Logistic Equation (logistic + equation)

Distribution by Scientific Domains


Selected Abstracts


Color Changes of Tomato Purees During Storage at Freezing Temperatures

JOURNAL OF FOOD SCIENCE, Issue 6 2002
S. Calligaris
ABSTRACT: The changes in color of unblanched and blanched tomato purees during storage at ,7 and ,18 °C were studied. They showed the typical sigmoidal-shape of radical reactions and were well described by the Logistic equation (R > 0.95; P < 10,3). After an initial induction time, a progressive increase in the bleaching rate was found for both unblanched and blanched frozen tomato purees. The color changes for the unblanched sample were statistically higher than those for the heated one. In the former case, the bleaching of carotenoids was attributed to both chemical and enzyme-catalyzed oxidation reactions. The effect of storage temperatures on color changes was appreciable only in the case of the unblanched tomato samples. [source]


A multivariate logistic regression equation to screen for dysglycaemia: development and validation

DIABETIC MEDICINE, Issue 5 2005
B. P. Tabaei
Abstract Aims To develop and validate an empirical equation to screen for dysglycaemia [impaired fasting glucose (IFG), impaired glucose tolerance (IGT) and undiagnosed diabetes]. Methods A predictive equation was developed using multiple logistic regression analysis and data collected from 1032 Egyptian subjects with no history of diabetes. The equation incorporated age, sex, body mass index (BMI), post-prandial time (self-reported number of hours since last food or drink other than water), systolic blood pressure, high-density lipoprotein (HDL) cholesterol and random capillary plasma glucose as independent covariates for prediction of dysglycaemia based on fasting plasma glucose (FPG) , 6.1 mmol/l and/or plasma glucose 2 h after a 75-g oral glucose load (2-h PG) , 7.8 mmol/l. The equation was validated using a cross-validation procedure. Its performance was also compared with static plasma glucose cut-points for dysglycaemia screening. Results The predictive equation was calculated with the following logistic regression parameters: P = 1 + 1/(1 + e,X) = where X = ,8.3390 + 0.0214 (age in years) + 0.6764 (if female) + 0.0335 (BMI in kg/m2) + 0.0934 (post-prandial time in hours) + 0.0141 (systolic blood pressure in mmHg) , 0.0110 (HDL in mmol/l) + 0.0243 (random capillary plasma glucose in mmol/l). The cut-point for the prediction of dysglycaemia was defined as a probability , 0.38. The equation's sensitivity was 55%, specificity 90% and positive predictive value (PPV) 65%. When applied to a new sample, the equation's sensitivity was 53%, specificity 89% and PPV 63%. Conclusions This multivariate logistic equation improves on currently recommended methods of screening for dysglycaemia and can be easily implemented in a clinical setting using readily available clinical and non-fasting laboratory data and an inexpensive hand-held programmable calculator. [source]


Comparison of the size selectivity of diamond (PA) and square (PE) mesh codends for deepwater crustacean species in the Antalya Bay, eastern Mediterranean

JOURNAL OF APPLIED ICHTHYOLOGY, Issue 4 2009
M. C. Deval
Summary The aim of this study was to compare selectivity results of currently used 44 mm nominal polyamide (PA) diamond mesh- and alternatively suggested 40 mm nominal polyethylene (PE) square mesh- codends in the deepwater crustacean trawl fishery in the Antalya Bay, eastern Mediterranean. Selectivity experiments were carried out during targeted trawling of four commonly harvested crustacean species: giant red shrimp Aristaeomorpha foliacea, ,blue and red' shrimp Aristeus antennatus, rose shrimp Parapenaeus longirostris, and pandalid shrimp Plesionika martia. A conventional bottom trawl of 600 meshes around the fishing circle was operated onboard a commercial stern trawler between 6 and 18 June 2007. Depth of the fishing area varied between 441 and 630 m. Data were collected using the covered codend technique, and analyzed using a logistic equation with maximum likelihood for individual and pooled hauls. The commercially used trawl codend was unable to release immature crustaceans. Selectivity parameters of the three species of crustaceans were distinctly lower when collected with the polyamide diamond mesh than with the polyethylene square mesh, except in the case of giant red shrimp for which values were similar. However, the present and previous results show that in square mesh codends, mesh sizes must be more than 40 mm in order to keep catches clear of specimens below minimum landing sizes or 50% sexual maturity sizes of crustaceans in the Mediterranean. This study suggests that regulating mesh size by requiring square mesh openings during deep water crustacean trawling of the eastern Mediterranean is essential for the release of immature individuals. [source]


Sorting grid trials to improve size selectivity of red mullet (Mullus barbatus) and annular sea bream (Diplodus annularis) in Turkish bottom trawl fishery

JOURNAL OF APPLIED ICHTHYOLOGY, Issue 3 2008
C. Ayd
Summary Sorting grids with two different bar spacings (12 mm and 14 mm) were tested to improve size selectivity of the commercially important fish species, red mullet (Mullus barbatus) and annular sea bream (Diplodus annularis), in Turkish bottom trawl fishery. Fishing trials were carried out with R/V ,Egesüf' between April and May 2003 in Izmir Bay, Aegean Sea, using a traditional bottom trawl. Selectivity data were collected by the top cover method and analyzed by means of a logistic equation with the maximum likelihood method. Selectivity parameters for individual hauls were obtained with the software program cc 2000. Mean selectivity was also estimated and compared using the EC Model software that takes between-haul variations into account. The codend catch size as an additional explanatory variable was used in the comparison. The Kolmogorov,Smirnov (K,S) test was also applied to detect differences between length-frequency distributions in the upper and lower bags of the 12 and 14 mm bar spacings for red mullet and annular sea bream. The mean L50 values of red mullet were 8.7 and 10.0 cm with the 12 and 14 mm grids, respectively. The L50 value of 14 mm was comparable with the L50 value of the codend mesh size; however, the 12 mm value was rather low. The mean L50 values of 12 and 14 mm bar spacings were 8.8 and 10.4 cm for annular sea bream, respectively; the value of 14 mm bar spacing was very close to 50% size at sexual maturity of the species (10.5 cm). The K,S test indicated length distributions of red mullet and annular sea bream in the 12 and 14 mm upper and lower bags as significantly different (P < 0.05). These results show that improving the size selectivity in a multi-species fishery using a single selective device is rather difficult. However, higher size selectivity can be obtained when considering the minimum landing size or the 50% sexual maturity size for a given species. [source]


Single Laboratory Method Performance Evaluation for the Analysis of Total Food Folate by Trienzyme Extraction and Microplate Assay

JOURNAL OF FOOD SCIENCE, Issue 5 2007
L. Chen
ABSTRACT:, Single laboratory method performance parameters, including the calibration curve, accuracy, recovery, precision, limit of detection (LOD), and limit of quantification (LOQ), were evaluated for the analysis of total food folate by the trienzyme extraction and microplate assay with Lactobacillus casei subsp. rhamnosus. Standard Reference Material (SRM) 1546 (meat homogenate), SRM 2383 (baby food composite), SRM 1846 (infant formula), Certified Reference Material (CRM) 121 (wholemeal flour), and CRM 485 (mixed vegetables), representing a broad selection of food matrices, were used to evaluate the performance of the method. A generated 4-parameter logistic equation of the calibration curve was y= (0.0705 , 1.0396)/(1 + (x/0.0165) 1.3072) + 1.0396 (P < 0.0001). The test of parallelism demonstrated that matrix components in the food extracts did not affect the accuracy. Measured values of the SRMs and CRMs were within their certified or reference values. Recoveries for all reference materials met the requirements of the AOAC guidelines for single laboratory validation. Precision measured as repeatability, including simultaneous and consecutive replicates for each SRM and CRM, met the Horwitz criterion. LOD and LOQ values were 0.3 and 0.6 ,g/100 g, respectively. The results showed that trienzyme digestion using ,-amylase, PronaseR, and conjugase from chicken pancreas coupled with a 96-well microplate assay provided a highly accurate, reproducible, and sensitive method for the determination of folate in a variety of foods. [source]


Existence, uniqueness, stochastic persistence and global stability of positive solutions of the logistic equation with random perturbation

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2007
Chunyan Ji
Abstract This paper discusses a randomized logistic equation (1) with initial value x(0)=x0>0, where B(t) is a standard one-dimension Brownian motion, and ,,(0, 0.5). We show that the positive solution of the stochastic differential equation does not explode at any finite time under certain conditions. In addition, we study the existence, uniqueness, boundedness, stochastic persistence and global stability of the positive solution. Copyright © 2006 John Wiley & Sons, Ltd. [source]


Robust parameter estimation during logistic modeling of batch and fed-batch culture kinetics

BIOTECHNOLOGY PROGRESS, Issue 3 2009
Chetan T. Goudar
Abstract Methods for robust logistic modeling of batch and fed-batch mammalian cell cultures are presented in this study. Linearized forms of the logistic growth, logistic decline, and generalized logistic equation were derived to obtain initial estimates of the parameters by linear least squares. These initial estimates facilitated subsequent determination of refined values by nonlinear optimization using three different algorithms. Data from BHK, CHO, and hybridoma cells in batch or fed-batch cultures at volumes ranging from 100 mL,300 L were tested with the above approach and solution convergence was obtained for all three nonlinear optimization approaches for all data sets. This result, despite the sensitivity of logistic equations to parameter variation because of their exponential nature, demonstrated that robust estimation of logistic parameters was possible by this combination of linearization followed by nonlinear optimization. The approach is relatively simple and can be implemented in a spreadsheet to robustly model mammalian cell culture batch or fed-batch data. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009 [source]


Variable Stoichiometry during the Laccase-Catalyzed Oxidation of Aqueous Phenol

BIOTECHNOLOGY PROGRESS, Issue 2 2007
Selvia Kurniawati
The oxidation of aqueous phenol through the catalytic action of laccase from Trametes versicolor was studied over a wide range of phenol concentrations and enzyme activities. The stoichiometric ratio, which is defined as the molar ratio of phenol transformed to oxygen consumed in the catalytic reaction, was found to increase with phenol concentration in the reaction mixture from a theoretical lower limit of 1 and to approach a theoretical upper limit of 4. A logistic equation was proposed to relate reaction stoichiometry to substrate concentration and was successfully used to relate these parameters over a range of phenol concentrations extending from approximately 0.15 to 8 mM. This expression was incorporated into two kinetic models in order to account for variations in reaction stoichiometry during the reaction and to extend the range over which the models may be accurately applied. The new models demonstrated an improved ability to predict concentrations of phenol and oxygen over time in a closed batch reaction system. [source]


Logistic Equations Effectively Model Mammalian Cell Batch and Fed-Batch Kinetics by Logically Constraining the Fit

BIOTECHNOLOGY PROGRESS, Issue 4 2005
Chetan T. Goudar
A four-parameter logistic equation was used to fit batch and fed-batch time profiles of viable cell density in order to estimate net growth rates from the inoculation through the cell death phase. Reduced three-parameter forms were used for nutrient uptake and metabolite/product formation rate calculations. These logistic equations constrained the fits to expected general concentration trends, either increasing followed by decreasing (four-parameter) or monotonic (three-parameter). The applicability of this approach was first verified for Chinese hamster ovary (CHO) cells cultivated in 15-L batch bioreactors. Cell density, metabolite, and nutrient concentrations were monitored over time and used to estimate the logistic parameters by nonlinear least squares. The logistic models fit the experimental data well, supporting the validity of this approach. Further evidence to this effect was obtained by applying the technique to three previously published batch studies for baby hamster kidney (BHK) and hybridoma cells in bioreactors ranging from 100 mL to 300 L. In 27 of the 30 batch data sets examined, the logistic models provided a statistically superior description of the experimental data than polynomial fitting. Two fed-batch experiments with hybridoma and CHO cells in benchtop bioreactors were also examined, and the logistic fits provided good representations of the experimental data in all 25 data sets. From a computational standpoint, this approach was simpler than classical approaches involving Monod-type kinetics. Since the logistic equations were analytically differentiable, specific rates could be readily estimated. Overall, the advantages of the logistic modeling approach should make it an attractive option for effectively estimating specific rates from batch and fed-batch cultures. [source]


Experimental and mathematical study of the influence of growth factors on the growth kinetics of adult human articular chondrocytes,

