1. Introduction
Kimchi is a traditional Korean food consisting of fermented salted vegetables (i.e., cabbage, radish) and ingredients such as spring onion, garlic, ginger, and red pepper powder (CODEX STAN 223-2001). Other fermented vegetable products similar to Kimchi are sauerkraut (fermented cabbage), pickled cucumbers, and Tsukenmono (preserved vegetables from Japan). Notably, fermented vegetable products are known for various health benefits around the world, and many studies have been conducted to prove such claims [
1,
2,
3].
While Kimchi was traditionally made in the home, it is now commodified and mass-produced owing to the rise of the nuclear families eating out and group meals. Korean cabbage Kimchi accounts for 75% of domestic Kimchi sales, from Korean Won (KRW) 677.4 billion in 2014 to KRW 807.3 billion in 2016 and have been increasing yearly. In addition, Kimchi exports reached US
$ 97.45 million in 2018, a 20% increase compared to the year before with the number of export destinations reaching 68 countries [
4].
Since Kimchi is a non-sterilized product, its fermentation continues during distribution. However, the taste and edibility period depend on the degree of fermentation. This makes it very difficult to ensure the quality of the product. Food is inevitably exposed to various temperature conditions from production to delivery. The temperature of the workshop where Kimchi is manufactured is kept below 10 °C, and the storage warehouse where it is kept until dispatch is typically 0–2 °C. Domestic sales are shipped in a refrigerated truck (0–5 °C) and then kept in refrigerated retail displays (2–10 °C) while exported Kimchi is transported by ship in a temperature controlled container. Extreme temperature control is required as the product is exposed to the external environment upon quarantine, customs clearance, warehouse transfer, and sale upon arrival.
Owing to the diverse temperature changes during distribution, the maturity and edibility of Kimchi cannot be confirmed until the packaging is opened. To solve this problem, Jung et al. [
5] developed a chitosan-based carbon dioxide indicator to evaluate the extent of ripening of Kimchi according to the concentration of carbon dioxide inside the packaging. Kim et al. [
6] aimed to identify the fermentation stage of Kimchi by evaluating the volatile organic compounds (VOCs) released using a colorimetric indicator and correlating the results with the physicochemical state of the Kimchi. These methods allow the consumer to roughly check the ripening of Kimchi via an indicator in the packaging at the time of purchase, but they do not allow quantitative information about the detailed ripening status. Therefore, it is important to inform consumers about the quality of their Kimchi by predicting how the freshness is affected by exposure to different temperatures and how long a certain level of quality can be maintained under a specified storage temperature.
The effects of external factors on the physical, chemical, and microbiological changes within food can be mathematically predicted and used for food safety and quality control assessment [
7,
8,
9]. Predictive models are developed using a combination of primary and secondary models. The primary model predicts the change in food quality index over time, and the secondary model considers the temperature dependence of the parameters calculated in the primary model. Subsequently, the accuracy of the model is verified by comparing it with observational data that was not used to develop the model (either fixed-or fluctuating-temperature quality observations) [
10,
11]. Such predictive models have been actively studied to surmise the growth or decline of microorganisms on food exposed to dynamic temperature changes [
12,
13,
14,
15]. However, these models could only describe the quality index change for the cases with a constant value at the stationary stage. They cannot be used for the cases where the quality index values at the stationary phase vary with storage temperature such as Kimchi acidity. Similar phenomena have been reported with microbial growth in beef [
16,
17]. Jaisan and Lee [
18] developed a kinetic model of Kimchi acidity change for the confining range between the lag and exponential growth phases, neglecting the stationary phase to avoid the difficulty of modeling it. Thus, for the case of the stationary phase, it is necessary to develop a methodology for producing a model that can describe acidity change from the lag to the stationary phases with the quality index varying with temperature history.
In this study, we analyzed the change of Kimchi quality according to temperature throughout the distribution process with several quality indices. Subsequently, we selected acidity as an appropriate freshness index that is dependent on temperature and has a high correlation coefficient with the sensory quality. Moreover, the selected freshness index is easily measured and reproducible in the field. We developed a dynamic prediction model to identify the freshness of Kimchi in a fluctuating-temperature environment (such as during distribution) by predicting mathematically selected quality index changes. In addition, we proposed a method for constructing food quality models using the mean kinetic temperature (MKT). The MKT represents the temperature history of the food at a given time as a single value. Finally, we verified the validity of the model by comparing the model prediction results with actual acidity measurements obtained when the Kimchi was exposed in a real fluctuating temperature environment.
The developed kinetic model uniquely treated the quality index at the stationary phase to be a function of MKT. It could successfully reproduce the observations under both constant and varying temperature conditions. This will help the suppliers decide on the sales and disposal of Kimchi in circulation based on the model prediction using the monitored temperature histories for their products. Both suppliers and consumers could prepare the temperature histories to make Kimchi of their favorite flavor. The developed model can also be applied to other products such as beef for which the quality index at the stationary phase changes with temperature histories.
2. Materials and methods
2.1. Sample Preparation
Kimchi samples used in this experiment were packed in 500 g units in polyethylene (PE) films immediately after production in a Kimchi manufacturing company (D Company, Seoul, Korea) and were transported in a refrigerated truck (2–5 °C). On arrival, the samples were stored in refrigeration units (Rei-technology Corporation, Anyang, Korea) at 0, 5, 10, and 20 °C. To reflect seasonal changes, Kimchi was purchased and tested in spring (March to May), summer (August to September), and winter (November to January), and the tests were labeled as experiments 1, 2 and 3, respectively.
According to the Codex Alimentarius, a collection of international food standards, the composition of acidity for fermented kimchi should not be more than 1%. Accordingly, the end of storage for Kimchi was generally selected to be the time for the acidity to approach the value of 1%. However, the observation period was extended to consider the plateaus of the stationary phase in this study. Kimchi generates carbon dioxide in the process of fermentation, and the polyethylene-made wrap could burst. These were considered in choosing the end of storage.
2.2. Quality Characteristics for Kimchi Ripening Index
To develop a prediction model that scientifically identifies the ripening of Kimchi during distribution, we first conducted experiments to evaluate a suitable ripening index. The experimental parameters chosen to reflect characteristics of Kimchi were pH, total acidity, Hunter color, hardness, aerobic count plate, lactic acid bacteria, and sensory characteristics.
2.2.1. PH and Acidity
A 500 g unit of Kimchi was pulverized in a blender for 1 min and then filtered with gauze. The pH of the sample was then measured using a pH meter (TA-70, DKK-TOA Corporation, Tokyo, Japan). The acidity was determined by measuring the amount of 0.1 N (
w/
v) NaOH consumed to neutralize the pH to 8.2 after taking 20 mL of Kimchi filtrate. This value was then converted into lactic acid content (%,
w/
w) using Equation (1).
2.2.2. Hunter Color
The chromaticity of the Kimchi was measured using a color meter (CR-200, Minolta Co., Osaka, Japan). A 100-g sample of Kimchi was pulverized for 1 min in a blender then placed in a petri dish (35 × 20 mm) for the measurement. The color values were expressed as L (lightness), a (redness), and b (yellowness) after adjusting to standard plate (L = 97.75, a = 0.49, b = 1.96) before each measurement.
2.2.3. Texture
The texture of the Kimchi was evaluated by measuring the hardness using a texture analyzer (TA-XT1, Stable Micro System Ltd., Godalming, England), and analyzed by the puncture test. Cabbage samples of 3 × 3 cm dimensions were cut from the area 5 cm below the root of the third cabbage leaf. For the measurement, the maximum strength received while penetrating 100% from the central portion of the crust was measured. The test conditions were as follows: a 3-mm cylindrical probe was used; the pre-test speed, test speed, and post-test speed were set to 3.0, 3.0, and 10.0 mm/s; and the distance was 15 mm.
2.2.4. Microbiological Analysis
To assess the aerobic and lactic acid bacteria, 10 g of Kimchi leaf and stem were taken and mixed with 90 mL of sterilized 0.85% NaCl solution. The mixture was homogenized in a bag mixer (Interscience Inc., Saint-Nom-la-Bretèche, France) for 1 min. One mL of the sample was taken and diluted stepwise with 9 mL of sterile 0.85% NaCl solution. For the aerobic count plate, 1 mL of the diluted solution was inoculated in a 3M Petrifilm plate (3M Co., Saint Paul, MN, USA) and cultured at 37 °C for 48 h, then the number of viable aerobic bacteria were measured in Colony-forming units (CFU/g). The number of lactic acid bacteria were also measured in Colony forming units (CFU/g) after culturing at 35 ± 1 °C for 48 h in MRS broth (Difco, Detroit, MI, USA).
2.2.5. Sensory Analysis
The sensory evaluation of Kimchi was carried out using a 9-point scale for 20 trained sensual assessors. In this case, the trained participants are selected from staff and researchers (5 males, 15 females, aged 30–60) at the Korea Food Research Institute. Beforehand, the participants were trained to differentiate kimchi qualities based on temperature and evaluate the appearance (softness), sour smell, sour taste, crunchiness, and overall ripeness of the Kimchi. For instance, “appearance” pertains to the color shade-softness of the Kimchi where “sour smell” described the sensation of typical generated flavor. The taste was used to obtain desired sour effects, and the ripeness was used to draw an overall freshness of the product. The intensity of each item was ranked from 1 (very low) to 9 (very strong); 3, 5, and 7 points were awarded for low, normal, and high intensities, respectively. The 3-g samples were provided in white polyethylene cups and numbered with three-digit randomly. Each sample was served one by one at room temperature.
2.2.6. Statistical Analysis
The results of the sensory evaluation were assessed using variance analysis conducted on SPSS Statistics 20 (IBM, Armonk, NY, USA). The significance of the difference was verified using Duncan’s multiple range test at the p < 0.05 level. In addition, Pearson’s correlation coefficient was used to correlate the quality characteristics of Kimchi and sensory ripening evaluation indices.
