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Kinetics of quality changes of green peas and white beans during thermal processing
Journal of Food Engineering 24 (1995) 361-377 Copyright O 1995 Elsevier Science Limited Printed in Great Britain. All rights reserved 0260-8774/95/$9.50 ELSEVIER
Kinetics of Quality Changes of Green Peas and White Beans During Thermal Processing A. Van Loey, A. Fransis, M. Hendrickx,* G. Maesmans & P. Tobback Katholieke Universiteit Leuven, Faculty of Agricultural Sciences, Centre for Food Science and Technology, Unit Food Preservation, Kardinaal Mercierlaan 92, B-3001 Heverlee, Belgium (Received 1 July 1993; accepted 2 February 1994)
ABSTRACT The design of optimal thermal processes relies on relevant and accurate kinetic data for bacterial inactivation and quality evolution. By use of taste panels, kinetic data for quality evolution of peas (Pisum sativum L., var. Wavette) and white beans (Phaseolus vulgaris, subsp, nanus Metz., var. Manteca de leon) were obtained. The thermal destruction kinetics of these quality attributes was described using two alternative models, the thermal death time model (z- and D-value) and the Arrhenius model (E a- and k-value). Kinetic parameters were estimated by use of three least squares methods: two-step linear regression, multiple linear regression and nonlinear regression. Multilinear regression analysis was selected for parameter estimation. The following temperature coefficients were obtained: colour of peas (z =26.4°C; E a = 102"4 k J/mole), hardness of peas (z =28"5°C, E~=94.9 kJ/mole) hardness of beans (z =21"3°C, Ea = 1308 kJ/mole) and appearance of beans (z =24"3°C, E~= 118.7 kJ/ mob;).
NOTATION a, b, c A C D Ea k n
Parameters to be estimated Quality parameter Cook value or process value of quality retention (min) Decimal reduction time (rain) Activation energy (J/mole) Reaction rate constant (min- ~) Reaction order
*To whom correspondence should be addressed. 361
362
R R 2 t
T T~f TDT Z
A. Van Loey, A. Fransis, M. Hendrickx, G. Maesmans, P. Tobback
Universal gas constant -- 1.9872 cal/(K mol) Coefficient of determination Time (min) Temperature (°C or K) Reference temperature (°C or K) Thermal death time Temperature dependence of the decimal reduction time (°C)
Subscripts ref Reference 0 Initial value INTRODUCTION Thermal processing of food results in an extended shelf-life but affects both the nutritional and the sensorial quality of the product. One of the challenges to the food canning industry is to minimize these quality losses, meanwhile providing an adequate process to achieve the desired degree of sterility. Optimization is possible because of the higher temperature dependence of the bacterial spore inactivation as compared to the rate of quality destruction, sensorial as well as nutritional (Lund, 1977). For sterilization of low-acid food, processed in the temperature range of 110-130°C, the heat resistance of CI. botulinum spores is chosen as a reference, characterized by a z-value of 10°C and a D12H-value of 0.21 min. A review on kinetic data of nutrient indices is given by Lund (1975), Hallstr6m et al. (1988), Holdsworth (1985, 1990) and Villota and Hawkes (1992); z-values range from 25 to 30°C and Dl2H-values from 100 to 1000 min. In contrast, quantification of sensory parameters is not as straightforward as it is for nutrients. Physical and chemical measuring techniques for sensory quality indicators are available (e.g. use of a colour difference meter to measure changes in green colour of peas; Hayakawa & Timbers, 1977), but there are some restrictions since the usefulness of an instrumental method as a substitute for subjective testing is determined by how well it correlates with sensory data, the assumption being that the latter is relevant. Physical and chemical measurements are usually linear correlated to the intensity whereas panel response could be nonlinear (Lund, 1982). Moreover, many quality attributes cannot be measured with reliability by use of objective instrumentation because of their inherent complexity. The perceptive response of a consumer to a food product is based on several interacting factors, while objective measurements only measure one factor (Sawyer, 1971). As a consequence, the temperature dependence of sensorial quality attributes should be determined using sensory analysis since objective measurements which highly correlate with an evaluation by a taste panel are still not available. Kinetic data on relevant quality attributes and obtained by use of taste panels are of extreme importance to optimize thermal processes. In the present study the temperature dependence of quality indicators (colour, hardness and appearance) for peas (Pisum sativum L., var. Wavette) and white beans ( Phaseolus vulgaris, subsp, nanus Metz., var. Manteca de leon) were
Thermal processing of green peas and white beans
363
determined within the temperature range of 90-122"C using a trained taste panel. A review of the literature shows that frequently kinetic parameters for these quality indicators are determined using objective methods (Hayakawa & Timbers, 1977; Quast & Da Silva, '1977; Lenz &Lund, 1980; Huang & Bourne, 1983; Rodrigo et al., 1983). Few studies appealed to a taste panel for the determination of these kinetic parameters (Timbers, 1971; Mansfield, 1974; both cited in Lund, 1975; Ohlsson, 1980a). MATERIALS A N D M E T H O D S Description of the products
Peas (Pisum sativum L., var. Wavette) were harvested in the summer of 1991 in Belgium. The unblanched peas were frozen in liquid nitrogen prior to processand stored at - 18°C. The mean diameter of the peas was 6"59 + 0"48 mm. e chemical composition is indicated in Table 1. White beans (Phaseolus vulgaris, subsp, nanus Metz., var. Manteca de leon) were harvested in the summer of 1991 in Spain. They were stored dry at 15°C. Before heat treatment, they were soaked in distilled and demineralized water at 15°C for at least 16 h. Preliminary experiments showed that beans reached maximal moisture content after 16 h. The mean sizes of the dry beans were 15.14+ 1.30 mm len~., 10"58+0"80 mm width and 8.71+0.80 mm height. The chemical composition is indicated in Table 1.
~
Heat treatment Thawed peas were heated in thermal death time cans (62 mm diameter and 7 mm height), each can containing + 10g of peas, while soaked beans were heated in small cans of 73 mm diameter and 27 mm height, each can containing + 50 g of beans. The use of flat cans reduced the existence of a temperature gradient in the can during heating so that the difference in heat treatment at the
TABLE 1 Chemical Composition of Peas (Pisum sativum L., var. Wavene) and White Beans (Phaseolus vulgaris, subsp, nanus Metz., var. Manteca de leon)
Composition
Peas
White beans
% Moisture % Proteins % Fat % Ash % Carbohydrates
78"80 5.28 0.30 1.83 13.79
58"46 9.44 0.55 3.59 27.96
The moisture content was determined by the difference of wet and dry weight, the concentration of proteins and fats by use of respectively the Kjeldhal method and the Soxhlet extraction, the percentage of ashes by burning in a furnace at 600°C and the amount of carbohydrates by subtraction.
364
A. Van Loey, A. Fransis, M. Hendrickx, G. Maesmans, P. Tobback
surface and in the centre of the cans was minimal. Before sealing, cans were filled with distilled and demineralized water; headspace was minimal. Cans were placed in a calibrated oil bath of 30 litres (Grant Instruments, Cambridge, Limited HB30). Processing temperatures were chosen to cover the temperature range used in the food industry, namely 90, 100, 110, 116 and 122°C. Samples were heated for pre-determined heating times. Immediately after heating, cans were cooled in ice water to minimize quality destruction during cooling. Prior to evaluation cans were stored at 4°C during _+48h.
