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Biopharmaceutics and
         PK
        Lab 5
Calculation of PK parameters using
one and two compartment model: IV
               bolus.
    Dr Sameh Rabea
Remember

   For 1st order kinetic one-compartment the
    equation will be:
      Cp= (Cp) 0 e –kt
Where: Cp: Y ; (Cp) 0 : intercept; t: X;    k: -slope x
   2.303; Slope= (logC2 – logC1)/t2-t1.
Or Ke = ln (C1/C2)/t2-t1
 The PK model:

       I.V.               Central          Ke
    injection          Compartment              Out.

   AUC= Cp0/ Ke
   Vdc= Dose/ Cp0.
   t ½= 0.693/ Ke.
   For 1storder kinetic two-compartment
    the equation will be:
        Cp= A e –αt + B e –βt
   Where A: intercept of line 1 and B
    intercept of line 2; α: distribution
    rate constant and β: elimination rate
    constant.
   The PK model:

     I.V.
            in     Central
                               K12
                                       Peripheral
                 Compartment          Compartment
     inj.
                               K 21

                     K2
Cp0= A + B
K2 = Cp0 / ( A/ α + B/ β )
K12= A.B (β- α) 2 / Cp0 (A β + B α)
K21= A β + B α / Cp0 .
   AUC= A/α + B/β .
   t ½= 0.693/ β.
   Vd c= Dose/Cp0= Dose/ A+B.
   Vd area= Dose/AUC. β
   Vd ss = Vdc + (K12/K21) Vdc
   Vd tissue= Vd area – Vdc.
   Therefore: Vd area> Vd ss > Vdc> Vd tissue.
   But Vd ss is not affected by elimination, so its
    represents true volume of distribution.
   CL = Vdc. Ke or CL= Vdc. Β.
Problem # 1

   A patient received 500 mg cefepime I.V
    bolus injection and numerous blood
    samples were drawn as the following:
Plotting Data
Time (hr)           Conc.( µ/ml)
   0.5                   38.2
   1                     21.6
   2                     11.6
   4                     5.0
   8                     1.4
   12                    0.2
   A- Test the order of this data.
   B- Write your model
   Calculate as many PK parameter as
    possible.
Problem # 2

   A patient received 300 mg I.V.
    dose of a drug. Several blood
    samples were collected and the
    following plasma concentrations
    were obtained:
Plotting Data
Time (hr)           Conc.( µ/ml)
   0.2                   5.6
   0.4                   4.6
   0.6                   3.8
   0.8                   3.2
   1                     2.8
   2                     1.8
   3                     1.35
   4                     1.2
   5                     1.06
   24                    0.0
   Test the order of this data.
   Write the model.
   Calculate PK parameters.
Problem # 3

   A patient received 350 mg I.V
    bolus dose of drug. Several
    blood samples were collected
    and the following plasma
    concentrations were obtained:
Plotting Data
Time (hr)          Conc. (µg/ml)
   0.5                   20.8
   1                     13.8
   1.5                   10
   2                     7.9
   3                     5.3
   6                     2.9
   8                      2
   10                    1.4
   A- Draw diagrammatic
    presentation describing PK
    model , and write your equation.
   Calculate the following PK parameters:
   A:
   B:
   α:
   β (Ke):
   t1/2 :
   AUC:
   Vdc:
   Vd area:

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Pk lab 5

  • 1. Biopharmaceutics and PK Lab 5 Calculation of PK parameters using one and two compartment model: IV bolus. Dr Sameh Rabea
  • 2. Remember  For 1st order kinetic one-compartment the equation will be:  Cp= (Cp) 0 e –kt Where: Cp: Y ; (Cp) 0 : intercept; t: X; k: -slope x 2.303; Slope= (logC2 – logC1)/t2-t1. Or Ke = ln (C1/C2)/t2-t1  The PK model: I.V. Central Ke  injection Compartment Out.  AUC= Cp0/ Ke  Vdc= Dose/ Cp0.  t ½= 0.693/ Ke.
  • 3. For 1storder kinetic two-compartment the equation will be:  Cp= A e –αt + B e –βt  Where A: intercept of line 1 and B intercept of line 2; α: distribution rate constant and β: elimination rate constant.
  • 4. The PK model: I.V. in Central K12 Peripheral Compartment Compartment inj. K 21 K2 Cp0= A + B K2 = Cp0 / ( A/ α + B/ β ) K12= A.B (β- α) 2 / Cp0 (A β + B α) K21= A β + B α / Cp0 .
  • 5. AUC= A/α + B/β .  t ½= 0.693/ β.  Vd c= Dose/Cp0= Dose/ A+B.  Vd area= Dose/AUC. β  Vd ss = Vdc + (K12/K21) Vdc  Vd tissue= Vd area – Vdc.  Therefore: Vd area> Vd ss > Vdc> Vd tissue.  But Vd ss is not affected by elimination, so its represents true volume of distribution.  CL = Vdc. Ke or CL= Vdc. Β.
  • 6. Problem # 1  A patient received 500 mg cefepime I.V bolus injection and numerous blood samples were drawn as the following:
  • 7. Plotting Data Time (hr) Conc.( µ/ml) 0.5 38.2 1 21.6 2 11.6 4 5.0 8 1.4 12 0.2
  • 8. A- Test the order of this data.  B- Write your model  Calculate as many PK parameter as possible.
  • 9. Problem # 2  A patient received 300 mg I.V. dose of a drug. Several blood samples were collected and the following plasma concentrations were obtained:
  • 10. Plotting Data Time (hr) Conc.( µ/ml) 0.2 5.6 0.4 4.6 0.6 3.8 0.8 3.2 1 2.8 2 1.8 3 1.35 4 1.2 5 1.06 24 0.0
  • 11. Test the order of this data.  Write the model.  Calculate PK parameters.
  • 12. Problem # 3  A patient received 350 mg I.V bolus dose of drug. Several blood samples were collected and the following plasma concentrations were obtained:
  • 13. Plotting Data Time (hr) Conc. (µg/ml) 0.5 20.8 1 13.8 1.5 10 2 7.9 3 5.3 6 2.9 8 2 10 1.4
  • 14. A- Draw diagrammatic presentation describing PK model , and write your equation.
  • 15. Calculate the following PK parameters:  A:  B:  α:  β (Ke):  t1/2 :  AUC:  Vdc:  Vd area: