scholarly journals Mathematical models describing disappearance of Lucerne hay in the rumen using the nylon bag technique

2021 ◽  
Vol 50 (5) ◽  
Author(s):  
V. Palangi ◽  
M. Macit ◽  
A.R. Bayat
Keyword(s):  
Mathematical Models ◽  
Crude Protein ◽  
Goodness Of Fit ◽  
Gompertz Model ◽  
Exponential Model ◽  
Parameter Estimates ◽  
Rumen Degradation ◽  
Degradation Data ◽  
Potential Use

It is essential to study the dynamics of rumen degradation of feeds before their potential use in formulating diets for ruminants. Various mathematical models have been developed to describe this degradation. The non-lagged exponential model (Model I), the lagged exponential model (Model II), the Gompertz model (Model III), and the generalized Mitscherlich model (Model IV) were examined using two alternative software (SAS and MATLAB) to determine their efficacy in accounting for variation in ruminal disappearance of dry matter (DM) and crude protein (CP) of lucerne hay from three cuttings. All models described DM degradability well (R2 >0.98). Only Models I and II converged when fitted to CP degradability data (R2 >0.98). It was concluded that any of these models could be used to describe the degradation of DM, whereas only Models I and II could be used to describe the degradation of CP from three cuttings of Lucerne hay. All the models that were fitted to the DM degradation data performed reasonably well, with only minor differences in goodness of fit. However, these models differed in values of the parameter estimates. Additionally, SAS failed to converge in the analyses of CP with Models III and IV, and MATLAB converged to nonsensical values with Model III. Model I might be recommended because it fitted the data well and required estimates of the fewest parameters Keywords: alfalfa hay, in situ digestion, model selection, nonlinear regression

scholarly journals In situ ruminal degradation of sallow tree leaves using different mathematical models

2021 ◽  
Vol 26 (3) ◽  
pp. e2170
Author(s):  
Valiollah Palangi
Keyword(s):  
Mathematical Models ◽  
Crude Protein ◽  
Dry Matter ◽  
Gompertz Model ◽  
Exponential Model ◽  
Salix Alba ◽  
Estimated Parameters ◽  
Ruminal Degradation ◽  
Ruminal Degradability

Objective. The objective of this study was to determine the in situ digestion parameters of sallow leaves (Salix Alba) as an alternative food, not commonly used in animal diets using mathematical models. Materials and methods. Four mathematical models were used to describe the ruminal disappearance of dry matter (DM) and crude protein (CP) of sallow leaves: non lagged exponential (Model I); lagged exponential (Model II); Gompertz (Model III), and generalized Mitscherlich (Model IV). Results. Results of DM and CP degradability characteristics showed that all the models fitted well (r2>0.98) to the disappearance data. There were minor differences between the models in terms of statistical evaluations. However, the models differed in the estimated parameters depending on the model’s nature and structure and the parameters included. Conclusions. Given that some models estimated negative values for the studied parameters, they were not biologically acceptable. For this reason, the only model I can be used for estimating the degradability of DM and CP of sallow leaves. In terms of effective degradability (ED) of DM, model III was not used in the calculations because of calculating negative values for part A. Sallow leaves constitute the largest possible proportion of the ruminal degradability fractions, and effective degradability can be used as a forage source in ruminant feeds.

scholarly journals Longitudinal Pattern of Aerenchyma Formation Using the Ti-Gompertz Model in Rice Adventitious Roots

2021 ◽  
Vol 12 ◽  
Author(s):  
Yun Chen ◽  
Guoming Li ◽  
Buhong Zhao ◽  
Yajun Zhang ◽  
Kun Liu ◽  
...  
Keyword(s):  
Adventitious Roots ◽  
Goodness Of Fit ◽  
Gompertz Model ◽  
Root Apex ◽  
Information Criterion ◽  
Ordinary Least Squares ◽  
Parameter Estimates ◽  
Aerenchyma Formation ◽  
Root Aerenchyma ◽  
Longitudinal Pattern

