Farm Animal Metabolism and Nutrition

An empirical multi-pool model

To fit gas curves, Groot et al. (1996) pro-
posed an equation of the form:

V= Vfi(1 + (Bi/t)Ci)
^1 (10.7)

in which Vfis the asymptotic gas volume
and Band Care positive constants. The
subscript i identifies the phase or pool. It
can be shown that B(units, h) is the time at
which one-half of the asymptotic gas
volume has appeared. Cis a dimensionless
switching constant that, together with B,
determines the shape of the gas profile.
When C ≤1, the curve has no point of
inflection and resembles an exponential
function; when C ≥1, the curve is
sigmoidal. Examples of these curve shapes
are given in Fig. 10.6. Two or, at most,
three pools will usually suffice to describe
a gas curve.
Equation 10.7 is also very versatile and
is best able to reproduce almost any
gas curve encountered in practice.
Unfortunately, the shape parameter C is
difficult to interpret in biological terms.

An empirical single-pool model

The first equation published as an alterna-

tive to the simple exponential equation

(Equation 10.4) treated the degradable sub-

strate as a single pool undergoing degrada-

tion at a fractional rate that was time

dependent (France et al., 1993). The concept

of a discrete lag (T, h) was retained and the

fractional rate of degradation, μ (h
^1 ) was

postulated to vary with time tas follows:

μ= 0 t< T

μ= b+ c(2 √t)
^1 t ≥T

No reason was provided for this hypo-

thetical relationship. If Vfis the asymptotic

gas volume, the equation describing

accumulated gas volume (V) with time (t)

becomes:

V= Vf{1 
exp[
b

(t
T) 
c(√t
√T)]} (10.8)

Equation 10.8 is quite limited in its applica-

tion and gives fits that are less satisfactory

than the multiple pool models described

above. For example, if the data sets graphed

220 P. Schofield

Fig. 10.5.Examples of single-pool logistic curves.