L.M.M. Tijskens

A dynamic and generic model of gas exchange of respiring produce: the effects of oxygen, carbon dioxide and temperature

Abstract A generic model is developed that describes rates of respiration and fermentation, in response to temperature and environmental gas conditions (oxygen and carbon dioxide). The mathematics of the model are based on Michaelis–Menten kinetics. Respiration is simplified as the effect of one enzymic reaction, inhibited by its own product, carbon dioxide. Both competitive, and uncompetitive inhibition are incorporated. Fermentation is modelled including the competitive inhibition of fermentation by both oxygen and carbon dioxide. Temperature dependence is introduced using Arrhenius equations for the maximum rates of oxygen consumption and carbon dioxide production. The model is generic in nature: it is applicable to different types of products (apple, chicory and tomato) at different conditions (in terms of O2, CO2 and temperature) and for different types of inhibition. This fitness is an indirect validation of the assumptions on which the model is based.

A generic model for keeping quality of vegetable produce during storage and distribution

Abstract A generic model on the keeping quality of perishable produce was formulated, based on the kinetics of the decrease of individual quality attributes. The model includes the effects of temperature, chilling injury and different levels of initial quality and of quality acceptance limits. Keeping quality of perishable produce was found to be inversely proportional to the sum of the rates of the separate reactions leading to quality decrease, irrespective of the kinetics of the decrease. In its static form, the model is useful for statistical analysis and for predicting keeping quality at constant conditions. In its dynamic form, it predicts keeping quality as a function of temperature, initial quality and quality acceptance limits. These limits are defined by personal, regional or national preferences. Calculation of the dynamic model requires only one simple numerical integral, even for multiple limiting attributes. Due to the fast numerical integration of that one integral, optimization of distribution chains with respect to produce quality over a broad time and space region becomes economically feasible. The model accounts for the behaviour of keeping quality of about 60 species of fruits and vegetables, including chilling-sensitive products, over a wide range of temperatures.

Modelling the change in colour of broccoli and green beans during blanching

Abstract The green colour of vegetables changes considerably during heat treatments like blanching. Green beans from two different countries and growing seasons, and the stems and florets of broccoli were heat-treated from 40 up to 96°C. The colour was monitored with the CIE-Lab system. Expressing the green colour as −a*/b* proved to considerably reduce the observed variance within measuring samples. It can be considered as a kind of internal standardisation. The colour was modelled by a simplified kinetic mechanism of two consecutive reactions: one that increases colour, one that degrades colour. First, all data sets were analysed separately using non-linear regression. The obtained percentage variance accounted for (R2adj) ranged from 75.7 to 90.8%. Allowing separate initial conditions but with the kinetic parameters in common, the data of the same vegetable type (green beans and broccoli separately) could be pooled and analysed together (R2adj=87.4 and 77.2%, respectively). The kinetic parameters obtained were so similar that a complete pooled and generic analysis was possible even for green beans and broccoli together. These findings greatly validate the developed model and indicate that the formation and degradation of visible colour in vegetables is governed by processes related to the colouring compounds (like chlorophyll and chlorophilides), irrespective of the vegetables under study.

Modelling colour of tomatoes during postharvest storage

Abstract The behaviour of tomato colour was studied during storage at both optimal and suboptimal temperature conditions. A mathematical model is developed describing the behaviour of tomato colour at different temperatures during storage and at harvest maturity stages. The mathematical description used in the model is a logistic (sigmoid) function with a correction for the actual biological age of the tomato. Accuracy in prediction of colour development is highly dependent on the stage of maturity. For tomatoes in the early breaker stage, prediction of colour and keeping quality is possible. In mature green stage, however, prediction will be inherently less accurate. Dynamically changing storage temperatures can be applied in the model by using the integration of the partial derivative.

Food process modelling.

Part 1 Principles of modelling: Fundamental approaches: Power and pitfalls of deductive modelling Problem decomposition Kinetic modelling Modelling of heat and mass transfer Combined discrete/continuous modelling. Part 2 Principles of modelling: Empirical approaches: Power and pitfalls of inductive modelling Data mining Modelling and prediction in an uncertain environment. Part 3 Applications: Agricultural production: Yield and quality prediction of vegetables Modelling and management of fruit production Dairy production Beef cattle production. Part 4 Applications: Processing technologies: Use of models in process development: the case of fermentation processes Improving modified atmosphere packaging through conceptual models Modelling thermal processes: cooling and freezing Modelling thermal processes: heating. Part 5 Applications: Safety and quality in the food chain: Modelling food quality Modelling microbiological safety Modelling use of time-temperature indicators in distribution and stock rotation Modelling the management of distribution centres Concepts of chain management and chain optimisation.