The longitudinal pattern of root aerenchyma formation of its relationship with the function of adventitious roots in rice remains unclear. In this study, the percentage of the aerenchyma area to the cross-sectional area (i.e., aerenchyma percentage) was fit with four non-linear models, namely, W0-Gompertz, Ti-Gompertz, logistic, and von Bertalanffy. Goodness-of-fit criteria such as the R2, the Akaike information criterion (AIC), and the Bayesian information criterion (BIC) were used to select the model. The bias of the parameters was evaluated using the difference between the ordinary least squares-based parameter estimates and the mean of 1,000 bootstrap-based parameter estimates and the symmetry of the distributions of these parameters. The results showed that the Ti-Gompertz model, which had a high goodness-of-fit with an R2 close to 1, lower AIC and BIC values, parameter estimates close to being unbiased, and good linear approximation, provided the best fit for the longitude pattern of rice aerenchyma formation with different root lengths among the competing models. Using the second- and third-order derivatives according to the distance from the root apex, the critical points of Ti-Gompertz were calculated. The rapid stage for aerenchyma formation was from the maximum acceleration point (1.38–1.76 cm from the root apex) to the maximum deceleration point (3.13–4.19 cm from the root apex). In this stage, the aerenchyma percentage increased by 5.3–15.7% per cm, suggesting that the cortical cells tended to die rapidly for the aerenchyma formation rather than for the respiration cost during this stage. Meanwhile, the volume of the aerenchyma of the entire roots could be computed using the integral function of the Ti-Gompertz model. We proposed that the longitudinal pattern of root aerenchyma formation modeled by the Ti-Gompertz model helped to deeply understand the relationship between the anatomical traits and physiological function in rice adventitious roots.

Evaluation of mathematical models to describe protein fraction degradation kinetics of various oilseed meals

2009 ◽  
Vol 2009 ◽  
pp. 171-171
Author(s):  
M Danesh Mesgaran ◽  
T Tashakkori ◽  
A Heravi Moussavi ◽  
S Danesh Mesgaran ◽  
A Vakili ◽  
...  
Keyword(s):  
Mathematical Models ◽  
Goodness Of Fit ◽  
Degradation Kinetics ◽  
Direct Method ◽  
Rapeseed Meal ◽  
Insoluble Protein ◽  
Degradation Kinetic ◽  
Negative Exponential ◽  
Kinetics Of

In situ procedure is a direct method of measuring the rumen degradation kinetic of a feed nutrient. Data obtained by this technique are generally analysed using an exponential curve (Ørskov and McDonald, 1979). However, very low attention has been paid to choice of mathematical model to fit the curves and goodness-of-fit of the model. Lopez et al. (1999) pointed out that the disappearance of some feed components, particularly structural carbohydrates, exhibits a larger variety of forms than for crude protein (CP). In the present study, two different mathematical models of a straight line or a negative exponential (France et al., 1990; and Ørskov and McDonald, 1979) were selected to evaluate in situ degradation kinetics of protein fractions including true protein (TP), neutral-detergent insoluble protein (NDIP) and acid-detergent insoluble protein (ADIP) of various oilseed meals (cottonseed meal (CSM), soyabean meal (SM) and rapeseed meal (RM)).

Effect of adding lignosulfonate and heat to canola screenings on ruminal and intestinal disappearance of dry matter and crude protein

2000 ◽  
Vol 80 (1) ◽  
pp. 215-219 ◽  
Author(s):  
Marina A. G. von Keyserlingk ◽  
E. Weurding ◽  
Mary Lou Swift ◽  
C. F. Wright ◽  
J. A. Shelford ◽  
...  
Keyword(s):  
Heat Treatment ◽  
Gastrointestinal Tract ◽  
Key Words ◽  
Crude Protein ◽  
Dry Matter ◽  
Holstein Cows ◽  
Lower Gastrointestinal Tract ◽  
Rumen Degradation ◽  
Heat Treated

The effect of adding 5% calcium lignosulfonate (LSO3) and heat to canola screenings on in situ ruminal and intestinal dry matter (DM) and crude protein (CP) disappearance in Holstein cows was investigated. Treatments consisted of untreated canola screenings, canola screenings that had been heated to 100 °C for 30 or 60 min and canola screenings that had 5% (wt wt−1) LSO3 added and were subsequently heated at 100 °C for 0, 30 or 60 min. Results indicate that treatment of canola screenings with 5% LSO3 and heated to 100 °C for 60 min was effective in reducing rumen degradation of DM and CP with a corresponding increase in disappearance in the lower gastrointestinal tract when compared to untreated and heat-treated canola screenings. Key words: Canola screenings, rumen by-pass protein, heat treatment, lignosulfonate

scholarly journals Classical Mathematical Models for Prediction of Response to Chemotherapy and Immunotherapy

2021 ◽  
Author(s):  
Narmin Ghaffari Laleh ◽  
Chiara Maria Lavinia Loeffler ◽  
Julia Grajek ◽  
Katerina Stankova ◽  
Alexander T. Pearson ◽  
...  
Keyword(s):  
Tumor Growth ◽  
Mathematical Models ◽  
Early Treatment ◽  
Goodness Of Fit ◽  
Tumor Volume ◽  
Human Tumor ◽  
Gompertz Model ◽  
Text Book ◽  
Response To Chemotherapy ◽  
Volume Measurements

