Abstract
Cold Plasma (CP) is an innovative non-thermal technique that maintains the quality of foods. The kinetics of natural microbiota viz. aerobic mesophiles (AM) and yeasts & molds (YM) were examined within the domain of 18–30 kV, 2–10 mm juice depth, and 0–4 min treatment time. A log reduction of 3.08 and 2.32 was achieved for AM and YM, respectively, at 30 kV/2 mm/4 min. The inactivation kinetics for AM and YM were established using different kinetic models, namely Weibull + tail, Geeraerd, log-logistic, biphasic, and Coroller models. First, the suitability of model was determined according to goodness of fit (Coefficient of determination (R2) and root mean square error (RMSE)) and validation indices (accuracy factor (Af) and bias factor (Bf)). The R2, RMSE, Af, and Bf values for the Weibull + tail, log-logistic, and Coroller models ranged between 0.939 and 0.999, 0.001–0.154, 1.001–1.086, and 0.992–1.024, respectively which were reported to be satisfactory in explaining the inactivation kinetics for AM and YM, respectively. Further, the most appropriate model was selected based on Akaike’s theory. The log-logistic model was the best fitting for AM and YM inactivation, showing the least akaike weight in 47.33 and 48.82% of the inactivation curves, respectively.
Supplementary Information
The online version contains supplementary material available at 10.1007/s13197-024-06091-0.
Keywords: Cold plasma, Kiwifruit juice, Kinetic models, Akaike theory
Highlights
The population of AM and YM were significantly affected by CP voltage, juice depth, and treatment time.
The population of AM and YM reduced by 3.08 and 2.32, respectively, after CP treatment.
The log-logistic model was best fitted for the AM and YM experimental datasets.
The YM was more CP-resistant than AM based on inactivation rate and time in log logistic model.
Supplementary Information
The online version contains supplementary material available at 10.1007/s13197-024-06091-0.
Introduction
Cold plasma (CP) is a novel technology that has emerged recently, aimed at preserving the quality and safety of food products. Plasma, the fourth phase of matter after solid, liquid, and gas, is formed by the ionization of gas particles. It is further classified as thermal plasma and cold plasma (non-thermal plasma). Thermal plasmas require high temperatures for their generation, while CP does not. At ambient temperature and atmospheric conditions, an electric charge is transferred to an inert gas like argon, helium, nitrogen, or air to produce CP. CP predominantly comprises electrons, electromagnetic radiation quanta, ions, as well as neutralized free radicals such as reactive oxygen species (ROS) and reactive nitrogen species (RNS) (Kopuk et al. 2022). The CP method has successfully eliminated sporulating and pathogenic microorganisms from food products. This novel technology has recently been shown to disinfect food and food-contact surfaces. The technique’s innovation comes from its wide range of production capabilities and potential applications, including direct or indirect plasma, non-thermal effects, functional coatings, plasma-treated water, and no adverse food quality effects (Sainz-García and Alba-Elías 2023). CP, which possesses strong antibacterial characteristics, can decrease the length of treatment and capitalize on low operational temperatures (ranging from 30 to 50 °C) to preserve the nutritional and sensory attributes of food products (Punia Bangar et al. 2022).
Kiwifruits belong to the Actinidiaceae family and Actinidia genus. It is also called Mihoutau, Macaque peach, and Chinese gooseberry. Numerous studies have shown that it includes nutrients that improve digestive, immunological, and metabolic health. It contains high levels of vitamins A, B, C, E, and K along with potassium, folate, dietary fiber, and other minerals (Chamorro et al. 2022). It is also rich in lutein, anthocyanins, flavonoids, and carotenoids. It is anti-diabetic, anti-cancerous, fertility, hepatoprotective, anti-ulcer, cataract-preventive, and macular degeneration-preventive (Pinto et al. 2020). Kiwifruit has gained popularity over the past two decades due to its medical benefits. It is usually eaten fresh, but juices, purees, sweets, fortified drinks, dried items, and frozen products are also available (Wang et al. 2021). Among various processed products, kiwifruit juice has gained significant popularity and consumer appeal, emerging as a prominent product within the market (Satpal et al. 2021). Nevertheless, the perishability of juice is inherent, resulting in a decrease in its worth due to a shortened duration of life. The primary cause of juice spoiling is the proliferation of naturally present microorganisms with osmophilic and acid-tolerant characteristics. Food-spoiling microorganisms can modify the sensory attributes of food, including its flavor, aroma, and appearance, to such a degree that it becomes unpleasant to the consumer. The degradation of kiwifruit juice is attributed to the presence of two significant microflora groups, namely aerobic mesophiles (AM) and yeasts & molds (YM) (D’Amato et al. 2011).
The mechanism of microbial inactivation by CP has been classified into two types: biological and physical. The biological mechanism includes DNA damage by UV radiation, lipid peroxidation, and protein modulation. The CP generation process produces UV light, which reacts with the cytosine and thymine of the DNA strand and turns it into dimer, affecting microorganism replication. The ROS produced reacts with membrane lipids (polyunsaturated fatty acids, PUFA) and also causes the oxidation of intracellular components (e.g., carbohydrates and proteins), leading to cell inactivation. Besides this, the hydroxyl radicals affect the function and structure of membrane protein, which is another mechanism for microbial inactivation. The physical mechanism involves the electrostatic disruption and electroporation. In electrostatic disruption, the charged particles accumulate over the cell membrane, generating the electrostatic force that disrupts the cell membrane, followed by cell death. On the other hand, the electroporation causes pore formation in the cell membrane due to the strong electric field generated by CP, which causes the leakage of cell content and, ultimately, cell death (Liao et al., 2017).
Moreover, scanty literature is available to understand the fundamental relationship between food microbial inactivation and CP exposure. Few studies have been conducted by Moritz et al. (2021), Hosseini et al. (2020), and Kang et al. (2021) regarding the inactivation of foodborne pathogens and spoilage microorganisms by CP treatment. Furthermore, the investigation into the applicability of models for predicting the kinetics of microbial inactivation after CP treatment of kiwifruit juice has not yet been conducted. Hence, this work aimed to evaluate and compare various mathematical models, including Weibull + tail, Coroller, Geeraerd, biphasic, and log-logistic models, to choose the most suitable model for analyzing the kinetics of microbial inactivation of AM and YM during CP treatment in kiwifruit juice.
Materials and methods
Kiwifruit juice preparation
Freshly kiwifruit (Actinidia deliciosa) was obtained from the local market in Tezpur, Assam, India, and subsequently placed into polythene bags. The polythene bags were conveyed in plastic crates to the Food Science and Technology Lab (FSTL) under the Agricultural and Food Engineering Department (AgFE) at the Indian Institute of Technology Kharagpur in West Bengal. Upon arrival, the fruits underwent preprocessing operations, specifically cleaning and sorting, before being stored in a deep freezer at -20 °C for subsequent study.
To prepare the juice, the frozen kiwifruit was allowed to thaw for 2 h at an ambient temperature of 25 °C. Following the thawing process, the kiwifruit underwent a series of procedures, including washing, peeling, and slicing into small pieces using a knife made of stainless steel. To obtain the juice from the kiwifruit, it was first triturated in a mixer grinder (Crompton, TD 71, Kolkata, India). The resulting mixture was then filtered using a three-layer muslin cloth.
