Propolis as a Natural Preservative for Frozen Fish Burgers: A Kinetic Study of Lipid Oxidation and Microbial Growth
محورهای موضوعی : Food and Health
Mohsen Mokhtarian
1
,
Mohsen Dalvi-Isfahan
2
,
Fatemeh Koushki
3
1 - Department of Food Engineering, Roudehen Branch, Islamic Azad University, Roudehen, Iran
2 - Department of Food Science and Technology, Faculty of Agriculture, Jahrom University, Iran
3 - Department of Food Engineering, Roudehen Branch, Islamic Azad University, Roudehen, Iran
کلید واژه: Propolis (Apis mellifera), / Lipid oxidation kinetics, / Microbial spoilage, / Frozen fish burger, / Sensory evaluation,
چکیده مقاله :
The kinetic mechanisms governing fatty acid (FA) degradation and microbial growth rate in seafood products are of paramount importance. This study evaluated the interactive effects of propolis incorporation at varying concentrations and storage duration on fatty acid oxidation kinetics and its inhibitory role in suppressing bacterial and fungal proliferation in frozen fish burger patties (FFB) stored at -18°C. The rates of fatty acid degradation and microbial growth in FFB during the storage period were found to follow zero-order kinetic models. After three months of storage, the treatment group containing 0.4% propolis (P-IV) exhibited the lowest growth rates (log10 CFU/g) for total viable count (3.66) and fungi (2.43). Correspondingly, this group displayed the lowest rate of peroxide value increase (k0 = 0.0462 meq O2/kg oil/day), indicative of minimal fatty acid oxidation, and received the highest sensory evaluation scores. The results demonstrate that incorporating 0.4% propolis into FFB and storing them at -18°C can effectively retard lipid oxidation and microbial proliferation, while concomitantly enhancing sensory quality for up to 86 days, which can be considered the optimal shelf life under these conditions.
The kinetic mechanisms governing fatty acid (FA) degradation and microbial growth rate in seafood products are of paramount importance. This study evaluated the interactive effects of propolis incorporation at varying concentrations and storage duration on fatty acid oxidation kinetics and its inhibitory role in suppressing bacterial and fungal proliferation in frozen fish burger patties (FFB) stored at -18°C. The rates of fatty acid degradation and microbial growth in FFB during the storage period were found to follow zero-order kinetic models. After three months of storage, the treatment group containing 0.4% propolis (P-IV) exhibited the lowest growth rates (log10 CFU/g) for total viable count (3.66) and fungi (2.43). Correspondingly, this group displayed the lowest rate of peroxide value increase (k0 = 0.0462 meq O2/kg oil/day), indicative of minimal fatty acid oxidation, and received the highest sensory evaluation scores. The results demonstrate that incorporating 0.4% propolis into FFB and storing them at -18°C can effectively retard lipid oxidation and microbial proliferation, while concomitantly enhancing sensory quality for up to 86 days, which can be considered the optimal shelf life under these conditions.
Propolis as a natural preservative for frozen fish burgers: A kinetic study of lipid oxidation and microbial growth
Mohsen Mokhtarian*1, Mohsen Dalvi-Isfahan*2, Fatemeh Koushki1
1. Department of Food Engineering, Roudehen Branch, Islamic Azad University, Roudehen, Iran
2. Department of Food Science and Technology, Faculty of Agriculture, Jahrom University, Iran
Running title: Kinetics of propolis preservation in frozen fish burgers
*Corresponding Authors:
Mohsen Mokhtarian
Mohsen Dalvi-Isfahan
Email: mokhtarian.mo@gmail.com & mokhtarian.mo@riau.ac.ir
Mohsen.dalvi@gmail.com & dalvi@jahromu.ac.ir
Tel: +98(935)-260-1788
https://orcid.org/0000-0003-4551-7065
https://orcid.org/0000-0002-9140-331X
Abstract
The kinetic mechanism of fatty acids (FA) degradation and microbial growth rate (MGR) in seafood are very important. In this research, the interaction effect of propolis addition (at different concentrations) and storage times on the FA oxidation kinetics and its inhibitory role on the suppression of bacterial/fungi growth of stored FFB at -18°C was evaluated. The FA degradation (or microbial growth) rates in FFB during storage period follows the zero-order kinetics. The lowest growth rate (log10 CFU/g) of total viable count (3.66) and fungi (2.43) of FFB was observed after three-months storage in the P-IV, that corresponded to the lowest degradation rate of peroxide value (k0=0.0462 meq O2/kg oil/day) and the highest sensory evaluation scores. Generally, adding 0.4% propolis to FFB and storing them at -18°C for up to 86 days (as the best shelf life) can effectively prevent lipid oxidation and microbial growth and improve sensory quality.