Sensory evaluation Evaluation method The evaluation technique used was variant of the QDA method (quantitative descriptive analysis), described by Stone et al. (1974). Both peas and beans were analysed using a randomized balanced block design with replication (Cochran & Cox, 1957). The panel members were asked to rank and rate the same at random coded (three digits) samples for a given characteristic by placing a vertical mark on a 14-5 cm scale. Two references were indicated at 1 cm of both ends: the fresh sample, coded 000 and the product processed at 100°C during 300 min, coded 300. The distance in mm between the reference coded 000 and the mark placed by the judge was a measure of the intensity of a treatment. Selection and training of the judges The selection of the judges was based on following criteria: the availability to participate in 80% or more of all sessions, a person's interest in the test program and motivation for sensory analysis, a general good health, no illness related to the sensory properties being measured and no antipathy against the product to be evaluated. The 12 selected panel members (six students and six staff members of the Unit Food Preservation at the KU Leuven, Belgium) had little or no experience in sensory analysis. They were well informed about the aim of the evaluation and about the test and the scaling method used during the evaluation. During the first session, judges could practice the use of the scale and discussion among panelists was encouraged to reveal any possible misunderstandings. The next training sessions took place in individual booths and samples representing large differences in intensity were presented, while later on differences between samples were refined. The minimal training period was determined using the sequential method (Meilgaard et al., 1988). As indicated in Fig. 1, training was completed after eight sessions. Performance evaluation began soon after training was initiated to identify problems among individual panelists. The sensorial capacity of the panel members was checked using two-out-of-five tests (Meilgaard et al., 1988)while the reliability could be assessed presenting duplicate samples and by replicating the ranking tests. Sample preparation and presentation Prior to evaluation, cans that had the same heat treatment were mixed to obtain homogeneous samples. Individual samples ( _+ 10 g of peas or + 20 g of white beans) were served in plastic cups (King disposables, 72 mm diameter and
Thermal processing of green peas and white beans
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22 m m height), coded with three random digits. During each session, panel members had to analyse six samples of different quality levels processed at the same temperarare. In order to eliminate distraction and prevent communication among panelists, evaluations took place in individual booths. Each booth was provided with a service hatch connected to the preparation room. Standardized daylight was used for the evaluation of colour of peas and appearance of white beans, while hardness of peas and white beans was examined under red light to mask differences in colour or in texture. For hardness testing, a dinner plate, a fork and a spoon were placed at the disposal of the judges. Data analysis Statistical analysis of the sensorial data First, residues of regression analysis were checked on normal distribution and homoscedasticity. Meeting both requirements, the following statistical techniques could be applied to control whether differences in quality level were detectable: the page-test (O'Mahony, 1986), the calculation of R-indices (O'Mahony et al., 1980; O'Mahony, 1986; Vie et al., 1991) and analysis of variance, combined with multiple comparison tests (Wonnacott & Wonnacott, 1985). The page-test and the calculation of R-indices were programmed in Turbo Pascal. A N O V A was performed on the Statistical Analysis System package (SAS, 1982). Performance of the panel as a whole was controlled using factor analysis and by calculating the Pearson's correlation matrix. Both methods were programmed using SAS (1982). Reaction order and parameter estimation The reaction order of the heat induced quality destruction was determined using nonlinear regression analysis on the sensorial data and by examining the tendency of residues. The thermal destruction kinetics of the quality indicators for peas and beans were described using two models: the thermal death time concept (Bigeiow,
366
A. Van Loey, A. Fransis, M. Hendrickx, G. Maesmans, P. Tobback
1921) (eqn ( 1 )) and the Arrhenius model (eqn (2)): D=
O r e f 10 / ~;°f-r I/:
(l )
where D is decimal reduction time (min); Dref is decimal reduction time at Tre~ (min); T is temperature (°C); Tref is reference temperature (°C); and z is temperature dependence of D-value (°C). k = k0 exp( - E a / R T )
(2)
where k is reaction rate constant (rain- l); k0 is reaction rate constant at T= oo (rain-l); Ea is activation energy (cal/mole); T is temperature (K); and R is 1"9872 cal/K mole. The kinetic parameters (k, Ea) and (D, Z) were estimated by use of three different least squares methods (Ratkowsky, 1983; Haralampu et aL, 1985): two-step linear regression, multiple linear regression and nonlinear regression. All calculations were performed using SAS (1982). The correctness of the z-values determined by the taste panel was validated using the Kramer test (Wonnacott & Wonnacott, 1985). RESULTS A N D DISCUSSION Statistical evaluation of the data and the panel members
Statistical analysis, including examination of the panel performance, was applied to the sensorial data. To evaluate whether differences in quality levels were detectable, two nonparametric tests (the page-test and the calculation of Rindices) and one parametric test (an analysis of variance) were used. The page-test (O'Mahony, 1986) is a related-sample nonparametric test to evaluate a ranked tendency. If the calculated L-value exceeds the tabled value, the null hypothesis (no ranked tendency) is rejected in favour of the alternative hypothesis. The tendency to be expected for a given temperature was the shortest process to be ranked first and further ranking according to the process time. Each test rejected the null hypothesis at a level of significance of 0.1%, a result which a ranking of the quality intensity according to the processing time justified. The R-index (O'Mahony et al., 1980; O'Mahony, 1986; Vie et al., 1991) is the probability of a given judge distinguishing correctly between two items. The greater the degree of difference, the higher the probability of discrimination. R-- 1 indicates samples which are perfectly distinguishable; R = 0.5 represents correct discrimination by accident. Intermediate values indicate the magnitude of discrimination by accident. At each temperature, R-indices were calculated for six processing times (Table 2). As indicated by Table 2, judges could distinguish between samples of a different quality level processed at a given temperature. Samples treate d during short times were clearly different for all quality indicators studied (R--1). Confusion appeared as processing time increased. The same tendency was found for the evaluation of samples treated at 90, 100, 110 and 122°C. As a consequence, colour, hardness and appearance decay faster in the beginning of the process, indicating a nonlinear degradation with time (nth order with n # 0).
