Abbreviation key: PRESS = prediction sums of squares, RMS = residual mean squares, RSS = residual sums of squares.

In contrast to digestion models that include a discrete lag phase, a compartmental digestion model was proposed. It assumed the existence of a lag compartment and a digestion compartment Substrate present in the digestion compartment was subject to first-order kinetics digestion. Flow of substrate from the lag compartment to the digestion compartment was proposed to be a first-order process and likely was affected by hydration of substrate, bacterial attachment, and colonization. The proposed model was compared with models that assumed the existence of a discrete lag phase. Parameter estimates for these models were obtained either through logaritlunic transformation of data or nonlinear regression. Statistically, there was no difference between the compartmental model and the nonlinear model with a discrete lag phase. Differences in parameter estimates between these two models were small. Residual mean squares were higher for the logaritlunically transformed models. Differences in parameter estimates between these models and the compartmental model depended on the structure of the experimental data. In a number of cases, the nonlinear parameters of the compartmental model converged to the same value, resulting in a different interpretation of the model. Residual mean squares for predicting rate of disappearance were lowest for the compartmental model. (Key words: digestion, models, rumen fermentation)

INTRODUCTION

Received April 6, 1990. Acccpled December 6, 1990. lSend correspondence 10 L. L. Berger, Department of Animal Sciences. University of Illinois. 1207 West Gregory Drive, Urbana, lL 61801.

1991 J Dairy Sci 74:2515-2529

Rumen in situ studies have been recognized as valuable tools for evaluating the nutritional value of feedstuffs. Although the usefulness of the results depends on factors like bag porosity, sample particle size, and bacterial contamination (11), its use is widespread. Different mathematical models have been employed to describe the results of in situ studies. Digestion of pure cellulose has been proposed to occur according to first-order kinetics (21). Two important assumptions in using first-order kinetics are that the pool of material is homogeneous and that disappearance can be described by a single fractional digestion rate constant. The chemical and morphological diversity of forages fed to livestock makes the first assumption untenable. Therefore, Waldo et al. (21) proposed that fiber could be characterized by two fractions- p0tentially digestible and indigestible. lbis concept was supported by the finding that NDF residues existed for beet pulp, dried brewers grains, ryegrass, and babassu meal after ruminal incubation for 42 d (15). For proteins, 0rskov and McDonald (13) distinguished a very rapidly degradable fraction. This fraction disappeared prior to the earliest removal of bags from the rumen. Basically, this fraction included soluble material and particles that were washed out of the bags. However, throughout the time span of incubation, one cannot distinguish between digestion and physicalloss of material. Because bags are washed thoroughly after incubation. no judgment can be made about the kinetics of solubilization. Substrate that is to be incubated thus can be fractionated as

2515

[1)

2516

VAN MlLGEN ET AL.

where fd is the potentially digestible fraction, fi is the indigestible fraction, and fs is the soluble fraction of the substrate. When substrate is incubated in the rumen, digestion usually is not considered to begin instantaneously. The period during which either no digestion occurs, or digestion occurs at a greatly reduced rate, is generally referred to as the lag phase (8). A model incorporating a lag phase can be described by residue

= fde-vkd(t -

t1)

+ fl'

[2]

where kci is the fractional digestion rate constant (h-l), tl is the discrete lag time (h), v = 0 for t < tl> and v = 1 for t ~ t}. Several factors have been proposed to affect lag time (1, 8, 20). Because enzymes can act only in aqueous environments, hydration of substrate seems to be an important factor determining the susceptibility to digestion. For insoluble fiber, bacterial attachment and colonization also are involved in the initiation of digestion. Once these limitations to digestion are overcome, digestion will start. However, because these limitations can be overcome within certain microenvironments (e.g., surface of particles, points of physical damage), one should consider partial substrate availability when describing digestion. Substrate may be digested as soon as it is placed in the rumen but at a very reduced rate. As more substrate is hydrated and more bacteria attach, rate of disappearance will increase. The model described by Equation [2] assumes that all limitations to digestion are overcome instantaneously at lag time. It does not account for the fact that these conditions can be met for a certain fraction of the substrate. The objective of this study was to identify a model that would account for partial substrate availability and thus would describe reduced initial digestion (in contrast to no initial digestion). This model then would be compared with other, commonly used models. MATERIALS AND METHODS Data

Data from six published and unpublished data sets were used. All studies were done with Journal of Dairy Science Vol. 74, No.8, 1991

ruminally cannulated cows or steers using a nylon bag incubation technique. Comparison of models describing digestion was based on DM disappearance. The data sets provided 112 digestion profiles (one for each animal-treatment combination) and included a total of 2729 observations. Data set 1 came from a study using wheat straw as substrate treated with different levels of alkaline hydrogen peroxide. Wheat straw was treated with 5N NaOH to achieve a pH of 11.5. Subsequently, samples were treated with 0, 1, 3, 5, or 10% (wt/wt) H2Ch, respectively. Untreated wheat straw was used as a control Data set 2 comprised data from a study on the efficacy of alkaline hydrogen peroxide treatment of various fibrous by-products. Treatments were control, 5% NaOIL and 5% NaOH plus 2% H2Ch, the latter with two time intervals between treatments. Data sets 3 through 5 were published by Erickson et al. (4), Klusmeyer et al. (6), and Schauff and Clark (17), respectively. Four forages, preserved at different DM contents, were used as data set 6. The experimental design of this data set was described by Nocek and English (12). A summary of the structure of the data sets is given in Table 1. Models

Model 1. Digestion of the potentially digestible fraction usually is considered to occur according to first-order kinetics and thus is intrinsically linear (3). Smith et al. (18) assumed that digestion of forage cell walls was completed after 72 h and that the residue at this time represented the indigestible fraction. If it is assumed that v = 1 for all observations, log transformation of data would make Equation [2] linear: In [

residue - f i f d

]

= kcit} - k