CP equipment and treatment
The CP equipment utilized in this study was a dielectric barrier discharge plasma system manufactured by Zeonics Systech Defence and Aerospace Engineers Private Limited, based in India, as depicted in Fig. S1. The CP system comprises a high-voltage generator, plasma chamber, and control panel (Pipliya et al. 2022). The discharge was initiated within the confined space between two copper electrodes, each having a thickness of 5 mm, which were enveloped by thick quartz plates serving as dielectric barrier plates. The kiwi juice was carefully transferred into a petri dish with a diameter of 90 mm, and the sample was exposed to CP. The distance between the upper electrode and the juice surface was maintained at a constant value of 6 mm. For kinetic modeling, the juice was exposed to CP voltage of 18, 24, and 30 kV at a depth of 2, 6, and 10 mm for 0–4 min.
Microbial analysis
The surviving population of two distinct groups of microorganisms, YM and AM, was enumerated using the serial dilution spread plate technique (Pipliya et al. 2023). The juice underwent serial dilution using sterile 0.1% peptone water, and then 0.1 ml of each dilution was evenly distributed throughout the agar surface within a petri plate. The incubation conditions for the plates associated with AM and YM were 37 °C for 24 to 36 h and 30 °C for 5 days, respectively. The quantification of the sample’s colony count was performed using colony-forming units (CFU), which were expressed as log10 CFU/mL.
Mathematical models
The non-linear regression analysis for microbiological deactivation data was conducted using the Origin Pro 8.5 software. The study employed five widely recognized models, including the log-logistic, Weibull + tail, Geeraerd, Coroller, and Biphaic models, to predict the kinetics of microbial group inactivation.
Weibull + tail model
The Weibull model, initially proposed by Albert and Mafart (2005), has undergone modifications and is now commonly known as the “Weibull + tail model.” The impact of tailing is taken into consideration. The kinetics of the decrease in microbial population over time (log10 CFU/mL) can be described by the following model (Eq. 1):
 |
1 |
Where the variables N0, Nres, α, and β correspond to the initial count of microbes, the count of residual microbes, the scale parameter, and the shape parameter, respectively. The scale parameter represents the duration needed for the one logarithmic decline in the microbial population, whereas the shape parameter characterizes the curvature of the inactivation curve, indicating whether it is concave (β < 1) or convex (β > 1).
Log-logistic model
The log-logistic equation was initially proposed by Cole et al. (1993) to characterize the non-linear inactivation of microorganisms. Subsequently, Chen and Hoover (2004) modified the equation to eliminate the direct utilization of diverse initial values and reduce the number of factors from four to three. The vitalistic model (Eq. 2) is employed to elucidate the non-linear dynamics involved in the deactivation of microorganisms.
 |
2 |
where σ = maximum inactivation rate, τ = log of time for maximum rate of inactivation, and A = distinction between lower and higher inactivation curve asymptotes.
Geeraerd model
Geeraerd model exhibits a log-linear pattern, regardless of the presence or absence of shoulder and/or tailing, illustrating a more gradual transition between phases. This model incorporates the concept of tailing, which pertains to populations that exhibit stability throughout time and do not experience significant subsequent inactivation (Geeraerd et al. 2000). The application of Geeraerd’s model version, as described by Eq. 3, is being attempted when the shoulder length is zero during the tailing phase.
 |
3 |
where k = inactivation rate constant for log-linear section, other parameters are the same as mentioned in Eq. 1.
Coroller model
The microbial population can be divided into two distinct subpopulations, each characterized by the Coroller model. This model is based on utilizing mixed Weibullian distributions (Coroller et al. 2006). The modified version of the Weibull distribution model (Eq. 4) for microbial resistance consists of four parameters.
 |
4 |
where δ = sensitivity (f) to resistive (1-f) fraction’s ratio, β = shape parameter, and α1 & α2 = scale parameter for subpopulations 1 & 2, respectively.
Biphasic model
Cerf (1977) proposed paradigm posits the coexistence of two populations exhibiting varying degrees of resistance. The model depicted in Eq. 5 is commonly referred to as the biphasic model. It employs a pair of first-order differential equations to describe the dynamics of the major subpopulation (N1) and the minor subpopulation (N2). This model is designed to handle scenarios where the parameters alter with time.
 |
5 |
where f = The sensitive initial population fraction corresponds to N1, 1-f = The resistant initial population fraction corresponds to N2, and k1 & k2 are the inactivation rates that correspond to subpopulations 1 & 2.
Statistical analysis
The statistical analysis was conducted using Origin Pro 8.5, a software developed by OriginLab Corporation based in Northampton, UK. The calculation of the coefficient of determination (R2) and root-mean-square error (RMSE) of the model was carried out as suggested by Kumar et al. (2024).
The predicted model was validated using several statistical variables, including accuracy (Af) and bias (Bf) factors. Equation 6 demonstrates Af, the degree of resemblance between predicted and observed data, with a value close to 1 indicating little deviations. Similarly, Eq. 7 represents Bf, the ability to forecast the observed experimental dataset both above (Bf > 1) and below (Bf < 1) the expected values (Pipliya et al. 2022).
 |
6 |
 |
7 |
Where yo, yp, and n are experimental values, predicted values, and number of experiments, respectively.
The utilization of the Akaike information criterion (AIC) (Eq. 8) is recommended for identifying the optimal model in such situations where observational data limitations prevent the selection of a single candidate model (Vega et al. 2016).
 |
8 |
Where m = number of observations, j = different model variables, and SSE= residual sum of square error.
Using Akaike information criteria, the best model is selected from the provided data set as per the procedure followed by Kumar et al. (2024). The Eqs. 9 and 10 were employed to determine the Akaike increment and Akaike weights.
 |
9 |
Where, AICmin = the minimum value obtained by the model that most accurately matches the data relative to all other models.
 |
10 |
where, 
for i = 1, 2, …, R denotes the collection of potential models, and it offers the likelihood of the model.
Results and discussion
Impact of CP exposure on microbial inactivation
The kiwifruit juice treated with CP showed a reduction in microbial populations in both the AM and YM groups (Fig. 1). This is apparent from the agar plates depicted in Fig. 2, which illustrate the comparison of microbial populations in untreated and CP-treated kiwifruit juice samples. Figure 1 showed a progressive decline in the number of surviving colonies of the AM and YM microbiological groups as the CP voltage and treatment time increased, whereas, in the case of juice depth, the AM and YM count decreased with the decrease in juice depth. At the juice depth of 2 mm and 4 min treatment time, the inactivation of AM and YM increased from 56.42 to 73.33% and from 35.91 to 66.66%, respectively, as the CP voltage increased from 18 to 30 kV. On the other hand, at the juice depth of 10 mm and 4 min treatment time, when the voltage was increased from 18 to 30 kV, the inactivation of AM and YM rose from 44.28 to 56.66% and 25.86 to 34.48%, respectively. The inactivation curves display the survival rates of two microbial groups, as shown in Fig. 3. Both types of microorganisms showed a curve pattern consisting of a modest shoulder (slow decay at the beginning of treatment), sigmoidal (significant deterioration), and tailing-effect (slow decay at later stages). The sharp decline at the start of exposure to CP indicates rapid cell death or faster inactivation rates, while the gradual decline towards the end suggests mild inactivation rates or a tailing effect. Further, at the process parameter of 30 kV CP-voltage, 10 mm juice depth, and 4 min treatment time, the reduction in microbial counts of AM and YM was reported to be 2.38 and 1.20 log CFU/mL, respectively, whereas keeping the CP-voltage and treatment time constant and changing the juice depth from 10 to 2 mm, the corresponding logarithmic reduction were 3.08 and 2.32 log CFU/mL, respectively.
