Compartment Model - Biopharmaceutics ppt

Compartment Model

1. School of Pharmacy
COMPARTMENT MODEL
By
Dr. B Sree Giri Prasad
HEAD OF DEPARTMENT
DEPARTMENT OF
PHARMACEUTICS

2. NNRG SCHOOL OF PHARMACY 2
CONTENTS
•Basic considerations in pharmacokinetics
•Compartment models
•One compartment model
•Assumptions
•Intravenous bolus administration
•Intravenous infusion
•Extravascular administration (zero order and first order
absorption model)

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BASIC CONSIDERATIONS IN
PHARMACOKINETICS
•Pharmacokinetic parameters
•Pharmacodynamic parameters
•Zero, first order & mixed order kinetic
•Rates and orders of kinetics
•Plasma drug conc. Time profiles
•Compartmental models – physiological model
•Applications of pharmacokinetics
•Non compartment model

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A TYPICAL PLASMA DRUG CONC. AND TIME CURVE
OBTAINED AFTER A SINGLE ORAL DOSE OF A DRUG,
SHOWING VARIOUS P'KINETIC AND P’DYNAMIC
PARAMETERS DEPICTED IN BELOW FIGURE

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PLASMA DRUG CONCENTRATION – TIME PROFILE
Effectiveness of Dosage Regimen
Concentration of Drug in the Body
Conc. at Site of
action
Conc. in whole Blood (Plasma, Serum), Saliva,
Urine, CSF
PK Parameters determine drug Conc.

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PHARMACOKINETIC PARAMETERS
Three important parameters useful in assessing the bioavailability of a drug
from its formulation are:
1.Peak plasma concentration ( c
max )
the point at which, maximum concentration of drug in plasma.
Units : µg/ml
• Peak conc. Related to the intensity of pharmacological response,
it should be above MEC but less than MSC.
• The peak level depends on administered dose and rate of
absorption and elimination.

7. NNRG SCHOOL OF PHARMACY 7
2.Time of peak concentration (t
max )
the time for the drug to reach peak concentration in plasma (after extra
vascular administration).
Units : hrs
•Useful in estimating onset of action and rate of absorption.
• Important in assessing the efficacy of single dose drugs used to
treat acute conditions (pain, insomnia ).

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3.Area under curve (AUC)
It represents the total integrated area under the plasma level-time profile and
expresses the total amount of the drug that comes into systemic circulation after
its administration.
Units : µg/ml x hrs
•Represents extent of absorption – evaluating the bioavailability of drug from its
dosage form.
•Important for drugs administered repetitively for treatment of chronic
conditions (asthma or epilepsy).

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PHARMACODYNAMIC PARAMETERS
1.Minimum effective concentration (MEC)
Minimum concentration of drug in plasma/receptor site required to produce
therapeutic effect.
Concentration below MEC – sub therapeutic level
Antibiotics- MEC
2.Maximum safe concentration(MSC)
Concentration in plasma above which adverse or unwanted effects are
precipitated.
•Concentration above MSC – toxic level

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3.Onset time
Time required to start producing pharmacological response.
Time for plasma concentration to reach mec after administrating drug
4.Onset of action
The beginning of pharmacologic response.
It occurs when plasma drug concentration just exceeds the required mec.
5.Duration of action
The time period for which the plasma concentration of drug remains above MEC
level.
6.Intensity of action
It is the minimum pharmacologic response produced by the peak plasma conc. Of
drug.
7.Therapeutic range the drug conc. Between MEC and MSC

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CONCEPT OF “HALF- LIFE”
½ Life = how much time it takes for blood levels of drug to decrease
to half of what it was at equilibrium
There are really two kinds of ½ life…
“Distribution” ½ life = when plasma levels fall to half what they were
at equilibrium due to distribution to/storage in body’s tissue reservoirs.
“Elimination” ½ life = when plasma levels fall to half what they were
at equilibrium due to drug being metabolized and eliminated.
It is usually the elimination ½ life that is used to determine dosing
schedules, to decide when it is safe to put patients on a new drug.

