dynamic conditions; particularly, when considering interactions of
dynamic variables. Also, such models can be difficult to validate when the rates of change or other
dynamic conditions differ from those of the experiments, even within the experimental space,
because most are based on best-fit outputs of a specific data set.
The log-linear approach has some constraints or weakness when applied in LMF. Standard
reference conditions that correspond to Dref and Tref for LMF are neither established nor generally
accepted. In addition, the input of other variables, such as aw, air velocity, and %MC, on the
reference conditions and ultimately the inactivation response is poorly understood. Although this
constraint can be avoided during the model fitting process, selection of the reference conditions
and fitting procedures could affect the value and reliability of the estimated parameters (Datta,
1993; Dolan & Mishra, 2013; Dolan, Valdramidis, & Mishra, 2013; Halder, Datta, & Geedipalli,
2007).

12

2.3.2.1 Optimization of reference conditions.
A common approach to optimize the reference conditions is based on error minimization
considering the range of conditions in which the experiment is performed (Datta, 1993). When
multiple parameters are involved, similar results can be achieved minimizing the correlation of the
parameters in the variance-covariance matrix (Dolan & Mishra, 2013; Dolan et al., 2013). Caution
must be taken when using this approach when the reference conditions are related to multiple
process or product variables that are dynamic. In those cases, multivariate optimization should be
performed (Garces-Vega, Jeong, Dolan, & Marks, 2016); performing stepwise optimization is
likely to result in partial minimums, which can lead to a less accurate parameter estimation.
2.3.2.2 Are traditional parameters truly constant?
Also, considering some parameters to be constant can lead to inaccurate parameter
estimation. ZT is commonly assumed to be constant, which appears to be valid and generally
accepted in high aw products (e.g., meats, milk) (Perez-Rodriguez & Valero, 2013). Recent
evidence suggests that ZT varies as a function of aw in LMF (Garces-Vega & Marks, 2015) (Figure
1). However, these relationships have not been previously reported, even though the trends
reported in Figure 1 can be significant for some products.

13

70
60

ZT (°C)

50
40
30
20
10

0
0

0.2

0.4

0.6

0.8

1

aw
Figure 1: Effect of aw on ZT for wheat flour (×) (Smith, 2014), peanut butter (◊), and low-fat peanut
butter (□) (He et al., 2013). - - best-fit lines plotted for reference only.

The relationship of ZT with aw and ultimately water in the product can have potential
impacts on parameter estimation and model performance. This relationship is product-dependent,
affecting both the magnitude and the direction in which the parameter is changing (e.g., In
traditional peanut butter, ZT decreases as aw decreases, while in low-fat peanut butter ZT decreases
as aw increases). Also, if the range of water in the product (i.e., aw or %MC) during the process is
wide enough to yield “large” changes in ZT, but is assumed to be constant, a larger uncertainty
(i.e., larger confidence intervals) in the estimated parameter can be expected, resulting in decreased
model robustness and confidence in predicting of food safety outcomes.
2.3.2.3 Secondary models involving water
Overall, water appears to play a significant role in bacterial inactivation kinetics in LMF,
and multiple approaches have been taken to model this effect. Both Jeong et al. (2009) and Casulli
(2016) showed that the traditional Bigelow model accounting only for temperature effects (eqn

14

[4]), is not suitable to model dynamic processes at different process humidities, because of the
insensitivity of the model towards this variable and some humidity-linked bias. The significant
differences in D-values because of aw presented above (See section 2.1), already show that a model
without a term to account for water (i.e., aw, %MC, process humidity, etc.) is likely to be
insufficient for LMF.
𝑡

𝑙𝑜𝑔(𝑁⁄𝑁0 ) = − ∫0 𝑑𝑡⁄{𝐷𝑟𝑒𝑓 ∙ 10[(𝑇𝑟𝑒𝑓 −𝑇(𝑡))

⁄𝑍𝑇 ]

}

[4]

The effect of process humidity, measured as a dew point, on lethality was described by
Jeong et al., (2009) (eqn [14] in section 3.4.5.1), showing a significant effect on the inactivation
response. The model accounted for process humidity, phenomenologically accounting for the
effect of condensing or evaporating water. However, that model assumed that condensation does
not affect the %MC of the product (i.e., no accumulation of water on the surface), which under
certain process condition may not be true (See Section 5.3). That model has been used successfully
to describe other inactivation responses for Salmonella and Enterococcus faecium in almonds and
pistachios (Casulli, 2016; Jeong et al., 2009; Jeong, Marks, & Ryser, 2011).
The effect of aw on Salmonella thermal inactivation in whey protein was described using a
Weibull primary model (Santillana Farakos et al., 2013). The secondary models for the δ and β
were proposed based on log-linear relationships of the parameters with temperature and aw.
Validation of their results was good for δ (i.e., R=0.97), but poor for β (i.e, R=0.03). Validation
based on other low-fat LMF data was also good (i.e., R=0.94), but exhibited a tendency to
under-predict inactivation.
Water activity remains the most common metric used to describe the effect of water in
food. Smith, Hildebrandt, Casulli, Dolan, & Marks, (2016) tried different inactivation model forms
to describe the inactivation of Salmonella in wheat flour, including a new model combining the

15

effect of temperature and aw. In those experiments, a modified version of the log-linear type model
proposed by Gaillard et al. (1998), disregarding the effect of pH, yielded the best fit and
performance. Villa-Rojas et al., (2013) tested a second-order polynomial model for temperature
and aw, for both log-linear and Weibull primary models, reporting good performance of the model.
However, the experiments were performed with product at high aw (i.e., > 0.70), which makes the
model uncertain/impractical for the aw of interest in LMF.
Recently other relationships between water in the product and inactivation parameters in
the secondary model have been explored. Garces-Vega & Marks (2015) showed a discontinuity in
plots of ZT vs. aw (Figure 2), suggesting that the discontinuity could be related to differences in the
inactivation kinetics when samples were processed after following adsorption or desorption paths.
The argument for that hypothesis is that discontinuity was observed around the native aw state of
the product; the trends (i.e., although based on only two points) above and below the native aw
appear to be different. Garces-Vega & Marks (2016) also showed a stronger correlation between
D-values and %MC than between D-value and aw across different LMF. Although these results
showed poor correlation for some products (i.e., ≪ 0.80), %MC generally had a better correlation
than aw (See Section 4.3). A model for inactivation of Salmonella in pistachios considering %MC
as a parameter following the similar log-linear relationships as those of Bigelow (1921) and Jeong
et al., (2009) was proposed recently (Casulli, 2016), showing that %MC was significant and
improved model performance. Therefore, it is necessary to better understand the effects of sorption
states and water in the product, by either aw or %MC, on the inactivation response of Salmonella
in LMF.

16

A
70

Regular fat

ZT (°C)

60
50
40
Low fat

30
0.1

0.3

0.5
aw

0.7

0.9

0.5
aw

0.7

0.9

B
30

ZT(°C)

25
20
15
10
0.1

0.3

Figure 2: Example of the discontinuity of ZT vs. aw. A) low-fat peanut butter (Garces-Vega &
Marks, 2015), data from He et al., (2013) B) wheat flour (Garces-Vega & Marks, 2015), data from
(Smith, 2014) . - - best-fit lines and shadow zones showed as reference only.
Other survival models for yeasts and lactic acid bacteria also have examined moisture
effects. In such approaches, the objective function is to maximize the survival and activity of the
microorganism of interest. In one example by Verbeek, Taekema, Meerdink, & van’t Riet, (1992),
an inactivation model consisting of two components, one for the temperature effect and one for a
desiccation effect, was proposed. The model was based on bacterial activity (i.e., acidification of

17

media from fermentation of sugars) rather than on bacterial population, which was a reasonable
approach for that kind of application but is not convenient from the food safety point of view.
However, they proposed and justified that %MC instead of aw was the critical variable affecting
inactivation during drying. Their approach was based on the temperature dependence of a w, not
the effect of aw on inactivation; they argued that aw was not the critical variable because bacterial
activity is not affected as aw is reduced by a reduction of temperature (the opposite effect of when
temperature is increased). However, their experiments at non-lethal temperature, which yielded a
reduction of bacterial activity, strongly support the idea that %MC has a significant effect on
bacterial inactivation.
2.3.3 Model performance and selection
The performance of a model is commonly understood as how accurately it describes the
experimental data. A common reported metric for model accuracy is the root mean square error
(RMSE). Although useful, this metric just gives a general idea of model performance, ignoring
trends in the accuracy of the predictions or clusters of data moving away from or getting closer to
the predicted values. Residual analysis, which is not commonly reported, can provide additional
information on the performance of models, allowing for the identification of areas of concern,
trends, outliers, and the potential effect of variables not included in the model, but known from the
experiments.
Metrics of performance based on the residuals of the predictions (i.e. bias factor, accuracy
factor, acceptable prediction zone) are also useful (Baranyi, Pin, & Ross, 1999; Oscar, 2005; Ross,
1996). However, they are rarely reported when evaluating models based on dynamic inactivation
data (i.e., models in which multiple variables are changing independently). Bias and accuracy
factor were developed to analyze the accuracy of the estimated parameters based on reported or
known parameter, not on individual points (Ross, 1996). However, the technique and meaning of
18

the metric have been used to evaluate model performance based on differences between the
observed and predicted values (Oscar, 2005). Interpretation of the results using these techniques
must be done carefully; identification of fail-dangerous and fail-safe prediction zones are subject
to how the data are analyzed (Ross, Dalgaard, & Tienungoon, 2000). Available criteria and
generally accepted values to describe a model output as fail-safe or fail-dangerous are based on
growth models. Extrapolation of such metrics to inactivation models implies additional challenges,
because of the nature of inactivation processes and the inherent risk associated with pathogens and
process validation.
Model selection processes and criteria are rarely reported in the inactivation literature.
Before-the-fact selection of a model is feasible both empirically and technically. Empirical
approaches are generally based on the shape of the response (i.e., linear or non-linear), and
realistically on the preference and capabilities of the individual performing the analysis. Technical
model selection can be done using multiple mathematical and statistical tools, including scaled
sensitivity coefficients and Fisher matrices (Bernaerts, Versyck, & Van Impe, 2000; Dolan et al.,
2013; Gil, Miller, Silva, & BrandĂŁo, 2014). However, these tools assume that the model being
tested is fundamentally correct, which is not always true. Consequently previous knowledge of the
parameters and variables involved in the model are needed with such information not always
available.
After-the-fact selection of a model is more commonly done, although still rarely reported.
Commonly, model selection involves both empirical and technical approaches, which may include
(in addition to the above-mentioned criteria) the coefficient of determination (R2), the correlation
matrix (i.e., variance-covariance matrix), the Akaike criteria of information (i.e., AIC, AICc for
small data sets), and other bias or accuracy metrics. R2 is the most commonly reported selection

19

criteria after RMSE, but R2 can provide deceiving information. As the number of parameters in
the model increases, R2 is likely to increase (while RMSE inherently decreases), making the model
appear “better”, without a cost-benefit analysis for the inclusion of additional parameters. AIC
compensates for this by “penalizing” the model for the increased number of parameters; more
likely models have smaller AIC values (indicating a “more likely correct” model).
Uncertainty measurements of the estimated parameters are also important in selecting a
model. Relative errors of the parameters (i.e. standard error of the parameter / estimated parameter
× 100), and confidence intervals of the estimate (i.e., 95% commonly used), provide evidence of
the validity of the estimated parameters (e.g., D-value ≠ 0, inactivation rate ≠ 0, β in the Weibull
model ≠ 1) and help to understand how much uncertainty in a model is affected by a given variable.
2.4

Summary
The independent topics of interest in this project (i.e., moisture sorption behaviors in LMF,

Salmonella thermal inactivation, predictive microbiology) are generally well understood.
However, their interactions, and particularly those interactions that affect the inactivation of
bacteria in LMF, remain relatively unexplored. Various efforts are underway among several peer
institutions to understand the influence of product characteristics and initial aw on bacterial
inactivation in LMF. However, the interactions of such factors with the process is incipient and
critical to real-world validation of pathogen reduction processes in the LMF industry.
The role of water and how to properly measure it in thermal inactivation applications is at
least questionable. There is no evidence yet quantifying the potential effect of sorption hysteresis
on the inactivation response of bacteria in/on LMF. If there is an effect that can be linked to either
aw or %MC, that metric should be considered as critical for describing the inactivation response
and used for generalized modeling purposes.

20

The effect of process parameters on inactivation of pathogens also remains highly under
reported, and extrapolation of the inactivation responses from nonpathogenic bacteria (i.e., lactic
acid bacteria) is in the best-case scenario unpractical. The effects of process moisture, drying
kinetics, and air velocity (and their interactions) on bacterial thermal inactivation are scarcely
known, and have yet to be quantitatively tested, reported, and modeled (likely because of the
difficulties involved in the isolation of these effects). However, these factors are critically
important in commercial-scale applications, and therefore to efforts needed to validate the efficacy
of such processes for pathogen reductions.

21

3

MATERIALS AND METHODS

This overall project consisted of two series of thermal inactivation experiments, one under
isothermal conditions (Study 1) and one under non-isothermal conditions (Study 2). The product,
the bacteria, and part of the inoculation procedure were the same for the two experiments. The
equilibration, heat treatments, and enumeration of surviving bacteria are described in detail for
each experiment. After enumerating the surviving bacteria, the inactivation responses were
described using thermal inactivation models, and the inactivation model parameters were
compared to elucidate the effect of product and process characteristics on microbial inactivation.
3.1

Product
Almonds (Nonpareil; industry size specification, 27 / 30; propylene oxide (PPO) treated)

were obtained from a commercial source (Select Harvest, Turlock, CA) and stored refrigerated
(~4°C) until use. Preliminary screening confirmed absence of quantifiable Salmonella in the
product (< 1 Log CFU/g).
3.2

Bacteria and Inoculum Preparation
Salmonella Enteritidis Phage Type 30 (Salmonella PT30) was used in this study.

