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Mathematical Modeling and Testing of Foods and Food Systems

Peleg, M.
University of Massachusetts - Amherst
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The project's primary goal is to develop new and improve existing mathematical models, mainly of two kinds: deterministic differential rate equations, and probabilistic models. Models of the first type are primarily intended for microbial growth and inactivation and the kinetics of nonlinear chemical and biochemical processes, which are associated with food safety, nutritional value, quality and shelf life. Models of the second type are primarily intended for microbial injury and spores germination, with emphasis on small groups of cells or spores. The work on stochastic models will also include the development of new applications of the Expanded Fermi Solution based on Monte Carlo simulations in microbial and chemical risk assessment.

Secondary goals of the project are the development of interactive program that will enable food scientists, technologists and engineering to solve practical quantitative problems and use computer simulations to resolve theoretical issues, and the development or improvement of methods to assess and interpret physical properties of foods. We expect that that the project will result in new mathematical models for quantitative microbiology, food reactions kinetics and mechanical properties of foods, produce improved versions of existing kinetic models, create new methods of calculation and a make a number of new programs available to professionals in the field through the Internet. Many of the latter will be in the form of interactive Wolfram Demonstrations, which are very user-friendly and freely downloadable from the Internet. The new methods and results will be published in scientific and technical journals, presented in professional meetings and described and explained in seminars and symposia held in academia and the food industry.

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The modeling effort will be based on three stages.

First: Models selection and investigation of their mathematical properties.

Second: Examination of the models capabilities and limitations with computer simulations based on realistic scenarios in food processing, preservation, transportation and storage.

Third: Testing the models' predictive ability with published data or with experimental data produced by other groups (within or outside the Massachusetts Agricultural Experiment Station). The modeled systems will be: microbial (growth, inactivation, germination, activation and their combinations), biochemical and chemical. The emphasis will be on systems whose evolution follows non-linear kinetics, i.e., where the momentary rate varies not only with temperature, pressure, pH, water activity, etc., but also with time. In microbial growth, inactivation, injury and germination kinetics, discrete stochastic models will also be developed, focused on the evolution of small cells and spores populations under changing conditions (favorable and hostile). The stochastic models will be related to existing continuous deterministic models developed for large microbial populations through the underlying probability rate functions. Software development, for model equations solution, systems simulations and physical and engineering calculations, will be primarily based on Mathematica (Wolfram Research, Champaign IL) and in special cases, MS Excel.

There will be two kinds of programs.

The first will consist of advanced and computation intensive programs the running of which requires having Mathematica installed on the user's computer. [As in the past, we'll publish the code, or make it available upon request, so that it can be implemented with other mathematical software.]

The second type will consist of interactive programs in the form of Wolfram Demonstrations, the use of which only requires downloading the free CDF Player from the Internet. Physical properties, especially rheological, will be determined in the Physical Properties Laboratory using equipment already in place. The focus will be on semi-liquid foods with time dependent characteristics using lubricated squeezing flow viscometry, and brittle foods with non-homogenous structure using a Universal testing machine. Existing models to describe, explain and predict them will be improved or new ones developed.

Funding Source
Nat'l. Inst. of Food and Agriculture
Project source
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Risk Assessment, Management, and Communication
Predictive Microbiology
Natural Toxins
Viruses and Prions
Bacterial Pathogens
Chemical Contaminants