• Title/Summary/Keyword: Gompertz growth model

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Validation of Predictive Liquid Model Systems for the Growth of Listeria monocytogenes and Yersinia enterocolitica on Pork at Various Temperatures

  • Rho, Min-Jeong;Chung, Myung-Sub;Kim, Jeong-Weon;Park, Ji-Yong
    • Food Science and Biotechnology
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    • v.14 no.1
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    • pp.42-45
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    • 2005
  • The present study was carried out to envisage the aerobic growth of Listeria monocytogenes and Yersinia enterocolitica on pork, which is one of the major meat sources in Korea. The results were compared with the previously developed predictive model systems for the verification of microbial growth in a real situation during pork processing. Pork loin samples (8.0 g, 5 mm thick) were aseptically prepared and inoculated with each pathogen by immersing into the respective inoculums for one min. Each of the samples were then wrapped with PE film and stored at 5, 10, and $15^{\circ}C$ up to 36 days to measure the growth profile of the respective pathogens. The growth parameters were calculated by using Gompertz equation and were compared with the previously reported data. The predicted generation time (GT) of L. monocytogenes at 5, 10 and $15^{\circ}C$ was 28.74, 7.85 and 4.02 hr, respectively, and for Y. enterocolitica was 10.29, 4.74 and 2.50 hr, at the same temperatures respectively. In this study, the GT values predicted on pork were slightly higher than the values predicted in other studies using liquid model systems. Unlike previous reports, both the pathogens were found to grow at $5^{\circ}C$ on pork. This finding recommends the necessity of controlling the growth of both the pathogens during the slaughtering process and distribution.

Estimation of Growth Curve Parameters for Body Weight and Length in Miniature Pigs

  • Kang, Hyun Sung;Nam, Ki Chang;Cabling, Meriam M.;Lee, Myeong Seop;Choi, Te Jung;Yoon, Jong Taek;Seo, Kang Seok
    • Journal of Animal Science and Technology
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    • v.54 no.6
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    • pp.395-400
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    • 2012
  • This study was conducted to estimate the growth curve parameters for the body weight (BW) and body length (BL) of miniature pigs in Korea. Growth curve parameters were estimated through a nonlinear regression model using Gompertz, Logistic, and von Bertalanffy methods. A total of 25 piglets were measured monthly from birth up to 15 months of age to estimate both body weight and length. Results showed that the estimated average values for the body weight (body length) were 31.83 kg (58.77 cm) for the mature weight (A), 3.06 (1.74) for the growth ratio (${\beta}$), and 0.28 (0.52) for the maturing rate (${\kappa}$). Average inflection points showing maximum growth rate estimated each month for body weight were 3.97 kg and 11.70 cm, while for the body length were 1.06 kg and 21.61 cm. Moreover, the estimated maturation rates of the body weight and length for the group of Sire 1 were 0.22 and 0.40 respectively, whereas for the group of Sire 2 these values were 0.34 and 0.39. On the other hand, for the groups of Dam 1, Dam 2, and Dam 3, maturation rates for their body weights were 0.26, 0.28 and 0.33 respectively, while for their body lengths these values were 0.43, 0.37, and 0.38, respectively. The study also indicated a negative relationship between the values of mature weight and maturity rate for the body weight will result to a higher inflection point which is in contrast for the body length where results show that a positive relationship between the values of mature length and the maturity rate will result to a higher inflection point. Furthermore, the growth performance of miniature pig varies across stages but using these estimated growth curve parameters could improve the genetic traits of miniature pig.

Estimation of Growth Curves and Suitable Slaughter Weight of the Liangshan Pig

  • Luo, Jia;Lei, Huaigang;Shen, Linyuan;Yang, Runlin;Pu, Qiang;Zhu, Kangping;Li, Mingzhou;Tang, Guoqing;Li, Xuewei;Zhang, Shunhua;Zhu, Li
    • Asian-Australasian Journal of Animal Sciences
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    • v.28 no.9
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    • pp.1252-1258
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    • 2015
  • The Liangshan pig is a traditional Chinese small-sized breed; it has a relatively long feeding period and low meat production ability but superior meat quality. This study utilized three non-linear growth models (Von Bertalanffy, Gompertz, and logistic) to fit the growth curve of Liangshan pigs from an unselected, random-bred pig population and estimate the pigs most suitable slaughter weight. The growth development data at 20 time points of 275 Liangshan pigs (from birth to 250 d) were collected. To analyze the relative gene expression related to development, seven slaughter weight phases (50, 58, 66, 74, 82, 90, and 98 kg) (20 pigs per phase) were examined. We found that the Liangshan pig growth curve fit the typical S-curve well and that their growth turning point was 193.4 days at a weight of 62.5 kg, according to the best fit Von Bertalanffy model based on the goodness of fit criteria. Furthermore, we estimated that the most suitable slaughter weight was 62.5 to 74.9 kg based on the growth curve and the relative expression levels of growth-related genes.

