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Woodward AP. Bayesian estimation in veterinary pharmacology: A conceptual and practical introduction. J Vet Pharmacol Ther 2024; 47:322-352. [PMID: 38385655 DOI: 10.1111/jvp.13433] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2023] [Revised: 01/22/2024] [Accepted: 01/24/2024] [Indexed: 02/23/2024]
Abstract
Sophisticated mathematical and computational tools have become widespread and important in veterinary pharmacology. Although the theoretical basis and practical applications of these have been widely explored in the literature, statistical inference in the context of these models has received less attention. Optimization methods, often with frequentist statistical inference, have been predominant. In contrast, Bayesian statistics have not been widely applied, but offer both practical utility and arguably greater interpretability. Veterinary pharmacology applications are generally well supported by relevant prior information, from either existing substantive knowledge, or an understanding of study and model design. This facilitates practical implementation of Bayesian analyses that can take advantage of this knowledge. This essay will explore the specification of Bayesian models relevant to veterinary pharmacology, including demonstration of prior selection, and illustrate the capability of these models to generate practically useful statistics, including uncertainty statements, that are difficult or impossible to obtain otherwise. Case studies using simulated data will describe applications in clinical trials, pharmacodynamics, and pharmacokinetics, all including multilevel modeling. This content may serve as a suitable starting point for researchers in veterinary pharmacology and related disciplines considering Bayesian estimation for their applied work.
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Affiliation(s)
- Andrew P Woodward
- Faculty of Health, University of Canberra, Canberra, Australian Capital Territory, Australia
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2
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de Beer D, Beelders T, Human C, Joubert E. Assessment of the stability of compounds belonging to neglected phenolic classes and flavonoid sub-classes using reaction kinetic modeling. Crit Rev Food Sci Nutr 2023; 63:11802-11829. [PMID: 35833472 DOI: 10.1080/10408398.2022.2096561] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
Phenolic compounds are known to degrade and/or undergo changes during food production and storage. Reaction kinetic modeling is generally used to define kinetic parameters of a food system and predict changes during thermal processing and storage. Data for phenolic acids and flavonoids, such as anthocyanins and flavan-3-ols, have been reviewed in detail, but the flavonoid sub-classes, dihydrochalcones and flavanones, have been mostly neglected. Other neglected phenolic classes are xanthones and benzophenones. The stability of these types of compounds is important as they are present in fruits and exposed to heat when processed into juice and jam. Other sources of the compounds are herbal teas, which are also subjected to thermal processing, either during the primary processing of the plant material, or the production of extracts for use as food ingredients. The theoretical background is given to understand the review of literature on these classes/sub-classes. Results of research on kinetic modeling are discussed in detail, while research on compound stability without the application of reaction kinetic modeling is briefly mentioned to provide context. The studies discussed included those focusing on heating during the processing and storage of model solutions, liquid foods, plant material, dried extracts, and extracts formulated with other food ingredients.
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Affiliation(s)
- Dalene de Beer
- Plant Bioactives Group, Post-Harvest & Agro-Processing Technologies, Agricultural Research Council Infruitec-Nietvoorbij, Stellenbosch, South Africa
- Department of Food Science, Stellenbosch University, Stellenbosch, South Africa
| | - Theresa Beelders
- Plant Bioactives Group, Post-Harvest & Agro-Processing Technologies, Agricultural Research Council Infruitec-Nietvoorbij, Stellenbosch, South Africa
- Department of Food Science, Stellenbosch University, Stellenbosch, South Africa
| | - Chantelle Human
- Plant Bioactives Group, Post-Harvest & Agro-Processing Technologies, Agricultural Research Council Infruitec-Nietvoorbij, Stellenbosch, South Africa
| | - Elizabeth Joubert
- Plant Bioactives Group, Post-Harvest & Agro-Processing Technologies, Agricultural Research Council Infruitec-Nietvoorbij, Stellenbosch, South Africa
- Department of Food Science, Stellenbosch University, Stellenbosch, South Africa
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3
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Choi WS. Problems and alternatives of testing significance using null hypothesis and P-value in food research. Food Sci Biotechnol 2023; 32:1-9. [PMID: 37363053 PMCID: PMC10227784 DOI: 10.1007/s10068-023-01348-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Revised: 05/12/2023] [Accepted: 05/16/2023] [Indexed: 06/28/2023] Open
Abstract
A testing method to identify statistically significant differences by comparing the significance level and the probability value based on the Null Hypothesis Significance Test (NHST) has been used in food research. However, problems with this testing method have been discussed. Several alternatives to the NHST and the P-value test methods have been proposed including lowering the P-value threshold and using confidence interval (CI), effect size, and Bayesian statistics. The CI estimates the extent of the effect or difference and determines the presence or absence of statistical significance. The effect size index determines the degree of effect difference and allows for the comparison of various statistical results. Bayesian statistics enable predictions to be made even when only a small amount of data is available. In conclusion, CI, effect size, and Bayesian statistics can complement or replace traditional statistical tests in food research by replacing the use of NHST and P-value.