Keywords: Propolis (Apis mellifera), Lipid oxidation kinetics, Microbial spoilage, Frozen fish burger, Sensory evaluation.
1. Introduction
Processed meat products like burger patties are highly perishable and susceptible to quality deterioration because of their preparation processes, such as cutting, grinding, mixing, and forming. These processes expose more surface area of the meat to oxygen and microorganisms, which can accelerate the oxidation and microbial growth, as well as cause mechanical injury to the tissues. This promotes biochemical changes and microbial contamination, which result in quality deterioration (Nie et al. 2022). The assessment and prediction of fish burger freshness (FBF) are important for ensuring safety, quality, and shelf life, as well as for reducing food waste and optimizing production and distribution processes (García et al. 2022). The FBF can be measured by various indicators, such as sensory attributes, pH, water activity (aw), total volatile basic nitrogen (TVB-N), thiobarbituric acid reactive substances (TBARS), and microbial counts (Shabani et al. 2021). However, the measuring of these indicators is often time-consuming, destructive, and requires skilled personnel and expensive equipment. Therefore, there is a need for rapid, non-destructive, and reliable methods to monitor and predict FBF (Walayat et al.2023). One of the emerging approaches for the FBF prediction is based on mathematical modeling, which uses mathematical equations to describe the changes in quality indicators as a function of time and other influencing factors, such as time, temperature, oxygen, packaging, and additives (García et al. 2022; Endoza et al. 2004).
There are different types of models that can be used to estimate the optimal storage time and conditions of burger patties based on their quality and safety parameters. Among them, the most well-known models are kinetic models such as the Arrhenius model, the Q10 model, and the Weibull model. For example, Quevedo et al. (2018) studied the quality changes of frozen industrial burgers stored at different temperatures. The authors used the Weibull model to fit the kinetics of oxidative rancidity, color, texture, and other indicators. The results verified that the shelf life of the burgers was mainly affected by the storage temperature and the oxidation process. Another modeling technique that was successfully utilized to predict the shelf life of chilled/supercooled pork was the entropy weight method (EWM). This method employs a holistic quality indicator that combines various quality indexes (such as microbial, chemical, and sensory) using a weighting method (Zhao et al. 2022).Regression techniques such as partial least squares (PLS) can also be utilized to estimate shelf life. PLSR can handle multiple predictors and responses, deal with collinearity and noise, and extract latent variables that capture the relationship between the quality attributes and the storage conditions (Ran et al. 2021). Marqueset al.(2022)used a PLS model to predict the sensory rancid taste, pH, and TBARS of grass carp burgers from the RGB pattern of digital images. They found that the models had high coefficients of determination (R2-value) and the low root mean square errors (RMSE) of prediction, indicating a good agreement between the predicted and observed values. Furthermore, Cui et al. (2023) reviewed the performance of various shelf life prediction models, such as neural network models and kinetic models, in the food field, and conducted a horizontal comparison of the modeling approaches. These studies demonstrate that the mathematical modeling to estimate freshness assessment can be applied at different levels of complexity and detail. The levels range from single quality indicators to multiple quality attributes, from raw to processed products in fish and sea products, and from static to dynamic conditions. Nevertheless, kinetic models are known as a superior technique for predicting and estimating shelf life of food products, such as fish burgers, because they can capture the effects of environmental factors, provide mechanistic insights, and facilitate prediction under different storage conditions (Choosuk et al. 2022).
This study aimed to elucidate the quality attributes of fish burger during storage by applying kinetic modeling. The factors that influenced the quality were the concentrations of propolis, a powerful antioxidant, and the duration of storage.
2. Material and Methods
2.1. Raw material preparation
Fresh cold fish (Oncorhynchus mykiss) with mean weight (800±100 g) and length (30±2 cm) were purchase from a local market and carried in cold-chain (at 1-4oC) to the Azad University laboratory. The required raw propolis (Apis mellifera L.) was prepared from Bee-Breeding Center.