Effects of Combined Treatment of Aqueous Chlorine Dioxide and Fumaric Acid on the Microbial Growth in Fresh-cut Paprika (Capsicum annuum L.) (신선편이 파프리카의 미생물 생장에 있어서 이산화염소수와 푸마르산 병합처리의 효과)

  • Jung, Seung-Hun;Park, Seung-Jong;Chun, Ho-Hyun;Song, Kyung Bin
    • Journal of Applied Biological Chemistry
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    • v.57 no.1
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    • pp.83-87
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    • 2014
  • The effects of combined treatment of aqueous chlorine dioxide ($ClO_2$) and fumaric acid on the microbial growth in fresh-cut paprika were investigated. After the combined treatment, the populations of total aerobic bacteria and inoculated Listeria monocytogenes in the paprika sample were reduced by 0.82 and 1.21 log CFU/g, respectively, compared to those of the control. In addition, after 10 d of storage at $10^{\circ}C$, the populations were decreased by 1.21 and 2.10 log CFU/g, respectively. The predictive model for the populations of total aerobic bacteria and L. monocytogenes in the paprika was applied during storage. The prediction equation using Gompertz model was appropriate, based on the statistical analysis such as accuracy factor and bias factor. These results suggest that the combined treatment of aqueous $ClO_2$ and fumaric acid can be an effective technology for microbial decontamination and it can improve microbial safety by decreasing maximum growth rate and increasing lag time of bacteria in the fresh-cut paprika.

Development of Predictive Growth Model of Listeria monocytogenes Using Mathematical Quantitative Assessment Model (수학적 정량평가모델을 이용한 Listeria monocytogenes의 성장 예측모델의 개발)

  • Moon, Sung-Yang;Woo, Gun-Jo;Shin, Il-Shik
    • Korean Journal of Food Science and Technology
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    • v.37 no.2
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    • pp.194-198
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    • 2005
  • Growth curves of Listeria monocytogenes in modified surimi-based imitation crab (MIC) broth were obtained by measuring cell concentration in MIC broth at different culture conditions [initial cell numbers, $1.0{\times}10^{2},\;1.0{\times}10^{3}\;and\;1.0{\times}10^{4}$, colony forming unit (CFU)/mL; temperature, 15, 20, 25, 37, and $40^{\circ}C$] and applied to Gompertz model to determine microbial growth indicators, maximum specific growth rate constant (k), lag time (LT), and generation time (GT). Maximum specific growth rate of L. monocytogenes increased rapidly with increasing temperature and reached maximum at $37^{\circ}C$, whereas LT and GT decreased with increasing temperature and reached minimum at $37^{\circ}C$. Initial cell number had no effect on k, LT, and GT (p > 0.05). Polynomial and square root models were developed to express combined effects of temperature and initial cell number using Gauss-Newton Algorism. Relative coefficients of experimental k and predicted k of polynomial and square root models were 0.92 and 0.95, respectively, based on response surface model. Results indicate L. monocytogenes growth was mainly affected by temperature and square root model was more effective than polynomial model for growth prediction.