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Affiliation(s)
- Won-Seok Choi
- Department of Food Science and Technology, Korea National University of Transportation, Jeungpyeong-gun, 27909 Chungbuk Republic of Korea
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4
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How many data points and how large an R-squared value is essential for Arrhenius plots? J Catal 2023. [DOI: 10.1016/j.jcat.2023.01.033] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
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5
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Application of the weibull model to describe the kinetic behaviors of thiol decolorizers in chlorogenic acid-lysine solutions. J FOOD ENG 2023. [DOI: 10.1016/j.jfoodeng.2022.111287] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Affan A, Zurada JM, Inanc T. Control-Relevant Adaptive Personalized Modeling From Limited Clinical Data for Precise Warfarin Management. IEEE OPEN JOURNAL OF ENGINEERING IN MEDICINE AND BIOLOGY 2023; 3:242-251. [PMID: 36846361 PMCID: PMC9955254 DOI: 10.1109/ojemb.2023.3240072] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2022] [Revised: 10/28/2022] [Accepted: 01/06/2023] [Indexed: 12/26/2023] Open
Abstract
Warfarin is a challenging drug to administer due to the narrow therapeutic index of the International Normalized Ratio (INR), the inter- and intra-variability of patients, limited clinical data, genetics, and the effects of other medications. Goal: To predict the optimal warfarin dosage in the presence of the aforementioned challenges, we present an adaptive individualized modeling framework based on model (In)validation and semi-blind robust system identification. The model (In)validation technique adapts the identified individualized patient model according to the change in the patient's status to ensure the model's suitability for prediction and controller design. Results: To implement the proposed adaptive modeling framework, the clinical data of warfarin-INR of forty-four patients has been collected at the Robley Rex Veterans Administration Medical Center, Louisville. The proposed algorithm is compared with recursive ARX and ARMAX model identification methods. The results of identified models using one-step-ahead prediction and minimum mean squared analysis (MMSE) show that the proposed framework effectively predicts the warfarin dosage to keep the INR values within the desired range and adapt the individualized patient model to exhibit the true status of the patient throughout treatment. Conclusion: This paper proposes an adaptive personalized patient modeling framework from limited patientspecific clinical data. It is shown by rigorous simulations that the proposed framework can accurately predict a patient's doseresponse characteristics and it can alert the clinician whenever identified models are no longer suitable for prediction and adapt the model to the current status of the patient to reduce the prediction error.
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Affiliation(s)
- Affan Affan
- Electrical and Computer Engineering DepartmentUniversity of LouisvilleLouisvilleKY40292USA
| | - Jacek M. Zurada
- Electrical and Computer Engineering DepartmentUniversity of LouisvilleLouisvilleKY40292USA
- Information Technology InstituteAcademy of Social Sciences90-193LodzPoland
| | - Tamer Inanc
- Electrical and Computer Engineering DepartmentUniversity of LouisvilleLouisvilleKY40292USA
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7
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Garre A, Pielaat A, Zwietering MH, den Besten HM, Smid JH. Critical comparison of statistical methods for quantifying variability and uncertainty of microbial responses from experimental data. Int J Food Microbiol 2022; 383:109935. [DOI: 10.1016/j.ijfoodmicro.2022.109935] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2022] [Revised: 09/09/2022] [Accepted: 09/14/2022] [Indexed: 11/17/2022]
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Garre A, Zwietering MH, van Boekel MAJS. The Most Probable Curve method - A robust approach to estimate kinetic models from low plate count data resulting in reduced uncertainty. Int J Food Microbiol 2022; 380:109871. [PMID: 35985079 DOI: 10.1016/j.ijfoodmicro.2022.109871] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2022] [Revised: 08/03/2022] [Accepted: 08/06/2022] [Indexed: 11/19/2022]
Abstract
A novel method is proposed for fitting microbial inactivation models to data on liquid media: the Most Probable Curve (MPC) method. It is a multilevel model that makes a separation between the "true" microbial concentration according to the model, the "actual" concentration in the media considering chance, and the actual counts on the plate. It is based on the assumptions that stress resistance is homogeneous within a microbial population, and that there is no aggregation of microbial cells. Under these assumptions, the number of colonies in/on a plate follows a Poisson distribution with expected value depending on the proposed kinetic model, the number of dilutions and the plated volume. The novel method is compared against (non)linear regression based on a normal likelihood distribution (traditional method), Poisson regression and gamma-Poisson regression using data on the inactivation of Listeria monocytogenes. The conclusion is that the traditional method has limitations when the data includes plates with low (or zero) cell counts, which can be mitigated using more complex (discrete) likelihoods. However, Poisson regression uses an unrealistic likelihood function, making it unsuitable for survivor curves with several log-reductions. Gamma-Poisson regression uses a more realistic likelihood function, even though it is based mostly on empirical hypotheses. We conclude that the MPC method can be used reliably, especially when the data includes plates with low or zero counts. Furthermore, it generates a more realistic description of uncertainty, integrating the contribution of the plating error and reducing the uncertainty of the primary model parameters. Consequently, although it increases modelling complexity, the MPC method can be of great interest in predictive microbiology, especially in studies focused on variability analysis.
