mathematical modeling of microbial growth in fresh filled pasta stored at different temperatures

MATHEMATICAL MODELING OF MICROBIAL GROWTH IN FRESH FILLED PASTA STORED AT DIFFERENT

TEMPERATURES

L. GIANNUZZI

Centro de Investigacibn y Desarrollo en Criotecnologia de Alimentos (CIDCA)

Facultad de Ciencias Exactas Universidad Nacional de La Plata

Calle 47 y I I6 (1900) La Plata, Argentina

Accepted for Publication May 14, 1998

ABSTRACT

Growth curves for a selection of pertinent microorganisms in ricotta and ricotta-filled ravioli were analyzed in terms of Gompertz’s model. The growth of Enterobacteriaceae, molds and yeasts and psychrotrophic microorganisms during storage at 0, 4, 8 and 10C was determined. Lag phase duration and specific growth rate were inversely related. The activation energies from an Arrhenius-type equation were calculated for the microorganisms under study. For ricotta samples, molds and yeasts were the most sensitive organisms showing E,, values of 74.60 KJoule/mol while Enterobacteriaceae and psychrotrophic microorganisms had E,, values of 24.30 and 25.70 KJoule/mol, respectively. For ricotta-filled ravioli samples, the three microorganisms showed activation energies in the range of 31.47-32.99 KJoule/mol; hence the temperature dependence of their growth rates was comparable. Results allow to predict microbial growth of different microorganisms in ricotta and ricotta-filled ravioli when exposed to different storage temperatures.

INTRODUCTION

Microbial spoilage of food is of great concern to producers, retailers and consumers. Growth of either pathogenic or spoilage organisms should be avoided for both safety and economic reasons.

Fresh filled pasta, particularly ravioli, are important products in Argentine- an market. The dough is prepared by mixing and mechanically kneading wheat

Telephone and FAX number: 54-21-249287/ 25-4853/ 89-0741, Email: 1edaQbiol.unlp.edu.ar

Journal of Food Processing Preservation 22 (1998) 433-447. All Rights Reserved. OCopyright I998 by Food & Nutrition Press, Inc., Trumbull, Connecticut. 433

434 L. GIANNUZZI

semolina, wheat flour, eggs, natural colors and preservatives and water. The filling is usually a mixture which may contain poultry, leafy vegetables, ricotta cheese, grated cheese, meat and spices. Since the manufacturing process for fresh pasta does not assure the elimination of microorganisms, good manufacturing practices procedure and hazard analysis and critical control points are highly recommended. The primary sources of contamination are raw ingredients and contamination during processing. Both the dough and the filling are good substrates for multiplication of microorganism and toxin production with a, = 0.93 and pH = 5.5 (Rodriguez ef al. 1991; Walsh ef al. 1974).

Predictive microbiology is emerging worldwide. The use of mathematical models to describe microorganisms' behavior is a helpful tool to improve food safety (Zwietering ef al. 1990; Buchanan 1993).

Generally, predictive models are built on the basis of data obtained from experiments run in liquid laboratory media. In these media, the values of different factors can be controlled more easily than in food products. The specific growth rate, and especially lag phase duration in a food, can be quite different from the values obtained in liquid media, even under the same environmental conditions. Thus, model validation in actual situations becomes a must before a model can be used for predictive purposes (McMeekin et al. 1992; Muermans ef al. 1993). At present, Gompertz equation has become the most widely used model to describe microbial growth (Gibson ef al. 1987; Gibson and Roberts 1989).

The goal of mathematical models, which allow calculation of lag phase and microbial growth rates, is to estimate microbial growth under storage conditions different from the originally tested ones (Buchanan 1993; Palumbo ef al. 1991, 1992).

