scholarly journals Method to generate growth and degrowth models obtained from combinations of existing models applied to agrarian sciences

2019 ◽  
Author(s):  
André Luiz Pinto dos Santos ◽  
Guilherme Rocha Moreira ◽  
Frank Gomes-Silva ◽  
Cícero Carlos Ramos de Brito ◽  
Maria Lindomárcia Leonardo da Costa ◽  
...  
Keyword(s):  
Least Squares Method ◽  
Kinetic Curve ◽  
Information Criterion ◽  
Compartment Model ◽  
Gas Production ◽  
Coefficient Of Determination ◽  
Von Bertalanffy ◽  
Absolute Deviation ◽  
Two Compartment Model

AbstractMathematical models that describe gas production are widely used to estimate the rumen degradation digestibility and kinetics. The present study presents a method to generate models by combining existing models and to propose the von Bertalanffy-Gompertz two-compartment model based on this method. The proposed model was compared with the logistic two-compartment one to indicate which best describes the kinetic curve of gas production through the semi-automatedin vitrotechnique from different pinto peanut cultivars. The data came from an experiment grown and harvested at the Far South Animal Sciences station (Essul) in Itabela, BA, Brazil and gas production was read at 2, 4, 6, 8, 10, 12, 14, 17, 20, 24, 28, 32, 48, 72, and 96 h after the start of thein vitrofermentation process. The parameters were estimated by the least squares method using the iterative Gauss-Newton process in the software R version 3.4.1. The best model to describe gas accumulation was based on the adjusted coefficient of determination, residual mean squares, mean absolute deviation, Akaike information criterion, and Bayesian information criterion. The von Bertalanffy-Gompertz two-compartment model had the best fit to describe the cumulative gas production over time according to the methodology and conditions of the present study.

scholarly journals New model of evaluation of sunflower and corn silages by the in vitro gas production technique

2020 ◽  
Vol 41 (4) ◽  
pp. 1373
Author(s):  
André Luiz Pinto dos Santos ◽  
Cícero Carlos Ramos de Brito ◽  
Guilherme Rocha Moreira ◽  
Frank Gomes-Silva ◽  
Moacyr Cunha Filho ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Least Squares Method ◽  
Kinetic Curve ◽  
Information Criterion ◽  
Gas Production ◽  
Corn Silage ◽  
Coefficient Of Determination ◽  
Von Bertalanffy ◽  
Production Technique

This study aimed to propose a model called Two-compartment Logistic-von Bertalanffy (LVB) and to identify among the proposed and Two-compartment Logistic (TL) models the one that has the best goodness of fit to the kinetic curve of cumulative gas production (CGP) of sunflower and corn silages alone and combined using the in vitro semi-automated gas production technique. A random block split-plot experimental design was employed in which the inoculums were the blocks, the incubation times were the split-plots, and the experimental diets were: CS - corn silage, SS - sunflower silage (as single roughage), and their mixtures, i.e., 340SS (660 g kg-1 corn silage and 340 g kg-1 sunflower silage) and 660SS (340 g kg-1 corn silage and 660 g kg-1 sunflower silage). The parameters were estimated by the least squares method using the iterative Gauss-Newton process in the software R version 3.4.1. The criteria adopted were: adjusted coefficient of determination (R2adj.), residual mean squares (RMS), mean absolute deviation (MAD), Akaike information criterion (AIC), Bayesian information criterion (BIC), and relative efficiency (RE). The TL model had higher R2adj. values compared to LVB, however, such difference may be considered negligible. The LVB model had RE above one, which indicates it is superior to the TL model, in addition to the lowest RMS, MAD, AIC, and BIC values, The Two-compartment Logistic-von Bertalanffy model had the best fit to describe the CGP over time according to the methodology and conditions of the present study.

scholarly journals Proposals of non-linear models to adjust in vitro gas production at different incubation times in cassava genotypes

2021 ◽  
Vol 43 ◽  
pp. e22
Author(s):  
André Luiz Pinto dos Santos ◽  
Frank Sinatra Gomes da Silva ◽  
Guilherme Rocha Moreira ◽  
Cícero Carlos Ramos de Brito ◽  
Maria Lindomárcia Leonardo da Costa ◽  
...  
Keyword(s):  
Linear Models ◽  
Least Squares Method ◽  
Logistic Models ◽  
Information Criterion ◽  
Gas Production ◽  
Coefficient Of Determination ◽  
Absolute Deviation ◽  
In Vitro Gas Production ◽  
The One

The present study aimed to propose new two-compartment models from the combination of the Gompertz, Logistic and Von Bertalanffy models and to identify between Gompertz and Logistic models, in their uni and two-compartiment versions, the one that presents the highest quality of fit to cumulative gas production curves of five cassava genotypes: Brasília, Engana Ladrão, Dourada, Gema de Ovo e Amansa Burro. The gas production readings were 2, 4, 6, 8, 10, 12, 14, 17, 20, 24, 28, 32, 48, 72, and 96 hours after the start of the in vitro fermentation process. The estimation of the parameters for the models was made by the least squares method through the Gauss-Newton iterative process. The selection of the best model to describe the gas accumulation was based on the adjusted coefficient of determination, residual mean squares, mean absolute deviation, Akaike information criterion and Bayesian information criterion. Among the adjusted models, the proposed models were the best to describe the accumulation of gases over time according to the methodology and conditions under which this study was developed.

scholarly journals Method to generate growth and degrowth models obtained from differential equations applied to agrarian sciences

2018 ◽  
Vol 39 (6) ◽  
pp. 2659 ◽  
Author(s):  
André Luiz Pinto dos Santos ◽  
Guilherme Rocha Moreira ◽  
Cicero Carlos Ramos de Brito ◽  
Frank Gomes-Silva ◽  
Maria Lindomárcia Leonardo da Costa ◽  
...  
Keyword(s):  
Differential Equations ◽  
Goodness Of Fit ◽  
Least Squares Method ◽  
Growth Curves ◽  
Information Criterion ◽  
Coefficient Of Determination ◽  
Absolute Deviation ◽  
Marquardt Algorithm ◽  
Maturation Rate ◽  
Biological Interpretation

This study aims to propose a method to generate growth and degrowth models using differential equations as well as to present a model based on the method proposed, compare it with the classic linear mathematical models Logistic, Von Bertalanffy, Brody, Gompertz, and Richards, and identify the one that best represents the mean growth curve. To that end, data on Undefined Breed (UB) goats and Santa Inês sheep from the works of Cavalcante et al. (2013) and Sarmento et al. (2006a), respectively, were used. Goodness-of-fit was measured using residual mean squares (RMS), Akaike information criterion (AIC), Bayesian information criterion (BIC), mean absolute deviation (MAD), and adjusted coefficient of determination . The models’ parameters (?, weight at adulthood; ?, an integration constant; ?, shape parameter with no biological interpretation; k, maturation rate; and m, inflection point) were estimated by the least squares method using Levenberg-Marquardt algorithm on the software IBM SPSS Statistics 1.0. It was observed that the proposed model was superior to the others to study the growth curves of goats and sheep according to the methodology and conditions under which the present study was carried out.

scholarly journals The use of the nonlinear models in the growth of pears of ‘Shinseiki’ cultivar

2017 ◽  
Vol 48 (1) ◽  
Author(s):  
Thais Destefani Ribeiro ◽  
Taciana Villela Savian ◽  
Tales Jesus Fernandes ◽  
Joel Augusto Muniz
Keyword(s):  
Logistic Model ◽  
Least Squares Method ◽  
Nonlinear Models ◽  
Logistic Models ◽  
Information Criterion ◽  
Fruit Weight ◽  
Coefficient Of Determination ◽  
Pear Fruit ◽  
Asian Pear ◽  
Residual Correlations

ABSTRACT: The goal of this study was to elucidate the growth and development of the Asian pear fruit, on the grounds of length, diameter and fresh weight determined over time, using the non-linear Gompertz and Logistic models. The specifications of the models were assessed utilizing the R statistical software, via the least squares method and iterative Gauss-Newton process (DRAPER & SMITH, 2014). The residual standard deviation, adjusted coefficient of determination and the Akaike information criterion were used to compare the models. The residual correlations, observed in the data for length and diameter, were modeled using the second-order regression process to render the residuals independent. The logistic model was highly suitable in demonstrating the data, revealing the Asian pear fruit growth to be sigmoid in shape, showing remarkable development for three variables. It showed an average of up to 125 days for length and diameter and 140 days for fresh fruit weight, with values of 72mm length, 80mm diameter and 224g heavy fat.

scholarly journals A COMPARISON OF NONLINEAR MODELS FOR DESCRIBING WEIGHT-AGE DATA IN ANGLO-NUBIAN DOES

2019 ◽  
Vol 32 (1) ◽  
pp. 251-258 ◽  
Author(s):  
Francisco Arthur Arré ◽  
José Elivalto Guimarães Campelo ◽  
José Lindenberg Rocha Sarmento ◽  
Luiz Antônio Silva Figueiredo Filho ◽  
Diego Helcias Cavalcante
Keyword(s):  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Nonlinear Models ◽  
Age Groups ◽  
Coefficient Of Determination ◽  
Group Model ◽  
Age Group ◽  
Von Bertalanffy ◽  
Absolute Deviation ◽  
Model Interaction

