• Biotechnology and Bioprocess Engineering:BBE
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• v.11 no.3
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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.

• Asian Pacific Journal of Cancer Prevention
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• v.15 no.22
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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.

• Journal of Forest and Environmental Science
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• v.8 no.1
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• pp.35-49
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• 1992

Three theoretical growth equations, i.e., the Mitscherlich, the Gompertz, and the Logistic equation, were applied to the radical stem growth of 50 jack pines (Pinus banksiana Lamb.). For the determination of the parameters in these equations, NELDER-MEAD's method was used, which is one of the direct-search methods of optimization. It has been known to be very convenient in dealing with the issues related to optimization, specifically where the number of parameters are less than 6. It was found that although all the equations did not appropriately work as expected, the Mitscherlich equation revealed the least discrapancy from the obsered value among three. Using these equations and the first certain period data, i. e., 35, 55, 75 years, the predection of radius of age 95 was investigated. Comparing to the observed value, the most valid equation was the Mitscherlich, and the next were the Gompertz and the Logistic, in order.

• Korean Journal of Agricultural Science
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• v.44 no.3
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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.

• Korean Journal of Poultry Science
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• v.49 no.4
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• pp.229-237
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• 2022

This study investigated the growth characteristics of four strains of newly developed synthetic Korean native commercial chickens (KNCs). We investigated a suitable growth curve model in KNCs and estimated the number of days to reach a 2 kg market weight. Body weight was measured at 2-week intervals from birth to 12 weeks of age. The growth curves were estimated using von Berteralanffy, Gompertz, and logistic functions. The results showed that males were significantly heavier than females at all ages, but there were no significant differences in body weight between strains, except at birth and 2 and 6 weeks of age. The coefficients of determination and adjusted determination of growth function had high goodness-of-fit (97.4~99.7). Of the growth curve parameters, the mature weight and growth ratio were higher in males than in females, but the maturity rate was similar in males and females. The inflection point occurred at approximately 7 weeks of age for females and 8 to 9 weeks of age for males. The weights estimated from the growth curve functions almost agreed with the actual weights, except for male weights estimated using the von Bertalanffy function. The coefficients of determination of the regression equations for weight to age were 0.9583 to 0.9746. The 8- and 10-week-old body weights estimated using the regression equation, and the 12-week-old weight estimated using the logistic function were most similar to the actual weight. Using these models, the estimated age of KNCs to reach 2 kg was 62.0~64.6 days for males and 74.9~78.6 days for females.

• Journal of Life Science
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• v.15 no.1 s.68
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• pp.15-20
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• 2005

The unstructured model was tested to describe mycelial growth, exopolysaccharide formation, and substrate consumption in submerged mycelial culture of Paeeiliomyees tenuipes C240. The Logistic equation for mycelial growth, the Luedeking-Piret equation for exopolysaccharide formation, and Luedeking­Piret-like equations for glucose consumptions were successfully incorporated into the model. The value of the key kinetic constants were: maximum specific growth rate ${\mu}m,\;0.7281\;h^{-1};$ growth­associated constant for exopolysaccharide production $(\alpha),\;0.1743g(g\;cells)^{-1}$; non-growth associated constant for exopolysaccharide production $(\beta),\;0.0019g(g\;cells)^{-1}\;;$ maintenance coefficient $(m_s),\;0.0572g\;(g\;cells)^{-1}$. When compared with batch experimental data, the model successfully provided a reasonable description for each parameter during the entire growth phase. The model showed that the production of exopolysaccharide in P. tenuipes C240 was growth-associated. The model tested in the present study can be applied to the design, scale-up, and control of fermentation process for other kinds of basidiomycetes or ascomycetes.

• The Korean Journal of Ecology
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• v.26 no.4
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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.

• Journal of Forest and Environmental Science
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• v.28 no.2
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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.

• Journal of Korean Society of Forest Science
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• v.86 no.2
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• pp.135-145
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• 1997

This study aimed at evaluating one curvilinear equation and nine non-linear equations for estimating stand growth characteristics(mean dbh, mean height and volume per ha) for the plantations of Pinus koraiensis and the natural stands of Quercus mongolica. The data were collected from 92 plots in Pines koraiensis stands and 83 plots in Quercus mongolica stands, and the site index of all the stands is 14. The curvilinear equation, $Y=at^be^{-c/t}$, used in preparing the yield tables was well fitted within the range of data, but was likely to give overestimates when extrapolating in old stage due to the tendency of linear increase. Among the non-linear equations, logistic equation and Sloboda equation gave overestimates in young stands and reached the asymptotic status early which means underestimates in old stage. Extrapolating in old stage, Hossfeld equation generally gave larger values than others due to its large estimates of parameter a, the maximum value. On the other hand, Bertalanffy equation gave underestimates in young and old stands and overestimates in middle-aged stands. The estimates with Korf equation was relatively low for Pinus koraiensis stands, and this tendency was more obvious in dbh growth of Quercus mongolica stands. Ueno-Ohzaki equation was liable to give over or underestimates depending on the value of parameter b when extrapolating in old stands. Considering the accuracy of estimates and the biological base of the growth equations, Gompertz equation, Chapman-Richards equation and Weibull equation were generally applicable for estimating the stand growth characteristics of both species in the whole range of stand ages including extrapolated range. To get more accurate and precise parameter estimates, more data, especially in old stands, should be required in further study.

• Biotechnology and Bioprocess Engineering:BBE
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• v.11 no.1
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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).