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PHARMACOKINETIC MODELS AND
COMPARTMENTS

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Pharmacokinetic Modelling
Compartment
Models
Non-Compartment
Models
Physiologic
Models
Caternary
Model
One compt.
Mamillary
Model
Multi
compt.
Two compt.
I. V
Bolus
Single oral Dose
I .V infusion
Intermittent I.V Infusion
Multiple Doses
I.V Bolus
Oral Drug
AUC, MRT, MAT, Cl,
V
SS

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PHARMACOKINETIC MODELS
Means of expressing mathematically or quantitatively, time course of
drug through out the body and compute meaningful pharmacokinetic
parameters.
Useful in :
•Characterize the behavior of drug in patient.
•Predicting conc. Of drug in various body fluids with dosage regimen.
•Calculating optimum dosage regimen for individual patient.
•Evaluating bioequivalence between different formulation.
•Explaining drug interaction.
Pharmacokinetic models are hypothetical structures that are used to
describe the fate of a drug in a biological system following its
administration.
Model
•Mathematical representation of the data.
•It is just hypothetical

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WHY MODEL THE
DATA ?
There are three main reasons due to which the data is
subjected to modelling.
1.Descriptive: to describe the drug kinetics in a simple way.
2.Predictive: to predict the time course of the drug after
multiple dosing based on single dose data, to predict the
absorption profile of the drug from the iv data.
3.Explanatory: to explain unclear observations.

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PHARMACOKINETIC MODELING IS USEFUL IN :-
•Prediction of drug concentration in plasma/ tissue/ urine at any point
of time.
•Determination of optimum dosage regimen for each patient.
•Estimation of the possible accumulation of drugs/ metabolites.
•Quantitative assessment of the effect of disease on drug’s adme.
•Correlation of drug concentration with pharmacological activity.
•Evaluation of bioequivalence.
•Understanding of d/i.

17. NNRG SCHOOL OF PHARMACY 17
COMPARTMENTAL
MODELS
•A compartment is not a real physiological or anatomic
region but an imaginary or hypothetical one consisting
of tissue/ group of tissues with similar blood flow &
affinity.
•Our body is considered as composed of several
compartments connected reversibly with each other.

18. NNRG SCHOOL OF PHARMACY 18
ADVANTAGES
•Gives visual representation of various rate processes involved in drug
disposition.
•Possible to derive equations describing drug concentration changes in each
compartment.
•One can estimate the amount of drug in any compartment of the system
after
drug is introduced into a given compartment.
DISADVANTAGES
•Drug given by IV route may behave according to single compartment
model
but the same drug given by oral route may show 2 compartment behaviour.
•The type of compartment behaviour i.E. Type of compartment model may
change with the route of administration.

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1.Central compartment
Blood & highly perfused tissues such as heart, kidney, lungs, liver,
etc.
2.Peripheral compartment
Poorly per fused tissues such as fat, bone, etc.
MODELS:
“OPEN” and “CLOSED” models:
•The term “open” itself mean that, the administered drug dose is
removed from body by an excretory mechanism ( for most
drugs, organs of excretion of drug is kidney)
•If the drug is not removed from the body then model refers as
“closed” model.
TYPES OF COMPARTMENT

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LOADING DOSE
•A drug dose does not show therapeutic activity unless it reaches the
desired steady state.
•It takes about 4-5 half lives to attain it and therefore time taken will
be too long if the drug has a long half-life.
•Plateau can be reached immediately by administering a dose that
gives the desired
steady state instantaneously before the commencement of
maintenance dose x
0
.
•Such an initial or first dose intended to be therapeutic is called as
priming dose or loading dose x
0,L
.

