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Development of predictive models for egg freshness and shelf-life under different storage temperatures

Development of predictive models for egg freshness and shelf-life under different storage... The objective of the present study was to develop models for egg freshness and shelf-life predictions for the selected evaluation indicators including egg weight, Haugh unit (HU), and albumen height. Experiments were carried out at different storage temperatures for a total period of 29–32 days. All data were collected and fitted in to Arrhenius equation for egg freshness, while the HU data were applied to a probability model for shelf-life prediction. The results showed that egg weight, albumen height, and HU decreased significantly, while albumen pH increased with the extension of storage time. The higher the storage temperature, the faster the egg quality decreased. In addition, the bias factor, accuracy factor, and the standard error of prediction were selected to verify the developed quality models. Maximum rescaled R-square statistic, the Hosmer–Lemeshow goodness-of-fit statistic, and the receiver operating characteristic curve were used to evaluate the goodness-of-fit of the developed probability model for the shelf-life of eggs, which indicated that the presented predictive models can be used to assess egg freshness and predict shelf-life during different storage temperatures. Keywords: Eggs; predictive models; probability model; shelf-life; freshness. complex physical, chemical, and physiological changes (Al-Obaidi Introduction et  al., 2011). They can also be contaminated by microorganisms, re- Eggs are a natural source of extremely rich nutrients such as proteins, sulting in spoilage (Stadelman. et  al., 1977; Suresh et  al., 2006), af- fats, minerals, and vitamins (Eke et al., 2013). During storage, poultry fecting their quality. Freshness is the most important characteristic eggs are constantly carrying out life activities, accompanied by various © The Author(s) 2021. Published by Oxford University Press on behalf of Zhejiang University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which per- mits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. 2 C. L. Quan et al. related to egg quality, and its decrease mainly depends on time and numbered individually. The eggs were placed blunt end up in the carton temperature (Yimenu et  al., 2018). Albumen height, albumen pH, pulp egg trays (each tray contains 30 egg specimens) and randomly div- and egg weight are the key indicators for evaluating freshness, and ided into 5 groups. Then the eggs were placed in the chambers directly are greatly affected by storage time and temperature (Lee et al., 2016; without any other packages under different constant temperatures Dong et al., 2017; Vivian et al., 2017). The Haugh unit (HU) is a widely (7, 17, 23, 37, and 40 °C) for 29–32 days. During the storage period, used indicator to measure egg quality, and is a comprehensive indicator random sampling was generally performed at 2–4  day intervals, or to reflect egg quality converted based on egg weight and protein height 4–6 day intervals at low temperature. At each sampling time in each (Suresh et al., 2006; Xavier et al., 2008; Dong et al., 2017). trial, 3 eggs were randomly selected and used for the measurements Storage conditions such as storage temperature, relative hu- of egg weight, albumen height, HU value, and pH. Experiments were midity, and storage time will affect egg quality (Yimenu et al., 2018). conducted in triplicate. Predictive modeling could provide a tool for applying scientific methods to describe the chemical and physical changes occurring in Experimental methods food under different environmental conditions. Several models have Egg quality evaluation been used to describe the effect of environmental conditions on egg Weight, albumen height, and HU values of sampling eggs at each freshness. The acceptability of the first-order reaction and Arrhenius sampling point were measured using an egg multi tester (EMT-7300, model for predicting the changes of eggs weight, yolk index, and air Robotmation Co., Ltd., Tokyo, Japan). After separating the yolk and room height at the storage temperature from 5 °C to 35 °C with high albumen, each egg was placed in a beaker and homogenized with a regression coefficients provided a reference for the storage and sale of glass rod. The pH values were measured using a pH meter (FE20, hen eggs (Yu and Wang, 2012). Du et al. (2018) selected HU, egg shell METTLER TOLEDO,  Zurich, Switzerland) and were recorded thickness, shell breaking strength and deformation, albumen height, when the reading was stabilized. and yolk film strength as research indicators to establish a prediction model for HU and albumen pH during storage, which provided a Freshness quality prediction models theoretical basis for egg detection. Yimenu et al. (2017) constructed The egg quality dynamics model is developed based on the equation primary and polynomial models for egg freshness (weight loss rate, of thermodynamics (Yu and Wang, 2012; Equation 1). yolk index, albumen index, and HU) under constant temperature from 5  °C to 30  °C. Subsequently, regression analysis was used to ln X=ln X −kt (1) study the impact of environmental factors (temperature, relative hu- midity, and air flow rate) on weight loss, HU, and S -ovalbumin con- where X is the quality index (egg weight, albumen height, pH, and tent by establishing predictive model for egg freshness under constant HU value) at storage time t (day); X is the initial value of each temperature storage (Yimenu et al., 2018). The relationship between quality indicator (egg weight, albumen height, pH, and HU value); egg quality and storage temperature can be understood through –1 k is the reaction rate constant (day ); and t is storage time (day). the study of the deterioration mechanism of poultry eggs, which k is a variable that changes with temperature, and its value is is reflected by the kinetic model and has practical significance for determined by Equation 2. Equation 2 is commonly referred to as improving storage conditions (Samli et  al., 2005). Although several the Arrhenius equation, and this expression has achieved remarkable models have been developed for egg freshness, they do not consider success in describing