Independent inoculums for each replicate (three for each study) were prepared. The Salmonella
culture was obtained from Dr. Linda Harris at the University of California Davis and stored
at -80°C in tryptic soy broth (Difco, BD, Franklin Lakes, NJ), containing 0.6% (wt/vol) yeast
extract (Difco, BD) and 20% glycerol until use. Salmonella PT30, was previously isolated from
almonds (Danyluk et al., 2007) linked to salmonellosis outbreaks (Isaacs et al., 2005), and used in
different studies related to inactivation and survival of Salmonella in low-moisture products (e.g.,
Abd, McCarthy, & Harris, 2012; Danyluk, Uesugi, & Harris, 2005; Izurieta & Komitopoulou,
2012; Jeong, Marks, & Orta-Ramirez, 2009; Jeong, Marks, & Ryser, 2011; Uesugi, Danyluk, &

22

Harris, 2006). Therefore, Salmonella PT30 is considered a reference strain for thermal inactivation
of Salmonella in LMF.
In general, the inoculation procedures of Danyluk et al.,(2005) were followed with minor
modifications. An aliquot (~0.1 ml) of the frozen culture was transferred to 9 ml of tryptic soy
broth (Difco, BD), containing 0.6% (wt/vol) yeast extract (Difco, BD) (TSB-YE), and incubated
at 37°C for ~24 h. Thereafter, 0.1 ml of the culture was transferred to another 9 ml of TSB-YE,
and incubated for another ~24 h at 37°C. After incubation, 1 ml of culture was streaked into 150
mm Ø by 15 mm plates of tryptic soy agar (Difco, BD) containing 0.6% (wt/vol) yeast extract
(Difco, BD) (TSA-YE), and incubated for ~24 h at 37°C. The resulting lawn plates were harvested
with two successive washes of 10 ml of 0.1% peptone water (Difco, BD) to generate the inoculum.
The inoculum was harvested from two lawn plates for each inoculation; the first plate was washed
the first time (10 ml peptone water) and the cell suspension collected; then washed for a second
time and the suspension cell recovered (~9 ml), then used as the first wash for the second plate and
the cell suspension collected; finally, the second plate was washed for a second time (10 ml of
peptone water) and the suspension cell collected (~9 ml).
3.3

Isothermal Experiments (Study 1)
In these experiments, the characteristic hysteresis of the sorption isotherms was used to

isolate the effects of aw and %MC on the thermal inactivation of Salmonella in almonds. The
general workflow is shown in Figure 3.

23

Figure 3: Flow diagram for isothermal experiment.
3.3.1 Inoculation
The inoculum (25 ml of the ~28 ml from 2 plates) was pelleted by centrifugation for 15
min at 5000 RPM (2996 × g RCF) (Sorvall RC 5B plus, rotor Sorvall SM-24, Waltham, MA), and
then re-suspended in 5 ml of 0.1% peptone water. The almonds and the Salmonella suspension
were mixed at a ratio of 5 ml / 200 g, shaken, and hand-massaged for 2 min to uniformly inoculate
the almonds. Thereafter the almonds were placed on trays containing a sheet of filter paper (Filter
paper Cat No. 09-802-18, Fisher Scientific, Pittsburgh, PA) in a single layer and let dry overnight
(14-15 h) in a biosafety hood. This procedure yielded inoculation levels of ~7.6 log CFU/g, on
samples that had 3.6% MC and 0.36 aw.
3.3.2 Equilibration
Sorption hysteresis was exploited to yield samples at three equilibration points that formed
two comparison pairs as follows: two groups of samples at the same aw but different %MC (a and

24

b in Figure 4), and two groups of samples with the same %MC but different aw (b and c in Figure

%MC (g H2O / 1 g Dry)

4).

Desorption
curve
b
c

d

Adsorption
curve

a
Initial
State
aw

Figure 4: Moisture equilibration states (a, b, and c) for the various samples subsequently subjected
to isothermal inactivation treatments.

To achieve these three different states, the inoculated product was placed in equilibration
chambers set at a target relative humidity. The equilibration system consisted of chambers (69 ×
51 × 51 cm) and a custom control system, comprised of relative humidity sensors inside each
equilibration chamber, a desiccation column, a hydration column, solenoid valves, air pumps, and
a computer-based control system that maintains the chamber relative humidity within Âą2% (Smith,
2014; Smith & Marks, 2015). Also, an electronic scale was placed inside each chamber, and the
weight of a 5-almond sample (~6 g) for each replicate was monitored during the process.
The inoculated samples were divided into two equilibration chambers set at 45% RH and
65% RH, respectively. After reaching equilibrium in ~10 days (i.e., change in weight during 3
days was < 0.1%) in an adsorption path (a in Figure 4), the samples in the 45% RH chamber were

25

treated as explained in the isothermal treatment section below. After reaching equilibrium in the
chamber set at 65% (d in Figure 4), the chamber %RH was adjusted down to 45%, and the samples
were allowed to equilibrate following a desorption path, after which equilibrium was reached in
~20 days (b in Figure 4); samples then were thermally treated as explained below. After treating
sub-samples at 45% RH (a), the chamber was adjusted to ~52% RH, and the remaining sample
was allowed to equilibrate, with the target %MC being the same as the sample that followed the
desorption path (b in Figure 4), but following an adsorption path in this case (c). After reaching
equilibrium (c in Figure 4), the samples were thermally treated as described below.
3.3.3 Isothermal treatment
Each thermal treatment consisted of seven samples of three inoculated and equilibrated
almonds each (~3.5 g), which were bagged in 4 oz bags (7.5 × 18.5 cm, 0.057 mm thick,
Whirl-PakÂŽ, Fort Atkinson, WI), vacuum sealed (VacMasterÂŽ, Overland Park, KS), and treated in
a water bath (NesLab, Waltham, MA) at 80°C for up to 60 min. One additional sample was
prepared, in which one almond was instrumented with a thin-wire type T thermocouple (Omega
Engineering, Inc. Stamford, CN); placing the tip of the thermocouple just under the skin of the
almond and securing it in place with a zip-tie (Figure 5) before placing the almond in a
vacuum-sealed bag. Temperature was logged using a hand-held data logger (Omega RDXL4SD)
at a frequency of 0.5 Hz. After the instrumented sample reached the process temperature (~80°C
¹ 1°C), the time zero sample was removed and immediately cooled by immersing the bag in an
ice-water bath. The remaining samples were individually retrieved from the hot water bath every
10 min and cooled thereafter.

26

Figure 5: Instrumented almond.

Initial and final aw and %MC were determined for three almonds. Water activity was
measured in a dew point water activity meter (Model 4TE AquaLab, WA). Moisture content was
determined following a gravimetric method (United Nations, 1991; USDA-FSIS, 2009), based on
the difference in weight between the wet and dry product after drying at 102°C for 18-24 h (DX400
Drying Oven, Yamato, Santa Clara, CA).
3.3.4 Enumeration of survivors
The treated and cooled almonds were aseptically removed from the treatment bags into
filter bags (7 oz, 9.5 × 18 cm, 0.076 mm thick, Whirl-Pak®) prefilled with peptone water (5 ml),
stomached for 3 min (Neutec™, Farmingdale, NY), and serially diluted 1:10 in 0.1% peptone
water. Appropriate dilutions were plated on tryptic soy agar (Difco, BD) supplemented with 0.6%
(wt/vol) yeast extract, 0.05% ammonium ferric citrate (Sigma-Aldrich, St. Louis, MO) and 0.03%
sodium thiosulfate (Sigma-Aldrich) (mTSA), and incubated at 37°C for 24h. The resulting
characteristic black center colonies (2-4 mm Ø) were counted, and the data were processed to
calculate the log CFU/g. For quality purposes, dilutions with fewer than 4 colonies (average of 2

27

plates) or plates with more than 250 colonies were not considered in the calculations (Garces-Vega
& Marks, 2014; Sutton, 2011).
3.3.5 Data analysis
3.3.5.1 Model fitting and comparison
The resulting inactivation curves depicting log N vs. time were fitted to the traditional
log-linear model (LLM) (Bigelow & Esty, 1920) (eqn [5]), and the Weibull model (Corradini &
Peleg, 2004) (eqn [6]), by ordinary least squares methodology using the fitnlm algorithm of
MatLabÂŽ (2016a),
𝑡

𝑙𝑜𝑔 (𝑁) = 𝑙𝑜𝑔(𝑁0 ) − 𝐷

[5]

where N is the population at time t; N0 is the population at time 0; and D is the decimal reduction
time.
𝑡 𝛽

𝑙𝑜𝑔(𝑁) = 𝑙𝑜𝑔(𝑁0 ) − (𝛿)

[6]

where N is the population at time t; N0 is the population at time 0; δ is the inactivation parameter;
and β is the shape parameter.
Model performance (goodness-of-fit) was evaluated based on root mean squared error
(RMSE), the 95% confidence intervals of the estimated parameters and their relative errors, and
analysis of residuals. Effect of the treatments on the inactivation response was assessed by an
analysis of covariance of the slopes of the log N vs. time lines.
3.3.5.2 Analysis of other secondary data sets
To further explore the potential relationship between aw and %MC with D-values, a search
was performed for Salmonella thermal inactivation data in LMF (at 80°C), with reported aw and
%MC, or sufficient information to estimate their values with moisture isotherms. Three suitable

28

data sets were acquired: almonds (Limcharoenchat, 2017), dates (Buchholz et al., 2016), and wheat
flour (Smith, 2014).
These data sets were used to fit the log-linear model (eqn [1]); to calculate the D-values.
The logarithm of the D-values vs aw and %MC was plotted. Visual analysis of the resulting trends
was performed, and the correlation coefficients of logD with aw and %MC for each product were
computed.
3.4

Non-Isothermal Experiments (Study 2)
In these experiments, the effects of process conditions (air velocity, process humidity, and

product %MC) on thermal inactivation of Salmonella on almonds under non-isothermal conditions
were studied in a pilot-scale impingement oven. The general workflow of the process is shown in
Figure 6.

Figure 6: Flow diagram for non-isothermal experiments.

29

3.4.1 Inoculation
The inoculum (25 ml) was hand-mixed with 400 g of almonds, which were then spread
over filtered paper (Filter paper Cat No. 09-802-18, Fisher Scientific) on trays, and let dry
overnight at room temperature in a biosafety hood. This procedure yielded inoculation levels of
~8 log CFU/g, and samples that were at ~ 0.40 aw.
3.4.2 Equilibration
To obtain samples at two representative aw conditions, the equilibration chambers were set
at target relative humidities of 25 and 65% RH. Samples were placed in the chambers on perforated
trays in a single layer and allowed to equilibrate. Equilibrium was evaluated in terms of aw and
weight stability. Product was in equilibrium when the change in weight during three days was less
than 0.1%. Water activity was measured and recorded but not used as the equilibrium criterion due
to observed higher instability and known dependence on temperature. Equilibrium was achieved
in ~7-10 days at 2.81 Âą 0.20% MC and aw 0.378 Âą 0.055, and 6.15 Âą 0.74% MC and aw 0.647 Âą
0.011 respectively. Samples were used within three days after equilibrium was reached.
3.4.3 Thermal treatment
3.4.3.1 Air velocity estimation
Direct measurements of air velocity in the oven were not feasible/reliable with the actual
configuration of the equipment and experimental conditions. An alternative approximation based
on heat transfer was used to estimate air velocities in the system. In general, a lumped parameter
approximation (Datta, 2002), approach was used (i.e., Biot number ranged from 0.0005 to
0.00021), the temperature profiles of an aluminum almond for five oven air velocity set-ups were
generated using dry air (i.e. < 3% Mv) at 121°C; temperature was recorded as described in section
3.4.3.2, in this case the thermocouple inserted in the center of the almond (i.e., between 50 and
148 data points per profile). The heat transfer convection coefficient h (eqn [7]) was estimated,

30

and air velocity calculations were done using the Nusselt and Reynolds number correlations (eqns
[8] to [12]) (Datta, 2002),
ℎ=

−𝑚∗𝐶𝑝∗∆(𝑇 ⁄𝑡)

[7]

𝐴

𝐷𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑙𝑒𝑠 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 = 𝐿𝑛((𝑇(𝑡) − 𝑇∞)/(𝑇𝑖 − 𝑇∞))

[8]

𝑁𝑢= −ℎ ∙ 𝑚 ∙ 𝐶𝑝⁄𝑘

[9]

𝑁𝑢𝐷 = 2 + (0.4 ∙ 𝑅𝑒 1⁄2 + 0.06 ∙ 𝑅𝑒 2⁄3 ) ∙ 𝑃𝑟 0.4

[10]

𝑁𝑢

𝑅𝑒 = (0.664∙𝑃𝑟1⁄3 )
𝑉=

2

[11]

𝑅𝑒∙𝜐

(𝑎∙𝑏)1.6 +(𝑎∙𝑐)1.6 +(𝑏∙𝑐)1.6

𝐴≈4∙𝜋∙(

[12]

𝐶𝐷

3

1⁄
1.6

)

[13]

where Cp is the heat capacity, m is the mass of the object, Δ (T/t) is the slope of the line
dimensionless temperature vs t, A is the surface area of the object (i.e., ellipsoid eqn [13]), a,b,and
c are radius of the ellipsoid, T(t) is the temperature at time t, Ti is the initial temperature, T∞ is the
temperature at equilibrium (i.e., air temperature), and CD was the characteristic dimension (i.e.,
0.0064 m, the thickness diameter).
The characteristics of the almond are reported in Table 2. Temperature was recorded as
described in Section 3.4.3 above, and transformed in the dimensionless form (eqn [8]), for each
set-up condition. The final experimental set-up was selected based on previous experiments, to
achieve a ratio of at least a 1.5 between the two different h values.

