Evaluation and Quantification of Heat Treatments Appliedto Food Preserves

Gonzalo Sacristán-Pérez-Minayo & Agustín León &

Juan Ignacio Reguera

Received: 1 April 2011 /Accepted: 16 September 2011 /Published online: 12 October 2011# Springer Science+Business Media, LLC 2011

Abstract The quantitative study of heat treatments forsterilisation uses the Bigelow model to calculate thesterilising value (F). Calculation of F requires theprevious determination of parameters D (decimal reduc-tion time at experimental temperature) and Z (thermal-death time parameter), obtained from the thermal-deathkinetics. Herein we compare two different methods,namely the Bigelow model and a predictive-type statisticalmethod, to calculate the sterilisation effect against Bacilluscoagulans spores when heat was applied to runner beanpreserves (variety: Helda). Samples were subjected tovarious autoclave treatments at working temperatures (Tai)of 105, 107, 110, and 115°C for periods from 3 to 35 min.The microorganism used was B. coagulans. Sterilisationachieved by these autoclave treatments was determined byusing the equation based on the Bigelow model (nprobe=Fz

Ti/DTi) where n is the fractional concentration of colony-forming units (or some quality factor), Fz

Ti is F attemperature Ti, and DTi is D at temperature Ti. TheBigelow model can be used to obtain Z (thermal-deathtime parameter), which is needed to calculate the tradi-

tional sterilisation factor F, but not to determine thereduction factor n for the heat treatments, particularlywhen microbial indicators with low decimal reductiontimes (D) are studied. The thermokinetic parameters for B.coagulans in runner bean solution resulted to be Z=10.64°Cand D121=0.0264 min (Af=1.04). Treatment at 115°C for20 min resulted in the most efficient sterilisation effect forB. coagulans.

Keywords Food preserves . Heat treatments . Bigelowmodel . Bacillus coagulans . Thermal-death kinetics

Introduction

The Bigelow model is frequently used to determine thethermokinetic parameters and the effects produced by heattreatments (Bigelow 1921). Microbial heat-death kineticswas first studied by Bigelow (1921) and Ball (1923), andlater by Stumbo (1973). The traditional Bigelow modelinvolves calculation of the sterilising value F, which itselfrequires the previous knowledge of parameters (decimalreduction time at experimental temperature), and Z (thermal-death time parameter), which are obtained from thethermal kinetics of the reference microorganism studied.Recent studies (León 2010) have pointed out that theBigelow model overestimates the effects produced to alarge degree, particularly when the sterilising effect isdetermined by using microorganisms with low D param-eters. Indeed, in these cases, the results provided bypredictive-type statistical models are more accurate toreflect the actual effects.

The thermal kinetics is based on quantifying the effect ofthe heat produced upon applying a constant temperature toa given point on a foodstuff as a function of the speed with

This work was presented at the XVII National Microbiology Congress(Valladolid, Spain) and recommended to the journal Food AnalyticalMethods.

G. Sacristán-Pérez-Minayo (*) : J. I. RegueraMicrobiology Section, Faculty of Sciences, University of Burgos,Pza. Misael Bañuelos s/n,09001 Burgos, Spaine-mail: gsacristan@ubu.es

A. LeónFood Technology Section, High School of AgriculturalEngineering, University of Valladolid,Avda. de Madrid 44,34004 Palencia, Spain

Food Anal. Methods (2012) 5:774–780DOI 10.1007/s12161-011-9307-0

which the changes caused by the increases of temperaturetake place. It can be formulated as:

dP

dt¼ �k � Pn

where P is the size of the property measured, k is aconstant of proportionality for that reaction, and n is thefractional concentration of colony-forming units (orsome quality factor). It is currently considered that,during analysis of properties of interest (changes to themicrobiota, nutritional components, or rheological prop-erties of the foodstuff), the n value is 1; thus, the kineticsin all these cases is of the first order (Arrhenius). In thecase of microbial heat-death kinetics, the property Pcorresponds to the number of viable bacteria and spores.In this case, the above equation can be expressed asfollows:

dN

dt¼ �k � N

Integrating the previous differential equation between aninitial time to and t

ZN

N0

dN

N¼ �k

Z t

0

dt ! Ln N � Ln No ¼ �k � t ! LnN0

N

� �

¼ k � t ! N0

N¼ e k�tð Þ

or

t ¼ logN0

N

� �� 2; 303

k

� �

or

t ¼ logN0

N

� �� D

where D is known as decimal reduction time, defined as theheating time at a constant temperature T required to reducea microbial population located at a specific point in thesubstrate tenfold. This equation indicates that a plot of thelogarithm of surviving microorganisms against exposuretime at a constant temperature T should be a straight linewith slope−1/D.