the temperature dependence of chemical reac- the stochastic variability of the freshness parameters. The probability tions (Ratkowsky et al., 1982): models were mainly applied for bacterial growth in published ref- erences (Koseki and Nonaka, 2012; Wang et al., 2017). Wang et al. k = k · exp(−E /RT ) 0 a absolute (2) (2017) developed the probability of the time to reach a certain level increase of Staphylococcus aureus on rice cakes at different temper- where k is the pre-exponential factor, R is the universal gas constant atures. However, the development of a probability model under dif- [8.3144 J/(mol·K)], T is the absolute temperature (K), and Ea is absolute ferent temperatures indicating the different time to reach a certain the activation energy (J/mol). HU value to predict the shelf-life of eggs has been rarely reported. In the present study, we used fresh eggs as experimental mater- Probability model development for the shelf-life of eggs ials to (1) study the effects of different storage temperatures (7, 17, In order to estimate the shelf-life of eggs at different temperatures, a 23, 37, and 40 °C) on the egg quality indices (egg weight, albumen probability model based on HU values was developed in this study. height, pH, and HU); (2) establish an egg quality (egg weight, al- For the probability model development, each sampling interval was bumen height, and HU) change model during storage according to marked with 0 or 1 to indicate whether or not an HU value of 60 the chemical kinetic model and the Arrhenius equation; and (3) de- was reached. The probability of HU values decrease to 60 was col- velop a logistic model based on HU value to predict the shelf-life of lected and fitted to a logistic regression model using R software (R eggs, so as to predict the probability of HU reaching 60. Core Team, 2020). The analyses were conducted with the glm func- tion in R software package Stats. The initial fitted model was shown as follows, after a minor modification according to the approach Materials and Methods described by Wang et al. (2017): Experimental materials and storage Freshly laid unfertilized and unwashed brown egg samples were Logit (P)=α +α ·T+α ·ln(t ) 0 1 2 HU (3) obtained directly from a local husbandry technology company (Qingdao, China), were then transferred to the laboratory at 4 °C on where P is the probability of an arbitrary decrease to HU value of the same day. The eggs used in this study were produced by laying hens 60, Logit (P)= ln [ P/(1−P)] , α −α are the coefficients to be es- 0 2 in conventional cages with similar bodyweights and aged 28–42 weeks. timated, T is the storage temperature, and t is the time at which the HU A total of 180 brown eggs with intact shells were used in each trial and decrement of HU value reached the set values. Modelling egg freshness and shelf-life 3 Verification model respectively, with loss rate of 23.04% and 32.15%. In contrast, The statistical indices including accuracy factor (A , Equation 4), the weight loss of eggs stored at 7, 17, and 23 °C was much less bias factor (B , Equation 5), and standard error of prediction (SEP, than those stored at 37 °C and 40  °C. The weight loss of eggs Equation 6)  were employed to evaluate the performance and reli- during storage will naturally occur due to water evaporation. ability of each model (Wang et al., 2017). Similar trends were reported by Akyurek and Okur (2009), Lee The proximity between the predicted value and the observed et  al. (2016), and Yeasmin et  al. (2014). The published studies value can be measured by A . The larger A , the less accurate the showed that there was no significant decrease under conditions of f f average estimate, while a value of 1 indicates that the predicted 2 °C and 12 °C within 10 days (Lee et al., 2016). Studies have re- value and the observed value are completely consistent (Lebert et al., vealed that the higher the temperature, the greater the evaporation 2000). The acceptable range of A values depended on the number loss of the solvent in the egg through the cracks of the eggshell, of variables in the predictive model, and A increases 0.10–0.15 for and the lighter the egg weight (Yeasmin et  al., 2014; Brodacki each variable (Ross, 1996). et al., 2019). Besides, it was also found that the egg weight reduc- tion was related to the egg white, eggshell porosity and thickness, ( | log(μ /μ )|/n) predicted observed and water conductivity (Brodacki et al., 2019). A = 10 (4) where μ represents observed values; μ represents pre- Changes on albumen height under different temperatures observed predictived dicted value; n is the number of sampling points each trial. As shown in Figure 1B, it was observed that the albumen height B is a measure of the extent of under- or over-prediction, and the decreased significantly due to storage period and temperature. The evaluation of the degree of deviation between the predicted value albumen height decreased from 17.5 mm to 6.5 mm at 7 °C, from and the contour. A B value range of 0.7–0.9 or 1.06–1.15 was con- 17.5 mm to 5.5  mm at 17  °C, and from 17.5 mm to 4.0  mm at sidered as acceptable (Ross et al., 2000; Wang et al., 2012). 23 °C during 29 days of storage, and the decline was further ex- panded while stored at 37 °C and 40 °C. Similar albumen heights ( log(μ /μ )/n) predicted observed were also reported by Lee et al. (2016) and Tabidi (2011). In this B = 10 (5) study, the albumen height decreased greatly in the first 4 days, and SEP can measure and verify the accuracy of predictive models. the subsequent changes became slower, indicating that the quality of the eggs dropped rapidly during the initial short storage period. In addition, during the 5  days of storage, the albumen height at 100 (μ − μ ) observed predictived SEP(%) = . 