1. PHARMACOKINETIC PARAMETERS OF
TWO COMPARTMENT OPEN MODEL
Seminar By
Ajmeera Divya
M. Pharmacy (Pharmaceutics)
St. Peter’s Institute of Pharmaceutical Sciences,
Hanmakonda.
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2. CONTENTS
I. INTRODUCTION
II. TWO COMPARTMENT OPEN MODEL - IV BOLUS
III. TWO COMPARTMENT OPEN MODEL - IV INFUSION
IV. TWO COMPARTMENT OPEN MODEL - EXTRAVASCULAR
ADMINISTRATION
V. CONCLUSION
VI. REFERENCES
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3. INTRODUCTION
PHARMACOKINETICS:
Pharmacon-Drug Kinesis-Motion/ Change of Rate
‘‘Pharmacokinetics is the study of kinetics of absorption,
distribution, metabolism and excretion (ADME) of drugs and their
corresponding pharmacologic, therapeutic, or toxic responses in
man and animals’’ (American Pharmaceutical Association, 1972).
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4. PHARMACOKINETIC MODELS
PHARMACOKINETIC
MODELS
COMPARTMENT NONCOMPARTMENT PHYSIOLOGICAL
MODEL MODEL MODEL

5. COMPARTMENT MODELS
•Compartment models are classical pharmacokinetic models that
simulate the kinetic process of drug ,absorption, distribution and
elimination with little physiologic detail.
OPEN AND CLOSED MODEL
Open: Administered drug dose is eliminated from the body by
an excretory mechanism.
Closed: The drug dose is not eliminated from the body.

6. COMPARTMENTS
Poorly
Highly Perfused
Perfused Tissue
Negligible
Perfused
Fat group
Tissue
Group
(a) Classification of human body into
compartments
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7. COMPARTMENT MODELS
COMPARTMENT
MODEL
MAMMILLARY CATERNARY
MODEL MODEL
(B) Classification of compartment model
based on arrangement
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8. TWO-COMPARTMENT OPEN MODEL
CENTRAL COMPARTMENT:
• Blood, extracellular fluid, and highly perfused tissues.
• The drug distributes rapidly and uniformly in the central
compartment.
TISSUE OR PERIPHERAL COMPARTMENT:
• Tissues in which the drug equilibrates more slowly.
• Drug transfer between the two compartments is assumed to take
place by first-order processes.
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9. TWO-COMPARTMENT OPEN MODEL
K12 Peripheral
Central
Model A: compartment
compartment
K21
KE
k12
Central Peripheral
Model B: compartment compartment
k21
kE
K12
Central Peripheral
Model C: compartment compartment
K21
KE KE

10. TWO COMPARTMENT OPEN MODEL-IV BOLUS
ADMINISTRATION:
k12
1 2
central peripheral
k21
kE
•After the iv bolus of a drug the decline in the plasma conc. is bi-
exponential.
•Two disposition processes- distribution and elimination.

11. Figure 1: Changes in the drug concentrations in the
central(plasma) and peripheral(tissue )compartment after
i.v. bolus of a drug that fits two-compartment model
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12. •The rate of change in drug concentration in the central
compartment is given as:
dCcdt = K21 Cp – K12 Cc – KE Cc (1)
Cc= drug concentration in central compartment
Cp= drug concentration in peripheral compartment
K12= first order distribution rate constant from central to
peripheral compartment
K21=FIRST order distribution rate constant from peripheral to
central compartment
KE= elimination rate constant from central compartment 12

13. • Extending the relationship X= Vd C
X=amount of drug in the body at any time t remaining to be
eliminated
C=drug concentration in plasma
Vd =proportionality const apparent volume of distribution
dCc = K21 Xp – K12 Xc – KE Xc
dt Vp Vc Vc (2)
Xc and Xp=amt of drug in C1 and C2
Vc and Vp=apparent volumes of C1 and C2

14. • The rate of change in drug concentration in the peripheral
component is given by:
dCp/dt=K12 Cc – K21 Cp (3)
=K12 Xc/ Vc – K21 Xp/Vp (4)
• Integration of the equations (3) and (4) gives conc of drug in
central and peripheral compartments at any given time t :
Cc = Xo/Vc [(K21 – α/ β-α ) e-αt + (K21- β/β-α) e-βt] (5)
Cp = Xo/ Vc [( K21 – α/β – α )e-αt + (K12 – b/α– β )e-βt] (6)
Xo = iv bolus dose
α and β = hybrid first order constants for rapid dissolution phase
and slow elimination phase respectively.

15. In simplified form
Cc = A e-αt + Be-βt
where,
A = X0/ Vc [K21 – α/ (β-α) ]
= Co/Vc [K21 – α/ (α-β)]
and
B = X0 /Vc [K21 – β/(α-β)]
= Co/Vc [K21 – β/(α-β)]
Co = plasma drug concentration immediately after
i.v. injection
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16. ASSESMENT OF TWO COMPARTMENT MODEL
METHOD OF RESIDUALS
C = A e-αt + B e-βt
C = B e-βt
log C = log B – βt/2.303
Figure 2: Resolution of the Bi exponential plasma concentration time curve by
this method of residual for a drug that follows two compartment kinetics on16
i.v
administration.