Fig. 1.
Variation in survival population of aerobic meshophiles (a-c) and yeasts & molds (d-f) with respect to treatment time (0–4 min) at different applied voltage (18–30 kV) and juice depth of (a, d) 2 mm, (b, e) 6 mm, and (c, f) 10 mm
Fig. 2.
Petri plates representing the growth of aerobic mesophiles in (a) untreated kiwifruit juice and (b) CP-treated kiwifruit juice sample; Yeasts & molds count in (c) untreated kiwifruit juice, and (d) CP-treated kiwifruit juice sample
Fig. 3.
Inactivation curve for kinetic data fitted to different models at 2 mm juice depth for aerobic mesophiles (a, b, and c) and yeasts and molds count (d, e and f)
The results were supported by Dasan et al. (2018), who showed a rapid initial decrease followed by a slower decline. Smet et al. (2016) found that a gradual reduction in the initial phases of Salmonella typhi treated in a liquid form was followed by a log-linear deactivation phase. The delayed inactivation process, in the beginning, may be due to a resistant group of microbes, indicating that the microbes need to reach a specific level of CP treatment before being significantly harmed. The data demonstrate that the process of microbial deactivation by CP is complex and influenced by different variables affecting the death kinetics of microorganisms. The results clearly show that CP effectively deactivated AM and YM in kiwifruit juice because of the juice’s transparency. Dasan and Boyaci (2018) confirmed that clear apple juice had greater efficacy in eliminating microbes than turbid tomato juice. Solid particles in juice can increase microbial cell resilience to reactive plasma species that kill bacteria during treatment due to turbidity. The greater acidity of kiwifruit juice is crucial in efficiently reducing the microbial population in juice samples. Microbial inactivation by plasma is significantly dependent on the pH levels of the liquid media undergoing treatment. Ikawa et al. (2010) said that antibacterial effects are significantly effective at a pH of 4.7 or below but become less effective or ineffective above this threshold. Their research indicates that a combination of a lower pH value (pH 3.5) and CP treatment is beneficial for microbial inactivation.
Inactivation kinetics of AM and YM during CP treatment
Figure 3 depicts the inactivation curves for the AM and YM, mostly consisting of log-linear and tailing phases. Based on the survival curve’s curvature, five models detailed in the methodology section have been chosen to investigate the kinetics of AM and YM inactivation of CP-treated kiwifruit juice.
Kinetic parameter evaluation for several models
The evaluation of different model parameters is made possible by the experimental data fitted to multiple models, as illustrate in Table 1.
Table 1.
Kinetic model parameters fitted to different mathematical models for aerobic mesophiles and yeasts & molds count
| Aerobic mesophiles | Yeasts and molds | |||||||
|---|---|---|---|---|---|---|---|---|
| Voltage (kV) | Voltage (kV) | |||||||
| Juice depth (mm) | 18 | 24 | 30 | 18 | 24 | 30 | ||
| Weibull + tail | α (min) | 2 | 1.32 ± 0.05 | 0.95 ± 0.11 | 0.84 ± 0.16 | 2.17 ± 0.16 | 2.15 ± 0.03 | 1.91 ± 0.02 |
| 6 | 1.5 ± 0.05 | 1.36 ± 0.08 | 1.02 ± 0.07 | 2.27 ± 0.11 | 2.23 ± 0.16 | 2.17 ± 0.02 | ||
| 10 | 1.82 ± 0.02 | 1.59 ± 0.02 | 1.37 ± 0.07 | 2.73 ± 0.03 | 2.47 ± 0.14 | 2.2 ± 0.08 | ||
| β | 2 | 1.14 ± 0.1 | 0.85 ± 0.13 | 0.91 ± 0.21 | 1.5 ± 0.29 | 1.51 ± 0.06 | 1.57 ± 0.04 | |
| 6 | 1.26 ± 0.12 | 1.06 ± 0.12 | 0.9 ± 0.09 | 1.84 ± 0.26 | 1.39 ± 0.22 | 1.59 ± 0.05 | ||
| 10 | 1.27 ± 0.04 | 1.35 ± 0.05 | 1.29 ± 0.15 | 2.05 ± 0.11 | 1.72 ± 0.23 | 1.6 ± 0.15 | ||
| Nres (CFU/mL) | 2 | 27.02 ± 5.2 | 19.6 ± 6.38 | 14.51 ± 3.02 | 11.42 ± 0.21 | 6.15 ± 0.39 | 2.47 ± 0.09 | |
| 6 | 33.79 ± 7.82 | 32.02 ± 5.41 | 24.16 ± 4.12 | 26.86 ± 2.69 | 13.77 ± 2.92 | 6.21 ± 0.06 | ||
| 10 | 45.82 ± 8.84 | 42.88 ± 6.22 | 37.78 ± 5.97 | 33.28 ± 0.21 | 23.11 ± 2.68 | 19.04 ± 1.37 | ||
| Geeraerd | k (min− 1) | 2 | 1.51 ± 0.1 | 1.73 ± 0.14 | 1.99 ± 0.17 | 0.91 ± 0.12 | 1 ± 0.11 | 1.33 ± 0.07 |
| 6 | 1.32 ± 0.09 | 1.73 ± 0.06 | 1.74 ± 0.12 | 0.77 ± 0.15 | 0.89 ± 0.1 | 0.98 ± 0.12 | ||
| 10 | 1.14 ± 0.05 | 1.29 ± 0.08 | 1.52 ± 0.1 | 0.52 ± 0.05 | 0.67 ± 0.13 | 0.88 ± 0.12 | ||
| Log (Nres) (log CFU/mL) | 2 | 1.28 ± 0.16 | 0.59 ± 0.28 | 0.39 ± 0.31 | 1.64 ± 0.3 | 0.95 ± 0.3 | 0.75 ± 0.22 | |
| 6 | 1.58 ± 0.23 | 1.34 ± 0.59 | 0.49 ± 0.3 | 1.94 ± 0.59 | 1.7 ± 0.23 | 0.85 ± 0.28 | ||
| 10 | 1.69 ± 0.89 | 1.49 ± 0.3 | 1.2 ± 0.22 | 2.05 ± 0.16 | 1.85 ± 0.89 | 1.56 ± 0.31 | ||
| Log- logistic | A (log CFU/ml) | 2 | -2.84 ± 0.02 | -3.33 ± 0.35 | -3.48 ± 0.38 | -1.42 ± 0.1 | -2.24 ± 0.11 | -3.49 ± 0.55 |
| 6 | -2.42 ± 0.02 | -3.21 ± 0.21 | -3.66 ± 0.23 | -1.22 ± 0.02 | -1.46 ± 0.11 | -2.14 ± 0.15 | ||
| 10 | -2.29 ± 0.48 | -2.47 ± 0.31 | -2.71 ± 0.01 | -1.11 ± 0.09 | -1.19 ± 0.04 | -1.4 ± 0.03 | ||
| τ (log min) | 2 | 0.27 ± 0.06 | 0.23 ± 0.07 | 0.18 ± 0.06 | 0.37 ± 0.04 | 0.31 ± 0.02 | 0.28 ± 0.07 | |
| 6 | 0.34 ± 0.05 | 0.33 ± 0.04 | 0.3 ± 0.04 | 0.38 ± 0.01 | 0.34 ± 0.04 | 0.33 ± 0.03 | ||