23, 37, and 40 °C decreased faster than those at 7 °C and 17 °C. Average(μ ) n observed (6) These results indicate that higher room temperature had a greater negative impact on albumen height. This is explained by the evap- For the probability model, the maximum rescaled R-square statistic, oration of water through the pores in the eggshell and the release the Hosmer–Lemeshow goodness-of-fit statistic, and the receiver of carbon dioxide (CO ) from the albumen, which would increase operating characteristic (ROC) curve were used to evaluate the 2 as temperature rises (Serrano et  al., 2016). Therefore, purchased goodness-of-fit of the developed model (Agresti, 2007). eggs should be stored at low temperature to slow down the rate of decline in egg quality. Statistical analysis All data of quality indicators obtained from each experiment with Haugh unit changes under different temperatures triplicates was transferred into a Microsoft Excel sheet for data ana- The HU values decreased with longer storage time at all storage lysis and charting. The data were analyzed using Tukey’s multiple temperatures except at 17  °C and 37  °C after 25  days, which range test to determine statistically significant differences (p<0.05). might be caused by the individual differences of eggs. In addition, Model development and model validation were conducted by the a greater decrease in the HU values was found at higher temper- OH-Fit Excel Add-In software (Ding et al., 2011). atures (23, 37, and 40 °C) compared with the lower temperatures (7 °C and 17 °C), as shown in Figure 1C. The decline of the HU of eggs during storage is due to the decomposition of carbonic acid in Results and Discussion the egg white, which produces CO and water released through the pores of the eggshell, causing the electrostatic complex between Changes in egg quality indicators during storage the lysozyme and ovomucin to rupture (Eke et al., 2013; Yimenu In this study, the impact of different constant temperature storage et al., 2017). conditions (7–40 °C) on the change of egg freshness indices was in- The HU has been considered as the gold standard of egg quality. vestigated. Storage temperature and time obviously affected almost According to the egg grades of the USA, the quality of eggs can all parameters of egg quality investigated in this study. Egg weight, be ranked as AA (≥72), A (71–60), B (59–30), C (<29) based on albumen height, and HU significantly decreased with the extension HU values. Eggs with HU value less <60 are considered unfit for of the storage time, while albumen pH increased. consumption (Nematinia and Mehdizadeh, 2018). As shown in Figure 1C, during the experimental period, the freshness of eggs Changes on egg weight under different temperatures was still AA grade eggs at 7 °C and 17 °C; the HU value of eggs Egg weight decreased slowly during storage for 0–25  days at 7, stored at 37 °C and 40 °C for about 10 days declines to 60 and 17, and 23  °C. The decrease was much faster during storage at they should not be eaten. Based on the results hereby presented, 37  °C and 40  °C. The difference between 7  °C and 17  °C was the higher the storage temperature of eggs, the faster the decline not significant (p >0.05) within 17  days. As shown in Figure 1A, of HU. These results are in agreement with those of Nematinia the weight of eggs stored at 37 °C and 40 °C were reduced from and Mehdizadeh, (2018), Liu et  al. (2016), and Yeasmin et  al. the initial (64.42±0.88)  g to (49.58±1.24)  g and (43.71±1.02)  g, (2014). 4 C. L. Quan et al. Figure 1. Changes of the evaluation indicators of eggs over time, under different temperatures. A, egg weight; B, albumen height; C, Haugh unit; D, albumen pH. Changes in albumen pH under different temperatures Table 1. Estimation of rate constants of egg quality and determin- The albumen pH value is another parameter representing egg quality. ation of coefficients at different temperatures The albumen pH of fresh egg is between 7.6 and 9.7 (Sharp, 1929). Egg weight Albumen height Haugh unit Figure 1D shows the changes in albumen pH of eggs stored at 7, 17, Tempera- 23, 37, or 40 °C for nearly one month. It can be seen from the figure –1 2 –1 2 –1 2 ture (°C) k (day ) R k (day ) R k (day ) R that the albumen pH decreased in the first 4 days after the egg was 7 0.001688 0.937 0.006283 0.846 0.004069 0.884 laid. It has been speculated that the possible reason for this is that a 17 0.001797 0.853 0.009087 0.818 0.006757 0.754 series of chemical changes have occurred after the eggs are separated 23 0.002086 0.890 0.016500 0.923 0.012570 0.889 from the hens’ internal environment, but the specifics are unknown. 37 0.009547 0.921 0.026470 0.911 0.016350 0.872 Albumen pH values increased significantly with further extension of 40 0.013400 0.950 0.026570 0.883 0.016870 0.733 storage time, probably because of the evaporation of egg moisture and the release of CO (Yimenu et al., 2017). Table 2. Arrhenius equation for egg weight, albumen height, and Overall increases in the albumen pH of all eggs was observed Haugh unit at the end of all storage experiments. The albumen pH of all eggs increased sharply after 4  days, which was consistent with previous Quality index Equation R studies (Lapao et  al., 1999; Dutta et  al., 2003). In particular, after 20 days of storage, the albumen pH of eggs at 40 °C showed a great Egg weight Y =14.35–5921.4X 0.856 Albumen height Y =7.4157–3584X 0.895 degree of fluctuation, while other samples showed no such trend. One Haugh unit Y =8.9118–3910.3X 0.952 possible reason is the interaction of various egg qualities (such as 3 moisture content, CO content, and albumen viscosity) under condi- Y , Y , and Y are the negative logarithms of the Arrhenius equation of the tions of high temperature and long storage time (Mathew et al., 2016). 1 2 3 change of egg weight, Haugh unit, and albumen height during egg storage; X is the reciprocal of the absolute temperature of the egg during storage, 1/K. Egg freshness quality prediction models The kinetic model of egg quality for egg weight, HU, and albumen the negative natural logarithms of both sides of the Arrhenius model height under different storage temperatures was established by using in Equation 2 and fitting it with the data in Table 1, the egg quality the first-order kinetic rate equation, and the reaction rate constant –1 2 kinetic model was obtained (Table 2). (k, day ), and coefficient determinations (R ) were obtained as Based on the data in Table 2, substituting the activation en- shown in Table 1. The pH values were excluded for model develop- ergy (E ) and the Arrhenius equation constant (K ) obtained in the ment because of the mismatch of albumen pH data. Then, by taking a 0 Modelling egg freshness and shelf-life 5 Table 3. Estimated parameters of the logistic regression for arbitrary Haugh decrease during storage period Coefficient Estimate Std. Error z value Pr(>|z|) Maximum rescaled R c (area under ROC curve) Hosmer–Lemeshow (goodness-of-fit) 0.7068 0.975795% CI: 3.549 with 8 df (P=0.8953) α –33.38 6.966 –4.792 1.65E–06 0.9499–0.9884 α 0.3457 0.066 5.239 1.61E–07 α 7.115 1.637 4.346 1.38E–05 Std., Standard; Pr, probability; CI, confidence interval; ROC, receiver operating characteristic; df, degree of freedom. Figure 2. According to the developed model, the shelf-life of eggs, while maintaining grade A  during storage at different temperatures, could be determined. Logit (P) values at each temperature can be obtained, and the probabilities to become lower than grade A could be generated subsequently. Based on the reported limits on the growth of bacteria (Presser et  al., 1998; Tienungoon et  al., 2000; Le Marc et  al., 2005; Hwang and Juneja, 2011; Wang et al., 2017) that P≤0.1 indicates an “unlikely” or “no” growth region, P>0.5 indicates a “likely” or growth region, while P values between 0.1 and 0.5 indicate an “uncertainty” region, we set a similar criterion for eggs’ shelf-life maintaining grade A. As shown in Figure 2, P≤0.1 indicates an “unlikely” region to be lower than grade A, P>0.5 indicates likely to be lower than grade A, and P values between 0.1 and 0.5 indicate an “uncertainty” region. Therefore, the eggs’ shelf-life could be calculated as follows: t = exp((33.38−0.3457×T)/7.115) shelf-life Figure 2. Probability of Haugh unit decrease to 60 at different temperatures. Solid and dashed lines represent the probability (P=0.5 and P=0.1) of reaching where T is the storage temperature, and t is shelf-life of eggs. shelf-life a Haugh unit of 60. According to the above equation, it is easy to predict shelf-life at different temperatures within the limits of the experimental design. Table 4. The parameters of validation for the predictive models at As shown in Figure 2, the likely shelf-life of eggs maintaining grade different temperature A at 7, 17, 23, 37 and 40 °C were 77.59, 47.73, 35.69, 18.06 and Quality index A B SEP (%) 15.61 days, respectively. The results showed that the logistic model f f developed in the present study could provide useful information for Egg weight 1.014 1.011 1.689 eggs storage management. Albumen height 1.062 0.988 6.465 Haugh unit 1.063 1.133 2.321 Verification of model Based on the evaluation indices (B , A , and SEP), the corresponding f f experiment into Equation 2, the prediction models for egg quality, deviation factor, predicted value deviation, and predicted standard egg protein height, and HU can be obtained as follows: deviation are obtained by comparing the predicted value with the measured value (Table 4). As shown in Table 4, the A values were −49231/RT absolute ln X = ln X −(1706577×e )×t egg weight 0 egg weight egg weight in the range 1.014–1.063 for egg weight, HU, and albumen height, and B ranged from 0.988 to 1.133, which were all acceptable. The −42575/RT A ranged from 1.0 to 1.15 and is acceptable because only tempera- absolute ln X = ln X −(201189×e )×t albumen height 0 albumen height albumen height ture was considered in the developed models (Wang and Oh, 2012). B values <0.7 or >1.15 are considered unacceptable (Tienungoon et −29797/RT absolute ln X =− ln X −(1662×e )×t Haugh unit 0 Haugh unit Haugh unit al., 2000). The smaller the value of SEP, the better the model can be used to predict data, and the maximum value in this study is no more than 7%. Results obtained in the present study indicated that the Development of logistic model for shelf-life of eggs established dynamic model could better describe the quality changes In order to determine the shelf-life of egg during a storage period, HU of eggs in the storage process. was selected as the index to develop a logistic model. As mentioned above, eggs will be ranked lower than grade A if the HU reaches less Conclusions than 60. Therefore, HU value of 60 was set to be the criterion to deter- mine the shelf-life of fresh eggs. The estimated parameters of the logistic In this study, under all temperature conditions considered, egg regression model’s HU decrease under different temperatures are pre- weight, albumen height, and HU continued to decrease with the sented in Table 3. The indices of goodness-of-fit of the model including extension of the storage period, while albumen pH gradually in- maximum rescaled R , area under receiver operating characteristic creased. A  noteworthy result was the visibility of a rapid decrease (ROC) curve, and Hosmer–Lemeshow goodness-of-fit are also listed in in the HU and the egg weight for short times at high temperatures. Table 3. The results obtained in this study showed that the developed Therefore, low-temperature storage or transportation is a better probability models were significant for the shelf-life prediction of eggs. choice for keeping the eggs fresh. Further research should be con- The cumulative probability distributions generated by the de- ducted to optimize fresh-keeping conditions to maximize the fresh- veloped logistic model at different temperatures are shown in keeping effects while reducing unnecessary waste. The developed 6 C. L. Quan et al. Koseki, S., Nonaka, J. (2012). Alternative approach to modeling bacterial lag quality models can be used to predict egg freshness changes in terms time, using logistic regression as a function of time, temperature, pH, and of egg weight, albumen height, and HU at temperatures of 7–40 °C sodium chloride concentration. Applied and Environmental Microbiology, during storage, and the logistic model was useful for the shelf-life 78(17): 6103–6112. predictions of eggs. The models presented in this study could simu- Lapao,  C., Gama,  L., Soares,  M. (1999). 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Journal of Transactions of the Chinese Society of Agricultural Engineering, 28(15): Food, Agriculture and Environment, 12(3&4): 87–92. 276–280. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Food Quality and Safety Oxford University Press

Development of predictive models for egg freshness and shelf-life under different storage temperatures

,; ,; ,; ,; ,; Forghani, Fereidoun; ,; ,; ,
Food Quality and Safety , Volume 5: 1 – Sep 7, 2021
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Oxford University Press
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© The Author(s) 2021. Published by Oxford University Press on behalf of Zhejiang University Press.