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Affiliation(s)
- Alberto Garre
- Food Microbiology, Wageningen University & Research, P.O. Box 17, 6700 AA Wageningen, the Netherlands
| | - Marcel H Zwietering
- Food Microbiology, Wageningen University & Research, P.O. Box 17, 6700 AA Wageningen, the Netherlands
| | - Martinus A J S van Boekel
- Food Quality & Design, Wageningen University & Research, P.O. Box 17, 6700 AA Wageningen, the Netherlands.
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9
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Multilevel modeling in food science: A case study on heat-induced ascorbic acid degradation kinetics. Food Res Int 2022; 158:111565. [DOI: 10.1016/j.foodres.2022.111565] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2022] [Revised: 05/29/2022] [Accepted: 06/22/2022] [Indexed: 11/24/2022]
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10
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Katsini L, Bhonsale S, Akkermans S, Roufou S, Griffin S, Valdramidis V, Misiou O, Koutsoumanis K, Muñoz López CA, Polanska M, Van Impe JF. Quantitative methods to predict the effect of climate change on microbial food safety: A needs analysis. Trends Food Sci Technol 2022. [DOI: 10.1016/j.tifs.2021.07.041] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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11
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Shrivastava C, Berry T, Cronje P, Schudel S, Defraeye T. Digital twins enable the quantification of the trade-offs in maintaining citrus quality and marketability in the refrigerated supply chain. NATURE FOOD 2022; 3:413-427. [PMID: 37118034 DOI: 10.1038/s43016-022-00497-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2021] [Accepted: 03/17/2022] [Indexed: 04/30/2023]
Abstract
Supply chains of fresh fruit must maintain a very narrow window of hygrothermal conditions after harvest. Any excursions outside this range can markedly lower the consumer acceptability of the fruit. However, the loss in fruit quality and marketability largely remains invisible to stakeholders throughout the supply chain. Here we developed a physics-based digital twin of citrus fruit to pinpoint when, why and to what extent fruit quality and marketability are reduced. Sensor data on 47 commercial shipments are thereby translated into actionable metrics for supply chain stakeholders by mapping the variability using principal component analysis. We unveiled a large spread (between 3% and 60%) in the shipments for different metrics of quality and marketability. Half of the shipments currently lie outside the ideal trade-off range between maintaining quality, killing fruit fly larvae and avoiding chilling injury. The digital twin technology opens the possibility to obtain the real-time coupling with sensor data to monitor food quality and marketability.
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Affiliation(s)
- Chandrima Shrivastava
- Empa, Swiss Federal Laboratories for Materials Science and Technology, Laboratory for Biomimetic Membranes and Textiles, St. Gallen, Switzerland
- University of Bern, ARTORG Center for Biomedical Engineering Research, Bern, Switzerland
| | - Tarl Berry
- Citrus Research International, Department of Horticultural Science, University of Stellenbosch, Stellenbosch, South Africa
| | - Paul Cronje
- Citrus Research International, Department of Horticultural Science, University of Stellenbosch, Stellenbosch, South Africa
| | - Seraina Schudel
- Empa, Swiss Federal Laboratories for Materials Science and Technology, Laboratory for Biomimetic Membranes and Textiles, St. Gallen, Switzerland
| | - Thijs Defraeye
- Empa, Swiss Federal Laboratories for Materials Science and Technology, Laboratory for Biomimetic Membranes and Textiles, St. Gallen, Switzerland.
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Sykes AL, Larrieu E, Poggio TV, Céspedes MG, Mujica GB, Basáñez MG, Prada JM. Modelling diagnostics for Echinococcus granulosus surveillance in sheep using Latent Class Analysis: Argentina as a case study. One Health 2022; 14:100359. [PMID: 34977321 PMCID: PMC8683760 DOI: 10.1016/j.onehlt.2021.100359] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2021] [Revised: 11/30/2021] [Accepted: 12/03/2021] [Indexed: 11/03/2022] Open
Abstract
Echinococcus granulosus sensu lato is a globally prevalent zoonotic parasitic cestode leading to cystic echinococcosis (CE) in both humans and sheep with both medical and financial impacts, whose reduction requires the application of a One Health approach to its control. Regarding the animal health component of this approach, lack of accurate and practical diagnostics in livestock impedes the assessment of disease burden and the implementation and evaluation of control strategies. We use of a Bayesian Latent Class Analysis (LCA) model to estimate ovine CE prevalence in sheep samples from the Río Negro province of Argentina accounting for uncertainty in the diagnostics. We use model outputs to evaluate the performance of a novel recombinant B8/2 antigen B subunit (rEgAgB8/2) indirect enzyme-linked immunosorbent assay (ELISA) for detecting E. granulosus in sheep. Necropsy (as a partial gold standard), western blot (WB) and ELISA diagnostic data were collected from 79 sheep within two Río Negro slaughterhouses, and used to estimate individual infection status (assigned as a latent variable within the model). Using the model outputs, the performance of the novel ELISA at both individual and flock levels was evaluated, respectively, using a receiver operating characteristic (ROC) curve, and simulating a range of sample sizes and prevalence levels within hypothetical flocks. The estimated (mean) prevalence of ovine CE was 27.5% (95%Bayesian credible interval (95%BCI): 13.8%-58.9%) within the sample population. At the individual level, the ELISA had a mean sensitivity and specificity of 55% (95%BCI: 46%-68%) and 68% (95%BCI: 63%-92%), respectively, at an optimal optical density (OD) threshold of 0.378. At the flock level, the ELISA had an 80% probability of correctly classifying infection at an optimal cut-off threshold of 0.496. These results suggest that the novel ELISA could play a useful role as a flock-level diagnostic for CE surveillance in the region, supplementing surveillance activities in the human population and thus strengthening a One Health approach. Importantly, selection of ELISA cut-off threshold values must be tailored according to the epidemiological situation.
