scholarly journals Modelling the Radial Growth of Geotrichum candidum: Effects of Temperature and Water Activity

2021 ◽  
Vol 9 (3) ◽  
pp. 532
Author(s):  
Martina Koňuchová ◽  
Ľubomír Valík
Keyword(s):  
Water Activity ◽  
Radial Growth ◽  
Goodness Of Fit ◽  
Growth Parameters ◽  
Growth Curves ◽  
Geotrichum Candidum ◽  
Coefficient Of Determination ◽  
Lag Phase ◽  
Growth Modelling ◽  
Effects Of Temperature

Modelling the growth of microorganisms in relation to environmental factors provides quantitative knowledge that can be used to predict their behaviour in foods. For this reason, the effects of temperature and water activity (aw) adjusted with NaCl on the surface growth of two isolates and one culture strain of Geotrichum candidum were studied. A dataset of growth parameters obtained from almost 600 growth curves was employed for secondary modelling with cardinal models (CMs). The theoretical minimal temperature resulting from the modelling of the mycelium proliferation rate ranged from −5.2 to −0.4 °C. Optimal and maximal temperatures were calculated and found to have narrow ranges of 25.4 to 28.0 °C and 34.2 to 37.6 °C, respectively. Cardinal aw values associated with radial growth (awmin from 0.948–0.960 and awopt from 0.992–0.993) confirmed the salt sensitivity of the species. Model goodness-of-fit was evaluated by the coefficient of determination R2, which ranged from 0.954 to 0.985, and RMSE, which ranged from 0.28 to 0.42. Substantially higher variability accompanied the lag time for growth modelling than the radial growth rate modelling despite the square root transformation of the reciprocal lag phase data (R2 = 0.685 to 0.808). Nevertheless, the findings demonstrate that the outputs of growth modelling can be applied to the quantitative evaluation of the roles of G. candidum in fresh cheese spoilage as well as the ripening of Camembert-type cheeses or various artisanal cheeses. Along with validation, the interactions with lactic acid bacteria can be included to improve the predictions of G. candidum in the future.

scholarly journals Modelling the Effect of Temperature on the Initial Decline during the Lag Phase of Geotrichum candidum

2021 ◽  
Vol 11 (16) ◽  
pp. 7344
Author(s):  
Ľubomír Valík ◽  
Petra Šipošová ◽  
Martina Koňuchová ◽  
Alžbeta Medveďová
Keyword(s):  
Death Rate ◽  
Goodness Of Fit ◽  
Practical Importance ◽  
Geotrichum Candidum ◽  
Effect Of Temperature ◽  
Coefficient Of Determination ◽  
Lag Phase ◽  
Square Root ◽  
Root Model ◽  
Square Root Model

The study of lag phase provides essential knowledge for food quality control. With respect to significance of Geotrichum candidum in the food context, the aim of this study was to quantitatively characterize the relationship between temperature (6–25 °C) and initial decline period during G. candidum lag phase. The decrease in G. candidum cells in the lag phase was primary modelled by Weibull’s model to define the first-decimal reduction time (δ). Subsequently, the lag death rate (LDR) values were recalculated from δ and further modelled by using Arrhenius equations, as well as a square root model, and the models’ suitability was proven by selected statistical indices. The square root model with the estimated parameters b = 0.016 °C−1 h−0.5 and Tmin = −0.72 °C showed better indices relating to goodness of fit based on a low root mean sum of square error (RMSE = 0.028 log CFU mL−1), a higher coefficient of determination (R2 = 0.978), and the lowest value of AIC (AIC = −38.65). The present study provides a solution to the possible application of secondary predictive models to the death rate dependence on temperature during the microbial lag phase. Despite limited practical importance, under specific conditions, it is possible to consider its use, for example, in exposure assessment.

scholarly journals Mathematical Models for Tumor Growth and the Reduction of Overtreatment