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Abstract

The objective of the present study was to develop models for egg freshness and shelf-life predictions for the selected evaluation indicators including egg weight, Haugh unit (HU), and albumen height. Experiments were carried out at different storage temperatures for a total period of 29–32 days. All data were collected and fitted in to Arrhenius equation for egg freshness, while the HU data were applied to a probability model for shelf-life prediction. The results showed that egg weight, albumen height, and HU decreased significantly, while albumen pH increased with the extension of storage time. The higher the storage temperature, the faster the egg quality decreased. In addition, the bias factor, accuracy factor, and the standard error of prediction were selected to verify the developed quality models. Maximum rescaled R-square statistic, the Hosmer–Lemeshow goodness-of-fit statistic, and the receiver operating characteristic curve were used to evaluate the goodness-of-fit of the developed probability model for the shelf-life of eggs, which indicated that the presented predictive models can be used to assess egg freshness and predict shelf-life during different storage temperatures. Keywords: Eggs; predictive models; probability model; shelf-life; freshness. complex physical, chemical, and physiological changes (Al-Obaidi Introduction et  al., 2011). They can also be contaminated by microorganisms, re- Eggs are a natural source of extremely rich nutrients such as proteins, sulting in spoilage (Stadelman. et  al., 1977; Suresh et  al., 2006), af- fats, minerals, and vitamins (Eke et al., 2013). During storage, poultry fecting their quality. Freshness is the most important characteristic eggs are constantly carrying out life activities, accompanied by various © The Author(s) 2021. Published by Oxford University Press on behalf of Zhejiang University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which per- mits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. 2 C. L. Quan et al. related to egg quality, and its decrease mainly depends on time and numbered individually. The eggs were placed blunt end up in the carton temperature (Yimenu et  al., 2018). Albumen height, albumen pH, pulp egg trays (each tray contains 30 egg specimens) and randomly div- and egg weight are the key indicators for evaluating freshness, and ided into 5 groups. Then the eggs were placed in the chambers directly are greatly affected by storage time and temperature (Lee et al., 2016; without any other packages under different constant temperatures Dong et al., 2017; Vivian et al., 2017). The Haugh unit (HU) is a widely (7, 17, 23, 37, and 40 °C) for 29–32 days. During the storage period, used indicator to measure egg quality, and is a comprehensive indicator random sampling was generally performed at 2–4  day intervals, or to reflect egg quality converted based on egg weight and protein height 4–6 day intervals at low temperature. At each sampling time in each (Suresh et al., 2006; Xavier et al., 2008; Dong et al., 2017). trial, 3 eggs were randomly selected and used for the measurements Storage conditions such as storage temperature, relative hu- of egg weight, albumen height, HU value, and pH. Experiments were midity, and storage time will affect egg quality (Yimenu et al., 2018). conducted in triplicate. Predictive modeling could provide a tool for applying scientific methods to describe the chemical and physical changes occurring in Experimental methods food under different environmental conditions. Several models have Egg quality evaluation been used to describe the effect of environmental conditions on egg Weight, albumen height, and HU values of sampling eggs at each freshness. The acceptability of the first-order reaction and Arrhenius sampling point were measured using an egg multi tester (EMT-7300, model for predicting the changes of eggs weight, yolk index, and air Robotmation Co., Ltd., Tokyo, Japan). After separating the yolk and room height at the storage temperature from 5 °C to 35 °C with high albumen, each egg was placed in a beaker and homogenized with a regression coefficients provided a reference for the storage and sale of glass rod. The pH values were measured using a pH meter (FE20, hen eggs (Yu and Wang, 2012). Du et al. (2018) selected HU, egg shell METTLER TOLEDO,  Zurich, Switzerland) and were recorded thickness, shell breaking strength and deformation, albumen height, when the reading was stabilized. and yolk film strength as research indicators to establish a prediction model for HU and albumen pH during storage, which provided a Freshness quality prediction models theoretical basis for egg detection. Yimenu et al. (2017) constructed The egg quality dynamics model is developed based on the equation primary and polynomial models for egg freshness (weight loss rate, of thermodynamics (Yu and Wang, 2012; Equation 1). yolk index, albumen index, and HU) under constant temperature from 5  °C to 30  °C. Subsequently, regression analysis was used to ln X=ln X −kt (1) study the impact of environmental factors (temperature, relative hu- midity, and air flow rate) on weight loss, HU, and S -ovalbumin con- where X is the quality index (egg weight, albumen height, pH, and tent by establishing predictive model for egg freshness under constant HU value) at storage time t (day); X is the initial value of each temperature storage (Yimenu et al., 2018). The relationship between quality indicator (egg weight, albumen height, pH, and HU value); egg quality and storage temperature can be understood through –1 k is the reaction rate constant (day ); and t is storage time (day). the study of the deterioration mechanism of poultry eggs, which k is a variable that changes with temperature, and its value is is reflected by the kinetic model and has practical significance for determined by Equation 2. Equation 2 is commonly referred to as improving storage conditions (Samli et  al., 2005). Although several the Arrhenius equation, and this expression has achieved remarkable models have been developed for egg freshness, they do not consider success in describing the temperature dependence of chemical reac- the stochastic variability of the freshness parameters. The probability tions (Ratkowsky et al., 1982): models were mainly applied for bacterial growth in published ref- erences (Koseki and Nonaka, 2012; Wang et al., 2017). Wang et al. k = k · exp(−E /RT ) 0 a absolute (2) (2017) developed the probability of the time to reach a certain level increase of Staphylococcus aureus on rice cakes at different temper- where k is the pre-exponential factor, R is the universal gas constant atures. However, the development of a probability model under dif- [8.3144 J/(mol·K)], T is the absolute temperature (K), and Ea is absolute ferent temperatures indicating the different time to reach a certain the activation energy (J/mol). HU value to predict the shelf-life of eggs has been rarely reported. In the present study, we used fresh eggs as experimental mater- Probability model development for the shelf-life of eggs ials to (1) study the effects of different storage temperatures (7, 17, In order to estimate the shelf-life of eggs at different temperatures, a 23, 37, and 40 °C) on the egg quality indices (egg weight, albumen probability model based on HU values was developed in this study. height, pH, and HU); (2) establish an egg quality (egg weight, al- For the probability model development, each sampling interval was bumen height, and HU) change model during storage according to marked with 0 or 1 to indicate whether or not an HU value of 60 the chemical kinetic model and the Arrhenius equation; and (3) de- was reached. The probability of HU values decrease to 60 was col- velop a logistic model based on HU value to predict the shelf-life of lected and fitted to a logistic regression model using R software (R eggs, so as to predict the probability of HU reaching 60. Core Team, 2020). The analyses were conducted with the glm func- tion in R software package Stats. The initial fitted model was shown as follows, after a minor modification according to the approach Materials and Methods described by Wang et al. (2017): Experimental materials and storage Freshly laid unfertilized and unwashed brown egg samples were Logit (P)=α +α ·T+α ·ln(t ) 0 1 2 HU (3) obtained directly from a local husbandry technology company (Qingdao, China), were then transferred to the laboratory at 4 °C on where P is the probability of an arbitrary decrease to HU value of the same day. The eggs used in this study were produced by laying hens 60, Logit (P)= ln [ P/(1−P)] , α −α are the coefficients to be es- 0 2 in conventional cages with similar bodyweights and aged 28–42 weeks. timated, T is the storage temperature, and t is the time at which the HU A total of 180 brown eggs with intact shells were used in each trial and decrement of HU value reached the set values. Modelling egg freshness and shelf-life 3 Verification model respectively, with loss rate of 23.04% and 32.15%. In contrast, The statistical indices including accuracy factor (A , Equation 4), the weight loss of eggs stored at 7, 17, and 23 °C was much less bias factor (B , Equation 5), and standard error of prediction (SEP, than those stored at 37 °C and 40  °C. The weight loss of eggs Equation 6)  were employed to evaluate the performance and reli- during storage will naturally occur due to water evaporation. ability of each model (Wang et al., 2017). Similar trends were reported by Akyurek and Okur (2009), Lee The proximity between the predicted value and the observed et  al. (2016), and Yeasmin et  al. (2014). The published studies value can be measured by A . The larger A , the less accurate the showed that there was no significant decrease under conditions of f f average estimate, while a value of 1 indicates that the predicted 2 °C and 12 °C within 10 days (Lee et al., 2016). Studies have re- value and the observed value are completely consistent (Lebert et al., vealed that the higher the temperature, the greater the evaporation 2000). The acceptable range of A values depended on the number loss of the solvent in the egg through the cracks of the eggshell, of variables in the predictive model, and A increases 0.10–0.15 for and the lighter the egg weight (Yeasmin et  al., 2014; Brodacki each variable (Ross, 1996). et al., 2019). Besides, it was also found that the egg weight reduc- tion was related to the egg white, eggshell porosity and thickness, ( | log(μ /μ )|/n) predicted observed and water conductivity (Brodacki et al., 2019). A = 10 (4) where μ represents observed values; μ represents pre- Changes on albumen height under different temperatures observed predictived dicted value; n is the number of sampling points each trial. As shown in Figure 1B, it was observed that the albumen height B is a measure of the extent of under- or over-prediction, and the decreased significantly due to storage period and temperature. The evaluation of the degree of deviation between the predicted value albumen height decreased from 17.5 mm to 6.5 mm at 7 °C, from and the contour. A B value range of 0.7–0.9 or 1.06–1.15 was con- 17.5 mm to 5.5  mm at 17  °C, and from 17.5 mm to 4.0  mm at sidered as acceptable (Ross et al., 2000; Wang et al., 2012). 23 °C during 29 days of storage, and the decline was further ex- panded while stored at 37 °C and 40 °C. Similar albumen heights ( log(μ /μ )/n) predicted observed were also reported by Lee et al. (2016) and Tabidi (2011). In this B = 10 (5) study, the albumen height decreased greatly in the first 4 days, and SEP can measure and verify the accuracy of predictive models. the subsequent changes became slower, indicating that the quality of the eggs dropped rapidly during the initial short storage period. In addition, during the 5  days of storage, the albumen height at 100 (μ − μ ) observed predictived SEP(%) = . 