Thermal processing of green peas and white beans
36 7
TABLE 2 R-index Values Derived from Evaluations of Samples of Six Processing Times (5, 15, 24, 32, 42 and 51 rain) at a Given Temperature (T= 116°C) for Colour, Hardness and Appearance of Peas and Beans
20 60 100 140 180
20
60
100
0
1 0
1 1 0
20
60
Colour of peas 140 1 1 0"497 0
180
220
1 1 0"535 0'531 0
1 1 0"885 0"882 0'816 0
I80
220
220
20 60 100 140 180
0
Hardness of peas l O0 140
1
1
1
1
1
0
1 0
1 0-427 0
1 0"312 0'299 0
1 0.511 0.462 0.611 0
20
60
100
140
180
220
0
1 0
1 1 0
1 1 1 0
1 1 1 0"809 0
1 I 1 0.917 0.719 0
20
60
180
220
0
0.924 0
1 1 1 0-916 0
1 1 1 0-996 0.962 0
220
Hardness of beans 20 60 100 140 180 220
20 60 100 140 180
220
Appearance of beans I00 140 0.993 0.814 0
1 1 1 0
368
A. Van Loey, A. Fransis, M. Hendrickx, G. Maesmans, P. Tobback
Analysis of variance of the sensorial data indicated differences between samples, processed at a given temperature during increased processing time, at the 0-1% level. Tukey HSD tests (Wonnacott & Wonnacott, 1985) pointed out, as the R-indices, that differences between samples treated during short times were obvious while samples undergoing longer heat treatment differed slightly. Performance of the individual judges (validity and reliability) was evaluated in the same way as it was tested during the training period, using two-out-of-five tests, by presenting duplicate test samples and replications. None of the panel members showed serious deviations in their judgements during the sessions. Factor analysis and the calculation of Pearson's correlation matrix examined the performance of the panel as a whole. The correlation matrix of appearance of beans is given in Table 3. The length of the vectors in the biplot presentation indicates a very good reconstruction in the two-dimensional plane. The high correlation of these vectors (representing different panel members) with factor l and the small angles between the vectors prove that all panelists judged the quality parameters in the same way. The same conclusion can be made by inspection of the correlation matrix in Table 3. All the judgements of the panel members were highly correlated with each other. Analogous results were obtained for colour and hardness evaluation of peas and for hardness evaluation of beans. Estimation of the reaction order
The reaction order of thermal destruction of the quality attributes was estimated by nonlinear regression analysis of the sensorial data. The results are given in Table 4. To verify these results for each quality indicator and for each temperature, a linear regression analysis was performed with the score values on one hand and with the logarithmic values on the other hand as a function of processing time. The tendency of residues as a function of time was a measure to determine if the
TABLE 3 Pearson's Correlation Matrix for the Evaluation of 12 Trained Judges of the Appearance of White Beans Krista Lieve Marc Domi Joris Suzy
Krista Lieve Marc Domi Joris Suzy Ilse Geert Joske Ann Lieve2 Leen
1
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Geert Joske Ann Lieve2 Leen
0.854 0.921 0.896 0"878 0.841 0"890 0.845 0.881 0"878 1 0.884 0.906 0"912 0"896 0.889 0.920 0"866 0.896 1 0.914 0"906 0-843 0"899 0.888 0.914 0'910 1 0"904 0"880 0"929 0-911 0.897 0"896 1 0.8600.908 0.902 0-911 0"920 1 0"845 0"898 0.860 0"838 1 0.894 0.873 0"920 1 0.896 0"920 1 0"872 1
0"886 0.850 0'855 0.915 0"885 0"880 0.889 0.893 0.862 0.881 0"846 0-891 0"894 0.875 0.870 0.880 0.873 0.861 0.893 0.892 1 0.866 1
Thermal processing of green peas and white beans
369
reaction was zero order or first order just as the coefficient of determination (R 2) of the linear regressions. The residues showed no systematic tendency and higher correlation coefficients were observed for first order reactions. Based on the results of nonlinear regression, the tendency of residues and the coefficient of determination, a first order reaction for the heat induced quality deterioration was assumed to calculate kinetic parameters: k/
logA = logA0
t
2.303 = logAo - ~
(3)
where A is quality at time t; A 0 is initial quality; k is reaction rate constant (min- t); t is time (min); and D is decimal reduction time (min). Determination of the kinetic parameters
Both the thermal death time (TDT) method and the Arrhenius model were considered to estimate the temperature dependence of the rate index (expressed as D or k), using three least squares regression methods. The most common method to estimate TDT or Arrhenius parameters is a successive two-step linear least squares fit. First, common logarithms of average score values are plotted versus heating times to obtain the reaction rate constant k and consequently the decimal reduction time D, since k= l n l 0 / D of the quality indicator at each temperature (Fig. 2). The second step in the Arrhenius model is to regress the natural logarithm of the reaction rate constant, Ink, versus the reciprocal of the absolute temperature, 1/T, to obtain the estimates of Ink0, the intercept and Ea/R, the slope index of the regression line (eqn (2)) (Fig. 3). In the TDT method, common logarithms of decimal reduction times are plotted against heating temperatures. From the linear regression equation the z-value can be derived (eqn (1)), representing the temperature change necessary to change the rate of the sensory quality deterioration one order of magnitude. The results of a two-step linear regression analysis are given in Tables 5 and 6. Two-step linear regression has the disadvantage of applying regression on regression coefficients. Errors on the first regression coefficients were not transformed to the second regression coefficients. Also, according to Haralampu et
TABLE 4 Estimates of the Reaction Order of the Heat Induced Quality Destruction of Peas and Beans, Using Nonlinear Regression Analysis
Peas: Colour Hardness Beans: Hardness Appearance
1-31 _+0-18 1.13 +-0.20 0.36 _+0.17 0.44 _+0' 16
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TABLE 5 Activation Energies (kJ/mole) and Reaction Rate Constants (min ~) at Reference Temperature ( Tref = 373 K) for Quality Deterioration of Peas and Beans Processed in the Temperature Range of 90-122°C Estimated Using Three Different Least Squares Methods
Two-step finear regression
MultUinear regression
Nonlinear regression
Activation energy (kJ/mole) Peas Colour Hardness Beans Hardness Appearance
103.7 _+0.4 92.8 _+0.8
102.4 _+ 1"7 94.9 _+ 1.7
85"4 _+3.4 89.9 _+3.0
102.0 _+ 1.3 102.8 _+2.5
130.8 _+ 1'3 118-7 _+ 1.3
97.0 _+6.1 95.1 _+5.4
Reaction rate c o n s t a n t kre f (10- "~rain- ~) at Tref = 373 K Peas Colour Hardness Beans Hardness Appearance
7"98 _+0"46 8.92 + 0.86
5.44 _+0'57 4.21 + 0.49
8"22 _+0"25 7"85 _+0.21
10.49_+0"44 10"69-+0"39
1.65 _+0-16 2"92_+0"26
7"64_+0"53 8'24+0-51
TABLE 6 Z-values (°C) and Decimal Reduction Times (min) at Reference Temperature ( Tre~= 100°C) for Quality Deterioration of Peas and Beans Processed in the Temperature Range of 90-122°C Estimated Using Three Different Least Squares Methods
Two-step linear regression
Multilinear regression
Nonlinear regression
z-value (°C) Peas Coiour Hardness Beans Hardness Appearance
25.9 + 0.5 29.2 + 0"8
26-5 + 0"8 28"5 + 0.8
32.0 + 1.3 30.2 + 1.0
27.6 + 0"9 27"4 + 1-6
21.3 _+0.4 24.3 + 0'5
29"0 + 1.8 29.5 _+ 1.7
Decimal reduction time Dre f (rain) at Trot = 100°C Peas Colour Hardness Beans Hardness Appearance
288-5 + 17-7 258"2 + 27"5
-429-6 + 40-7 554"0 + 58"4
280"2 _+8"2 295"2 + 8'1
219"8 + 9 ' 5 215"3 + 8"3
1416"5_+ 127'4 794"3 + 64.9
300"0+20"6 278"3 + 17-1
Thermal processing of green peas and white beans
373
al. (1985) and Cohen and Saguy (1985), two-step linear regression gives the least accurate estimates for Arrhenius parameters, probably because it estimates too many intermediate values and because it does not consider the data set as a whole. To overcome this inaccuracy, another least squares method was used, namely a multiple linear regression analysis. This regression technique gains strength by estimating fewer parameters and by analysing the data set as a whole (Haralampu et al., 1985 ). By substituting eqn ( 1 ) in eqn ( 3 ) and eqn (2) in eqn ( 3 ) and subsequently taking the common logarithms, eqns (4) and (5) can easily be derived:
log log
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Estimated values of z and Ea by multiple linear regression are reported in Tables 5 and 6. Deviation from one of the estimated c-parameters can be taken as a measure of accuracy of the regression. In both cases (TDT and Arrhenius) c was estimated as 1.05 which indicated a rather accurate regression analysis. Haralampu et al. (1985) indicated biased but very precise regression coefficients using multilinear regression analysis to estimate Arrhenius parameters. Bias could appear because the reaction rate estimates were not independent (i.e. they are correlated through the multiple linear regression), thus violating an assumption of least squares regression. However, Haralampu et al. (1985) preferred mutlilinear regression to two-step linear regression. The third method, nonlinear regression, estimated z- and E~-values using the Marquardt procedure. As for mult'dinear regression, it performed a single regression on all data without calculating rates at each temperature. Equations (4) and (5) together with the derivatives of I n ( A / A o) to kre~and E~ for Arrhenius parameters and to Dref and z for TDT parameters are required as input equations. Results of the previous two methods were used as first estimates for z and E~. The results of a nonlinear regression analysis are reported in Tables 5 and 6. Nevertheless, one must be aware that also the estimates of a nonlinear regression can be biased. Least squares estimators in linear models are unbiased, normally distributed and achieve the mimimum variance bound given the
374
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assumption of an independent homoscedastic normally distributed error. For nonlinear models, the least squares estimators have these properties only asymptotically, i.e. for infinite sample size (Ratkowsky, 1983). Secondly, good starting values are vital according to Myers (1990). Poor values may converge in a local minimum of the error mean squares function. As E a- and z-values differ according to the least squares method applied, the question arises of which values can be used if all restrictions of the methods are considered. Least accurate estimates, largest confidence intervals, estimation of unnecessary parameters and regression on regression coefficients made the twostep linear regression inferior to the other methods. While Myers (1990) favoured nonlinear regression, the arguments of Ratkowsky (1983) are a plea to linearize data. The possibility of biased estimates injures the multilinear regression technique while problems with convergence and dependence of the estimated parameters on the initial values makes the nonlinear regression less attractive. Since calculations in multiple regression are less complex than in the nonlinear case and indications of accurate estimations were present, results of multiple linear regression analysis were selected. A review of kinetic data of quality indices of peas and beans is presented in Table 7. Frequently, kinetic parameters of quality indices are determined using objective methods. Only few studies appeal to a subjective determination of kinetic parameters. All parameters obtained (Tables 5 and 6) are within the range cited in literature. Differences in methods of evaluation, species and variety of peas and beans make a strict comparison of literature data and Tables 5 and 6 irrelevant. The influence of the variety of beans on kinetic parameters for the heat induced hardness degradation of beans was studied by Quast and Da Silva ( 1977). Evaluation of the z-values
To evaluate the correctness of the determined z-values, the judges had to evaluate a series of samples of the same quality level processed at different temperatures (T= 100, 110, 116 and 122°C). Processing times were calculated according to the method described by Ohlsson ( 1980a, b) using the z-values for quality deterioration previously determined by the taste panel. The panel members were asked to rank the samples on the same scale as used for the determination of the kinetic parameters. Each treatment was evaluated in duplicate for each quality attribute. The Kramer test (Wonnacott & Wonnacott, 1985) was used to check if the panel as a whole was able to pin-point differences between the samples. No differences were found which meant that either the ranked data were insufficient to indicate differences or -- and this is only hypothetical because statistical tests are not designed to indicate similarities -that quality levels were really the same. It was concluded that the panel members could not distinguish between samples of the same quality level processed at different temperatures. CONCLUSION Based on the results of nonlinear regression, tendency of residues and the coefficient of determination, a first order reaction was assumed for the thermal
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A. Van Loey, A. Fransis, M. Hendrickx, G. Maesmans, P. Tobback
destruction of quality indicators of peas and white beans (colour, hardness and appearance) evaluated by a trained taste panel. Kinetic parameters of two different models (the TDT method and the Arrhenius model) were estimated by use of three different least squares methods (two-step linear regression, multiple linear regression and nonlinear regression). Large confidence intervals, estimation of unnecessary parameters and regression on regression coefficients made two-step linear regression inferior to the other two methods. The results of multiple regression were suggested since calculations were less complex compared to nonlinear regression analysis and indications of accurate estimations were present. This research on kinetics provides relevant data for optimizing thermal processes of peas and beans in terms of hardness, appearance and colour. ACKNOWLEDGEMENTS This research has been performed as part of the Food-linked Agro-industrial Research programme (project AGRF-CT90-0018), supported by the European Commission. This research was also funded by the 'Vlaamse Executive' (project EG/FLAIR/20).
REFERENCES Bigelow, W. D. (1921). The logarithmic nature of thermal death time curves. J. Infectious Diseases, 29, 528-36. Cochran, W. G. & Cox, G. M. (1957). Experimental Design (2nd edn). John Wiley, New York. Cohen, E. & Saguy, 1. (1985). Statistical evaluation of Arrhenius model and its applicability in prediction of food quality losses. J. Food Proc. Preserv., 9, 273-90. Hallstr6m, B., Skj61debrand, C. & Tr~igardh, C. (1988). Heat Transfer & Food Products. Elsevier Applied Science, London, p. 26. Haralampu, S. G., Saguy, I. & Karel, M. (1985). Estimation of Arrhenius model parameters using three least squares methods. J. Food Proc. Preserv., 9, 129-43. Hayakawa, K.-I. & Timbers, G. E. (1977). Influence of heat treatment on the quality of vegetables: changes in visual green color. J. Food Sci., 42 (3), 778-81. Holdsworth, S. D. (1985). Optimisation of thermal processing -- A review. J. Food Eng., 4,89-116. Holdsworth, S. D. (1990). Kinetic data -- What is available and what is necessary. In Processing and Quality of Foods, Vol. 1: HTST Processing. Elsevier Applied Science, London, pp. 74-89. Huang, Y. T. & Bourne, M. C. (1983). Kinetics of thermal softening of vegetables. J. Texture Stud., 14, 1-9. Lenz, M. K. &Lund, D. B. (1980). Experimental procedures for determining destruction kinetics of food components. Food Technol., 34, 51. Lund, D. B. (1975). Effects of heat processing on nutrients. In Nutritional Evaluation of Food Processing, ed. R. S. Harris & E. Karmas. AVI Publishing, Westport, CT, pp. 205-40. Lund, D. B. (1977). Maximizing nutrient retention. Food Technol., 31 (2), 71-8. Lund, D. B. (1982). Quantifying reactions influencing quality of foods: Texture, flavour and appearance. 9'. Food Proc. Preserv., 6, 133-53.