Growth and Predictive Model of Wild-type Salmonella spp. on Temperature and Time during Cut and Package Processing in Cold Pork Meats (냉장돈육 가공공정 온도와 시간에서의 Wild-type Salmonella spp.의 성장특성 및 예측모델)

  • Song, Ju Yeon;Kim, Yong Soo;Hong, Chong Hae;Bahk, Gyung Jin
    • Journal of Food Hygiene and Safety
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    • v.28 no.1
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    • pp.7-12
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    • 2013
  • This study presents the influence on growth properties determined using a novel predictive growth model of wild-type Salmonella spp. KSC 101 by variations in the temperature and time during cut packaging in cold, uncooked pork meat. The experiment performed for model development included an arrangement of different temperatures ($0^{\circ}C$, $5^{\circ}C$, $10^{\circ}C$, $15^{\circ}C$, and $20^{\circ}C$) and time durations (0, 1, 2, and 3 hours) that reflect actual pork-cut and packaging processes. No growth was observed at $0^{\circ}C$ and $5^{\circ}C$, whereas some growth was observed at $10^{\circ}C$, $15^{\circ}C$, and $20^{\circ}C$, with a mean increase of only 0.34 log CFU/g. The growth observed at $20^{\circ}C$ was more robust than that observed at $15^{\circ}C$, but the difference was not statistically significant (p > 0.05). However, compared with PMP (Pathogen Modeling Program), the wild-type Salmonella spp. KSC 101 showed a more rapid growth. We used the Gompertz 4 parameter equation as the primary model, and the exponential decay formula as the secondary model. The estimated $R^2$ values were 0.99 or higher. The developed model was evaluated by comparison of the experimental and predictive values, and the values were in agreement with the ${\pm}0.5$ log CFU/g, although the RMSE (Root mean square error) value was 0.103, which indicates a slight overestimation. Therefore, we suggest that the developed predictive growth model would be useful as a tool for evaluating sanitation criteria in pork cut-packaging processes.

Development of a Predictive Growth Model of Staphylococcus aureus and Shelf-life Estimation of Cooked Mung Bean Sprouts Served in School Foodservice Operations (학교급식에서 제공되는 숙주나물의 Staphylococcus aureus 성장예측모델 개발 및 섭취유효기간 설정)

  • Park, Hyoung-Su;Kim, Min-Young;Jeong, Hyun-Suk;Park, Ki-Hwan;Ryu, Kyung
    • Journal of the Korean Society of Food Science and Nutrition
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    • v.38 no.11
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    • pp.1618-1624
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    • 2009
  • This study was conducted to estimate the shelf-life of cooked mung bean sprouts contaminated with Staphylococcus aureus according to storage temperatures after cooking in school foodservice operations. A predictive growth model of S. aureus in cooked mung bean sprouts prepared using a standard recipe was developed at 4 storage temperatures (5, 15, 25, and 35${^{\circ}C}$). To determine the effect of vinegar on the shelf-life of cooked mung bean sprouts, the growth of S. aureus in sprouts prepared using vinegar and the standard recipe were compared. The $R^2$ values of the specific growth rate (SGR) and lag time (LT) determined using the Gompertz model were greater than 0.90 at all temperatures except 5${^{\circ}C}$, which confirmed that it would be appropriate to use these parameters for a secondary model. The secondary model, which indicates changes in LT and SGR values according to storage temperatures, was calculated using response surface models. The compatibility of the developed model was confirmed by calculating $R^2$, Bf, Af and MSE values as statistic parameters. The $R^2$ values of LT and SGR were 0.94 or higher, and the MSE, Bf and Af values were 0.02 and 0.002, 0.97 and 1.03, and 1.31 and 1.10, respectively, with high statistical compatibility. The growth rate of S. aureus was higher when the standard recipe was used than when vinegar was used at all temperatures. Indeed, no growth of S. aureus was observed in mung bean sprouts prepared using vinegar. Based on the model developed, cooked mung bean sprouts prepared using the standard recipe for school foodservice should be stored at 10${^{\circ}C}$ or less. Additionally, sprouts stored at 25 or 35${^{\circ}C}$ should be consumed within 6 or 12 hours after cooking. Finally, the addition of vinegar will prevent the growth of S. aureus in cooked mung bean sprouts.

Prediction of Listeria monocytogenes Growth Kinetics in Sausages Formulated with Antimicrobials as a Function of Temperature and Concentrations

  • Bang, Woo-Suk;Chung, Hyun-Jung;Jin, Sung-Sik;Ding, Tian;Hwang, In-Gyun;Woo, Gun-Jo;Ha, Sang-Do;Bahk, Gyung-Jin;Oh, Deog-Hwan
    • Food Science and Biotechnology
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    • v.17 no.6
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    • pp.1316-1321
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    • 2008
  • This study was conducted to develop a model to describe the effect of antimicrobials [potassium sorbate (PS), potassium lactate (PL), and combined PL and sodium diacetate (SDA, PLSDA)] on the growth parameters of Listeria monocytogenes such as specific growth rate (SGR) and lag phase periods (LT) in air-dried raw sausages as a function of storage temperature (4, 10, 16, and $25^{\circ}C$). Results showed that the SGR of L monocytogenes was dependent on the storage temperature and level of antimicrobials used. The most effective treatment was the 4% PLSDA, followed by the 2% PLSDA and 4% PL and 0.2% PS exhibited the least antimicrobial effect. Increased growth rates were observed with increasing storage temperatures from 4 to $25^{\circ}C$. The growth data were fitted with a Gompertz equation to determine the SGR and LT of the L. monocytogenes. Six polynomial models were developed for the SGR and LT to evaluate the effect of PS (0.1, 0.2%) and PL (2,4%) alone and PLSDA (2, 4%) on the growth kinetics of L. monocytogenes from 4 to $25^{\circ}C$.

Development of Predictive Mathematical Model for the Growth Kinetics of Staphylococcus aureus by Response Surface Model

  • Seo, Kyo-Young;Heo, Sun-Kyung;Lee, Chan;Chung, Duck-Hwa;Kim, Min-Gon;Lee, Kyu-Ho;Kim, Keun-Sung;Bahk, Gyung-Jin;Bae, Dong-Ho;Kim, Kwang-Yup;Kim, Cheorl-Ho;Ha, Sang-Do
    • Journal of Microbiology and Biotechnology
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    • v.17 no.9
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    • pp.1437-1444
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    • 2007
  • A response surface model was developed for predicting the growth rates of Staphylococcus aureus in tryptic soy broth (TSB) medium as a function of combined effects of temperature, pH, and NaCl. The TSB containing six different concentrations of NaCl (0, 2, 4, 6, 8, and 10%) was adjusted to an initial of six different pH levels (pH 4, 5, 6, 7, 8, 9, and 10) and incubated at 10, 20, 30, and $40^{\circ}C$. In all experimental variables, the primary growth curves were well ($r^2=0.9000$ to 0.9975) fitted to a Gompertz equation to obtain growth rates. The secondary response surface model for natural logarithm transformations of growth rates as a function of combined effects of temperature, pH, and NaCl was obtained by SAS's general linear analysis. The predicted growth rates of the S. aureus were generally decreased by basic (pH 9-10) or acidic (pH 5-6) conditions and higher NaCl concentrations. The response surface model was identified as an appropriate secondary model for growth rates on the basis of correlation coefficient (r=0.9703), determination coefficient ($r^2=0.9415$), mean square error (MSE=0.0185), bias factor ($B_f=1.0216$), and accuracy factor ($A_f=1.2583$). Therefore, the developed secondary model proved reliable for predictions of the combined effect of temperature, NaCl, and pH on growth rates for S. aureus in TSB medium.

Development and Validation of Predictive Models of Esherichia coli O157:H7 Growth in Paprika (파프리카에서 병원성 대장균의 성장예측 모델 개발 및 검증)

  • Yun, Hyejeong;Kim, Juhui;Park, Kyeonghun;Ryu, Kyoung-Yul;Kim, Byung Seok
    • Journal of Food Hygiene and Safety
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    • v.28 no.2
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    • pp.168-173
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    • 2013
  • This study was carried out to develop and validate predictive models of E. coli O157:H7 growth. Growth data of E. coli O157:H7 in Paprika were collected at 12, 24, 30 and $36^{\circ}C$. The population increased into 3.0 to 3.8 log10 CFU/g within 4 days, then continued to increase at a slower rate through 10 days of storage at $12^{\circ}C$. The lag time (LT) and maximum specific growth rate (SGR) obtained from each primary model was then modeled as a function of temperature using Davey and square root equations, respectively. For interpolation of performance evaluation, growth data for a mixture of E. coli O157:H7 were collected at time intervals in paprika incubated at the different temperatures, which was not used in model development. Results of model performance for interpolation data demonstrated that induced secondary models showed acceptable goodness of fit. Relative errors in the LT and SGR model for interpolation data (18 and $27^{\circ}C$) was 100%, which show acceptable goodness of fit and validated for interpolation. The primary and secondary models developed in this study can be used to establish tertiary models to quantify the effects of temperature on the growth of E. coli O157:H7 in paprika.