23, 37, and 40 °C decreased faster than those at 7 °C and 17 °C. Average(μ ) n observed (6) These results indicate that higher room temperature had a greater negative impact on albumen height. This is explained by the evap- For the probability model, the maximum rescaled R-square statistic, oration of water through the pores in the eggshell and the release the Hosmer–Lemeshow goodness-of-fit statistic, and the receiver of carbon dioxide (CO ) from the albumen, which would increase operating characteristic (ROC) curve were used to evaluate the 2 as temperature rises (Serrano et  al., 2016). Therefore, purchased goodness-of-fit of the developed model (Agresti, 2007). eggs should be stored at low temperature to slow down the rate of decline in egg quality. Statistical analysis All data of quality indicators obtained from each experiment with Haugh unit changes under different temperatures triplicates was transferred into a Microsoft Excel sheet for data ana- The HU values decreased with longer storage time at all storage lysis and charting. The data were analyzed using Tukey’s multiple temperatures except at 17  °C and 37  °C after 25  days, which range test to determine statistically significant differences (p<0.05). might be caused by the individual differences of eggs. In addition, Model development and model validation were conducted by the a greater decrease in the HU values was found at higher temper- OH-Fit Excel Add-In software (Ding et al., 2011). atures (23, 37, and 40 °C) compared with the lower temperatures (7 °C and 17 °C), as shown in Figure 1C. The decline of the HU of eggs during storage is due to the decomposition of carbonic acid in Results and Discussion the egg white, which produces CO and water released through the pores of the eggshell, causing the electrostatic complex between Changes in egg quality indicators during storage the lysozyme and ovomucin to rupture (Eke et al., 2013; Yimenu In this study, the impact of different constant temperature storage et al., 2017). conditions (7–40 °C) on the change of egg freshness indices was in- The HU has been considered as the gold standard of egg quality. vestigated. Storage temperature and time obviously affected almost According to the egg grades of the USA, the quality of eggs can all parameters of egg quality investigated in this study. Egg weight, be ranked as AA (≥72), A (71–60), B (59–30), C (<29) based on albumen height, and HU significantly decreased with the extension HU values. Eggs with HU value less <60 are considered unfit for of the storage time, while albumen pH increased. consumption (Nematinia and Mehdizadeh, 2018). As shown in Figure 1C, during the experimental period, the freshness of eggs Changes on egg weight under different temperatures was still AA grade eggs at 7 °C and 17 °C; the HU value of eggs Egg weight decreased slowly during storage for 0–25  days at 7, stored at 37 °C and 40 °C for about 10 days declines to 60 and 17, and 23  °C. The decrease was much faster during storage at they should not be eaten. Based on the results hereby presented, 37  °C and 40  °C. The difference between 7  °C and 17  °C was the higher the storage temperature of eggs, the faster the decline not significant (p >0.05) within 17  days. As shown in Figure 1A, of HU. These results are in agreement with those of Nematinia the weight of eggs stored at 37 °C and 40 °C were reduced from and Mehdizadeh, (2018), Liu et  al. (2016), and Yeasmin et  al. the initial (64.42±0.88)  g to (49.58±1.24)  g and (43.71±1.02)  g, (2014). 4 C. L. Quan et al. Figure 1. Changes of the evaluation indicators of eggs over time, under different temperatures. A, egg weight; B, albumen height; C, Haugh unit; D, albumen pH. Changes in albumen pH under different temperatures Table 1. Estimation of rate constants of egg quality and determin- The albumen pH value is another parameter representing egg quality. ation of coefficients at different temperatures The albumen pH of fresh egg is between 7.6 and 9.7 (Sharp, 1929). Egg weight Albumen height Haugh unit Figure 1D shows the changes in albumen pH of eggs stored at 7, 17, Tempera- 23, 37, or 40 °C for nearly one month. It can be seen from the figure –1 2 –1 2 –1 2 ture (°C) k (day ) R k (day ) R k (day ) R that the albumen pH decreased in the first 4 days after the egg was 7 0.001688 0.937 0.006283 0.846 0.004069 0.884 laid. It has been speculated that the possible reason for this is that a 17 0.001797 0.853 0.009087 0.818 0.006757 0.754 series of chemical changes have occurred after the eggs are separated 23 0.002086 0.890 0.016500 0.923 0.012570 0.889 from the hens’ internal environment, but the specifics are unknown. 37 0.009547 0.921 0.026470 0.911 0.016350 0.872 Albumen pH values increased significantly with further extension of 40 0.013400 0.950 0.026570 0.883 0.016870 0.733 storage time, probably because of the evaporation of egg moisture and the release of CO (Yimenu et al., 2017). Table 2. Arrhenius equation for egg weight, albumen height, and Overall increases in the albumen pH of all eggs was observed Haugh unit at the end of all storage experiments. The albumen pH of all eggs increased sharply after 4  days, which was consistent with previous Quality index Equation R studies (Lapao et  al., 1999; Dutta et  al., 2003). In particular, after 20 days of storage, the albumen pH of eggs at 40 °C showed a great Egg weight Y =14.35–5921.4X 0.856 Albumen height Y =7.4157–3584X 0.895 degree of fluctuation, while other samples showed no such trend. One Haugh unit Y =8.9118–3910.3X 0.952 possible reason is the interaction of various egg qualities (such as 3 moisture content, CO content, and albumen viscosity) under condi- Y , Y , and Y are the negative logarithms of the Arrhenius equation of the tions of high temperature and long storage time (Mathew et al., 2016). 