31

Table 2: Characteristics of the aluminum almond.
Characteristic
Density (kg/m3)
Specific heat Cp (kJ/kg×K)
Thermal Conductivity k
(W/(m×K)) at 121°C, interpolated
Mass (kg)
Length (m)
Thickness (m)
Width (m)

Value
2700
0.91
222
0.0025
2.12×10-2
6.38×10-3
1.13×10-2

Reference
(ToolBox, 2016a)
(ToolBox, 2016b)
(ToolBox, 2016b)
Measured
(Aydin, 2003)
(Aydin, 2003)
(Aydin, 2003)

3.4.3.2 Heat treatment and experimental design
The heat treatments were performed in a custom-built, computer-controlled,
laboratory-scale, moist-air convection oven (Jeong et al., 2009). Almonds (~10 g, 13 almonds)
from each equilibration condition were removed from the equilibration chambers, immediately
spread on wire trays and placed in the oven treatment chamber. For the oven, air temperature and
dew point (DMP246, Vaisala, Woburn, MA) (as a measure of process humidity) were recorded
for each treatment.
To monitor the surface temperature of the almonds, one almond was instrumented with a
thin-wire type T thermocouple (Omega Engineering, Inc. Stamford, CN) as described in Section
3.3.3, and the temperature was logged using a hand-held data logger (Omega RDXL4SD) at a
frequency of 0.5 Hz. After each processing time, aw and %MC were measured using three almonds
as described in Section 3.3.3 above.
Eight treatments were performed in triplicate (Table 3). Samples with different initial aw
values were treated in the oven simultaneously on two different racks to reduce variability among
processes, and to minimize the length of the experiments. Casulli (2016) failed to see a significant
effect when treating pistachios with this configuration, and preliminary trials with almonds
indicated that the effect of tray location was negligible. Treatment times were estimated based on
32

the previous work of Jeong et al. (2009). Low-humidity processes were carried out for 60 min,
sampling product every 10 min; high-humidity processes were carried out for 6 min, sampling
product every minute.
3.4.4 Enumeration of survivors
Immediately after thermal processing the almonds (~8 g) were aseptically transferred to
filter bags (7 oz, 9.5 × 18 cm, 0.076 mm thick, Whirl-Pak®) prefilled with chilled peptone water
(10 ml) to stop the bacterial inactivation, and refrigerated at 4°C until final processing (< 4 h). For
final processing, samples were stomached for 3 min (Neutec™) and serially diluted 1:10 in 0.1%
peptone water. Appropriate dilutions were plated as previously described in section 3.3.4.

Table 3: Non-isothermal treatments experimental design.
Treatment

Air Temperature

A
B
C
D
E
F
G
H

121°C
121°C
121°C
121°C
121°C
121°C
121°C
121°C

Process
Humidity
(% Mv)
30
30
30
30
<3
<3
<3
<3

Air Velocity

Initial
aw @ 25°C

low
high
low
high
low
high
low
high

0.65
0.65
0.45
0.45
0.65
0.65
0.45
0.45

3.4.5 Model parameter estimation and evaluation
3.4.5.1 Models and model fitting
Number of survivor were transformed into the logarithmic form and normalized based on
the initial population of each replicate and experimental condition (i.e., the population of untreated
samples enumerated on the day of testing). The resulting inactivation curves were used to fit the

33

Bigelow-type models presented below. The models were fitted using ordinary least squares (OLS)
methodologies with the fitnlm algorithm of MatLabÂŽ; the numerical integration was performed
using the trapezoidal method, with the trapz function of MatLabÂŽ.
𝑡

𝑁

𝑙𝑜𝑔 (𝑁 ) = − ∫0 (
0

𝑑𝑡
{[𝑇𝑟𝑒𝑓 −𝑇𝑠 (𝑡)]⁄𝑍𝑇 }+{[(𝑇𝑑,𝑟𝑒𝑓 −𝑇𝑑 )−(𝑇𝑟𝑒𝑓 −𝑇𝑠 (𝑡))]⁄𝑍𝑀 }

𝑡

𝑁

𝑙𝑜𝑔 (𝑁 ) = − ∫0 (
0

{[𝑇𝑟𝑒𝑓 −𝑇𝑠 (𝑡)]⁄𝑍𝑇 }+{[(𝑇𝑑,𝑟𝑒𝑓 −𝑇𝑑 )−(𝑇𝑟𝑒𝑓 −𝑇𝑠 (𝑡))]⁄𝑍𝑀 }+((%𝑀𝐶𝑟𝑒𝑓 −%𝑀𝐶)⁄𝑍𝑀𝐶 )

0

𝑑𝑡

𝑡

0

𝑑𝑡
{[𝑇𝑟𝑒𝑓 −𝑇𝑠 (𝑡)]⁄(𝑍𝑀𝐶 × 2√1−%𝑀𝐶(𝑡))}+{[(𝑇𝑑,𝑟𝑒𝑓 −𝑇𝑑 )−(𝑇𝑟𝑒𝑓 −𝑇𝑠 (𝑡))]⁄𝑍𝑀 }

[16]

)

[17]

𝐷𝑟𝑒𝑓 ∗10

(1−𝛾𝑉 ×𝑉)∙𝑑𝑡

𝑡

𝑁

𝑙𝑜𝑔 (𝑁 ) = − ∫0 (
0

{[𝑇𝑟𝑒𝑓 −𝑇𝑠 (𝑡)]⁄𝑍𝑇 }+{[(𝑇𝑑,𝑟𝑒𝑓 −𝑇𝑑 )−(𝑇𝑟𝑒𝑓 −𝑇𝑠 (𝑡))]⁄𝑍𝑀 }

)

[18]

𝐷𝑟𝑒𝑓 ∗10

(1−𝛾𝑉 ×𝑉)∙𝑑𝑡

𝑡

𝑙𝑜𝑔 (𝑁 ) = − ∫0 (
0

)

{[𝑇𝑟𝑒𝑓 −𝑇𝑠 (𝑡)]⁄(𝑍𝑇0 −𝑍𝑀𝐶 ×%𝑀𝐶(𝑡))}+{[(𝑇𝑑,𝑟𝑒𝑓 −𝑇𝑑 )−(𝑇𝑟𝑒𝑓 −𝑇𝑠 (𝑡))]⁄𝑍𝑀 }

𝐷𝑟𝑒𝑓 ∗10

𝑙𝑜𝑔 (𝑁 ) = − ∫0 (

𝑁

) [15]

𝐷𝑟𝑒𝑓 ∗10

𝑙𝑜𝑔 (𝑁 ) = − ∫0 (

𝑁

[14]

dt

𝑡

𝑁

)

𝐷𝑟𝑒𝑓 ∗10

{[𝑇𝑟𝑒𝑓 −𝑇𝑠 (𝑡)]⁄(𝑍𝑀𝐶 × 2√1−%𝑀𝐶(𝑡))}+{[(𝑇𝑑,𝑟𝑒𝑓 −𝑇𝑑 )−(𝑇𝑟𝑒𝑓 −𝑇𝑠 (𝑡))]⁄𝑍𝑀 }

)

[19]

𝐷𝑟𝑒𝑓 ∗10

In all of the above models, log(N/N0) is the normalized population at time t; Dref is the Dvalue at the reference condition; Tref is the reference temperature; Td,ref is the dew point reference;
%MCref is the moisture content reference; Td is the measured dew point, Ts(t) is the product surface
temperature at time t, %MC(t) is the moisture content a time t; V is the categorical variable for air
velocity (i.e., 1 high air velocity, 0 low air velocity); and ZT, ZM, ZMC, ZT0, and ÎłV are model
parameters.
The models were coded for identification purposes. Table 4 shows the code corresponding
to each model, the parameters to be estimated, and the reference for each model

34

Table 4: Models acronyms and parameters to be estimated for each of the models.
Equation
13
14
15
16
17
18

Model code
DLM
DLMC
DLMCM
DLMCM2
DLMV
DLMCM2V

Parameters Estimated
ZT, ZM
ZT, ZM, ZMC
ZT, ZM, ZT0, ZMC
ZT, ZM, ZMC
ZT, ZM, ÎłV
ZT, ZM, ZMC, ÎłV

Reference
(Jeong et al., 2009)
(Casulli, 2016)
New/Proposed
New/Proposed
New/Proposed
New/Proposed

3.4.5.2 Input data
Some of the input variables for the models were treated differently than in previous work
of Jeong et al., (2009) and Casulli, (2016). In this study, the dew point (Td) was estimated as the
average of the recorded dew point (i.e. recorded every 10 s) during the whole series of experiments
for each experimental condition (n ~ 1500 for low humidity processes, n ~ 380 for high humidity
processes). Also, oven temperature was recorded for quality purposes and was confirmed to be
within 121 ¹ 2°C during the experiments.
The %MC was recorded at a different rate than the surface temperature (See Section 3.4.3).
To perform the numerical integration necessary to fit the models with the parameter ZMC, a linear
interpolation of the average %MC of the three replicates was performed to fill the gaps. Although,
fitting a drying model to the %MC vs t data (Casulli, 2016) was considered; the observed behavior
(See Section 5.3) of %MC lead to the interpolation approach as more feasible.
Reference conditions (i.e., Tref, Td,ref, and %MCref) were initially extracted from previous
work (Casulli, 2016; Jeong et al., 2009). To minimize the correlation among parameters, Tref and
Td,ref were optimized using a multivariate optimization based on the DLM model and used in the
parameter estimation for all other models. Visual and numerical evaluation of the minimized
variance-covariance entries were done to select the final Tref (80°C) and Td,ref (55°C). %MCref (i.e.,

35

1 g H2O/g dry) was not optimized because of the performance of the DLMC model; however, the
different values or %MCref that were tested yielded similar model performance.
3.4.5.3 Model performance and selection
Performance of the model was evaluated based on root mean squared error (RMSE), and
analysis of residuals. Also, the 95% confidence intervals of the estimated parameters, and their
relative errors were considered, and the scaled sensitivity coefficients (SSC) were considered as
indicators of model identifiability (Beck & Arnold, 1977, 2007; Dolan & Mishra, 2013; Dolan et
al., 2013).
SSC corresponds to the partial derivative of the parameter multiplied by the estimated
parameter (eqn [20]) (Beck & Arnold, 1977, 2007). Large SSCs in comparison with the response
variable, and SSCs that are uncorrelated with each other (i.e., ratios among SSCs non-constant,
non-parallel lines when plotted SSCs vs time), are indicative of model parameter identifiability,
𝜒𝛽′ 𝑖 = 𝛽𝑖 ×

𝜕𝑓(𝑡,𝛽𝑖 )
𝜕𝛽𝑖

[20]

where χβi is the SSC vector, βi is the parameter, and ∂ represents the partial derivative of the model
for that parameter.
SSC commonly are analyzed on a plot. To represent the different experimental conditions
used in this experiment; simulated temperature, dew point, and %MC profiles were generated and
can be seen in Figure 7. Actual experiments were performed at constant process humidity (i.e.,
constant dew point), however, is not possible to estimate a parameter associated with a variable
without variance. Therefore, the dew point profiles (increasing and decreasing) account for the
variance on the experiment where two nominal levels of process humidity were used in the actual
experiments.

36

Figure 7: Simulated profiles for temperature, dew point (Increasing and decreasing) and %MC.

To compare the models that performed very closely, the corrected Akaike Information
Criteria (AICc) was used (eqn [21]) (Motulosky & Chritopoulos, 2003). Models with smaller AICc
are most likely to be correct (Myung, Balasubramaniam, & Pitt, 2000),
𝑆𝑆

(𝑘+1)

𝐴𝐼𝐶𝑐 = 𝑛 ∙ 𝑙𝑛 ( 𝑛 ) + 2 ∙ 𝑘 + 𝑛−𝑘−1

[21]

where n is the number of data points, k is the number of parameters in the model, and SS is sum of
squares from the fitting algorithm. AICc values were retrieved from the output of the fitnlm
algorithm of MatLabÂŽ.

37

4

RELATIONSHIPS OF WATER ACTIVITY AND MOISTURE CONTENT TO
THE INACTIVATION KINETICS OF SALMONELLA IN LOW-MOISTURE
FOODS
Water in a food is recognized as one of the main drivers, after temperature, of the thermal

inactivation response of pathogens in LMF. However, the relationships between %MC or a w and
the thermal inactivation response remain unclear. To improve our understanding of such
relationships, the effect of moisture adsorption/desorption on the inactivation kinetics of
Salmonella on almonds was assessed. Additionally, a re-analysis of published thermal resistance
results was conducted to further elucidate the relationships between aw and %MC and Salmonella
inactivation kinetics.
4.1

Sample Characteristics
The inoculated and equilibrated almonds prepared for thermal treatment consisted of

samples at three different %MC / aw sorption states (Table 5 and Figure 8). The samples exhibited
the characteristic hysteresis between the adsorption and desorption isotherms. A deviation from
the expected aw at room temperature was observed, which was slightly lower in each case than the
relative humidity in the chambers.
Equilibrium conditions were achieved within ~10 days after the chambers were adjusted
to the desired %RH. Variability in %MC and aw among replicates appeared to change between the
different conditions tested (Table 5). These effects were particularly noticed between the sorption
and desorption samples at 45% RH, in which the variability in %MC after adsorption to 65% RH
and desorption to 45% RH was around six times larger than for adsorption directly to 45% RH.
Also, twice as much variability was observed for adsorption at 52% RH, indicating that variability
in %MC may be affected by the process (i.e., adsorption or desorption) as well as the path to the
equilibrium state. The effects on aw were smaller, at about 0.006 units for all the conditions.

38

Table 5: Chambers and product characteristics for the isothermal experiments. Mean Âą standard
deviation (n = 3).
Isothermal State
Initial Sample
Adsorption
Desorption
Adsorption

Chamber % RH
NA
45%
45%
52%

aw
0.359 Âą 0.011
0.419 Âą 0.007
0.427 Âą 0.006
0.458 Âą 0.006

% MC
3.6 Âą 0.24
3.9 Âą 0.05
4.3 Âą 0.28
4.2 Âą 0.11

5.0%

4.5%

%MC

0.427, 4.3%

0.458, 4.2%

4.0%

0.419, 3.9%
3.5%
0.4

0.41

0.42

0.43

0.44
aw

0.45

0.46

0.47

0.48

Figure 8: Product condition at processing time. Adsorption 45% RH (◊), desorption 45% RH (○),
and adsorption 52% RH (□). The error bars represent the 95% confidence interval of the measured
aw and %MC.

Considering the time required to equilibrate the samples of each condition some products
remained in the chambers for ~30-40 days. This storage period could affect the inactivation
response and the initial population of Salmonella over time. Analysis of the data from
Steinbrunner, Limcharoenchat, Marks, & Jeong, (2017), suggested some effect of storage between
the time of equilibration and the 7th week of storage (P < 0.05). However, their long-term study,

39

up to 27 weeks, indicated that the effect of storage on thermal resistance of Salmonella on almonds
is negligible, (P > 0.05), whit similar results reported by Abd, McCarthy,
& Harris, (2012). The effect on microbial population also has been discussed and reported
previously. Reductions of ~1 log CFU/g over 150 days (Uesugi et al., 2006), and a rate of reduction
of -0.007 log CFU/g/day (Kimber, Kaur, Wang, Danyluk, & Harris, 2012), are similar to the
reductions observed in this experiment which were on the order of 0.5 log CFU/g between the time
of inoculation and the last sample treated (i.e., 40 days).
4.2

Inactivation Results
The inactivation curves showed a reasonable linear trend (Figure 9). Fitting of the log-

linear and Weibull models to the data were reasonable (Table 6). However, based on the higher
uncertainty in the parameters of the Weibull model, as well as the lack of homogeneity or
systematic variability in the shape factor (β), all further analysis were based on the log-linear model
results.