| 10 | 0.4 ± 0.1 | 0.37 ± 0.07 | 0.33 ± 0.04 | 0.46 ± 0.03 | 0.39 ± 0.01 | 0.37 ± 0.02 | ||
| σ (log CFU/ml* log min− 1) | 2 | -3.15 ± 0.48 | -3.26 ± 0.21 | -3.84 ± 0.02 | -1.99 ± 0.26 | -2.77 ± 0.06 | -4.31 ± 0.15 | |
| 6 | -3.03 ± 0.08 | -3.22 ± 0.09 | -3.6 ± 0.02 | -1.82 ± 0.1 | -2.01 ± 0.11 | -2.8 ± 0.04 | ||
| 10 | -2.73 ± 0.01 | -3.02 ± 0.31 | -3.23 ± 0.17 | -1.77 ± 0.04 | -1.78 ± 0.05 | -1.96 ± 0.11 | ||
| Biphasic | f | 2 | 0.99 ± 0.03 | 0.98 ± 0.02 | 0.99 ± 0.02 | 0.95 ± 0.03 | 0.95 ± 0.02 | 0.95 ± 0.02 |
| 6 | 0.99 ± 0.04 | 0.99 ± 0.01 | 0.98 ± 0.02 | 0.96 ± 0.04 | 0.95 ± 0.01 | 0.95 ± 0.02 | ||
| 10 | 0.99 ± 0.01 | 0.99 ± 0.05 | 0.99 ± 0.01 | 0.97 ± 0.01 | 0.96 ± 0.05 | 0.96 ± 0.01 | ||
| k1 (min− 1) | 2 | 1.82 ± 0.1 | 2.51 ± 0.19 | 2.82 ± 0.32 | 1.06 ± 0.68 | 1.13 ± 0.11 | 1.25 ± 0.21 | |
| 6 | 1.54 ± 0.09 | 1.75 ± 0.08 | 2.34 ± 0.12 | 0.96 ± 0.16 | 1.03 ± 0.13 | 1.12 ± 0.14 | ||
| 10 | 1.27 ± 0.08 | 1.54 ± 0.11 | 1.84 ± 0.17 | 0.84 ± 0.07 | 0.94 ± 0.12 | 0.98 ± 0.18 | ||
| k2 (min− 1) | 2 | 0.07 ± 0.02 | 0.61 ± 0.23 | 0.66 ± 0.51 | 0.84 ± 0.14 | 0.73 ± 0.16 | 0.94 ± 0.17 | |
| 6 | 0.13 ± 0.06 | 0.48 ± 0.05 | 0.61 ± 0.22 | 0.72 ± 0.11 | 0.82 ± 0.12 | 0.56 ± 0.11 | ||
| 10 | 0.19 ± 0.02 | 0.05 ± 0.03 | 0.09 ± 0.03 | 0.77 ± 0.12 | 0.64 ± 0.09 | 0.8 ± 0.09 | ||
| Coroller | δ | 2 | 1.67 ± 0.21 | 3.95 ± 0.18 | 4.78 ± 0.17 | 0.75 ± 0.08 | 1.16 ± 0.06 | 2.38 ± 0.21 |
| 6 | 1.52 ± 0.07 | 2.32 ± 0.05 | 3.62 ± 0.41 | 0.68 ± 0.07 | 0.76 ± 0.11 | 1.27 ± 0.17 | ||
| 10 | 1.43 ± 0.04 | 2.04 ± 0.03 | 2.76 ± 0.07 | 0.61 ± 0.09 | 0.84 ± 0.06 | 0.86 ± 0.04 | ||
| α1 (min) | 2 | 1.28 ± 0.03 | 1.07 ± 0.05 | 0.68 ± 0.09 | 1.99 ± 0.16 | 1.91 ± 0.13 | 1.74 ± 0.23 | |
| 6 | 1.43 ± 0.06 | 1.26 ± 0.04 | 1.12 ± 0.04 | 2.07 ± 0.07 | 1.99 ± 0.09 | 1.73 ± 0.11 | ||
| 10 | 1.82 ± 0.03 | 1.59 ± 0.03 | 1.34 ± 0.05 | 2.73 ± 0.07 | 2.04 ± 0.05 | 1.94 ± 0.09 | ||
| α2 (min) | 2 | 5.25 ± 0.08 | 4.61 ± 0.04 | 3.01 ± 0.06 | 6.94 ± 0.08 | 6.22 ± 0.11 | 4.51 ± 0.15 | |
| 6 | 6.03 ± 0.12 | 4.79 ± 0.11 | 3.71 ± 0.08 | 7.06 ± 0.13 | 6.98 ± 0.09 | 6.48 ± 0.11 | ||
| 10 | 6.89 ± 0.13 | 5.08 ± 0.12 | 4.51 ± 0.08 | 9.07 ± 0.07 | 7.71 ± 0.08 | 7.5 ± 0.11 | ||
| β | 2 | 1.35 ± 0.09 | 0.69 ± 0.05 | 0.65 ± 0.08 | 2.14 ± 0.09 | 1.69 ± 0.07 | 1.57 ± 0.01 | |
| 6 | 1.48 ± 0.07 | 1.44 ± 0.08 | 0.74 ± 0.08 | 2.3 ± 0.04 | 1.96 ± 0.07 | 1.72 ± 0.06 | ||
| 10 | 1.27 ± 0.06 | 1.35 ± 0.07 | 1.53 ± 0.09 | 2.05 ± 0.11 | 2.23 ± 0.08 | 1.9 ± 0.06 | ||
Note Estimated kinetic parameters are reported as mean ± standard error
The Weibull + tail differs from the Weibull model because the former model considers the tailing behavior in the survival curve, which is explained by a new parameter, log10(Nres). This model is adaptable and flexible for analyzing survival curves and other common non-linear processes. The aforementioned factors led to the selection of this model to illustrate the inactivation kinetics of AM and YM after CP treatment. The experimental values were fitted to Eq. 1, and the shape factor (β), residual microbial population (Nres), and scale parameter (α) of the Weibull + tail model were determined. In this model, α represents the duration of the first one-log reduction (Panigrahi et al. 2021). The increase in CP voltage from 18 to 30 kV decreased the α value for AM from 1.32 to 0.84 min and 1.82 to 1.37 min at the juice depth of 2 and 10 mm, respectively. Similarly, the α value for AM decreased from 1.82 to 1.32 and 1.37 to 0.84 with the decrease in the juice depth from 10 to 2 mm at the CP-voltage of 18 and 30 kV, respectively. The α value for YM also followed the same trend as of AM with respect to the CP-voltage and juice depth. It can be said that the α decreased with the increase of CP-voltage and with the decrease of juice depth. The lower α depicts higher microbial inactivation, which implies that high CP-voltage and low juice depth favored microbial inactivation. The β of AM and YM ranged between 0.85 and 1.34 and 1.49 to 2.05, respectively, at various combinations of CP-voltage and juice depth. The results indicated that the YM inactivation curves concave downward for all voltage and juice depth applications (β > 1). The downward concavity (β > 1) may be explained by cumulative damage to the surviving population, increasing the susceptibility of the survivor cells to the lethal treatment (Pipliya et al. 2023). The quantity of viable or residual bacterial colonies following CP treatment is denoted as log10 (Nres). When the CP voltage was enhanced from 18 to 30 kV, the value of Nres for AM reduced from 27.02 to 14.51 and 45.82 to 37.78, at the depth of 2 and 10 mm, respectively. Similarly, the value of Nres for YM ranged between 2.47 and 33.27 for different combinations of CP-voltage and juice depth. After CP treatment, the Weibull + tail curve indicated that certain resistant microorganisms continued to exist in the residual microbial log10 (Nres) populations. In contrast to other microbes, these exhibited greater resistance to CP due to cellular agglomeration mechanisms that shielded interior cells from external damage (Cheng et al. 2020).