2.2. Production of fish burger patties
Initially, the prepared fish were washed by tap water. After the heads of the fish were removed, they were peeled, deboned, and their intestines were removed. Next, the lean meat was cut into fillets, and a homemade meat grinder (Panasonic, MK-ZJ3500, Japan) was used to mince them (with 5 mm particle sizes).
The ingredients of salt (2%), mixed spices (2%, including curry powder, pepper, and turmeric), bread powder (5%), sugar (0.5%), garlic powder (1.5%) and onion powder (4.0 %) were uniformly mixed (as supplements) and then, they were subjected to ultraviolet light (at 200-280 nm) for 20 min for decontamination. According to the standard recipe of fish burger, 85% (w/w) of minced fish fillet was combined with 15% (w/w) of additives to form a consistent paste. Next, the paste was mixed with propolis powder at various concentrations (from zero to 0.4%). Round and circular burgers (with 1 cm thickness, 10 cm diameter and 100 g±5 weight) were prepared from the fish pastes. The burgers were packed in polyethylene bags by hand and frozen at -18oC for three months. The quality of the frozen fish burgers (FFB) was assessed at various time points (0, 30, 60 and 90 days) (Shabani et al. 2021).
2.3. Measuring peroxide values of FFB’s oil during storage
The oil was extracted from each FFB sample by Soxhlet extractor at less 20oC (for inhibition of lipid oxidation), in accordance to method of Shabani et al. (2021). The iodometric titration method used to measure the peroxide value (PV) of the extracted oil.
2.4. Microbiological analysis
The microbiological analyses on the sample were conducted at 0, 30, 60 and 90 days during storage at -18oC. Total viable bacteria (TVC) of each sample were enumerated by using plate count agar (Fater-riz-pardaz, B630, Iran) followed by incubation at 37oC for 48 h (INSO 2015). The fungi (mold and yeast) of FFB samples were enumerated by using Yeast Extract Glucose Cholranphenicol Agar after their inoculation using the surface plate technique. The inoculated plates were incubated at 25oC for 5-7 days before enumeration (INSO 2008). At the end of the incubation period, plates with 30 to 300 colonies were counted. The results were expressedLog10 CFU/g of the sample.
2.5. Data fitting and model validation
2.5.1. Quality kinetic modeling of FFB in frozen storage
The radical oxidation mechanism (formation of hydroperoxides) along with the microbial growth rate (MGR) in the FFB are the most destructive reactions that lead to a decline in the product quality during the storage period. We monitored the changes of the PV and the TVC during the storage period to determine the microbial and the oxidation reaction orders, as well as the shelf life estimation of the FFB. Table 1 shows different models used to display the changes in the increasing PVs (or TVCs) of different FFB samples during storage and to find out their reaction orders (from zero-order to second-order).
Table 1.
The coefficient of determination (R2) and mean relative deviation or P(%) used to assign the best and supreme model for the order of lipid oxidation reaction (or MGR). For quality fit, the R2-value should be higher and the P(%) should be lower. These parameters can be calculated by Equations (1) and (2). It should be noted that, the Microsoft Excel version 2007 was used to data fitting.
(1)
(2)
Where, θp,i is predicted data, θe,i is observed data, 
is average of predicted data and N is the number of observation (Mokhtarian and Garmakhany 2017; Tavakolipour and Mokhtarian 2012).
2.5.2. Shelf-life prediction of FFB in frozen storage
The shelf life of produced fish burger affected by process and storage conditions. By and large, after knowing the key parameters, the shelf life of the FFB can be calculated by the equations are inserted in Table 1 (Choosuk et al. 2022).
2.6. Consumer preference
The sensory quality of the FFB (after three months storage) was assessed by 15 trained and experienced panelists (men and women) aged 20 to 30 years. They were given random samples of raw fish burger (each weighing about 20 g) labeled with 3-digit random numbers. They rated sensory attributes (mainly aroma), organoleptic characteristics (general appearance, texture, and visual color) and overall acceptability of FFB according to the method described by Stone and Sidel (2004). The panelists used a 5-point hedonic scale (1=extremely dislike, 2=dislike, 3=neutral, 4=like and 5=extremely like) to score different properties and their means were considered for final evaluation (Mokhtarian el al. 2017; Reis et al. 2017).