Classical mathematical models of tumor growth have shaped our understanding of cancer and have broad practical implications for treatment scheduling and dosage. However, even the simplest text-book models have been barely validated in real world-data of human patients. In this study, we fitted a range of differential equation models to tumor volume measurements of patients undergoing chemo-therapy or cancer immunotherapy for solid tumors. We used a large dataset of 1472 patients with three or more measurements per target lesion, of which 652 patients had six or more data points. We show that the early treatment response shows only moderate correlation with the final treatment re-sponse, demonstrating the need for nuanced models. We then perform a head-to-head comparison of six classical models which are widely used in the field: the Exponential, Logistic, Classic Bertalanffy, General Bertalanffy, Classic Gompertz and General Gompertz model. Several models provide a good fit to tumor volume measurements, with the Gompertz model providing the best balance between goodness of fit and number of parameters. Similarly, when fitting to early treatment data, the general Bertalanffy and Gompertz models yield the lowest mean absolute error to forecasted data, indicating that these models could potentially be effective at predicting treatment outcome. In summary, we pro-vide a quantitative benchmark for classical textbook models and state-of-the art models of human tumor growth. We publicly release an anonymized version of our original data, providing the first benchmark set of human tumor growth data for evaluation of mathematical models.

scholarly journals Effect of extrusion on the rumen undegradable protein fraction of lupins

2021 ◽  
Vol 50 (6) ◽  
Author(s):  
T.S. Brand ◽  
L. Jordaan
Keyword(s):  
Crude Protein ◽  
Lupinus Albus ◽  
Maximum Temperature ◽  
Rumen Degradation ◽  
Ruminant Diets ◽  
Outflow Rate ◽  
Ruminal Degradation ◽  
Ruminant Animals ◽  
Rumen Undegradable Protein

Lupins are highly degradable in the rumen, and do not provide enough bypass protein for high-producing ruminant animals. The effects of extrusion on dry matter (DM) and crude protein (CP) rumen degradability of Lupinus albus and Lupinus angustifolius were determined in situ. Samples of both types of lupin were extruded at maximum temperature, which reached 116 °C. Six Dohne Merino wethers fitted with rumen cannulas were used in this trial. Samples were incubated in the rumen at intervals of 0, 2, 4, 12, 36, and 48 hours. This procedure was repeated in two sheep per treatment and in three periods, giving a total of six observations for each variable. Extrusion lowered the soluble fraction of CP and increased the potential degradable fraction without affecting its rate of degradation. It also lowered the effective degradability of CP of both types of lupin by 28% at an outflow rate of 0.08% per hour. No differences were observed between types. Extrusion modified the ruminal degradation parameters and decreased effective rumen degradation, especially at faster outflow rates. Thus, the rumen undegradable protein (RUP) fraction of lupins was increased by extrusion and lupins could be used more efficiently in ruminant diets. This study showed that the benefits of extrusion could be reached at a relatively low temperature of 116 °C to reduce the possibility of heat damage.

Effect of particle size on in situ ruminal disappearances of pea (Pisumsativum) organic matter, proteins and starch in dairy cows

2000 ◽  
Vol 80 (1) ◽  
pp. 203-206 ◽  
Author(s):  
C. Bayourthe ◽  
R. Moncoulon ◽  
F. Enjalbert
Keyword(s):  
Particle Size ◽  
Organic Matter ◽  
Dairy Cows ◽  
Crude Protein ◽  
Rumen Degradation ◽  
Pea Flour ◽  
Effect Of Particle Size ◽  
Pea Seeds ◽  
In Sacco

Ruminal disappearance characteristics of OM, CP and starch relative to particle size of dehulled pea seeds were determined using the in sacco method. Fine grinding (≤502 µm) highly increased the rapidly CP and starch degradable fractions and the rate of degradation of these nutrients. Key words: Pea flour, particle size, rumen degradation, crude protein, starch

The use of the rumen degradation characteristics of hay as predictors of its voluntary intake by sheep

1991 ◽  
Vol 52 (1) ◽  
pp. 133-139 ◽  
Author(s):  
M. D. Carro ◽  
S. Lopez ◽  
J. S. Gonzalez ◽  
F. J. Ovejero
Keyword(s):  
Crude Protein ◽  
Soluble Fraction ◽  
Live Weight ◽  
Exponential Model ◽  
Multiple Regression Model ◽  
Rumen Degradation ◽  
Degradation Characteristic ◽  
Voluntary Intake ◽  
The Relationship ◽  
Variance Explained