The Geeraerd model is alternatively known as the log-linear plus-tail model. The Geeraerd model explains both the slope (k) of the linear portion defined by the inactivation rate constant and the tailing referred to as residual survivability (Nres). The k value for AM increased from 1.51 to 1.98 and 1.14 to 1.51 as the CP-voltage increased from 18 to 30 kV at the juice depth of 2 and 10 mm, respectively. Similarly, for YM, the k value ranged between 0.52 and 1.33 under different treatment conditions. In contrast, the residual population log10 (Nres) for AM and YM exhibited values from 0.39 to 1.68 and 0.75 to 2.04, respectively, while the corresponding voltage range was 18 to 30 kV. The higher residual population magnitude of YM compared to AM provided clear evidence that YM was less vulnerable to CP treatment-induced inactivation. In accordance with the trajectory of k and Nres, the microbial cell has become more susceptible to severe CP effects.
In particular, the log-logistic model depicts nonlinear survival graphs incorporating a tailing effect. A and τ exhibit an inverse relationship with CP voltage but directly correlate with juice depth. Conversely, σ positively correlates with CP voltage and juice depth throughout treatment. The difference between the lower and upper asymptotes (A) ranged from − 2.29 to -3.47 and − 1.11 to -3.49 for AM and YM, respectively. The maximal inactivation rates for AM ranged from − 2.73 to -3.83, whereas for YM, they ranged from − 1.76 to -4.31. It was determined that a lower juice depth and a higher applied CP voltage caused a higher rate of microorganism inactivation. On the other hand, the log time required for maximal inactivation rate for AM and YM varied from 0.17 to 0.39 and 0.27 to 0.45, respectively. It was noted that treatment conditions involving high voltage and low juice depth necessitated a shorter log time to achieve the highest inactivation rate.
Due to the consideration of non-zero activity during prolonged treatments, inactivation modeling frequently utilizes the biphasic model, a derivative of the first-order kinetic model. The model incorporates a subset of survivors (f) with higher apparent resistance (f) in comparison to the other subset (1-f) to account for curves containing resistances of different subpopulations (Panigrahi et al. 2021). Compared to the AM, YM exhibited a low value for the f (0.95–0.97) parameter, suggesting that more microorganisms demonstrated resistance to the CP treatment. Conversely, the higher f values (0.98–0.99) in the AM suggested the presence of a higher sensitive subpopulation. Compared to the AM treatment, the CP treatment resulted in the lowest f value in kiwifruit inoculated with YM, indicating the presence of a higher resistant subpopulation.
The k1 and k2 inactivation rates for AM were 1.27 to 2.81 and 0.05 to 0.66, respectively. The inactivation rates k1 and k2 for YM exhibited corresponding ranges of 0.84 to 1.25 and 0.55 to 0.94, respectively. Significantly higher k1 values were observed compared to k2, suggesting the presence of a tail in the late phase and exceptionally high inactivation rates during the initial minutes of treatment. As a result, it was deduced that cells with higher resistance were less affected than cells with lower susceptibility over a reduced time. Throughout the inactivation procedure, various simultaneous phenomena may occur, each of which has the potential to impact the microorganism population.
The Coroller model furnishes comprehensive insights into the interaction dynamics between sensitive and resistant subpopulations. The durations between the first decimal reduction and the resistant and sensitive subpopulations are denoted as α2 and α1, correspondingly. The α1 values for AM reduced from 1.28 to 0.67 and 1.82 to 1.34 at the juice depth of 2 and 10 mm, respectively, after enhancing the voltage from 18 to 30 kV. For YM, the α1 values varied from 1.98 to 1.73 and 2.72 to 1.94 at the juice depth of 2 and 10 mm, respectively, upon increasing the CP voltage from 18 to 30 kV. On the other hand, the α2 values for AM and YM ranged between 3.01 and 6.88 and 4.51–9.06, respectively, at corresponding different treatment conditions. The resistant subpopulation required significantly more time than the sensitive subpopulation to perform the first decimal reduction. The results suggested that a significant proportion of the microbial population exhibited sensitivity and perished within minutes of receiving CP treatment. Furthermore, as the applied voltage increased, the proportion of susceptible cells (δ) exhibited a significant increase exceeding 1. This finding was consistent with both natural microbiotas and indicated that the majority of the population consisted of sensitive cells. A second phase of inactivation generally results in a deceleration of progress and can exhibit either a linear or non-linear pattern, which defines the majority of survival curves. The model demonstrated a high degree of correspondence with the inactivation patterns (sigmoidal-type curves), which exhibited a distinct decline after the second decay and a plateau subsequent to the initial decay (Ferrario et al. 2013).
Validation and performance assessment of different models
The survival and inactivation curves for AM and YM, which were fitted to different models, are illustrated in Fig. 3. A summary of the statistical parameters utilized to assess the model’s performance is presented in Tables 2 and 3. Statistical indices (R2 and RMSE) indicated that nearly all models accurately fitted the experimental dataset. Experiments involving the inactivation of microorganisms consistently yielded RMSE, Af, and Bf values that were well within the expected range. The log-logistic model effectively represented the data by accounting for over 99.5% of the variability in response to the inactivation of AM and YM in CP-treated kiwifruit juice, as indicated by its R2 > 0.995 and RMSE < 0.001. In the same way, the experimental data are modelled by the Coroller and Weibull + tail model, as evidenced by R2 values exceeding 0.939 and RMSE values falling below 0.154. Depending on the different combinations of CP voltage, juice depth, and the types of microbial groups, biphasic and Geeraerd also exhibited R2 values in the ranges of 0.938–0.998 and 0.869–0.993, respectively, that accurately suited the survival data. It indicated that these two models might account for between 86.9% and 99.8% of the variability in the experimental dataset.
Table 2.
