The document discusses the one-compartment open model used to describe drug distribution and elimination following administration. It describes the model assumptions of rapid distribution throughout a single homogeneous compartment and first-order elimination. It then discusses four specific models: intravenous bolus dosing, continuous intravenous infusion, extravascular administration with zero-order absorption, and extravascular administration with first-order absorption. Key parameters like elimination rate constant, half-life, volume of distribution, and clearance are also defined.

1. Mrs. Arti Majumdar
ONE COMPARTMENT MODEL

2. CONTENTS
 Introduction
 Types of one compartment open model:
1. One compartment open model, I. V. bolus
administration
2. One compartment open model, continuous I.V.
infusion
3. One compartment open model, E.V.
Administration, zero order absorption
4. One compartment open model E.V.
Administration, first order absorption

3. ONE COMPARTMENT OPEN MODEL
(Instantaneous Distribution Model)
 The time course of drug concentration determined after the
administration can be satisfactorily explained by assuming
the body as single well mixed compartment with first order
disposition process. The term open indicates that the input
and output are unidirectional.
 One – compartment open model is generally used to
describe plasma levels following administration of a single
dose of a drug.

4. ONE COMPARTMENT MODEL IS BASED
UPON FOLLOWING ASSUMPTIONS
 The body is considered as a single kinetically homogenous
unit that has no barriers to movement of drug.
 Applied for drugs that distributes rapidly throughout the
body.
 Elimination is a first order process with first order rate
constant.
 Drugs move dynamically in and out of the compartment.
 The rate of input is greater than rate of output.
 Any change in plasma drug concentration reflects
proportional change in drug concentration throughout the
body.
However the model does not assume that the drug
concentration in plasma is equal to that in other body tissues.

5. TYPES OF ONE COMPARTMENT OPEN
MODEL
 Depending upon the rate of input, Following one
compartment open models can be defined:
1. One compartment open model, I. V. bolus
administration
2. One compartment open model, continuous I.V.
infusion
3. One compartment open model, E.V. Administration,
zero order absorption
4. One compartment open model E.V. Administration,
first order absorption

6. One-compartment open model
Intravenous Bolus Administration
 When drug that distributes rapidly in the body is
given in the form of a rapid intravenous injection, 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

7.  The rate of drug presentation to the body is given by following
expression
dX/dt= Rate in (availability)- Rate out (elimination) (1)
 Since rate in or absorption is absent, the equation becomes
dX/dt= -Rate out (2)
 If rate out or elimination follows first order kinetics then
dX/dt= -KE X (3)
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

8. 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 due to distribution, the
phase being called as elimination phase. Elimination
phase can be characterized by 4 parameters-
1. Elimination rate constant
2. Apparent volume of distribution
3. Elimination half life
4. Clearance

9. Elimination rate constant (KE)
 Elimination rate constant represents the fraction of drug removed
per unit of time
 KE has a unit of reciprocal of time (e.g. minute-1, hour-1, and day-1)
 With first-order elimination, the rate of elimination is directly
proportional to the serum drug concentration
 The equation for elimination rate
dX/dt= -KE X …..3
now integrating this equation 3
lnX= ln X0 - KE t.........4
Where X0= amount of drug at time t = zero. Above equation
can also be written in the following exponential format as
X=Xoe- KE t …………5
 Above equation shows that disposition of drug in one
compartment kinetics is monoexponential.

10. Elimination rate constant (KE)
 Equation 4 can be written in common logarithm (log to
the base 10 form) as
logX = log X0 – KEt/2.303………..6
 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
X= Vd C………….7
 Where Vd = proportionality constant popularly known
as the apparent volume of distribution
So equation 6 can be written as
logC = log C0 – KEt/2.303………..8

11. One-compartment open model

12. Elimination half life (t1/2)
 The elimination half life is sometimes called ‘‘biological
half-life’’ of a drug
 The elimination half life is defined as the time taken for
the amount of unchanged drug in the body as well as
plasma concentration (h, min, day, etc.) to reduce to half
(or 50%) of the initial amount of drug.
 The elimination half life is a secondary parameter that
depends upon primary parameters clearance and
volume of distribution.
t1/2 = 00.693 ………9
KE
t1/2 = 00.693Vd ………10
ClT

13. Apparent Volume of Distribution (Vd)
 Apparent volume of distribution may be defined as the
hypothetical volume of body fluids into which a drug is
distributed.
 The volume of distribution represents a volume that must
be considered in estimating the amount of drug in the body
from the concentration of drug found in the sampling
compartment.
 In general, drug equilibrates rapidly in the body. When
plasma or any other biologic compartment is sampled and
analyzed for drug content, the results are usually reported
in units of concentration instead of amount
 Each individual tissue in the body may contain a different
concentration of drug due to differences in drug affinity for
that tissue. Therefore, the amount of drug in a given location
can be related to its concentration by a proportionality
constant that reflects the volume of fluid in which the drug
is dissolved.

