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Dynamic Modelling and Simulation of Food Systems

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A special issue of Foods (ISSN 2304-8158). This special issue belongs to the section "Food Engineering and Technology".

Deadline for manuscript submissions: closed (30 June 2022) | Viewed by 32664

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Special Issue Editors

Dr. Carlos Vilas

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Guest Editor

Process Engineering Group, IIM-CSIC (Spanish National Research Council), 36208 Vigo, Spain
Interests: mathematical modelling; advanced control; model-based optimization; food processes; food quality and safety; parameter estimation

Dr. Míriam R. García

E-Mail Website
Co-Guest Editor

Process Engineering Group, IIM-CSIC (Spanish National Research Council), 36208 Vigo, Spain
Interests: predictive microbiology; modelling and optimization of food quality and safety; fresh fishery products; antimicrobial resistance; cleaning and disinfection; model identification; process engineering

Dr. Jose A. Egea

E-Mail Website
Co-Guest Editor

Centro de Edafología y Biología Aplicada del Segura (CEBAS-CSIC), Campus Universitario de Espinardo, E-30100 Murcia, Spain
Interests: modelling and optimization of agri-food processes; optimization in engineering and biotechnology; parameter estimation; optimal experimental design; data analysis; metaheuristics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

There are several factors that guide consumers’ choice of food products. Although price remains the main criterion, pleasure, convenience, and health are important driving factors of food market evolution. Food enterprises are making significant efforts to manufacture products that meet consumers’ demands without compromising safety standards. The food industry is also searching for means to improve the efficiency of the transformation and conservation processes by minimizing energy consumption, process duration, and waste generation. Food processes are very complex systems with highly non-linear dynamics and interactions among several time and spatial scales. Mathematical modeling and simulation are key elements that allow us to gain a deeper understanding of food processes and enable the use of tools such as optimization and real-time control to improve their efficiency.

This Special Issue aims to gather research developing dynamic mathematical models describing relevant factors of food processes. We invite authors to submit original research papers or comprehensive review papers related with the mathematical modeling of food processes from the perspectives of food safety (chemical or microbiological), food quality (organoleptic or nutritional), cleaning and disinfection, energy consumption, and resources waste. The Special Issue is not limited to model development, and we also welcome papers that use mathematical models to improve food processes. This includes decision-making tools, optimization, characterization of uncertainty/variability of model predictions, model simulation techniques, software sensors, and software development.

Dr. Carlos Vilas
Guest Editor
Dr. Míriam R. García
Dr. Jose A. Egea
Co-Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Foods is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2900 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

dynamic modeling, simulation and optimization
model identification
software sensors
process engineering
predictive microbiology
food quality and safety
numerical methods
food variability

Published Papers (14 papers)

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Editorial

Jump to: Research, Review

5 pages, 211 KiB

Open AccessEditorial

Dynamic Modelling and Simulation of Food Systems: Recent Trends and Applications

by Jose A. Egea, Míriam R. García and Carlos Vilas

Foods 2023, 12(3), 557; https://0-doi-org.brum.beds.ac.uk/10.3390/foods12030557 - 27 Jan 2023

Cited by 1 | Viewed by 1716

Abstract

Several factors influence consumers’ choices of food products [...] Full article

(This article belongs to the Special Issue Dynamic Modelling and Simulation of Food Systems)

Research

Jump to: Editorial, Review

14 pages, 12620 KiB

Open AccessArticle

Multiobjective Optimization of a Frying Process Balancing Acrylamide Formation and Quality: Solution Analysis and Uncertainty Propagation

by Jose Lucas Peñalver-Soto, María Muñoz-Guillermo, Alberto Garre, Asunción Iguaz, Pablo S. Fernández and Jose A. Egea

Foods 2022, 11(22), 3689; https://0-doi-org.brum.beds.ac.uk/10.3390/foods11223689 - 17 Nov 2022