Such plots are known as survival plots and can beobtained by measuring the thermal history or behaviour ofa very small volume of a suspension of cells or spores whenexposed to a temperature T, with the heat resistance beingcharacterised by the parameter D. The different techniquesused to determine the heat resistance of microorganisms aredescribed below.

In real-life heat treatments, N0 is termed the initialinfection level, and the reduction factor is designated as nand is given by

n ¼ logN0 � logNf ¼ logN0

Nf

� �

The reduction factor n is designed such that thetreatment results in a sufficiently small population Nf thatthe foodstuff poses no health risk after its application. Theheat treatment can be expressed as a function of the aboveparameters (t=n×D). When different temperatures areassayed, D can be determined for each one, and valuesplotted in a semi-logarithmic scale as a function of the testtemperature also giving a linear plot. The parameter Z is ameasure of the relative heat-resistance capacity of themicrobial population and represents the temperature in-crease, required to reduce the reduction tenfold.

Calculation of the Sterilising Factor F

It is convenient to differentiate between ideal and realtreatments. Since although theoretically the effect ofheating is analysed by assuming that a constant temperatureis applied and that this heat reaches a certain point in thefoodstuff immediately, in fact, temperature changes occurduring an autoclave cycle, and their effect in a given pointdepends upon several characteristics. This critical pointshould be taken into account carefully.

The goal in ideal treatments is to calculate the lethaleffect (or duration) of a treatment tTi applied at aconstant temperature Ti by comparing it with another“reference” treatment. This reference treatment (tTref) isdefined by a given microorganism, a reference tempera-ture Tref, and a reducing effect of n units. The lethalityratio for the two treatments can be determined from theequivalent treatment effect plot for the reference treatmenttTref obtained at the reference temperature Tref for areduction factor.

tTI ¼ tT ref � 10Tref�Ti

Zð Þ

In order to make comparisons between the effect of twotreatments, the term basic lethal unit has been adopted forthe lethality of a treatment tTref applied at the referencetemperature Tref for 1 min (tTref=1 min) and a reductiveeffect of n units for the reference microorganism concerned.The lethality of a generic treatment tTi at a temperature Tiwith the same reductive effect n can be expressed as afunction of the lethality of the reference treatment using thequotient:

LTi ¼tT reftT i

Food Anal. Methods (2012) 5:774–780 775

This quotient is known as the modification ratio orlethality coefficient. Taking into account that tTref=1 minand the equation for tTi describing the lethality ratiobetween two treatments described above, the value of thelethality coefficient is given by the following expression:

LTi ¼ 10Ti�Tref

Z

� �

If the treatment tTi lasts for t minutes, the lethal effect is:

FT i ¼ LTi � t

The process described above is useful for a treatment atconstant temperature where the heating and cooling timesare negligible. In practice, this assumption is clearlyunuseful for real treatments as any such treatment neces-sarily involves a heating stage, followed by a period wherethe target temperature is maintained and then a coolingstage. Current practice for the heat treatment of food isbased on applying the most appropriate heating and coolingconditions such that the inevitable degradation of thenutrient and organoleptic quality factors are minimisedwith the aim of achieving a microbiologically safe andorganoleptically stable product (Casp and Abril 1999). Inlight of this, it is therefore necessary to determine the effectof the temperatures achieved during each of these threestages at the point in the foodstuff which warms up theslowest (critical point) and to calculate the lethal effect atthat point (Holdsworth and Simpson 2007). Indeed, thesterilising effect is studied at the critical point. A real heattreatment process can be considered to consist of a series ofindividual treatments produced by each of the temperaturesinvolved such that each temperature has a differentmodification ratio at the critical point. In this case, theoverall sterilising effect or F value is calculated bysumming the products of the modification ratios for eachtemperature during the time for which each is applied.

The sterilising effect F is normally assigned character-istic indices, in this case a subscript for the referencetemperature used and a superscript representing the char-acteristic Z parameter for the reference microorganism:

FZTref

¼X

10Ti�Tref

Zð Þ�Δ ti

In order to compare the effects produced by varioustreatments, it is interesting to characterise them on the basisof the working temperature (Tai) applied and the duration oreffect produced by that temperature: T t (time during whichTai is maintained or process time). Under these conditions,the expression for the reduction factor achieved by thetreatment is as follows:

n ¼ tZTaiDTai

Fresh vegetables have a short shelf life and are commonlykept under conditions which reduce their quality in a shortperiod of time before they are cooked or consumed. Due to theseasonal dependence of their harvesting, conservation tech-nologies must be applied to ensure that they maintain theirnutritional and organoleptic properties and to extend theirshelf life (Giannakourou and Taoukis 2003). The vastmajority of runner beans are either frozen or heat treatedrather than being consumed fresh (García et al. 2000). Thecurrent project was designed to study the spoilage micro-organisms found in runner bean (Phaseolus vulgaris)preserves, especially the survival of Bacillus coagulans.The preserve herein studied had a pH between 4.5 and 5since it contains lemon juice (Cameron and Esty 1940).

Spore-forming aerobic and anaerobic bacteria are chieflyresponsible for spoilage of vegetable preserves at these pHvalues, the genus Bacillus being the most common. Most ofthem are mesophiles although a few are thermophiles (55–70°C). Some of them are facultative anaerobes andsubsequently able to grow in hermetically sealed containers.Spoilage is commonly associated with Bacillus with acid andgas production (Bacillus macerans and Paenibacilluspolymyxa), or fermentation of carbohydrates with productionof acid but no gas (Bacillus stearothermophilus (pH>5) andB. coagulans (pH up to 4.2)) (Buchanan and Gibbons 1974).Spore-forming anaerobes are soil inhabitants and found invegetables. Some of them are saccharolytic and producelarge volumes of gas resulting in bloating of the packaging(Notermans 1993).

B. coagulans is responsible for the spoilage processknown as “flat souring” or “simple fermentation” inmedium- and low-acid vegetable preserves, which consistsof an attack on carbohydrates and gas-free acid production.Herein we compare the results obtained when using twodifferent models, namely the Bigelow model and apredictive-type statistical model, to calculate the sterilisa-tion effect against B. coagulans for heat treatments appliedto extra-thin runner bean preserves (variety: Helda).

Material and Methods

Bacterial Strain

B. coagulans 12T spores were obtained from the SpanishType Culture Collection (CECT). The preparation of B.coagulans spores suspension was performed according tothe manufacturer's instructions.

Autoclave Sterilisation Treatments

Trimmed runner beans cut into 2-cm pieces and blanched at85°C for 1.5 min were used to prepare the preserves used

776 Food Anal. Methods (2012) 5:774–780

herein. Cylindrical tin cans (425 mL) were used. The meancharacteristic weights of the preserves were 350 (netweight) and 200 g (drained weight). The brine was preparedusing water, NaCl (2% w/v), sugar (20 g/L), and lemonjuice (to a pH of 5). It was added to the containercontaining the product whilst hot (85 °C) and immediatelyafter placement of the probe described below. The contain-ers were sealed using an Ezquera 2026 sealer.

The containers were then submitted to a series ofautoclave treatments at the working temperatures (Tai)105, 107, 110 and 115°C for times (tai) of between 3 and35 min. A 30-L vertical autoclave (Autester E-30 Dry-PV;JP Selecta S.A., Barcelona, Spain) was used. Temperaturewas measured every 2 min.

The containers were removed from the autoclave at theend of the plateau phase after forced steam removal andimmersed in a cold water bath until the temperature haddropped to 35°C to avoid overcooking. A wireless probewas used to measure the product temperature at the criticalpoint in the container.

The probe's “xVacq” software was used to obtain theheat-penetration graphs for each treatment. In light of thepH of the preserve (5), B. coagulans was chosen as theindicator to evaluate the degree of sterilisation obtainedwith each treatment, and the procedure described by Hayes(1992) and Brennan et al. (1998), which establishes arecommended reduction factor of 5 or higher, was followedto select the best treatment.

The sterilising effects produced by these autoclavetreatments were determined using formula (4) based onthe Bigelow model, whereas the statistical method used realreduction factor data (nreal) obtained from the kinetics of B.coagulans at constant temperature.

Heat-Death Kinetics for B. coagulans

A direct method known as the mixing or flask method,consisting of heating a solution containing a small number

of spores and a large amount of substrate, was used toanalyse the heat death of B. coagulans. Since the substrateis heated before inoculation of the spores, inertia times arenegligible (Brown et al. 1988).

A solution of extra-thin runner beans prepared withwater (50% w/v), NaCl (2% w/v), sucrose (20 g/L) andlemon juice (to a pH of 5) was used. This mixture wasfinely triturated with a mixer, sterilised at 121°C for 15 minand filtered using a Millipore–MilliQ apparatus fitted with a0.40-μm filter and used to measure growth.