2.7. Data analysis
The Statistix version 8 (Analytical Software Inc., Tallahassee, FL 32312, USA) program was applied to make analysis of variances (ANOVA) and perform least significant difference (LSD) test for different treatments at the confidence level of 99%.
3. Results and Discussion
3.1. Interaction effect of propolis concentration and storage days on peroxide value of FFB
One of the most common chemical reactions of oil or fat-based products is auto-oxidation that takes place due to various agents during storage. The fat oxidation (in other words, formation of hydro-peroxide) of unsaturated fatty acids (USFA) and specifically polyunsaturated fatty acids (PUFA) in FFB (fish finger burger) during storage has direct effect on its quality (Srinivasan and Kirk Lindsay 2017; Hu and Jacobsen 2016). The major method for measuring the lipid oxidation in FFB is peroxide value (PV), such that the increase of this index leads to severe degradation of USFA in FFB (Shabani et al. 2021). The results of mean comparison of PV-value of FFB during 3 months storage at -18°C are given in Figure 1-A.The results showed that interaction effects of type FFB (I, II, III & IV) and extension of storage days both had a positive effect (p<0.05) on changing the PV-value of FFB (Figure 1-A). The lowest PV-value of FFB during the entire storage period was observed in relation to P-IV sample (corresponding to the FFB sample containing 0.4% of the propolis). As well, the result indicated that in all the examined samples, increasing the days of storage from zero to 90 days caused an increase in the PV-value. The obtained results from the literature indicated that, adding natural herbal plants (such as oregano, green tea, sage, and laurel) to ready-to-eat products like FFB reduce the progress of lipid oxidation (Shavisi et al. 2017; Ozogul and Uçar 2013). According to Connell (1975), the permissible PV should be between 10 to 20 meq O2/[kg oil] to have an acceptable fat rancidity for consumption of foodstuff. Furthermore, adding organic compounds (such as herbal extracts with considerable TPC) to fish products considerably delay increasing their PV during storage time.
3.2. Interaction effect of propolis concentration and storage days on total viable count of FFB
The bacterial growth is the main mode of product spoilage, and counting the bacteria is important as one of the quality indicators of fish finger burger (FFB). The interactive effect of propolis concentration and storage days on total viable count (TVB) of FFB within the three months storage time at -18°C is shown in Figure 1-B. The results showed that the type of FFB (I,II, III & IV) and days of storage had a significant effect (p<0.05) on changing the TVB of FFB (Figure 1-B). As seen, the lowest and highest TVB of FFB belonged to P-IV (at first day of storage) and P-I (after 90-days of storage), respectively. This state is mainly due to the inhibitory effect of propolis (especially the hydroxyl groups of phenolic compounds) on normal activity of bacterial cell membrane via binding to the walls of cells (Shabani et al. 2021). Similar finding was reported by Çoban and Keleştemur (2017). They used the essential oil of Zataria multiflora Boiss (at level of 0.4% w/v) in catfish fish burger (CFB) formulation. Their results indicated that the microbial load of the CFB was reduced significantly in comparison to the control sample. Furthermore, the result indicated that in all the examined samples, increasing the days of storage from zero to 90 days caused an increase in the TVB. The obtained results from the literature indicated that, adding natural herbal plants (such as propolis, oregano, green tea, sage, and laurel) to ready-to-eat products like FFB reduce the progress of lipid oxidation (Shavisi et al. 2017; Ozogul and Uçar 2013). According to Connell (1975), the permissible TVB should be between 10 to 20 meq O2/[kg oil] to have an acceptable fat rancidity for consumption of foodstuff. Furthermore, adding organic compounds (such as herbal extracts with considerable TPC) to fish products considerably delay increasing their TVB during storage time.
