[4-1015-C] Food Safety (1)

[4-1015-C-05] Development of Calculation Framework for Stochastic Prediction of Uncertainty and Variability in Survival Spore Numbers during Non-isothermal Inactivation by Second-order Monte Carlo Simulation

*Hiroki Abe¹, Kento Koyama¹, Kohei Takeoka¹, Shinya Doto¹, Shuso Kawamura¹, Shige Koseki¹ (1. Hokkaido University(Japan))

キーワード：Predictive microbiology, Dynamic model, Stochastic model, Bootstrap method, Markov chain Monte Carlo, Weibull model, Thermal inactivation

Although thermal inactivation is one of the control measures for microbial contamination in foods, thermal processing at a high temperature or long-time heating induces chemical and physical reactions in foods that reduce product quality. To determine minimum processing condition, mathematical models need to appropriately describe the bacterial behavior during inactivation; the log-linear model, generally used, based on D-value (Decimal reduction time) would lead to overestimation or underestimation of thermal death time. In addition, the conventional kinetic predictive models disregard the variability and uncertainty of bacterial death behavior, although various mathematical models (log-linear or non-log-linear models) have been used to describe reduction behaviors during bacterial inactivation. In this context, “uncertainty” represents the lack of perfect knowledge of the parameter value; “variability” represents the true heterogeneity of the population that is a consequence of the physiological system. The importance of uncertainty and variability of biological and natural phenomena is widely recognized in the context of the guidance of quantitative microbial risk assessment. Few studies have been performed to separately evaluate and describe the variability and the uncertainty in population dynamics of microbial inactivation. This study aimed to develop a stochastic bacterial survival model considering both the “variability” and “uncertainty” from kinetic data. The developed model estimates the variance of survival behavior during non-isothermal inactivation. Furthermore, the estimated bacterial death behaviors were validated with the observed survival counts data. The spores of Bacillus simplex were heated under fifteen isothermal conditions (pH: 5.4, 5.8, 6.2, 6.6 and 7.0; Temperature: 80, 85 and 90°C); the changes in the survival spore count were experimentally determined. The uncertainty in fitted Weibullian parameters was estimated from statistical resampling one thousand replicates of the survival spore counts in each thermal condition by the non-parametric bootstrap method. One thousand replicates of the secondary models were described by estimated parameters. The secondary models describe the relationship between Weibullian parameters and pH and/or heating temperature. In contrast, individual cell heterogeneity of the death spore counts in an infinitesimal time interval was described as “variability” by Markov chain Monte Carlo (MCMC) method based on a binomial distribution. The second-order Monte Carlo (2DMC) simulation estimated the changes in the survival spore behavior during non-isothermal heating with both the variations. In parallel, the variance in survival kinetics of survival spore counts during non-isothermal heating was observed to compare with the prediction of survival counts. The uncertainty of the Weibullian parameter estimations and individual heterogeneity of the death spore counts in an infinitesimal time interval was successfully described. Furthermore, in all of three non-isothermal histories, the variances in the survival spore counts during processing periods were successfully described by the developed 2DMC model. The MCMC successfully described stochastic results in the bacterial reduction behaviors during not only isothermal but also non-isothermal from kinetic data. In conclusion, the 2DMC model enabling to describe both the uncertainty and variability in thermal inactivation will play an important role in appropriate risk assessment for bacterial survival.