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Key Words
- Argentina
- BCI, Bayesian Credible Interval
- Bayesian inference
- CE, Cystic Echinococcosis
- CI, Confidence Interval
- DALY, Disability-adjusted life year
- Diagnostics
- ELISA, Enzyme-Linked Immunosorbent Assay
- Echinococcosis
- JAGS, Just Another Gibbs Sampler
- LCA, Latent class analysis
- Latent class analysis
- MCAR, Missing completely at random
- MCMC, Markov Chain Monte Carlo
- OD, Optical density
- ROC, Receiver Operating Characteristic
- SD, Standard deviation
- Surveillance
- USD, United States Dollar
- WB, Western blot
- WHO, World Health Organization.
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Affiliation(s)
- Abagael L. Sykes
- London Centre for Neglected Tropical Disease Research and MRC Centre for Global Infectious Disease Analysis, School of Public Health, Imperial College London, London, UK
| | - Edmundo Larrieu
- Facultad de Ciencias Veterinarias, Universidad Nacional de La Pampa, General Pico, Argentina
- Escuela de Veterinaria, Universidad Nacional de Río Negro, Choele Choel, Argentina
| | | | | | | | - Maria-Gloria Basáñez
- London Centre for Neglected Tropical Disease Research and MRC Centre for Global Infectious Disease Analysis, School of Public Health, Imperial College London, London, UK
| | - Joaquin M. Prada
- Faculty of Health and Medical Sciences, University of Surrey, Guildford, UK
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13
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Kinetics of heat-induced changes in dairy products: Developments in data analysis and modelling techniques. Int Dairy J 2022. [DOI: 10.1016/j.idairyj.2021.105187] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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14
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Paul A, Gaiani C, Cvetkovska L, Paris C, Alexander M, Ray C, Francius G, EL-Kirat-Chatel S, Burgain J. Deciphering the impact of whey protein powder storage on protein state and powder stability. J FOOD ENG 2022. [DOI: 10.1016/j.jfoodeng.2022.111050] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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15
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Smid J, van der Swaluw-Dekker C, Ueckert J, de Vries E, Pielaat A. Bayesian global regression model relating product characteristics of intermediate moisture food products to heat inactivation parameters for Salmonella Napoli and Eurotium herbariorum mould spores. Int J Food Microbiol 2022; 370:109638. [DOI: 10.1016/j.ijfoodmicro.2022.109638] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2021] [Revised: 03/03/2022] [Accepted: 03/19/2022] [Indexed: 11/27/2022]
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Andrewes P. Predicting the shelf-life of microbially-stabilised dairy products: What are the roles of stability studies, storage trials, ‘accelerated’ trials, and dairy science? Int Dairy J 2022. [DOI: 10.1016/j.idairyj.2021.105239] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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17
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Adebo OA, Oyedeji AB, Adebiyi JA, Chinma CE, Oyeyinka SA, Olatunde OO, Green E, Njobeh PB, Kondiah K. Kinetics of Phenolic Compounds Modification during Maize Flour Fermentation. Molecules 2021; 26:molecules26216702. [PMID: 34771110 PMCID: PMC8587012 DOI: 10.3390/molecules26216702] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2021] [Revised: 11/01/2021] [Accepted: 11/01/2021] [Indexed: 11/16/2022] Open
Abstract
This study aimed to investigate the kinetics of phenolic compound modification during the fermentation of maize flour at different times. Maize was spontaneously fermented into sourdough at varying times (24, 48, 72, 96, and 120 h) and, at each point, the pH, titratable acidity (TTA), total soluble solids (TSS), phenolic compounds (flavonoids such as apigenin, kaempferol, luteolin, quercetin, and taxifolin) and phenolic acids (caffeic, gallic, ferulic, p-coumaric, sinapic, and vanillic acids) were investigated. Three kinetic models (zero-, first-, and second-order equations) were used to determine the kinetics of phenolic modification during the fermentation. Results obtained showed that fermentation significantly reduced pH, with a corresponding increase in TTA and TSS. All the investigated flavonoids were significantly reduced after fermentation, while phenolic acids gradually increased during fermentation. Among the kinetic models adopted, first-order (R2 = 0.45–0.96) and zero-order (R2 = 0.20–0.82) equations best described the time-dependent modifications of free and bound flavonoids, respectively. On the other hand, first-order (R2 = 0.46–0.69) and second-order (R2 = 0.005–0.28) equations were best suited to explain the degradation of bound and free phenolic acids, respectively. This study shows that the modification of phenolic compounds during fermentation is compound-specific and that their rates of change may be largely dependent on their forms of existence in the fermented products.