Table 6: Model fitting summary for the log-linear and Weibull models based on three independent
replicates. Estimated parameters, relative error of the parameters and RMSE of the model.
Isothermal
State
Adsorption 45 %
Desorption 45 %
Adsorption 52 %

Log-Linear Model
D value RSE
RMSE
(min)
%
15.74
8.6
0.25
16.02
11.0
0.35
18.04
18.3
0.69

δ
16.16
8.10
3.97

Weibull Model
RSE
RSE
β
%
%
30.3
1.02
20.8
50.6
0.68
23.3
102.6
0.47
36.4

RMSE
0.26
0.31
0.55

An analysis of covariance (Appendix C) indicated non-significant differences in the rate of
inactivation (i.e., slopes) among the three experimental conditions (P > 0.05). Additionally,
independent pairwise comparisons of the D-values from samples with the same aw but different
%MC, and the same %MC but different aw did not indicate significant differences (P > 0.05).
40

To further understand the results, the expected differences in D-value were estimated from
the data of Limcharoenchat (2017). The estimated difference was on the order of 1.3 min.
Unfortunately, given the uncertainty resulting from the present data (i.e., greater than Âą 2 min), it
therefore was not possible to detect differences of that magnitude in the D-values. These
observation highlights the need to improve the accuracy and reliability of the present methodology
to estimate D-values, especially for comparison purposes. Other studies involving LMF reported
similar or larger uncertainties in the estimated D-values for the log-linear model, and δ values for
the Weibull model (Ma et al., 2009; Santillana Farakos, Hicks, & Frank, 2014; Smith & Marks,
2015).

Figure 9: Thermal inactivation results. Log reductions (○), log-linear predicted inactivation (˗),
95% confidence interval (- -). A: Adsorption at 45 %RH, B: Desorption at 45 %RH, and C:
Adsorption at 52 %RH.
The relationship between aw and temperature could help elucidate some of these results.
Despite recent progress in measuring aw at high temperatures (i.e., between ~60°C and ~80°C)
41

(Syamaladevi, Tadapaneni, et al., 2016), the relationships between high-temperature aw and
inactivation kinetics (i.e., D-value) of Salmonella in LMF are not yet well described or reported.
Very few studies have reported aw at high temperatures. The experimental space is reduced at high
temperature (i.e., the aw range of LMF at high temperature is smaller than at room temperature).
Additionally, limited commercial equipment is available to perform aw measurements at
high-temperature (although there are prototypes), and other methodological constraints limit the
applicability of this concept. Also, many industrial processes are performed above temperatures at
which aw cannot be measured consistently (i.e., > 100°C), making the aw methodology unsuitable
for real-time industrial applications.
4.3

Analysis of Data from Other Studies
Analysis of published (Buchholz et al., 2016; Smith, 2014) and in-house (Limcharoenchat,

2017) data sets (See Appendix D) for Salmonella thermal inactivation in LMF was conducted.
Inactivation kinetics (i.e., D-values), aw, and %MC were reported, which enabled a comparison of
the inactivation kinetics of Salmonella as a function of aw and %MC. Most studies only reported
aw; thus, %MC needed to be estimated from reported isotherms. However, adsorption and
desorption isotherms are rarely found for LMF; commonly only one sorption isotherm is reported,
because of the relevance of the adsorption or desorption process for quality control.
The effect of aw and %MC on thermal resistance appears to be highly product specific.
Distinctive patterns for D80°C were observed for aw and %MC (Figure 10). In general, an inverse
relationship was observed; as aw or %MC increased the log(D-value) decreased, indicating greater
thermal resistance with decreasing moisture. Salmonella in wheat flour appeared to be more
sensitive to changes in both aw and %MC, while Salmonella on dates appeared to be less sensitive
to changes in both metrics. Salmonella on almonds appears to be more sensitive to changes in
%MC than aw. Note that the aw reported and used in this analysis was measured at room
42

temperature, not at 80ÂşC. Therefore, the aforementioned temperature effects on a w definitely

1.6

1.6

1.2

1.2

Log(D(min))

Log(D(min))

influence these relationships, and need to be further investigated.

0.8
0.4
0.0
-0.4
0.00

0.8
0.4
0.0
-0.4

0.25

0.50
aw

0.75

1.00

0.0

0.1
0.2
0.3
0.4
%MC (g H2O / g Dry)

Figure 10: Relationship of log(D80°C) with aw and %MC. ○ Almonds (Limcharoenchat, 2017), □
wheat flour (Smith, 2014), and ◊ dates (Buchholz et al., 2016), dotted lines (- -) are plotted for
reference only.

Table 7: Correlation coefficients of log(D80°C) vs. aw and %MC of some representative
low-moisture foods.
Date
Flour
Almonds

aw
-0.404
-0.957
-0.551

%MC
-0.395
-0.952
-0.610

A comparison of the correlation coefficients shows little difference between %MC and aw
(i.e. ≤ 0.05 units). In almonds, %MC appears to be more strongly correlated with log(D80°C), while
in dates aw appears to be slightly stronger; in flour, the correlation is practically the same (Table
7). However, the correlation coefficients were not equally high; and were in fact quite low for

43

dates, suggesting that other variables or interactions among variables could better explain the
changes in D-value for Salmonella in these products under these conditions.
These results, reinforce the need to consider the sorption state of products to estimate the
thermal inactivation kinetics and the development of inactivation models to validate processes.
Considering the varying behavior of the different products, development of a single approach to
predict Salmonella inactivation broadly across multiple LMF appears unlikely.

44

5

MODELING TEMPERATURE, MOISTURE, AND AIR VELOCITY EFFECTS
ON SALMONELLA INACTIVATION DURING DYNAMIC THERMAL
PROCESSES OF LOW-MOISTURE FOODS
This experiment assessed thermal inactivation of Salmonella on almonds in a

laboratory-scale, moist-air convection oven, considering: two air velocities, two process
humidities, and two initial levels of water in the product. The resulting inactivation data were used
to estimate the parameters of multiple secondary models coupled with a log-linear primary
inactivation model considering dynamic conditions. The initial resulting parameters and the
analysis of residuals showed that a model accounting for product temperature and process humidity
described the inactivation accurately, but there was significant bias due to air velocity and water
in the product. Further attempts to model the effect of air velocity and water in the product were
performed and analyzed, and the results are described in this chapter.
5.1

Sample Equilibration
Equilibration, defined as an average change in mass of the control sample of less than

0.05% during 3 days, was achieved within 10 days after placing the inoculated samples in the
equilibration chambers. Equilibrium %MC and aw are reported in Table 8; samples were thermally
treated within 40 days of equilibration. Rare deviations from equilibrium (i.e., random change in
the mass of one of the replicates) were observed over time after equilibrium was reached, but
samples returned to the equilibrium state within a day or two, and were not used until the 3-day
criterion described above was satisfied again.

Table 8: Summary of equilibrium conditions (mean Âą standard deviation)
aw
%MC (g H2O / g dry)

25% RH
0.378 Âą 0.055
0.028 Âą 0.002

45

65% RH
0.647 Âą 0.011
0.061 Âą 0.007

Discrepancies between the target and measured aw were larger for the samples at 25% RH,
around 0.128 aw units above the target, than for the sample at 65% RH, which was 0.003 aw units
below. The reasons for these discrepancies may be attributed to differences in the mechanism of
adsorption and desorption, mass transfer differences between the surface and the body of the nut,
and uncertainty in the %RH sensors. Variability in the %MC appeared to be larger, but was around
10% of the measured %MC, which is consistent with expected variability of the methodology and
the measuring system. Also, variability in samples reaching equilibrium by desorption was greater
than for those in an adsorption path, similarly to what was observed in Section 4.1, which supports
the idea that variability in the equilibrium conditions can be affected by the equilibration process
(i.e., adsorption or desorption).
5.2

Air Velocity Estimation
The aluminum almond temperature curves from different operation set points controlled

with a variable speed blower (i.e., V1, V2, V3, V4, and V5, where V1 was the maximum speed at
which the oven was stable and V5 was the minimum speed at which the blower did not stop) were
recorded and analyzed to estimate the heat transfer coefficients (h) of the system. Plots of the
natural logarithm of the dimensionless temperature vs. time exhibited a reasonable linear trend
(Figure 11), suggesting that the relationship described by eqn [7] is valid only for the linear portion
of the temperature curves. The slopes and h values were estimated in the data range starting at 20
s and extending to 120, 130, 200, 200, and 250 s for the five-different operation set points (Table
9).

46

Ln(Dimenssionless Temperature)

0.5
0

-0.5

V5

-1

-1.5
-2

V4

-2.5

V1

-3

V2

V3

-3.5
0

50

100

150 200
Time (s)

250

300

Figure 11: Dimensionless temperature profiles

Table 9: Estimated slopes and convective heat transfer coefficient (h) for the operational set points
tested.
Set point
V1
V2
V3
V4
V5

R2
>0.99
>0.99
>0.99
>0.99
>0.99

Slope
-0.023 Âą 0.000
-0.020 Âą 0.000
-0.014 Âą 0.001
-0.011 Âą 0.001
-0.010 Âą 0.001

h (W / m2 × °C)
104.5
90.6
61.9
51.4
43.8

The resulting h values were reasonable for the system under study, given that every case
involved forced air convection of individual almonds. In order to test the effect of air velocity
within the experimental design, the set-points V1 and V5 were selected. The ratio of h values
obtained between the high (i.e., V1) and low velocities (i.e., V5) was 2.4, which supports the
premise that the two air velocity conditions were very different. Final estimations of the air velocity
were not used for numerical analysis, because the Nu-Re correlation (for 30,000 < Re < 150,000 )
published for an ellipsoid (Mohsenin, 1980) is not valid at the Re achieved in the experiment (i.e.,
Re ranged from ~190 to ~1250); also, estimations based on alternative geometries yielded distinct

47

velocities (i.e., spherical geometry yielded air velocities of 4.95 and 0.75m/s, while flow over a
flat plate yielded 4.7 and 0.82 m/s (See Appendix E). Also, h value calculations were direct and
presumed to be fairly accurate, given that they were derived from the measured variables, while
the calculated air velocities are the result of iterative calculations and assumed geometrical
configurations.
5.3

Changes in Product Temperature, Water Activity and Product Moisture Content
during Processing
The eight experimental treatments (i.e., oven conditions) (Table 3) yielded significantly

different product histories, as reflected in the temperature (Figure 12), %MC (Figure 13), and aw
profiles (Figure 14). Temperature appeared to be more regular at the higher velocity, as well as at
lower humidity. The effect of the different initial water content in the product was observed (not
shown), and considered later during fitting of the models. Moisture content and aw showed similar
results (Figure 13 and Figure 14), with several trends of importance to the process. In general, a
declining moisture history was observed; however, the experiments that were performed at high
humidity (i.e., 30% Mv) exhibited an increase in %MC and aw during the first 2-3 min of
processing, because of condensation of water on the product surface. Also, this transient increase
in %MC appears to be larger at low velocity, which is consistent with the temperature profiles,
which showed a slower heating rate for the low velocity (Figure 12-B and Figure 12-D).

48

0

Temperature (°C)

Temperature (°C)

hV

1200
2400
Time (s)

HV

0

C

140
120
100
80
60
40
20
0

B

140
120
100
80
60
40
20
0

3600

100

200
Time (s)

300

hv

400

D

140

Temperature (°C)

Temperature (°C)

A

140
120
100
80
60
40
20
0

120
100
80
60

Hv

40
20
0

0

1200
2400
Time (s)

3600

0

100

200

300

400

Time (s)

Figure 12: Examples of temperature profiles. A, high-velocity low-humidity (hV), B, high-velocity
high-humidity (HV), C, low-velocity low-humidity (hv), and D, low-velocity high-humidity (Hv).

%MC (g H2O / g Dry)

0.07
Hv

0.06
0.05
HV

0.04
0.03

hv

hV

Hv
HV

hv

0.02
0.01

hV

0

0

600

1200

1800
Time (s)

2400

3000

3600

Figure 13: Moisture content histories. The letters corresponds to the process humidity (H = high
(30% Mv, h = low < 3% Mv), and the air velocity (V = high, v =low).

49

aw

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

Hv
Hv

HV

hV

hv

HV

hV

hv

0

600

1200

1800
Time (s)

2400

3000

3600

Figure 14: Water activity histories. The letters corresponds to the process humidity (H = high (30%
Mv, h = low < 3% Mv), and the air velocity (V = high, v =low).

The transient increase in %MC continued after the dew point was reached (which was ~20
s at high velocity and ~80 s at low velocity). This observation is likely due to limitations in the
measurement of %MC and the mass transfer phenomenon that occurred during the process. The
measurements of %MC were done for three whole / intact almonds, but water condensation and
initial adsorption of moisture occurs only on the surface of the product (i.e., almond skin). This
explains the observed high peaks in aw, meaning that there was a relatively large amount of water
on the surface of the almonds that increased the product vapor pressure and therefore yielded larger
aw values. This phenomenon is linked to what Limcharoenchat, James, Hall, & Marks, (2016),
reported as partial equilibration of the product, when differences were seen between the aw of intact
and split almonds. Those experiments required long equilibration periods (i.e., ~10 days) to
achieve the same aw readings for intact and split almonds. Also, higher velocity air means a thinner
boundary layer and lower external resistance to water transfer to / from the product surface, thereby

50

increasing the impact of the air conditions on product surface moisture and the associated bacterial
inactivation (discussed below).
Although the %MC and aw profiles show similar trends, some important differences were
noted. Considering the %MC profiles, %MC increased more at low than at high velocity,
suggesting that air velocity is affecting the condensation and retention of water on the product
which is consistent with mass transfer theory. Also, product having a lower initial water content
appears to be retaining larger amounts of water, with an increase in %MC of ~0.75% in comparison
to ~0.50% for the high initial water content samples. Regarding the aw histories, differences due
to initial water in the product were also observed. The increase in aw readings was slower at high
velocity (close to a minute for the low initial water product), and was basically undetectable for
the high initial water content product, indicating that these samples underwent what was
effectively and exclusively drying.
In the low humidity processes the increase in %MC and aw did not occur because the dew
point of the process (i.e., < 22°C) was below the initial temperature of the product, implying that
the product goes into instantaneously drying. However, differences were seen between the high
and low-velocity processes. In Figure 13 low-velocity %MC appears to be above high-velocity
%MC, but the gap across the process is similar which is an effect of the initial %MC of each
product and the differences in drying rate midway through the process. In Figure 14, the effects on
aw are consistent with the previous statement, but the product processed at higher velocity showed
a larger aw. This was unexpected, but can be explained by the variability of the process at those
conditions as can be seen in Figure 12C, where temperature fluctuate as the control system made
adjustments controlling temperature and process humidity, while at high air velocity (Figure 12A)

51

the effect is not noticeable (likely because of better mixing of air throughout the oven and sample
chamber).
The effect of condensation during processing, and the differences in %MC and aw in this
type of application, have not been previously reported. Previous work using this same system
either ignored these two factors, assuming that any condensation was immediately swept away
from the product surface and not adsorbed (Jeong, Marks, & James, 2017; Jeong et al., 2009, 2011;
Limcharoenchat, Marks, & Jeong, 2014), or treated the system as a drying process based on
observation (Casulli, 2016). The present results point to the need for measuring and monitoring
processes more closely during the initial stages, when condensation can occur, because it could
have a meaningful effect on bacterial inactivation, product characteristics and functionality.
5.4

Microbial Inactivation Curves
Microbiologically, declining population curves observed for the eight experimental

conditions (Figure 15) exhibit a generally linear trend, even though product experienced dynamic
conditions (due to the counter-acting effects of increasing temperature and decreasing moisture).
The experiments at higher process humidity (i.e., 30% Mv) achieved lethality about ten times faster
than the low-humidity processes (i.e., <3% Mv). The effect of air velocity appears to be weaker
compared to product humidity; lethality at low velocity appeared to be smaller than at high
velocity, particularly in high-humidity processes, differences in reductions were 2 to 3 logs.

52

Figure 15: Observed inactivation curves. Individual plots are coded as follow: process humidity (H = high, h = low), for air velocity (V
= high, v = low), 25 and 65 for %RH of equilibration respectively.

53

The differences among replicates were within ~1 log CFU/g; however, there are sample
points in which differences between replicates were up to 3 log CFU/g. Part of this variability is
linked to uncertainty in the process (i.e., temperature and process humidity control), and another
part to experimental error. The observed variability is similar to that seen for comparable
experiments (Casulli, 2016; Jeong et al., 2009; Limcharoenchat et al., 2014), who reported
differences of 1 and 2 log CFU/g between replicates.
5.5

Parameter Estimation - Model Fitting
The inactivation curves were fitted globally to the DLM model [14] (Table 10), which only

accounted for surface temperature and process humidity (i.e., dew point). The RSME (0.61 log
N/N0) was acceptable. The relative error of ZT (24%), and the variance-covariance correlation of
ZT and ZM (0.99) were large, indicating high uncertainty for ZT. This observation is partially
consistent with the SSC analysis (Figure 16), in which ZT and ZM are uncorrelated for the
high-humidity part of the simulated processed but are almost symmetrical for most low-humidity
part. However, interpretation of SSC plots for such data sets and experiments is more complex
because of the multiple dynamic conditions involved, which is more difficult than visualization of
a single SSC plot for an entire data set. The single data set SSC depicted allows a better
understanding of some of the intricacies of parameter estimation but, cannot be considered as an
independent evaluation tool for the entire global fitting process.

Table 10: Estimated values, relative standard error (RSE) and P-values for the DLM model
parameters.
Parameter
Tref (°C)
Tdref (°C)
Dref (s)
ZT (°C)
ZM (°C)

Estimate
80
55
182
69.1
61.9
54

RSE %

P-value

2.89
23.7
9.62

2.28×10-73
4.14×10-5
2.11×10-19

Residual analysis showed distinctive trends among the residuals at high and low velocity
as well as at high and low initial water content in the product (Figure 17). The mean residual
differences were 0.6 log N/N0, based on air velocities, and 0.5 log N/N0, between the two initial
product water contents. The effects of low and high air velocity and water in the product were
confirmed by ANOVA of the residuals, which indicated significant differences (P < 0.05) between
the two levels of the variables.

Dref

Dref
ZM

ZT

ZT

Yobs

ZM

Yobs

Figure 16: SSC for the DLM model with decreasing (left) and increasing (right) dew point.

55

Figure 17: Observed vs. fitted log CFU/g for the DLM model by %Mv, air velocity, and initial
water content in the product. (○) High level, (+) low level.

Fitting the DLM model confirmed the effects of product surface temperature (ZT = 69.1°C),
and process humidity (ZM = 61.9°C) on Salmonella inactivation. However, the large relative error
of ZT and high-level correlation of ZT and ZM raises concerns about the identifiability of the ZT
parameter (Beck & Arnold, 1977, 2007; Dolan et al., 2013). Although, the reference conditions
were optimized to minimize correlation of the parameters (Datta, 1993), it was not possible to
reduce the correlation any further; reference plots of the optimization are in Appendix H. Despite
these limitations, the performance of the model in terms of RMSE (i.e., 0.61 log N/N0), the mean
95% confidence intervals within Âą0.22 log N/N0, and the 95% prediction interval within Âą1.9 log
N/N0, indicate that the model could be useful for comparison purposes. However, its applicability
to predict thermal inactivation, and to validate processes, in real-life scenarios is not encouraged
or recommended at this time, without further testing of model robustness.
Differences in the estimated parameters can be observed in similar previous studies and
analyses (Garces-Vega et al., 2016; Jeong et al., 2009). Such differences can be, at least partially,
explained by differences in the experimental conditions and product preparation. However, the

56

general trends that indicate that results from this study are consistent with previous results. The
estimated Dref value (i.e., 182 s at 80ÂşC) is consistent with those of Jeong et al., (2009), falling
within the interval of their estimations for the processes at dry and low humidities (i.e., 5% Mv
(957 s) and 30-50% Mv (55.7 s) correspondingly, all at 82ÂşC). In contrast, ZT and ZM were about
twice as large as those reported by Jeong et al., (2009), which could be due to differences in the
air velocity and impingement system setup (i.e., sample positioning, fan damper set-up, etc.). In
all of these studies, ZT and ZM are relatively close and of the same order of magnitude. Jeong et al.,
(2009) reported a ZT of 14.7°C and 21.7°C and a ZM of 27.9°C and 34.2°C for the dry and low
moisture processes, respectively. Garces-Vega et al. (2016) included the whole data set from Jeong
et al., (2009) and reported a ZT of 32.4°C and a ZM 42.4°C. Finally the present study yielded a ZT
of 69.1°C and a ZM of 61.9°C.
Residual analysis of the fitted model (Figure 17), shows different trends for the high and
low velocity data. The mean residuals for the two groups are significantly different (i.e., -0.31 log
N/N0, 0.28 log N/N0 for high and low-velocity, respectively) (P < 0.05), as well as when comparing
the mean residuals for the low (i.e., 0.23 log N/N0) and high (i.e., -0.25 log N/N0) initial product
water content (P < 0.05). Significant differences in residuals suggest the need/opportunity for
additional model terms to account for air velocity and %MC effects.
The mean residual difference was larger between the air velocities (i.e., 0.6 log N/N0 vs 0.5
log N/N0), so a modified model accounting for air velocity as a categorical factor was considered
eqn [18] (DLMV). The model fit the data well; and the separation of the mean residuals due to air
velocity was reduced to a non-significant 0.04 log N/N0 (Figure 18). Compared to the DLM model,
the RMSE improved (0.51 vs 0.61 log N/N0), as did the AICc (i.e., 230.8 DLMV vs 285.5 DLM).
However, the correlation between ZT and ZM remained large (> 0.95), and relative errors of the

57

parameters increased, ~30% for ZT (Table 11). Also, separation between the mean residuals due to
initial product water content (0.50 log N/N0), remained significant (P < 0.05).

Table 11: Estimated values, relative standard error (RSE) and P-values for the DLMV model
parameters.
Parameter
Tref (°C)
Tdref (°C)
Dref (s)
ZT (°C)
ZM (°C)
ÎłV

Estimate
80
55
219
106
70.9
-0.39

RSE %

P-value

3.85
30.1
9.21
15.0

3.75×10-57
1.14×10-3
1.37×10-20
4.84×10-10

Figure 18: Observed vs. fitted log(N/N0) for the DLMV model by %Mv, air velocity, and initial
water content in the product. (○) High level, (+) low level.

The Îł parameter in the DLMV model suggests that the inactivation rate is higher at higher
air velocity, independent of the effect of T(t). Including the Îł parameter yielded a 1.39 times faster
kill than at low velocity, indicating that other factors should be considered in the inactivation
process. The heat transfer effect is accounted for in the surface temperature and the temperature
component of the model. The observed air velocity effects are independent of temperature.
Because the effect of moisture in the process is associated with condensation and surface

58

temperature, the moisture effect is dependent on the heat transfer phenomenon. Therefore, there
should be a linkage between air velocity and other phenomena that can explain such effects, such
as the dynamic mass transfer phenomena. However, the differentiated trends observed based on
the initial product water content suggest possible independent effects due to air velocity and mass
transfer.
Given that mass transfer in this process is mainly associated with the gain and loss of water
to/from the product, then a model that includes %MC as a parameter should logically be
considered. Casulli (2016) proposed a model with a %MC term for pistachios and demonstrated
that the new model performed better than the DLM model. Additionally, other models based on
aw to represent the effect of water in the product as a result of mass transfer were tested but did not
outperform the model with the %MC term. However, when that model eqn [15] (DLMC) was
fitted to the data of this experiment, the fitting did not improve over that of the DLM model (See
Appendix I). The estimated ZMC parameter was very large making the effect of %MC ~0.
Garces-Vega & Marks (2015, 2016) showed a significant effect of aw on the ZT parameter
under isothermal conditions (Figure 2), as well as a discontinuity that may be linked to the
adsorption/desorption state of the samples. This observation suggests that using %MC as an
independent variable instead of aw might be phenomenologically preferred. From that premise and
observations from (Limcharoenchat, 2017), an alternative model eqn [16] (DLMCM) considering
ZT as a linear function of %MC was considered (See Appendix I) but did not fit properly.
Considering that ZT is expected to have a theoretical maximum when %MC is zero, a square-root
model with a maximum at zero eqn [17] (DLMCM2) also was considered. The fitting was
satisfactory (Table 12), with RMSE = 0.61 log N/N0, and relative errors of the parameters similar
to those in the DLM model (i.e., < 10% for Dref and ZM : > 20% ZMC). The variance-covariance

59

correlation between ZMC and ZM was also large (> 0.95) like that of ZT and ZM in the DLM model.
These results might be expected, because the model is basically applying a variable substitution
but not changing the general structure of the model (DLM vs DLMCM2). Also, within the range
of experimental conditions, evaluation of the section (𝑍𝑀𝐶 × 2√𝑀𝐶𝑟𝑒𝑓 − %𝑀𝐶(𝑡)) yielded a small
difference (i.e.~70.5 to ~68.8°C), which is consistent with the estimated parameter and the
parameters in the DLM model (69.1°C).

Table 12: Estimated values, relative standard error (RSE) and P-values for the DLMCM2 model
parameters.
Parameter
Tref (°C)
Tdref (°C)
MCref
Dref (s)
ZMC (°C)
ZM (°C)

Estimate
80
55
1
181
71.2
62.1

RSE %

P-value

2.89
23.7
9.60

2.49×10-73
4.38×10-5
1.90×10-19

The analysis of residuals (not shown) was like that of the DLM model, which is consistent
with estimated parameters and the estimated effects of ZMC in the model. Separation of mean
residuals based on air velocity and initial water in the product remained significant (P < 0.05) in
both cases.
The two models based on %MC (DLMCM and DLMCM2) were also tested, with the
measured aw at 25°C substituted for %MC as an independent variable (not shown). In both cases,
model performance was comparable to that of the DLMCM and DLMCM2 models, which is
expected of because the inherent relationship between %MC and aw. However, the AICC
comparison (Table 13) was inconclusive for the DLMCM model, and slightly favorable for the
DLMCM2 model using %MC as the water metric. The other performance parameters (i.e., RMSE,

60

the relative error of the parameters, variance-covariance matrices) were marginally favorable to
the model that used %MC as the water metric.

Table 13: AICc comparison for the DLMCM and DLMCM2 models using %MC and a w as the
metric of water in the product.
Model
DLMMC
DLMMC
DLMMC2
DLMMC2

Water Metric
aw
%MC
aw
%MC

AICc
285.6
285.7
289.3
285.6

While no major differences between the DLM and DLMMC models were observed, a
merged model consisting of the DLMV and DLMMC2 models was tested (DLMMC2V). The
model fit well to the data (Table 14), with model performance comparable to the DLMV model,
with RMSE = 0.51 log N/N0. Also, no difference was seen in the AICc which was 230.7, for the
DLMMCV model vs 230.8 for the DLMV model.

Table 14: Estimated values, relative standard error (RSE) and P-values for the DLMCM2V model
parameters
Parameter
Tref (°C)
Tdref (°C)
MCref
Dref (s)
ZMC (°C)
ZM (°C)
ÎłV

Estimate
80
55
1
218.
109
70.9
-0.39

RSE %

P-Value

3.87
30.0
9.19
14.9

6.26×10-57
1.10×10-3
1.15×10-20
4.60×10-10

The analysis of residuals did not show any major improvement in model performance. The
differences in mean residuals split by the experimental variables of interest remained as in the

61

DLMV model, 0.03 log N/N0 for high vs low air velocity and 0.5 log N/N0 for high vs low initial
product water content.