17. PHARMACOKINETIC PARAMETERS
1. AREA UNDER THE CURVE
2. VOLUME OF DISTRIBUTION
3. RATE CONSTANTS OF DRUG
TRANSFER
4. HALF LIFE
5. CLEARANCE
6. ELIMINATION CONSTANT
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18. • By proper substitution of the following values, the above
listed parameters can be evaluated:
C0 = A + B
KE = αβC0
A β + Bα
K12 = A B (β - α)2
C0 (A β + B α)
K21 = A β + B α
C0

19. • Area Under the Curve :
(AUC) = A + B
α β
• Apparent volume of Central compartment :
Vc = X0/ C0 = X0/KE(AUC)
• Apparent volume of Peripheral compartment :
VP= VcK12/K21
• Apparent volume of distribution at steady state or equilibrium :
Vd,ss = VC +VP 19

20. • Apparent volume of distribution from area :
Vd,area = X0
βAUC
• Haif life :
t1/2=0.693/β
• Total systemic Clearence :
ClT = β Vd
• Renal Clearence :
ClR =dXU /dt = KE VC
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21. TWO-COMPARTMENT OPEN MODEL
INTRAVENOUS INFUSION
R0 1 K12 2
Central
Peripheral
K21
KE
• The plasma or central compartment concentration of a drug
when administered as constant rate (zero order) i.v.infusion is
given as:
C = R0 [1+(KE -β)e-αt +(KE - α)e-βt]
VC KE β–α α- β

22. • At steady state (i.e.at time infinity) the second and the third term
in the bracket becomes zero and the equation reduces to:
Css = R0
VC KE
Now
VC KE = Vd β
CSS = R0 = R0
Vdβ ClT
• The loading dose
X0,L = Css Vc = R0/KE

23. TWO-COMPARTMENT OPEN MODEL-
EXTRAVASCULAR ADMINISTRATION
Ka 1 K12 2
Central peripheral
K21
KE
• The plasma concentration at any time t for a drug that enters the
body by a first-order absorption process and distributed according
to two compartment model is given by :
C = N e-kαt + L e-at + M e-βt
C = Absorption + Distribution + Elimination
exponent exponent exponent

24. Where
•Ka is the first order absorption constant
•α and β are hybrid first order constants for the rapid
distribution phase and slow elimination phase respectively
•L,M,N are hypothetical coefficients.
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25. True plasma
conc
log N Back extrapolated
log L distribution curve
log M
First residual
curve Back extra polated
elimination
log C
Slope =-Ka/2.303
t
figure3:Semi log plot of C versus t of a drug
with two compartment characteristics if
administered extravascularly
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26. CONCLUSION
• Pharmacokinetic models predict drug disposition after drug
administration.
•Statistical methods are used for the estimation and data
interpretation of pharmacokinetic parameters
• Useful in Drug formulation and treatment regimen
• The drug behaviour within the body might be able to fit different
compartmental models depending upon the route of drug
administration.
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27. REFERENCES
•Milo Gibaldi, Donald Perrier,pharmacokinetics, 2nd Edition, 1-89
•Leon Shargel, Susanna W.U Pong, Andrew Bc.Yu, Applied Bio-
Pharmaceutics And Pharmacokinetics, 5th Edition ,51-105
•M.Blomhoj, T.H.Kjeldsen,j.Ottensen, Compartmental Modeling,1-32
•Sunil S. Jambamkar, Sunil. B. Jaiswal , Basic Pharmacokinetis
( Pharmaceutical Press) ,185- 289
•Aldo Rescigno , Foundations of The Pharmacokinetics, 135 -149
•P.L.Madan, Biopharmaceutics And Pharmacokinetics, 1st Edition ,
173 -282
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28. •Steven B Heymfield, Steven Litchman, Richard. N. Baumgartner, Jack
Wong, Body Compositions Of Human, American Journal Of Clinical
Nutrition, 52-59
•Joseph T.Dipiro, William, Spruill, concepts In Clinical
Pharmacokinetics, 4th Edition, 19-45
• V. Venkateswar Rao, Fundamentals of Biopharmaceutics And
Pharmacokinetics, 109-196
•H.P.Tipnis, Amritha Bajaj, Principles And Application Of
Biopharmaceutics And Pharmacokinetics, 213-259
•Dm.Brahmamkhar, Sunil.B.Jaiswal, Biopharmaceutics And
Pharmacokinetics : A Treatise, 212-272
•J.S Kulakarni. Ap .Pawar, Vp Shedbalkar, Biopharmaceutics And
Pharmacokinetics Cbs Publisher, 165-193 28

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