Weibull distribution function based on an empirical mathematical model for inactivation of Escherichia coli by pulsed electric fields

Abstract

The pulsed electric field inactivation kinetics of Escherichia coli suspended in orange juices with three different concentrations of carrot juice (0, 20, and 60%) was studied. Electric field strengths ranged from 25 to 40 kV/cm, and treatment times ranged from 40 to 340 μs. Experimental data were fitted to Bigelow, Hülsheger, and Weibull distribution functions, and the Weibull function provided the best fit (with the lowest mean square error). The dependency of each model's kinetic constant on electric field strength and carrot juice concentration was studied. A secondary model was developed to describe the relationship of Weibull parameters a and n to electric field strength and carrot juice concentration. An empirical mathematical model based on the Weibull distribution function, relating the natural logarithm of the survival fraction to treatment time, electric field strength, and carrot juice concentration, was developed. Parameters were estimated by a nonlinear regression. The results of this study indicate that the error rate for the model's predictions was 6.5% and that the model was suitable for describing E. coli inactivation.