JOURNAL OF CELLULAR PHYSIOLOGY, Issue 3 2005
Andrea Barbero
This study aimed at determining how kinetic parameters of adult human articular chondrocytes (AHAC) growth are modulated by the growth factor combination TGF,1, FGF-2, and PDGF BB (TFP), recently shown to stimulate AHAC proliferation. AHAC, isolated from cartilage biopsies of three individuals, were cultured in medium without (CTR) or with TFP. For growth curves, AHAC were seeded at 1,000 cells/cm2 and cultured for 12 days, with cell numbers measured fluorimetrically in the same wells every 12 h. For microcolony tests, AHAC were seeded at 2.5 cells/cm2 and cultured for 6 days, with cell numbers determined for each microcolony by phase contrast microscopy every 8 h. A mathematical model combining delay and logistic equations was developed to capture the growth kinetic parameters and to enable the description of the complete growth process of the cell culture. As compared to CTR medium, the presence of TFP increased the number of cells/well starting from the fifth day of culture, and a four-fold larger cell number was reached at confluency. For single microcolonies, TFP reduced the time for the first cell division by 26.6%, the time for subsequent cell divisions (generation time) by 16.8%, and the percentage of quiescent cells (Qc) by 42.5%. The mathematical model fitted well the experimental data of the growth kinetic. Finally, using both microcolony tests and the mathematical model, we determined that prolonged cell expansion induces an enrichment of AHAC with shorter first division time, but not of those with shorter generation time. © 2005 Wiley-Liss, Inc. [source]


Robust parameter estimation during logistic modeling of batch and fed-batch culture kinetics

BIOTECHNOLOGY PROGRESS, Issue 3 2009
Chetan T. Goudar
Abstract Methods for robust logistic modeling of batch and fed-batch mammalian cell cultures are presented in this study. Linearized forms of the logistic growth, logistic decline, and generalized logistic equation were derived to obtain initial estimates of the parameters by linear least squares. These initial estimates facilitated subsequent determination of refined values by nonlinear optimization using three different algorithms. Data from BHK, CHO, and hybridoma cells in batch or fed-batch cultures at volumes ranging from 100 mL,300 L were tested with the above approach and solution convergence was obtained for all three nonlinear optimization approaches for all data sets. This result, despite the sensitivity of logistic equations to parameter variation because of their exponential nature, demonstrated that robust estimation of logistic parameters was possible by this combination of linearization followed by nonlinear optimization. The approach is relatively simple and can be implemented in a spreadsheet to robustly model mammalian cell culture batch or fed-batch data. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009 [source]


Logistic Equations Effectively Model Mammalian Cell Batch and Fed-Batch Kinetics by Logically Constraining the Fit

BIOTECHNOLOGY PROGRESS, Issue 4 2005
Chetan T. Goudar
A four-parameter logistic equation was used to fit batch and fed-batch time profiles of viable cell density in order to estimate net growth rates from the inoculation through the cell death phase. Reduced three-parameter forms were used for nutrient uptake and metabolite/product formation rate calculations. These logistic equations constrained the fits to expected general concentration trends, either increasing followed by decreasing (four-parameter) or monotonic (three-parameter). The applicability of this approach was first verified for Chinese hamster ovary (CHO) cells cultivated in 15-L batch bioreactors. Cell density, metabolite, and nutrient concentrations were monitored over time and used to estimate the logistic parameters by nonlinear least squares. The logistic models fit the experimental data well, supporting the validity of this approach. Further evidence to this effect was obtained by applying the technique to three previously published batch studies for baby hamster kidney (BHK) and hybridoma cells in bioreactors ranging from 100 mL to 300 L. In 27 of the 30 batch data sets examined, the logistic models provided a statistically superior description of the experimental data than polynomial fitting. Two fed-batch experiments with hybridoma and CHO cells in benchtop bioreactors were also examined, and the logistic fits provided good representations of the experimental data in all 25 data sets. From a computational standpoint, this approach was simpler than classical approaches involving Monod-type kinetics. Since the logistic equations were analytically differentiable, specific rates could be readily estimated. Overall, the advantages of the logistic modeling approach should make it an attractive option for effectively estimating specific rates from batch and fed-batch cultures. [source]