1 2 3 change of egg weight, Haugh unit, and albumen height during egg storage; X is the reciprocal of the absolute temperature of the egg during storage, 1/K. Egg freshness quality prediction models The kinetic model of egg quality for egg weight, HU, and albumen the negative natural logarithms of both sides of the Arrhenius model height under different storage temperatures was established by using in Equation 2 and fitting it with the data in Table 1, the egg quality the first-order kinetic rate equation, and the reaction rate constant –1 2 kinetic model was obtained (Table 2). (k, day ), and coefficient determinations (R ) were obtained as Based on the data in Table 2, substituting the activation en- shown in Table 1. The pH values were excluded for model develop- ergy (E ) and the Arrhenius equation constant (K ) obtained in the ment because of the mismatch of albumen pH data. Then, by taking a 0 Modelling egg freshness and shelf-life 5 Table 3. Estimated parameters of the logistic regression for arbitrary Haugh decrease during storage period Coefficient Estimate Std. Error z value Pr(>|z|) Maximum rescaled R c (area under ROC curve) Hosmer–Lemeshow (goodness-of-fit) 0.7068 0.975795% CI: 3.549 with 8 df (P=0.8953) α –33.38 6.966 –4.792 1.65E–06 0.9499–0.9884 α 0.3457 0.066 5.239 1.61E–07 α 7.115 1.637 4.346 1.38E–05 Std., Standard; Pr, probability; CI, confidence interval; ROC, receiver operating characteristic; df, degree of freedom. Figure 2. According to the developed model, the shelf-life of eggs, while maintaining grade A  during storage at different temperatures, could be determined. Logit (P) values at each temperature can be obtained, and the probabilities to become lower than grade A could be generated subsequently. Based on the reported limits on the growth of bacteria (Presser et  al., 1998; Tienungoon et  al., 2000; Le Marc et  al., 2005; Hwang and Juneja, 2011; Wang et al., 2017) that P≤0.1 indicates an “unlikely” or “no” growth region, P>0.5 indicates a “likely” or growth region, while P values between 0.1 and 0.5 indicate an “uncertainty” region, we set a similar criterion for eggs’ shelf-life maintaining grade A. As shown in Figure 2, P≤0.1 indicates an “unlikely” region to be lower than grade A, P>0.5 indicates likely to be lower than grade A, and P values between 0.1 and 0.5 indicate an “uncertainty” region. Therefore, the eggs’ shelf-life could be calculated as follows: t = exp((33.38−0.3457×T)/7.115) shelf-life Figure 2. Probability of Haugh unit decrease to 60 at different temperatures. Solid and dashed lines represent the probability (P=0.5 and P=0.1) of reaching where T is the storage temperature, and t is shelf-life of eggs. shelf-life a Haugh unit of 60. According to the above equation, it is easy to predict shelf-life at different temperatures within the limits of the experimental design. Table 4. The parameters of validation for the predictive models at As shown in Figure 2, the likely shelf-life of eggs maintaining grade different temperature A at 7, 17, 23, 37 and 40 °C were 77.59, 47.73, 35.69, 18.06 and Quality index A B SEP (%) 15.61 days, respectively. The results showed that the logistic model f f developed in the present study could provide useful information for Egg weight 1.014 1.011 1.689 eggs storage management. Albumen height 1.062 0.988 6.465 Haugh unit 1.063 1.133 2.321 Verification of model Based on the evaluation indices (B , A , and SEP), the corresponding f f experiment into Equation 2, the prediction models for egg quality, deviation factor, predicted value deviation, and predicted standard egg protein height, and HU can be obtained as follows: deviation are obtained by comparing the predicted value with the measured value (Table 4). As shown in Table 4, the A values were −49231/RT absolute ln X = ln X −(1706577×e )×t egg weight 0 egg weight egg weight in the range 1.014–1.063 for egg weight, HU, and albumen height, and B ranged from 0.988 to 1.133, which were all acceptable. The −42575/RT A ranged from 1.0 to 1.15 and is acceptable because only tempera- absolute ln X = ln X −(201189×e )×t albumen height 0 albumen height albumen height ture was considered in the developed models (Wang and Oh, 2012). B values <0.7 or >1.15 are considered unacceptable (Tienungoon et −29797/RT absolute ln X =− ln X −(1662×e )×t Haugh unit 0 Haugh unit Haugh unit al., 2000). The smaller the value of SEP, the better the model can be used to predict data, and the maximum value in this study is no more than 7%. Results obtained in the present study indicated that the Development of logistic model for shelf-life of eggs established dynamic model could better describe the quality changes In order to determine the shelf-life of egg during a storage period, HU of eggs in the storage process. was selected as the index to develop a logistic model. As mentioned above, eggs will be ranked lower than grade A if the HU reaches less Conclusions than 60. Therefore, HU value of 60 was set to be the criterion to deter- mine the shelf-life of fresh eggs. The estimated parameters of the logistic In this study, under all temperature conditions considered, egg regression model’s HU decrease under different temperatures are pre- weight, albumen height, and HU continued to decrease with the sented in Table 3. The indices of goodness-of-fit of the model including extension of the storage period, while albumen pH gradually in- maximum rescaled R , area under receiver operating characteristic creased. A  noteworthy result was the visibility of a rapid decrease (ROC) curve, and Hosmer–Lemeshow goodness-of-fit are also listed in in the HU and the egg weight for short times at high temperatures. Table 3. The results obtained in this study showed that the developed Therefore, low-temperature storage or transportation is a better probability models were significant for the shelf-life prediction of eggs. choice for keeping the eggs fresh. Further research should be con- The cumulative probability distributions generated by the de- ducted to optimize fresh-keeping conditions to maximize the fresh- veloped logistic model at different temperatures are shown in keeping effects while reducing unnecessary waste. The developed 6 C. L. Quan et al. Koseki, S., Nonaka, J. (2012). Alternative approach to modeling bacterial lag quality models can be used to predict egg freshness changes in terms time, using logistic regression as a function of time, temperature, pH, and of egg weight, albumen height, and HU at temperatures of 7–40 °C sodium chloride concentration. Applied and Environmental Microbiology, during storage, and the logistic model was useful for the shelf-life 78(17): 6103–6112. predictions of eggs. The models presented in this study could simu- Lapao,  C., Gama,  L., Soares,  M. (1999). 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Journal

Food Quality and Safety – Oxford University Press

Published: Sep 7, 2021

Keywords: Eggs; predictive models; probability model; shelf-life; freshness

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