14. Apparent Volume of Distribution (Vd)
 Drugs which binds selectively to plasma proteins, e.g.
Warfarin have apparent volume of distribution smaller
than their real volume of distribution
 Drugs which binds selectively to extravascular tissues,
e.g. Chloroquines have apparent volume of distribution
larger than their real volume of distribution. The Vd of
such drugs is always greater than 42 L (Total body
water)
 In order to determine the apparent volume of
distribution of a drug, it is necessary to have
plasma/serum concentration versus time data.
………11

15. Apparent Volume of Distribution (Vd)

16. Clearance (Cl)
 Clearance is a measure of the removal of drug from the body.
 Plasma drug concentrations are affected by the rate at which drug
is administered, the volume in which it distributes, and its
clearance.
 A drug’s clearance and the volume of distribution determine its half
life.
 It is the most important parameter in clinical drug applications and
is useful in evaluating the mechanism by which a drug is eliminated
by the whole organism or by a particular organ.
 For One compartment pharmacokinetics , clearance is calculated
using:
Cl = K/Vd
Cl= dX/dt
C
………12
………13

17. Clearance (Cl)
 Clearance (expressed as volume/time) describes the
removal of drug from a volume of plasma in a given unit
of time (drug loss from the body)
 Clearance does not indicate the amount of drug being
removed. It indicates the volume of plasma (or blood)
from which the drug is completely removed, or cleared,
in a given time period.
 Figures in the following two slides represent two ways
of thinking about drug clearance:
 In the first Figure, the amount of drug (the number of
dots) decreases but fills the same volume, resulting in a
lower concentration

18. Clearance (Cl)
The amount of drug (the number of dots) decreases but
fills the same volume, resulting in a lower concentration

19. Clearance (Cl)
Another way of viewing the same decrease would be to
calculate the volume that would be drug-free if the
concentration were held constant as presented in the
second Figure

20. Clearance (Cl)
 The most general definition of clearance is that it is ‘‘a
proportionality constant describing the relationship
between a substance’s rate of elimination (amount per
unit time) at a given time and its corresponding
concentration in an appropriate fluid at that time.’’
 Clearance can also be defined as ‘‘the theoretical volume
of blood (plasma or serum) or other biological fluids
from which the drug is completely removed per unit
time.’’
 It is expressed as ml/min or ltr/hrs

21. Clearance (Cl)
 Drugs can be cleared from the body by different
pathways, or organs, including hepatic
biotransformation and renal and biliary excretion.
 Total body clearance of a drug is the sum of all the
clearances by various mechanisms.
ClT= ClR +ClH + Clothers ………14
ClT=KEX………….15
C
ClT= 0.693Vd………….16
T1/2

22. ONE COMPARTMENT INTRAVENOUS
INFUSION
 Rapid i.v. injection is unsuitable when the drug has
potential to precipitate toxicity or when
maintenance of a stable concentration or amount of
drug in the body is desired. In such a situation, the
drug (for example, several antibiotics, theophylline,
procainamide, etc.) is administered at a constant
rate (zero-order) by i.v. infusion.
 In contrast to the short duration of infusion of an
i.v. bolus (few seconds), the duration of constant
rate infusion is usually much longer than the half-
life of the drug.

23. Advantages of zero-order infusion
of drugs
 Ease of control of rate of infusion to fit
individual patient needs.
 Prevents fluctuating maxima and minima
(peak and valley) plasma level, desired
especially when the drug has a narrow
therapeutic index.
 Other drugs, electrolytes and nutrients
can be conveniently administered
simultaneously by the same infusion line
in critically ill patients.

24. The model can be represented as:
Ro= Zero order rate of drug infusion
Ke= First order elimination rate constant

25. Estimation of pharmacokinetic parameters
 At any time during infusion , the rate of change in amt. of
drug in the body , dx/dt is the difference between the zero
order rate of drug infusion Ro and first order rate
elimination , ‐Ke X:
dx/dt = R0‐ KeX .........1
(X=amount of drug in the body at any time t remaining to be
eliminated.)
Integration and rearrangement of above equation yields:-
X=Ro/Ke(1-e-Ket) …..2
As a constant relationship exists in between drug
conc in plasma C & X. Thus:
X=VdC
Vd is a Proportionality constant(apparent volume of
distribution)

26. Rearranging the eqn we get:-
C= Ro/KeVd(1-e-Ket)…..3
C = Ro/Clt(1-e-Ket)…..4
The total body clearance, Clt, also called as total
systemic clearance, is an additive property of
individual organ clearances.

27.  At the start of constant rate infusion, the amount of
drug in the body is zero, & hence there is no
elimination.
 As time passes, the amount of drug in the body rises
gradually(elimination rate is less than the rate of
infusion) until a point after which the rate of
elimination = rate of infusion i.e. the concentration
of drug in plasma approaches a constant value
called as steady state or infusion equilibrium.