B. coagulans 12T spores were obtained from the SpanishType Culture Collection (CECT) and resuscitated in aliquid medium (tryptic soy broth; Oxoid CM 129, Basing-stoke, UK). The concentration and purity of B. coagulansspore suspensions were assessed during storage.

Tubes containing inoculated runner bean solution weresubjected to treatments in a water bath at constanttemperature, cooled in cold water and the spores counted.Counts were performed by duplicate; test temperatures (Tai)were 80, 90 and 95°C, with time intervals (treatment times;tai) of between 5 and 40 min. Each experiment was repeatedthree times.

logN = 8.44 - 0.047 tai

logN= 8.3302 – 0.1322 tai

4

5

6

7

8

9

0 10 20 30 40

tai (min)

log N

Tai= 80 oC

Tai= 90 oC

Tai= 95 oC

logN = 8.1025 - 0.0052 tai

Fig. 1 Survival curves for B. coagulans in runner bean solution(pH 5) at 80, 90 and 95°C

0

0.5

1

1.5

2

2.5

3

3.5

4

0 10 20 30 40

nre

al

tnreal ⋅DTai (min)

nreal = 0.1323 tnreal⋅D95

Tai = 80 °C

Tai = 90 °C

Tai = 95 °C

Fig. 3 Linearised survival curves for B. coagulans (the equation forthe survival curve at 95 °C for nreal is shown)

log DTai= 9.7964 – 0.094Tai

0.00

0.50

1.00

1.50

2.00

2.50

75 80 85 90 95 100

Tai (oC)

log DTai

Fig. 2 Equivalent heat-death treatment curves for B. coagulans inrunner bean solution (pH 5). D121=0.0264 min, Z=10.64°C

Food Anal. Methods (2012) 5:774–780 777

Results and Discussion

Heat-Death Kinetics for B. coagulans

The results of the tests performed at constant temperatureas regards the heat-death indicators for B. coagulans inextra-thin runner beans (variety: Helda) are shown inFigs. 1, 2 and 3. The survival curves for B. coagulansobtained by linear regression and the decimal reductiontimes at the test temperatures used can be seen in Fig. 1(D80=192.31 min, D90=21.28 min and D95=7.56 min).Figure 1 shows the heat-death plots for B. coagulans at 80,90 and 95°C.

The correlation coefficient, which measures the rela-tive ratio between the variables, was greater than 0.95 inall cases, thus indicating that the variables are stronglyinter-related, and as the value of p was less than 0.05 in

all cases, this relationship can be established with aconfidence level of 95%. The standard and absoluteerrors, which are used to evaluate the validity of thepredictive model based on these results, were lower atlower test temperatures (Table 1).

The values for Z (Z=10.64°C) and the decimal reductiontime at a temperature of 121°C (D121=0.0264 min) areshown in Fig. 2.

The value obtained for the decimal reduction time of B.coagulans (D121=0.0264 min) was within the rangesreported by Stumbo (1973) and Brennan et al. (1998)(0.01<D121<0.07). In contrast, the value calculated for theZ parameter (Z=10.64°C) was lower than the rangeproposed by Stumbo (1973) (14<Z<18) but slightly higherthan the value reported by Brennan et al. (1998) (Z=10°C).Correlation coefficient was −0.999913 and R2 (percent) was99.9825.

Table 2 Analysis of the validityof the heat-death kinetics forB. coagulans

nprobe Correction factorderived from the Bigelowmodel, n*real real theoreticalreduction factor

Autoclave treatment (process time at 95°C) Survival curve at 95°C Relative error (%)nreal=0.1323 tnreal�D95

Treatment tZ95(min) nprobe n*real

105°C–3 min 36.92 5.05 4.88 3.31

105°C–7 min 71.92 9.83 9.52 3.31

105°C–10 min 92.86 12.69 12.29 3.31

105°C–20 min 182.32 24.92 24.12 3.31

105°C–30 min 270.20 36.93 35.75 3.31

107°C–3 min 52.31 7.21 6.92 4.24

107°C–6 min 99.34 13.70 13.14 4.24

107°C–10 min 177.94 24.54 23.54 4.24

107°C–20 min 266.76 36.79 35.29 4.24

107°C–30 min 424.35 58.52 56.14 4.24

110°C–3 min 94.98 13.20 12.57 5.01

110°C–10 min 264.26 36.71 34.96 5.01

110°C–15 min 404.10 56.14 53.46 5.01

110°C–25 min 686.58 95.39 90.83 5.01

110°C–35 min 961.66 133.60 127.23 5.01

115°C–3 min 316.10 43.40 41.82 3.78

115°C–10 min 835.45 114.71 110.53 3.78

115°C–20 min 1,636.78 224.73 216.55 3.78

115°C–30 min 2,373.41 325.87 314.00 3.78

Table 1 Equations for the survival curves for B. coagulans and their statistical coefficients