2018 ◽  
Vol 80 (01) ◽  
pp. 072-078 ◽  
Author(s):  
Berdine Heesterman ◽  
John-Melle Bokhorst ◽  
Lisa de Pont ◽  
Berit Verbist ◽  
Jean-Pierre Bayley ◽  
...  
Keyword(s):  
Tumor Growth ◽  
Mathematical Models ◽  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Age At Onset ◽  
Growth Curves ◽  
Magnetic Resonance Images ◽  
Coefficient Of Determination ◽  
Growth Data ◽  
Significant Difference

Background To improve our understanding of the natural course of head and neck paragangliomas (HNPGL) and ultimately differentiate between cases that benefit from early treatment and those that are best left untreated, we studied the growth dynamics of 77 HNPGL managed with primary observation. Methods Using digitally available magnetic resonance images, tumor volume was estimated at three time points. Subsequently, nonlinear least squares regression was used to fit seven mathematical models to the observed growth data. Goodness of fit was assessed with the coefficient of determination (R 2) and root-mean-squared error. The models were compared with Kruskal–Wallis one-way analysis of variance and subsequent post-hoc tests. In addition, the credibility of predictions (age at onset of neoplastic growth and estimated volume at age 90) was evaluated. Results Equations generating sigmoidal-shaped growth curves (Gompertz, logistic, Spratt and Bertalanffy) provided a good fit (median R 2: 0.996–1.00) and better described the observed data compared with the linear, exponential, and Mendelsohn equations (p < 0.001). Although there was no statistically significant difference between the sigmoidal-shaped growth curves regarding the goodness of fit, a realistic age at onset and estimated volume at age 90 were most often predicted by the Bertalanffy model. Conclusions Growth of HNPGL is best described by decelerating tumor growth laws, with a preference for the Bertalanffy model. To the best of our knowledge, this is the first time that this often-neglected model has been successfully fitted to clinically obtained growth data.

scholarly journals Method to generate growth and degrowth models obtained from differential equations applied to agrarian sciences

2018 ◽  
Vol 39 (6) ◽  
pp. 2659 ◽  
Author(s):  
André Luiz Pinto dos Santos ◽  
Guilherme Rocha Moreira ◽  
Cicero Carlos Ramos de Brito ◽  
Frank Gomes-Silva ◽  
Maria Lindomárcia Leonardo da Costa ◽  
...  
Keyword(s):  
Differential Equations ◽  
Goodness Of Fit ◽  
Least Squares Method ◽  
Growth Curves ◽  
Information Criterion ◽  
Coefficient Of Determination ◽  
Absolute Deviation ◽  
Marquardt Algorithm ◽  
Maturation Rate ◽  
Biological Interpretation

This study aims to propose a method to generate growth and degrowth models using differential equations as well as to present a model based on the method proposed, compare it with the classic linear mathematical models Logistic, Von Bertalanffy, Brody, Gompertz, and Richards, and identify the one that best represents the mean growth curve. To that end, data on Undefined Breed (UB) goats and Santa Inês sheep from the works of Cavalcante et al. (2013) and Sarmento et al. (2006a), respectively, were used. Goodness-of-fit was measured using residual mean squares (RMS), Akaike information criterion (AIC), Bayesian information criterion (BIC), mean absolute deviation (MAD), and adjusted coefficient of determination . The models’ parameters (?, weight at adulthood; ?, an integration constant; ?, shape parameter with no biological interpretation; k, maturation rate; and m, inflection point) were estimated by the least squares method using Levenberg-Marquardt algorithm on the software IBM SPSS Statistics 1.0. It was observed that the proposed model was superior to the others to study the growth curves of goats and sheep according to the methodology and conditions under which the present study was carried out.

scholarly journals Choice of non-linear models to determine the growth curve of meat-type quail

2021 ◽  
Vol 51 (2) ◽  
Author(s):  
Marta Jeidjane Borges Ribeiro ◽  
Fabyano Fonseca Silva ◽  
Maíse dos Santos Macário ◽  
José Aparecido Santos de Jesus ◽  
Claudson Oliveira Brito ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Linear Models ◽  
Growth Curves ◽  
Information Criterion ◽  
Metabolizable Energy ◽  
Coefficient Of Determination ◽  
Parameter Estimates ◽  
Coturnix Coturnix ◽  
Non Linear ◽  
Meat Type

