Mathematical models for the effects of pH, temperature, and sodium chloride on the growth of Bacillus stearothermophilus in salty carrots

Estimating the shelf life and safety of any food product is an important part of food product development. Predictive food microbiology reduces the time and expense associated with conventional challenge and shelf life testing. The purpose of this study was to characterize and model germination, outgrowth, and lag (GOL) time and the exponential growth rate (EGR) of Bacillus stearothermophilus in salty carrot medium (SCM) as a function of pH, temperature, and NaCl concentration. B. stearothermophilus is a spore- forming thermophilic organism associated with flat sour spoilage of canned fonds. A split-split plot design was used to measure the effects and interactions of pH (5.5 to 7.0), temperature (45 to 60°C), and NaCl (0 to 1%) on the growth kinetics of B. stearothermophilus in SCM. A total of 96 experiments were analyzed, with individual curve parameters determined by using the Gompertz equation. Quadratic polynomial models for GOL time and EGR of B. stearothermophilus in terms of temperature, pH, and NaCl were generated by response surface analysis. The r² values for the GOL time and EGR models were 0.917 and 0.916, respectively. These models provide an estimate of bacterial growth in response to combinations of the variables studied within the specified ranges. The models were used to predict GOL times and EGRs for additional experimental conditions. The accuracy of these predictions validated the model's predictive ability in SCM.