Neel desai (one compartment iv bolus parmacokinetic model)

SSR COLLEGE OF PHARMACY.
Presented by:
Neel Desai.
Enrollment No-
19SSRMPH08
M. Pharm Sem: 2
Pharmaceutics
NEEL DESAI. 2019-2020;SSRCP
1 Roll NO.:19SSRMPH08 ;Subject Seminar. Sem.II,M.Pharm Pharmaceutics

Contents:
• Introduction Of One Compartment Open Model
• I.V. Bolus Administration
• Estimation of Pharmacokinetic Property
• Elimination Rate Constant
• Elimination Half Life
• Apparent Volume Of Distribution
• Clearance
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Roll NO.:19SSRMPH08 ;Subject Seminar. Sem.II,M.Pharm Pharmaceutics

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• The simplest route of drug administration from a
modeling perspective is a rapid intravenous injection (IV
bolus).
• The one-compartment open model offers 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 (ie, the model is "open"), and the body acts like a
single, uniform compartment.

• The simplest kinetic model that describes drug
disposition in the body is to consider that the drug is
injected all at once into a box, or compartment, and that
the drug distributes instantaneously and homogenously
throughout the compartment.
• Drug elimination also occurs from the compartment
immediately after injection.
• In reality the body is infinitely more complex than a
single compartment.

6
• In the body, when a drug is given in the form of an IV bolus, the
entire dose of drug enters the bloodstream immediately, and the
drug absorption process is considered to be instantaneous.
• In most cases, the drug distributes via the circulatory system to
potentially all the tissues in the body.
• Uptake of drugs by various tissue organs will occur at varying
rates, depending on:
1. The blood flow to the tissue.
2. The lipophilicity of the drug.
3. The molecular weight of the drug.
4. The binding affinity of the drug for the tissue mass.

7

The one-compartment open model is the simplest model with the below
assumptions:-
1) The body as a single, kinetically homogenous unit that has no barriers to the
movement of drug.
2) Final distribution equilibrium between the drug the plasma and other body fluids
is attained instantaneously and maintained at all times. This model thus applies
only to those drugs that distribute rapidly throughout the body.
3) Drug move dynamically in and out of this compartment.
4) Elimination is a first order process with 1st order rate constant.
5) The anatomical reference compartment is the plasma and concentration of
drug in plasma is representative of drug concentration in all body tissues. i.e. any
change in plasma drug concentration reflects a proportional change in drug
concentration throught out the body.
However, the model does not assume that the drug concentration in plasma is
equal to that in other body tissue. The term OPEN indicates that the input
(availability) and output (elimthe ination) are unidirectional and that drug can be
eliminated from the body. Fig. shows such a one- compartment model.
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One-compartment open model is generally used to describe plasma levels
following administration of a single dose of a drug.
Depending upon the input, several one-compartment open models
can be defined:-
• One-Compartment open model, intravenous bolus administration
• One-Compartment open model, continuous intravenous infusion
• One-Compartment open model, extravascular administration, zero-order
absorption, and
• One-Compartment open model, extravascular administration, first-order
absorption.
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When a drug that distributes rapidly in the body is given in the form of a rapid
intravenous injection (i.e. i.v. bolus or slug), it takes about one to three minutes for
complete circulation and therefore the rate of absorption is neglected in
calculations. The model can be depicted as follows:
10

11

The general expression for rate of drug presentation to the
body is:-
dX = Rate in (availability) – Rate out (elimination) …(1)
dt
Since rate in or absorption is absent, the equation becomes;
dX = -Rate out ….(2)
dt
If the rate out or elimination follows first-order kinetics, then:
dX = -KE X …(3)
dt
Where KE = first-order elimination rate constant, and
X = 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.
12

13

For a drug that follows one-compartment kinetics and administered as rapid. i.v.
injection, the decline in plasma drug concentration is only due to elimination of
drug from the body (and not due to distribution), the phase being called as
elimination phase.
Elimination phase can be characterized by 3 parameters :–
1. Elimination rate constant.
2. Elimination half-life.
3. Clearance.
14

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• Integration of equation (3) yields:
Where, Xo= amount of drug at time t = zero i.e.
the initial amount of drug injected.
• Equation (4) can also be written in the exponential form
as:
• This equation shows one compartment kinetics is
monoexponential.

17
• It is a pharmacokinetic parameter that permits the use of plasma
drug concentration in place of total amount of drug in the body by
equation (6) therefore becomes:
where Co= plasma drug concentration immediately after i.v.
injection
• Equation (8) is that of a straight line and indicates that semi
logarithmic plot of log C vs t, will be linear with Y-intercept as log
C0

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• Transforming equation (4) into common logarithms (log base 10)
we get:
• Since it is difficult to determine directly the amount of drug in the
body X, advantage is taken of the fact that a constant relationship
exists between drug concentration in plasma C and X, thus
where, Vd = proportionality costant popularly known as the
apparent volume of distribution.