Low storage temperatures play a major role in extending product shelf-life but refrigeration temperatures are hardly kept constant during food handling. Temperature effects on microbial stability has been studied quantitatively by computer supported models based on heat transfer and microbial growth estimations (McMeekin and Olley 1986; Fu et al. 1991; Almonacid-Merino and Torres 1993; Li and Torres 1993). The effectiveness of chilling storage as a preservation method depends on the initial quality of the raw material and time- temperature conditions. Commonly, during food transportation thermal oscillations reduce product shelf-life (Field 1989).

The objectives of the present work were (1) to analyze the effect of storage temperature (0, 4, 8 and 1OC) on microbial growth parameters obtained by fitting a mathematical model to experimental counts of different microorganisms (Enterobacten'aceae, psychrotrophic microorganisms and molds and yeast) growing in ricotta and ricotta-filled ravioli and (2) to evaluate the effect of temperature on the lag phase and the specific growth rate parameters using different equations. This information allows the prediction of microbial growth

TEMPERATURE EFFECT ON MICROBIAL GROWTH 435

under conditions different from those tested experimentally but within the studied range of temperatures.

MATERIAL AND METHODS

The samples of ricotta and ricotta-filled ravioli were obtained from an Italian-style fresh pasta manufacturing plant in La Plata region, Argentina. Storage experiments were performed at 0, 4, 8 and 1OC. Sample temperatures were measured by inserting needle-type thermocouple sensors attached to a Fluke 2240 C Data Logger. The pH was determined with an Ingold lot 405 m4 electrode. The moisture content was determined gravimetrically in duplicate by drying at 105C (under atmospheric pressure) until constant weight. The results were expressed as g of water per 100 g of initial sample. The water activity (aJ of samples was assessed in a Novasina Thermoconstanter Humidat TH2/TH1 that measures the equilibrium air relative humidity over the food sample in a small thermostatized sealed chamber. The relative humidity (RH) sensor, was calibrated with saturated solutions of K2Cr207, BaC1,.2H20, NaCl and MgN0,.6H20, with relative humidities of 98, 90, 75 and 53%, respectively.

Microbiological Determinations

Samples of 20 g were homogenized for 1 mia with 180 mL of 0.1% peptone water in a stomacher. Dilutions with 0.1 % peptone water were then performed to prepare the culture media for the following microbial determinations:

(1) Psychrotrophic microorganisms: 1 mL of the necessary dilutions was inoculated in Plate Count Agar (Merck) and incubated at 4C for 7 days.

(2) Enterobacteriaceae counts: 0.1 mL of the necessary dilutions was inoculated in Bilk red violet glucose agar (Merck) and incubated at 37C for 12 to 24 h.

(3) Mold and yeast count: 0.1 mL of the necessary dilutions was inoculated in YGC Agar (Yeast extract, Glucose, Cloramphenicol), (Merck) with incubation at 25C for 5 days.

Determinations were made in duplicate and the results were expressed as Log N (N: Colony Forming Units expressed as logCFU/g).

Microbial Growth Modeling

The finished product (ricotta-filled ravioli) and a raw material (ricotta, constituent of the filling) were both stored at 0, 4, 8 and 1OC. During these

436 L. GIANNUZZI

storage experiments, samples of ricotta and ravioli were periodically taken to quantify Enterubacteriaceue, psychrotrophic microorganisms and molds and yeasts. The modified-Gompertz equation was applied to experimental data counts (Gibson et al. 1987):

(1) log N = log No + c - exp(-exp(-b(t-m)))

where:

log N

NO

C

b

m

is the decimal logarithm of microbial counts at time t [log (CFU/g)].

the initial count (approximately equivalent to the initial number of bacteria) [log (CFU/g)].

is the difference in log counts between the inoculum and the stationary phase [log (CFU/g)]

is the relative maximum growth rate at time m [days]-'.

is the time required to reach the maximum growth rate [days].