22. NNRG SCHOOL OF PHARMACY 22
CALCULATION OF LOADING DOSE
•After e.V. Administration, cmax is always smaller than that achieved after i.V.
And hence loading dose is proportionally smaller.
•For the drugs having a low therapeutic indices, the loading dose may be divided
into smaller doses to be given at a various intervals before the first maintenance
dose.
•A simple equation for calculating loading dose is : x
o,l = css,av vd
F
•When vd is not known, loading dose may be calculated by the following
equation :
x
o,l = 1_ X
o
(1 – e
-ket
) (1 – e
-kat
)
•Given equation applies when ka >> ke and drug is distributed rapidly.
•When drug is given i.V. Or when absorption is extremely rapid, the absorption
phase is neglected and the above equation reduces to accumulation index:

23. ASSUMPTIONS
1.One compartment
The drug in the blood is in rapid equilibrium with drug in the extra-vascular
tissues. This is not an exact representation however it is useful for a number
of drugs to a reasonable approximation.
2.Rapid mixing
We also need to assume that the drug is mixed instantaneously in blood or
plasma.
3.Linear model
We will assume that drug elimination follows first order kinetics.
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24. LINEAR MODEL - FIRST ORDER KINETICS
•FIRST-
ORDER
KINETICS
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25. MATHEMATICALLY
•This behavior can be expressed mathematically
as :
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26. ONE COMPARTMENT MODEL
One compartment model can be defined :
•One com. Open model –i.V. Bolus.
•One com. Open model -cont. Intravenous infusion.
•One com. Open model -extra vas. Administration (zero-order
absorption)
•One com. Open model - extra vas. Administration (First-order
absorption )
•INTRAVENOUS (IV) BOLUS ADMINISTRATION
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27. RATE OF DRUG PRESENTATION TO BODY IS:
•dx =rate in (availability)–rate out( Eli)
dt
•Since rate in or absorption is absent, equation becomes dx = - rate out
dt
•If rate out or elimination follows first order kinetic
Dx/dt = -k
ex (eq.1)
ELIMINATION PHASE:
Elimination phase has three parameters:
•Elimination rate constant
•Elimination half life
•Clearance
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28. ELIMINATION RATE
CONSTANT
•Integration of equation (1)
•In x = ln xo – k
e t(eq.2)
Xo = amt of drug injected at time t = zero i.e.
Initial
amount of drug injected
X=xo e
-ket ( eq.3)
•Log x= log xo – k
e t
2.303 (eq.4)
•Since it is difficult to directly determine amount of drug in body x, we use
relationship that exists between drug conc. In plasma C and X; thus
(eq. 5)•X = v
d C
•So equation-8 becomes
log c = log co –k
e t
2.303 (eq.6)
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8

