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Abstract：
Kinetic models are nowadays a basic tool to ensure food safety. Most models used in predictive microbiology have model parameters, whose precision is crucial to provide meaningful predictions. Kinetic parameters are usually estimated based on experimental data, where the experimental design can have a great impact on the precision of the estimates. In this sense, Optimal Experiment Design (OED) applies tools from optimization and information theory to identify the most informative experiment under a set of constrains (e.g. mathematical model, number of samples, etc). In this work, we develop a methodology for the design of optimal isothermal inactivation experiments. We consider the two dimensions of the design space (time and temperature), as well as a temperature-dependent maximum duration of the experiment. Functions for its application have been included in the bioOED R package. We identify design patterns that remain optimum regardless of the number of sampling points for three inactivation models (Bigelow, Mafart and Peleg) and three model microorganisms (Escherichia coli, Salmonella Senftenberg and Bacillus coagulans). Samples at extreme temperatures and close to the maximum duration of the experiment are the most informative. Moreover, the Mafart and Peleg models require some samples at intermediate time points due to the non-linearity of the survivor curve. The impact of the reference temperature on the precision of the parameter estimates is also analysed. Based on numerical simulations we recommend fixing it to the mean of the maximum and minimum temperatures used for the experiments. The article ends with a discussion presenting guidelines for the design of isothermal inactivation experiments. They combine these optimum results based on information theory with several practical limitations related to isothermal inactivation experiments. The application of these guidelines would reduce the experimental burden required to characterize thermal inactivation.
摘要：
如今，动力学模型是确保食品安全的基本工具。预测微生物学中使用的大多数模型都有模型参数，其精度对于提供有意义的预测至关重要。动力学参数通常根据实验数据进行估计，实验设计会对估计的精度产生很大影响。在这个意义上,最佳实验设计（OED）应用来自优化和信息理论的工具来识别一组约束下的信息最丰富的实验（例如数学模型，样品数量,etc).在这项工作中,我们开发了一种设计最佳等温失活实验的方法。我们考虑设计空间的两个维度（时间和温度），以及与温度相关的实验最大持续时间。其应用功能已包含在bioOEDR包中。我们确定了无论三个失活模型的采样点数量如何都保持最佳的设计模式(Bigelow，Mafart和Peleg)和三种模式微生物(大肠杆菌，Senftenberg沙门氏菌和凝结芽孢杆菌）。在极端温度和接近实验的最大持续时间的样品是最有益的。此外，由于幸存者曲线的非线性，Mafart和Peleg模型在中间时间点需要一些样本。还分析了参考温度对参数估计精度的影响。根据数值模拟，我们建议将其固定为实验所用的最高和最低温度的平均值。本文最后讨论了等温失活实验设计的指南。他们将基于信息论的这些最佳结果与与等温失活实验有关的几个实际限制相结合。这些指南的应用将减少表征热失活所需的实验负担。