From these parameters, the following information was derived:

Specific growth rate p = b - c/ exp (1) [log (CFU/g) days-'], Lag phase duration (LPD) = m - (l/b) [days] Maximum population density MPD = log No + c [log (CFU/g)]

Statistical Analysis

Data fits obtained from Gompertz model were performed by means of a statistical software (Systat, Inc 1990). The Systat software calculates the set of parameters with the lowest residual sum of squares (RSS) and their 95% confidence interval. It also provides for each data fit, the sum of squares, the degree of freedom (DF) and the mean square due to the regression and due to the residual variation. The error propagation procedure was used to calculate the error of the derived parameters p and LPD (Himmelblaum 1970).

RESULTS AND DISCUSSION

Fitting of Mathematical Model to Microbial Growth Curves

Since the water activity (a,,,) of ricotta filling and ricotta-filled ravioli varied between 0.97 and 0.96 with a moisture content (wet basis) of 30-31 %, and pH between 5.8-6.2, these foods were good substrates for microbial growth.


Figures 1 a, b, c, and 2 a, b and c show the fitting of Gompertz model to experimental data of microbial growth in ricotta as raw material and ricotta- filled ravioli, respectively. In all cases, a good agreement between experimental data and fitted values was obtained; a minimum of 10 data points were determined per curve and each point was the mean of two microbial counts.

The final microbial counts were similar to data reported by Pasolini er al. (1981) who examined 250 samples of pasta produced by 15 different manufacturers. In fact 30% of the samples were shown to have bacterial counts above lo9 CFU/g and molds contamination of the same order in 11 % of the samples. The frequency of samples contaminated with coliforms was rather high (7 1 % , from 3 to 1100 microorganisms/g). A survey performed on fresh pasta by Spicher (1976) in the former Federal Republic of Germany on 74 samples from 6 manufacturers showed microbial contamination levels similar to those of the previously cited authors.

The derived parameters: exponential microbial growth rate (p) , lag phase duration (LPD) and maximum population density (MPD) for microorganisms growing in ricotta and ricotta-filled ravioli samples are shown in Table 1. In ricotta samples, psychrotrophic microorganisms grew at the highest rates, with p values ranging from 1.95 log (CFU/g) days-' to 2.80 log (CFU/g) days-'. Lag phase duration diminished from 1.06 days to 0.11 days for 0 and lOC, respectively. Enrerobacreriaceae showed p and LPD values of 0.94 log (CFU/g) days-' and 3.78 days at OC, respectively; at 1OC the corresponding values were 1.58 log (CFU/g) days-' and 0.86 days. Molds and yeast grew at the lowest rates with p values of 0.18 log (CFU/g) days-' at OC and 0.62 log (CFU/g) days-' at 1OC; LPD values were 1.43 days at OC and 0.92 days at 1OC.

In ricotta filled ravioli samples, psychrotrophic microorganisms grew at the highest rates. For psychrotrophic microorganisms when temperature increased from 0 to lOC, p values changed from 1.63 log (CFU/g)days-' to 2.55 (log CFU/g)days-' and LPD decreased from 1.11 days to 0.18 days. Enrerobacreria- ceae grew at the lowest rates (0.65 log (CFU/g) days-' at OC and 1.07 log (CFU/g)days-' at lOC); LPD decreased from 1.71 days to 0.22 days when temperature increased from 0 to IOC. Molds and yeast showed j~ values of 0.59 log (CFU/g)days-' at OC and 0.98 log (CFU/g) days -' at 1OC; LPD values were 1.29 days at OC and 0.15 days at 1OC.

The initial counts and MPD were higher in ricotta-filled ravioli samples than in ricotta for all microorganisms considered. Psychrotrophic microorganisms were the microorganisms with the highest MPD values ranging from 8.69 logCFU/g to 9.00 logCFU/g. Enferobacreriuceae showed MPD values of 7.53 logCFU/g and 8.22 logCFU/g at 0 and lOC, respectively. Molds and yeast showed the lowest values of MPD with 6.40 logCFU/g at OC and 7.06 log CFU/g at 1OC (Table 1).