Cited by 1 | Viewed by 1206

Abstract

In this study, we performed multi-objective model-based optimization of a potato-frying process balancing between acrylamide production and a quality parameter (yellowness). Solution analysis revealed that, for most of the Pareto solutions, acrylamide levels exceeded the EFSA recommendation. Almost equivalent optimal solutions were found for moderate processing conditions (low temperatures and/or processing times) and the propagation of the uncertainty of the acrylamide production model parameters led to Pareto fronts with notable differences from the one obtained using the nominal parameters, especially in the ranges of high values of acrylamide production and yellowness. These results can help to identify processing conditions to achieve the desired acrylamide/yellowness balance and design more robust processes allowing for the enhancement of flexibility when equivalent optimal solutions can be retrieved. Full article

(This article belongs to the Special Issue Dynamic Modelling and Simulation of Food Systems)

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20 pages, 459 KiB

Open AccessArticle

Parameter Estimation of Dynamic Beer Fermentation Models

by Jesús Miguel Zamudio Lara, Laurent Dewasme, Héctor Hernández Escoto and Alain Vande Wouwer

Foods 2022, 11(22), 3602; https://0-doi-org.brum.beds.ac.uk/10.3390/foods11223602 - 11 Nov 2022

Cited by 2 | Viewed by 1382

Abstract

In this study, two dynamic models of beer fermentation are proposed, and their parameters are estimated using experimental data collected during several batch experiments initiated with different sugar concentrations. Biomass, sugar, ethanol, and vicinal diketone concentrations are measured off-line with an analytical system while two on-line immersed probes deliver temperature, ethanol concentration, and carbon dioxide exhaust rate measurements. Before proceeding to the estimation of the unknown model parameters, a structural identifiability analysis is carried out to investigate the measurement configuration and the kinetic model structure. The model predictive capability is investigated in cross-validation, in view of opening up new perspectives for monitoring and control purposes. For instance, the dynamic model could be used as a predictor in receding-horizon observers and controllers. Full article

(This article belongs to the Special Issue Dynamic Modelling and Simulation of Food Systems)

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16 pages, 4875 KiB

Open AccessArticle

Effect of Cold- and Hot-Break Heat Treatments on the Physicochemical Characteristics of Currant Tomato (Solanum pimpinellifolium) Pulp and Paste

by Kandi Sridhar, Hilal A. Makroo and Brijesh Srivastava

Foods 2022, 11(12), 1730; https://0-doi-org.brum.beds.ac.uk/10.3390/foods11121730 - 13 Jun 2022

Cited by 3 | Viewed by 2281

Abstract

Currant tomato (Solanum pimpinellifolium), an underutilized wild species of modern tomato, was investigated to determine the physicochemical properties and understand the effect of cold- and hot-break heat treatments on physicochemical characteristics. Moreover, a new Arrhenius-type equation was used to model the temperature-dependent viscosity of currant tomato pulp and paste. The currant tomato’s porosity, surface area, and lycopene content were 40.96 ± 0.84%, 663.86 ± 65.09 mm², and 9.79 ± 1.88 mg/100 g, respectively. Cold- and hot-break heat treatments had a significant (p < 0.05) effect on tomato pulp and paste color change (0.09 to 0.26; 0.19 to 1.96), viscosity (0.06 to 0.02 Pa.s; 0.85 to 0.37 Pa.s), and lycopene content (9.70 to 9.07 mg/100 g; 9.60 to 9.37 mg/100 g), respectively. An Arrhenius-type equation described the temperature-dependent viscosity of currant tomato pulp and paste with activation energy (E_a) ranging from 7.54 to 11.72 kJ/mol and 8.62 to 8.97 kJ/mol, respectively. Principal component analysis (PCA) revealed a total of variance 99.93% in tomato pulp and paste as affected by the cold- and hot-break heat treatments. Overall, the findings may provide knowledge for design graders and process optimization to develop currant tomato-based products. Full article

(This article belongs to the Special Issue Dynamic Modelling and Simulation of Food Systems)

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18 pages, 935 KiB

Open AccessArticle

Consideration of Maintenance in Wine Fermentation Modeling

by Alain Rapaport, Robert David, Denis Dochain, Jérôme Harmand and Thibault Nidelet

