Primary model for biomass growth prediction in batch fermentation

Abstract

Predictive models may be considered a tool to ensure food quality as they provide insights that support decision making on the design of processes, such as fermentation. Objective: To formulate a mathematical model that describes the growth of lactic acid bacteria (LAB) in batch fermentation. Methodology: Based on real-life experimental data from eight LAB strains, we formulated a primary model in the form of a third-degree polynomial function that successfully describes the four phases observed in LAB growth, i.e., lag, exponential, stationary, and death. Our cubic mathematical model allows us to understand the fundamental nonlinear dynamics of LAB as well as its time-variant dependencies. Parameters of the model are written in terms of initial biomass, maximum biomass, maximum growth rate, and lag phase duration. Further, a statistical analysis was performed to compare our cubic primary model with the ones proposed by Gompertz, Baranyi, and Vázquez-Murado by computing the coefficient of determination(R2), the residual sum of squares (RSS), and the Akaike Information Criterion (AIC). Results: The average statistical results from the cubic model are as follows: R2 = 0.820 providing a better fit than the other three models, RSS = 0.658 and AIC = −6.499, where both values are lower than the other models considered in this study. Conclusion: The cubic primary model formulated in this work describes the behavior of biomass as it accurately represents the four phases of biomass growth in batch fermentation process.