• 제목/요약/키워드: logistic growth equations

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Kinetics and Modelling of Cell Growth and Substrate Uptake in Centella asiatica Cell Culture

  • Omar, Rozita;Abdullah, M.A.;Hasan, M.A.;Rosfarizan, M.;Marziah, M.
    • Biotechnology and Bioprocess Engineering:BBE
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    • 제11권3호
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    • pp.223-229
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    • 2006
  • In this study, we have conducted kinetics and modelling studies of Centella asiatica cell growth and substrate uptake, in an attempt to evaluate cell growth for a better understanding and control of the process. In our bioreactor cultivation experiment, we observed a growth rate of 0.18/day, a value only 20% higher than was seen in the shake flask cultivation trial. However, the observed maximum cell dry weight in the shake flask, 10.5g/L, was 14% higher than was achieved in the bioreactor. Ninety seven percentage confidence was achieved via the fitting of three unstructured growth models; the Monod, Logistic, and Gompertz equations, to the cell growth data. The Monod equation adequately described cell growth in both cultures. The specific growth rate, however, was not effectively predicted with the Logistic and Gompertz equations, which resulted in deviations of up to 73 and 393%, respectively. These deviations in the Logistic and Gompertz models may be attributable to the fact that these models were developed for substrate-independent growth and fungi growth, respectively.

Modeling Age-specific Cancer Incidences Using Logistic Growth Equations: Implications for Data Collection

  • Shen, Xing-Rong;Feng, Rui;Chai, Jing;Cheng, Jing;Wang, De-Bin
    • Asian Pacific Journal of Cancer Prevention
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    • 제15권22호
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    • pp.9731-9737
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    • 2014
  • Large scale secular registry or surveillance systems have been accumulating vast data that allow mathematical modeling of cancer incidence and mortality rates. Most contemporary models in this regard use time series and APC (age-period-cohort) methods and focus primarily on predicting or analyzing cancer epidemiology with little attention being paid to implications for designing cancer registry, surveillance or evaluation initiatives. This research models age-specific cancer incidence rates using logistic growth equations and explores their performance under different scenarios of data completeness in the hope of deriving clues for reshaping relevant data collection. The study used China Cancer Registry Report 2012 as the data source. It employed 3-parameter logistic growth equations and modeled the age-specific incidence rates of all and the top 10 cancers presented in the registry report. The study performed 3 types of modeling, namely full age-span by fitting, multiple 5-year-segment fitting and single-segment fitting. Measurement of model performance adopted adjusted goodness of fit that combines sum of squred residuals and relative errors. Both model simulation and performance evalation utilized self-developed algorithms programed using C# languade and MS Visual Studio 2008. For models built upon full age-span data, predicted age-specific cancer incidence rates fitted very well with observed values for most (except cervical and breast) cancers with estimated goodness of fit (Rs) being over 0.96. When a given cancer is concerned, the R valuae of the logistic growth model derived using observed data from urban residents was greater than or at least equal to that of the same model built on data from rural people. For models based on multiple-5-year-segment data, the Rs remained fairly high (over 0.89) until 3-fourths of the data segments were excluded. For models using a fixed length single-segment of observed data, the older the age covered by the corresponding data segment, the higher the resulting Rs. Logistic growth models describe age-specific incidence rates perfectly for most cancers and may be used to inform data collection for purposes of monitoring and analyzing cancer epidemic. Helped by appropriate logistic growth equations, the work vomume of contemporary data collection, e.g., cancer registry and surveilance systems, may be reduced substantially.