62

6

CONCLUSIONS

The sorption state of low-moisture food products must be considered in the estimation of
bacterial inactivation kinetics, model development, and process validation. Although the
experimental results from this study were inconclusive, analysis of these and prior data support
the need to better understand the role of this variable in the inactivation kinetics of Salmonella in
low-moisture foods.
While aw is an excellent metric to describe the effects of water in foods, regarding microbial
growth and growth boundaries, it appears to be insufficient to describe the effects of water on
thermal inactivation of pathogens on LMF, in a manner that is universal across products. Until the
validity of these metrics is better elucidated, it is necessary to report both variables for thermal
inactivation of pathogens in LMF, as well as to analyze the results under the light of both scenarios
(i.e., inactivation kinetics as functions of aw and %MC).
Given the small difference in D-values expected for the experiments performed in this
study, better methodologies need to be developed to estimate inactivation kinetics. Variability of
the plate counts, and the effect of other factors such as come-up times during the heating process,
etc., affected the results, making the analysis and comparison challenging.
The relationship of aw, and %MC with the thermal inactivation kinetics of Salmonella in
LMF are different. Further analysis is need to more accurately identify which metric is adequate
to describe the effect of water in the product in thermal inactivation process.
The %MC is likely to be a better metric for product water content. %MC is independent of
temperature; can be measured in real-time during processing (but the equipment is expensive); and
appears to be better correlated with the inactivation kinetics of Salmonella in LMF. These
characteristics make %MC better suited for process monitoring and validation.

63

The effect of air velocity on the thermal resistance of Salmonella on low-moisture
particulates is significant. While it is not possible to conclusively propose, and select the best
generalizable model using only the data from this study (because of limitations in the experimental
domain), the model provides sufficient evidence considering air velocity as a variable, to support
that hypothesis. These results also support the premise that air velocity is affecting the inactivation
process beyond just the heat transfer phenomena, given that the thermal effect is already accounted
for in the surface temperature term of the models.
The effect of water in the product is also significant in open, air-heated systems. The
improved model that accounts for air velocity still exhibited residual trends that support that
hypothesis. The models tested suggest that %MC could have some advantage over aw to account
for product water effects; however, the results remain inconclusive, as the different models tested
did not outperform the DLM or DLMV models, only marginally affecting model outputs.
The resulting models are valuable tools to understand the effects of product and process
variables on pathogen inactivation in LMF. Also, the overall results of this study clearly
demonstrate that the effects of process variables appear to be as diverse as the products in this food
category. Therefore, further work is necessary to establish generalized models that can be used
commercially for low-moisture process design or validation. Use of the reported models and
parameters in industrial scenarios is not yet encouraged, until further model testing and
independent validation is completed.

64

7

FUTURE WORK AND RECOMMENDATIONS

Further analysis is necessary to test the hypothesis that either aw or %MC is the superior
metric for product water effects on pathogen thermal inactivation kinetics in low-moisture foods.
This should specifically include tests with multiple other products, particularly those with smaller
and larger hysteresis between adsorption and desorption isotherms. Ultimately, the original
hypothesis could be better tested using low-moisture foods with a larger sorption hysteresis.
Comparisons of the inactivation kinetics at other temperatures is necessary, particularly
above 100°C, where aw measurements are not feasible. Estimation and comparison of ZT-values
considering the sorption hysteresis, including temperatures above 100°C, could be useful to
elucidate some of the relationships of %MC and aw with thermal inactivation kinetics.
Establishing sorption equilibrium product characteristics is extremely important to the
overall challenge of low-moisture food pasteurization. Products that are uniform in size and shape
(e.g., nuts, dried fruit pieces) are likely to perform better than those prone to breakage in handling,
or those in which less homogeneous inoculation is likely to occur (e.g., powders, butter, and small
particulates materials). It would be extremely helpful in future research studies to evaluate whether
using change of weight as a measurement of equilibrium could help to reduce variability of the
inactivation response of Salmonella in those products.
For the oven-heating (open air) thermal tests, reliable quantification of air velocity is
desirable to develop a quantitative model accounting for this characteristic. Future studies should
include additional levels of air velocity, given that this effect is unlikely to be linear, based on the
trends observed. Additionally, the utility of the model could be further tested by repeating similar
experiments with food products of multiple particle sizes, in order to more directly test how air
velocity affects the relative sensitivity of the inactivation process to product vs. process moisture.

65

When designing experiments of this type, with multiple dynamic variables, more attention
should be given to the sampling points during the non-isothermal stage of the process, in order to
improve the identifiability of the temperature-dependent parameters. Use of non-regular time
intervals to take samples may be a reasonable solution, using shorter time intervals at the beginning
of the process ensure adequate sampling during the non-isothermal part of the process. Although,
this approach requires an increased in number of samples, further optimization of the experiments
is recommended.
An assessment of the effect of air velocity at non-lethal temperatures would be interesting,
to isolate the effect of any desiccation effect (i.e., %MC changes) from the effect of temperature
in the inactivation response of Salmonella in low-moisture foods. This approach was taken
previously by Lievense et al. (1994, 1992) to elucidate the effect of drying on the inactivation (i.e.,
reduction of microbial activity) of lactic acid bacteria, and could be significant in understanding
the effects of %MC, air velocity, and rate of dehydration (i.e., mass transfer phenomenon) on
thermal resistance of Salmonella in low-moisture foods.
The effect of product and process water on Salmonella thermal inactivation in lowmoisture products remains unsolved, in terms of a universally applicable metric or modeling
solution. There are hints suggesting that the relative effects of water in the product and the process
are linked to the mass transfer phenomenon that occurs during dynamic temperature and moisture
processes. A better understanding of how mass transfer is occurring, particularly in the early stages
of the processes, where %MC and aw increased for the high humidity treatments, is necessary. The
development of a coupled heat and mass transfer model considering the change in %MC as water
condenses on the product surface could be useful to elucidate those effects in relation to bacterial

66

inactivation, and to ultimately develop a generalized model that works across the low-moisture
product category.

67

APPENDICES

68

Survival plate counts for the isothermal experiments
The data sets corresponding to the isothermal inactivation curves in 4.1 are presented in
Table 15; the three data points later identified as outliers (based on leverage residual analysis) are
highlighted by * in the first column.
Table 15: Inactivation data of the isothermal experiments.
STATE

CHAMBER %RH

REPLICATE

TIME (min)

LOG (CFU/g)

Adsorption

45

1

0

5.88

Adsorption

45

1

10

5.58

Adsorption

45

1

20

4.93

Adsorption

45

1

30

3.56

Adsorption

45

1

40

3.37

Adsorption

45

1

50

2.59

Adsorption

45

1

60

2.30

Adsorption

45

2

0

5.80

Adsorption

45

2

10

5.94

Adsorption

45

2

20

4.59

Adsorption

45

2

30

4.97

Adsorption

45

2

40

4.44

Adsorption

45

2

50

2.97

Adsorption

45

2

60

2.19

*Adsorption

45

3

0

6.91

Adsorption

45

3

10

5.50

Adsorption

45

3

20

5.09

Adsorption

45

3

30

3.45

Adsorption

45

3

40

4.45

Adsorption

45

3

50

3.68

Adsorption

45

3

60

2.29

Desorption

45

1

0

6.30

Desorption

45

1

10

4.80

Desorption

45

1

20

4.44

Desorption

45

1

40

3.90

Desorption

45

1

50

3.57

Desorption

45

1

60

2.28

Desorption

45

2

0

6.62

Desorption

45

2

10

5.93

Desorption

45

2

30

4.34

Desorption

45

2

40

3.70

Desorption

45

2

60

2.65

Desorption

45

3

0

5.87

69

Table 15 (cont’d)
STATE

CHAMBER %RH

REPLICATE

TIME (min)

LOG (CFU/g)

Desorption

45

3

10

5.33

Desorption

45

3

20

3.74

Desorption

45

3

30

3.14

Desorption

45

3

40

2.47

Desorption

45

3

60

1.89

*Adsorption

52

1

0

7.56

Adsorption

52

1

10

4.98

Adsorption

52

1

20

4.15

Adsorption

52

1

30

4.12

Adsorption

52

1

40

3.21

Adsorption

52

1

60

3.22

Adsorption

52

2

0

5.85

Adsorption

52

2

10

4.98

Adsorption

52

2

30

3.47

Adsorption

52

2

40

3.71

*Adsorption

52

2

50

4.32

Adsorption

52

2

60

2.76

Adsorption

52

3

0

5.64

Adsorption

52

3

10

4.85

Adsorption

52

3

20

4.79

Adsorption

52

3

30

2.64

Adsorption

52

3

50

1.79

70

Example almond surface histories from the isothermal experiments
Example of the isothermal temperature profiles of the experiments in 4.2 are presented in
Figure 12. The different lines correspond to the three replicates, with the × marking the come-up
time (i.e., where T > 79°C and the “time zero” samples are pulled).

90
80

70

Temperature (°C)

60
50
40
30
20
10
0
0

10

20

30
40
Time (min)

50

60

Figure 19: Example almond surface temperature histories from the isothermal experiments.

71

70

Analysis of covariance effect of water metrics
Results of the analysis of covariance for the effect of the a w and %MC on the inactivation
kinetics of Salmonella in almonds Table 16 and Table 17.

Table 16: ANOVA table of the analysis of covariance.
Source
Group
Time (min)
Group*Time (min)
Error

d.f.
2
1
2
46

Sum Sq
2.34
69.8
0.187
13.2

Mean Sq
1.17
69.8
0.093
0.287

F
4.07
243.1
0.325

Prob > F
0.02
< 0.001
0.724

Table 17: Coefficients estimates of the analysis of covariance.
Term
Intercept
A
B
C
Slope
A
B
C

Estimate
5.84
-0.106
0.278
-0.172
-0.059
0.004
-0.001
-0.003

Std. Err.
0.13
0.188
0.184
0.189
0.004
0.005
0.005
0.005

72

T
44.07
-0.565
1.511
-0.909
-15.58
0.771
-0.137
-0.610

Prob > |T|
< 0.001
0.575
0.138
0.368
<0.001
0.445
0.892
0.545

Secondary data for analysis of aw and %MC on D-values.
The data-sets used to estimate D-values and compare the effects of aw and %MC on thermal
inactivation of Salmonella in low-moisture products in 4.3 are presented in Table 18.

Table 18: Data from other products; dates (Buchholz et al., 2016), wheat flour (Smith, 2014), and
almonds (Limcharoenchat, 2017).
Product
Dates
Dates
Dates
Dates
Dates
Dates
Dates
Dates
Flour
Flour
Flour
Flour
Flour
Flour
Flour
Flour
Flour
Flour
Flour
Flour
Almonds
Almonds
Almonds
Almonds
Almonds
Almonds
Almonds
Almonds
Almonds

aw
0.461
0.453
0.455
0.635
0.644
0.656
0.280
0.234
0.582
0.582
0.582
0.427
0.427
0.427
0.310
0.310
0.310
0.687
0.687
0.687
0.450
0.450
0.450
0.250
0.250
0.250
0.633
0.635
0.654

%MC (g H2O/g Dry)
0.191
0.188
0.189
0.276
0.283
0.291
0.137
0.125
0.188
0.188
0.188
0.167
0.167
0.167
0.149
0.149
0.149
0.204
0.204
0.204
0.041
0.041
0.041
0.031
0.031
0.031
0.058
0.058
0.061

73

D (min)
0.709
0.950
1.567
0.847
0.734
1.052
0.846
1.009
1.551
1.268
1.346
5.189
5.302
7.866
12.022
8.401
14.475
1.277
1.428
1.182
26.93
24.09
21.21
17.12
21.75
21.00
12.15
6.17
13.48

Log(D)
-0.149
-0.022
0.195
-0.072
-0.134
0.022
-0.073
0.004
0.191
0.103
0.129
0.715
0.724
0.896
1.080
0.924
1.161
0.106
0.155
0.073
1.430
1.382
1.327
1.233
1.337
1.322
1.084
0.791
1.130

Air velocity calculations
The thermal properties of aluminum and air, and characteristics of the aluminum almond
used to perform the heat transfer calculations are presented in Table 19.

Table 19: Thermal properties used in the air velocity estimation.
Aluminum Thermal Properties
Density- ρ -(kg/m3)
Specific Heat- cp -(kJ/(kg×K))
Thermal Conductivity- k -(W/(m×K))

2700
0.91
222

Air Thermal Properties at 120°C
Kinematic Viscosity- ν -(m2/s)
Expansion Coefficient- b -(1/K)
Thermal Conductivity- k -(W/(m×K))
Prandtl's Number- Pr -

2.52×10-05
2.55×10-03
0.0328
0.7

The resulting estimated air velocities for the different set points are in Table 20:

Table 20: Air velocity estimation results and intermediate calculations.
Set Point
Slope
h (W/(m2×K)
Nu Estimated
Re
Velocity ∞ (m/s)
Re
Velocity ∞ (m/s)
Re
Velocity ∞ (m/s)

V1
V2
V3
-0.02
-0.02
-0.01
104.5
90.6
61.9
20.3
17.6
12.0
Assuming Spherical Geometry
1252
940
421
4.95
3.72
1.67
Assuming Slab Geometry
1188
894
417
4.70
3.54
1.65
Assuming Ellipsoid Geometry
916
709
358
3.62
2.81
1.42

74

V4
-0.01
51.4
10.0

V5
-0.01
43.8
8.5

278
1.10

191
0.75

288
1.14

208
0.82

257
1.01

192
0.76

Microbial populations, almond aw (measured at room temperature), and
%MC from the air velocity experiments
The data set from the air velocity experiments used to do parameter estimation in 5.5 is
presented in Table 21.

Table 21: Inactivation data and grouping variables from the non-isothermal experiments.
Times
(s)
0

Log
(CFU/g)
8.05

60

Log(N/N0)

aw

%MC

%v/v (°C)

%v/v (g)

Air V.

