This document summarizes one and two compartment open models for extravascular drug administration. It describes how compartment models are used to simplify drug distribution and elimination processes in the body. A one compartment open model is presented, showing drug absorption from extravascular administration followed by distribution and elimination from the body compartment. Equations are provided to describe drug behavior under zero-order and first-order absorption. Methods for estimating the absorption rate constant like residuals and Wagner-Nelson are also summarized. Finally, a two compartment open model is briefly introduced.

1. A SEMINAR ON ONE & TWO
COMPARTMENT OPEN MODEL
EXTRA VASCULAR
ADMINISTRATION
PRESENTED BY
SANKAR DASARI
M PHARM ,PHCETS ,1 YR 2 SEM
MALLAREDDY COLLEGE OF PHARMACY
GUIDED BY
Dr. SATYA BRATA BHANJA sir

2. Pharmacokinetic models are used to simplify all the
processes that occur during drug administration that
include drug distribution and elimination in the body.
Compartment models – Classical pharmacokinetic models
That stimulate the kinetic processes of drug A,D and E
Compartment models broadly categorised into two types
Single compartment model
2
One compartment model
Multiple compartment model which includes
Two compartment model
Three compartment model

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5. 5

6. 6

7. One Compartment Open model extra
vascular administration can be shown
in a diagrammatic way by the
following diagram
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8. Normal and semi log plots depicting one compartment
open model extra vascular administration
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9. 9

10. In One Compartment open model
 EXTRAVASCULAR ADMINISTRATION
When drug is administered by extravascular route,
absorption is prerequisite for its therapeutic activity. The
rate of absorption may be described mathematically as
zero-order or first-order process.
After e.v. administration, the rate of change in the amount
of drug in the body is given by
dx = Rate of absorption – Rate of elimination
dt
dX = dXev - dxe
dt dt dt
10

11. • During absorption phase, the rate of absorption is
greater than elimination phase.
dXev > dxe
dt dt
• At peak plasma concentration,
dXev = dxe
dt dt
• During post absorption phase,
dXev < dxe
dt dt
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12. ZERO-ORDER ABSORPTION MODEL
R0 KE
Drug Blood Excretion
This model similar to that of constant rate infusion and
all equation which applies to it are applicable to this
model.
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13. FIRST-ORDER ABSORPTION MODEL
Ka KE
Drug Blood Excretion
first order
From equ. dX = dXev - dxe
dt dt dt
Differentiating above equ. We get,
dX = Ka Xa – KEX, Ka= absorption rate const.
dt Xa= amt of drug remaining
to be absorbed.
Integrating above equ.,
X =
[ K T K t ]
K FX - - -
( - )
a o e E e a
K K
a E
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14. ABSORPTION RATE CONSTANT
This can be calculated by METHOD OF RESIDUALS.
Method is also known as Feathering, stripping and
peeling.
Drug that folllows one- compartment kinetics and
administered e.v. , the concentration of drug in plasma
is expressed by biexponential equation:
Assuming A = Log Ka F X 0
Vd (Ka – KE)
C = A e-kEt – A e-Kat
14

15. During the elimination phase, when absorption is most
over, Ka >>KE
C = A e-Ket
In log form above equation is
Log C = Log A - Ket
2.303
Where, C = back extraplotted plasma conc. Values.
Substracting true plasma conc. From extraploted one,
log(C – C ) =Cδ = Log A - Ket
2.303
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16. 16

17. This method works best when difference between Ka
KE is large (Ka/KE >3)
If KE/Ka > 3 , the terminal slope estimates Ka and not
KE whereas the slope of residuals line gives Ke and not
Ka.
This is called as flip-flop phenomenon since the slopes
of the two lines have exchanged their meanings.
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18. Wagner Nelson Method for Estimation of Ka
The method involves determination of ka from percent un absorbed- time plots
and does not required assumption of zero or first- order absorption
After oral administration of single dose of drug at any given time ,the amount
of drug in the body X and the amount of drug eliminated from the body XE
.Thus:
X=VdC ,
The total amount of drug absorbed into systemic circulation from time zero to
infinite can be given as :
Since at t = ∞, ,the above equation reduce to :
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19. The fraction of drug absorbed at any time t is given as:
Percent drug unabsorbed at any time is therefore:
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21. Two compartment open model
extra vascular administration
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26. References:
1.D.M. Brahmankar, compartment model in
Biopharmaceutics and Pharmacokinetics, Vallabh
prakashan, second editon, 2009; p:
2.Applied Biopharmaceutics and Pharmaceutics
26
sixth edition
LEON SHARGEL