Microbial growth models: A general mathematical approach to obtain μ max and λ parameters from sigmoidal empirical primary models

Daniel Angelo Longhi,Gláucia Maria Falcão De Aragão,Francieli Dalcanton,João Borges Laurindo,Bruno Augusto Mattar Carciofi

doi:10.1590/0104-6632.20170342s20150533

Daniel Angelo Longhi, Gláucia Maria Falcão De Aragão + Show 3 more

Open Access

https://doi.org/10.1590/0104-6632.20170342s20150533

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Abstract

Abstract – Empirical sigmoidal models have been widely applied as primary models to describe microbial growth in foods. In predictive microbiology, the maximum specific growth rate ( µ max ) and the lag phase (λ) are the parameters of some models and have been considered as biological parameters. The objective of the current study was to propose mathematical equations to obtain the parameters μ max and λ for any sigmoidal empirical growth model. In a case study, the performance was compared of two models based on empirical parameters and two models based on biological parameters. These models were fitted to experimental data for Lactobacillus plantarum in six isothermal conditions. Some advantages of the proposed approach were the practical and biological interpretation of these parameters, and the useful information of the secondary modeling describing the dependence of µ max and λ with the temperature. Keywords : predictive microbiology; mathematical modelling; secondary models; food safety.

Highlights

In predictive microbiology, the maximum specific growth rate and the lag phase (λ) are parameters present in some models and are supposed to have biological meaning (Zwietering et al, 1990)
The parameter μmax is defined as the slope of the tangent line at the inflection point and the parameter λ is defined as the intercept of this tangent line with the value of the initial microbial count (Pirt, 1975; Zwietering et al, 1990)
Both are the main parameters of the mathematical models used to describe microbial growth over time for a single set of environmental conditions, and such models are called primary models (Whiting and Buchanan, 1993)

Summary

Introduction

The maximum specific growth rate (μmax) and the lag phase (λ) are parameters present in some models and are supposed to have biological meaning (Zwietering et al, 1990). The parameter μmax is defined as the slope of the tangent line at the inflection point and the parameter λ is defined as the intercept of this tangent line with the value of the initial microbial count (Pirt, 1975; Zwietering et al, 1990) Both are the main parameters of the mathematical models used to describe microbial growth over time for a single set of environmental conditions, and such models are called primary models (Whiting and Buchanan, 1993). Obtaining great fits for the secondary models can be considered as important as obtaining great fits for primary models

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Results