Biopharmaceutics

1. MULTICOMPARTMENT MODELS
Prepared By
Girijesh Kumar Pandey
M.Pharm. (Pharmaceutics)

2. Contents
• Introduction
• Two-Compartment Open model
• Intravenous bolus administration
• Intravenous Infusion
• Extra vascular administration
• Conclusion
• References

3. Introduction
• One compartment is described by mono-
exponential term i.e. elimination.
• For large class of drugs this terms is not sufficient
to describe its disposition.
• It needs a bi- or multi- exponential terms
• The body is composed of a heterogeneous group
of tissues each with different degree of blood
flow and affinity for drug and therefore different
rates of elimination.
• Multi-compartment characteristics are best
described by administration as i.v. bolus.

4. Two Compartment Model
• The simplest and commonest is the two compartment
model which classifies the body tissues in two
categories :
1) Central compartment or Compartment 1
2) Peripheral or Tissue Compartment or Compartment 2.
• Compartment 1 comprises of blood and highly
perfused tissues like liver, lungs, kidneys, etc.
• Elimination usually occurs from this compartment.
• Compartment 2 comprises of poorly perfused and slow
equilibriating tissues such as muscles, skin, adipose,
etc.

5. Two Compartment Model
• General Grouping of Tissue According to Blood
Supply

6. Two Compartment Model
• Depending upon the compartment from
which the drug is eliminated, the 2
compartment model can be further
categorised into :
- With elimination from Central compartment
- With elimination from peripheral
compartment
- With elimination from both the
compartments

7. Two Compartment Model

8. Two compartment Open model-
I.V. bolus administration:
• Elimination from central compartment
1 Central 2 Peripheral
• After the iv bolus of a drug the decline in the
plasma conc. is bi-exponential.
• Two disposition processes- distribution and
elimination.
• These two processes are only evident when a
semilog plot of C vs t is made.

9. Two compartment Open model-
I.V. bolus administration:
• Model Structure for Two Compartment Model

10. Two compartment Open model-
I.V. bolus administration:
• Where, X 0 = IV bolus dose administered
C c = X 1 = amount of drug in the central compartment
C p = X 2 = amount of drug in the peripheral compartment
k 12 = rate constant for transfer of drug from the central to the
peripheral compartment
k 21 = rate constant for transfer of drug from the peripheral to
the central compartment
k E = first order elimination rate constant.
Elimination of drug out of the central compartment

11. Two compartment Open model-
I.V. bolus administration:
• The second, slower rate process, is called as the post-
distributive or elimination phase.
• In contrast to central compartment, the conc of drug in
the peripheral compartment first increases and reaches
its max.
• The Rate change in drug conc. in the central
compartment is given by,
• Extending the relationship X= V d C
• Where, V c and V p = apparent volumes of C1 and C2

12. Two compartment Open model-
I.V. bolus administration:
• The rate of change in drug conc in the
peripheral component is given by:
• On integration equation gives conc. of drug in
central and peripheral compartments at given
time t :

13. Two Compartment Open Model –
Intravenous Infusion
• The plasma or central compartment conc of a
drug when administered as constant rate (0
order) i.v. infusion is given as:

14. Two Compartment Open Model –
Intravenous Infusion
• At steady state the second and the third term
in the bracket becomes zero and the equation
reduces to: Now, The loading dose

15. Two-Compartment Open Model-
Extravascular administration
• First - Order Absorption
• The model can be depicted as follows :
• The rate of change in drug conc. in the central
compartment is described by three exponents :
An absorption exponent, and
• Two usual exponents that describe drug
disposition.

16. Two-Compartment Open Model-
Extravascular administration
• The plasma conc at time t is,
• Where, L, M & N are coefficients

17. Conclusion
• The future should involve the use of models
capable of incorporating physico -chemical data
and biological information .
• Compartment modelling is useful in Characterize
the behavior of drug in patient, predicting conc.
of drug in various body fluids with dosage
regimen , calculating optimum dosage regimen
for individual patient, evaluating bioequivalence
between different formulation, explaining drug
interaction.

18. References
• D.M.Brahmankar & S.B. Jaiswal , Biopharmaceutics &
pharmacokinetics. A.treatise , First edition, Vallabh
Prakashan, P.No . 290-299,
• Leu and febiger , Biopharmaceutics & clinical
pharmacokinetics by Milo Giberldi , Fourth edition,
Philadelphis , 1991. P.No . 213-230.
• Leon shargel and Andrew Yu, A pplied Biopharmaceutics
and pharmacokinetics, Fourth edition. page no. 47-62.
• Milo Gibaldi , Biopharmaceutics and clinical
pharmacokinetics Fourth edition . page no.14-23,
• http://www.authorstream.com/Presentation/abhijit_26-
1830737-multi-compartment-models/