• Title/Summary/Keyword: Gompertz Growth Model

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Development of Kinetic Models Describing Kinetic Behavior of Bacillus cereus and Staphylococcus aureus in Milk

  • Kim, Hyoun Wook;Lee, Sun-Ah;Yoon, Yohan;Paik, Hyun-Dong;Ham, Jun-Sang;Han, Sang-Ha;Seo, Kuk-Hwan;Jang, Aera;Park, Bum-Young;Oh, Mi-Hwa
    • Food Science of Animal Resources
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    • v.33 no.2
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    • pp.155-161
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    • 2013
  • This study developed predictive models to evaluate the kinetic behaviors of Bacillus cereus and Staphylococcus aureus in milk during storage at various temperatures. B. cereus and S. aureus (3 Log CFU/mL) were inoculated into milk and stored at $10^{\circ}C$, $15^{\circ}C$, $20^{\circ}C$, and $30^{\circ}C$, as well as $5^{\circ}C$, $15^{\circ}C$, $25^{\circ}C$, and $35^{\circ}C$, respectively, while bacterial populations were enumerated. The growth data were fitted to the modified Gompertz model to estimate kinetic parameters, including the maximum specific growth rate (${\mu}_{max}$; Log CFU/[$mL{\cdot}h$]), lag phase duration (LPD; h), lower asymptote ($N_0$; Log CFU/mL), and upper asymptote ($N_{max}$; Log CFU/mL). To describe the kinetic behavior of B. cereus and S. aureus, the parameters were fitted to the square root model as a function of storage temperature. Finally, the developed models were validated with the observed data, and Bias (B) and Accuracy (A) factors were calculated. Cell counts of both bacteria increased with storage time. Primary modeling yielded the following parameters; ${\mu}_{max}$: 0.14-0.75 and 0.06-0.51 Log CFU/mL/h; LPD: 1.78-14.03 and 0.00-1.44 h, $N_0$: 3.10-3.37 and 2.09-3.07 Log CFU/mL, and $N_{max}$: 7.59-8.87 and 8.60-9.32 Log CFU/mL for B. cereus and S. aureus, respectively. Secondary modeling yielded a determination of coefficient ($R^2$) of 0.926.0.996. B factors were 1.20 and 0.94, and A factors were 1.16 and 1.08 for B. cereus and S. aureus, respectively. Thus, the mathematical models developed here should be useful in describing the kinetic behaviors of B. cereus and S. aureus in milk during storage.

Development of Predictive Growth Models for Staphylococcus aureus and Bacillus cereus on Various Food Matrices Consisting of Ready-to-Eat (RTE) Foods

  • Kang, Kyung-Ah;Kim, Yoo-Won;Yoon, Ki-Sun
    • Food Science of Animal Resources
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    • v.30 no.5
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    • pp.730-738
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    • 2010
  • We developed predictive growth models for Staphylococcus aureus and Bacillus cereus on various food matrices consisting primarily of ready-to-eat (RTE) foods. A cocktail of three S. aureus strains, producing enterotoxins A, C, and D, or a B. cereus strain, were inoculated on sliced bread, cooked rice, boiled Chinese noodles, boiled bean sprouts, tofu, baked fish, smoked chicken, and baked hamburger patties at an initial concentration of 3 log CFU/g and stored at 8, 10, 13, 17, 24, and $30^{\circ}C$. Growth kinetic parameters were determined by the Gompertz equation. The square-root and Davey models were used to determine specific growth rate and lag time values, respectively, as a function of temperature. Model performance was evaluated based on bias and accuracy factors. S. aureus and B. cereus growth were most delayed on sliced bread. Overall, S. aureus growth was significantly (p<0.05) more rapid on animal protein foods than carbohydrate-based foods and vegetable protein foods. The fastest growth of S. aureus was observed on smoked chicken. B. cereus growth was not observed at 8 and $10^{\circ}C$. B. cereus growth was significantly (p<0.05) more rapid on vegetable protein foods than on carbohydrate-based foods. The secondary models developed in this study showed suitable performance for predicting the growth of S. aureus and B. cereus on various food matrices consisting of RTE foods.