29. K
E = KE + KM +KB +KL +….. (Eq.7)
(K
E is overall elimination rate constant)
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30. ELIMINATION HALF LIFE
T
1/2 = 0.693
K
E (eq.8)
•Elimination half life can be readily obtained from the graph of
log c versus t
•Half life is a secondary parameter that depends upon the
primary
parameters such as clearance and volume of distribution.
•T
1/2 = 0.693 V
d
Cl
T (eq.9)
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31. APPARENT VOLUME OF
DISTRIBUTION
•Defined as volume of fluid in which drug appears to be
distributed.•Vd= amount of drug in the body
= Plasma drug concentration
x
C
(eq.10)
Vd = xo/co
=I.V.Bolus dose/co(eq.11)
•Example: 30 mg i.V. Bolus, plasma conc.= 0.732
mcg/ml. =30000mcg/0.732mcg/ml
…….12.A
•Vol. Of dist. =
30mg/0.732mcg/ml
= 41 liter.
•For drugs given as i.V.Bolus,
V
d (area)=xo/K
E.Auc
•For drugs admins. Extra. Vas.
V
d (area)=f xo/k
e.Auc
……..12.B
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32. CLEARANCE
Clearance =rate of elimination
Plasma drug conc.. (Or)cl=dx /dt
C…….,(eq.13)
Thus, renal clearance
Hepatic clearance=
=rate of elimination by
kidney
C
rate of elimination by liver
C
Other organ clearance = rate of elimination by organ
C
Total body clearance:
Cl
t = cl
r + cl
h + cl
other ……,(eq.14)
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33. •According to earlier definition
cl = dx /dt
C
•Submitting eq.1 dx/dt = K
E X , above eq. Becomes ,cl
t = K
E X/ C .., (Eq
15)
•By incorporating equation 1 and equation for vol. Of dist. ( Vd= X/C ) we can
get
cl
t =K
E vd(eq.16)
•Parallel equations can be written for renal and hepatic clearance.
(eq.17)
(eq.18)
Cl
h =km vd
Cl
r =ke vd
•But, K
E=
0.693/t
1/2
•So,
cl
t = 0.693 vd
(eq.19)
t
1/2
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34. •For non compartmental method which follows one compartmental
kinetic is :
•For drug given by i.V. Bolus
cl
t = xo…..20.A
Auc
•For drug administered by e.V.
Cl
t = f xo …..20.B
Auc
…….(eq. 21)
•For drug given by i.V. Bolus
renal clearance = xu∞
auc
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35. ORGAN CLEARANCE
•Rate of elimination by organ= rate of presentation to the organ – rate of
exit from the organ.
•Rate of elimination =q. C
in- Q.C
out
(Rate of extraction)=Q (c
in- c
out)
Cl
organ=rate of extraction/c
in
=q(c
in-c
out)/c
in
…………… .(eq 22)=Q.Er
•Extrac
tion
ratio:
ER=
(c
in-
c
out)/ c
in
•ER is an index of how efficiently the eliminating organ clear the
blood
flowing through it of drug.
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36. According to ER, drugs can be classified as
•Drugs with high ER (above 0.7)
•Drugs with intermediate ER (between 0.7-0.3)
•Drugs with low ER (below 0.3)
•The fraction of drug that escapes removal by organ is expressed
as F= 1- ER
•Where f=systemic availability when the eliminating organ is
liver.
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37. HEPATIC
CLEARANCE
Cl
h = cl
t – cl
r
Can also be written down from eq 22
Cl
h= Q
H ER
H
Q
H= hepatic blood flow. ER
H = hepatic
extraction ratio.
Hepatic clearance of drug can be
divided into two groups :
1.Drugs with hepatic blood flow rate-
limited clearance
2.Drugs with intrinsic capacity- limited
clearance
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38. HEPATIC BLOOD FLOW
•F=1-er
h
= AUC
oral
AUC
i.V
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39. INTRINSIC CAPACITY CLEARANCE
•Denoted as cl
int, it is defined as the inherent ability of an organ to
irreversibly remove a drug in the absence of any flow limitation.
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40. ONE COMPARTMENT OPEN MODEL:
INTRAVENOUS INFUSION
•Model can be represent as : ( i.v infusion)
Drug
…eq 23
…eq 24
Dx/dt =r
o-k
ex
X=r
o/k
e(1-e
-ket)
Since X =v
dc
C= r
o/k
evd(1-e
-ket) …eq 25
= R
o/cl
t(1-e
-ket)…eq 26
Blood & other
Body tissues
R
0
Zero order
Infusion
rate
K
E
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41. •At steady state. The rate of change of amount of drug in the body is zero ,eq
23 becomes
Zero=r
o-k
ex
ss
K
ex
ss=r
o
C
ss=r
o/k
ev
d
=R
o/cl
t i.E
…27
…28
…29
infusion rate ....30
…31
Clearance
Substituting eq. 30 in eq. 26
•C=c
ss(1-e
-
ket) Rearrangement yields:
•[C
ss-c]=e
-
ket
.
...32
…33
C
ss
Log
C
SS-C
C
ss
=-k
et
2.303
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42. •If n is the no. Of half lives passed since the start of infusion(t/t
1/2)
•Eq. Can be written as
•C=C
SS [1-(1/2)
n]…34
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43. INFUSION PLUS LOADING DOSE
XO,L=C
SSV
D …35
…36
•SUBSTITUTION OF C
SS=R
O/K
EV
D
•XO,L=R
O/K
E
•C=XO,L/V
D E
-KET+ R
O/K
EV
D(1-E
-KET) …
37
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44. ONE COMPARTMENT OPEN MODEL
EXTRA VASCULAR
ADMINISTRATION
•When drug administered by extra vascular route (e.G. Oral, i.M,
rectal ),
absorption is prerequisite for its therapeutic activity.
NNRG SCHOOL OF PHARMACY 44

