Noncompartment Model - Pharmacokinetics
Dr C. V. S. Subrahmanyam
Principal
Gokaraju Rangaraju College of Pharmacy
Hyderabad
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Noncompartment Model - Pharmacokinetics
Objectives of this session
The participant shall be able to:
- Explain the concepts of noncompartment
model
- Explain the differences between
compartment and noncompartment models
- Describe different pharmacokinetic
parameters in noncompartment model
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Noncompartment Model - Pharmacokinetics
Noncompartmen model pharmacokinetics is a
new approach devised to study the time
course of drug in the body based on the
statistical moment theory
Model independent method
Overcomes some of the drawbacks
associated with classical compartment
modeling
Peak plasma drug concentration, Cmax
Time of peak concentration, tmax
Area under the curve, AUC
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Noncompartment Model - Pharmacokinetics
Cmax
Graphic
method
Equation: Cmax is a function of several factors
F KaD
Cmax =
(e-k10tmax – e-katmax)
V1(ka – k10)
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Noncompartment Model - Pharmacokinetics
Cmax
First point Cmax
It raises a question about the measurement
of true Cmax, because of insufficient early
sampling times
It requires a carefully chosen pilot study
Early time points between 3 to 15 minutes
Followed by additional sample collection (two
to five) in the first hour
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Noncompartment Model - Pharmacokinetics
tmax
Graphic
method
Eq: tmax is a function of several factors
2.303 log (ka /k10)
tmax =
Grcp
(ka – k10)
CVS
AUC
Area of one trapezoid =
(1/2)(Cn-1 + Cn)(tn – tn-1)
Area under the curve, AUC =
Grcp
(areas of the trapezoids) CVS
Noncompartment Model - Pharmacokinetics
AUC
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Noncompartment Model – AUC
[AUC]0 = [AUC]0t +
C t*
Z
Where Ct* = last measurable Ct, g/ml
Z = termination elimination rate constant, h-1
Elimination rate constant is calculated
separately
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Noncompartment Model - Pharmacokinetics
Applications
Useful for estimating certain pharmacokinetic
parameters without specifically
referring to any models
Estimating PK parameters
Clearance
Bioavailability
Apparent volume of distribution
Fraction of dose of drug absorbed
Mean absorption time
Mean resident time,
Average plasma steady state conc. of drug
or its metabolite
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Noncompartment Model - Pharmacokinetics
Advantages
Derivation of PK parameters is easy, because
of simple algebraic equations
Mathematical treatment remains same, for
drug or metabolite, provided elimination
follows first order kinetics
Drug disposition kinetics need not be
described in detail
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Noncompartment Model - Pharmacokinetics
Disadvantages
a) Information regarding plasma drug
concentration-time profile is expressed as
an average
b) Generally not useful for describing the
time course of drug in the blood
c) It is applicable only for linear
pharmacokinetics
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Noncompartment and Compartment models –
Comparison
Compartment models
Noncompartment models
These require elaborate
assumptions to fit the data.
Curve fitting of experimental
data using computers. It is a
tedious method.
Time course changes in C1 can
be predicted precisely.
Applicable to linear and
nonlinear pharmacokinetics
C1 - time profile is regarded as
expressions of exponents.
Do not require assumptions to
compartment model.
Simple algebraic equations. No
curve fitting and no computers.
Time course changes in C1
cannot be predicted precisely.
Applicable to linear
pharmacokinetics.
C1 – time profile is regarded as
statistical distribution.
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Noncompartment and Compartment models –
Comparison
Compartment models
Noncompartment models
These are useful for most of
the situations, though
assumptions of modeling are
involved.
Particularly useful for the
applications of clinical
pharmacokinetics,
bioavailability, and
bioequivalence studies.
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Noncompartment Model –
Statistical Moment Theory
Approach is based on the statistical moment
theory
Categorisation of moments
Zero Moment
Zero moment of a drug concentration in
plasma versus time curve is referred to
as the total area under concentration
from zero to infinity, or simply AUC
[AUC]0 =  C dt
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Noncompartment Model –
Statistical Moment Theory
Area of trapezoid =
(1/2)(Cn-1 + Cn)(tn – tn-1)
Area under the curve, AUC =
(areas of the trapezoids)
[AUC]0 = [AUC]0t +
C t*
Z
Where Ct* = last measurable Ct, g/ml
Z = termination elimination rate constant, h-1
Elimination rate constant is calculated
separately
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Noncompartment Model –
Statistical Moment Theory
Applications
Used for calculating bioavailability and
drug clearance
First Moment
First moment of a plasma drug concentration
- time profile is referred to as mean
residence time (MRT)
MRT =
[AUMC]0
[AUC]0
=
 t x C. dt
 C.dt
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Noncompartment Model –
Statistical Moment Theory
Area of one trapezoid
Area under the curve, AUC
[AUC]0 = [AUC]0t +
t*Ct*
+
C*
Z
Z2
Where Ct* = last measurable Ct, g/ml
Z = termination elimination rate constant, h-1
Elimination rate constant is calculated
separately
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Noncompartment Models – Analysis
I.v. bolus injection – Calculation of AUC
and AUMC
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Noncompartment Models – Analysis
I.v. bolus injection - AUC
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Noncompartment Models – Analysis
I.v. bolus injection - AUMC
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Noncompartment Models – Analysis
Oral product - Calculation of AUC and
AUMC
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Noncompartment Models – PK Parameters
Oral product - AUC
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Noncompartment Models – PK Parameters