Rep

aw0

Code

0.00

0.340

0.025

68.3

H

H

1

0.25

HH125

7.72

-0.33

0.453

0.029

68.3

H

H

1

0.25

HH125

120

6.42

-1.64

0.283

0.027

68.3

H

H

1

0.25

HH125

180

5.66

-2.39

0.305

0.023

68.3

H

H

1

0.25

HH125

240

5.31

-2.75

0.300

0.027

68.3

H

H

1

0.25

HH125

300

4.88

-3.17

0.261

0.025

68.3

H

H

1

0.25

HH125

0

7.55

0.00

0.640

0.059

68.3

H

H

1

0.65

HH165

60

6.18

-1.37

0.690

0.063

68.3

H

H

1

0.65

HH165

120

5.41

-2.14

0.515

0.056

68.3

H

H

1

0.65

HH165

180

5.35

-2.19

0.480

0.055

68.3

H

H

1

0.65

HH165

240

4.90

-2.65

0.512

0.054

68.3

H

H

1

0.65

HH165

300

3.19

-4.36

0.456

0.055

68.3

H

H

1

0.65

HH165

0

8.11

0.00

0.403

0.029

67.1

H

H

2

0.25

HH225

60

7.43

-0.67

0.539

0.030

67.1

H

H

2

0.25

HH225

120

6.47

-1.63

0.368

0.027

67.1

H

H

2

0.25

HH225

180

6.25

-1.86

0.317

0.025

67.1

H

H

2

0.25

HH225

240

5.50

-2.61

0.311

0.030

67.1

H

H

2

0.25

HH225

300

5.17

-2.93

0.298

0.026

67.1

H

H

2

0.25

HH225

0

7.65

0.00

0.649

0.063

67.1

H

H

2

0.65

HH265

60

6.59

-1.06

0.636

0.061

67.1

H

H

2

0.65

HH265

120

6.15

-1.50

0.536

0.056

67.1

H

H

2

0.65

HH265

180

5.53

-2.12

0.496

0.060

67.1

H

H

2

0.65

HH265

240

4.80

-2.85

0.499

0.058

67.1

H

H

2

0.65

HH265

300

4.37

-3.29

0.439

0.053

67.1

H

H

2

0.65

HH265

0

8.19

0.00

0.521

0.027

67.8

H

H

3

0.25

HH325

60

7.33

-0.86

0.488

0.031

67.8

H

H

3

0.25

HH325

120

6.94

-1.25

0.285

0.027

67.8

H

H

3

0.25

HH325

180

7.01

-1.18

0.321

0.029

67.8

H

H

3

0.25

HH325

240

6.24

-1.95

0.319

0.027

67.8

H

H

3

0.25

HH325

300

5.25

-2.94

0.267

0.023

67.8

H

H

3

0.25

HH325

360

5.26

-2.93

0.293

0.028

67.8

H

H

3

0.25

HH325

75

Table 21 (cont’d)
Times
(s)
0

Log
(CFU/g)
7.96

60

Log(N/N0)

aw

%MC

%v/v (°C)

%v/v (g)

Air V.

Rep

aw0

Code

0.00

0.642

0.056

67.8

H

H

3

0.65

HH365

6.96

-1.00

0.459

0.056

67.8

H

H

3

0.65

HH365

120

6.37

-1.59

0.574

0.056

67.8

H

H

3

0.65

HH365

180

5.96

-2.01

0.567

0.064

67.8

H

H

3

0.65

HH365

240

5.00

-2.97

0.476

0.054

67.8

H

H

3

0.65

HH365

300

3.67

-4.29

0.485

0.050

67.8

H

H

3

0.65

HH365

360

4.78

-3.19

0.419

0.048

67.8

H

H

3

0.65

HH365

0

7.97

0.00

0.364

0.032

18.6

L

H

1

0.25

LH125

1200

5.80

-2.16

0.175

0.019

18.6

L

H

1

0.25

LH125

1800

5.19

-2.78

0.136

0.010

18.6

L

H

1

0.25

LH125

2400

4.39

-3.58

0.141

0.014

18.6

L

H

1

0.25

LH125

3000

4.33

-3.63

0.163

0.013

18.6

L

H

1

0.25

LH125

3600

3.49

-4.48

0.129

0.016

18.6

L

H

1

0.25

LH125

0

6.92

0.00

0.670

0.068

18.6

L

H

1

0.65

LH165

600

7.22

0.29

0.361

0.088

18.6

L

H

1

0.65

LH165

1800

4.16

-2.76

0.218

0.009

18.6

L

H

1

0.65

LH165

2400

3.78

-3.14

0.239

0.031

18.6

L

H

1

0.65

LH165

3000

1.90

-5.02

0.261

0.030

18.6

L

H

1

0.65

LH165

0

7.91

0.00

0.397

0.027

19.0

L

H

2

0.25

LH225

600

6.67

-1.24

0.176

0.019

19.0

L

H

2

0.25

LH225

1200

6.07

-1.84

0.278

0.022

19.0

L

H

2

0.25

LH225

1800

5.30

-2.60

0.158

0.016

19.0

L

H

2

0.25

LH225

2400

5.24

-2.67

0.168

0.015

19.0

L

H

2

0.25

LH225

3000

4.93

-2.98

0.172

0.016

19.0

L

H

2

0.25

LH225

3600

3.30

-4.60

0.144

0.010

19.0

L

H

2

0.25

LH225

0

7.77

0.00

0.651

0.065

19.0

L

H

2

0.65

LH265

1200

4.61

-3.16

0.376

0.034

19.0

L

H

2

0.65

LH265

1800

3.72

-4.05

0.238

0.039

19.0

L

H

2

0.65

LH265

2400

3.73

-4.04

0.235

0.030

19.0

L

H

2

0.65

LH265

3000

3.62

-4.15

0.183

0.022

19.0

L

H

2

0.65

LH265

3600

2.05

-5.72

0.106

0.024

19.0

L

H

2

0.65

LH265

0

8.21

0.00

0.378

0.027

18.5

L

H

3

0.25

LH325

600

7.32

-0.88

0.201

0.024

18.5

L

H

3

0.25

LH325

1200

6.67

-1.53

0.166

0.014

18.5

L

H

3

0.25

LH325

1800

6.17

-2.03

0.148

0.017

18.5

L

H

3

0.25

LH325

2400

5.47

-2.73

0.160

0.012

18.5

L

H

3

0.25

LH325

3000

2.78

-5.42

0.168

0.017

18.5

L

H

3

0.25

LH325

3600

4.34

-3.87

0.123

0.010

18.5

L

H

3

0.25

LH325

0

8.05

0.00

0.656

0.041

18.5

L

H

3

0.65

LH365

1800

4.53

-3.52

0.218

0.028

18.5

L

H

3

0.65

LH365

76

Table 21 (cont’d)
Times
(s)
2400

Log
(CFU/g)
4.89

3000

Log(N/N0)

aw

%MC

%v/v (°C)

%v/v (g)

Air V.

Rep

aw0

Code

-3.16

0.225

0.024

18.5

L

H

3

0.65

LH365

4.71

-3.34

0.120

0.012

18.5

L

H

3

0.65

LH365

3600

2.64

-5.41

0.159

0.021

18.5

L

H

3

0.65

LH365

0

7.63

0.00

0.339

0.026

67.3

H

L

1

0.25

HL125

60

7.84

0.21

0.684

0.039

67.3

H

L

1

0.25

HL125

120

7.86

0.23

0.704

0.037

67.3

H

L

1

0.25

HL125

180

7.06

-0.57

0.557

0.036

67.3

H

L

1

0.25

HL125

240

6.69

-0.94

0.523

0.029

67.3

H

L

1

0.25

HL125

300

6.57

-1.06

0.459

0.034

67.3

H

L

1

0.25

HL125

360

5.24

-2.39

0.345

0.033

67.3

H

L

1

0.25

HL125

0

7.58

0.00

0.645

0.065

67.3

H

L

1

0.65

HL165

60

7.06

-0.52

0.834

0.073

67.3

H

L

1

0.65

HL165

120

6.71

-0.87

0.742

0.063

67.3

H

L

1

0.65

HL165

180

6.15

-1.43

0.746

0.073

67.3

H

L

1

0.65

HL165

240

4.99

-2.59

0.693

0.063

67.3

H

L

1

0.65

HL165

300

5.14

-2.44

0.654

0.061

67.3

H

L

1

0.65

HL165

360

4.59

-2.99

0.593

0.066

67.3

H

L

1

0.65

HL165

0

7.86

0.00

0.347

0.029

66.9

H

L

2

0.25

HL225

60

7.83

-0.02

0.532

0.032

66.9

H

L

2

0.25

HL225

120

5.95

-1.90

0.719

0.038

66.9

H

L

2

0.25

HL225

180

6.64

-1.21

0.606

0.035

66.9

H

L

2

0.25

HL225

240

6.07

-1.79

0.516

0.034

66.9

H

L

2

0.25

HL225

300

5.89

-1.97

0.461

0.034

66.9

H

L

2

0.25

HL225

360

5.15

-2.71

0.428

0.033

66.9

H

L

2

0.25

HL225

0

7.67

0.00

0.648

0.064

66.9

H

L

2

0.65

HL265

60

6.71

-0.96

0.799

0.065

66.9

H

L

2

0.65

HL265

180

5.10

-2.58

0.793

0.067

66.9

H

L

2

0.65

HL265

240

5.15

-2.53

0.730

0.070

66.9

H

L

2

0.65

HL265

300

5.26

-2.41

0.604

0.071

66.9

H

L

2

0.65

HL265

360

4.84

-2.84

0.562

0.059

66.9

H

L

2

0.65

HL265

0

8.03

0.00

0.376

0.030

67.3

H

L

3

0.25

HL325

60

7.73

-0.30

0.694

0.039

67.3

H

L

3

0.25

HL325

120

7.63

-0.39

0.615

0.034

67.3

H

L

3

0.25

HL325

180

7.23

-0.79

0.578

0.034

67.3

H

L

3

0.25

HL325

240

6.18

-1.85

0.524

0.037

67.3

H

L

3

0.25

HL325

300

5.97

-2.05

0.482

0.034

67.3

H

L

3

0.25

HL325

360

5.80

-2.22

0.461

0.033

67.3

H

L

3

0.25

HL325

0

8.36

0.00

0.637

0.061

67.3

H

L

3

0.65

HL365

60

7.27

-1.09

0.840

0.071

67.3

H

L

3

0.65

HL365

180

6.63

-1.73

0.775

0.068

67.3

H

L

3

0.65

HL365

77

Table 21 (cont’d)
Times
(s)
240

Log
(CFU/g)
5.71

300

Log(N/N0)

aw

%MC

%v/v (°C)

%v/v (g)

Air V.

Rep

aw0

Code

-2.65

0.721

0.075

67.3

H

L

3

0.65

HL365

6.08

-2.28

0.608

0.054

67.3

H

L

3

0.65

HL365

360

6.10

-2.26

0.583

0.058

67.3

H

L

3

0.65

HL365

0

8.43

0.00

0.331

0.028

11.8

L

L

1

0.25

LL125

600

7.81

-0.62

0.138

0.022

11.8

L

L

1

0.25

LL125

1200

7.61

-0.81

0.105

0.020

11.8

L

L

1

0.25

LL125

1800

6.60

-1.83

0.084

0.017

11.8

L

L

1

0.25

LL125

2400

6.36

-2.07

0.091

0.016

11.8

L

L

1

0.25

LL125

3000

6.56

-1.87

0.068

0.014

11.8

L

L

1

0.25

LL125

3600

5.89

-2.54

0.072

0.013

11.8

L

L

1

0.25

LL125

0

8.14

0.00

0.651

0.062

11.8

L

L

1

0.65

LL165

600

7.03

-1.11

0.343

0.056

11.8

L

L

1

0.65

LL165

1200

6.44

-1.70

0.293

0.036

11.8

L

L

1

0.65

LL165

1800

6.57

-1.57

0.171

0.037

11.8

L

L

1

0.65

LL165

2400

5.59

-2.55

0.179

0.028

11.8

L

L

1

0.65

LL165

3000

5.25

-2.89

0.149

0.025

11.8

L

L

1

0.65

LL165

3600

4.27

-3.87

0.090

0.016

11.8

L

L

1

0.65

LL165

0

8.25

0.00

0.429

0.031

16.4

L

L

2

0.25

LL225

600

8.11

-0.14

0.226

0.026

16.4

L

L

2

0.25

LL225

1200

7.60

-0.66

0.208

0.020

16.4

L

L

2

0.25

LL225

1800

7.03

-1.22

0.163

0.018

16.4

L

L

2

0.25

LL225

2400

6.33

-1.92

0.157

0.019

16.4

L

L

2

0.25

LL225

3000

5.75

-2.51

0.144

0.019

16.4

L

L

2

0.25

LL225

0

8.20

0.00

0.626

0.063

16.4

L

L

2

0.65

LL265

600

7.50

-0.70

0.415

0.050

16.4

L

L

2

0.65

LL265

1200

6.75

-1.45

0.300

0.050

16.4

L

L

2

0.65

LL265

1800

6.19

-2.01

0.256

0.052

16.4

L

L

2

0.65

LL265

2400

5.58

-2.62

0.235

0.051

16.4

L

L

2

0.65

LL265

3000

4.67

-3.53

0.262

0.033

16.4

L

L

2

0.65

LL265

0

8.44

0.00

0.318

0.028

12.4

L

L

3

0.25

LL325

600

8.16

-0.28

0.138

0.025

12.4

L

L

3

0.25

LL325

1200

7.89

-0.55

0.133

0.021

12.4

L

L

3

0.25

LL325

1800

7.18

-1.26

0.117

0.019

12.4

L

L

3

0.25

LL325

2400

6.79

-1.64

0.095

0.017

12.4

L

L

3

0.25

LL325

3000

6.49

-1.95

0.119

0.021

12.4

L

L

3

0.25

LL325

0

8.34

0.00

0.646

0.070

12.4

L

L

3

0.65

LL365

600

7.74

-0.61

0.291

0.049

12.4

L

L

3

0.65

LL365

1200

7.02

-1.32

0.225

0.040

12.4

L

L

3

0.65

LL365

1800

6.67

-1.68

0.222

0.037

12.4

L

L

3

0.65

LL365

2400

5.78

-2.56

0.159

0.031

12.4

L

L

3

0.65

LL365

78

Table 21 (cont’d)
Times
(s)
3000

Log
(CFU/g)
6.12

3600

5.38

Log(N/N0)

aw

%MC

%v/v (°C)

%v/v (g)

Air V.

