Development of a mathematical model to predict pool sizes and rates of digestion of 2 pools of digestible neutral detergent fiber and an undigested neutral detergent fiber fraction within various forages

The digestion of neutral detergent fiber treated with amylase and sodium sulfite and ash corrected (aNDFom) has been described as a single digestible pool and a fraction undigested in ruminants. Further, most models that predict rate and extent of digestion of aNDFom in the rumen assume first-order processes, in which the rates of digestion and passage are proportional to the pool size of aNDFom consumed and digested. Data exist demonstrating that the undigested fraction of aNDFom is not well described by a fixed coefficient and varies by maturity and agronomic growing conditions of the plant. Thus, our objective was to improve the prediction of digestible aNDFom (pdNDF) and to quantify, using a minimum number of fermentation time points, 2 pools of digestible aNDFom, pdNDF(1) and pdNDF(2), and their respective rates. Based on fermentations from 0 to 240 h among 34 forages (grasses, conventional and brown midrib corn silages, and alfalfas), 3 pools were described by aNDFom(t) = pdNDF(1) x e(-k1(t-L)) + pdNDF(2) x e(-k2(t-L)) + uNDF, where aNDFom(t), is the residue at time t; L is the lag; k(1) is the rate of digestion of pdNDF(1); k(2) is the rate of digestion of pdNDF(2); and uNDF the unavailable NDF on an aNDFom basis. A nonlinear estimation allowed the computation of the pool size and respective digestion rates. Using 3 time points from the digestion curve, 30, 120, and 240 h, as the fermentation endpoints to represent uNDF, we optirnized the same model in Vensim (Ventana Simulation Environment; Ventana Systems Inc., Belmont, MA) to obtain rates and pool sizes of aNDFom. In addition, the same optimization was also performed with 2 time-points arid a forage type-specific range for uNDF. Parameters (with and without uNDF) obtained per forage using Vensim were compared by fitting kinetics data from the nonlinear calculations, using coefficients of determination and residual mean squares at convergence for ranking purposes for the whole equation and mean squared prediction errors for specific parameters. The highest coefficient of determination (0.98) and lowest mean square prediction error [0.0927 (NDF-1)(2)] were obtained when using 48, 120, and 240 h of aNDFom residues or when using 30 and 120 h and a range for the forage-specific uNDFom. Correlations were in all cases consistently high for all kinetic parameters, ranging from 0.76 to 0.99. Results demonstrated that an adequate description of the heterogeneity of aNDFom disappearance was possible without multiple fermentation time points. The equation was fit to all data generated; however, because of the variable nature of pool sizes and rates, forage-specific equations should be developed for better estimations of the forage specific pool sizes and uNDF estimation. This study further describes the heterogeneous nature of aNDFom disappearance and provides an approach for estimating the individual pool sizes and rates of digestion for application for diet formulation.