PHA 5127

Problem Set "One Compartment Model with i.v. Injection Only Urinary Elimination

 

A 70 kg patient was given a bolus i.v. injection of 1000 mg of a drug. The drug is not bound to plasma proteins and is excreted unchanged solely into the urine. When the plasma concentration (Cp) was assayed, the following data was obtained.

 

time t[min]

Cp[mg/ml]
  • 5
    •
  • 32.7
    •
  • 10
    •
  • 32.0
    •
  • 15
    •
  • 31.3
    •
  • 25
    •
  • 30.0
    •
  • 50
    •
  • 27.1
    •
  • 100
    •
  • 22.0
    •
  • 150
    •
  • 17.8
    •
  • 200
    •
  • 14.5
    •
  • 250
    •
  • 11.8
    •
  • 300
    •
  • 9.55
    •
  • 350
    •
  • 7.95
    •
  • 400
    •
  • 6.30
    •
  • 500
    •
  • 4.15
    •
  • 600
    •
  • 2.74
    •
  • 800
    •
  • 1.19
    •
  • 1000
    •
  • 0.52
    •

     

    1. Plot the plasma data on linear coordinate paper and estimate t1/2 and Vd.

    2. Plot the plasma data on semilogarithmic paper and determine ke, t1/2 and Vd.

    3. Match the following pharmacokinetic parameters with its units

    (A)

    		kren

    (1) min
    (B) Cltot (2) l/sec
    (C) t1/2 (3) m3
    (D) Vd (4) 1/hr
         

    4. A drug was given as an i.v. -bolus injection. The following plasma levels were measured.

    Plasma Cp[ng/ml]
    time [h]  
    1 317.5
    2 252.0
    3 200.0
    4 158.8
    6 100.0
    8 63.0
    10 39.7
    12 25.0
    14 15.8

     

    Assuming a one-compartment-body model and first order kinetics determine from the data given above:

    4-a Elimination rate constant

    4-b Plasma elimination half-life

    5. Explain why volume of distribution and clearance are independent parameters.

    6. A patient was admitted into the hospital in status asthmaticus. She received a starting infusion of 320 mg theophylline over 30 min. 30 min and 5 hours after the stop of the infusion, plasma levels were determined to be 11.5 and 6.7 mg/L respectively. Calculate the theophylline half-life for this patient.

    7. In the following, pairs of pharmacokinetic parameters are listed. Mark whether the following correlations are always true are false for a one compartment body model.

    (a) T F kren<ke
    (b) T F D=U¥
    (c) T F Cpo* Vd=D
    (d) T F t=0.693/ke
    (e) T F Clren=kren*D/Cpo

     

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