Model performance evaluation based on validation indices and goodness of fit parameters for aerobic mesophiles
| Voltage (kV) | Voltage (kV) | Voltage (kV) | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 18 | 24 | 30 | ||||||||||||||
| Juice depth (mm) | Af | Bf | AIC | R 2 | RMSE | Af | Bf | AIC | R 2 | RMSE | Af | Bf | AIC | R 2 | RMSE | |
| 2 | 1.021 | 1.005 | -37.679 | 0.996 | 0.034 | 1.029 | 1.004 | -31.883 | 0.988 | 0.062 | 1.046 | 1.008 | -26.227 | 0.971 | 0.108 | |
| Weibull + tail | 6 | 1.023 | 1.006 | -38.403 | 0.996 | 0.032 | 1.031 | 1.008 | -34.596 | 0.993 | 0.047 | 1.022 | 1.004 | -35.074 | 0.994 | 0.045 |
| 10 | 1.011 | 0.997 | -49.022 | 0.999 | 0.011 | 1.01 | 0.997 | -47.942 | 0.999 | 0.012 | 1.029 | 1.008 | -34.915 | 0.994 | 0.045 | |
| 2 | 1.086 | 0.959 | -21.114 | 0.925 | 0.181 | 1.142 | 0.915 | -17.442 | 0.881 | 0.261 | 1.136 | 0.921 | -15.564 | 0.869 | 0.315 | |
| Geeraerd | 6 | 1.082 | 0.972 | -22.466 | 0.925 | 0.158 | 1.036 | 1.015 | -33.985 | 0.992 | 0.05 | 1.119 | 0.93 | -19.099 | 0.916 | 0.221 |
| 10 | 1.053 | 0.995 | -28.553 | 0.97 | 0.086 | 1.08 | 0.981 | -22.845 | 0.927 | 0.152 | 1.093 | 0.977 | -20.652 | 0.918 | 0.189 | |
| 2 | 1.001 | 0.999 | -62.869 | 0.999 | 0.003 | 1.014 | 1.001 | -37.414 | 0.996 | 0.035 | 1.022 | 1.002 | -31.244 | 0.99 | 0.066 | |
| Log-logistic | 6 | 1.002 | 0.999 | -62.794 | 0.999 | 0.003 | 1.01 | 1.001 | -44.025 | 0.999 | 0.018 | 1.007 | 1.001 | -44.5 | 0.999 | 0.017 |
| 10 | 1.025 | 0.996 | -38.297 | 0.995 | 0.032 | 1.03 | 0.996 | -34.274 | 0.992 | 0.048 | 1.001 | 1.002 | -70.169 | 0.999 | 0.001 | |
| 2 | 1.034 | 1.019 | -34.097 | 0.992 | 0.049 | 1.02 | 1.005 | -36.828 | 0.995 | 0.038 | 1.037 | 1.012 | -29.424 | 0.985 | 0.079 | |
| Biphasic | 6 | 1.049 | 1.027 | -32.475 | 0.986 | 0.058 | 1.036 | 1.016 | -34.057 | 0.992 | 0.05 | 1.015 | 1.005 | -40.324 | 0.998 | 0.026 |
| 10 | 1.047 | 1.03 | -34.41 | 0.989 | 0.048 | 1.058 | 1.036 | -30.386 | 0.978 | 0.071 | 1.063 | 1.038 | -28.795 | 0.977 | 0.084 | |
| 2 | 1.002 | 1.002 | -58.278 | 0.999 | 0.004 | 1.051 | 1.011 | -27.271 | 0.968 | 0.098 | 1.068 | 1.016 | -22.7 | 0.939 | 0.154 | |
| Coroller | 6 | 1.003 | 1.003 | -58.859 | 0.999 | 0.004 | 1.004 | 1.004 | -54.52 | 0.999 | 0.006 | 1.05 | 1.012 | -28.266 | 0.977 | 0.088 |
| 10 | 1.011 | 0.997 | -49.021 | 0.999 | 0.011 | 1.01 | 0.997 | -47.941 | 0.999 | 0.012 | 1.004 | 1.004 | -56.944 | 0.999 | 0.005 | |
Table 3.
Model performance evaluation based on validation indices and goodness of fit parameters for yeasts and molds
| Voltage (kV) | Voltage (kV) | Voltage (kV) | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 18 | 24 | 30 | ||||||||||||||
| Juice depth (mm) | Af | Bf | AIC | R 2 | RMSE | Af | Bf | AIC | R 2 | RMSE | Af | Bf | AIC | R 2 | RMSE | |
| 2 | 1.058 | 1.021 | -36.341 | 0.985 | 0.039 | 1.017 | 1.008 | -48.082 | 0.999 | 0.012 | 1.002 | 0.999 | -70.032 | 0.999 | 0.001 | |
| Weibull + tail | 6 | 1.053 | 1.026 | -40.547 | 0.993 | 0.026 | 1.045 | 1.015 | -38.587 | 0.99 | 0.031 | 1.013 | 1.006 | -51.692 | 0.999 | 0.008 |
| 10 | 1.005 | 0.999 | -58.146 | 0.999 | 0.004 | 1.051 | 1.024 | -41.955 | 0.994 | 0.022 | 1.03 | 1.012 | -43.708 | 0.997 | 0.019 | |
| 2 | 1.111 | 1.066 | -31.253 | 0.952 | 0.066 | 1.103 | 1.074 | -29.755 | 0.967 | 0.076 | 1.139 | 1.104 | -24.845 | 0.954 | 0.124 | |
| Geeraerd | 6 | 1.053 | 1.026 | -40.547 | 0.993 | 0.026 | 1.085 | 1.049 | -33.662 | 0.968 | 0.052 | 1.12 | 1.085 | -28.761 | 0.958 | 0.084 |
| 10 | 1.204 | 1.153 | -31.33 | 0.919 | 0.065 | 1.152 | 1.098 | -31.883 | 0.942 | 0.062 | 1.113 | 1.069 | -31.68 | 0.953 | 0.063 | |
| 2 | 1.024 | 1.006 | -42.628 | 0.996 | 0.021 | 1.012 | 0.996 | -49.694 | 0.999 | 0.01 | 1.034 | 0.987 | -37.862 | 0.998 | 0.034 | |
| Log-logistic | 6 | 1.007 | 1.003 | -57.543 | 0.999 | 0.005 | 1.019 | 1.004 | -44.738 | 0.997 | 0.017 | 1.02 | 0.993 | -45.273 | 0.999 | 0.016 |
| 10 | 1.043 | 0.977 | -47.079 | 0.998 | 0.013 | 1.012 | 1.004 | -53.739 | 0.999 | 0.007 | 1.012 | 0.996 | -47.911 | 0.999 | 0.012 | |
| 2 | 1.102 | 1.059 | -31.924 | 0.959 | 0.061 | 1.079 | 1.024 | -31.023 | 0.979 | 0.067 | 1.122 | 1.081 | -25.563 | 0.964 | 0.116 | |
| Biphasic | 6 | 1.15 | 1.111 | -30.945 | 0.938 | 0.068 | 1.078 | 1.042 | -34.406 | 0.974 | 0.048 | 1.117 | 1.083 | -28.818 | 0.961 | 0.084 |
| 10 | 1.09 | 1.037 | -35.138 | 0.973 | 0.044 | 1.136 | 1.102 | -32.815 | 0.95 | 0.056 | 1.092 | 1.063 | -33.519 | 0.969 | 0.052 | |
| 2 | 1.015 | 1.005 | -44.875 | 0.998 | 0.017 | 1.016 | 0.992 | -46.244 | 0.999 | 0.015 | 1.014 | 0.997 | -43.21 | 0.999 | 0.02 | |
| Coroller | 6 | 1.024 | 0.999 | -44.485 | 0.998 | 0.017 | 1.023 | 1.005 | -44.031 | 0.997 | 0.018 | 1.026 | 1.015 | -44.002 | 0.998 | 0.018 |
| 10 | 1.086 | 1.015 | -39.045 | 0.986 | 0.03 | 1.038 | 1.026 | -43.724 | 0.996 | 0.019 | 1.025 | 0.989 | -42.618 | 0.996 | 0.021 | |
When the accuracy factor (Af) equals 1, the prediction model corresponds to the experimental data. The log-logistic model exhibited accuracy factor values close to 1 for both the microbiological groups (AM & YM), indicating that it reproduces experimental observations with minimal deviation across all CP voltage and juice depth conditions. Af values close to 1 were observed for all applied CP voltage and juice depth conditions except the Geeraerd model in the case of AM and YM and the biphasic in the case of YM only, indicating that the accuracy of the remaining models was also acceptable. The observed outcome can be accounted by the relationship where experimental observation forecasting becomes less reliable as the Af value increases (Vega et al. 2016). When measurements and predictions perfectly align, the model’s dependability is indicated by a bias factor of 1 (Pipliya et al. 2022). Tables 2 and 3 show that the log-logistic model provided a satisfactory fit for both survival curves, with Bf values close to 1. Weibull + tail, biphasic, and Coroller models exhibit appropriate Bf values for all applied voltages for AM and Weibull + tail and Coroller models for YM microbial groups. The Bf values in the Geeraerd model are somewhat more than 1 for AM and YM and the Bf values in the biphasic model for YM, making it less dependable for predicting experimental results properly.