3.3. Interaction effect of propolis concentration and storage days on fungi of FFB
The ANOVA showed that the FFB’s kind (I, II, III & IV) and days of storage, had an effect (p<0.05) on the fungi (mold and yeast) of FFB (Figure 1-B). Even though the growth rate of fungi in the control sample or P-I (without propolis) after 90 days of freeze-storage under -18oC reached to 2.94 log10 CFU/g, the lowest amount of fungi (2.43 log10 CFU/g) was observed in the stored sample of P-IV (~18% reduction compared to the control sample) under similar conditions (Figure 1-C). As seen, these values are lower than the corresponding values for the TVC, which represents the lower growth rate of fungi. This event is mainly due to a more effective effect of propolis in destroying fungi (mold and yeast) than on bacteria (or TVC). In addition, due to the fastidious nature of fungi, and due to the presence of abundant nutritious compounds in the FFB, the growth of the TVC is higher than that of the fungi, and they can use better and more nutrient sources (Frazier et al. 2013). Furthermore, it should be noted that, the growth of the fungi in all the FFB samples is lower than the permissible value (i.e. 3 log10 CFU/g) announced by the Iranian national standard during the entire storage period (INSO 2016). Özvural et al. (2016) could reduce the mesophilic bacteria and yeast of hamburger patties stored at 4oC for 8 days to 7.64 and 10.20 log10 CFU/g, respectively. These values were significantly lower than their respective control samples when they combined patties with 5% green tea extract. Almuhayawi (2020) stated that propolis had antimicrobial efficacy against bacteria, viruses, fungi and protozoa. He claim that the most abundant antimicrobial compounds of propolis are related to terpenoid lupeol, flavonoids (fisetin, quercetin, pinocembrin, apigenin),phenolic compounds (kaempferide, cinnamic acid) etc.
Figure 1.
3.2. Kinetics modeling of FFB’s lipid and microbial degradation
To achieve the optimal storage conditions of FFB enriched with various amounts of propolis concentration (from zero to 0.4%), the kinetic changes of the quality control indicators degradation of FFB were monitored in terms of chemical (fatty acid oxidation and monohydroperoxide formation or MHP) and microbial (microbial growth rate or TVC) properties during three months of storage at -18oC. Table 2 shows the kinetic data for the peroxide value and the total viable count in FFB when they were fitted by zero, first and second order reactions. The results showed that the changes in the concentration of MHP (or TVC) in FFB during the storage period follow by the zero-order kinetic reaction (this claim is confirmed by examining the ratio of [R2/P]). According to Table 2, it is vividly seen that the degradation rate (k0) of fatty acids and the growth rate of TVC ranged between 0.0462 and 0.1283 meq O2/(kg oil/day) and from 0.0148 to 0.0170 log10 CFU/g/day, respectively. Quevedo et al. (2018) investigated the kinetic modeling (by Weibull model) of frozen industrial burgers based on PV formation at -18oC. Their results indicated that the kinetic rate of PV formation in the burger was 0.009 meq O2/(kg oil/day), which this value confirms our obtained results.
The best storage time (or shelf life) in which the quality characteristics of the product (especially in terms of the degree of rancidity and microbial load) are preserved and the consumer will receive the most nutritional properties from the product by consuming it, is calculated by Equation (ts=(C0-C)/k0). According to the chemical (i.e. PV) and microbial (i.e. TVC) quality control indicators (QCIs) and with considering the reaction constant (k0) for the zero-order kinetic model (as the best model), the shelf life of product (P-IV) (as the best treatment and containing 0.4% propolis concentration) was determined ~86 days for both QCIs.
Table 2.
3.4. Sensory properties of FFB
The scores of appearance and organoleptic attributes for the uncooked FFB with different concentrations of propolis stored three months at -18oC are given in Table 3. The overall acceptance scores of FFB made with different levels of propolis concentration were significantly (p<0.05) higher than the control samples (Table 3). While the control sample of FFB (or P-I) obtained 58% of the total possible sensory scores, those made with 0.1, 0.2 and 0.4% gained respectively about 72.5, 87 and 96% of the maximum scores. Additionally, the ANOVA outcomes confirmed that the FFB made with propolis (at different concentrations) had significantly better general appearance, aroma, color, texture, and overall acceptance than those made without propolis (control samples).
Table 3.
3.5. The effects of propolis concentration on peroxide value, microbial activities and overall acceptance of FFB during frozen storage
The added propolis not only affects the chemical parameters (especially PV) and the microbial activities (TVC and fungi), but also affects the organoleptic properties (mainly appearance, aroma, color and texture) of FFB in frozen storage. Furthermore, when the propolis concentration in FFB increased (from zero to 0.4%), the production rate of PV diminished significantly after the samples stored three months at -18oC (Figure 2). High and positive Pearson correlation (r=+0.9969 & R2=0.9938) between the PV and reaction constant of model or k0 (which represents a strong and consistent dependence of the two parameters) confirmed the relation between these two parameters.