28. Plasma concentration-time profile for a drug given by constant rate i.v.
infusion (the two curves indicate different infusion rates Ro and 2Ro for
the same drug)

29. AT STEADY STATE
 At steady state, the rate of change of amount of
drug in the body is zero. So eqn 1 becomes:-
Zero=Ro-KeXss
KeXss=Ro …….5
Css=Ro/Kevd….6
Css=Ro/Clt i.e infusion rate/clearance ….7
Xss= amount of drug in the body at steady state.
Css= amount of drug in plasma at steady state.

30.  Substituting the value ofCss =Ro/Clt in eqn 4:
C=Css(1-e-ket)…..8
 Rearrangement yields:
[Css-c]=e-Ket
Css
log CSS-C = -Ket …….9
Css 2.303

31.  The time to reach steady state concentration is
dependent upon the elimination half life .
 If n is the number of half-lives passed since the start of
infusion, then the eqn 7 can be written as:-
C=CSS [1-(1/2)n]………10

32.  It takes very long time for the
drugs having longer half lives
before the steady state
concentration is reached.(Eg:-
Phenobarbital)
 An I.V. loading dose is given to
yield the desired steady-state
immediately upon injection
prior to starting the infusion.
 It should then be followed
immediately by I.V. infusion at a
rate enough to maintain this
concentration.

33.  So the equation for computing the loading dose Xo,L can be
given:
 As X = VdC, the loading dose Xo,L can be given:
X0,L = C ss Vd…..11
 Substitution of Css = Ro/KEVd from equation 6 in above
equation yields another expression for loading dose in
terms of infusion rate:
X0,L =Ro/KE…….12
 The equation describing the plasma concentration-time
profile following simultaneous i.v. loading dose (i.v. bolus)
and constant rate i.v. infusion is the sum of two equations
describing each process
…….13

34.  If we substitute CssVd for Xo,L and CssKEVd for Ro
in above equation and simplify it, it reduces to
C = Css …..14
 indicating that the concentration of drug in plasma
remains constant (steady) throughout the infusion
time.

35. EXTRAVASCULAR ADMINISTRATION
 When a drug is administered by extravascular route
(e.g. oral, i.m., rectal, etc.), absorption is a prerequisite
for its therapeutic activity.
 The rate of absorption may be described
mathematically as a zero-order or first-order process.
A large number of plasma concentration- time profiles
can be described by a one- compartment model with
first-order absorption and elimination. However,
under certain conditions, the absorption of some
drugs may be better described by assuming zero-
order (constant rate) kinetics.

36. Distinction between zero-order and first-order
absorption processes. Figure a is regular plot, and Figure
b a semilog plot of amount of drug remaining to be
absorbed (ARA) versus time t.

37.  Zero-order absorption is characterized by a
constant rate of absorption. It is independent of
amount remaining to be absorbed (ARA), and its
regular ARA versus t plot is linear with slope equal to
rate of absorption while the semilog plot is described
by an ever-increasing gradient with time.
 In contrast, the first-order absorption process is
distinguished by a decline in the rate with ARA i.e.
absorption rate is dependent upon ARA; its regular plot
is curvilinear and semilog plot a straight line with
absorption rate constant as its slope.

38.  After e.v. administration, the rate of change in the
amount of drug in the body dX/dt is the difference
between the rate of input (absorption) dXev/dt and
rate of output (elimination) dXE/dt.
 dX/dt = Rate of absorption – Rate of elimination

39.  For a drug that follows one-compartment kinetics,
the plasma concentration-time profile is
characterized by absorption phase, post-absorption
phase and elimination phase.

40.  During the absorption phase, the rate absorption is
greater than the rate of elimination
 At peak plasma concentration , the rate of absorption
equals the rate of elimination and the change in
amount of drug in the body is zero
 Post absorption is characterized by
 After completion of drug absorption, its rate becomes
zero and the plasma level time curve is characterized
only by the elimination phase.

41. Zero-Order Absorption Model
 This model is similar to that for constant rate infusion.
 All equation that explain the plasma concentration – time
profile for constant rate i.v. infusion are also applicable to
this model.

42. First order Absorption Model Extravascular
Administration
 A drug that enters the body by a first order absorption
process gets distributed in the body according to one -
compartment kinetics and is eliminated by a first - order
process, the model can be depicted as follows

43. •Integration of eque. (5) gives
Transforming in to concentration terms, the eque. becomes
Where, F= fraction of drug absorbed systemically after e.v.
administration .

44. REFERENCES
 Brahmankar D. M., Jaiswal S.B., Biopharmaceutics &
Pharmacokinetics A Treatise, Second Edition 2009
Published by Vallabh Prakashan .
 Milo Glibaldi Biopharmaceutics and Clinical Pharmaceutics,
Reprint 2006 , Fourth Edition published by Pharma book
syndicate, Hyderabad