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Meilgaard, M., Civille, G. V. & Carr, B. T. (1988). Sensory Evaluation Techniques. CRC Press, Boca Raton, FL. Myers, R. H. (1990). Classical and Modern Regression with Applications (2nd edn). PWSKENT Publishing Co. Ohlsson, T. (1980a). Temperature dependence of sensory quality changes during thermal processing. J. Food Sci., 45,836-9, 847. Ohlsson, T. (1980b). Optimal sterilisation temperature for flat containers. J. Food Sci., 45,848-52, 859. O'Mahony, M. (1986). Sensory Evaluation of Food." Statistical Methods and Procedures. Marcel Dekker, New York. O'Mahony, M., Garske, S. & Klapman, K. (1980). Rating and ranking procedures for short-cut signal detection multiple difference tests. J. Food Sci., 45, 392-3. Quast, D. C. & Da Silva, S. D. (1977). Temperature dependence of the cooking rate of dry legumes. J. Food Sci., 42 (2), 370-4. Ratkowsky, D. A. (1983). Nonlinear Regression Modeling. A Unified Practical Approach. Marcel Dekker, New York. Rodrigo, M., Safon, J., Lorenzo, E & Autor, M. J. (1983). An approach to optimize the heat sterilization of canned beans by a rotary cooker. In Proc. 6th Int. Congress of Food Science and Technology, Dublin, pp. 187-8. SAS (1982). SAS User's Guide: Statistics (1982 edn). SAS Institute Inc., Cary, NC. Sawyer, F. M. (1971). Interaction of sensory panel and instrumental measurement. Food Technol., 25 (3), 51-2. Stone, H.. Sidel, J., Oliver, S., Woolsey, A. & Singleton, R. C. (1974). Sensory evaluation by quantitative descriptive analysis. Food Technol., 28 ( 11 ), 24-33. Vie, A., Gulli, D. & O'Mahony, M. (1991). Alternative hedonic measures. J. Food Sci., 56 (1), 1-5, 46. Villota, R. & Hawkes, J. G. (1992). Reaction kinetics in food systems. In Handbook of Food Engineering, Marcel Dekker, New York, chap. 2, pp. 65-123. Wonnacott, R. J. & Wonnacott, T. H. (1985). Introductory Statistics (4th edn). John Wiley, New York.
Kinetics of Quality Changes of Green Peas and White Beans During Thermal Processing A. Van Loey, A. Fransis, M. Hendrickx,* G. Maesmans & P. Tobback Katholieke Universiteit Leuven, Faculty of Agricultural Sciences, Centre for Food Science and Technology, Unit Food Preservation, Kardinaal Mercierlaan 92, B-3001 Heverlee, Belgium (Received 1 July 1993; accepted 2 February 1994)
ABSTRACT The design of optimal thermal processes relies on relevant and accurate kinetic data for bacterial inactivation and quality evolution. By use of taste panels, kinetic data for quality evolution of peas (Pisum sativum L., var. Wavette) and white beans (Phaseolus vulgaris, subsp, nanus Metz., var. Manteca de leon) were obtained. The thermal destruction kinetics of these quality attributes was described using two alternative models, the thermal death time model (z- and D-value) and the Arrhenius model (E a- and k-value). Kinetic parameters were estimated by use of three least squares methods: two-step linear regression, multiple linear regression and nonlinear regression. Multilinear regression analysis was selected for parameter estimation. The following temperature coefficients were obtained: colour of peas (z =26.4°C; E a = 102"4 k J/mole), hardness of peas (z =28"5°C, E~=94.9 kJ/mole) hardness of beans (z =21"3°C, Ea = 1308 kJ/mole) and appearance of beans (z =24"3°C, E~= 118.7 kJ/ mob;).
NOTATION a, b, c A C D Ea k n
Parameters to be estimated Quality parameter Cook value or process value of quality retention (min) Decimal reduction time (rain) Activation energy (J/mole) Reaction rate constant (min- ~) Reaction order
*To whom correspondence should be addressed. 361
362
R R 2 t
T T~f TDT Z
A. Van Loey, A. Fransis, M. Hendrickx, G. Maesmans, P. Tobback
Universal gas constant -- 1.9872 cal/(K mol) Coefficient of determination Time (min) Temperature (°C or K) Reference temperature (°C or K) Thermal death time Temperature dependence of the decimal reduction time (°C)
Subscripts ref Reference 0 Initial value INTRODUCTION Thermal processing of food results in an extended shelf-life but affects both the nutritional and the sensorial quality of the product. One of the challenges to the food canning industry is to minimize these quality losses, meanwhile providing an adequate process to achieve the desired degree of sterility. Optimization is possible because of the higher temperature dependence of the bacterial spore inactivation as compared to the rate of quality destruction, sensorial as well as nutritional (Lund, 1977). For sterilization of low-acid food, processed in the temperature range of 110-130°C, the heat resistance of CI. botulinum spores is chosen as a reference, characterized by a z-value of 10°C and a D12H-value of 0.21 min. A review on kinetic data of nutrient indices is given by Lund (1975), Hallstr6m et al. (1988), Holdsworth (1985, 1990) and Villota and Hawkes (1992); z-values range from 25 to 30°C and Dl2H-values from 100 to 1000 min. In contrast, quantification of sensory parameters is not as straightforward as it is for nutrients. Physical and chemical measuring techniques for sensory quality indicators are available (e.g. use of a colour difference meter to measure changes in green colour of peas; Hayakawa & Timbers, 1977), but there are some restrictions since the usefulness of an instrumental method as a substitute for subjective testing is determined by how well it correlates with sensory data, the assumption being that the latter is relevant. Physical and chemical measurements are usually linear correlated to the intensity whereas panel response could be nonlinear (Lund, 1982). Moreover, many quality attributes cannot be measured with reliability by use of objective instrumentation because of their inherent complexity. The perceptive response of a consumer to a food product is based on several interacting factors, while objective measurements only measure one factor (Sawyer, 1971). As a consequence, the temperature dependence of sensorial quality attributes should be determined using sensory analysis since objective measurements which highly correlate with an evaluation by a taste panel are still not available. Kinetic data on relevant quality attributes and obtained by use of taste panels are of extreme importance to optimize thermal processes. In the present study the temperature dependence of quality indicators (colour, hardness and appearance) for peas (Pisum sativum L., var. Wavette) and white beans ( Phaseolus vulgaris, subsp, nanus Metz., var. Manteca de leon) were
Thermal processing of green peas and white beans
363
determined within the temperature range of 90-122"C using a trained taste panel. A review of the literature shows that frequently kinetic parameters for these quality indicators are determined using objective methods (Hayakawa & Timbers, 1977; Quast & Da Silva, '1977; Lenz &Lund, 1980; Huang & Bourne, 1983; Rodrigo et al., 1983). Few studies appealed to a taste panel for the determination of these kinetic parameters (Timbers, 1971; Mansfield, 1974; both cited in Lund, 1975; Ohlsson, 1980a). MATERIALS A N D M E T H O D S Description of the products
Peas (Pisum sativum L., var. Wavette) were harvested in the summer of 1991 in Belgium. The unblanched peas were frozen in liquid nitrogen prior to processand stored at - 18°C. The mean diameter of the peas was 6"59 + 0"48 mm. e chemical composition is indicated in Table 1. White beans (Phaseolus vulgaris, subsp, nanus Metz., var. Manteca de leon) were harvested in the summer of 1991 in Spain. They were stored dry at 15°C. Before heat treatment, they were soaked in distilled and demineralized water at 15°C for at least 16 h. Preliminary experiments showed that beans reached maximal moisture content after 16 h. The mean sizes of the dry beans were 15.14+ 1.30 mm len~., 10"58+0"80 mm width and 8.71+0.80 mm height. The chemical composition is indicated in Table 1.