Foods 2022, 11(12), 1682; https://0-doi-org.brum.beds.ac.uk/10.3390/foods11121682 - 08 Jun 2022

Cited by 2 | Viewed by 1474

Abstract

We show that a simple model with a maintenance term can satisfactorily reproduce the simulations of several existing models of wine fermentation from the literature, as well as experimental data. The maintenance describes a consumption of the nitrogen that is not entirely converted into biomass. We show also that considering a maintenance term in the model is equivalent to writing a model with a variable yield that can be estimated from data. Full article

(This article belongs to the Special Issue Dynamic Modelling and Simulation of Food Systems)

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13 pages, 18069 KiB

Open AccessFeature PaperArticle

Use of Food Spoilage and Safety Predictor for an “A Priori” Modeling of the Growth of Lactic Acid Bacteria in Fermented Smoked Fish Products

by Angela Racioppo, Daniela Campaniello, Milena Sinigaglia, Antonio Bevilacqua, Barbara Speranza and Maria Rosaria Corbo

Foods 2022, 11(7), 946; https://0-doi-org.brum.beds.ac.uk/10.3390/foods11070946 - 25 Mar 2022

Cited by 3 | Viewed by 2561

Abstract

Fermentation is one of the oldest methods to assure the safety and quality of foods, and to prolong their shelf life. However, a successful fermentation relies on the correct kinetics depending on some factors (i.e., ingredients, preservatives, temperature, inoculum of starter cultures). Predictive microbiology is a precious tool in modern food safety and quality management; based on the product characteristics and the conditions occurring in food processing, the inactivation of or increase in microbial populations could be accurately predicted as a function of the relevant intrinsic or extrinsic variables. The main aim of this study was the optimization of the formula of a smoked fermented fish product using predictive modeling tools (tertiary and secondary models) in order to define the role of each factor involved in the formulation and assure a correct course of fermentation. Product optimization was conducted through the software Food Spoilage and Safety Predictor (FSSP), by modeling the growth of lactic acid bacteria (LAB) as a function of some key parameters such as temperature, pH, salt, liquid smoke, carbon dioxide, and nitrites. The variables were combined through a fractional design of experiments (DoE) (3^k-p), and the outputs of the software, i.e., the maximal growth rate (μ_max) and the time to attain the critical threshold (t_crit), were modeled through a multiple regression procedure. The simulation, through FSSP and DoE, showed that liquid smoke is the most critical factor affecting fermentation, followed by temperature and salt. Concerning temperature, fermentation at 20–25 °C is advisable, although a low fermentation temperature is also possible. Other parameters are not significant. Full article

(This article belongs to the Special Issue Dynamic Modelling and Simulation of Food Systems)

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13 pages, 2757 KiB

Open AccessArticle

Dynamics of Microbial Inactivation and Acrylamide Production in High-Temperature Heat Treatments

by Jose Lucas Peñalver-Soto, Alberto Garre, Arantxa Aznar, Pablo S. Fernández and Jose A. Egea

Foods 2021, 10(11), 2535; https://0-doi-org.brum.beds.ac.uk/10.3390/foods10112535 - 21 Oct 2021

Cited by 2 | Viewed by 1824

Abstract

In food processes, optimizing processing parameters is crucial to ensure food safety, maximize food quality, and minimize the formation of potentially toxigenic compounds. This research focuses on the simultaneous impacts that severe heat treatments applied to food may have on the formation of harmful chemicals and on microbiological safety. The case studies analysed consider the appearance/synthesis of acrylamide after a sterilization heat treatment for two different foods: pureed potato and prune juice, using Geobacillus stearothermophilus as an indicator. It presents two contradictory situations: on the one hand, the application of a high-temperature treatment to a low acid food with G. stearothermophilus spores causes their inactivation, reaching food safety and stability from a microbiological point of view. On the other hand, high temperatures favour the appearance of acrylamide. In this way, the two objectives (microbiological safety and acrylamide production) are opposed. In this work, we analyse the effects of high-temperature thermal treatments (isothermal conditions between 120 and 135 °C) in food from two perspectives: microbiological safety/stability and acrylamide production. After analysing both objectives simultaneously, it is concluded that, contrary to what is expected, heat treatments at higher temperatures result in lower acrylamide production for the same level of microbial inactivation. This is due to the different dynamics and sensitivities of the processes at high temperatures. These results, as well as the presented methodology, can be a basis of analysis for decision makers to design heat treatments that ensure food safety while minimizing the amount of acrylamide (or other harmful substances) produced. Full article