Oral product - AUMC
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Noncompartment Model –
Second Moment
Statistical Moment Theory
Second moment is referred to as variance of
the mean residence time (VRT) of the
drug in the body
t2.C dt
(1–MRT)2 C dt
VRT =
=
 C dt
AUC
Higher moments are prone to unacceptable
level of errors
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Noncompartment Models – PK Parameters
Mean Residence Time – Half Life
Mean residence time (MRT) defined as the
average amount of time spent by the
drug in the body before being eliminated
MRT =
AUMC
AUC
=
 t x C. dt
 C.dt
MRT represents the time for 63.2% of drug
eliminated when given i.v. bolus injection
It is analogous to plasma elimination half life,
t1/2, i.e., 50% elimination
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Noncompartment Models – PK Parameters
Mean Residence Time – Half Life
Like half life, MRT is a function of both
distribution and elimination
1
MRT =
k10
Plasma elimination half life, t1/2 =
0.693
k10
Plasma elimination half life, t1/2 = 0.693MRT
In two compartment model, concept of MRT
would be still useful, because of non
compartment model
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Noncompartment Models – PK Parameters
Mean Residence Time – Half Life
MRTiv is used for comparison. For eg: following
constant rate of infusion
MRTiv = MRTinst -
T
2
Where T = duration of infusion, h
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Noncompartment Models – PK Parameters
Apparent Volume of Distribution at Steady State
Apparent volume of distribution (V1ss) is
independent of drug elimination
AUMC
V1ss =
doseiv
(AUC)2
This equation is applicable to i.v. bolus
administration
It solely reflects the anatomic space occupied
by the drug and the relative degree of drug
binding in blood and extravascular space
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Noncompartment Models – PK Parameters
Apparent Volume of Distribution at Steady State
If drug is given by short term constant rate i.v.
infusion
Infused dose (AUMC)
V1ss =
(AUC)2
Infused dose x 
V1ss =
2(AUC)
Since infused dose is equal to R0
V1ss =
R0 x  (AUMC)
2(AUC)2
=
R0 2
2(AUC)
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Noncompartment Models – PK Parameters
Drug Clearance (Cl)
Clearance is defined as the ratio of the dose
after a single i.v. injection to the total area
under the drug concentration – time curve
After a single i.v. bolus injection
Doseiv
Cl =
AUC
Since infused dose is equal to R0
Cl =
R0
C1ss
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Noncompartment Models – PK Parameters
Mean Absorption Time (MAT) - Drug Absorption
MAT is defined as the differences in mean
residence time (MRT) after different modes
of administration
MAT = MRTni – MRTiv
MRTni = mean residence time of drug by non-
instantaneous route, h
MRTiv = mean residence time of drug by i.v.
bolus injection, h
Same equation is used for i.m. injection
Absorption follows first order kinetics
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Noncompartment Models – PK Parameters
Mean Absorption Time (MAT)
1
MAT =
ka
Absorption half life, t1/2 =
0.693
ka
Absorption half life, t1/2 = 0.693MAT
When absorption follows zero order
MAT =
T
2
T = time over which absorption takes place, h
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Noncompartment Models – PK Parameters
MAT - Applications
Used for the comparison of dosage forms
Eg: comparison of furosemide dosage forms
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Noncompartment Models – PK Parameters
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Noncompartment Models – PK Parameters
Steady State Plasma Drug Concentration
The C1ss is a function of the effective rate
of dosing and total body clearance of the
drug in a patient
In continuous infusion
C1ss =
Ro
Cl
In multiple dosage regimen
AUCss
Cavss =

When absorption follows zero order
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Noncompartment Models – PK Parameters
Steady State Plasma Drug Concentration
Average plasma drug concentration at steady
state, Cavss
F x dosing rate
Cavss =
Cl
If a drug is given in a dose of 400 mg every
8 hours, dosing rate is 400/8, i.e., 50
mg/hour
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Noncompartment Models – PK Parameters
Predicting the Time to Steady State
Time required for the drug to reach steady
state, i.e., 99%, takes 6.65 half lives.
 In extravascular route (or prolonged
release drug products), the time required
to attain ss takes longer than predicted by
biological half life
 In multicompartment disposition, time
required to attain to ss is shorter than
that predicted by terminal half life
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Noncompartment Models – PK Parameters
Predicting the Time to Steady State
In noncompartment models, when the drug is
administered repetitive dosing, fss
AUC0’
fss =
AUC
AUC = area under the curve in single dose
Bioavailability
Bioavailability refers to the fractional dose of
a dosage form reaches systemic circulation
For i.v. bolus injection, bioavailability is
referred as unity (=1)
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Noncompartment Models – PK Parameters
Bioavailability
Bioavailability (F) of a dosage form
AUCoral Div
Absolute bioavailability, F =
AUCiv Doral
Equation assumes equal clearances in oral
and i.v. doses
Relative bioavailability, Fr, may be
expressed by comparing the zero
moments of a product with a standard
product
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Noncompartment Models – PK Parameters
Fraction of Drug Metabolised, fm
Fraction of a drug metabolized, fm, is equal
to ratio of zero moments of the metabolite,
administered the drug to the metabolite
directly
Fraction metabolized, fm =
AUCx1
AUC1
AUCx1 = AUC of metabolite, when drug is
administered by i.v. bolus injection,
zero to infinity time, g.h/ml
AUC1 = AUC of metabolite, when metabolite
is administered by i.v. bolus injection, Grcp
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Noncompartment Models – PK Parameters
Fraction of Drug Metabolised, fm
Metabolite is administered in equimolar i.v.
dose
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