~
Heat treatment Thawed peas were heated in thermal death time cans (62 mm diameter and 7 mm height), each can containing + 10g of peas, while soaked beans were heated in small cans of 73 mm diameter and 27 mm height, each can containing + 50 g of beans. The use of flat cans reduced the existence of a temperature gradient in the can during heating so that the difference in heat treatment at the
TABLE 1 Chemical Composition of Peas (Pisum sativum L., var. Wavene) and White Beans (Phaseolus vulgaris, subsp, nanus Metz., var. Manteca de leon)
Composition
Peas
White beans
% Moisture % Proteins % Fat % Ash % Carbohydrates
78"80 5.28 0.30 1.83 13.79
58"46 9.44 0.55 3.59 27.96
The moisture content was determined by the difference of wet and dry weight, the concentration of proteins and fats by use of respectively the Kjeldhal method and the Soxhlet extraction, the percentage of ashes by burning in a furnace at 600°C and the amount of carbohydrates by subtraction.
364
A. Van Loey, A. Fransis, M. Hendrickx, G. Maesmans, P. Tobback
surface and in the centre of the cans was minimal. Before sealing, cans were filled with distilled and demineralized water; headspace was minimal. Cans were placed in a calibrated oil bath of 30 litres (Grant Instruments, Cambridge, Limited HB30). Processing temperatures were chosen to cover the temperature range used in the food industry, namely 90, 100, 110, 116 and 122°C. Samples were heated for pre-determined heating times. Immediately after heating, cans were cooled in ice water to minimize quality destruction during cooling. Prior to evaluation cans were stored at 4°C during _+48h.
Sensory evaluation Evaluation method The evaluation technique used was variant of the QDA method (quantitative descriptive analysis), described by Stone et al. (1974). Both peas and beans were analysed using a randomized balanced block design with replication (Cochran & Cox, 1957). The panel members were asked to rank and rate the same at random coded (three digits) samples for a given characteristic by placing a vertical mark on a 14-5 cm scale. Two references were indicated at 1 cm of both ends: the fresh sample, coded 000 and the product processed at 100°C during 300 min, coded 300. The distance in mm between the reference coded 000 and the mark placed by the judge was a measure of the intensity of a treatment. Selection and training of the judges The selection of the judges was based on following criteria: the availability to participate in 80% or more of all sessions, a person's interest in the test program and motivation for sensory analysis, a general good health, no illness related to the sensory properties being measured and no antipathy against the product to be evaluated. The 12 selected panel members (six students and six staff members of the Unit Food Preservation at the KU Leuven, Belgium) had little or no experience in sensory analysis. They were well informed about the aim of the evaluation and about the test and the scaling method used during the evaluation. During the first session, judges could practice the use of the scale and discussion among panelists was encouraged to reveal any possible misunderstandings. The next training sessions took place in individual booths and samples representing large differences in intensity were presented, while later on differences between samples were refined. The minimal training period was determined using the sequential method (Meilgaard et al., 1988). As indicated in Fig. 1, training was completed after eight sessions. Performance evaluation began soon after training was initiated to identify problems among individual panelists. The sensorial capacity of the panel members was checked using two-out-of-five tests (Meilgaard et al., 1988)while the reliability could be assessed presenting duplicate samples and by replicating the ranking tests. Sample preparation and presentation Prior to evaluation, cans that had the same heat treatment were mixed to obtain homogeneous samples. Individual samples ( _+ 10 g of peas or + 20 g of white beans) were served in plastic cups (King disposables, 72 mm diameter and
Thermal processing of green peas and white beans
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22 m m height), coded with three random digits. During each session, panel members had to analyse six samples of different quality levels processed at the same temperarare. In order to eliminate distraction and prevent communication among panelists, evaluations took place in individual booths. Each booth was provided with a service hatch connected to the preparation room. Standardized daylight was used for the evaluation of colour of peas and appearance of white beans, while hardness of peas and white beans was examined under red light to mask differences in colour or in texture. For hardness testing, a dinner plate, a fork and a spoon were placed at the disposal of the judges. Data analysis Statistical analysis of the sensorial data First, residues of regression analysis were checked on normal distribution and homoscedasticity. Meeting both requirements, the following statistical techniques could be applied to control whether differences in quality level were detectable: the page-test (O'Mahony, 1986), the calculation of R-indices (O'Mahony et al., 1980; O'Mahony, 1986; Vie et al., 1991) and analysis of variance, combined with multiple comparison tests (Wonnacott & Wonnacott, 1985). The page-test and the calculation of R-indices were programmed in Turbo Pascal. A N O V A was performed on the Statistical Analysis System package (SAS, 1982). Performance of the panel as a whole was controlled using factor analysis and by calculating the Pearson's correlation matrix. Both methods were programmed using SAS (1982). Reaction order and parameter estimation The reaction order of the heat induced quality destruction was determined using nonlinear regression analysis on the sensorial data and by examining the tendency of residues. The thermal destruction kinetics of the quality indicators for peas and beans were described using two models: the thermal death time concept (Bigeiow,
366
A. Van Loey, A. Fransis, M. Hendrickx, G. Maesmans, P. Tobback
1921) (eqn ( 1 )) and the Arrhenius model (eqn (2)): D=
O r e f 10 / ~;°f-r I/:
(l )
where D is decimal reduction time (min); Dref is decimal reduction time at Tre~ (min); T is temperature (°C); Tref is reference temperature (°C); and z is temperature dependence of D-value (°C). k = k0 exp( - E a / R T )
(2)
where k is reaction rate constant (rain- l); k0 is reaction rate constant at T= oo (rain-l); Ea is activation energy (cal/mole); T is temperature (K); and R is 1"9872 cal/K mole. The kinetic parameters (k, Ea) and (D, Z) were estimated by use of three different least squares methods (Ratkowsky, 1983; Haralampu et aL, 1985): two-step linear regression, multiple linear regression and nonlinear regression. All calculations were performed using SAS (1982). The correctness of the z-values determined by the taste panel was validated using the Kramer test (Wonnacott & Wonnacott, 1985). RESULTS A N D DISCUSSION Statistical evaluation of the data and the panel members
Statistical analysis, including examination of the panel performance, was applied to the sensorial data. To evaluate whether differences in quality levels were detectable, two nonparametric tests (the page-test and the calculation of Rindices) and one parametric test (an analysis of variance) were used. The page-test (O'Mahony, 1986) is a related-sample nonparametric test to evaluate a ranked tendency. If the calculated L-value exceeds the tabled value, the null hypothesis (no ranked tendency) is rejected in favour of the alternative hypothesis. The tendency to be expected for a given temperature was the shortest process to be ranked first and further ranking according to the process time. Each test rejected the null hypothesis at a level of significance of 0.1%, a result which a ranking of the quality intensity according to the processing time justified. The R-index (O'Mahony et al., 1980; O'Mahony, 1986; Vie et al., 1991) is the probability of a given judge distinguishing correctly between two items. The greater the degree of difference, the higher the probability of discrimination. R-- 1 indicates samples which are perfectly distinguishable; R = 0.5 represents correct discrimination by accident. Intermediate values indicate the magnitude of discrimination by accident. At each temperature, R-indices were calculated for six processing times (Table 2). As indicated by Table 2, judges could distinguish between samples of a different quality level processed at a given temperature. Samples treate d during short times were clearly different for all quality indicators studied (R--1). Confusion appeared as processing time increased. The same tendency was found for the evaluation of samples treated at 90, 100, 110 and 122°C. As a consequence, colour, hardness and appearance decay faster in the beginning of the process, indicating a nonlinear degradation with time (nth order with n # 0).