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Affiliation(s)
- Oluwafemi Ayodeji Adebo
- Department of Biotechnology and Food Technology, Doornfontein Campus, Faculty of Science, University of Johannesburg, Doornfontein, P.O. Box 17011, Johannesburg 2028, South Africa; (J.A.A.); (S.A.O.); (E.G.); (P.B.N.)
- Correspondence: (O.A.A.); (A.B.O.); (K.K.); Tel.: +27-115596261 (O.A.A.); +27-744113712 (A.B.O.); +27-115596915 (K.K.)
| | - Ajibola Bamikole Oyedeji
- Department of Biotechnology and Food Technology, Doornfontein Campus, Faculty of Science, University of Johannesburg, Doornfontein, P.O. Box 17011, Johannesburg 2028, South Africa; (J.A.A.); (S.A.O.); (E.G.); (P.B.N.)
- Correspondence: (O.A.A.); (A.B.O.); (K.K.); Tel.: +27-115596261 (O.A.A.); +27-744113712 (A.B.O.); +27-115596915 (K.K.)
| | - Janet Adeyinka Adebiyi
- Department of Biotechnology and Food Technology, Doornfontein Campus, Faculty of Science, University of Johannesburg, Doornfontein, P.O. Box 17011, Johannesburg 2028, South Africa; (J.A.A.); (S.A.O.); (E.G.); (P.B.N.)
| | - Chiemela Enyinnaya Chinma
- Department of Food Science and Technology, Federal University of Technology, P.M.B 65, Minna 920001, Nigeria;
- Africa Center of Excellence for Mycotoxin and Food Safety, Federal University of Technology, P.M.B 65, Minna 920001, Nigeria
| | - Samson Adeoye Oyeyinka
- Department of Biotechnology and Food Technology, Doornfontein Campus, Faculty of Science, University of Johannesburg, Doornfontein, P.O. Box 17011, Johannesburg 2028, South Africa; (J.A.A.); (S.A.O.); (E.G.); (P.B.N.)
| | - Oladipupo Odunayo Olatunde
- Department of Food and Human Nutritional Sciences, Faculty of Agricultural and Food Sciences, University of Manitoba, Winnipeg, MB R3T 2N2, Canada;
| | - Ezekiel Green
- Department of Biotechnology and Food Technology, Doornfontein Campus, Faculty of Science, University of Johannesburg, Doornfontein, P.O. Box 17011, Johannesburg 2028, South Africa; (J.A.A.); (S.A.O.); (E.G.); (P.B.N.)
| | - Patrick Berka Njobeh
- Department of Biotechnology and Food Technology, Doornfontein Campus, Faculty of Science, University of Johannesburg, Doornfontein, P.O. Box 17011, Johannesburg 2028, South Africa; (J.A.A.); (S.A.O.); (E.G.); (P.B.N.)
| | - Kulsum Kondiah
- Department of Biotechnology and Food Technology, Doornfontein Campus, Faculty of Science, University of Johannesburg, Doornfontein, P.O. Box 17011, Johannesburg 2028, South Africa; (J.A.A.); (S.A.O.); (E.G.); (P.B.N.)
- Correspondence: (O.A.A.); (A.B.O.); (K.K.); Tel.: +27-115596261 (O.A.A.); +27-744113712 (A.B.O.); +27-115596915 (K.K.)
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Effect of Alternative Preservation Steps and Storage on Vitamin C Stability in Fruit and Vegetable Products: Critical Review and Kinetic Modelling Approaches. Foods 2021; 10:foods10112630. [PMID: 34828909 PMCID: PMC8619176 DOI: 10.3390/foods10112630] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2021] [Revised: 10/25/2021] [Accepted: 10/26/2021] [Indexed: 01/20/2023] Open
Abstract
Vitamin C, a water-soluble compound, is a natural antioxidant in many plant-based products, possessing important nutritional benefits for human health. During fruit and vegetable processing, this bioactive compound is prone to various modes of degradation, with temperature and oxygen being recognised as the main factors responsible for this nutritional loss. Consequently, Vitamin C is frequently used as an index of the overall quality deterioration of such products during processing and post-processing storage and handling. Traditional preservation methods, such as thermal processing, drying and freezing, are often linked to a substantial Vitamin C loss. As an alternative, novel techniques or a combination of various preservation steps ("hurdles") have been extensively investigated in the recent literature aiming at maximising Vitamin C retention throughout the whole product lifecycle, from farm to fork. In such an integrated approach, it is important to separately study the effect of each preservation step and mathematically describe the impact of the prevailing factors on Vitamin C stability, so as to be able to optimise the processing/storage phase. In this context, alternative mathematical approaches have been applied, including more sophisticated ones that incorporate parameter uncertainties, with the ultimate goal of providing more realistic predictions.
