Mathematical models for the trimethylamine (TMA) formation on packed cod fish fillets at different temperatures

•Evaluation of models for the formation of trimethylamine at different temperatures.•Temperature mainly influences the parameters for the maximum TMA formation rate.•The differences in initial quality are crucial for the TMA formation profile.•Differences in initial quality need to be adequately incorporated in a TMA model.•A dynamic model with potential to predict TMA content at dynamic temperatures.

The microbial formation of trimethylamine (TMA) can be used as a quality indicator compound to predict the freshness of fish during its shelf life. In a supply chain with fluctuating temperatures, mathematical models will be valuable tools to simulate this formation as a function of temperature and time. These models are essential to link sensor data on the formation of TMA to the actual freshness of fish. Existing models for the formation of TMA in fish needed improvements and secondary models for the effect of temperature on the formation of TMA are lacking in the literature. Three different approaches were evaluated on their ability to simulate the experimental observed TMA formation at 4 different temperatures (0, 5, 10 and 15 °C). In the first approach the existing models were improved and the temperature effect was modelled by an empirical model using four parameters. This model is able to simulate the TMA formation at static temperatures. Since TMA is produced on fresh cod fillets by the micro-organisms Shewanella putrefaciens and Photobacterium phosphoreum the microbial Baranyi-Roberts model was initially used for modelling the TMA formation, but this model was found to be too complex (too many correlated parameters that could not be estimated). In the third approach it was seen that a simplified Baranyi-Roberts model with only three parameters could be used to predict the TMA formation with equal accuracy. The influence of the temperature on the parameter μmax was modelled using the extended square root model of Ratkowsky and the differences in TMA formation profiles of different batches could be described by the batch specific parameter N0 representing the initial quality. The presented dynamic model is valuable in predicting the formation of TMA in a fresh fish supply chain with dynamic temperatures. This model has the potential to be used to link sensor data of TMA in the headspace to the actual freshness status of the fish.