.

1. One compartment open model: IV bolus
administration
■ Presented by: (Group 3)
■ Nadia Hia Sraboni (B170606016 )
■ Md. Emran Hossain (B170606017)
■ K H Muntasir Feroz (B170606018)
■ Selim Mia (B170606019)
■ Hasibur Rahman (B170606020)
Batch: 9th
Session: 2017-2018
Department of
Pharmacy
Jagannath University
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2. Contents
■ Introduction
■ One compartment model: IV bolus administration
■ Body as one compartment model
■ Pharmacokinetic parameters
■ Elimination rate constant
■ Apparent volume of distribution
2

3. Introduction
Pharmacokinetic compartment models are used to simplify
all the kinetic processes that occur during drug
administration that include drug distribution and elimination
from the body. One compartment model is the simplistic
view of pharmacokinetic model that will allow us to study
different important parameters of pharmacokinetics once IV
bolus is administered.
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4. One compartment open model: IV Bolus
administration
■ The one compartment open model is the simplest way to describe
the process of drug distribution and elimination in the body. This
model assumes that the drug can enter or leave the body.
Therefore is called open model and the entire body acts like a
single uniform compartment.
■ The simplest route of drug administration from a modeling
perspective is a rapid intravaneous injection.
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5. Body as one compartment model
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6. Estimation of pharmacokinetic parameters-IV
bolus administration
■ For a drug that follows one compartment kinetics and administered
as rapid iv injection. The decline in plasma drug concentration is
only due to elimination of drug from the body and not dew to
distribution, the phase being called as elimination phase.
Elimination phase can be characterized by 4 parameters;
 Elimination rate constant
 Apparent volume of distribution
 Elimination half life
 Clearance
6

7. Elimination rate
constant
■ Elimination rate constant
represents the fraction of
drug removed per unit of
time.
■ It is proportional to the rate
at which the drug
concentration in the body
declines over time.
■ Apparent volume of
distribution is described as
the hypothetical value of
body fluids into which a drug
is distributed.
Apparent volume of
distribution
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8. Elimination half life
■ It is defined as the time taken for the amount of drug in the body as
well as plasma concentration to decline by one half or 50% of it’s
initial volume.
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9. Clearance
■ In pharmacology, clearance is a pharmacokinetic
measurement of the volume of plasma from which a
substance is completely removed per unit time. Usually
clearance is measured in L/h or mL/min
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10. DB ,VD
IV
k
Figure: Pharmacokinetic model for a drug administered by
rapid intravaneous injection. DB = drug in body; VD =
apparent volume of distribution; k= elimination rate constant
The one compartment model that describes the
distribution and elimination after an IV bolus dose is
given:
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11. What is elimination rate constant?
■ Drug elimination means removal of drugs from body by the process of
metabolism and excretion.
■ Several routes of elimination of drug by metabolism or excretion.
■ The elimination rate constant (k) is the fraction of the drug in the body
which is removed per unit time.
K=km+ ke
km=first order rate process of metabolism
Ke=First order rate process of excretion
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12. First order elimination kinetics
■ First order kinetics occur when a constant proportion of the drug is eliminated per unit time.
■ Rate of elimination is proportional to the concentration of drug in the body.
■ The higher the concentration, the greater the amount of drug eliminated per unit time
■ So the elimination rate constant follow the First order process.
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13. Continued
■ Expression for rate of drug elimination in the body is:-
dDB/dt=Rate in (absorption)-Rate out(elimination)
■ Since rate in or absorption is absent, the equation becomes:-
dDB/dt=-rate out -----------(1)
■ If the rate out or elimination follows first-order kinetics , then:-
dDB/dt=-kDB -----------(2)
Where,
K= first order elimination rate constant
DB=amount of drug in the body at any time t remaining to be eliminated.
■ Negative sign indicates that the drug is being lost from the body.
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14. Equation for elimination rate constant
Integration of equation (2),
Slove=-k
-----(3)
t
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15. Apparent volume of distribution
 The volume in which the drug seems to be distributed is
termed the apparent volume of distribution.
 It assumes that the drug is theoretically rapidly and
uniformly distributed in the body throughout the apparent
volume.
 It is called apparent volume of distribution as the value is
theoretical and does not have a true physiologic meaning
in terms of an anatomic space.
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16. Equation for apparent volume of distribution
In a one-compartment model, the volume of distribution (Vd)
is calculated from the following equation:
VD=
𝑡𝑜𝑡𝑎𝑙 𝑑𝑜𝑠𝑒 𝑎𝑑𝑚𝑖𝑛𝑖𝑠𝑡𝑒𝑟𝑒𝑑
𝐶𝑝
0
Where, Cp
0 represents the plasma drug concentration
immediately after injection.
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17. continued…….
Apparent volume of distribution (VD) relates the concentration of drug in
plasma(CP) with the amount of the drug in the body(DB).
DB=VDCP ---------(4)
From previous slide equation 3 is (lnDB – lnDB
o = -kt)
Substituting equation (3) into equation 4, a similar expression based
on drug concentration in plasma is obtained for the first order decline
of drug plasma levels:
lnCP= −𝑘𝑡 + 𝑙𝑛𝐶𝑃0 (5)
Equation (5) can also be expressed as
CP=CP
0𝑒−𝑘𝑡
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18. VD
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19. Calculation of volume of distribution
■ For one compartment model , volume of distribution
can be calculated by
VD=Dose/Cp
o= DB
o/Cp
o
[Here,
C P
O= Instantaneous drug
concentration in plsama After drug
equilibrium at t=0
D B
O=amount of drug in the body when
t=0]
Figure:Semilog graph giving the value of CP
O By
extrapolation
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20. We know that , rate of drug elimination is
dDB/dt=-KDB
Substituting equation DB =VDCP, We can say that
dDB /dt=-KVDCP
dDB=-kVDCP dt.......(1)
As both k and VD are constant, equation 1 can be
written as
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21. The integral of CPdt means the area under the curve
represented by AUC
After integration,the equation becomes,
..
From this equation, we can find out volume of distribution if we have the
value of area under curve which can be further calculated from trapezoidal
rule 21

22. Trapezoidal rule and AUC
If we plot plasma concentrations of drug and time intervals in a
graph,we can find a trapezoidal area and by integrating the area we
can calculate AUC
Figure: Elimination of drug from plsama after iv
adminisration
Plasma
drug
level(Microgram/ml/
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23. Significance of Vd
 The apparent volume of distribution is not a true physiologic volume. Most
drugs have an apparent volume of distribution smaller than or equal to our
body mass.
 The apparent volume of distribution is dependent on Cpo
.
 For a given dose, a very small Cpo
may be occur in the body due to
concentration of drug in peripheral tissues and organ.
 The apparent VD is a volume term that can be expressed as a simple
volume or in terms of percent of body weight.
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24. Continued....
■ If VD is a very large number (i.e 100% of body weight ) then it may
be assumed that the drug is concentrated in certain tissue
compartment.
■ The apparent volume of distribution in considering the relative
amounts of drug in the vascular and in the extra-vascular tissues.
■ For each drugs, the apparent volume of distribution is a constant.
In certain pathologic cases, the apparent volume of distribution for
the drug may be altered if the distribution of the drug is changed.
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25. Thank You
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