Fundamental models and disciplines

Fundamental-oriented models can be built in many ways and within many scientific disciplines. Disciplines, however, are a result of the deep-rooted urge of man and scientists to bring some order to our view and perception of the world. Nature, on the other hand, does not have or need disciplines at all. Processes occurring in nature "naturally" comply with the laws of nature. The ultimate drive of science is to detect and understand these laws, and to convert that understanding into some practical application in order to increase the quality of our lives. So, within the realm of each discipline, the same laws of nature will be present and known in one form or another. The direct consequence is that, in modelling and understanding processes of nature, it does not really matter which particular discipline is used as a framework, as long as its rules are used consistently and thoroughly. For chemists, the choice of kinetic modelling is self-evident.

The general rules of kinetic modelling are summarised and described in van Boekel and Tijskens (2001). The rules of the discipline and the laws of nature in the area of chemistry were all discovered and formulated in the early days of chemical discoveries, and theories were formulated. They are now a standard part of textbooks on chemistry, physical chemistry, kinetics and enzyme kinetics (Chang, 1981; Fersht, 1984; Whittaker, 1994; etc.) Although this knowledge has been available for so many years, when building empirical models old-fashioned style, it is the first information that consistently is not used at all. Every time new data need to be analysed, mathematical and statistical relations are invented and tested all over again, and the model with the statistical best fit to the data at hand is chosen to represent the behaviour of that system, without recourse to any expert knowledge whatsoever. Modern science is based on the most important rule of all: the repeatability of a process. That is, in the same conditions the same process will occur at the same rate. In making models, we should use this, the very basis of science, and search for process rate constants that are true constants for any condition encountered. In other words, rate constants of processes will be the same for the same processes, no matter what the conditions are.

Some general rules can be drawn up when modelling the complexity of interacting processes that occur in nature. When trying to model interactive processes, it is of the utmost importance to apply the old Roman rule "divide et impera" (divide and rule). In modern terminology, that is problem decomposition. Having used this technique almost unconsciously for several years in developing process-oriented models, a young information technologist devoted a major part of his PhD thesis to developing a more consistent, understandable and applicable system in that respect (Sloof, 1999; Sloof, 2001). Still, the process of detecting possible and plausible mechanisms in rather unstructured data is apparently quite a difficult task for most people. In our opinion, that, rather than the necessary requirements of mathematical skills or product expertise, is what makes a good modeller.

Another general rule for developing process-oriented models is the consistent application at all costs of the laws of a particular discipline. Adapting mathematical equations, whether at the level of differential equations or at the level of functions or analytical solutions of these differential equations, invariably changes the fundamental nature of a model into an empirical one. Changes are only permitted at the level of developing appropriate mechanisms. Changes at a mathematical level inevitably prevent any further development along fundamental lines. Process-oriented modelling does offer not only the advantage of an increased understanding of processes and interactions, it also ensures a reusability of models and, above all, the transferability of parameter values to all kinds of different situations and conditions in which the product is used. And that is the ultimate goal of modelling: providing a prediction of future behaviour of products from any provenance, from any growing conditions and in any circumstances during the food supply chain.

Based on these ideas, using the vast knowledge product experts already have on the processes which take place and the applicability of the laws of the various disciplines, modelling product behaviour and food quality is not at all difficult - it merely takes a lot of time and effort. The reason why this technique has not been used consistently in every case is the idea that our food is too complex to be described by these simple principles.

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