Thermal processing of green peas and white beans
36 7
TABLE 2 R-index Values Derived from Evaluations of Samples of Six Processing Times (5, 15, 24, 32, 42 and 51 rain) at a Given Temperature (T= 116°C) for Colour, Hardness and Appearance of Peas and Beans
20 60 100 140 180
20
60
100
0
1 0
1 1 0
20
60
Colour of peas 140 1 1 0"497 0
180
220
1 1 0"535 0'531 0
1 1 0"885 0"882 0'816 0
I80
220
220
20 60 100 140 180
0
Hardness of peas l O0 140
1
1
1
1
1
0
1 0
1 0-427 0
1 0"312 0'299 0
1 0.511 0.462 0.611 0
20
60
100
140
180
220
0
1 0
1 1 0
1 1 1 0
1 1 1 0"809 0
1 I 1 0.917 0.719 0
20
60
180
220
0
0.924 0
1 1 1 0-916 0
1 1 1 0-996 0.962 0
220
Hardness of beans 20 60 100 140 180 220
20 60 100 140 180
220
Appearance of beans I00 140 0.993 0.814 0
1 1 1 0
368
A. Van Loey, A. Fransis, M. Hendrickx, G. Maesmans, P. Tobback
Analysis of variance of the sensorial data indicated differences between samples, processed at a given temperature during increased processing time, at the 0-1% level. Tukey HSD tests (Wonnacott & Wonnacott, 1985) pointed out, as the R-indices, that differences between samples treated during short times were obvious while samples undergoing longer heat treatment differed slightly. Performance of the individual judges (validity and reliability) was evaluated in the same way as it was tested during the training period, using two-out-of-five tests, by presenting duplicate test samples and replications. None of the panel members showed serious deviations in their judgements during the sessions. Factor analysis and the calculation of Pearson's correlation matrix examined the performance of the panel as a whole. The correlation matrix of appearance of beans is given in Table 3. The length of the vectors in the biplot presentation indicates a very good reconstruction in the two-dimensional plane. The high correlation of these vectors (representing different panel members) with factor l and the small angles between the vectors prove that all panelists judged the quality parameters in the same way. The same conclusion can be made by inspection of the correlation matrix in Table 3. All the judgements of the panel members were highly correlated with each other. Analogous results were obtained for colour and hardness evaluation of peas and for hardness evaluation of beans. Estimation of the reaction order
The reaction order of thermal destruction of the quality attributes was estimated by nonlinear regression analysis of the sensorial data. The results are given in Table 4. To verify these results for each quality indicator and for each temperature, a linear regression analysis was performed with the score values on one hand and with the logarithmic values on the other hand as a function of processing time. The tendency of residues as a function of time was a measure to determine if the
TABLE 3 Pearson's Correlation Matrix for the Evaluation of 12 Trained Judges of the Appearance of White Beans Krista Lieve Marc Domi Joris Suzy
Krista Lieve Marc Domi Joris Suzy Ilse Geert Joske Ann Lieve2 Leen
1
llse
Geert Joske Ann Lieve2 Leen
0.854 0.921 0.896 0"878 0.841 0"890 0.845 0.881 0"878 1 0.884 0.906 0"912 0"896 0.889 0.920 0"866 0.896 1 0.914 0"906 0-843 0"899 0.888 0.914 0'910 1 0"904 0"880 0"929 0-911 0.897 0"896 1 0.8600.908 0.902 0-911 0"920 1 0"845 0"898 0.860 0"838 1 0.894 0.873 0"920 1 0.896 0"920 1 0"872 1
0"886 0.850 0'855 0.915 0"885 0"880 0.889 0.893 0.862 0.881 0"846 0-891 0"894 0.875 0.870 0.880 0.873 0.861 0.893 0.892 1 0.866 1
Thermal processing of green peas and white beans
369
reaction was zero order or first order just as the coefficient of determination (R 2) of the linear regressions. The residues showed no systematic tendency and higher correlation coefficients were observed for first order reactions. Based on the results of nonlinear regression, the tendency of residues and the coefficient of determination, a first order reaction for the heat induced quality deterioration was assumed to calculate kinetic parameters: k/
logA = logA0
t
2.303 = logAo - ~
(3)
where A is quality at time t; A 0 is initial quality; k is reaction rate constant (min- t); t is time (min); and D is decimal reduction time (min). Determination of the kinetic parameters
Both the thermal death time (TDT) method and the Arrhenius model were considered to estimate the temperature dependence of the rate index (expressed as D or k), using three least squares regression methods. The most common method to estimate TDT or Arrhenius parameters is a successive two-step linear least squares fit. First, common logarithms of average score values are plotted versus heating times to obtain the reaction rate constant k and consequently the decimal reduction time D, since k= l n l 0 / D of the quality indicator at each temperature (Fig. 2). The second step in the Arrhenius model is to regress the natural logarithm of the reaction rate constant, Ink, versus the reciprocal of the absolute temperature, 1/T, to obtain the estimates of Ink0, the intercept and Ea/R, the slope index of the regression line (eqn (2)) (Fig. 3). In the TDT method, common logarithms of decimal reduction times are plotted against heating temperatures. From the linear regression equation the z-value can be derived (eqn (1)), representing the temperature change necessary to change the rate of the sensory quality deterioration one order of magnitude. The results of a two-step linear regression analysis are given in Tables 5 and 6. Two-step linear regression has the disadvantage of applying regression on regression coefficients. Errors on the first regression coefficients were not transformed to the second regression coefficients. Also, according to Haralampu et
TABLE 4 Estimates of the Reaction Order of the Heat Induced Quality Destruction of Peas and Beans, Using Nonlinear Regression Analysis
Peas: Colour Hardness Beans: Hardness Appearance
1-31 _+0-18 1.13 +-0.20 0.36 _+0.17 0.44 _+0' 16
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TABLE 5 Activation Energies (kJ/mole) and Reaction Rate Constants (min ~) at Reference Temperature ( Tref = 373 K) for Quality Deterioration of Peas and Beans Processed in the Temperature Range of 90-122°C Estimated Using Three Different Least Squares Methods
Two-step finear regression
MultUinear regression
Nonlinear regression
Activation energy (kJ/mole) Peas Colour Hardness Beans Hardness Appearance
103.7 _+0.4 92.8 _+0.8
102.4 _+ 1"7 94.9 _+ 1.7
85"4 _+3.4 89.9 _+3.0
102.0 _+ 1.3 102.8 _+2.5
130.8 _+ 1'3 118-7 _+ 1.3
97.0 _+6.1 95.1 _+5.4
Reaction rate c o n s t a n t kre f (10- "~rain- ~) at Tref = 373 K Peas Colour Hardness Beans Hardness Appearance
7"98 _+0"46 8.92 + 0.86
5.44 _+0'57 4.21 + 0.49
8"22 _+0"25 7"85 _+0.21
10.49_+0"44 10"69-+0"39
1.65 _+0-16 2"92_+0"26
7"64_+0"53 8'24+0-51
TABLE 6 Z-values (°C) and Decimal Reduction Times (min) at Reference Temperature ( Tre~= 100°C) for Quality Deterioration of Peas and Beans Processed in the Temperature Range of 90-122°C Estimated Using Three Different Least Squares Methods
Two-step linear regression
Multilinear regression
Nonlinear regression
z-value (°C) Peas Coiour Hardness Beans Hardness Appearance
25.9 + 0.5 29.2 + 0"8
26-5 + 0"8 28"5 + 0.8
32.0 + 1.3 30.2 + 1.0