The effects of temperature and senescence on the accumulation of reducing sugars during storage of potato (Solanum tuberosum L) tubers: A mathematical model

Abstract A dynamic mathematical model based on underlying physiological processes is developed to describe, analyze and predict the storage behaviour of potato ( Solanum tuberosum L.) tubers in terms of accumulation of reducing sugars. The data necessary for calibration and validation of the model were gathered during long term storage experiments over a wide range of storage temperatures for several seasons and cultivars. Although the model is based on a considerable simplification of the occurring physiological processes, it is capable of accounting for about 95% of the storage behaviour, including both cold-induced and senescent sweetening. The concept is postulated that the state of maturity at time of harvest determines storage behaviour through the initial amount of enzyme (or enzyme system) responsible for cold-induced sweetening.

Biological Variance, Burden or Benefit

Based on theoretical considerations, a new approach to deal with the variation in properties and quality attributes inherently occurring in all products and batches is presented. It leads to a better understanding of the processes involved and enables the mathematical description and modelling of the observed phenomena. The effect of variation in harvest maturity on the composition of batches drawn from a larger population is used as an example to elucidate the effects of external conditions. These external conditions include the rate constant of the process (directly linked to temperature and controlled atmosphere (CA) conditions), the magnitude of the variation in the larger population and the size of the batches. These theoretical examples show that the standard advice of statisticians to increase the number of individuals in a batch or sample does indeed increase the reliability of data analysis based on mean values. It also shows that the so obtained estimate may well give a complete false picture of the real value. An overview is given for ways to avoid the generation of biological variance, as well as ways to decrease the effects of biological variance already present. This new approach shows how biological variance should be tackled, and even possibly turned into a benefit. A number of practical examples is provided and described briefly to underpin the validity of the approach presented. These examples relate to sources of variation (sweetening of potatoes), to the behaviour of variation during postharvest treatment (colour of apples, keeping quality of cucumbers) and to sophisticated means of dealing with biological variance without too much explicit knowledge of the mechanisms involved (dynamic control system, soil irrigation).

Activity of pectin methyl esterase during blanching of peaches

The activity of pectin methyl esterase (PE) in peaches during blanching treatments was modelled and analysed. It was postulated that the enzyme exists in two configurations, one bound and one soluble. The bound configuration can be converted into the soluble configuration. These two configurations have a different susceptibility to temperature. All rate constants of reaction were modelled as dependent on temperature according to the Arrhenius law. Despite the daily measuring variance, the variance accounted for by the model in multivariate nonlinear regression analysis was more than 90%. The obtained parameter values were highly comparable for two consecutive seasons. An analysis of the data of the two seasons combined was feasible with the kinetic parameters estimated in common, without losing information with a tremendous increase in predictive power.

Kinetics of polygalacturonase activity and firmness of peaches during storage

The activity of endo-polygacturonase (PG) in peaches during storage at different constant temperatures is shown to be the result of a formation from some inactive predecessor and a denaturation or decay into an inactive form. This whole process strongly resembles the normally encountered turnover. On these premises, a process-oriented mathematical model is formulated. The variance accounted for by the model in multivariate nonlinear regression analysis is more than 80% for the data gathered in two successive seasons. Analysis of the data from both seasons combined did not decrease the descriptive power of the model, regardless the fact that the maturity at harvest and the initial level of enzyme activity showed major differences. The values of the parameters obtained from the data of both seasons combined were comparable with those of the individual seasons. The effect of the action of PG on the firmness of peaches was also modelled and analysed with an variance accounted for of almost 90%. The parameters obtained with respect to denaturation of the enzyme were highly comparable.

The effect of harvest time on the accumulation of reducing sugars during storage of potato (Solanum tuberosum L.) tubers: Experimental data described, using a physiological based, mathematical model

SummaryThe physiological based mathematical model describing the storage behaviour of potato (Solanum tuberosum) tubers was examined to determine its ability to explain the changing storage behaviour as a function of harvest time for ten different cultivars. Between 90 to 98% of the observed variance was accounted for. This confirmed the models concept that the maturity at time of harvest determines the storage behaviour through the initial amount of the enzyme (or enzyme system) responsible for cold induced sweetening.