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Capecci S, Wang Y, Delgado J, Casson Moreno V, Mignot M, Grénman H, Murzin DY, Leveneur S. Bayesian Statistics to Elucidate the Kinetics of γ-Valerolactone from n-Butyl Levulinate Hydrogenation over Ru/C. Ind Eng Chem Res 2021. [DOI: 10.1021/acs.iecr.1c02107] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
- Sarah Capecci
- Normandie Université, INSA Rouen, UNIROUEN, LSPC, EA4704, 76000 Rouen, France
- Dipartimento di Ingegneria Chimica, Civile, Ambientale e dei Materiali, Alma Mater Studiorum—Università di Bologna, via Terracini 28, 40131 Bologna, Italy
| | - Yanjun Wang
- Normandie Université, INSA Rouen, UNIROUEN, LSPC, EA4704, 76000 Rouen, France
| | - Jose Delgado
- Normandie Université, INSA Rouen, UNIROUEN, LSPC, EA4704, 76000 Rouen, France
- Laboratory of Industrial Chemistry & Reaction Engineering, Department of Chemical Engineering, Johan Gadolin Process Chemistry Centre, Åbo Akademi University, FI-20500 Åbo-Turku, Finland
| | - Valeria Casson Moreno
- Dipartimento di Ingegneria Chimica, Civile, Ambientale e dei Materiali, Alma Mater Studiorum—Università di Bologna, via Terracini 28, 40131 Bologna, Italy
| | - Mélanie Mignot
- COBRA UMR CNRS 6014, Normandie Université, INSA de Rouen, avenue de l’Université, Saint-Etienne-du-Rouvray 76800, France
| | - Henrik Grénman
- Laboratory of Industrial Chemistry & Reaction Engineering, Department of Chemical Engineering, Johan Gadolin Process Chemistry Centre, Åbo Akademi University, FI-20500 Åbo-Turku, Finland
| | - Dmitry Yu. Murzin
- Laboratory of Industrial Chemistry & Reaction Engineering, Department of Chemical Engineering, Johan Gadolin Process Chemistry Centre, Åbo Akademi University, FI-20500 Åbo-Turku, Finland
| | - Sébastien Leveneur
- Normandie Université, INSA Rouen, UNIROUEN, LSPC, EA4704, 76000 Rouen, France
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Koyama K, Ranta J, Takeoka K, Abe H, Koseki S. Evaluation of Strain Variability in Inactivation of Campylobacter jejuni in Simulated Gastric Fluid by Using Hierarchical Bayesian Modeling. Appl Environ Microbiol 2021; 87:e0091821. [PMID: 34047637 PMCID: PMC8315736 DOI: 10.1128/aem.00918-21] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 05/16/2021] [Indexed: 11/20/2022] Open
Abstract
This study was conducted to quantitatively evaluate the variability of stress resistance in different strains of Campylobacter jejuni and the uncertainty of such strain variability. We developed Bayesian statistical models with multilevel analysis to quantify variability within a strain, variability between different strains, and the uncertainty associated with these estimates. Furthermore, we measured the inactivation of 11 strains of C. jejuni in simulated gastric fluid with low pH, using the Weibullian survival model. The model was first developed for separate pH conditions and then analyzed over a range of pH levels. We found that the model parameters developed under separate pH conditions exhibited a clear dependence of survival on pH. In addition, the uncertainty of the variability between different strains could be described as the joint distribution of the model parameters. The latter model, including pH dependency, accurately predicted the number of surviving cells in individual as well as multiple strains. In conclusion, variabilities and uncertainties in inactivation could be simultaneously evaluated and interpreted via a probabilistic approach based on Bayesian theory. Such hierarchical Bayesian models could be useful for understanding individual-strain variability in quantitative microbial risk assessment. IMPORTANCE Since microbial strains vary in their growth and inactivation patterns in food materials, it is important to accurately predict these patterns for quantitative microbial risk assessment. However, most previous studies in this area have used highly resistant strains, which could lead to inaccurate predictions. Moreover, variability, including measurement errors and variability within a strain and between different strains, can contribute to predicted individual-level outcomes. Therefore, a multilevel framework is required to resolve these levels of variability and estimate their uncertainties. We developed a Bayesian predictive model for the survival of Campylobacter jejuni under simulated gastric conditions taking into account the variabilities and uncertainties. We demonstrated a high correspondence between predictions from the model and empirical measurements. The modeling procedure proposed in this study recommends a novel framework for predicting pathogen behavior, which can help improve quantitative microbial risk assessment during food production and distribution.
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Affiliation(s)
- Kento Koyama
- Graduate School of Agricultural Science, Hokkaido University, Sapporo, Japan
| | - Jukka Ranta
- Risk Assessment Unit, Finnish Food Authority, Helsinki, Finland
| | - Kohei Takeoka
- Graduate School of Agricultural Science, Hokkaido University, Sapporo, Japan
| | - Hiroki Abe
- Graduate School of Agricultural Science, Hokkaido University, Sapporo, Japan
| | - Shige Koseki
- Graduate School of Agricultural Science, Hokkaido University, Sapporo, Japan
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22
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Hiura S, Abe H, Koyama K, Koseki S. Bayesian Generalized Linear Model for Simulating Bacterial Inactivation/Growth Considering Variability and Uncertainty. Front Microbiol 2021; 12:674364. [PMID: 34248886 PMCID: PMC8264593 DOI: 10.3389/fmicb.2021.674364] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2021] [Accepted: 05/17/2021] [Indexed: 11/24/2022] Open
Abstract
Conventional regression analysis using the least-squares method has been applied to describe bacterial behavior logarithmically. However, only the normal distribution is used as the error distribution in the least-squares method, and the variability and uncertainty related to bacterial behavior are not considered. In this paper, we propose Bayesian statistical modeling based on a generalized linear model (GLM) that considers variability and uncertainty while fitting the model to colony count data. We investigated the inactivation kinetic data of Bacillus simplex with an initial cell count of 105 and the growth kinetic data of Listeria monocytogenes with an initial cell count of 104. The residual of the GLM was described using a Poisson distribution for the initial cell number and inactivation process and using a negative binomial distribution for the cell number variation during growth. The model parameters could be obtained considering the uncertainty by Bayesian inference. The Bayesian GLM successfully described the results of over 50 replications of bacterial inactivation with average of initial cell numbers of 101, 102, and 103 and growth with average of initial cell numbers of 10–1, 100, and 101. The accuracy of the developed model revealed that more than 90% of the observed cell numbers except for growth with initial cell numbers of 101 were within the 95% prediction interval. In addition, parameter uncertainty could be expressed as an arbitrary probability distribution. The analysis procedures can be consistently applied to the simulation process through fitting. The Bayesian inference method based on the GLM clearly explains the variability and uncertainty in bacterial population behavior, which can serve as useful information for risk assessment related to food borne pathogens.
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Affiliation(s)
- Satoko Hiura
- Graduate School of Agricultural Science, Hokkaido University, Sapporo, Japan
| | - Hiroki Abe
- Graduate School of Agricultural Science, Hokkaido University, Sapporo, Japan
| | - Kento Koyama
- Graduate School of Agricultural Science, Hokkaido University, Sapporo, Japan
| | - Shige Koseki
- Graduate School of Agricultural Science, Hokkaido University, Sapporo, Japan
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van Boekel MAJS. To pool or not to pool: That is the question in microbial kinetics. Int J Food Microbiol 2021; 354:109283. [PMID: 34140188 DOI: 10.1016/j.ijfoodmicro.2021.109283] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2021] [Revised: 05/19/2021] [Accepted: 05/30/2021] [Indexed: 11/17/2022]
Abstract
Variation observed in heat inactivation of Salmonella strains (data from Combase) was characterized using multilevel modeling with two case studies. One study concerned repetitions at one temperature, the other concerned isothermal experiments at various temperatures. Multilevel models characterize variation at various levels and handle dependencies in the data. The Weibull model was applied using Bayesian regression. The research question was how parameters varied with experimental conditions and how data can best be analyzed: no pooling (each experiment analyzed separately), complete pooling (all data analyzed together) or partial pooling (connecting the experiments while allowing for variation between experiments). In the first case study, level 1 consisted of the measurements, level 2 of the group of repetitions. While variation in the initial number parameter was low (set by the researchers), the Weibull shape factor varied for each repetition from 0.58-1.44, and the rate parameter from 0.006-0.074 h. With partial pooling variation was much less, with complete pooling variation was strongly underestimated. In the second case study, level 1 consisted of the measurements, level 2 of the group of repetitions per temperature experiment, level 3 of the cluster of various temperature experiments. The research question was how temperature affected the Weibull parameters. Variation in initial numbers was low (set by the researchers), the rate parameter was obviously affected by temperature, the estimate of the shape parameter depended on how the data were analyzed. With partial pooling, and one-step global modeling with a Bigelow-type model for the rate parameter, shape parameter variation was minimal. Model comparison based on prediction capacity of the various models was explored. The probability distribution of calculated decimal reduction times was much narrower using multilevel global modeling compared to the usual single level two-step approach. Multilevel modeling of microbial heat inactivation appears to be a suitable and powerful method to characterize and quantify variation at various levels. It handles possible dependencies in the data, and yields unbiased parameter estimates. The answer on the question "to pool or not to pool" depends on the goal of modeling, but if the goal is prediction, then partial pooling using multilevel modeling is the answer, provided that the experimental data allow that.