438

2-

L. GIANNUZZI

’“I 8 a’

00-0 Time (days)

o- Time (days)

FIG. 1 . FITTING OF THE GOMPERTZ MODEL TO MICROBIAL COUNTS OF DIFFERENT MICROORGANISMS GROWING IN RICOTTA SAMPLES AT

0 (v), 4 (m), 8 ( 0 ) AND 10 ( A ) C, (a) Enterobacteriaceae (b) psychrotrophic microorganisms and (c) molds and yeasts


88 J a'

I

O O b 1 4 6 8 10 Time (days)

00 - 0 2 4 6 8 Time (days)

00- 0 2 4 6 8 Time (days)

FIG. 2. FITTING OF THE GOMPERTZ MODEL TO MICROBIAL COUNTS OF DIFFERENT MICROORGANISMS GROWING IN RAVIOLI SAMPLES AT

0 (T), 4 (m), 8 ( 0 ) and 10 ( A ) C (a) Enterobacteriaceae (b) psychrotrophic microorganisms and (c) molds and yeasts

440 L. GIANNUZZI

TABLE 1. DERIVED PARAMETERS p (SPECIFIC MICROBIAL GROWTH RATE), LPD (LAG PHASE

DURATION) AND MPD (MAXIMUM POPULATION DENSITY) OBTAINED FROM GOMPERTZ PARAMETERS

Ricotta samples Ricotta tilled ravioli samples

T("C) 11 ASE LPD ASE MPD 11 ASE LPD ASE MPD

0 0.94 0.01 3.78 0.01 5.54 0.65 0.10 1.71 0.12 7.53

Enterobacteriaceae 4 1.31 0.02 3.89 0.03 6.25 0.69 0.09 0.90 0.32 7.40

8 1.10 0.04 1.75 0.10 6.40 0.86 0.14 0.47 0.12 8.30

10 1.58 0.05 0.86 0.03 7.05 1.07 0.02 0.22 0.10 8.22

0 0.18 0.01 1.43 0.21 3.07 0.59 0.01 1.29 0.02 6.40

Moulds and Yeast 4 0.45 0.01 0.98 0.04 4.46 0.79 0.06 0.34 0.01 6.58

8 0.53 0.04 0.90 0.04 4.65 0.95 0.05 0.16 0.05 6.77

10 0.62 0.01 0 . E 0.04 4.91 0.98 0.02 0.15 0.04 7.06

0 1.95 0.04 1.06 0.02 8.36 1.63 0.04 1.11 0.02 8.69

Psychotrophic 4 1.96 0.04 0.03 0.04 8.10 1.55 0.03 0.19 0.04 8.55

microorganisms 8 2.56 0.44 0.07 0.06 8.90 2.24 0.04 0.23 0.06 8.56

10 2.80 0.54 0.11 0.05 9.% 2.55 0.15 0.18 0.05 9.00

11: log(CFtJ/g)days-l, LPD : days. MPD: log(CFU/g). ASE: average standard error.

Effect of Storage Temperature on Microbial Growth Parameters

specific growth rate (p) was interpreted by the following equations: Specific Growth Rate. Effect of storage temperature (0,4, 8 and 1OC) on

Arrhenius Model.

p = A * exp (-E,/RT) (2)

where p is the specific growth rate [log(CFU/g) days-'], T the absolute temperature [OK], E, the activation energy [KJoule/mol], A is the preexponential factor [log(CFU/g)days-'1 and R the gas constant [8.31 Joule/"K moll.


Linear Model.

p = pLo + dT (3)

where p is the specific growth rate [log(CFU/g) days-'] evaluated at T ["C], p,, is the specific growth rate at OC [log (CFU/g) days-', d is slope of the linear regression [log (CFU/g) days-' ("C)-'1 (Li and Torres 1993; Spencer and Baines 1 964).

Square Root Equation. Ratkowsky et al. (1983) proposed the following relationship:

where g is a regression coefficient [log CFU/g days-']'' "C-l, T' is the incubation absolute temperature [OK], To' is a conceptual temperature, with no metabolic meaning for psychrophiles, psychrotrophs and mesophiles (Ratkowsky ef al. 1983). Equation (4) was modified as follows:

where p is derived by extrapolating the linear regression to zero [log CFU/g days-']'', q is the slope of the regression line [log (CFUIg) days-"]" "C-', and T is temperature [ "C] .

As an example, Fig. 3 a, b and c show the Arrhenius, the linear and the square root equation models for molds and yeasts in ricotta-filled ravioli samples, respectively. Table 2 summarizes the regression coefficients (R') obtained by applying the three models to microbial growing in ricotta and ricotta filled ravioli samples. For both psychotrophic microorganisms and Enterobacte- riaceae the highest correlation coefficients were obtained with Arrhenius model. For yeast and molds, linear model equation showed higher correlation coefficients. Concerning the Arrhenius model, the activation energy of a microorganism can be seen as a measure of the sensitivity of its growth rate to temperature changes. For ricotta samples, Table 2, shows that molds and yeasts were the most sensitive, with E, values of 74.60 KJoule/mol, while Enterobacte- riaceae and psychrotrophic microorganism had lower E, values 24.30 and 25.70 KJoule/mol, respectively. In ricotta-filled ravioli samples, the three microorganisms presented activation energies in the range of 3 1.47-32.99 KJoule/mol, so the sensitivity to temperature of their growth rates was comparable (Table 2).

Lag Phase Duration (LPD). As long as product shelf-life is concerned, the lag phase duration (LPD) of damage-causing microorganisms is an important

442 L. GIANNUZZI

parameter. Zwietering and coworkers (1991) modified the extended Ratkowsky model to describe the lag time as function of temperature. The effect of temperature on LPD reflects how the adaptation period of microorganisms to

2 06- 08 -

i

_ _ 3 2 34 36 38 1

VT 103 ( 0 K-1 1 10,

n7 I

0

3051 I I I I

,., 0 2 4 6 8 10 b- T(OC 1

b"t I 1 05 L I I I I J

0 2 4 6 8 10 T(OC1

FIG. 3. APPLICATION OF: (a) ARRHENIUS MODEL (b) LINEAR MODEL (c) SQUARE ROOT MODEL TO EVALUATE TEMPERATURE DEPENDENCE

SPECIFIC MICROBIAL GROWTH RATE FOR MOLDS AND YEAST IN RAVIOLI SAMPLES

ON


TABLE 2. APPLICATION OF ARRHENIUS, LINEAR AND SQUARE ROOT MODELS TO

EVALUATE TEMPERATURE EFFECT ON SPECIFIC GROWTH RATE OF DIFFERENT MICROORGANISMS GROWING IN RICO'ITA AND

RICOTTA-FILLED RAVIOLI SAMPLES

Arrhenius model equaiion (2) Linear model equation (3) Square mot model equation

microorganisms Sample InA E, Rz c d p q p R2

~ c h m ~ h i c RI 11.76 25.70 0.88 1.82 0.09 087 1.35 0.03 087

RRI 14.36 31.70 0.81 1.45 0\09 0.81 1.21 0.04 0.80

Mould and RI 31.33 74.60 0.86 0.21 0.04 0.94 0.46 0.03 0.91

Yeast RFR 14.04 32.99 0.94 0.61 0.04 0.97 0.78 0.02 0.97

Enierobacteriaceae RI 10.84 24.30 0.58 0.98 0.04 0.55 0.99 0.02 0.26

RFR 13.38 31.47 0.91 0.60 0.04 0.85 0.78 0.02 0.87

RI: rimtta samples, RFR rimtta-lilted ravioli samples

A: log(CFU/g)days'. E,: Kjoule/mol, k: log(CFU/g) days-', d log(CFU/g)dayd T' q:(logCFv/gdays')'~C'.p:(logcFu/g)da~~')'~

their new environment changes with temperature. In this regard, the adaptation rate is the reciprocal of LPD (Li 1988; Li and Torres 1993), and was fitted to an Arrhenius-type model.

l/LPD = D exp(-Ew/RT) (6)

where 1/LPD is the adaptation rate [days-'] at T [OK], D is the preexponential factor[days-'1, EL,, is the activation energy [KJoule/mol], R the gas constant [8.31 Joule/"K moll. As an example, Fig. 4 shows the linear fit of the adaption rate of yeast and molds in ricotta-filled ravioli samples as a function of temperature. A linear relationship was obtained for all microorganisms studied, with correlation coefficients (R') ranging from 0.55 to 0.97 (Table 3). Yeast and molds had lower EL,, values (3.35-3.36 KJoule/mol). For ricotta samples, psychrotrophic microorganisms were most sensitive with EL,, values of 14.91 KJoule/mol and for ricotta-filled ravioli samples, Enterobucferiaceue were most sensitive with EL,, values of 15.19 KJoule/mol.

444 L. GIANNUZZI

FIG. 4. ARRHENIUS PLOT OF THE ADAPTATION RATE (1ILPD) FOR MOLDS AND YEASTS IN RAVIOLI SAMPLES

TABLE 3. APPLICATION OF THE ARRHENIUS MODELS TO EVALUATE TEMPERATURE

EFFECT ON LAG PHASE DURATION (LPD) OF DIFFERENT MICROORGANISMS GROWING IN RICOTTA AND

RICOTTA-FILLED RAVIOLI SAMPLES

Microorganisms Samples In D E m RZ

Psychrotrophic RI 55.62 14.91 0.55

RFR 45.22 12.26 0.66

Moulds and Yeast RI 1 1 . 9 4 3.35 0.78

RFR 12.07 3.36 0.92

Entp. obwreriaceae RI 40.44 11.5 0.93

RFR 55.01 15. 19 0.97

R1: ricotta samples, RFR: ricotta-filled ravioli samples

D: days-', EI.m: Kjoule/mol,

TEMPERATURE EFFECT ON MICROBIAL QROWTH 445

Correlation Between Lag Phase Duration (LPD) and the Reciprocal of Specific Growth Rate (I(.). An early report by Cooper (1963) noted that in some examples the ratio of growth rate to generation time was nearly constant. This suggested a linear relationship between lag time and the reciprocal of specific growth rate, that was confirmed in the present work for the different microorganisms growing in ricotta and ricotta-filled ravioli. A linear relationship between LPD and l /p was proposed for all the cases, and the correlation coefficients obtained ranged from 0.61 and 0.93. An example is shown in Fig. 5 for yeast and molds in ricotta and ravioli samples. Similar regressions were obtained for the other studied microorganisms with correlation coefficients R2 ranging between 0.869 and 0.998. Li and Torres (1993) also found a linear relationships for P. fluorexens growing in a media with NaCl or glycerol as the a, controlling solute.

The present work allowed prediction of microbial growth under different temperatures by means of activation energy values for LPD and p , derived from Arrhenius type model. On the basis that microbial testing of foods is expensive and time consuming, mathematical models become a useful tool to provide a matrix of microbial growth responses to a broad range of storage conditions often observed in the distribution chain of the product.

0 1 2 3 4 5 6

l/p(log CFU4) days-'

FIG. 5 . CORRELATION OF LAG PHASE DURATION (LPD) AND THE RECIPROCAL OF SPECIFIC GROWTH RATE FOR MOLDS AND YEASTS IN ( W ) RAVIOLI AND

( 0 ) RICOTTA SAMPLES

446 L. GIANNUZZI

ACKNOWLEDGMENTS

The authors gratefully acknowledge the financial support of the Consejo Nacional de investigaciones Cientificas y Ttcnicas de Argentina (CONICET).

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mathematical modeling of microbial growth in fresh filled pasta stored at different temperatures

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