### Dosage calculations

Dosage calculations are complicated by the extra terms in the equations however
some calculations are still reasonably straightforward. The dose required for
a particular initial plasma concentration can be calculated if V_{1} is known.
Thus:
DOSE = V_{1} * Cp^{0}(required)

To achieve an initial Cp of 20 mg/L given V_{1} = 30 liter would require a DOSE =
20 * 30 = 600 mg.

Alternately if a dose of 500 mg is given and the V_{1} value is 16 L, the expected
Cp^{0} can be calculated.

Cp^{0} = 500/16 = 31.3 mg/L

If the A, B, , and values are known or calculated, then the
plasma concentration at any time after a single IV dose can be calculated.

The plasma concentration achieved after a continuous IV infusion is given by
the same equation described for the one compartment model, i.e.:-

k0 = Cp^{ss }*^{ }clearance = Cp^{ss *} V_{1} * kel =
Cp^{ss }*^{ }V_{area} *

If a plasma concentration of 30 mg/L is required and V_{1} = 15 L and kel is 0.2
hr^{-1}
then the required infusion rate can be readily determined.

k0 = 30 x 15 x 0.2 = 90 mg/hr

**Figure XIX-10 Linear Plot of Cp Versus Time With IV Bolus and Infusion to Give 30 mg/L**

Since the time to
reach the steady state concentration is controlled by the value this
could mean a slow approach to the desired value, thus an IV bolus loading dose
may be useful. Unfortunately this calculation is not straight forward as you
found in the lab experiment.

With V_{1} = 15 L, kel = 0.2 hr^{-1},
and required Cp = 30 mg/L

Bolus DOSE = 15 x 30 = 450 mg and

Infusion Rate = k0 = 30 x 15 x 0.2 = 90 mg/hr

**Figure XIX-11 Linear Plot with Higher and Lower Bolus Dose**

As you can see (Figure XIX-10 above) this
gives quite a dip in the Cp versus time curve.

With Bolus DOSEs, either 600 or 300 mg (shown in Figure XIX-11) the curves may or
may not be better depending on the therapeutic range of the drug.

**Figure XIX-12, Linear Plot of Cp Versus Time With Fast and Slow Infusion**

Another alternative is to give a fast infusion followed by the maintenance
infusion. Here 1200 mg was given over 4 hours (at 300 mg/hr) before switching
to the slower 90 mg/hr maintenance rate.

This page was last modified: 12 February 2001
Copyright 2001 David W.A. Bourne