Nonlinear mixed models for characterization of growth trajectory of New Zealand rabbits raised in tropical climate

  • de Sousa, Vanusa Castro;Biagiotti, Daniel;Sarmento, Jose Lindenberg Rocha;Sena, Luciano Silva;Barroso, Priscila Alves;Barjud, Sued Felipe Lacerda;de Sousa Almeida, Marisa Karen;da Silva Santos, Natanael Pereira
    • Animal Bioscience
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    • v.35 no.5
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    • pp.648-658
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    • 2022
  • Objective: The identification of nonlinear mixed models that describe the growth trajectory of New Zealand rabbits was performed based on weight records and carcass measures obtained using ultrasonography. Methods: Phenotypic records of body weight (BW) and loin eye area (LEA) were collected from 66 animals raised in a didactic-productive module of cuniculture located in the southern Piaui state, Brazil. The following nonlinear models were tested considering fixed parameters: Brody, Gompertz, Logistic, Richards, Meloun 1, modified Michaelis-Menten, Santana, and von Bertalanffy. The coefficient of determination (R2), mean squared error, percentage of convergence of each model (%C), mean absolute deviation of residuals, Akaike information criterion (AIC), and Bayesian information criterion (BIC) were used to determine the best model. The model that best described the growth trajectory for each trait was also used under the context of mixed models, considering two parameters that admit biological interpretation (A and k) with random effects. Results: The von Bertalanffy model was the best fitting model for BW according to the highest value of R2 (0.98) and lowest values of AIC (6,675.30) and BIC (6,691.90). For LEA, the Logistic model was the most appropriate due to the results of R2 (0.52), AIC (783.90), and BIC (798.40) obtained using this model. The absolute growth rates estimated using the von Bertalanffy and Logistic models for BW and LEA were 21.51g/d and 3.16 cm2, respectively. The relative growth rates at the inflection point were 0.028 for BW (von Bertalanffy) and 0.014 for LEA (Logistic). Conclusion: The von Bertalanffy and Logistic models with random effect at the asymptotic weight are recommended for analysis of ponderal and carcass growth trajectories in New Zealand rabbits. The inclusion of random effects in the asymptotic weight and maturity rate improves the quality of fit in comparison to fixed models.

Kinetic Behavior of Salmonella on Low NaNO2 Sausages during Aerobic and Vacuum Storage

  • Ha, Jimyeong;Gwak, Eunji;Oh, Mi-Hwa;Park, Beomyoung;Lee, Jeeyeon;Kim, Sejeong;Lee, Heeyoung;Lee, Soomin;Yoon, Yohan;Choi, Kyoung-Hee
    • Food Science of Animal Resources
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    • v.36 no.2
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    • pp.262-266
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    • 2016
  • This study evaluated the growth kinetics of Salmonella spp. in processed meat products formulated with low sodium nitrite (NaNO2). A 5-strain mixture of Salmonella spp. was inoculated on 25-g samples of sausages formulated with sodium chloride (NaCl) (1.0%, 1.25%, and 1.5%) and NaNO2 (0 and 10 ppm) followed by aerobic or vacuum storage at 10℃ and 15℃ for up to 816 h or 408 h, respectively. The bacterial cell counts were enumerated on xylose lysine deoxycholate agar, and the modified Gompertz model was fitted to the Salmonella cell counts to calculate the kinetic parameters as a function of NaCl concentration on the growth rate (GR; Log CFU/g/h) and lag phase duration (LPD; h). A linear equation was then fitted to the parameters to evaluate the effect of NaCl concentration on the kinetic parameters. The GR values of Salmonella on sausages were higher (p<0.05) with 10 ppm NaNO2 concentration than with 0 ppm NaNO2. The GR values of Salmonella decreased (p<0.05) as NaCl concentration increased, especially at 10℃. This result indicates that 10 ppm NaNO2 may increase Salmonella growth at low NaCl concentrations, and that NaCl plays an important role in inhibiting Salmonella growth in sausages with low NaNO2.

Effects of Temperature and Packaging on the Growth Kinetics of Clostridium perfringens in Ready-to-eat Jokbal (Pig's Trotters)

  • Park, Hee-Jin;Na, Yu-Jin;Cho, Joon-Il;Lee, Soon-Ho;Yoon, Ki-Sun
    • Food Science of Animal Resources
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    • v.34 no.1
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    • pp.80-87
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    • 2014
  • Ready-to-eat (RTE) Jokbal (Pig's trotter), which consists of pig's feet cooked in soy sauce and various spices, is a very popular and widely sold in Korean retail markets. Commercially, the anaerobically packed Jokbal have also become a popular RTE food in several convenience stores. This study evaluates the effects of storage temperature and packaging methods for the growth of C. perfringens in Jokbal. Growth kinetic parameters of C. perfringens in aerobically and anaerobically packed Jokbals are determined at each temperature by the modified Gompertz equation. The lag time, specific growth rate, and maximum population density of C. perfringens are being analyzed as a function of temperature and packaging method. The minimum growth temperature of C. perfringens in aerobically and anaerobically packed Jokbal is $24^{\circ}C$ and $18^{\circ}C$, respectively. The C. perfringens in Jokbal did not grow under conditions of over $50^{\circ}C$ regardless of the packaging methods, indicating that the holding temperature of Jokbal in markets must be maintained at above $50^{\circ}C$ or below $18^{\circ}C$. Growth of C. perfringens in anaerobically packed Jokbal is faster than in aerobically packed Jokbal when stored under the same conditions. This indicates that there are a higher risks associated with C. perfringens for anaerobically packed meat products.

Growth and Production of Mactra veneriformis (Bivalvia) on the Songdo Tidal Flat, West Coast of Korea (서해 송도 갯벌에서의 동죽(Mactra veneriformis: Bivalvia)의 성장과 생산)

  • 신현출;고철환
    • 한국해양학회지
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    • v.30 no.5
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    • pp.403-412
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    • 1995
  • The present study was performed to determine th growth and production of Mactra veneriformis on the Songdo tidal flat off Inchon. west coast of Korea. Monthly samples were collected from Marc 1989 to September 1990. The size distributions of shell length showed unimodal patterns from March to August 1989. The binodal pattern after September 1989 indicated a recruitment of young clams during this period. The density fluctuated irregularly, but showed a decreasing pattern over time on the whole. The density of the year class 1989 increased markedly after February 1990. The growth in shell length showed three phases during a year, a fast growth phase in spring, a slow growth phase in summer and autumn, and a lag phase in winter. The annual increment in shell length reduced with age. The flesh dry weight showed a peak in late spring just before the spawning period, and another peak in autumn. The length of annuli and the back-calculated flesh dry weight were used to describe the annual growth. The growth in shell length fitted to the von Bertalanffy model and the flesh dry weight to the Gompertz model. The absolute growth rate of the shell length reduced gradually with age. The year class 1985 had the highest L, and the yeat class 1986 the lowest L. The annual growth in weight showed a typical sigmoid curve. The growth rate was maximum at the age of 2 to 3. Year classes of 1984 and 1985 had higher values of W and higher absolute growth rates than those of 1986 and 1987. Maximum absolute growth rates of 1986 and 1987 year classes were recorded at younger ages than 1984 and 1985 year classes. The annual relative growth rates of length and weight decreased exponentially with age. Biomass in flesh dry weight increased till spring and thereafter decreased progressively. Maximum biomass was 134.6g m/SUP -2/ in August 1990. The biomass of 1989 yeat class occupied highest proportion in total biomass. Annual production in flesh dry weight from March 1989 to March 1990 was 67.9 g m/SUP -2/ year/SUP -1/. Cumulative production of 1989 year class was highest among all year classes, and that of year class 1984 was lowest. The production is high in spring and autumn, and very low in summer and winter.

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Cell Disruption of Microalgae by Low-Frequency Non-Focused Ultrasound (저주파 초음파를 이용한 미세조류 파쇄)

  • Bae, Myeong-Gwon;Choi, Jun-Hyuk;Park, Jong-Rak;Jeong, Sang-Hwa
    • Journal of the Korean Society of Manufacturing Process Engineers
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    • v.19 no.2
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    • pp.111-118
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    • 2020
  • Recently, bioenergy research using microalgae, one of the most promising biofuel sources, has attracted much attention. Cell disruption, which can be classified as physical or chemical, is essential to extract functional ingredients from microalgae. In this study, we investigated the cell disruption efficiency of Chlorella sp. using low-frequency non-focused ultrasound (LFNFU). This is a continuously physical method that is superior to chemical methods with respect to environmental friendliness and low processing cost. A flat panel photobioreactor was employed to cultivate Chlorella sp. and its growth curve was fitted both with Logistic and Gompertz models. The temporal change in cell reduction by cell disruption using LFNFU was fitted with a Logistic model. The experimental conditions that were investigated were the initial concentration of microalgal cells, relative amplitude of output ultrasound waves, processing volume of microalgal cells, and initial pH value. The optimal conditions for the most efficient cell disruption were determined through the various tests.

Growth Curves Fitting for Body Weight and Backfat Thickness of Swine by Sex (성별에 따른 돼지 체중 및 등지방두께 성장곡선 추정)

  • Choi, Te-Jeong;Seo, Kang-Seok;Choi, Je-Gwan;Kim, Si-Dong;Cho, Kwang-Hyun;Choe, Ho-Sung
    • Food Science of Animal Resources
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    • v.28 no.2
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    • pp.187-195
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    • 2008
  • The purpose of this study was to establish proper shipping weight and backfat thickness by applying the growth model to backfat thickness, measured by means of not only body weight, but also ultrasonography, and predicting the changes by age. Three breeds, i.e. Duroc, Landrace, and Yorkshie, were analyzed, and the Gompertz, logistic, and Von Bertalanffy model were used for inference with the parameter of the growth model being sex. As a result, both body weight and backfat thickness showed different growth curve parameters and characteristics at inflection points depending on model selection and sex. As for backfat thickness, in estimating the inflection point, unlike the case of body weight, the inflection ages of the boars of the Duroc breed was earlier than that of sows, whereas the inflection ages of the sows of the Landrace and Yorkshire breeds was earlier than that of boars. More than anything else, in the analysis of the changes in backfat thickness according to body weight, as the body weight reached 145kg, the backfat thickness showed much variation as great as 1.7-3.2 cm in each breed and sex. In addition, unlike the other breeds, the boars of the Landrace breed showed an exponential type of relationship between body weight and backfat thickness. As they grow to become 100 kg or heavier, abrupt change in back fat thickness was confirmed. If the growth of body weight and backfat thickness is understood and the genetic relationship is taken advantage of like this, it would be possible to set desired body weight and backfat thickness, and thus help effectively set the shipping time. If not only the phenotype, but also genetic parameters about growth characteristics are estimated and analyzed additionally, more effective data can be generated.

Prediction of Growth of Escherichia coli O157 : H7 in Lettuce Treated with Alkaline Electrolyzed Water at Different Temperatures

  • Ding, Tian;Jin, Yong-Guo;Rahman, S.M.E.;Kim, Jai-Moung;Choi, Kang-Hyun;Choi, Gye-Sun;Oh, Deog-Hwan
    • Journal of Food Hygiene and Safety
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    • v.24 no.3
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    • pp.232-237
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    • 2009
  • This study was conducted to develop a model for describing the effect of storage temperature (4, 10, 15, 20, 25, 30 and $35^{\circ}C$) on the growth of Escherichia coli O157 : H7 in ready-to-eat (RTE) lettuce treated with or without (control) alkaline electrolyzed water (AIEW). The growth curves were well fitted with the Gompertz equation, which was used to determine the specific growth rate (SGR) and lag time (LT) of E. coli O157 : H7 ($R^2$ = 0.994). Results showed that the obtained SGR and LT were dependent on the storage temperature. The growth rate increased with increasing temperature from 4 to $35^{\circ}C$. The square root models were used to evaluate the effect of storage temperature on the growth of E. coli O157 : H7 in lettuce samples treated without or with AIEW. The coefficient of determination ($R^2$), adjusted determination coefficient ($R^2_{Adj}$), and mean square error (MSE) were employed to validate the established models. It showed that $R^2$ and $R^_{Adj}$ were close to 1 (> 0.93), and MSE calculated from models of untreated and treated lettuce were 0.031 and 0.025, respectively. The results demonstrated that the overall predictions of the growth of E. coli O157: H7 agreed with the observed data.

A Study on the Yolk Absorption and Early Growth in the Alevin of Rainbow Trout, Oncorhynchus mykiss (무지개송어, Oncorhynchus mykiss 자어의 난황흡수 및 초기성장에 관한 연구)

  • Park, In-Seok;Im, Jae-Hyun;Zhang, Chang-Ik
    • Korean Journal of Ichthyology
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    • v.8 no.1
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    • pp.49-55
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    • 1996
  • The growth of total length(TL), total weight(TW) and somatic weight(SW) of rainbow trout, Oncorhynchus mykiss alevin at yolk absorption period was expressed by the Gompertz growth model as $TLt=2.7e^{-1.24{\cdot}e^{-0.11t}}(r^{2}=0.66)$, $TWt=1.8e^{-2.03{\cdot}e^{-0.11t}}(r^{2}=0.66)$ and $SWt=1.8e^{-5.41{\cdot}e^{-0.13t}}(r^{2}=0.83)$ respectively. Yolk length, yolk height and yolk volume of rainbow trout decreased linearly. The relative growth of total weight-total length, somatic weight-total length, yolk length-total length, yolk height-total length, yolk volume-total length, yolk weight-total length, yolk weight-total weight, yolk weight-yolk height and yolk weight-yolk length at yolk absorption period revealed the pattern of yolk absorption in rainbow trout.

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