(This article belongs to the Special Issue Dynamic Modelling and Simulation of Food Systems)

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17 pages, 3800 KiB

Open AccessArticle

Prediction in the Dynamics and Spoilage of Shewanella putrefaciens in Bigeye Tuna (Thunnus obesus) by Gas Sensors Stored at Different Refrigeration Temperatures

by Zhengkai Yi and Jing Xie

Foods 2021, 10(9), 2132; https://0-doi-org.brum.beds.ac.uk/10.3390/foods10092132 - 09 Sep 2021

Cited by 13 | Viewed by 2169

Abstract

Shewanella putrefaciens have a faster growth rate and strong spoilage potential at low temperatures for aquatic products. This study developed a nondestructive method for predicting the kinetic growth and spoilage of S. putrefaciens in bigeye tuna during cold storage at 4, 7 and 10 °C by electronic nose. According to the responses of electronic nose sensor P30/2, the fitted primary kinetic models (Gompertz and logistic models) and secondary model (square root function model) were able to better simulate the dynamic growth of S. putrefaciens, with high R² and low RMSE values in the range of 0.96–0.99 and 0.021–0.061, respectively. A partial least squares (PLS) regression model based on both electronic nose sensor response values and electrical conductivity (EC) values predicted spoilage of S. putrefaciens in bigeye tuna more accurately than the PLS model based on sensor signal values only. In addition, SPME/GC-MS analysis suggested that 1-octen-3-ol, 2-nonanone, 2-heptanone, dimethyl disulfide and methylamine, N, N-dimethyl- are the key VOCs of tuna inoculated with S. putrefaciens. Full article

(This article belongs to the Special Issue Dynamic Modelling and Simulation of Food Systems)

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14 pages, 2249 KiB

Open AccessArticle

Dynamic Thermal Properties Estimation Using Sensitivity Coefficients for Rapid Heating Process

by Anbuhkani Muniandy, Patnarin Benyathiar, Dharmendra K. Mishra and Ferhan Ozadali

Foods 2021, 10(8), 1954; https://0-doi-org.brum.beds.ac.uk/10.3390/foods10081954 - 22 Aug 2021

Cited by 4 | Viewed by 2952

Abstract

Thermal conductivity determination of food at temperatures > 100 °C still remains a challenge. The objective of this study was to determine the temperature-dependent thermal conductivity of food using rapid heating (TPCell). The experiments were designed based on scaled sensitivity coefficient (SSC), and the estimated thermal conductivity of potato puree was compared between the constant temperature heating at 121.10 °C (R12B10T1) and the rapid heating (R22B10T1). Temperature-dependent thermal conductivity models along with a constant conductivity were used for estimation. R22B10T1 experiment using the k model provided reliable measurements as compared to R12B10T1 with thermal conductivity values from 0.463 ± 0.011 W m⁻¹ K⁻¹ to 0.450 ± 0.016 W m⁻¹ K⁻¹ for 25–140 °C and root mean squares error (RMSE) of 1.441. In the R12B10T1 experiment, the analysis showed the correlation of residuals, which made the estimation less reliable. The thermal conductivity values were in the range of 0.444 ± 0.012 W m⁻¹ K⁻¹ to 0.510 ± 0.034 W m⁻¹ K⁻¹ for 20–120 °C estimated using the k model. Temperature-dependent models (linear and k models) provided a better estimate than the single parameter thermal conductivity determination with low RMSE for both types of experiments. SSC can provide insight in designing dynamic experiments for the determination of thermal conductivity coefficient. Full article

