Stochastic Modeling of Thermal Death Kinetics of a Cell Population Revisited

Abstract

Microorganisms as well as plant and animal cells involved in various biochemical processes are discrete entities whose sizes are mesoscopic. Thus, their number concentration (density) continually fluctuates, especially when it is small; such is the case at the tail end of thermal disinfection. It is, therefore, highly desirable and even essential to introduce the concept and methodology of stochastic processes in the instruction of biochemical engineering. It is indeed appropriate for major textbooks in the field to include these subjects. In fact, the thermal disinfection is commonly adopted to illustrate the application of stochastic processes in these textbooks, but only the mean (the first moment) of the fluctuating number concentration is analytically obtained and numerically presented in the majority of such textbooks; apparently, only one presents the variance (the second moment about the mean). 

To gain deeper insight into the stochastic nature of any phenomenon or process of interest, as manifested in fluctuations of the characteristic property of concern, it would be immensely useful to evaluate the quantities defined in terms of the moments of the distribution of this fluctuating property higher than the second order. In this contribution, the skewness (third moment about the mean over the third power of the standard deviation) and kurtosis (fourth moment about the mean over the fourth power of the standard deviation) of the distribution of fluctuations in the number concentration of cells are evaluated for the same example of thermal disinfection; these results would supplement what is given in the currently available textbooks.