ABSTRACT The objective of this study was to determine the optimum age at last weighing and compare the goodness of fit of nonlinear models used to fit longitudinal weight-age data to describe the growth pattern of Anglo-Nubian does. Weights of 104 animals from birth to 60 months of age were grouped into 10 age groups at six-month intervals. In each age group, parameters A (asymptotic weight), B (integration constant), and K (maturity index) were estimated using the Brody, Gompertz, logistic, and von Bertalanffy models. Data were analyzed using analysis of variance in a factorial design (10 age groups × 4 nonlinear models). The age group × model interaction was not significant. Mean estimates of A, B, and K were significantly different between age groups up to 30 months (p < 0.05), indicating that the estimated curve is affected by weights taken before this age independent of the model. The values of mean squared error (MSE), mean absolute deviation (MAD), coefficient of determination (R2) and Rate of convergence (RC) at each age group up to 30 months were compared to determine the goodness of fit of nonlinear models. The ranking of fit was logistic, Brody, von Bertalanffy, and Gompertz. The logistic and Brody models respectively estimated the smallest and largest asymptotic weight. Longitudinal weight records taken until 30 months of age are most appropriate for estimating the growth of Anglo-Nubian does using nonlinear models.

scholarly journals Kinetics of In Vitro Gas Production and Fitting Mathematical Models of Corn Silage

Fermentation ◽  
2021 ◽  
Vol 7 (4) ◽  
pp. 298
Author(s):  
Camila da Silva Zornitta ◽  
Luis Carlos Vinhas Ítavo ◽  
Camila Celeste Brandão Ferreira Ítavo ◽  
Geraldo Tadeu dos Santos ◽  
Alexandre Menezes Dias ◽  
...  
Keyword(s):  
Mathematical Models ◽  
Gas Production ◽  
Feed Additives ◽  
Corn Silage ◽  
Feed Additive ◽  
Coefficient Of Determination ◽  
Production Data ◽  
In Vitro Gas Production ◽  
Kinetics Of

This study aimed at examining the effects of rumen inoculum of steers receiving different combinations of ionophore and probiotics in their diets on in vitro gas production of corn silage. The fitting of gas production was performed with five mathematical models and its kinetics was evaluated. Four crossbred steers (403.0 ± 75.5 kg body weight) with ruminal cannula were assigned to a 4 × 4 Latin square design. The additives used were Monensin sodium (Rumensin® 100, 3 g/day), Bacillus toyonensis (Micro-Cell Platinum® 109, 1 g/day) and Saccharomyces cerevisiae boulardii (ProTernative®20, 0.5 g/day). Additives were arranged into the following treatments, supplied daily into total mixed diet: (1) Monensin; (2) Monensin + B. toyonensis; (3) Monensin + S. boulardii; and (4) B. toyonensis + S. boulardii. The gas production data were fitted into the models of Gompertz, Groot, Ørskov, Brody, Richards, and Dual-pool Logistic. A perfect agreement between observed and predicted values in curves of accumulated in vitro gas production was observed in the Groot and Richards models, with higher coefficient of determination (R2 = 0.770 and 0.771, respectively), concordance correlation coefficient (CCC = 0.871 and 0.870, respectively), and root mean square error of prediction (RMSEP = 1.14 and 1.15, respectively). Evaluating the feed additives throughout the Groot model, the B. toyonensis + S. boulardii treatment presented higher VF (12.08 mL/100 mg of DM; p = 0.0022) than Monensin and Monensin + S. boulardii (9.16 and 9.22 mL/100 mg of DM, respectively). In addition, the fractional rate of gas production (k) was higher (p = 0.0193) in B. toyonensis + S. boulardii than in Monensin, not presenting a statistical difference (p > 0.05) from the other two treatments. Additionally, with the time of beginning to gas production, the lag time (λ), was greater (p < 0.001) with Monensin and Monensin + B. toyonensis than with Monensin + S. boulardii and B. toyonensis + S. boulardii. The combination of Monensin and probiotics (B. toyonensis + S. boulardii) resulted in better kinetics of degradation of corn silage, being that the Groot and Richards models had the best fit for estimates of the in vitro gas production data of corn silage tested with different feed additive combinations.

