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Pharmacokinetic problems-Pharmacology

Pharmacokinetic exercises 
  1. In a 70kg test subject an oral 80mg dose of verapamil was administered. However because of extensive biotransformation during the first pass through portal circulation, the bioavailability was only 25%. Calculate the amount of the dose of the drug reaching the systemic circulation. 
    
   A.   Bioavailability is 25%
= x 80 = 20 mg
= 20 mg reaches systemic circulation 

  1. A new antibiotic is being tested in clinical trials. The following pharmacokinetic parameters have been previously determined.

Volume of distribution (vd) = 5L
Half-life: 3Hours.  
Plasma concentration=0.1mg/ml.  
  1. Calculate the elimination constant
  2. Calculate the loading dose.

  1. Elimination constant is given by the formula
Ke  
  1. Loading dose is given by the formula
LD = Vd CP
     = 5L 0.1mg/ml = 5000ml X 0.1mg/ ml 
     = 500 mg 
  
Vd = apparent volume of distribution in litres
Cp = plasma concentration in mg/ml

  1. A drug X needs to be administered for a patient with renal failure. This drug is entirely eliminated through kidney. The creatinine clearance in this patient is 20ml/min. The normal dose for an adult is 200mg/day. Considering the normal creatinine clearance to be 100ml/min, calculate the new dose to be administered in this patient
Corrected dose

  1. What maintenance dose should be administered intravenously for drug every 6hours to eventually obtain an average steady state concentration of 4mg/L. Given that Clearance = 80 ml/min

Maintenance dose =
Cpss = 4 mg /litre
Clearance = 80 ml / min = 0.08 litre/min
Bioavailability =
Therefore      Maintenance Dose = 4mg
Therefore     dose every 6th hourly would be   

  1. A normal volunteer will receive a new drug in phase –I clinical trial. The clearance & volume of distribution of the drug in this subject are 1.386 ml/min and 8L respectively. What is the plasma half-life?

 t ½  = 0.693      =  
             Ke

Ke =

t1/2 =

  1. The kidney actively secretes a new antibiotic and apparent Vd is 3.5 litres in the normal adult. The clearance of this drug is 60ml/min 

a). What is the plasma half-life of this drug.

Cl = 60 ml/ min = 0.060 L/min

t1/2 =   
0.693 X3.5L
      0.06 l/min

  =  40.425 min

  1. Calculate the loading dose for a given by IV route that has a long t1/2 where goal is to achieve a plasma concentration of 1.2mg/dl. The Vd at steady state is 40liters.

        loading dose = Cp x Vd
= 1.2 x40 x10 = 480mg

  1. Mr white is admitted to a hospital with complaints of fever, productive cough and chest pain. A diagnosis of pneumonia due to gram negative bacteria is made, based on clinical examination and sputum culture. The physician orders gentamicin  to be administered. The clearance and volume of distribution of gentamicin is 4.7L/h and 20 L respectively. 
  1. What is the maintenance dose to be administered intravenously every 8th hourly to obtain an average steady state plasma concentration of 0.05 mg/ml
  2. What is the loading dose to be administered intravenously to achieve a plasma concentration of 3 mg/L ?

Maintenance dose =
      = 0.05mg/ml X 4.7L/ hr 
      1

= 50mg/litre X 4.7 Litre / hr

= 235 mg/hr 

Therefore     dose every 8th hourly would be 235mg/hr X 8 = 1880mg 

loading dose = Cp x Vd
= 3 mg/L x20L = 60mg

  1. A 74 year old patient with a myocardial infarction has a cardiac arrhythmia. A continuous slow iv infusion of lidocaine is started at 8 AM at a rate of 1.92 mg per minute.  The average pharmacokinetic parameters of lidocaine are:  Vd = 77 L; CL = 640 mL/min; t1/2 = 1.8 h.  
a.What is the expected average steady state plasma concentration?  
b.What is the loading dose to be administered intravenously to achieve a plasma concentration of 0.0005 mg/ml ?

Maintenance dose =
Maintenance dose : 1.92 mg/min
Vd = 77 L; CL = 640 mL/min; t1/2 = 1.8 h

Plasma concentration  = Maintenance dose X bioavailability 
Clearance 

= 1.92 mg/min X 1   =0.003mg/ml
640ml/min

loading dose = Cp x Vd = 0.0005mg/ml X 77L = 0.0005 X 77000 = 38.5mg

10.A patient is brought to the emergency ward with a history of ingestion of a large number of phenobarbitone tablets about 1 hours earlier. Measurement of plasma concentration reveals a concentration of 0.50mg/ml. Assuming the Vd of phenobarbitone to be 40L and the half life to be 100 hrs, how much of phenobarbitone did the patient consume? 

Cp = 0.50mg/ml
Vd = 40 L 
T1/2 = 100 Hr

loading dose = Cp x Vd
= 0.50 mg/ml X 40L = 0.50 X 1000 X 40 = 20,000 mg = 20gm


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