(This article belongs to the Special Issue Dynamic Modelling and Simulation of Food Systems)

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22 pages, 5199 KiB

Open AccessArticle

Dynamic Modeling of Carnobacterium maltaromaticum CNCM I-3298 Growth and Metabolite Production and Model-Based Process Optimization

by Cristian Puentes, Amélie Girardeau, Stephanie Passot, Fernanda Fonseca and Ioan-Cristian Trelea

Foods 2021, 10(8), 1922; https://0-doi-org.brum.beds.ac.uk/10.3390/foods10081922 - 19 Aug 2021

Cited by 3 | Viewed by 1848

Abstract

Carnobacterium maltaromaticum is a species of lactic acid bacteria found in dairy, meat, and fish, with technological properties useful in food biopreservation and flavor development. In more recent years, it has also proven to be a key element of biological time–temperature integrators for tracking temperature variations experienced by perishable foods along the cold-chain. A dynamic model for the growth of C. maltaromaticum CNCM I-3298 and production of four metabolites (formic acid, acetic acid, lactic acid, and ethanol) from trehalose in batch culture was developed using the reaction scheme formalism. The dependence of the specific growth and production rates as well as the product inhibition parameters on the operating conditions were described by the response surface method. The parameters of the model were calibrated from eight experiments, covering a broad spectrum of culture conditions (temperatures between 20 and 37 °C; pH between 6.0 and 9.5). The model was validated against another set of eight independent experiments performed under different conditions selected in the same range. The model correctly predicted the growth kinetics of C. maltaromaticum CNCM I-3298 as well as the dynamics of the carbon source conversion, with a mean relative error of 10% for biomass and 14% for trehalose and the metabolites. The paper illustrates that the proposed model is a valuable tool for optimizing the culture of C. maltaromaticum CNCM I-3298 by determining operating conditions that favor the production of biomass or selected metabolites. Model-based optimization may thus reduce the number of experiments and substantially speed up the process development, with potential applications in food technology for producing starters and improving the yield and productivity of the fermentation of sugars into metabolites of industrial interest. Full article

(This article belongs to the Special Issue Dynamic Modelling and Simulation of Food Systems)

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20 pages, 4633 KiB

Open AccessArticle

Dynamic Modeling of the Impact of Temperature Changes on CO₂ Production during Milk Fermentation in Batch Bioreactors

by Jožef Ritonja, Andreja Goršek, Darja Pečar, Tatjana Petek and Boštjan Polajžer

Foods 2021, 10(8), 1809; https://0-doi-org.brum.beds.ac.uk/10.3390/foods10081809 - 05 Aug 2021

Cited by 2 | Viewed by 1972

Abstract

Knowledge of the mathematical models of the fermentation processes is indispensable for their simulation and optimization and for the design and synthesis of the applicable control systems. The paper focuses on determining a dynamic mathematical model of the milk fermentation process taking place in a batch bioreactor. Models in the literature describe milk fermentation in batch bioreactors as an autonomous system. They do not enable the analysis of the effect of temperature changes on the metabolism during fermentation. In the presented extensive multidisciplinary study, we have developed a new mathematical model that considers the impact of temperature changes on the dynamics of the CO₂ produced during fermentation in the batch bioreactor. Based on laboratory tests and theoretical analysis, the appropriate structure of the temperature-considered dynamic model was first determined. Next, the model parameters of the fermentation process in the laboratory bioreactor were identified by means of particle swarm optimization. Finally, the experiments with the laboratory batch bioreactor were compared with the simulations to verify the derived mathematical model. The developed model proved to be very suitable for simulations, and, above all, it enables the design and synthesis of a control system for batch bioreactors. Full article

(This article belongs to the Special Issue Dynamic Modelling and Simulation of Food Systems)