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Affiliation(s)
- M A J S van Boekel
- Food Quality & Design Group, Wageningen University & Research, the Netherlands.
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24
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Koseki S, Koyama K, Abe H. Recent advances in predictive microbiology: theory and application of conversion from population dynamics to individual cell heterogeneity during inactivation process. Curr Opin Food Sci 2021. [DOI: 10.1016/j.cofs.2020.12.019] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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25
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Microbial Modeling Needs for the Nonthermal Processing of Foods. FOOD ENGINEERING REVIEWS 2020. [DOI: 10.1007/s12393-020-09263-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
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Georgalis L, Garre A, Fernandez Escamez PS. Training in tools to develop Quantitative Risk Assessment using Spanish ready-to-eat food examples. EFSA J 2020; 18:e181103. [PMID: 33294042 PMCID: PMC7691611 DOI: 10.2903/j.efsa.2020.e181103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Unsafe food poses global health threats, potentially endangering consumers. The great majority of people will experience a food-borne disease at some point in their lives. Ready-to-eat (RTE) food is the one intended by the producer or the manufacturer for direct human consumption without the need for cooking or other processing effective to eliminate or reduce the concentration of pathogenic microorganisms. Prepared foods are often complex and may contain multiple components that make them vulnerable for growth of pathogenic microorganisms. Among all the pathogenic microorganisms that may be present in RTE foods, Listeria monocytogenes is of special interest because it is the causative agent of listeriosis and it has the ability to survive and replicate at refrigeration and low pH conditions. We performed a quantitative microbial risk assessment (QMRA) in RTE dry-fermented sausage to measure the risk of listeriosis associated to the consumption of this product. The starting point of our investigation was the storage at the factory, after the end-product was produced and before distribution to retail. The stochastic model was implemented in MicroHibro, an online tool for QMRA. Because L. monocytogenes concentration and prevalence can vary greatly between different studies and different types of fermented sausages, we tested different scenarios to show the importance of low prevalence and concentration of the pathogen at the final product. Our results show that the risk estimates are very sensitive to the modelling hypotheses used to describe this process. Therefore, the development of accurate probabilistic models describing the initial concentration of L. monocytogenes shall largely reduce the uncertainty associated to the QMRA of listeriosis in this type of product.
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Garre A, Zwietering MH, den Besten HMW. Multilevel modelling as a tool to include variability and uncertainty in quantitative microbiology and risk assessment. Thermal inactivation of Listeria monocytogenes as proof of concept. Food Res Int 2020; 137:109374. [PMID: 33233076 DOI: 10.1016/j.foodres.2020.109374] [Citation(s) in RCA: 32] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2020] [Revised: 05/27/2020] [Accepted: 05/31/2020] [Indexed: 12/13/2022]
Abstract
Variability is inherent in biology and also substantial for microbial populations. In the context of food safety risk assessment, it refers to differences in the response of different bacterial strains (between-strain variability) and different cells (within-strain variability) to the same condition (e.g. inactivation treatment). However, its quantification based on empirical observations and its incorporation in predictive models is a challenge for both experimental design and (statistical) analysis. In this article we propose the use of multilevel models to quantify (different levels of) variability and uncertainty and include them in the predictions. As proof of concept, we analyse the microbial inactivation of Listeria monocytogenes to thermal treatments including different levels of variability (between-strain and within-strain) and uncertainty. The relationship between the microbial count and time was expressed using a (non-linear) Weibullian model. Moreover, we defined stochastic hypotheses to describe the different types of variation at the level of the kinetic parameters, as well as in the observations (microbial counts). The model parameters (kinetic parameters and variances) are estimated using Bayesian statistics. The multilevel approach was compared against an analogous, single-level model. The multilevel methodology shrinks extreme parameter estimates towards the mean according to uncertainty, thus mitigating overfitting. In addition, this approach enables to easily incorporate different levels of variation (between-strain and/or within-strain variability and/or uncertainty) in the predictions. On the other hand, multilevel (Bayesian) models are more complex to define, implement, analyse and communicate than single-level models. Nevertheless, their ability to incorporate different sources of variability in predictions make them very suitable for Quantitative Microbial Risk Assessment.
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Affiliation(s)
- Alberto Garre
- Food Microbiology, Wageningen University & Research, P.O. Box 17, 6700 AA Wageningen, the Netherlands
| | - Marcel H Zwietering
- Food Microbiology, Wageningen University & Research, P.O. Box 17, 6700 AA Wageningen, the Netherlands
| | - Heidy M W den Besten
- Food Microbiology, Wageningen University & Research, P.O. Box 17, 6700 AA Wageningen, the Netherlands.
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