A generalized compartmental model to estimate the fibre mass in the ruminoreticulum: 1. Estimating parameters of digestion

Parameters related to the microbial digestion of nutrients in the ruminoreticulum have been estimated by fitting mathematical models to degradation profiles generated from kinetic studies. In the present paper, we propose a generalized compartmental model of digestion (GCMD) based on implicit theoretical concepts and the gamma probability density function to estimate fibre digestion parameters. The proposed model is consistent to a broader compartmental model presented in a companion paper that integrates aspects of fibre digestion and passage. Different versions of the GCMD were generated by increasing the integer order of time dependency of the gamma function. These versions were fitted to 192 published fibre degradation profiles that were obtained using an in vitro fermentation technique. The quality of fit was evaluated based on the frequency of minimum sum of squares of errors (SSE), the number of runs of signs of residuals, and its likelihood probability calculated according to the Akaike's Information Criterion. The likelihood of the proposed model was also compared to a discrete lag time model (DLT), which is commonly used to interpret fibre degradation profiles. The GCMD had superior quality of fit compared to the DLT and was considered more likely in describing 68.75% of the profiles evaluated. Only 9.38% of the degradation profiles that were fitted to the DLT model had a lower SSE. Even though the degradation profiles studied were generated by incubating feed samples up to 96h, the true asymptotic limit of fibre degradation can only be achieved by long-term fermentations. This fact leads to questioning the uniformity of the potentially digestible fibre fraction and a further approach based on GCMD-type model was used to account for its heterogeneous nature.