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a) Cartesian plot of drug that follows one-compartment kinetics and
given by rapid injection b) Semi logarithmic plot for the rate of
elimination in a one-compartment model

…10(a)
…10(b)
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• The elimination or removal of drug from the body is the sum of
urinary excretion, metabolism, biliary excretion, pulmonary
excretion and other mechanisms involved therein.
• Thus, KE is an additive property of rate constant for each of this
processes and better called as overall elimination rate constant.
• The fraction of drug excreted unchanged in urine Fe and fraction
of drug metabolized Fm can be given as

21

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• Elimination half life : Also called as biological half life.
• The time taken for the amount of drug in the body as well as
plasma concentration to decline by one- half or 50% its initial value.
• It is expressed in Time.
• Half life expressed by following equation:
• The half – life is a secondary parameter that depends upon the
primary parameter clearance & apparent volume of distribution.
• According to following equation:

23

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• The two separate & independent pharmacokinetic characteristics of a
drug distribution of a drug since, they are closely related with the
physiological mechanism of body, they are called as primary
parameters.
• Modification of equation (7) defined apparent volume of distribution :
• The best and the simplest way of estimating Vd of a drug is
administering it by rapid i.v. injection, determining the resulting
plasma concentration immediately by using the following equation:
X0 i.v. bolus dose
Vd = ----- = --------------------- …(14)(for drugs that obey one Compartmnt Kinetics)
C0 C0
x
Vd C

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• A more general, a more useful non-compartmental method that
can be applied to many compartment models for estimating the
Vd is:
For drugs given as i.v. bolus,
For drugs administered extravascularly (e.v.)
X0 = dose administered
F = fraction of drug absorbed into the systemic circulation.

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…(17
)NEEL DESAI. 2019-2020;SSRCP
• Clearance is defined as “the theoretical volume of body fluid
containing drug from which the drug is completely removed in a
given period of time.” It is expressed in ml/min or lit/hr.
• Clearance : Clearance is the most important parameter in clinical
drug applications & is useful in evaluating the mechanism by which
a drug is eliminated by the whole organisms or by a particular
organ.
• Clearance is a parameter that relates plasma drug concentration
with the rate of drug elimination according to following equations-

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• Clearance at an individual organ level is called as organ clearance
• It can be estimated by dividing the rate of elimination by each
organ with the concentration of drug presented to it. Thus,

x
Vd C
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• The total body clearance, ClT = ClR +ClH + Clother .
• Clearance by all organs other than kidney is some times known
as nonrenal clearance ClNR .
• It is the difference between total clearance and renal clearance
according to earlier an definition(equation(17).
• Substituting dX/dt = KEX from equ.3 in above equ.we get
• Since X/C = Vd ( from equation 13) the equ. (21) can be written as

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• Parallel equation can be written for renal and hepatic clearance as:
• Since, KE= 0.693/t1/2 ( from equa. 11), clearance can be related to
half life by the following equation

Identical equations can be written for renal clearance and
hepatic clearance in which cases the half life will be urinary
excretion half-life for unchanged drug and metabolism half-life
respectively. Equa. (22) shows that as clearance time
decreases, as in renal insufficiency, half life of the drug
increases. As the clearance time takes into account volume of
drug changes in Vd as in obesity like condition will reflect
changes in clearance time.
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Books:-
1. Brahmankar DM. and Jaiswal SB. Biopharmaceutics and Pharmacokinetics-A
Treatise; 3rd edition; Vallabh Prakashan, Delhi, pg 260-284.
2. Shargel L., Wu-Pong S. and Yu AB. Applied Biopharmaceutics &
Pharmacokinetics; 5th Edition; pg 51-68.
3. Jambhekar SS. and Breen PJ. Basic Pharmacokinetics ; Pharmaceutical Press,
pg 29-52.
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Articles:-
1. Yu RH & Cao YX, “A method to determine pharmacokinetic parameters
based on andante constant rate intravenous infusion.” Scientific Reports
2017.
2. Jalali MB. , “Some methods for estimating parameters of linear one
compartment open models with bolus intravenous injection and constant rate
intravenous infusion using urinary excretion data.” Int. J. Pharm. 1982, 1, 91-
94.
3. Tarek AA. , “Pharmacokinetics of drugs following IV Bolus, IV Infusion, and
Oral Administration.” In. Tech. 2015.
4. Gaur A., Saini SP., Garg S. and Srivastava A., “Pharmacokinetics of ofloxacin
after a single intravenous bolus dose in neonatal calves.” J. Vet. Pharmacol.
Ther. 2004, 2.
5. Hill SA., “Pharmacokinetics of drug infusions” Br. J. Anaesth. 2004, 3, 76-80.
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