scholarly journals Growth models for morphological traits of sunn hemp

2017 ◽  
Vol 38 (5) ◽  
pp. 2933
Author(s):  
Cláudia Marques de Bem ◽  
Alberto Cargnelutti Filho ◽  
Giovani Facco ◽  
Denison Esequiel Schabarum ◽  
Daniela Lixinski Silveira ◽  
...  
Keyword(s):  
Morphological Traits ◽  
Logistic Models ◽  
Information Criterion ◽  
Coefficient Of Determination ◽  
Percentage Error ◽  
Mean Absolute Deviation ◽  
Absolute Deviation ◽  
Sunn Hemp ◽  
Number Of Leaves ◽  
Second Period

The objective of the present study was to fit Gompertz and Logistic nonlinear to descriptions of morphological traits of sunn hemp. Two uniformity trials were conducted and the crops received identical treatment in all experimental area. Sunn hemp seeds were sown in rows 0.5 m apart with a plant density of 20 plants per row meter in a usable area of 52 m × 50 m. The following morphological traits were evaluated: plant height (PH), number of leaves (NL), stem diameter (SD), and root length (RL). These traits were assessed daily during two sowing periods—seeds were sown on October 22, 2014 (first period) and December 3, 2014 (second period). Four plants were randomly collected daily, beginning 7 days after first period and 13 days after for second period, totaling 94 and 76 evaluation days, respectively. For Gompertz models the equation was used y=a*e^((?-e?^((b-c*xi))and Logistic models the equation was used yi= a/(1+e^((-b-c*xi)). The inflection points of the Gompertz and Logistic models were calculated and the goodness of fit was quantified using the adjusted coefficient of determination, Akaike information criterion, standard deviation of residuals, mean absolute deviation, mean absolute percentage error, and mean prediction error. Differences were observed between the Gompertz and Logistic models and between the experimental periods in the parameter estimate for all morphological traits measured. Satisfactory growth curve fittings were achieved for plant height, number of leaves, and stem diameter in both models using the evaluation criteria: coefficient of determination (R²), Akaike information criterion (AIC), standard deviation of residuals (SDR), mean absolute deviation (MAD), mean absolute percentage error (MAPE), and mean prediction error (MPE).

Single Dose Administration of rFVIIa and NN1731 in Two Hemophilia A Dogs.

Blood ◽  
2007 ◽  
Vol 110 (11) ◽  
pp. 3144-3144 ◽  
Author(s):  
Mirella Ezban ◽  
Lone Frost ◽  
Dorthe Viuff ◽  
Judi Møss ◽  
Mark Kloos ◽  
...  
Keyword(s):  
Hemophilia A ◽  
Ex Vivo ◽  
Compartment Model ◽  
Initial Distribution ◽  
Coagulation Assays ◽  
Two Compartment Model ◽  
Dose Study ◽  
Related Proteins

Abstract Introduction: The objective of this pilot study was to evaluate and compare the pharmacokinetic and pharmacodynamic (PK/PD) profile of rFVIIa and NN1731 in two hemophilia A dogs. In addition, it was the aim to evaluate the use of TEG for monitoring rFVIIa/NN1731 activity after in vivo administration and to compare with ex vivo spiking data from a previous study. NN1731 is a new rFVIIa analoge with enhanced activity (Allen et al. Arterioscler. Thromb. Vasc. Biol.2007;27:683–689). In hemophilia patients as well as hemophilia dogs the clot formation is impaired and reflected in coagulation assays such as thromboelastography (TEG) and APTT. The choice of hemophilia dogs is based upon the knowledge that the pharmacokinetics of human coagulations factors (FVIII, FIX and rFVIIa) as well as the effective dose is similar to that in humans. In normal dogs, it is not possible to evaluate the effect of these procoagulant proteins in coagulation assays as no impaired clotting is observed. Methods: rFVIIa and NN1731 (280 μg/kg IV) were administered to two hemophilia dogs on separate days and plasma samples collected at different time points. FVIIa activity was measured by the FVIIa clot assay and values were used for pharmacokinetic assessment. The same pharmacokinetic models, a non-compartmental method and a two compartment model, respectively, were used as was the case in the First Human Dosing (FHD) trial of NN1731 (NN1731–1639). Analysis of PD markers in dogs included: APTT, PT and whole blood thromboelastography analysis, recently developed for use in hemophilia dogs. Results: Based on the FVIIa activity profile in the two dogs it was observed that the values obtained at the first time point (C5 min), were higher after treatment with NN1731 than after rFVIIa. All activity based assays including TEG demonstrated that NN1731 was cleared faster than rFVIIa., FVIIa activity (FVIIa clot assay), showed a rapid initial distribution and/or elimination of FVIIa activity (t1/2α:0.3 h) followed by a less rapid elimination phase (t½β:3.5 h). Similar profile and values were obtained for NN1731 in the FHD dose study (J. Møss et al, ISTH, 2007) Conclusions: This study indicates that in hemophilia A dogs, NN1731 and rFVIIa have distinct PK profiles and very similar to what is observed in man. All activity assays show the same qualitative profile, the FVIIa clot assay being the most sensitive assay. The TEG data obtained in vivo are in accordance with the values obtained after in vitro spiking. The data support the use of hemophilia dogs for evaluating the pharmacokinetic and pharmacodynamic profiles of FVIIa related proteins.