Because of this, it is difficult to compare and assess each model’s overall performance based on validation indices and goodness of fit metrics. Therefore, more factors need to be looked at in this context.
Identifying the most suitable model based on AIC, Δi and Wi statistical indices
The model’s prediction error is estimated by the AIC. In addition, it is a statistical metric employed to order and select the possible model that best fits the data. These indicators were put in place since it was difficult to determine which one was better using the statistical metrics that had been previously mentioned. When the AIC (Δi = 0) values are small, the model will best match the observed data (Panigrahi et al. 2021). Tables S1 and S2 display the AIC, Δi, and Wi values for each suggested model. Geeraerd and biphasic models showed Δi greater than 10 for all cases except at 24 kV/2 mm, 30 kV/6 mm, and 30 kV/2 mm for AM. These models received little support and cannot be used to fit the microbial kinetic based on the Akaike increment rule of thumb. For that specific data set, the model with the lowest AIC (i.e., Δi = 0) and the largest weightage is considered the best (Panigrahi et al. 2021). The Akaike weights value of the log-logistic model was found to be 47.33% and 48.82% for AM and YM, respectively, which is higher than that of other models. Therefore, the log-logistic model was established as the best-fit model for predicting the inactivation of AM and YM in the CP-treated juice, based on evidence ratios (which measure the likelihood of one model compared to another) and weights of evidence. On the other hand, the Coroller and Weibull + tail models were deemed acceptable as a second option for understanding the inactivation of AM and YM, respectively, in CP-treated kiwifruit juice.
Conclusion
This study aims to illustrate the impact of CP treatment on the natural microbiota in kiwifruit juice. After CP treatment, the AM and YM were inactivated by 3.08 and 2.32 log CFU/mL at 30 kV/2 mm/4 min. According to model parameters and data, although the treatment period at which the population’s share of CP-sensitive members rose and the bulk of them perished, a small percentage of resistant cells continued to exist undamaged while CP-voltage climbed. The fit values of all the models used to forecast the antimicrobial activity of CP-voltage over time were comparable, as measured by statistical measures (R2 and RMSE). Further, based on the Af and Bf values, the biphasic and Geeraerd models were unsuitable for fitting the inactivation kinetic data. Then, the AIC, Δi, and Wi parameters were used to complete the model selection interpretation. The log-logistic model was the best kinetic model for predicting AM and YM kinetics experimental data. For the log-logistic model, the maximum inactivation rate (σ) increased with the increase in CP-voltage and decreased with the increase in juice depth. The highest value of σ was reported at maximum CP-voltage and minimum juice depth because the severity of CP treatment is maximum at maximum CP-voltage and minimum juice depth. Moreover, the log time (τ) decreased with the increase in CP-voltage and increased with the increase in the juice depth. In addition, the τ of YM is more than AM, and the σ of AM is more than YM for the corresponding CP-voltage and juice depth, which shows that the YM is more CP-resistant than AM. It was anticipated that the kinetic models for inactivation would find extensive use in the food process engineering of kiwifruit juice processing.
Electronic supplementary material
Below is the link to the electronic supplementary material.
Authors contribution
Sitesh Kumar: Research plan, experimentation, data analysis, and manuscript preparation. Sunil Pipliya: Manuscript corrections and technical suggestions. Prem Prakash Srivastav: Supervision, research plan, technical suggestions. Brijesh Srivastava: Fund allocation, Project monitoring.
Funding
The authors would like to acknowledge the financial support of the National Agricultural Science Fund (NASF), Indian Council of Agricultural Research (ICAR), Ministry of Agriculture and Farmers Welfare, Govt. of India and Indian Institute of Technology (IIT) Kharagpur.
Data availability
All data generated or analyzed during this study are included in this published article.
Code availability
Not applicable.
Declarations
Consent for publication
The authors hereby consent to publication of the work.
Ethical approval
The Author warrants that the work has not been published before in any form, that the Work is not being concurrently submitted to and is not under consideration by another publisher. All the authors read and agreed to the submission of this manuscript to the “Journal of Food Science and Technology”.
Consent to participate
Not applicable.
Conflict of interest
The authors have declared no conflict of interest.
