Clinical Pharmacokinetic Equations and Calculations Prof. Henny Lucida, PhD, Apt

Basic equations LOADING DOSE: LD = Css x Vd MAINTENANCE DOSE: MD = Css x Cl

CLEARANCE: Cl = ke x Vd HALF-LIFE: t1/2 = 0.693/ke

 

Intravenous bolus equations

Intravenous bolus  

Continuous iv infusion  

Non iv/extravascular  

Css av, any route of adm  

Problems: 1. A physician wants to give theophylline to a young male asthmatic patient (age 29, 80 kg). According to the literature, t1/2 elimination of the drug is 5 hours and the Vd app is equal to 50% of body weight. The plasma level of theophylline required to provide adequate airway ventilation is approximately 10 mg/mL. The physician wants the patient to take medication every 6 hours around the clock. What dose of theophylline would you recommend? (F=1) If you were to find that theophylline is available to you only in 225 mg capsules, what dosage regimen would you recommend?

Mr JM, a nonsmoking 60 kg patient with chronic obstructive pulmonary disease, is to be started on an oral regimen of aminophylline (85% of which is theophylline). The pharmacokinetic parameter values for a typical patient population with this disease are: F = 1 (for theophylline), Vd = 0.5 L/kg and CL = 40 mL/hr/kg. Desain an oral dosage regimen of aminophylline (100 and 200 mg tablets are marketed) for this patient to attain and maintain a plasma conc with ther window 10-20 mg/L. Abs theophylline is complete and rapid

2. The t1/2 elimination of an antibiotic is 3 hours and the Vd app is 20% of body weight. The therapeutic window for this drug is from 2 to 10 mg/mL. Adverse toxicity is often observed at drug concentrations above 15 mg/mL. The drug will be given by multiple IV bolus injections. Calculate the dose for an adult male patient (68 yo, 82 kg) with normal renal function to be given every 8 hours.

3. An antibiotic drug is to be given to an adult male patient (75 kg, 58 years old) by IV infusion. The drug is supplied in sterile vials containing 30 mL of the antibiotic solution at a concentration of 125 mg/mL. What rate (mL/min) would you infuse this patient to obtain a Css of 20 mg/mL? What loading dose would you suggest? Assume: one-compartment model, Vd = 0.5L/kg and t1/2 elimination = 3 hours

Equations for iv infusion

Equations for iv infusion X0 = Css * Vd

4. For prolonged surgical procedures, succinylcholine chloride is given by iv infusion for sustained muscle relaxation.A typical initial dose is 20 mg followed by continuous infusion of 4 mg/min. The infusion must be individualized because of variation in the kinetics of metabolism of succinylcholine. Estimate the elimination half-lives of succinylcholine in patients requiring 0.4 mg/min and 4 mg/min, respectively, to maintain 20 mg in the body.

5. Calculate the excretion rate at steady state for a drug given by iv infusion at a rate of 30 mg/hr. The Css is 20 mg/mL. If the rate of infusion were increased to 40 mg/hr, what would be the new Css? Assume first order elimination kinetics and a one compartment model.

6. A patient with renal dysfunction received a dose of vancomycin 6. A patient with renal dysfunction received a dose of vancomycin. Cp were 22 and 15 mg/L at 24 and 48 hours after infusion respectively. Determine when the concentration would reach 10 mg/L! a. 54 hours b. 72 hours c. 96 hours d. 128 hours

7. If the Cp just after a gentamicin dose is 10 mg/L and the patient’s elimination rate constant is 0.15/hr, predict what the Cp will be 8 hours later! a. 6.0 mg/L b. 3.0 mg/L c. 1.5 mg/L d. 1.0 mg/L

8.