• Title/Summary/Keyword: Gompertz 모델식

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Development of Predictive Growth Model of Vibrio parahaemolyticus Using Mathematical Quantitative Model (수학적 정량평가모델을 이용한 Vibrio parahaemolyticus의 성장 예측모델의 개발)

  • Moon, Sung-Yang;Chang, Tae-Eun;Woo, Gun-Jo;Shin, Il-Shik
    • Korean Journal of Food Science and Technology
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    • v.36 no.2
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    • pp.349-354
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    • 2004
  • Predictive growth model of Vibrio parahaemolyticus in modified surimi-based imitation crab broth was investigated. Growth curves of V. parahaemolyticus were obtained by measuring cell concentration in culture broth under different conditions ($Initial\;cell\;level,\;1{\times}10^{2},\;1{\times}10^{3},\;and\;1{\times}10^{4}\;colony\;forming\;unit\;(CFU)/mL$; temperature, 15, 25 37, and $40^{\circ}C$; pH 6, 7, and 8) and applying them to Gompertz model. Microbial growth indicators, maximum specific growth rate (k), lag time (LT), and generation time (GT), were calculated from Gompertz model. Maximum specific growth rate (k) of V. parahaemolyticus increased with increasing temperature, reaching maximum rate at $37^{\circ}C$. LT and GT were also the shortest at $37^{\circ}C$. pH and initial cell number did not influence k, LT, and GT values significantly (p>0.05). Polynomial model, $k=a{\cdot}\exp(-0.5{\cdot}((T-T_{max}/b)^{2}+((pH-pH_{max)/c^{2}))$, and square root model, ${\sqrt{k}\;0.06(T-9.55)[1-\exp(0.07(T-49.98))]$, were developed to express combination effects of temperature and pH under each initial cell number using Gauss-Newton Algorism of Sigma plot 7.0 (SPSS Inc.). Relative coefficients between experimental k and k Predicted by polynomial model were 0.966, 0.979, and 0.965, respectively, at initial cell numbers of $1{\times}10^{2},\;1{\times}10^{3},\;and\;1{\times}10^{4}CFU/mL$, while that between experimental k and k Predicted by square root model was 0.977. Results revealed growth of V. parahaemolyticus was mainly affected by temperature, and square root model showing effect of temperature was more credible than polynomial model for prediction of V. parahaemolyticus growth.

Comparison of Regression Models for Estimating Ventilation Rate of Mechanically Ventilated Swine Farm (강제환기식 돈사의 환기량 추정을 위한 회귀모델의 비교)

  • Jo, Gwanggon;Ha, Taehwan;Yoon, Sanghoo;Jang, Yuna;Jung, Minwoong
    • Journal of The Korean Society of Agricultural Engineers
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    • v.62 no.1
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    • pp.61-70
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    • 2020
  • To estimate the ventilation volume of mechanically ventilated swine farms, various regression models were applied, and errors were compared to select the regression model that can best simulate actual data. Linear regression, linear spline, polynomial regression (degrees 2 and 3), logistic curve, generalized additive model (GAM), and gompertz curve were compared. Overfitting models were excluded even when the error rate was small. The evaluation criteria were root mean square error (RMSE) and mean absolute percentage error (MAPE). The evaluation results indicated that degree 3 exhibited the lowest error rate; however, an overestimation contradiction was observed in a certain section. The logistic curve was the most stable and superior to all the models. In the estimation of ventilation volume by all of the models, the estimated ventilation volume of the logistic curve was the smallest except for the model with a large error rate and the overestimated model.

Prediction of Seedling Emergence and Early Growth of Eleocharis kuroguwai Ohwi under Evaluated Temperature (상승된 온도 조건에서 올방개(Eleocharis kuroguwai)의 출아 및 초기생장 예측)

  • Kim, Jin-Won;Moon, Byeong-Chul;Lim, Soo-Hyun;Chung, Ji-Hoon;Kim, Do-Soon
    • Korean Journal of Weed Science
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    • v.30 no.2
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    • pp.94-102
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    • 2010
  • Field and pot experiments were conducted to investigate seedling emergence and early growth of Eleocharis kuroguwai panted on different dates. Non-linear regression analyses of observed data against effective accumulated temperature (EAT) with the Gompertz model showed that the Gompertz model works well in describing seedling emergence and early growth of E. kuroguwai regardless of planting date and soil burial depth. EATs required for 50% of the maximum seedling emergence of E. kuroguwai planted at 1, 3 and 5 cm soil burial depth in the pot experiment were estimated to be 54.5, 84.0 and $118.0^{\circ}C$, respectively, and $56.7^{\circ}C$ when planted at 1 cm in the field experiment. EATs required for 50% of the maximum leaf number of E. kuroguwai planted at 1, 3 and 5 cm soil burial depth in the pot experiment were estimated to be 213.3, 249.0 and $291.6^{\circ}C$, respectively, and $239.5^{\circ}C$ when planted at 1 cm in the field experiment. Therefore, models developed in this study thus predicted that if rotary tillage with water is made on 27 May under $+2^{\circ}C$ elevated temperature condition, dates for 50% of the maximum seedling emergence, 5 leaf stage and 5 cm plant height of E. kuroguwai buried at 3 cm soil depth were predicted to be 2 June, 10 June and 12 June. These dates are 1 day earlier for the seedling emergence and 3 days earlier for the early growth as compared with current temperature condition, suggesting that earlier application of herbicides is required for effective control of E. kuroguwai.