Footnotes
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
References
- Albert I, Mafart P (2005) A modified Weibull model for bacterial inactivation. Int J Food Microbiol 100(1–3):197–211. 10.1016/J.IJFOODMICRO.2004.10.016 [DOI] [PubMed] [Google Scholar]
- Cerf O (1977) A REVIEW tailing of Survival curves of bacterial spores. J Appl Bacteriol 42(1):1–19. 10.1111/J.1365-2672.1977.TB00665.X [DOI] [PubMed] [Google Scholar]
- Chamorro F, Carpena M, Fraga-Corral M, Echave J, Riaz Rajoka MS, Barba FJ, Cao H, Xiao J, Prieto MA, Simal-Gandara J (2022) Valorization of Kiwi agricultural waste and industry by-products by recovering bioactive compounds and applications as food additives: a circular economy model. Food Chem 370:131315. 10.1016/J.FOODCHEM.2021.131315 [DOI] [PubMed] [Google Scholar]
- Chen H, Hoover DG (2004) Use of Weibull model to describe and predict pressure inactivation of Listeria monocytogenes Scott A in whole milk. Innovative Food Sci Emerg Technol 5(3):269–276. 10.1016/J.IFSET.2004.03.002 [Google Scholar]
- Cheng JH, Lv X, Pan Y, Sun DW (2020) Foodborne bacterial stress responses to exogenous reactive oxygen species (ROS) induced by cold plasma treatments. Trends Food Sci Technol 103(July):239–247. 10.1016/j.tifs.2020.07.022 [Google Scholar]
- Cole MB, Davies KW, Munro G, Holyoak CD, Kilsby DC (1993) A vitalistic model to describe the thermal inactivation of Listeria monocytogenes. J Ind Microbiol 12(3–5):232–239. 10.1007/BF01584195 [Google Scholar]
- Coroller L, Leguerinel I, Mettler E, Savy N, Mafart P (2006) General model, based on two mixed weibull distributions of bacterial resistance, for describing various shapes of inactivation curves. Appl Environ Microbiol 72(10):6493–6502. 10.1128/AEM.00876-06/ASSET/1A7CAA78-2154-4CFE-9513-72271C5B4963/ASSETS/GRAPHIC/ZAM0100671700007.JPEG [DOI] [PMC free article] [PubMed] [Google Scholar]
- D’Amato D, Sinigaglia M, Corbo MR (2011) Microbial characterization of lightly processed Kiwifruit and Fruit Based salads in Relation to Packaging Atmosphere. Food Sci Technol Res 17(6):529–536. 10.3136/FSTR.17.529 [Google Scholar]
- Dasan BG, Boyaci IH (2018) Effect of Cold Atmospheric plasma on inactivation of Escherichia coli and Physicochemical properties of Apple, Orange, Tomato juices, and Sour Cherry Nectar. Food Bioprocess Technol 11(2):334–343. 10.1007/s11947-017-2014-0 [Google Scholar]
- Dasan BG, Yildirim T, Boyaci IH (2018) Surface decontamination of eggshells by using non-thermal atmospheric plasma. Int J Food Microbiol 266(July 2017):267–273. 10.1016/j.ijfoodmicro.2017.12.021 [DOI] [PubMed] [Google Scholar]
- Ferrario M, Alzamora SM, Guerrero S (2013) Inactivation kinetics of some microorganisms in apple, melon, orange and strawberry juices by high intensity light pulses. J Food Eng 118(3):302–311. 10.1016/j.jfoodeng.2013.04.007 [Google Scholar]
- Geeraerd AH, Herremans CH, Van Impe JF (2000) Structural model requirements to describe microbial inactivation during a mild heat treatment. Int J Food Microbiol 59(3):185–209. 10.1016/S0168-1605(00)00362-7 [DOI] [PubMed] [Google Scholar]
- Hosseini SM, Rostami S, Samani H, B., Lorigooini Z (2020) The effect of atmospheric pressure cold plasma on the inactivation of Escherichia coli in sour cherry juice and its qualitative properties. Food Sci Nutr 8(2):870–883. 10.1002/fsn3.1364 [DOI] [PMC free article] [PubMed] [Google Scholar]
- Ikawa S, Kitano K, and, S. H.-P. P., & (2010) undefined. (2010). Effects of pH on bacterial inactivation in aqueous solutions due to low-temperature atmospheric pressure plasma application. Wiley Online LibraryS Ikawa, K Kitano, S HamaguchiPlasma Processes and Polymers, 2010•Wiley Online Library, 7(1), 33–42. 10.1002/ppap.200900090
- Kang JH, Bai J, Min SC (2021) Inactivation of indigenous microorganisms and salmonella in Korean rice cakes by in-package cold plasma treatment. Int J Environ Res Public Health 18(7):3360. 10.3390/IJERPH18073360/S1 [DOI] [PMC free article] [PubMed] [Google Scholar]
- Kopuk B, Gunes R, Palabiyik I (2022) Cold plasma modification of food macromolecules and effects on related products. Food Chem 382:132356. 10.1016/J.FOODCHEM.2022.132356 [DOI] [PubMed] [Google Scholar]
- Kumar S, Pipliya S, Srivastav PP, Srivastava B (2024) Modeling the inactivation kinetics of polyphenol oxidase and peroxidase during the cold plasma treatment of kiwifruit juice. J Food Process Eng 47(2):e14542. 10.1111/JFPE.14542 [Google Scholar]
- Liao, X., Liu, D., Xiang, Q., Ahn, J., Chen, S., Ye, X., & Ding, T. (2017). Inactivation mechanisms of non-thermal plasma on microbes: A review. Food control, 75, 83-91.
- Moritz M, Wiacek C, Weihe T, Ehlbeck J, Weltmann KD, Braun PG (2021) Effect of cold atmospheric pressure plasma treatment of eggshells on the total bacterial count inoculated Salmonella Enteritidis and selected quality parameters. Plasma Processes Polym 18(1):2000061. 10.1002/PPAP.202000061 [Google Scholar]
- Panigrahi C, Mishra HN, De S (2021) Modelling the inactivation kinetics of Leuconostoc mesenteroides, Saccharomyces cerevisiae and total coliforms during ozone treatment of sugarcane juice. LWT 144:111218. 10.1016/J.LWT.2021.111218 [Google Scholar]
- Pinto D, Delerue-Matos C, Rodrigues F (2020) Bioactivity, phytochemical profile and pro-healthy properties of Actinidia arguta: a review. Food Res Int 136:109449. 10.1016/J.FOODRES.2020.109449 [DOI] [PubMed] [Google Scholar]
- Pipliya S, Kumar S, Srivastav PP (2022) Inactivation kinetics of polyphenol oxidase and peroxidase in pineapple juice by dielectric barrier discharge plasma technology. Innovative Food Sci Emerg Technol 80(February):103081. 10.1016/j.ifset.2022.103081 [Google Scholar]
- Pipliya S, Kumar S, Srivastav PP (2023) Modeling of the inactivation kinetics of aerobic mesophiles and yeasts and molds natural microbiota in nonthermal plasma-treated pineapple (Ananas comosus) juice. J Food Sci 88(9):3905–3919. 10.1111/1750-3841.16721 [DOI] [PubMed] [Google Scholar]
- Punia Bangar S, Trif M, Ozogul F, Kumar M, Chaudhary V, Vukic M, Tomar M, Changan S (2022) Recent developments in cold plasma-based enzyme activity (browning, cell wall degradation, and antioxidant) in fruits and vegetables. Compr Rev Food Sci Food Saf 21(2):1958–1978. 10.1111/1541-4337.12895 [DOI] [PubMed] [Google Scholar]
- Sainz-García E, Alba-Elías F (2023) Advances in the application of cold plasma technology in Foods. Foods 12(7):1388. 10.3390/foods12071388 [DOI] [PMC free article] [PubMed] [Google Scholar]
- Satpal D, Kaur J, Bhadariya V, Sharma K (2021) Actinidia deliciosa (Kiwi fruit): a comprehensive review on the nutritional composition, health benefits, traditional utilization, and commercialization. J Food Process Preserv 45(6):e15588. 10.1111/JFPP.15588 [Google Scholar]
- Smet C, Noriega E, Rosier F, Walsh JL, Valdramidis VP, Van Impe JF (2016) Influence of food intrinsic factors on the inactivation efficacy of cold atmospheric plasma: impact of osmotic stress, suboptimal pH and food structure. Innovative Food Sci Emerg Technol 38:393–406. 10.1016/j.ifset.2016.09.028 [Google Scholar]
- Vega S, Saucedo D, Rodrigo D, Pina C, Armero C, Martínez A (2016) Modeling the isothermal inactivation curves of Listeria innocua CECT 910 in a vegetable beverage under low-temperature treatments and different pH levels. 22(6):525–535. 10.1177/1082013215624807 [DOI] [PubMed]
- Wang S, Qiu Y, Zhu F (2021) Kiwifruit (Actinidia spp.): a review of chemical diversity and biological activities. Food Chem 350:128469. 10.1016/J.FOODCHEM.2020.128469 [DOI] [PubMed] [Google Scholar]
Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
Data Availability Statement
All data generated or analyzed during this study are included in this published article.
Not applicable.