45. ONE COMPARTMENT MODEL: EXTRA
VASCULAR ADMIN ( ZERO
ORDER ABSORPTION)
•This model is similar to that for constant rate
infusion.
Drug at site
zero order elimination
on
oRate of drug absorption as in case of CDDS , is constant and continues
until the amount of drug at the absorption site (Ex. GIT) is depleted.
oAll equations for plasma drug conc. Profile for constant rate i.V. Infusion
are also applicable to this model.
Blood & other
Body tissues
R0
Absor
pti
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46. ONE COMPARTMENT MODEL: EXTRA
VASCULAR ADMIN ( FIRST ORDER
ABSORPTION)
Blood & other
Body tissues
Drug at
site
K
EK
a
First order
absorption
elimination
•Drug that enters the body by first order absorption process gets distributed
in the body according to one compartment kinetic and is eliminated by first
order process.
•The model can be depicted as follows and final equation is as follows
C=K
a F X
o/V
d (K
a-K
E) [e
-Ket
-e
-Kat
] …41
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47. MULTI- COMPARTMENT
MODELS
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48. •Ideally a true pharmacokinetic model should be the one with a rate constant for
each tissue undergoing equilibrium.
•Therefore best approach is to pool together tissues on the basis of similarity in
their distribution characteristics.
•The drug disposition occurs by first order.
•Multi-compartment characteristics are best described by administration as i.v
bolus and observing the manner in which the plasma concentration declines with
time.
The no. Of exponentials required to describe such a plasma level-time profile
determines the no. Of kinetically homogeneous compartments into which a drug
will distribute.
The simplest and commonest is the two compartment model which classifies the
body tissues in two categories :
1.Central compartment or compartment 1
2.Peripheral or tissue compartment or compartment 2.
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49. THEORY: The working equations can be derived from the mass balance
equation: Gives the following eqaution with time and mass balance
•Above equation Integrating
gives
•
To the equation amount absorbed VERSUS TIME
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CALCULATING K
a
using Wagner- Nelson
Method (Bioavailability Parameters)