Effect of O2 affinity on arterial PO2 in animals with central vascular shunts

1982 ◽  
Vol 53 (6) ◽  
pp. 1360-1364 ◽  
Author(s):  
S. C. Wood
Keyword(s):  
Body Temperature ◽  
Compartment Model ◽  
Congenital Defects ◽  
Arterial Blood ◽  
Venous Shunt ◽  
Two Compartment Model ◽  
Ectothermic Vertebrate ◽  
The Right ◽  
Dissociation Curves

Central vascular or intracardiac shunts result in venous admixture and reduced saturation of systemic arterial blood. This is pronounced in most species of amphibians and reptiles and may occur as congenital defects in homeotherms. A two-compartment model is useful to analyze the effects of shunt on O2 transport. The PO2 of a mixture of pulmonary (ideal) and mixed venous (shunt) blood will be a function of the resulting O2 saturation, analogous to the principle of the “mixing method” in vitro. Furthermore, for a given saturation, the PO2 of systemic arterial blood (PaO2) should be inversely related to the O2 affinity of the mixed blood. The present study tested this two-compartment model of shunt in animals with normally occurring right-to-left shunts (amphibians and reptiles) and with dogs having artificial shunts. The O2 dissociation curves (ODC) of the blood were manipulated by varying body temperature and blood pH. For any level of saturation of systemic arterial blood, the PaO2 was found to increase with factors that shifted the ODC to the right. This experimental support of mathematical models of shunting and PaO2 suggests that animals with intracardiac or central vascular shunts are benefited by low-O2-affinity blood, a condition that is common in amphibians and reptiles. For an individual ectothermic vertebrate, an increase in O2 demand due to increased body temperature would, because of decreased O2 affinity, be accompanied and perhaps facilitated by an increase in PaO2 if saturation remained constant.

Comparison of storage- and signal-limited models of pancreatic insulin secretion

1980 ◽  
Vol 238 (5) ◽  
pp. R378-R389 ◽  
Author(s):  
M. D. O'Connor ◽  
H. Landahl ◽  
G. M. Grodsky
Keyword(s):  
Insulin Secretion ◽  
Physiological Mechanism ◽  
Compartment Model ◽  
Single Step ◽  
Two Compartment Model ◽  
Pulse Type ◽  
Glucose Test ◽  
Glucose Stimulated Insulin Secretion ◽  
Mathematical Relationships

Kinetic patterns of glucose-stimulated insulin secretion from the in vitro perfused pancreas were used to test different types of secretion models of similar complexity. A storage-limited, two-compartment model, modified slightly from that previously, was compared with signal-limited models incorporating delta or feedback characteristics. Mathematical relationships for all models were fixed by single-step, dose-response experiments and models were compared in a series of glucose test patterns including steps, step restimulations, staircases, pulses, ramps, and ramp restimulations. The work quantifies previously unreported characteristics of hypersensitivity and low-glucose rest/restimulation behavior in the pancreas. All models simulated staircase and ramp experiments. The two-compartment model contains an inherent hypersensitivity factor required for repeated pulse-type experiments. However, the kinetics of hypersensitivity were too rapid to be simulated in all types of pulse and ramp/pulse experiments by the restricted refilling characteristics as written into this model. The signal-limited, delta-feedback model did not inherently produce potentiation, but required add-on modification that then more closely simulated some pulse and ramp/pulse experiments. This model simulated experimental negative spikes, whereas the storage-limited model would require additional complexity to do so. These and other results suggest that both storage- and signal-limited models, although currently insufficient, could be elaborated to simulate available data. Therefore, a choice between the two to describe the underlying physiological mechanism of multiphasic insulin secretion is premature. The alternate possibility that the secretion mechanism may be reflected by a combination of the two models is presented.

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