### Parameter determination

#### Method of residuals

Values for all these parameters can be determined by first calculating A, B,
, and . For this we can use the method of residuals (in a
similar fashion to determining ka and kel for the one compartment model after
oral administration). By definition is greater than then as
t -->
, e^{-*t} -->
0 faster than e^{-
* t}. Therefore if the ratio / is large enough (greater
than 5) the terminal data points will fall on the line

Cp^{late} = B * e^{- * t}

This equation is similar to the equation for the late plasma concentration
values after oral administration with a one compartment model. This line will
be linear if plotted on semi-log
graph paper.

From the slope of this line a value of can be determined. The t_{1/2}
calculated as 0.693/ is often called the biological half-life
or terminal half-life.
It is the half-life
describing the terminal elimination of the drug from plasma. [For the one
compartment model the biological half-life
is equal to 0.693/kel].

**Figure XIX-4, Semi-Log Plot of Cp Versus Time Showing Cp**^{late} Extrapolated Back to B

The
difference between the Cp^{late} values at early times and the actual
data at early times is again termed the 'residual'

Residual = Cp - Cp^{late} = A * e^{-*t}

**Figure XIX-5, Semi-Log Plot of Cp Versus Time Showing Residual Line and Line**

From the slope of the
residual line the value of can be calculated with the A read off the
concentration axis. With A, B, , and calculated we can
calculate the microconstants given the formulas.

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