직접탐색법(直接探索法)을 이용한 이론적(理論的) 생장함수(生長函數)의 적용(適用) (Theoretical Growth Equations and Their Application with a Direct Search Method)

  • 서옥하
    • Journal of Forest and Environmental Science
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    • 제8권1호
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    • pp.35-49
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    • 1992
  • 대표적(代表的)인 이론적(理論的) 생장함수(生長函數)인 Mitscherlich, Gompertz, Logistic 함수(函數)를 jack pine (Pinus banksiana Lamb.) 50본의 반경생장(半徑生長)에 적용(適用)하여 보았다. 각함수(函數)의 계수(係數)값을 구하기 위해서는 최적화(最適化) 문제(問題)를 해결(解決)하는데 사용(使用)되는 직접탐구법(直接探究法)의 한 종류(種類)인 NELDER와 MEAD에 의한 제안(提案)된 방법(方法)을 이용(利用)하였다. 이는 특히 변수(變數)가 5 내지 6개 이하인 최적화(最適化) 문제(問題)를 해결(解決)하기 위한 효율적(效率的)인 방법(方法)이다. 모든 함수(函數)가 처음 예상(豫想)했던 것보다는 정확(精確)하게 실측치(實測値)와 일치(一致)되지는 않았지만 세가지 함수(函數)중에서 Mitscherlich 함수(函數)가 실측치(實測値)와 오차(誤差)가 가장적었다. 또 초기의 일정기간(一定期間) (1~35년, 1~55년, 1~95년)의 수목반경(樹木半徑) 실측치(實測値)를 자료(資料)로 하여, 3가지 생장양수(生長兩數)에 의해 추정(推定)한 최종(最終) 96년에서의 반경(半徑)을 실측치(實測値)와 비교(比較)해 본 결과(結果) Mischerlich, Gompertz, Logistic함수(函數)의 순(順)으로 적합(適合)한 것으로 나타났다.

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Growth curve estimates for wither height, hip height, and body length of Hanwoo steers (Bos taurus coreanae)

  • Park, Hu-Rak;Eum, Seung-Hoon;Roh, Seung-Hee;Sun, Du-Won;Seo, Jakyeom;Cho, Seong-Keun;Lee, Jung-Gyu;Kim, Byeong-Woo
    • 농업과학연구
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    • 제44권3호
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    • pp.384-391
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    • 2017
  • Growth curves in Hanwoo steers were estimated by Gompertz, Von Bertalanffy, Logistic, and Brody nonlinear models using growth data collected by the Hanwoo Improvement Center from a total of 6,973 Hanwoo (Bos taurus coreanae) steers 6 to 24 months old that were born between 1996 and 2015. The data included three parameters: A, mature size of body measurement; b, growth ratio; and, k, intrinsic growth rate. Nonlinear regression equations for wither height according to Gompertz, Von Bertalanffy, Logistic, and Brody models were $Y_t=144.7e^{-0.5869e^{-0.00301t}}$, $Y_t=145.3(1-0.1816e^{-0.00284t})^3$, $Y_t=143.1(1+0.7356e^{-0.00352t})^{-1}$, and $Y_t=146.8(1+0.4700e^{-0.00249t})^1$, respectively, while those for hip height were $Y_t=144.5e^{-0.5549e^{-0.00312t}}$, $Y_t=145.0(1-0.1724e^{-0.00295t})^3$, $Y_t=143.1(1+0.6863e^{-0.00360t})^{-1}$, and $Y_t=146.2(1+0.4501e^{-0.00263t})^1$, respectively. Equations for body length $Y_t=174.1e^{-0.8342e^{-0.00289t}}$, $Y_t=175.8(1-0.2500e^{-0.00265t})^3$, $Y_t=170.0(1+1.1548e^{-0.00363t})^{-1}$, and $Y_t=180.3(1+0.6077e^{-0.00215t})^1$, respectively, for the same models. Among the four models, the Brody model resulted in the lowest mean square error, with mean square errors of 31.79, 30.57, and 42.13, respectively, for wither height, hip height, and body length. Also, an estimated birth wither height, birth hip height, and birth body length (77.98, 80.57, and 70.97 cm, respectively) were lower in the Brody model than in other models. An inflection point was not observed during the growth phase of Hanwoo steer according to the growth curves calculated using Gompertz, Von Bertalanffy, and Logistic models. Based on the results, we concluded that the regression equation using the Brody model was the most appropriate among the four growth models. To obtain more accurate parameters, however, using data from a wider production period (from birth to shipping) would be required, and the development of a suitable model for body conformation traits would be needed.

신품종 토종닭의 계통과 성별에 따른 성장 특성에 관한 연구 (A Study on Growth Pattern in a New Synthetic Korean Native Commercial Chicken by Sex and Strains)

  • 김기곤;최은식;손시환
    • 한국가금학회지
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    • 제49권4호
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    • pp.229-237
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    • 2022
  • 본 연구는 신품종 토종종계로부터 생산된 토종실용닭 4계통의 성장 특성을 규명하고 출하일령 추정에 적합한 모형을 제시하고자 실시하였다. 체중은 발생시부터 12주령까지 2주 간격으로 개체별로 측정하였으며 성장곡선의 추정은 Von Berteralanffy, Gompertz 및 Logistic 모형을 이용하였다. 분석 결과, 발생시 체중을 제외한 모든 주령에서 수컷이 암컷보다 무겁게 나타났고, 계통 간 체중은발생시, 2주령 및 6주령을 제외하고는 차이가 없는 것으로 나타났다. 모든 성장곡선 모형의 결정계수와 수정된 결정계수는 97.4~99.7로 높은 적합도를 나타내었다. 성장곡선 모수 중성숙체중과 성장률은 수컷이 암컷보다 높게 나타났고, 성숙률은 암컷과 수컷이 비슷한 값을 보였다. 변곡점은 모형과 계통 별 차이가 있으나 암컷은 약 7주령, 수컷은 8~9주령으로 나타나 성별 간 10일 정도의 차이를 나타내었다. 성장곡선 모형의 거의 대부분은 실제 체중과 잘 일치하나, Von Bertalanffy 모형에서 수컷의 체중이 실제 체중과 다소의 차이를 보였다. 출하일령 예측을 위한 회귀함수의 결정계수는 0.9583~0.9746으로 나타나 예측 값에 대한 신뢰도가 높게 나타났다. 성장 곡선과 회귀식을 사용하여 추정한 주령 별 체중 값은 8주령과 10주령은 회귀식을 이용한 추정 값이, 12주령 체중은 Logistic 모형으로 추정한 값이 실제 체중과 가장 비슷하게 나타났다. 이러한 성장곡선에 따른 토종닭의 2 kg 도달일령의 평균 예측일수는 수컷이 62.0~64.6일, 암컷은 74.9~78.6일로 추정된다.

동충하초 Paecilomyces tenuipes C240의 균사체 배양에 의한 세포외 다당체 생산의 동력학적 연구 (A Kinetic Study for Exopolysaccharide Production in Submerged Mycelial Culture of an Entomopathogenic Fungus Paecilomyces tenuipes C240)

  • ;윤종원
    • 생명과학회지
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    • 제15권1호
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    • pp.15-20
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    • 2005
  • 동충하초 Paecilomyces tenuipes C240의 균사체 배양과정에서 균사체 성장, 세포외 다당체 생산, 기질감소 속도를 표현할 수 있는 동력학적 모델을 제시하였다. 균사체 성장은 Logistic식을, 세포외 다당체 생산은 Luedeking-Piret 식을, 기질소모는 Luedeking-Piret 유사식을 각각 적용함으로써, 전체 균사체 배양과정을 예측할 수 있었다. 모델식에서 사용된 주요 kineti, constant들은 다음과 같다: 균사체의 최대 비성장속도${\mu}m,\;0.7281\;h^{-1};$; 다당체 생산에서의 growth-associated constant $(\alpha),\;0.1743g(g\;cells)^{-1}$; non-growth-associated constant $(\beta),\;0.0019g(g\;cells)^{-1}\;;$ maintenance coefficient ($(m_s),\;0.0572g\;(g\;cells)^{-1}$·5L 발효조에서 얻은 균사체 성장, 세포외 다당체 생산, 기질감소 속도자료들을 모델에서 예측한 결과와 비교한 결과 서로 잘 일치하는 것으로 보아, 본 연구에서 제안된 모델식은 이 동충하초 균사체 배양공정의 scale-up등의 프로세스 설계에 응용가능 할 것이며, 다른 종류의 동충하초 균사체 배양공정에도 적용가능 할 것으로 판단된다.