50. WAGNER-NELSON METHOD
•Taking this to infinity where cp equals
0
•Finally (A
max - A), the amount remaining to be absorbed can also be
expressed as the amount remaining in the GI, xg
•We can use this equation to look at the absorption process. If, and only
if, absorption is a single first order process
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51. WAGNER-NELSON METHOD
•Example data for the method of wagner-nelson kel (from IV data) = 0.2
hr
-
Time (hr)Plasma
Concentratio
Column 3 Column 4Column 5
kel * AUC
A/V
[Col2 +
(A
max - A)/V
n ΔAUC AUC Col5]
(mg/L)
0.0 0.0 0.0 0.0 0.0 0.0 4.9
1.0 1.2 0.6 0.6 0.12 1.32 3.58
2.0 1.8 1.5 2.1 0.42 2.22 2.68
3.0 2.1 1.95 4.05 0.81 2.91 1.99
4.0 2.2 2.15 6.2 1.24 3.44 1.46
5.0 2.2 2.2 8.4 1.68 3.88 1.02
6.0 2.0 2.1 10.5 2.1 4.1 0.8
8.0 1.7 3.7 14.2 2.84 4.54 0.36
10.0 1.3 3.0 17.2 3.44 4.74 0.16
12.0 1.0 2.3 19.5 3.9 4.9 -
∞ 0.0 5.0 24.5 4.9 4.9 -
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52. WAGNER-NELSON METHOD
•The data (A
max-A)/V versus time can be plotted on semi-log and linear
graph paper
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53. WAGNER-NELSON METHOD
•Plotting (A
max-A)/V versus time produces a straight line on semi-log graph paper
and a curved line on linear graph paper. This would support the assumption that
absorption can be described as a single first process. The first-order absorption
rate constant, ka, can be calculated to be 0.306 hr
-1
from the slope of the line on
the semi-log graph paper.
ADVANTAGES:
•The absorption and elimination processes can be quite similar and accurate
determinations of ka can still be made.
•The absorption process doesn't have to be first order. This method can be used to
investigate the absorption process.
DISADVANTAGES:
•The major disadvantage of this method is that you need to know the elimination
rate constant, from data collected following intravenous administration.
•The required calculations are more complex.
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54. RESIDUAL METHOD (OR )
FEATHERING TECHNIQUE
•Absowhen a drug is administered by extravascular route,
absorption is a prerequisite for its therapeutic activity.
•The absorption rate constant can becalculated
bythe methodof residuals.
•The technique is also known as feathering, peeling and
stripping.
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φ It is commonly used in pharmacokinetics to resolve a
multiexponential curve into its individual components.
φ For a drug that follows one-compartment kinetics and administered
extravascularly, the concentration of drug in plasma is expressed
by a biexponential equation.

55. C=
????????????????????????0
????????????( − )
???????????? ????????????
[e-K
E
t
– e-K
a
t
] (1)
If KaFX0/Vd(Ka-KE) = A, a hybrid constant, then: C = A e
-K
E
t – A e
-K
a
t(2)
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eliminationphase,whenabsorptionisφDuringthe
almostover,K
a<<K
E andthevalueofsecond
exponential e
-Katapproacheszerowhereasthefirst
exponential e
-K
E
t retains some finite value.
φ At this time, the equation (2) reduces to:
??????
−
=
?????? ??????
−
??????????????????(3)
φ In log form, the above equation is:Log C
−
= log A -
??????????????????
2.303
(4)
Where , C
− = back extrapolated plasma concentration values
φA plot of log C versus t yield a biexponential curve with a terminal linear
phase having slope –K
E/2.303
φBack extrapolation of this straight line to time zero yields y- intercept
equal to log A.

56. Plasma conc.-Time profile after oral administration of a
single dose of a drug
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57. φ Subtraction of true plasma concentration values i.e. equation (2)
from the extrapolated plasma concentration values i.e. equation (3)
yields a series of residual concentration value C
τ.
(C
− - C) = C
τ = A e
-K
a
t
(5)
φ In log form , the equation
is:
τ 2.303
log C = log A -
????????????
??????
(6)
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φ A plot of log C
τ versus t yields a straight line with slope - K
a
/2.303 and y-intercept log A.
φ Thus, the method of residual enables resolution of the
biexponential plasma level-time curve into its two exponential
components.
φ The technique works best when the difference between K
a and K
E
is large (K
a/K
E ≥ 3).