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17 pages, 1670 KiB

Open AccessArticle

A Population Balance Model to Describe the Evolution of Sublethal Injury

by Simen Akkermans, Davy Verheyen, Cindy Smet and Jan F. M. Van Impe

Foods 2021, 10(7), 1674; https://0-doi-org.brum.beds.ac.uk/10.3390/foods10071674 - 20 Jul 2021

Cited by 4 | Viewed by 2406

Abstract

The detection and quantification of sublethal injury (SI) of pathogenic microorganisms has become a common procedure when assessing the efficiency of microbial inactivation treatments. However, while a plethora of studies investigates SI in function of time, no suitable modelling procedure for SI data has been proposed thus far. In this study, a new SI model structure was developed that relies on existing microbial inactivation models. This model is based on the description of inactivation kinetics between the subpopulations of healthy, sublethally injured and dead cells. The model was validated by means of case studies on previously published results, modelled by different inactivation models, i.e., (i) log-linear inactivation; (ii) biphasic inactivation; and (iii) log-linear inactivation with tailing. Results were compared to those obtained by the traditional method that relies on calculating SI from independent inactivation models on non-selective and selective media. The log-linear inactivation case study demonstrated that the SI model is equivalent to the use of independent models when there can be no mistake in calculating SI. The biphasic inactivation case study illustrated how the SI model avoids unrealistic calculations of SI that would otherwise occur. The final case study on log-linear inactivation with tailing clarified that the SI model provides a more mechanistic description than the independent models, in this case allowing the reduction of the number of model parameters. As such, this paper provides a comprehensive overview of the potential and applications for the newly presented SI model. Full article

(This article belongs to the Special Issue Dynamic Modelling and Simulation of Food Systems)

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Review

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26 pages, 766 KiB

Open AccessReview

Assessment and Prediction of Fish Freshness Using Mathematical Modelling: A Review

by Míriam R. García, Jose Antonio Ferez-Rubio and Carlos Vilas

Foods 2022, 11(15), 2312; https://0-doi-org.brum.beds.ac.uk/10.3390/foods11152312 - 02 Aug 2022

Cited by 13 | Viewed by 3323

Abstract

Fish freshness can be considered as the combination of different nutritional and organoleptic attributes that rapidly deteriorate after fish capture, i.e., during processing (cutting, gutting, packaging), storage, transport, distribution, and retail. The rate at which this degradation occurs is affected by several stress variables such as temperature, water activity, or pH, among others. The food industry is aware that fish freshness is a key feature influencing consumers’ willingness to pay for the product. Therefore, tools that allow rapid and reliable assessment and prediction of the attributes related to freshness are gaining relevance. The main objective of this work is to provide a comprehensive review of the mathematical models used to describe and predict the changes in the key quality indicators in fresh fish and shellfish during storage. The work also briefly describes such indicators, discusses the most relevant stress factors affecting the quality of fresh fish, and presents a bibliometric analysis of the results obtained from a systematic literature search on the subject. Full article

(This article belongs to the Special Issue Dynamic Modelling and Simulation of Food Systems)

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23 pages, 997 KiB

Open AccessReview

The Inclusion of the Food Microstructural Influence in Predictive Microbiology: State-of-the-Art

by Davy Verheyen and Jan F. M. Van Impe

Foods 2021, 10(9), 2119; https://0-doi-org.brum.beds.ac.uk/10.3390/foods10092119 - 08 Sep 2021

Cited by 7 | Viewed by 2326

Abstract

Predictive microbiology has steadily evolved into one of the most important tools to assess and control the microbiological safety of food products. Predictive models were traditionally developed based on experiments in liquid laboratory media, meaning that food microstructural effects were not represented in these models. Since food microstructure is known to exert a significant effect on microbial growth and inactivation dynamics, the applicability of predictive models is limited if food microstructure is not taken into account. Over the last 10–20 years, researchers, therefore, developed a variety of models that do include certain food microstructural influences. This review provides an overview of the most notable microstructure-including models which were developed over the years, both for microbial growth and inactivation. Full article

(This article belongs to the Special Issue Dynamic Modelling and Simulation of Food Systems)

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