Tai (°C) Equations for the survival curves Correlation coefficient R2 (%) Standard error Absolute error p value

80 log N=8.1025−0.0052 tai –0.999342 99.8685 0.0029453 0.00201462 <0.01

90 log N=8.44−0.047 tai –0.955082 91.2181 0.19386 0.115938 <0.05

95 log N=8.3302−0.1322 tai –0.985566 97.1341 0.308427 0.212797 <0.05

778 Food Anal. Methods (2012) 5:774–780

Validity Analysis of the Heat-Death Kinetics for B.coagulans

The results obtained using this method, which involvesdetermining the process times for the treatments at thehighest temperature used in the heat-death tests (in our case,95°C) and introducing them into the equation for thecorresponding survival curve, compare the reduction factorsobtained using the relative error function (percent).

The initial data used to obtain the linear survival curvesrequired to perform the previous correction can be found inTable 2. The corresponding graphs and the equation for thesurvival curve at 95°C for nreal are shown in Fig. 3.

The absolute value for the slope of the linearised survivalcurve at a temperature of 95°C was the same as that for thecorresponding survival curve (Fig. 1). The independent termwhen performing this type of correction is always zero.

The equation for the corrective factor required to applythe statistical method was as follows:

npred ¼ f Tai;Fð Þ ¼ �12:85þ 0:147911 � Tai þ 0:04485

�FðR2 ¼ 74:97Þ

It can be seen from Table 3 that the degree of oversizingof the Bigelow model was very high in all cases andincreased with treatment temperature. Indeed, for the boldand underlined treatment (treatment selected for n≥5), itwas higher than 4.280%.

In summary, the validity of these tests has been analysed,and the error arising when quantifying the autoclavetreatments using the Bigelow model was determined. TheBigelow model is a method for calculating the effects ofheat treatments that uses statistical estimates involving adouble use of the logarithmic function. However, it is wellknown that the use of such logarithm-based methods whendesigning process for the food industry can lead to poorlydimensioned results (Nevares 2002). In such cases, theproportional results provided by predictive-type statisticalmodels are considered to better reflect reality.

In this study, the behaviour of the Bigelow modelwhen used to calculate the sterilisation effect of heattreatments applied to extra-thin runner bean preserves(variety: Helda) has been studied. Finally, the values ofthe thermokinetic values for B. coagulans in runner beansolution (pH 5), as calculated on the basis of the resultsobtained in the present research, were Z=10.64°C andD121=0.0264 min (Af=1.04). Of the treatments analysedin this study, that which involved heating the sample to115°C for 20 min resulted in the best sterilisation effect(n≥5) for B. coagulans. As a final conclusion, theBigelow model can be used to obtain the Z parameter,which in turn can be used to calculate the traditionalsterilisation factor F but not the reduction factor nobtained by heat treatments in light of the large errorsinvolved, especially when microbial indicators with a lowdecimal reduction time are to be quantified (D).

Table 3 Oversizing of theBigelow model and selection ofthe ideal treatment

Treatment Process time Bigelow method Statistical method Oversizing

Tai (°C) tai (min) FZTai

(min) nprobe npred (%)

105 3 4.24 5.05 2.87 75.96

105 7 8.26 9.83 3.05 222.30

105 10 10.66 12.69 3.16 301.58

105 20 20.93 24.92 3.62 588.40

105 30 31.02 36.93 4.07 807.37

107 3 3.90 7.21 3.15 128.89

107 6 7.40 13.70 3.31 313.90

107 10 13.25 24.54 3.57 587.39

107 20 19.87 36.79 3.87 850.65

107 30 31.60 58.52 4.39 1,233.03

110 3 3.69 13.20 3.59 267.69

110 10 10.28 36.71 3.88 846.13

110 15 15.72 56.14 4.13 1,259.32

110 25 26.71 95.39 4.62 1,964.72

110 35 37.41 133.60 5.10 2,519.61

115 3 4.17 43.40 4.35 897.70

115 10 11.01 114.71 4.65 2,366.88

115 20 21.57 224.73 5.13 4,280.70

115 30 31.28 325.87 5.56 5,760.97

Food Anal. Methods (2012) 5:774–780 779

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