Similarly, the producing rate of TVC and fungi significantly decreased when the samples of prepared FFBs stored at the same conditions (Figure 2). While the PV, TVC and fungi of the FFB sample (with 0.4% of propolis concentration) reduced respectively to ~32, ~4, and ~8.5% after three months storage at -18oC, its total acceptance scores (for organoleptic properties) increased >65% in comparison with the control sample.
Figure 2.
4. Conclusion
This study demonstrates the potential of mathematical modeling to provide accurate and reliable predictions of fish freshness in fish burger patties, as well as to optimization of food processes. The outcomes indicated that the peroxide value and the total viable count can all be able to estimate the shelf life of FFB when stored at -18oC. The frozen fish burgers treated with 0.4% of propolis powder (i.e. P-IV) that were stowed at -18oC for a prolonged period (up to 3 months) had the lowest rate of lipid-oxidation and microbial growth, and these samples indicated the highest score of overall acceptance as well. A zero-order kinetic response was used to evaluate the reaction of the PV-value, and TVC change during frozen storage. In addition, according to the results, the changing rate of the PV-value (as primary oxidation products) was faster than the microbial attributes (~32% for PV vs. ~4% for TVC, in the sample of P-IV). In a nutshell, rancidity is one of the first quality control indexes that can be recognized when fish burgers start to lose their quality, and it can be controlled by diminishing the storage time and adding the natural preservatives (in acceptable level).
Statements and Declarations
Data Availability: The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.
Funding: The authors did not receive support from any organization for the submitted work. This study was conducted at the personal expense of the authors and had no sponsorship.
Financial interests: The authors declare they have no financial interests.
Conflict of Interest: The authors declare that they have no conflict of interest.
Ethical Approval: This article does not contain any studies with animals performed by any of the authors.
Patient Consent Statement: Not applicable.
Informed Consent: Not applicable.
Author Contribution
Mohsen Mokhtarian: Formal Analysis, Methodology, Extraction data, Formal Analysis, Writing Original Draft, and Supervision.
Mohsen Dalvi-Isfahan: Conceptualization, Writing Original Draft, and Supervision.
Fatemeh Koushki: Conceptualization, and Methodology.
ORCID and Mail Addresses of Authors
1) Mohsen Mokhtarian
Email: mokhtarian.mo@riau.ac.ir & mokhtarian.mo@gmail.com
https://orcid.org/0000-0003-4551-7065
2) Mohsen Dalvi-Isfahan
Email: mohsen.dalvi@gmail.com
https://orcid.org/0000-0002-9140-331X
3) Fatemeh Koushki
Email: Koushki.eng@gmail.com
https://orcid.org/0000-0003-4266-0085
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Figures Captions:
Figure 1. The interaction effects of different propolis concentration (from zero to 0.4%) and storage days (up to 90 days) on the peroxide values (A), the total viable count (B) and the fungi (C) of FFB in frozen storage at -18oC.
Figure 2. The effects of fortifying FFB by adding propolis from zero (P-I) to 0.4% (P-IV) on chemical (PV in meq O2/kg oil) and microbial (TVC and fungi, all in log10CFU/g) properties along with their overall acceptance scores of organoleptic evaluation after three months storage (at -18oC).
(A)
(B)
(C)
Figure 1. The interaction effects of different propolis concentration (from zero to 0.4%) and storage days (up to 90 days) on the peroxide values (A), the total viable count (B) and the fungi (C) of FFB in frozen storage at -18oC.
Figure 2. The effects of fortifying FFB by adding propolis from zero (P-I) to 0.4% (P-IV) on chemical (PV in meq O2/kg oil) and microbial (TVC and fungi, all in log10CFU/g) properties along with their overall acceptance scores of organoleptic evaluation after three months storage (at -18oC).
Tables Captions:
Table 1. The different forms of quality kinetics models along with its shelf life for different order reactions.
Table 2. Kinetic parameters for FFB’s lipid oxidation (or microbial growth rate) after three months at -18oC storage.
Table 3. The scores of organoleptic attributes(*1) of the FFB including different amount of propolis concentration after three months storage at -18oC.
Table 1. The different forms of quality kinetics models along with its shelf life for different order reactions.
