Mathematical modeling applied to ruminal digestion and gas production in vitro

Abstract

The ruminal digestion performed by ruminants is one of the essential and most important processes for the use of dietary nutrients. However, the use of mathematical models applied to digestion kinetics has been widely applied to provide prediction of animal performance, maximize the use of nutrients and reduce nutritional losses due to excreta and a reduction in the cost of animal production. In this context, it aimed to conduct a literature review on the use of mathematical models and to analyze comparisons of different models to predict ruminal digestion. The in vitro gas production technique provides direct measurement of the ruminal digestion rate associated with gas production and the respective gravimetric measurement of the food or diet under test. Nonlinear models are chosen to evaluate ruminal digestion due to a better interpretation of biological parameters, they produce exponential and sigmoidal growth equations. However, the most suitable model for evaluation depends on the type of food or diet. The two-compartment logistical model presents a better adjustment of the gas production curve, mainly for foods with a high proportion of fiber. Among this, single-compartment models can be well applied to evaluate the degradation kinetics of foods with low fibrous carbohydrate content. Therefore, the choice of the most appropriate model is up to the researcher to assess which model best suits the chemical-chemical composition of the food or diet.

<i>In-Vitro </i>Fermentation of Browsable Native Shrubs in New Zealand

“…Nonlinear mathematical models are widely used to fit in vitro gas production to describe the fermentation kinetics of ruminant feeds [14]. The nonlinear models vary in structure, parameters, time zero behavior, lag period, points of inflection, and fermentation gas pools [3,14]. Description of some nonlinear models commonly used to fit in vitro gas production can be found in [3,11,13,14].…”

“…The nonlinear models vary in structure, parameters, time zero behavior, lag period, points of inflection, and fermentation gas pools [3,14]. Description of some nonlinear models commonly used to fit in vitro gas production can be found in [3,11,13,14]. However, the exponential and sigmoidal models are preferred because they are robust in relating gas production to microbial mass and substrate levels [11] and can be structured to accommodate more than one fermentation gas pool [14].…”

“…Description of some nonlinear models commonly used to fit in vitro gas production can be found in [3,11,13,14]. However, the exponential and sigmoidal models are preferred because they are robust in relating gas production to microbial mass and substrate levels [11] and can be structured to accommodate more than one fermentation gas pool [14]. Single pool models are better predictors of fermentation kinetics of simple substrates and are suggested for feeds with low fibre, while multipool models are better descriptor of heterogenous substrate and considers each substrate fraction independently and are recommended for feeds with high fibre [14].…”

“…Non-linear mathematical functions, mainly exponential and sigmoidal, are preferred because of their ability to model microbial growth and have parameters that can be biologically explained [11][12][13]. However, the suitability of the mathematical function in estimating fermentation kinetic parameters depends on the nutritive composition of the feed substrate [3,13,14]. Single compartment models, also referred to as single pool functions assume a constant rate of fermentation and are mainly suited for feed substrates with homogenous nutrients, while dual pool functions considers two rates of fermentation and are suitable for feed substrates with heterogenous nutrients [11][12][13][14].…”

“…However, the suitability of the mathematical function in estimating fermentation kinetic parameters depends on the nutritive composition of the feed substrate [3,13,14]. Single compartment models, also referred to as single pool functions assume a constant rate of fermentation and are mainly suited for feed substrates with homogenous nutrients, while dual pool functions considers two rates of fermentation and are suitable for feed substrates with heterogenous nutrients [11][12][13][14]. Application of both single and dual pool non-linear functions is common in feed evaluation because natural feeds consumed by sheep contain a mixture of substrates that vary in nutrient composition [11].…”