ABSTRACTEleven sun-cured hays with crude protein (CP) and neutral-detergent fibre (NDF) concentrations ranging from 57 to 207 and 428 to 744 g/kg dry matter (DM) respectively, were used to study the relationship between the DM and NDF degradation characteristics and the voluntary DM intake (VDMI) by sheep.The VDMI was measured in the last 10 days of a 21-day period using 50 mature ewes in five groups of 10 ewes per group, with a mean live weight (LAY) of 55 kg and ranged from 41·2 to 69·8 g/day per kg LW075. Disappearanc e rates of DM and NDF were measured by incubating samples in nylon bags in the rumens of three hay-fed rumen-cannulated ewes for 3, 6, 9, 15, 24, 48 and 72 h and by fitting the exponential model Y = a + b (1 — e-ct) to the results. Potential degradabilities (defined as a + b) for DM and NDF ranged from 679 to 868 and from 445 to 808 g/kg respectively.The VDMI was significantly correlated with the soluble fraction of DM (aDM; P < 0·05) and the rate of degradation of DM (cDM; P < 0·01) and NDF (cNDF; P < 0·01). The inclusion of aDM and cDM ni a multiple regression model resulted in the equation: VDMI = 21·3 + 0·0733 (s.e. 0·01577) aDM + 138 (s.e. 26·0) cDM (R2 = 0·897; residual s.d. = 2·79), with a significant increase of the variance explained by one single degradation characteristic (P < 0·05). The prediction was not improved by adding the constant cNDF to the equation (P > 0·05). These results indicate the possibility of predicting the VDMI of hays by sheep from the rumen soluble fraction (aDM) and the rate of degradation (cDM) of DM.

scholarly journals A MODIFIED METHOD FOR DETERMINATION OF IN SITU RUMEN DEGRADATION OF FEEDSTUFFS

1987 ◽  
Vol 67 (1) ◽  
pp. 93-102 ◽  
Author(s):  
G. DE BOER ◽  
J. J. MURPHY ◽  
J. J. KENNELLY
Keyword(s):  
Crude Protein ◽  
Dry Matter ◽  
Holstein Cows ◽  
Polyester Mesh ◽  
Rumen Degradation ◽  
Modified Method ◽  
Constant Rate ◽  
Mesh Bag

In situ rumen dry matter (DM) and crude protein (CP) disappearance of various feed-stuffs was studied in Holstein cows. Comparisons of nylon bag size, method of containment within the rumen, and washing technique were made to develop a system which would reduce labor and improve precision among and within laboratories. Bags (7.0 × 11.0 cm) were suspended individually in the rumen by fishing line, or placed in a polyester mesh bag before being put in the rumen. No differences were observed between method of suspension in the rumen. The polyester mesh bag was then used to contain two nylon bag types (3.5 × 5.5 cm, 1-g sample (BT1); 7.0 × 11.0 cm; 5-g sample (BT2)) for incubation in the rumen. Small bags (BT1) were heat-sealed. Dry matter and CP disappearances from BT1 were lower than from BT2. These differences were attributed to washing technique as the larger bag (BT2) was washed more vigorously. A mechanical washing wheel was designed and built to reduce variability due to washing by hand. Bags washed by machine followed by hand washing had slightly higher DM and CP disappearances than bags washed by machine only; however, these differences did not significantly influence effective degradability. Feedstuffs were reincubated in small bags and large bags, and bags were mechanically washed. Dry matter and CP disappearance and effective rumen degradabilities of DM- and CP, assuming a constant rate of outflow, were not significantly different between bag types. Use of heat-sealed small bags (3.5 × 5.5 cm), containing 1-g samples incubated in the rumen within a polyester mesh bag, and a mechanical washer, provides a system for measuring in situ DM and CP disappearance from nylon bags which reduces labor input, can potentially improve consistency among and within laboratories, and facilitates high sample throughput. Key words: In situ, rumen, degradability, mechanical washer, Holstein cows

scholarly journals Variation of in situ rumen degradation of crude protein and amino acids and in vitro digestibility of undegraded feed protein in rapeseed meals

animal ◽  
2013 ◽  
Vol 7 (7) ◽  
pp. 1119-1127 ◽  
Author(s):  
H. Steingass ◽  
G. Kneer ◽  
G. Wischer ◽  
M. Rodehutscord
Keyword(s):  
Amino Acids ◽  
Crude Protein ◽  
In Vitro Digestibility ◽  
Rumen Degradation ◽  
Feed Protein
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