The Determination and Prediction of Pine to Oak Forest Succession in Sugadaira, Central Japan

  • Jun, Kato;Hayashi, Ichiroku
    • The Korean Journal of Ecology
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    • 제26권4호
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    • pp.155-163
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    • 2003
  • In order to analyze the succession process from a pine forest to an oak forest, the tree growth of Pinus densiflora and Quercus mongolica ssp. crispula was monitored in a permanent quadrat for 23 years. The measurements were carried out for the stem diameter (DBH) of Pinus densiflora between 1977 and 1999 and for the height of Quercus mongolica ssp. crispula saplings between 1998 and 2000. The floristic composition and the locations of the individual P. densiflora and Q. mongolica ssp. crispula trees and saplings in the quadrat were recorded. P densiflora and Q. mongolica ssp. crispula individuals were randomly distributed within the quadrat. The relative growth rates (RGR) of DBH in P. densiflora were 0.085 $yr^{-1}$ for large trees and 0.056 $yr^{-1}$ for small trees in 1977. The RGR of height for Q. mongolica ssp. crispula was 0.122 $yr^{-1}$. The growth curve for DBH of P. densiflora was approximated by the logistic equation: $$DBH(t) = 30 {[1+1.16exp(-0.13 t)]}^{-1}$$ where DBH (t) the DBH (cm) in year t and t is the number of years since 1977. The growth in height of P. densiflora and Q. mongolica ssp. crispula was described by following equations: $$H (t) = 20.2 {[1+0.407exp(-0.137 t)]}^{-1} (P. densiflora)$$ $$H (t) = 30 {[1+20.7exp(-0.122 t)}^{-1} (Q. mongolica ssp. crispula)$$ Where H (t) is the tree height (m) in year t and t is the number of years since 1977 in P. densiflora and 1998 in Q. mongolica ssp. crispula. With these equations we predicted that the height of Q. mongolica ssp. crispula increases from 2 m in 1999 to 20 m in 2029. Therefore, Q. mongolica ssp. crispula and P. densiflora will be approximately the same height in 2029. The years required for succession from a pine forest to an oak forest are expected 33 with the range between 23 and 44 years.

Crown Ratio Models for Tectona grandis (Linn. f) Stands in Osho Forest Reserve, Oyo State, Nigeria

  • Popoola, F.S.;Adesoye, P.O.
    • Journal of Forest and Environmental Science
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    • 제28권2호
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    • pp.63-67
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    • 2012
  • Crown ratio is the ratio of live crown length to tree height. It is often used as an important predictor variable for tree growth equation. It indicates tree vigor and is a useful parameter in forest health assessment. The objective of the study was to develop crown ratio prediction models for Tectona grandis. Based on the data set from the temporary sample plots, several non linear equations including logistics, Chapman Richard and exponential functions were tested. These functions were evaluated in terms of coefficient of determination ($R^2$) and standard error of the estimate (SEE). The significance of the estimated parameters was also verified. Plot of residuals against estimated crown ratios were observed. Although the logistic model had the highest $R^2$ and the least SEE, Chapman-Richard and Exponential functions were observed to be more consistent in their predictive ability; and were therefore recommended for predicting crown ratio in the stand.

비선형(非線型) 생장함수(生長函數)를 이용(利用)한 임분생장(林分生長) 추정(推定) (Stand Growth Estimation Using Nonlinear Growth Equations)

