# Identification of the Kinetic Parameters of Thermal Micro-Organisms Inactivation
## 1 Introduction  
The processes of thermal sterilization of biotechnological equipment, food products, medical materials, life support systems, etc., are based on both vegetative bacterial cells and their spore deaths at high temperatures. The high-temperature extent of exposure depends on the type of bacterial culture, concentration, physical condition and other factors. In particular, as concerns food products, heat treatment of milk is a mandatory requirement nowadays. The death of the vegetative cells of micro-organisms when heated at a temperature range of 65-95 \({}^{\circ}\)C is called pasteurization. Thermal exposure at temperatures above 120 \({}^{\circ}\)C is called ultra-pasteurization (destruction of spore cultures [1]). The problem in both cases is to minimize the loss of food nutritional value [2, 3]. Some types of bacteria are pathogens or spoilage agents and form spores with increased resistance. Their inactivation is an important factor in the development of food-processing technologies [4, 5]. As a mathematical basis for describing the nonlinear dynamics of the number of micro-organisms contained in food products [5, 6], the approaches of chemical kinetics (transition state theory) are successfully used. Models of chemical reactions occurring in gas-liquid and heterogeneous media adequately describe the biochemistry of many processes. This makes it possible to use well-established methods for the solutions to the physical chemistry problems of embryogenesis [7, 8] and analysis of the life cycle of micro-organisms [9, 10, 11]. Many applications of the original and modified forms of the Arrhenius equation have been reported. These mathematical forms of the Arrhenius equation are used in various models: the growth rate of bacterial cultures; the respiration of plant leaves; the temperature dependence of the heart rate of amphibians; the kinetics of food spoilage, etc., [12]. As an example, the modeling of the behavior dynamics of living organisms is described by the kinetics of molecular reactions [13], and biological systems can be used to obtain certain values of the rate constants and activation energy. To solve applied problems for quantitative estimation of the efficiency of thermal sterilization modes and predication of thermal inactivation, mathematical models are widely used: most important models consider the relevant features of these processes. The physiological, biochemical and physical properties of micro-organisms regulated by temperature, as well as effective modes of food processing, have been discussed [14]. Since the appearance of the original (1889) Arrhenius equation, many models have arisen to describe the population dynamics of organisms, the rate of enzymatic reactions and other temperature-dependent processes. Empirical approaches have been improved, and models based on the thermodynamic principles of biomolecular processes have become more complicated. In particular, the criteria for evaluating the applicability of various approaches to studying the mechanisms of micro-organism inactivation are given [15]. New mathematical models were obtained by modifying the Arrhenius function, applying the Eyring-Polanyi transition state theory considering the diffusion and heat transfer equations [16; 17; 18]. The multifactorial model of extended quasi-chemical kinetics describes the continuous dynamics of some micro-organisms of bacterial cultures from the beginning of growth to the moment of complete inactivation [19]. These models enables to predict the growth or inactivation of micro-organisms as a function of environmental factors such as temperature, pH and water activity [20]. Structural models have been proposed, to describe microbial inactivation during heat treatment [21]. We note that in publications on similar subject matter, aspects related to the description of the model and the practical implementation of computational procedures are not considered together.