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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 V1 is known. Thus:

DOSE = V1 * Cp0(required)

To achieve an initial Cp of 20 mg/L given V1 = 30 liter would require a DOSE = 20 * 30 = 600 mg.

Alternately if a dose of 500 mg is given and the V1 value is 16 L, the expected Cp0 can be calculated.

Cp0 = 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 = Cpss * clearance = Cpss * V1 * kel = Cpss * Varea *

If a plasma concentration of 30 mg/L is required and V1 = 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 V1 = 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

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