Parameter estimation for dynamic microbial inactivation: which model, which precision?

Ordinary least squares (OLS) one-step regression and the sequential procedure were applied to estimate the dynamic thermal microbial inactivation parameters of Escherichia coli K12 using the differential form of five different models. The best-performing models based on their statistical assessment were, in order: Geeraerd et al. sublethal (7 parameters), Geeraerd et al. stress adaptive (7 parameters); reduced Geeraerd et al. (6 parameters), Weibull (6 parameters), and the first-order model (5 parameters) all integrated with the secondary Bigelow model. The statistics used to evaluate the models were: lowest AICc, minimum root mean square error (RMSE); distribution of residuals; asymptotic relative errors of parameters; scaled sensitivity coefficients; and sequential estimation. RMSE for the first-order model was more than twice that for Geeraerd et al. sublethal model, showing that the first-order model was inappropriate for these data. The optimum reference temperature (Tref) for the secondary model (Bigelow type) was interpolated by estimating all other parameters for different fixed Tref values, and choosing Tref that minimized the correlation coefficient between AsymDref and z. The advantage of finding the optimum Tref was that it minimized the relative error for AsymDref. Scaled sensitivity coefficients of the Geeraerd et al. sublethal model revealed that a) none of the parameters was linearly correlated with others, and b) that the most easily estimated parameters were the three initial microbial concentrations logN(0), followed by AsymDref , z, logCc(0), and sublethal β. The sequential method was also applied to estimate updated parameter values by successively adding each data point. Sequential results showed that each parameter reached a constant after ∼2.5 log reductions. These results show that a) parameters may be affected by rate of heating, and b) dynamic microbial inactivation parameters can be estimated accurately and precisely, directly from few experiments, potentially eliminating the need to apply isothermal parameters to dynamic industrial processes.