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.

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Ingestion of mycotoxins by animals causes damage to the production system and can still be transferred to animal products, including milk. Due to its carcinogenic and genotoxic potential, the intake of mycotoxins, especially aflatoxins, is relevant to human health. The use of mycotoxin-absorbing agents has gained attention in dairy cattle nutrition. Therefore, it aimed to conduct a literature review on the use of mycotoxin absorbers in the dairy cattle diet. Mycotoxin absorbing agents can be of organic or inorganic origin, the inorganic ones being the most studied. Inorganic and organic agents have been shown to be effective in reducing the transfer of aflatoxin M1 to milk. However, the inclusion of mixed agents (organic and inorganic) is promising as a potential for mycotoxin absorption. In general, organic, inorganic and mixed absorbents showed positive results in improving the antioxidant and inflammatory status in the liver.

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