Van Impe J F, Nicolaï B M, Martens T, De Baerdemaeker J, Vandewalle J
ESAT-Department of Electrical Engineering, Katholieke Universiteit Leuven, Belgium.
Appl Environ Microbiol. 1992 Sep;58(9):2901-9. doi: 10.1128/aem.58.9.2901-2909.1992.
Many sigmoidal functions to describe a bacterial growth curve as an explicit function of time have been reported in the literature. Furthermore, several expressions have been proposed to model the influence of temperature on the main characteristics of this growth curve: maximum specific growth rate, lag time, and asymptotic level. However, as the predictive value of such explicit models is most often guaranteed only at a constant temperature within the temperature range of microbial growth, they are less appropriate in optimization studies of a whole production and distribution chain. In this paper a dynamic mathematical model--a first-order differential equation--has been derived, describing the bacterial population as a function of both time and temperature. Furthermore, the inactivation of the population at temperatures above the maximum temperature for growth has been incorporated. In the special case of a constant temperature, the solution coincides exactly with the corresponding Gompertz model, which has been validated in several recent reports. However, the main advantage of this dynamic model is its ability to deal with time-varying temperatures, over the whole temperature range of growth and inactivation. As such, it is an essential building block in (time-saving) simulation studies to design, e.g., optimal temperature-time profiles with respect to microbial safety of a production and distribution chain of chilled foods.
文献中已报道了许多S形函数，用于将细菌生长曲线描述为时间的显式函数。此外，还提出了几种表达式来模拟温度对该生长曲线主要特征的影响：最大比生长速率、延迟期和渐近水平。然而，由于此类显式模型的预测价值通常仅在微生物生长温度范围内的恒定温度下才能得到保证，因此它们不太适用于整个生产和分销链的优化研究。本文推导了一个动态数学模型——一个一阶微分方程，将细菌数量描述为时间和温度的函数。此外，还纳入了在高于生长最高温度的温度下细菌数量的失活情况。在恒温的特殊情况下，该解与相应的Gompertz模型完全一致，最近的几份报告已对该模型进行了验证。然而，这个动态模型的主要优点是它能够在整个生长和失活温度范围内处理随时间变化的温度。因此，它是（节省时间的）模拟研究中的一个重要组成部分，例如设计关于冷藏食品生产和分销链微生物安全性的最佳温度-时间曲线。
