• 제목/요약/키워드: 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
    • 한국축산식품학회지
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    • 제33권2호
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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
    • 한국축산식품학회지
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    • 제30권5호
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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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    • 제35권5호
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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
    • 한국축산식품학회지
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    • 제36권2호
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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
    • 한국축산식품학회지
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    • 제34권1호
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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.

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

  • 신현출;고철환
    • 한국해양학회지
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    • 제30권5호
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    • pp.403-412
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    • 1995
  • 본 연구에서는 한국 서해 인천 연안의 송도 갯벌 조간대에 서식하는 동죽(Mactra veneriformis)의 성장과 생산을 조사하였다. 표품은 1989년 3월부터 1990년 9월까지 월별로 채집하였다. 각장은 1989년 3월부터 8월까지 단일 규모 모드를 보였보였다. 1989년 9월부터는 1990년 9월부터는 작은 개체들이 출현하기 시작하여 이중모드를 보 였다. 서식밀도는 다소 불규칙적으로 변동하였으나, 대체로 시간이 경과함에 따라 감 소하는 경향을 보였다. 1989 연도군의 서식밀도는 1990년 2월 이후 급격히 증가하였 다. 각장은 봄에 성장이 빠르고, 산란기 이후 여름과 가을에 둔화되며, 겨울에 성장을 멈추었다. 성장률은 연령이 증가될수록 감소하였다. 중량은 산란기 직전에 늦봄에 최 대값을 보이고, 가을에 2차 최대값을 나타내었다. 윤장과 이로부터 역계산한 육질부 건중량으로 연성장을 분석하였다. 각장은 vov bertalanffy 성장 모델에, 건중량은 Gompertz 성장모델에 잘 적합되었다. 1985년군의 L∽가 가장 높고, 1986년 군이 가장 낮았다. 중량의 성장률은 2∼3세에서 최대값을 나타내었다. 1984년군과 1985년군의 W ∽와 성장률이 높았고, 1986년군과 1987년군이 낮았다. 최대성장률이 나타나는 연령은 1986년군과 1987년군이 더 빨랐다. 각장과 중륭의 상대 성장률은 연령에 따라 지수함 수적으로 감소하였다. 육질부 건중량의 생물량은 모든 연령군에서 봄에 높았다가 산란 기 이후 감소하여 겨울에 최저치를 보였다. 생물량은 1990년 8월에 134.6g·m/SUP -2/ 으로 가장 높았다. 1989년도군이 가입한 이후에는 1989년군의 생물량이 총 생물량의 변동을 지배하였다. 1989년 3월부터 1990년 3월까지의 연소연량은 67.9g·m/SUP -2/· y/SUP -1/이었다. 조사기간동안 1989년도군의 누적 생산량이 가장 높았고, 1984년군이 가장 적었다. 생산량은 봄과 가을에 증가하였고, 여름과 겨울에 0의 값을 보였다.

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

  • 배명권;최준혁;박종락;정상화
    • 한국기계가공학회지
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    • 제19권2호
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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.

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

  • 최태정;서강석;최재관;김시동;조광현;최호성
    • 한국축산식품학회지
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    • 제28권2호
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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
    • 한국식품위생안전성학회지
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    • 제24권3호
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    • pp.232-237
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    • 2009
  • 본 연구는 오염된 양상치를 알카리전해수로 세척한 처리구와 비처리구에 오염된 E. coli O157 : H7균이 다양한 온도 (4, 10, 15, 20, 25, 30, $35^{\circ}C$)에 저장할 경우 이균의 specific growth rate (SCR) 과 lag time (LT) 생육변수에 미치는 영향을 조사하기 위한 모델을 개발하기 위하여 수행되었다. E. coli O157 : H7의 specific growth rate (SGR) 과 lag time (LT)를 결정하기 위해 생육도를 Gompertz 식을 사용하여 fitting한 결과, $R^2$값이 0.994로 나타났다. 실험값으로부터 얻은 SGR과 LT는 저장온도에 의존하는 것으로 나타났으며 $4^{\circ}C$에서 $35^{\circ}C$까지 온도가 증가할수록 성장 속도가 증가하는 것으로 나타났다. AIEW 처리구 또는 비처리구의 양상치 에서 E. coli O157 : H7의 성장 kinetics에 대한 저장 온도의 효과를 평가하기 위해 SRG에 대한 두개의 모델을 개발하였다. 유도된 2개의 모델 검증은 $R^2$, $R^2_{Adj}$ (adjusted determination coefficient) 및 MSE (mean square error)를 적용하였으며, 그 결과 $R^2$, $R^2_{Adj}$가 1 (>0.93)에 근접하였으며, 알카리 전해수 처리구 및 비처리구 양상치 모델의 MSE는 각각 0.031, 0.025로 나타났다. 따라서, 본연구에서 개발된 모델의 생육변수는 실험 치에서 얻은 E. coli O157 : H7의 생육변수 결과와 매우 유사한 것으로 나타났다.

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

  • 박인석;임재현;장창익
    • 한국어류학회지
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    • 제8권1호
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    • pp.49-55
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    • 1996
  • 무지개송어, Oncorhynchus mykiss 난황자어의 부상기 이전까지의 부화일수에 따른 전장(TL)성장식은 $TLt=2.7e^{-1.24{\cdot}e^{-0.11t}}(r^{2}=0.66)$, 전중(TW)성장식은 $TWt=1.8e^{-2.03{\cdot}e^{-0.11t}}(r^{2}=0.66)$, 체세포중량(SW)성장식은 $SWt=1.8e^{-5.41{\cdot}e^{-0.13t}}(r^{2}=0.83)$로 나타났다. 부화일수 경과에 따른 난황장, 난황고, 난황부피는 감소를 나타내는 직선식이였다. 전중-전장, 체세포중량-전장, 난황장-전장, 난황고-전장, 난황부피-전장, 난황중-전장, 난황중-전중, 난황중-난황고 및 난황중-난황장의 성장형질간의 상대성장식은 부화일 경과에 따라 난황홉수 경향을 반영하였다.

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