  • 손영모;이경학;정영교
    • 한국산림과학회지
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    • 제86권2호
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    • pp.135-145
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    • 1997
  • 본 연구의 목적은 잣나무인공림과 신갈나무천연림에 있어 직경, 수고 및 재적생장을 설명할 수 있는 비선형생장식(非線形生長式) 추정과 이들 식의 논리적 타당성을 검정하기 위한 것이다. 이를 위해 전국에 분포한 지위지수 14인 임분에서 조사한 자료를 가지고 수확표 조제시 사용하였던 곡선식(曲線式) $Y=at^be^{-c/t}$와 9가지 비선형생장식(非線形生長式)을 적용, 분석하였으며 그 결과를 요약하면 다음과 같다. 먼저 수확표에서 사용된 곡선식은 자료범위내에서는 잘 적합시키고 있지만, 범위 이상에서는 직선적인 증가를 보이고 또 점근선(漸近線)을 가지고 있지 않아 과대치를 줄 위험이 있다. 비선형식중 Logistic식과 Sloboda식은 어린 임분에 있어 과대추정치를 나타내고 있는데 이는 식의 구조상 원점을 지나지 않기 때문이다. 또 이들 식은 타 식에 비하여 조기에 점근선에 도달하는 것으로 나다났다. 그리고 Gompertz식과 Ueno-Ohzaki식도 원점을 지나지 않는 식의 구조를 가지고 있다. 또한 Hossfeld식은 전반적으로 자료범위 이상의 임령에서는 여타 비선형식보다 큰 추정치를 주는데 이는 도달할 수 있는 최대치를 나타내는 모수 a값의 추정치가 크기 때문이다. 따라서 이 식은 범위 이상의 추정시 과대치를 주기 쉽다. 반면 Bertalanffy식은 임분의 유령기(幼齡基)와 노령기(老齡期)에서는 과소치, 그리고 그 사이에서는 과대추정치를 주고 있어, 식의 적용이 부적당한데, 이는 이 식이 동물의 생장추정을 위하여 개발된 것이기 때문이다. Korf식은 잣나무임분 생장추정시 노령기에 있어 과대추정치를 주는 경향이 있으며, 이는 신갈나무의 직경생장 추정시 확연하게 나타나고 있다. Ueno-Ohzaki식은 식의 구조상 모수 b에 따라 자료범위 밖의 노령기에 있어 직선적 상승 또는 조기 점근에 도달하고 있어 과대 휴은 과소치를 주기 쉽다. 전반적으로 잣나무와 신갈나무임분의 생장추정식으로는 Gompertz식, Chapman-Richards식 및 Weibull식이 현 자료범위 뿐만 아니라 범위밖의 유령림이나 노령림에 있어서도 가장 바람직한 식이라고 판단된다. 그리고 임목의 생장이란 시간이 지남에 따라 sigmoid curve를 그러므로 추후 생장식 도출에 있어서는 기존의 직선 및 곡선식보다 비선형식에 의한 것이 타당할 것이며, 앞으로 비선형식의 모수 추정, 특히 최대값인 모수 a의 정확한 추정을 위해서는 노령림에 대한 자료의 보완이 요구된다.

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Kinetics of Kojic Acid Fermentation by Aspergillus flavus Link S44-1 Using Sucrose as a Carbon Source under Different pH Conditions

  • Rosfarizan M.;Ariff A.B.
    • Biotechnology and Bioprocess Engineering:BBE
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    • 제11권1호
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    • pp.72-79
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    • 2006
  • Kojic acid production by Aspergillus flavus strain S44-1 using sucrose as a carbon source was carried out in a 250-mL shake flask and a 2-L stirred tank fermenter. For comparison, production of kojic acid using glucose, fructose and its mixture was also carried out. Kojic acid production in shake flask fermentation was 25.8 g/L using glucose as the sole carbon source, 23.6 g/L with sucrose, and 6.4 g/L from fructose. Reduced kojic acid production (13.5 g/L) was observed when a combination of glucose and fructose was used as a carbon source. The highest production of kojic acid (40.2 g/L) was obtained from 150 g/L sucrose in a 2 L fermenter, while the lowest kojic acid production (10.3 g/L) was seen in fermentation using fructose as the sole carbon source. The experimental data from batch fermentation and resuspended cell system was analysed in order to form the basis for a kinetic model of the process. An unstructured model based on logistic and Luedeking-Piret equations was found suitable to describe the growth, substrate consumption, and efficiency of kojic acid production by A. flavus in batch fermentation using sucrose. From this model, it was found that kojic acid production by A. flavus was not a growth-associated process. Fermentation without pH control (from an initial culture pH of 3.0) showed higher kojic acid production than single-phase pH-controlled fermentation (pH 2.5, 2.75, and 3.0).