Derivation of the Microbial Inactivation Rate Equation from an Algebraic Primary Survival Model Under Constant Conditions
Abstract
:1. Introduction
2. Materials and Methods
2.1. Definitions of Food Process System, System State, and Path of State Change
2.2. The Path-Independent Microbial Inactivation Rate
2.3. The Path-Dependent Microbial Inactivation Rate
2.4. Statistical Analysis
3. Results and Discussion
3.1. The Relationship Between an Inactivation Rate Equation and an Algebraic Primary Model Under Constant Conditions
3.2. A Revisit to Previous Studies
3.2.1. The Application of the Path-Independent Inaction Rate Equation
3.2.2. The Application of the Path-Dependent Inaction Rate Equations
3.2.3. Case Studies
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Reference | Inactivation Rate Equation | Survival Model Under Constant Processing Conditions |
---|---|---|
Chick [15] | ||
Buckow, Isbarn, Knorr, Heinz and Lehmacher [16] | ||
Zhu and Chen [54] | ||
Koseki and Yamamoto [14] |
Data Source | Bacteria | Food Matrix | Isothermal Treatment | Processing Conditions | Temperature Range | RMSE [Equation (7)] | RMSE [Equation (9)] | |
---|---|---|---|---|---|---|---|---|
Case I [32] | Figure 2(a) | Bacillus sporothermodurans IC4 spores | McIlvaine pH7 | 115 °C, 120 °C, 125 °C, 130 °C | HR = 1 °C/min | 110–124 °C | 1.45 | 2.54 |
Figure 2(e) | HR = 10 °C/min | 110–130 °C | 0.382 | 0.762 | ||||
Figure 3(a) | CR = 1 °C/min | 110–126 °C | 6.82 | 5.95 | ||||
Figure 3(b) | CR = 10 °C/min | 110–130 °C | 0.437 | 0.584 | ||||
Figure 2(b) | McIlvaine pH5 | HR = 1 °C/min | 110–124 °C | 0.228 | 0.975 | |||
Figure 2(f) | HR = 10 °C/min | 110–130 °C | 0.812 | 2.08 | ||||
Figure 2(c) | McIlvaine pH3 | HR = 1 °C/min | 110–124 °C | 0.355 | 0.447 | |||
Figure 2(g) | HR = 10 °C/min | 110–130 °C | 1.15 | 0.851 | ||||
Figure 2(d) | Courgette soup | HR = 1 °C/min | 110–124 °C | 0.395 | 1.69 | |||
Figure 2(h) | HR = 10 °C/min | 110–130 °C | 0.836 | 2.46 | ||||
Case II [29] | Figure 3(e) | Geobacillus stearothermophilus T26 | Distilled water | 120 °C, 122.5 °C, 125 °C, 127.5 °C | HR = 1 °C/min | 90–130 °C | 1.41 | 1.69 |
Figure 3(f) | HR = 20 °C/min | 0.874 | 1.12 | |||||
Figure 4(c) | With heating, holding and cooling | 83–122.5 °C | 1.43 | 1.62 | ||||
Case III [33] | Figure 6 | Listeria monocytogenes | Ground beef | 57 °C, 60 °C, 63 °C, 66 °C | HR = 1.72 °C/min | 30–65 °C | 0.389 | 7.56 |
Case IV [59] | Figure 6(a) | Staphylococcus aureus | Peptone water, performed in the thermoresistometer Mastia | 55 °C, 57.5 °C, 60 °C, 62.5 °C | Programmed to simulate the heating profile obtained in the heat exchanger with a product flow of 700 mL/min. | 30–65 °C | 0.914 | 1.80 |
Figure 6(b) | Salmonella senftenberg | 30–65 °C | 0.832 | 2.08 |
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Zhu, S.; Li, B.; Chen, G. Derivation of the Microbial Inactivation Rate Equation from an Algebraic Primary Survival Model Under Constant Conditions. Foods 2025, 14, 1980. https://doi.org/10.3390/foods14111980
Zhu S, Li B, Chen G. Derivation of the Microbial Inactivation Rate Equation from an Algebraic Primary Survival Model Under Constant Conditions. Foods. 2025; 14(11):1980. https://doi.org/10.3390/foods14111980
Chicago/Turabian StyleZhu, Si, Bing Li, and Guibing Chen. 2025. "Derivation of the Microbial Inactivation Rate Equation from an Algebraic Primary Survival Model Under Constant Conditions" Foods 14, no. 11: 1980. https://doi.org/10.3390/foods14111980
APA StyleZhu, S., Li, B., & Chen, G. (2025). Derivation of the Microbial Inactivation Rate Equation from an Algebraic Primary Survival Model Under Constant Conditions. Foods, 14(11), 1980. https://doi.org/10.3390/foods14111980