Estimation of Population Ecological Characteristics of Small Yellow Croaker, Pseudosciaena polyactis off Korea (한국근해 참조기의 자원생태학적 특성치 추정)

  • ZHANG Chang-Ik;KIM Yong-Mun;YOO Sin-Jae;PARK Cha-Soo;KIM Su-Am;KIM Chong-Kwan;YOON Seong-Bong
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.25 no.1
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    • pp.29-36
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    • 1992
  • This paper deals with the estimation of population ecological parameters, including growth parameters, survival rates, instantaneous coefficient of natural mortality and age at first capture, of the small yellow-croaker, Pseudosciaena Polyactis in Korean waters, which determine fluctuations in stock abundance. For describing the growth of the small yellow croaker, von Bertalanffy growth equation was recommended for the purpose of stock assessment, although the Gompertz model yielded the closest fit. The survival rate (S) of the croaker was estimated to be 0.219 (variance=0.0000262), and the instantaneous coefficient of natural mortality (M) was 0.4 $year^{-1}$. From the estimates of S and M, the instantaneous coefficient of fishing mortality (F) was calculated to be 1.11$year^{-1}$ implying an impact from fishing three times that of natural mortality. Finally, the age at first capture $(t_{c})$ was estimated to be 0.602.

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Development of Predictive Growth Model of Imitation Crab Sticks Putrefactive Bacteria Using Mathematical Quantitative Assessment Model (수학적 정량평가모델을 이용한 게맛살 부패균의 성장 예측모델의 개발)

  • Moon, Sung-Yang;Paek, Jang-Mi;Shin, Il-Shik
    • Korean Journal of Food Science and Technology
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    • v.37 no.6
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    • pp.1012-1017
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    • 2005
  • Predictive growth model of putrefactive bacteria of surimi-based imitation crab in the modified surimi-based imitation crab (MIC) broth was investigated. The growth curves of putrefactive bacteria were obtained by measuring cell number in MIC broth under different conditions (Initial cell number, $1.0{\times}10^2,\;1.0{\times}10^3$ and $1.0{\times}10^4$ colony forming unit (CFU)/mL; temperature, $15^{\circ}C,\;20^{\circ}C\;and\;25^{\circ}C$) and applied them to Gompertz model. The microbial growth indicators, maximum specific growth rate constant (k), lag time (LT) and generation time (GT), were calculated from Gompertz model. Maximum specific growth rate (k) of putrefactive bacteria was become fast with rising temperature and fastest at $25^{\circ}C$. LT and GT were become short with rising temperature and shortest at $25^{\circ}C$. There were not significant differences in k, LT and GT by initial cell number (p>0.05). Polynomial model, $k=-0.2160+0.0241T-0.0199A_0$, and square root model, $\sqrt{k}=0.02669$ (T-3.5689), were developed to express the combination effects of temperature and initial cell number, The relative coefficient of experimental k and predicted k of polynomial model was 0.87 from response surface model. The relative coefficient of experimental k and predicted k of square root model was 0.88. From above results, we found that the growth of putrefactive bacteria was mainly affected by temperature and the square root model was more credible than the polynomial model for the prediction of the growth of putrefactive bacteria.

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.

Effects of Air-flow Rate on Bio-drying of Food waste (송풍량이 음식물쓰레기 발효건조에 미치는 영향)

  • Yoo, Jung-Suk;Yoon, Young-Man
    • Journal of the Korea Organic Resources Recycling Association
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    • v.26 no.2
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    • pp.65-73
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    • 2018
  • This study was carried out for 20 days in a bio-drying batch reactor under the blowing conditions of 0.75, 1.00, 1.25, and $1.50L/min{\cdot}kg$ in order to optimize the operating conditions for the bio-drying of food wastes. The decomposition rate of organic matter during the bio-drying operation period was analyzed using modified Gompertz model. The maximum organic degradation (P) was 2.31, 2.52, 2.27 and 1.88 kg at air flow rates of 0.75, 1.00, 1.25 and $1.50L/min{\cdot}kg$, and the maximum organic degradation rate was 0.33, 0.45, 0.28, and 0.18 kg/day at 1.00, 1.25 and $1.50L/min{\cdot}kg$, respectively, showing excellent organic decomposition efficiency at a air flow rate of $1.00L/min{\cdot}kg$. The lag growth phase time (${\lambda}$) of the bio-drying reactor was 2.10, 1.48, 1.15, and 1.06 days at 0.75, 1.00, 1.25 and $1.50L/min{\cdot}kg$, respectively. The water removal rate in the operation of bio-drying reactor of food waste increased with the increase of air flow rate from the early stage of bio-drying to the middle stage, and the highest water removal rate was observed at the air flow rate of $1.00L/min{\cdot}kg$ at the end of bio-drying. The optimum air flow rate condition of bio-drying reactor was $1.00L/min{\cdot}kg$.

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.

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.