# 2.2: Pharmacokinetics II - Dosing

USE OF PHARMACOKINETIC PARAMETERS TO ESTIMATE DOSING REGIMENS

You have decided to prescribe a new drug GOOD-4U® to your patient, Ms. H.S.T., who weighs 70 kg and has normal renal function. The population average pharmacokinetic parameters for GOOD-4U are: Vd = 0.6 l/kg (about total body water), ClT = 60.6 ml/min. Therapeutic efficacy generally occurs at Cp of 2.38 μg/ml; side effects begin to occur with Cp of 5.0 μg/ml.

You decide to administer a single dose of 100 mg by iv injection.

1. Assuming rapid distribution in the Vd, are you expecting to produce side effects (hint: what is the initial C0)?

No, assuming a single compartment system, the 100 mg will distribute in 42 liters to achieve an initial Cp of 2.38 μg/ml. See Fig. 1.

2. How long before 94% of the dose is eliminated (hint: what is the half-life)?

The half-life computed from the total clearance and Vd is 8 hours; 94% of the dose is eliminated in about 4 half-lives, 32 hours.

3. A complete urine collection from the time of dosing until 16 hr later contains 37.5 mg of the drug. To what extent is the renal function of Ms. H.S.T. of importance to the total clearance of this drug?

Computation of the renal clearance indicates that it is about 50% of the total clearance. At 16 hr, which is 2 half-lives, 75 mg should have been eliminated by all clearance mechanisms. Half of that is appearing in the urine suggesting the renal clearance is 30 ml/min. The drug must be extensively bound to plasma proteins and/or is substantially reabsorbed after glomerular filtration. It is reasonable to predict that reduction of the patient’s creatinine clearance by 50% will reduce total clearance by at least 25%.

One week later you decide to administer GOOD-4U® by constant iv infusion to achieve the therapeutic effect.

The minimum loading dose would be (2.38.μg/ml)(42 liters) or 100 mg.

5. What infusion rate would you prescribe?

To achieve a Css of 2.38 μg/ml, given a total clearance of 60.6 ml/min, the infusion rate should be 144.2 μg/min. See Fig. 4.

If instead you had administered 100 mg by iv injection every 8 hours:

6. At steady-state what would be the Cmax?

The drug is given repeatedly at a dosing interval which in this case equals the elimination half-life. The drug will accumulate to twice the initial C0, ie. 4.76

μg/ml. You can prove that from the equation provided (cf. Figure 5).

$$\bf{C}_{\bf{max}_{ss}}={\bf{C}_0\over1-f}$$

7. At steady-state would the Cmin be sufficient to achieve continuous therapeutic efficacy throughout the regimen?

Yes, since Cmin will be 2.38 μg/ml. At steady-state the input from each dose equals the output over the dosing interval. Since each dose adds 2.38 μg/ml, the Cmax,ss drops by 2.38 μg/ml to a Cmin of 2.38 μg/ml. Or approached another way, the dosing interval equals one half-life so Cmin will be 50% of Cmax! See Fig. 5.