Rep

aw0

Code

-2.22

0.136

0.027

12.4

L

L

3

0.65

LL365

-2.96

0.135

0.029

12.4

L

L

3

0.65

LL365

79

Temperature profiles
Summary of the temperature profiles used in the experiments; the frequency adjusted to show 20 data points per curve.
Table 22: Summary of temperature profiles of the non-isothermal experiments.
Time

HH125

HH165

HH225

HH265

HH325

HH365

HL125

HL165

HL225

HL265

HL325

HL365

0

32.9

31.8

32.5

28.3

29.5

29.3

25.3

24.0

33.9

29.6

32.0

35.5

18

69.2

67.9

76.7

76.2

80.6

69.3

59.6

59.2

63.5

63.8

59.9

59.7

36

76.6

75.8

84.5

83.9

87.3

75.6

64.5

65.2

68.3

69.7

65.6

65.1

54

82.5

83.0

90.3

90.7

93.9

81.3

67.5

68.0

70.4

71.8

68.7

67.7

72

85.7

89.6

96.4

101.8

98.0

87.9

68.8

70.5

73.7

75.9

71.3

67.3

90

90.3

94.8

99.7

105.1

102.6

92.8

70.5

72.5

75.1

77.3

73.0

70.4

108

94.7

98.8

102.7

107.9

106.2

96.3

71.8

74.9

76.6

78.4

74.9

70.9

126

100.5

102.7

105.0

109.9

110.5

98.4

76.2

78.7

77.9

76.1

77.5

74.6

144

103.7

105.2

107.2

111.6

112.5

102.3

77.9

80.2

79.3

77.7

78.9

74.9

162

106.3

107.3

109.4

113.1

113.9

104.7

79.7

81.9

80.9

79.3

80.8

75.8

180

108.4

109.1

110.7

114.0

114.9

106.7

81.8

83.2

82.7

80.8

81.6

74.7

198

108.9

109.1

114.3

113.5

115.8

106.9

82.3

83.8

82.6

82.3

87.0

78.2

216

110.6

110.5

114.9

114.6

116.8

108.4

84.3

85.4

84.2

83.6

88.4

80.8

234

112.0

111.7

115.6

115.5

118.2

110.4

86.2

87.1

85.8

84.7

89.9

82.4

252

115.4

110.4

112.2

115.7

117.8

113.0

87.7

84.2

88.2

90.0

96.4

82.7

270

116.2

111.6

113.6

116.4

118.4

113.8

89.5

86.1

89.7

91.4

97.8

84.5

288

116.9

112.5

114.0

117.6

118.6

114.9

91.1

87.9

91.2

92.7

99.2

85.7

306

116.9

116.8

114.6

117.0

117.7

113.4

93.8

87.5

92.5

92.6

101.9

88.5

324

117.5

117.2

114.6

117.0

118.2

114.3

95.4

89.2

93.7

93.7

102.8

89.7

342

118.0

117.8

114.6

117.0

113.4

114.9

97.0

90.9

95.0

95.3

103.7

91.1

360

118.4

118.1

114.6

117.0

118.4

115.6

98.4

92.4

96.1

96.5

104.5

92.3

80

Table 22 (cont’d)
Time

LH125

LH165

LH225

LH265

LH325

LH365

LL125

LL165

LL225

LL265

LL325

LL365

0

30.7

29.2

30.9

30.0

29.2

28.7

27.1

25.9

28.2

27.0

29.8

28.7

180

110.5

62.8

64.0

61.3

70.5

54.7

49.5

44.7

49.7

38.7

46.6

44.1

360

118.3

74.6

76.3

73.0

82.6

70.7

57.2

51.9

57.3

44.2

54.0

50.3

540

119.7

82.9

84.3

81.7

90.0

79.1

63.3

57.8

63.0

49.2

60.4

55.8

720

120.2

89.6

90.8

88.3

95.6

86.2

68.2

63.0

67.8

53.8

66.0

61.0

900

120.2

95.2

96.0

93.7

100.6

92.0

73.1

67.5

71.7

58.1

70.9

65.0

1080

120.3

99.3

100.0

98.3

103.9

96.5

77.1

72.2

75.4

62.3

75.1

69.2

1260

120.4

102.9

103.5

101.9

106.6

100.8

80.6

76.0

78.8

66.0

78.8

73.0

1440

120.4

105.6

106.5

105.0

108.7

103.6

83.9

79.7

81.7

69.7

82.2

76.4

1620

120.4

108.1

108.7

107.5

110.4

106.3

86.9

83.1

84.5

73.2

85.1

79.4

1800

120.4

110.0

110.7

109.5

111.8

108.1

89.6

86.0

87.0

76.3

87.8

82.4

1980

120.3

111.6

112.2

111.3

113.1

110.2

91.9

88.8

89.3

79.3

90.3

85.1

2160

120.4

112.9

113.5

112.7

114.4

111.5

94.3

91.1

91.5

82.1

92.5

87.5

2340

120.3

114.1

114.6

113.8

115.5

112.8

96.3

93.3

93.5

84.7

94.6

89.9

2520

120.5

115.0

115.5

114.8

116.3

113.8

98.2

95.3

95.4

86.9

96.5

92.0

2700

120.5

115.8

116.2

115.6

117.0

114.7

100.0

97.2

97.2

89.3

98.2

93.9

2880

120.4

116.5

116.8

116.3

117.6

115.5

101.6

98.9

98.9

91.4

99.8

95.8

3060

120.6

117.0

117.3

116.8

118.0

116.2

103.1

100.5

100.5

93.3

101.3

97.3

3240

120.4

117.5

117.8

117.3

118.4

116.7

104.5

102.0

101.7

95.1

102.6

98.9

3420

120.6

117.8

118.2

117.7

118.7

117.2

105.7

103.3

103.2

96.7

103.9

100.3

3600

120.0

118.1

118.5

118.0

118.9

117.6

106.9

104.5

104.5

98.3

105.1

101.6

81

Reference conditions optimization
To minimize the correlation among parameters of the inactivation models, a matrix of the
reference conditions was created, the model fitted through all possible combinations changing the
reference conditions simultaneously, selecting the conditions in which the entrance of the variance
covariance matrix where minimized by exploration of the resulting response surface and contour
plots.
ZT - ZM

DRef - ZT

Figure 20: Optimization contour plots for the DLM model.

82

Figure 20 (cont’d)
DRef - ZM

83

Scaled sensitivity coefficients
The SSC plots for the model DLMV and DLMCM2V, are reported here. SSC for the model
DLMV are similar to those of the DLM model with a visible because of the different air velocities.
Because air velocity was considered in the model as a categorical variable the simulated profiles
used to estimate the SSC consider low velocity for the first 600 s and high velocity for the later
600 s. The SSC for the CLMCM2V model, show a significant correlation among ZT and ZM, in
the decreasing due point conditions, and lower correlation in the increasing, however difficult, the
parameters remain identifiable with larger level of uncertainty.

Dref
Dref

ZM

ZT

Îłv

Îłv

ZT
Yobs

ZM
Yobs

Figure 21: SSC for the DLMV model.

84

ZMC
ZMC
ZM
Dref
Dref
Îłv
Îłv
ZM

Yobs

Yobs

Figure 22: SSC for DLMCM2V model.

In the SSC at under decreasing dew point (Figure 22 left) the SSC for ÎłV is not visible,
meaning it cannot be identifiable under those conditions. Is visible and identifiable in the
increasing dew point (Figure 22 right), indicating that is more likely to be identifiable based on
data from high process humidity and high velocity.

85

Estimated parameters of other models tested
The following model were tested but are not presented in the main document because of
poor performance or the lack of improvement in the final outputs.
Model DLMC eqn [15] was previously used by Casulli, (2016) to describe the effect of
changing %MC in the inactivation of Salmonella in pistachios. However, the model did not fit the
data of this experiment properly, estimated values for ZMC were very large making the general
effect of %MC insignificant.

Table 23: Estimated parameter for the DMLC model eqn [15].
Tref
Tdref
MCref
Dref
ZT
ZM
ZMC

Estimate
80
55
1
182
68.9
61.9
1.72×108

SE

t-Stat

p-Value

5.26
16.3
5.95
1.18×10-15

34.58
4.23
10.40
1.46×1023

2.31×10-73
4.01×10-5
2.03×10-19
0

Number of observations: 153, Error degrees of freedom: 150
Root Mean Squared Error: 0.615
R-Squared: 0.802, Adjusted R-Squared 0.8
F-statistic vs. constant model: 304, p-value = 1.61e-53

Model DLMMC eqn [16], considers ZT as linear function of %MC. ZT0 corresponds to the
theoretical ZT at 0% MC (i.e., 77.5°C), ZMC to the slope, and %MC(t) to the moisture content (g
H2O/g Dry) at any time. It was disregarded because the estimated ZMC had a very large standard
error that indicated that the parameter was not different from 0 and therefore makes the effect of
temperature undetermined.

86

Table 24: Estimated parameters of the DLMMC model eqn [16].
Tref
Tdref
MCref
Dref
ZMC
ZM

Estimate
80
55
1
185.15
-205.35
62.11

SE

t-Stat

p-Value

6.47
302.99
5.09

28.62
-0.68
12.194

1.21×10-62
0.50
3.37×10-24

Number of observations: 153, Error degrees of freedom: 150
Root Mean Squared Error: 0.614
R-Squared: 0.803, Adjusted R-Squared 0.8
F-statistic vs. zero model: 647, p-value = 1.47e-85

87

MatLabÂŽ Code
These are the commented example codes that were used in this dissertation. Examples of
the formatted data source had been added when convenient to facilitate the use of the programs.
clc
clear all
close all
format compact
global TP Tref Tdref zT zM
%% DATA IMPORT
[~, ~, raw] = xlsread('location of the data’); % Adjust the path as necessary

The data was set up as follow to be imported:
Times

LogRaw

Log(CFU/g)

aw

%MC

%v/v (ẋ)

%v/v (g)

Air V.

Rep

aw0

Code

0

8.05

0.00

0.340

0.025

68.3

H

H

1

0.25

HH125

60

7.72

-0.33

0.453

0.029

68.3

H

H

1

0.25

HH125

…

…

…

…

…

…

…

…

…

…

…

3000

6.12

-2.22

0.136

0.027

12.4

L

L

3

0.65

LL365

3600

5.38

-2.96

0.135

0.029

12.4

L

L

3

0.65

LL365

raw(cellfun(@(x) ~isempty(x) && isnumeric(x) && isnan(x),raw)) = {''};
cellVectors = raw(:,[7,8,11]);
raw = raw(:,[1,2,3,4,5,6,9,10]);
data1 = reshape([raw{:}],size(raw));
data = table;
data.Times = data1(:,1);
data.LogRaw=data1(:,2);
data.LogCFUg = data1(:,3);
data.aw = data1(:,4);
data.MC = data1(:,5);
data.vv = data1(:,6);
data.vvg = cellVectors(:,1);
data.AirV = cellVectors(:,2);
data.Rep = data1(:,7);
data.aw0 = data1(:,8);
data.Code = cellVectors(:,3);
clearvars data1 raw cellVectors;
% This code generates a table with the data
%% REFERENCE CONDITIONS
Tref=80; % Optimized to reduce correlation in the DLM model
Tdref=55; % Optimized to reduce correlation in the DLM model
%% GLOBAL FITTING
% Loading Temperature Profiles

88

The excel file has 1 tab for each condition; the tab label is consistent with the code used
to identify each data set to match the inactivation data and the temperature, aw, and %MC
profiles. Each tab has the information arrange as follow:
Time (s)

Temperature (°C)

%MC

aw

0.0

31.8

0.059453

0.643733

2.0

48.3

0.059471

0.642113

…

…

…

…

358.0

118.3

0.047912

0.420021

360.0

118.1

0.047749

0.41865

tl=unique(data.Code); % Identify the tabs that need to import from excel
file.
for i=1:length(tl)
TP{i}=xlsread('location of the data’,tl{i}); % Adapt path as necessary
end
%% GLOBAL DDM FITTING
Dref=100; % Initial value estimated from previous works
zT=32.4; % Initial value From Garces et.al. 2016 (ICPMF)
zM=60; % Initial value estimated based in optimal conditions from Jeong
et.al., 2009.
dll=fitnlm([data.Times,data.vv],data.LogCFUg,@DDM,[Dref zT zM ]) % This code
perform the fitting using nlinfit and generates a cell array with the result
of the fitting and other parameter estimation useful data.
R=corrcov(dll.CoefficientCovariance) % Generates the variance-covariance
matrix.
%% FUNCTION DDM
function y=DDM(beta,x)
global TP Tref Tdref
Dref =beta(1);
zT=beta(2);
zM=beta(3);
t=x(:,1);
td=x(:,2);
for l=1:length(t)
if t(l)==0;
N(l)=0;
else
for k=1:size(TP,2)
ST=[TP{1,k}];
li=find(ST(:,1)==t(l));
a=(Tref-ST(1:li,2))./zT;
b=((Tdref-td(l))-(Tref-ST(1:li,2)))./zM;
EqS= 1./(Dref*10.^(a+b));
N(l)=-trapz(ST(1:li,1),EqS);
if l<length(t)
if t(l+1)==0
k=k+1;

89

end
end
end
end
end
y=N';
end
%% CATEGORICAL EFFECT OF AIR VELOCITY
zV=0.5; % Initial value for the effect of air velocity
VarV=strcmp(data.AirV,'H'); % Transform the variable data.AirV to 0 and 1
dllV=fitnlm([data.Times,data.vv,VarV],data.LogCFUg,@DDMVel,[Dref zC zM zV ])
R=corrcov(dllV.CoefficientCovariance)
%% FUNCTION DDMVel
function y=DDMVel(beta,x)
global TP PI Tref Tdref MCref
Dref =beta(1);
zT=beta(2);
zM=beta(3);
zV=beta(4);
t=x(:,1);
td=x(:,2);
V=x(:,3);
for l=1:length(t)
if t(l)==0;
N(l)=0;
else
for k=1:size(TP,2)
ST=[TP{1,k}];
li=find(ST(:,1)==t(l));
a=(Tref-ST(1:li,2))./(zT);
b=((Tdref-td(l))-(Tref-ST(1:li,2)))./(zM);
EqS= (1-zV.*V(l))./(Dref*10.^(a+b));
N(l)=-trapz(ST(1:li,1),EqS);
if l<length(t)
if t(l+1)==0
k=k+1;
end
end
end
end
end
y=N';
end

90

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91

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