Evaluation of Different Dose-Response Models for High Hydrostatic Pressure Inactivation of Microorganisms

Modeling microbial inactivation is central to optimizing food preservation techniques. Traditional methods rely on time-dependent inactivation curves under fixed pressure and temperature. However, these methods require long processing times at low pressure, which increases costs. This gap motivated the exploration of dose-response modeling, where pressure is varied while time remains constant. Prior research has shown that microbial survival can be predicted using various mathematical models. However, no prior work had resolved which model best fits dose-response data for high-pressure inactivation. The need for efficient modeling is clear, especially in industrial applications where time and pressure settings must be optimized. This paper addresses the lack of comparative analysis among models used for HHP inactivation. By evaluating different models, the study contributes a new perspective on how to streamline microbial inactivation modeling.

This study aimed to compare the effectiveness of four mathematical models in describing microbial inactivation under high hydrostatic pressure. The goal was to determine which model best fits the dose-response data when pressure varies and time is fixed. The specific problem addressed is the inefficiency of traditional time-based inactivation modeling at low pressure. The motivation stems from the need to reduce processing costs in food preservation. By using a fixed time and varying pressure, the researchers sought to identify a more practical modeling approach. The study also aimed to calculate the pressure required for 5 log₁₀ inactivation (P₅) for each model. This approach allows for the comparison of microbial pressure resistance across species. The findings could guide the design of future HHP experiments and industrial processing protocols.

The researchers compiled 49 dose-response curves from published studies on microbial inactivation by high hydrostatic pressure. Each curve included at least 4 log₁₀ reduction and five data points, including atmospheric pressure (0.1 MPa). The holding time was limited to 10 minutes to ensure practical relevance. Four models were fitted to the data: Discrete, Shoulder, Fermi equation, and Weibull. Each model was evaluated for goodness of fit using adjusted R² and mean square error (MSE). The pressure value needed for 5 log₁₀ inactivation (P₅) was calculated for all models. The Shoulder model and Fermi equation produced identical parameters and P₅ values. The Discrete model showed similar or identical results to the Fermi equation in some cases. The Weibull model had the lowest fit quality, with the lowest R² and highest MSE.

The Shoulder model and Fermi equation produced identical parameter values and P₅ estimates, indicating strong agreement between the two. The Discrete model showed similar or identical results to the Fermi equation in some cases, suggesting overlapping behavior. The Weibull model had the lowest fit quality, with the lowest adjusted R² and highest MSE values. The Fermi equation had the best fit, with the highest R² and lowest MSE values. These results suggest that the Fermi equation is the most suitable model for dose-response HHP inactivation data. The Shoulder model performed equally well, indicating it is a viable alternative. The P₅ values calculated from each model can guide the design of HHP experiments and comparisons between microorganisms. The study highlights the importance of selecting the right model for accurate predictions.

The study found that the Fermi equation and Shoulder model provided the best fit for dose-response HHP inactivation data. The Discrete model showed similar results in some cases but was not as consistent. The Weibull model performed poorly, with the lowest fit quality. These findings suggest that the Fermi equation is the most reliable model for this type of data. The Shoulder model is a close alternative. The P₅ values calculated from each model can be used to compare microbial pressure resistance and guide future experiments. The study supports the use of dose-response modeling over traditional time-based methods. The findings may help optimize HHP processing in food preservation. The procedure can also be extended to enzyme inactivation by HHP.