2 compartments model

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: