For Helping Purpose only

1. Two Compartment Open Model
Presented by :- Sulekha (M.pharma)
DEPARTMENT OF PHARMACEUTICAL SCIENCES
GURU JAMBHESHWAR UNIVERSITY OF SCIENCE AND TECHNOLOGY,
HISAR

2. Two Compartment Open Model
• Compartment :- A compartment is not a real
physiological or anatomic region but an
imaginary or hypothetical consisting of group
of tissues.
• In this model, the drug distribute into 2
compartments i.e. Central compartment and
Peripheral compartment.
• Central Compartment or Compartment 1 : -
Comprising of blood and highly perfused
tissues like liver, lungs, etc.

3. • Peripheral or Tissue or Compartment 2 :-
Comprising of poorly perfused and slow
equilibrating tissues such as muscles, skin,
adipose, etc.
• There are several possible two compartment
model-
Model A :-
1
Central
Compartment
2
Peripheral
Compartment
K12
K21
KE

4. Model B :-
Model C :-
1
Central Compartment
2
Peripheral Compartment
K12
K21
1
Central Compartment
2
Peripheral Compartment
K12
K21
KE
KE
KE

5. Two Compartment Open Model
Intravenous Bolus Administration
• The model can be depicted as follows :-
• Let K12 and K21 the first order distribution rate
constants depicting drug transfer between the
central and peripheral compartment.
• The rate of change in drug concentration in the
central compartment is given by :-
K21Cp – K12Cc – KECc
1
Central Compartment
2
Peripheral
Compartment
K12
K21
KE
1

6. Extending the relationship X = VdC to the above
eqn , we have
K21XP K12Xc KEXc
VP Vc Vc
Where, Xc and XP are the amt. of drug in the
central and peripheral compartment
respectively. VP and XP are the apparent volume
of the central and peripheral compartment is
given by :
2
Cc
3
4

7. Integration of eqn 2 and 4 yields eqns that describe
the concentration of drug in the central and
peripheral compartment at any given time t.
Where Xo = i.v. bolus dose, where α & β are hybrid
constants and k12 & K21 called as micro-
constants and their relationship is given as:-
α + β = K12 + K21 + KE
αβ = K21 KE
5
6
7
8

8. eqn 5 can be written in simple form as :-
Cc = Ae-αt – Be-βt
 Method Of Residual :- The bioexponential eqn 9
can be resolved into individual components by
method of residual. When distribution is more
rapid than elimination the rate constant α is
greater than β, the term e-αt approaches to zero
and eqn reduces to:-
C´ = Be-βt
In log form,
log C´= log B -
9
10
11

9. where C´ is back extrapolated plasma
concentration values & a semi- log plot of C v/s t
yields terminal linear phase of curve having
slope & t1/2 or elimination phase is given as:
t1/2 =
subtraction of extrapolated plasma
concentration values from corresponding
through plasma concentration values a series of
residual concentrations
Cr = C - C´ = Ae-αt 12

10. In log form,
logCr = logA –
A number of pharmacokinetic parameter at t = 0
eqn 9 reduces to
Co = A + B
KE =
K12 =
K21 =
13
14
15
16
17

12. Two Compartment Open Model
Intravenous Infusion
The model can be depicted as follows
The plasma or central Compartment concentration
of a drug that fits two compartment model when
administered as constant rate i.v. infusion, is
given by eqn
1
Central Compartment
2
Peripheral
compartment
K12Ro
K21
KE

13. At the steady state, the second and third term
becomes zero and the eqn reduces to
Css
The loading dose Xo,L Css immediately at the
start of infusion can be calculated from the
equation:-
Xo,L = CssVC

14. Two Compartment Open Model
Extra vascular Administration
The model cab be depicted as follows:-
For a drug which enters the body by first order
absorption process & distribution acc. to two
Compatment model, the rate of change of drug
concentration in Cc is described by 3 exponents.
1
Central
Compartment
Ka
2
Peripheral
Compartment
K12
K21
KE

15. (1). Absorption exponent
(2). Elimination exponent
(3). Distribution exponent
The plasma concentration at time t, is given by –
C = Ne-Kat + Le-αt + e-βt
Where, N, L & M are coefficient.
The 3- exponents can be resolved stepwise by
method of residual.
Absorption rate constant Ka can be determined
by the method of Residual and Loo- Riegelman
method.

16. • Determination of absorption rate constant Ka by
Loo-Riegelman method using 2COM.
After oral administration of a dose of a drug that
exhibits two compartment model kinetics, the
amount of drug absorbed is calculated as the
sum of the amt. of drug in the central
compartment (XC ), XP (tissue compartment) and
amt. of drug eliminated by all routes XE .
XA = XC + XP + XE
Each of these terms, may be expressed in terms of
kinetic constant & plasma drug concentration as
follows:-
1

17. XC = VC +CC
XP = VP +CP
XE = KEVC
Substitute the above expression of XC & XE in eqn 1
XA = VCCC + XP + XEVC
By dividing the equation 5 by VC , we obtain
At t = ꝏ, we obtain equation 7
2
3
4
5
6
7

18. Dividing equation 6 & 7
A plot of fraction of drug unabsorbed v/s time
gives as the slope from which absorption
rate constant is obtained.
8

19. Importance
(1). Two Compartment Model predict drug
disposition after drug administration.
(2). Useful in drug formulation & treatment
regimen.