ABSTRACT: The objective of this study was to compare non-linear models fitted to the growth curves of quail to determine which model best describes their growth and check the similarity between models by analyzing parameter estimates.Weight and age data of meat-type European quail (Coturnix coturnix coturnix) of three lines were used, from an experiment in a 2 × 4 factorial arrangement in a completely randomized design, consisting of two metabolizable energy levels, four crude protein levels and six replicates. The non-linear Brody, Von Bertalanffy, Richards, Logistic and Gompertz models were used. To choose the best model, the Adjusted Coefficient of Determination, Convergence Rate, Residual Mean Square, Durbin-Watson Test, Akaike Information Criterion and Bayesian Information Criterion were applied as goodness-of-fit indicators. Cluster analysis was performed to check the similarity between models based on the mean parameter estimates. Among the studied models, Richards’ was the most suitable to describe the growth curves. The Logistic and Richards models were considered similar in the analysis with no distinction of lines as well as in the analyses of Lines 1, 2 and 3.

Moisture Sorption Characteristics of Ready-to-eat Chicken Wheat Crisps Prepared Using Resistant Starch and Chicken Powder with Wheat Flour

2017 ◽  
Vol 2 (2) ◽  
pp. 163 ◽  
Author(s):  
Shefali Bhardwaj ◽  
V. K. Shiby ◽  
M. C. Pandey ◽  
Natarajan Gopalan
Keyword(s):  
Surface Area ◽  
Water Activity ◽  
Goodness Of Fit ◽  
Moisture Sorption ◽  
Isosteric Heat ◽  
Coefficient Of Determination ◽  
Sorption Data ◽  
Temperature Equilibrium ◽  
Increasing Temperature ◽  
Parameter Values

Fibre and protein enriched chicken wheat crisps were evaluated for their adsorption behaviour at a temperature range of 5 °C - 40 °C and a water activity range of 0.1-0.9. Sigmoid type II isotherm was obtained for the product and the sorption data was fitted to 3 models namely BET, GAB, and Peleg model. Each model was statistically evaluated by means of root mean square (%) and coefficient of determination (R2). Peleg and GAB gave the best fits for the moisture sorption data evaluated on the basis of regression analyses and goodness of fit. Surface area of adsorption was evaluated using parameter values obtained from the BET model and the surface area decreased with increase in temperature. Equilibrium moisture content at a particular water activity and isosteric heat of sorption were seen to decrease with increasing temperature. We conclude that the chicken wheat crisps can be stored at 25 °C for a better shelf life.

scholarly journals Growth of Staphylococcus aureus 2064 described by predictive microbiology: From primary to secondary models

2019 ◽  
Vol 12 (2) ◽  
pp. 175-181
Author(s):  
Alžbeta Medveďová ◽  
Adriana Havlíková ◽  
Ľubomír Valík
Keyword(s):  
Staphylococcus Aureus ◽  
Growth Rate ◽  
Specific Growth Rate ◽  
Water Activity ◽  
Goodness Of Fit ◽  
Specific Growth ◽  
Growth Curves ◽  
Extended Model ◽  
Predictive Microbiology ◽  
Temperature Range

Abstract The growth of Staphylococcus aureus 2064 isolate in model nutrient broth was studied as affected by temperature and water activity using principles and models of predictive microbiology. Specific rates resulting from growth curves fitted by the Baranyi model were modelled by the secondary Ratkowsky model for suboptimal temperature range (RTKsub) as well as the Ratkowsky extended model (RTKext) and cardinal model (CM) in the whole temperature range. With the biological background of the RTKext model, cardinal values of temperature Tmin = 6.06 °C and Tmax = 47.9 °C and water activity aw min = 0.859 were calculated and validated with cardinal values estimated by CM (Tmin = 7.72 °C, Tmax = 46.73 °C, aw min = 0.808). CM also provided other cardinal values, Topt = 40.63 °C, aw opt = 0.994, as well as optimal specific growth rate of 1.97 h–1 (at Topt and aw opt). To evaluate the goodness of fit of all models, mathematical and graphical validation was performed and the statistical indices proved appropriateness of all the secondary models used.

scholarly journals Isotonic regression analysis of Guzerá cattle growth curves

Revista CERES ◽  
2018 ◽  
Vol 65 (1) ◽  
pp. 24-27 ◽  
Author(s):  
Adriano Rodrigues ◽  
Lucas Monteiro Chaves ◽  
Fabyano Fonseca Silva ◽  
Idalmo Pereira Garcia ◽  
Darlene Ana Souza Duarte ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Least Squares Method ◽  
Age Groups ◽  
Growth Curves ◽  
Generalized Least Squares ◽  
Isotonic Regression ◽  
Coefficient Of Determination ◽  
Linear Regression Models ◽  
Generalized Least Squares Method

ABSTRACT The objective of this study was to apply data transformation via isotonic regression in growth curves studies of Guzerá cattle whose data presented disturbances characterized by decreased body weight in certain age groups. Weight-age data were collected on newly weaned Guzerá males according to the methodology of weight gain tests (WGT) defined by the Brazilian Association of Zebu Breeders (ABCZ). The Logistic, Von Bertalanffy and Gompertz models were fitted to weight-age data using the generalized least squares method for non-linear regression models through the Gauss-Newton algorithm. The proposed transformation based on isotonic regression theory proved to be efficient; and the Logistic model was the best to describe the growth of animals, with a high percentage of convergence (100%) and goodness of fit assessed by the mean squared error (MSE) and the coefficient of determination (R2).

Growth Variation Among Species and Strains of Listeria in Culture Broth

1994 ◽  
Vol 57 (9) ◽  
pp. 765-769 ◽  
Author(s):  
WERNER B. BARBOSA ◽  
LAURA CABEDO ◽  
HEIDI J. WEDERQUIST ◽  
JOHN N. SOFOS ◽  
GLENN R. SCHMIDT
Keyword(s):  
Growth Parameters ◽  
Phosphate Buffer Solution ◽  
Growth Curves ◽  
Culture Broth ◽  
Lag Phase ◽  
Gompertz Function ◽  
Buffer Solution ◽  
Phase Duration ◽  
Growth Variation ◽  
Increasing Temperature

Culture suspensions of 45 species and strains of Listeria were prepared in tryptic soy broth with 0.6% yeast extract (TSBYE) for 24 h at 37°C, and were then diluted with phosphate buffer solution and standardized to 0.10 ± 0.01 absorbance at 600 nm. Spectrophotometer tubes containing 5 ml of TSBYE (pH 7.2) were inoculated with 0.1 ml of the standardized cultures and incubated at 4, 10 or 37°C. Absorbance readings were taken during storage. Growth curves were fitted using the Gompertz function, and growth parameters were calculated. There were major differences in lag phase duration (LPD), generation time (GT) and exponential growth rate (EGR) among species and strains of Listeria tested. Values for LPD and GT decreased (P &lt;0.05) with increasing temperature of incubation, while EGR and maximum population density (MPD) values increased. Lag phase duration and GT values at a given temperature were lower for Listeria monocytogenes compared to other Listeria spp. At 4°C, LPDs for L. monocytogenes strains ranged from 69.8 to 270.8 h. Of the L. monocytogenes cultures tested, strain Scott A had the longest average (209.8 ± 0.1) h LPD at 4°C. At l0°C, LPDs ranged from 36.5 to 68.9 h, with Scott A being again one of the strains with the longest average LPD (62.8 ± 0.7 h). At 37°C, LPDs ranged from 4.4 to 11.1 h. Variation was also observed in GT and EGR, especially at 4°C. Although there were major variations in growth parameters due to strain and temperature, no significant (P &gt;0.05) trends were observed in average values among different serotypes of L. monocytogenes tested.

Growth of Listeria monocytogenes in a Model High-Moisture Cheese on the Basis of pH, Moisture, and Acid Type

2020 ◽  
Vol 83 (8) ◽  
pp. 1335-1344
Author(s):  
SARAH K. ENGSTROM ◽  
CHRISTIE CHENG ◽  
DENNIS SEMAN ◽  
KATHLEEN A. GLASS
Keyword(s):  
Lactic Acid ◽  
Listeria Monocytogenes ◽  
Citric Acid ◽  
Ph Value ◽  
Growth Parameters ◽  
Growth Curves ◽  
Lag Phase ◽  
High Moisture ◽  
Contrast Model ◽  
Acid Type

ABSTRACT High-moisture, low-acid cheeses have been shown to support Listeria monocytogenes growth during refrigerated storage. Prior studies suggest that organic acids vary in their antilisterial activity and that cheeses of lower pH delay growth longer than those of higher pH; however, no standard pH value for Listeria control in cheese exists. The objective of this research was to create a predictive model to include the effects of acid type, pH, and moisture on the growth of L. monocytogenes in a model cheese system. Cream, micellar casein, water, lactose, salt, and acid (citric, lactic, acetic, or propionic) were combined in 32 formulations targeting 4 pH values (5.25, 5.50, 5.75, and 6.00) and two moisture levels (50 and 56%). Each was inoculated with 3 log CFU/g L. monocytogenes (five-strain mixture) after which 25-g samples were vacuum sealed and stored 8 weeks at 4°C. Triplicate samples were enumerated on modified Oxford agar weekly in duplicate trials. Model cheeses formulated with acetic and propionic acids inhibited growth (i.e., no observed increase in L. monocytogenes populations over 8 weeks) at pH ≤5.75, while those formulated with lactic acid inhibited growth at pH 5.25 only. In contrast, all model cheeses formulated with citric acid supported growth. Resulting growth curves were fitted for lag phase and growth rate before constructing models for each. The pH and acid type were found to significantly affect both growth parameters (P &lt; 0.05), while moisture (50 to 56%) was not statistically significant in either model (P ≥ 0.05). The effects of acetic and propionic acid were not significantly different. In contrast, model cheeses made with citric acid had significantly shorter lag phases than the other acids tested, but growth rates after lag were statistically similar to model cheeses made with lactic acid. These data suggest propionic ∼ acetic &gt; lactic &gt; citric acids in antilisterial activity within the model cheese system developed and can be used in formulating safe high-moisture cheeses. HIGHLIGHTS

scholarly journals Comparison of Primary Models to Predict Microbial Growth by the Plate Count and Absorbance Methods

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
María-Leonor Pla ◽  
Sandra Oltra ◽  
María-Dolores Esteban ◽  
Santiago Andreu ◽  
Alfredo Palop
Keyword(s):  
Growth Rate ◽  
Goodness Of Fit ◽  
Microbial Growth ◽  
Growth Parameters ◽  
Growth Curves ◽  
Food Microbiology ◽  
Plate Count ◽  
Three Phase ◽  
Primary Model ◽  
Almost All

The selection of a primary model to describe microbial growth in predictive food microbiology often appears to be subjective. The objective of this research was to check the performance of different mathematical models in predicting growth parameters, both by absorbance and plate count methods. For this purpose, growth curves of three different microorganisms (Bacillus cereus, Listeria monocytogenes, andEscherichia coli) grown under the same conditions, but with different initial concentrations each, were analysed. When measuring the microbial growth of each microorganism by optical density, almost all models provided quite high goodness of fit (r2>0.93) for all growth curves. The growth rate remained approximately constant for all growth curves of each microorganism, when considering one growth model, but differences were found among models. Three-phase linear model provided the lowest variation for growth rate values for all three microorganisms. Baranyi model gave a variation marginally higher, despite a much better overall fitting. When measuring the microbial growth by plate count, similar results were obtained. These results provide insight into predictive microbiology and will help food microbiologists and researchers to choose the proper primary growth predictive model.

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