58. THREE COMPARTMENT MODEL
AND APPLICATIONS OF
PHARMACOKINETIC
PARAMETERS IN DOSAGE
DEVELOPMENT
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59. THREE COMPARTMENT
MODEL
•Gibaldi & feldman described a three compartment open model to
explain the influence of route of administration .I.E. Intravenous
vs. Oral, on the area under the plasma concentration vs. Time
curve.
•Portman utilized a three compartment model which included
metabolism & excretion of hydroxy nalidixic acid.
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60. CENTRAL
COMPARTMENT
TISSUE
COMPARTMENT
DEEP TISSUE
COMPARTMENT
DRUG INPUT
THREE COMPARTMENT MAMMILLARY
MODEL
TISSUE
COMPARTMENT
CENTRAL
COMPARTMENT
DEEP
TISSUE
COMPARTMENT
K
10
DRUG OUTPUT
K
21 K
13
K
12
K
31
K
10
THREE COMPARTMENT
CATENARY MODEL
RAPID IV
DRUG INPUT
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61. Three compartment model consist of the following compartments .
Central compartment.
Tissue compartment.
Deep tissue compartment.
In this compartment model drug distributes most rapidly in to first or
central compartment.
Less rapidly in to second or tissue compartment .
Very slowly to the third or deep tissue compartment. The third
compartment is poor
in tissue such as bone & fat.
•Each compartment independently connected to the central compartment.
•Notari reported the tri exponential equation c=a e-
t
+ b e
-βt
+ c e
-γt
•A,B,C are the y-intercept of extrapolated lines.
•Α,β,γ are the rate constants
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62. RAPID I.V BOLUS - ADMINISTRATION
•When the drug is administered by i.V the drug will rapidly distributed
in C.C,less rapidly in to T.C. Very slowly in to deep tissue
compartment. Plasma profile
•When the drug is administered by i.V the plasma conc. Will increased
in c.C
this is first order release.
•Theconc. Of drug in c.C. Exhibits an initial distribution this is very
rapid.
•Drug in central compartment exhibits an initial distribution this is very
rapid .
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63. Pharmacokinetic
Parameters
Bioloigical half-life ::
•It is defined as the time taken for the amount of drug in the body as well
as
plasma to decline by one half or 50% its initial value.
•Concentration of drug in plasma as a function of time is c=a e
- t
+ b e
-β t
+
c e
-γ t
•In this equation α>β>γ some time after the distributive phase (i.e. When
time become large) the two right hand side terms values are equal to zero.
•The eq.. Is converted in to
c=a e
-αt
Taking the natural logarithm on both sides
the rate constant of this straight line is ‘α’ and biological half life is t
1/2
=0.693/α
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64. VOLUME OF CENTRAL
COMPARTMENT
•At time=0
C=A e
–α t+ B e
–β t+ C e
–γ t
This equation becomes
C
O = A+B+C -----1
C
O =conc. Of plasma immediately after the i.V administration
•When administered the dose is not distributed in tissue compartment.
•Therefore the drug is present in c.C only .
•If D is dose administered then C
O = D /V
C---------2 V
c=volume of drug in c.C
Combining the 1&2 eq.. We get V
c = d/c
o (c
o----- conc. Of drug in plasma)
ELIMINATION RATE CONSTANT:
Drug that follows three compartment kinetics and administered by i.V injection
the decline in the plasma drug conc. Is due to elimination of drug from the three
compartments. K
e=(a+b+c) α β γ/a β γ +b α γ+ cα β
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65. PHYSIOLOGICALLY BASED
PHARMACOKINETIC MODELS
•Blood flow rate limited or perfusion rate
limited model.
•Drawn on the basis of anatomic and
physiologic data.(More realistic)
•Organs or tissues having no perfusion are
excluded.
•Drug movement to a particular region is
much more rapid than its rate of delivery
to that region by blood - perfusion rate
limited model.
•Thus, applicable to highly membrane
permeable drugs, i.e. Low molecular
weight, poorly ionized and highly lipophilic
drugs.
•For highly polar, ionized and charged drugs,
the model is referred to as membrane
permeation rate limited.
81
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66. 82
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67. REFERENCES
BIOPHARMACEUTICS AND PHARMACOKINETICS. P L MADAN, 1
ST
EDN
BIOPHARMACEUTICS AND PHARMACOKINETICS.
D.M BRAHMANKAR AND SUNIL. B .JAISWAL, 1
ST
EDN
APPLIED BIOPHARMACEUTICS AND PHARMACOKINETICS LEON
SHARGEL AND ANDREW YU, 4
TH
EDN.
BIOPHARMACEUTICS AND CLINICAL PHARMACOKINETICS BY MILO
GIBALDI, 4
TH
EDN.
WWW.GOOGLE.COM
WWW.BOOKS.GOOGLE.COM
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