27.6 + 0"9 27"4 + 1-6
21.3 _+0.4 24.3 + 0'5
29"0 + 1.8 29.5 _+ 1.7
Decimal reduction time Dre f (rain) at Trot = 100°C Peas Colour Hardness Beans Hardness Appearance
288-5 + 17-7 258"2 + 27"5
-429-6 + 40-7 554"0 + 58"4
280"2 _+8"2 295"2 + 8'1
219"8 + 9 ' 5 215"3 + 8"3
1416"5_+ 127'4 794"3 + 64.9
300"0+20"6 278"3 + 17-1
Thermal processing of green peas and white beans
373
al. (1985) and Cohen and Saguy (1985), two-step linear regression gives the least accurate estimates for Arrhenius parameters, probably because it estimates too many intermediate values and because it does not consider the data set as a whole. To overcome this inaccuracy, another least squares method was used, namely a multiple linear regression analysis. This regression technique gains strength by estimating fewer parameters and by analysing the data set as a whole (Haralampu et al., 1985 ). By substituting eqn ( 1 ) in eqn ( 3 ) and eqn (2) in eqn ( 3 ) and subsequently taking the common logarithms, eqns (4) and (5) can easily be derived:
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Estimated values of z and Ea by multiple linear regression are reported in Tables 5 and 6. Deviation from one of the estimated c-parameters can be taken as a measure of accuracy of the regression. In both cases (TDT and Arrhenius) c was estimated as 1.05 which indicated a rather accurate regression analysis. Haralampu et al. (1985) indicated biased but very precise regression coefficients using multilinear regression analysis to estimate Arrhenius parameters. Bias could appear because the reaction rate estimates were not independent (i.e. they are correlated through the multiple linear regression), thus violating an assumption of least squares regression. However, Haralampu et al. (1985) preferred mutlilinear regression to two-step linear regression. The third method, nonlinear regression, estimated z- and E~-values using the Marquardt procedure. As for mult'dinear regression, it performed a single regression on all data without calculating rates at each temperature. Equations (4) and (5) together with the derivatives of I n ( A / A o) to kre~and E~ for Arrhenius parameters and to Dref and z for TDT parameters are required as input equations. Results of the previous two methods were used as first estimates for z and E~. The results of a nonlinear regression analysis are reported in Tables 5 and 6. Nevertheless, one must be aware that also the estimates of a nonlinear regression can be biased. Least squares estimators in linear models are unbiased, normally distributed and achieve the mimimum variance bound given the
374
A. Van Loey, A. Fransis, M. Hendrickx, G. Maesmans, P. Tobback
assumption of an independent homoscedastic normally distributed error. For nonlinear models, the least squares estimators have these properties only asymptotically, i.e. for infinite sample size (Ratkowsky, 1983). Secondly, good starting values are vital according to Myers (1990). Poor values may converge in a local minimum of the error mean squares function. As E a- and z-values differ according to the least squares method applied, the question arises of which values can be used if all restrictions of the methods are considered. Least accurate estimates, largest confidence intervals, estimation of unnecessary parameters and regression on regression coefficients made the twostep linear regression inferior to the other methods. While Myers (1990) favoured nonlinear regression, the arguments of Ratkowsky (1983) are a plea to linearize data. The possibility of biased estimates injures the multilinear regression technique while problems with convergence and dependence of the estimated parameters on the initial values makes the nonlinear regression less attractive. Since calculations in multiple regression are less complex than in the nonlinear case and indications of accurate estimations were present, results of multiple linear regression analysis were selected. A review of kinetic data of quality indices of peas and beans is presented in Table 7. Frequently, kinetic parameters of quality indices are determined using objective methods. Only few studies appeal to a subjective determination of kinetic parameters. All parameters obtained (Tables 5 and 6) are within the range cited in literature. Differences in methods of evaluation, species and variety of peas and beans make a strict comparison of literature data and Tables 5 and 6 irrelevant. The influence of the variety of beans on kinetic parameters for the heat induced hardness degradation of beans was studied by Quast and Da Silva ( 1977). Evaluation of the z-values
To evaluate the correctness of the determined z-values, the judges had to evaluate a series of samples of the same quality level processed at different temperatures (T= 100, 110, 116 and 122°C). Processing times were calculated according to the method described by Ohlsson ( 1980a, b) using the z-values for quality deterioration previously determined by the taste panel. The panel members were asked to rank the samples on the same scale as used for the determination of the kinetic parameters. Each treatment was evaluated in duplicate for each quality attribute. The Kramer test (Wonnacott & Wonnacott, 1985) was used to check if the panel as a whole was able to pin-point differences between the samples. No differences were found which meant that either the ranked data were insufficient to indicate differences or -- and this is only hypothetical because statistical tests are not designed to indicate similarities -that quality levels were really the same. It was concluded that the panel members could not distinguish between samples of the same quality level processed at different temperatures. CONCLUSION Based on the results of nonlinear regression, tendency of residues and the coefficient of determination, a first order reaction was assumed for the thermal
Thermal processing of green peas and white beans
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A. Van Loey, A. Fransis, M. Hendrickx, G. Maesmans, P. Tobback
destruction of quality indicators of peas and white beans (colour, hardness and appearance) evaluated by a trained taste panel. Kinetic parameters of two different models (the TDT method and the Arrhenius model) were estimated by use of three different least squares methods (two-step linear regression, multiple linear regression and nonlinear regression). Large confidence intervals, estimation of unnecessary parameters and regression on regression coefficients made two-step linear regression inferior to the other two methods. The results of multiple regression were suggested since calculations were less complex compared to nonlinear regression analysis and indications of accurate estimations were present. This research on kinetics provides relevant data for optimizing thermal processes of peas and beans in terms of hardness, appearance and colour. ACKNOWLEDGEMENTS This research has been performed as part of the Food-linked Agro-industrial Research programme (project AGRF-CT90-0018), supported by the European Commission. This research was also funded by the 'Vlaamse Executive' (project EG/FLAIR/20).
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