2.3. Model Development
2.3.1. Primary Model
Acidity was selected as the most suitable ripening index of Kimchi during storage. The acidity shows sigmoidal growth with time. The Gompertz, Hill and Wright, and Logistic, and Baranyi and Roberts models can be used to express sigmoidal growth. Herein, the Baranyi and Roberts model was selected as the primary model to express this change.
where
is the acidity (%);
is a factor indicating the physiological food quality;
is elapsed time;
is food temperature;
is the maximum acidity growth rate at temperature
; and
is the maximum acidity value at temperature
(%). The initial conditions of
and
were used to integrate the first-order differential equations in Equations (2) and (3). Under the fixed temperature condition, the maximum acidity value at a given temperature condition (
) does not change.
2.3.2. Secondary Model
The secondary model describes the effect of environmental conditions on the parameters analyzed in the primary model. The most commonly used models are the Polynomial, Square root, and Ratkowski models. Herein, the Polynomial model was used to analyze the influence of
on temperature.
where
,
, and
are variables for minimizing the difference between the experimental and predicted values, determined using the optimization packages [
19,
20] of the open-source statistical program, R [
21].
2.3.3. Dynamic Model Using Mean Kinetic Temperature (MKT) in Fluctuating-Temperature Environments
A dynamic model was developed to predict the change in acidity (%) under fluctuating temperature conditions. First, the acidity values were measured under two fluctuating temperature profiles. The first fluctuation was between 0 and 10 °C at 24 h intervals for 20 days, and the second was between 5 and 15 °C at 24 h intervals for 14 days.
If
is constant, it is easy to predict the change in acidity under fluctuating temperature conditions, as the changes of
and
over time can be obtained considering the influence of the instantaneous temperature on
as described by Corradini et al. [
22]. However, if
is a function of temperature, then
must change according to the change in temperature. That is,
should decrease with time as the temperature decreases in the stationary phase where
is constant. However, the
value observed in a given phase does not decrease even if the temperature decreases. Therefore, we devised a dynamic model which is modified to
by using the MKT. The MKT is obtained by integrating the effects of various temperature changes over a certain period on the acidity value; therefore, it tends not to change easily when the temperature changes instantaneously. Thus,
does not change according to the instantaneous temperature, as it is determined by the overall temperature history, as shown in Equation (5).
Herein, we calculated MKT from the acidity value at time
after identifying the relationship between
and
over time under fixed temperature conditions (0, 5, 10, 15, and 20 °C). The MKT at the starting point of the fluctuating temperature condition,
, is equal to the initial temperature under the fixed temperature condition. Therefore, the rate of acidity change at
can be obtained using Equations (2) to (4) at the initial temperature and MKT. The acidity value
at time
can be obtained considering the elapsed time. For a given acidity value
at time
, the constant temperature profile that best matches the fluctuating temperature profile is determined as the MKT. An example of the MKT calculation is shown in
Figure 1. After five days, the acidity of the Kimchi was 0.546, and the MKT was 9.77 °C. Please refer to Kim et al. [
23] for the detailed process of MKT calculation.
2.3.4. Comparison between Observations and Predictions
The accuracy of the predicted values was verified by comparing them to the observed values using the bias factor
and accuracy factor
(Equation (6)).
and
are equal to 1 when the predicted and observed values are exactly the same; thus, the closer to 1, the higher the accuracy of the model [
24].
4. Conclusions
We developed a method to predict Kimchi ripening according to temperature to provide information on how the ripening changes during distribution. The physicochemical changes were analyzed according to temperature, and acidity (%) was selected as an appropriate freshness index. Acidity (%) is dependent on temperature and correlates well with the sensory data. Moreover, it is easy to measures and reproducible in the field. A predictive model was developed using the Baranyi and Roberts and Polynomial models to mathematically predict the change of acidity (the selected quality index) over time. When the developed model was applied with fluctuating temperature conditions, the acidity value of the Kimchi predicted by the model decreases as the temperature changes from high to low. To solve this problem, a method using a mean kinetic temperature (MKT) is proposed. The results show that the accuracy of the model is high, since , which show the similarity between the measured and predicted values, are close to 1. It was confirmed that there is no great variation in the maximum acidity change when using MKT, since the MKT does not change much if the temperature changes in the stationary phase where the maximum acidity is constant. This study provides important information on the development of models to predict changes in food quality index under fluctuating temperature conditions.
The developed kinetic model uniquely treated the quality index at the stationary phase to be a function of MKT. It could successfully reproduce the observations under both constant and varying temperature conditions. The suppliers could decide on the sales and disposal of Kimchi in circulation based on the model prediction using the monitored temperature histories for their products. Both suppliers and consumers could prepare the temperature histories to make Kimchi of their favorite flavor. The developed model can be applied to other products such as beef for which the quality index at the stationary phase changes with temperature histories. Further investigations for the possible applications of the model on other foods and verification are necessary. At the moment, beef also has similar temperature-dependent stationary phase levels problems [
16,
17].