Noncompartment Model - Pharmacokinetics
Dr C. V. S. SubrahmanyamPrincipal
Gokaraju Rangaraju College of PharmacyHyderabad
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- Explain the concepts of noncompartment
model- Explain the differences between
compartment and noncompartment models- Describe different pharmacokinetic
parameters in noncompartment model
Noncompartment Model - PharmacokineticsObjectives of this session
The participant shall be able to:
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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
Noncompartment Model - Pharmacokinetics
Time of peak concentration, tmax
Area under the curve, AUC Grcp
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Noncompartment Model - Pharmacokinetics
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Cmax
Graphic
method
Equation: Cmax is a function of several factors
F KaDCmax = (e-k10tmax – e-katmax)
V1(ka – k10)
Noncompartment Model - Pharmacokinetics
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Cmax First point Cmax
It raises a question about the measurement
of true Cmax, because of insufficient early
sampling timesIt requires a carefully chosen pilot studyEarly time points between 3 to 15 minutesFollowed by additional sample collection (two
to five) in the first hour
Noncompartment Model - Pharmacokinetics
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tmax
Eq: tmax is a function of several factors 2.303 log (ka /k10)
tmax = (ka – k10)
Graphic
method
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AUC
Area of one trapezoid =
(1/2)(Cn-1 + Cn)(tn – tn-
1)Area under the curve, AUC =
(areas of the trapezoids)
Noncompartment Model – AUC Ct*
[AUC]0 = [AUC]0
t + Z
Z = termination elimination rate constant, h-1
Where Ct* = last measurable Ct, g/ml
Elimination rate constant is calculated
separately
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Noncompartment Model - PharmacokineticsUseful for estimating certain pharmacokinetic
parameters without specifically
referring to any models
Bioavailability Clearance
Apparent volume of distributionFraction of dose of drug absorbedMean absorption time
Mean resident time,
Applications
Average plasma steady state conc. of drug
or its metabolite
Estimating PK parameters
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Noncompartment Model - PharmacokineticsAdvantages
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 - PharmacokineticsDisadvantages
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 bloodc) It is applicable only for linear
pharmacokinetics
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Noncompartment and Compartment models –
ComparisonCompartment models Noncompartment models
These require elaborate assumptions to fit the data.
Do not require assumptions to compartment model.
Curve fitting of experimental data using computers. It is a tedious method.
Simple algebraic equations. No curve fitting and no computers.
Time course changes in C1 can be predicted precisely.
Time course changes in C1 cannot be predicted precisely.
Applicable to linear and nonlinear pharmacokinetics
Applicable to linear pharmacokinetics.
C1 - time profile is regarded as expressions of exponents.
C1 – time profile is regarded as statistical distribution.
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Noncompartment and Compartment models –
ComparisonCompartment 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
theoryCategorisation of moments
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
Zero Moment
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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) Ct*
[AUC]0 = [AUC]0
t + Z
Z = termination elimination rate constant, h-1
Where Ct* = last measurable Ct, g/ml
Elimination rate constant is calculated
separatelyGrcp
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Noncompartment Model –
Statistical Moment Theory Application
s Used for calculating bioavailability and
drug clearance
First moment of a plasma drug concentration
- time profile is referred to as mean
residence time (MRT)
First Moment
[AUMC]0 t x C. dt
MRT = = [AUC]0
C.dt Grcp
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Noncompartment Model –
Statistical Moment Theory Area of one
trapezoidArea under the curve, AUC t*Ct* C*
[AUC]0 = [AUC]0
t + + Z Z
2
Z = termination elimination rate constant, h-1
Where Ct* = last measurable Ct, g/ml
Elimination rate constant is calculated
separately
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Noncompartment Model –
Statistical Moment Theory Second Moment
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 dtVRT = =
C dt AUC Higher moments are prone to
unacceptable
level of errors
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Noncompartment Models – PK Parameters Mean Residence Time – Half LifeMean residence time (MRT) defined as the
average amount of time spent by the
drug in the body before being eliminated
MRT represents the time for 63.2% of drug
eliminated when given i.v. bolus injectionIt is analogous to plasma elimination half life,
t1/2, i.e., 50% elimination
AUMC t x C. dt
MRT = = AUC
C.dt
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Noncompartment Models – PK Parameters Mean Residence Time – Half LifeLike half life, MRT is a function of both
distribution and elimination 1MRT =
k10 0.693Plasma elimination half life, t1/2 =
k10Plasma elimination half life, t1/2 = 0.693MRTIn two compartment model, concept of MRT
would be still useful, because of non
compartment model Grcp
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Noncompartment Models – PK Parameters Mean Residence Time – Half LifeMRTiv is used for comparison. For eg: following
constant rate of infusion T
MRTiv = MRTinst - 2 Where T = duration of infusion,
h
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Noncompartment Models – PK Parameters
AUMCV1
ss = doseiv (AUC)2
Apparent Volume of Distribution at Steady State Apparent volume of distribution (V1
ss) is
independent of drug elimination
This equation is applicable to i.v. bolus
administrationIt solely reflects the anatomic space occupied
by the drug and the relative degree of drug
binding in blood and extravascular space Grcp
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Noncompartment Models – PK Parameters
Infused dose (AUMC)V1
ss = (AUC)2
Apparent Volume of Distribution at Steady State If drug is given by short term constant rate i.v.
infusion
Infused dose x V1
ss = 2(AUC)
R0 x (AUMC) R0 2
V1ss = = 2(AUC)2 2(AUC)
Since infused dose is equal to R0
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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 DoseivCl =
AUC
R0 Cl =
C1ss
Since infused dose is equal to R0
After a single i.v. bolus injection
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Noncompartment Models – PK Parameters Mean Absorption Time (MAT) - Drug
AbsorptionMAT is defined as the differences in
mean
residence time (MRT) after different modes
of administrationMRTni = mean residence time of drug by
non-
instantaneous route, h
MRTiv = mean residence time of drug by i.v.
bolus injection, h
MAT = MRTni – MRTiv
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) 1MAT =
ka 0.693
Absorption half life, t1/2 = kaAbsorption half life, t1/2 =
0.693MAT
TMAT =
2
When absorption follows zero order
T = time over which absorption takes place, h
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Noncompartment Models – PK Parameters MAT - Applications
Used for the comparison of dosage formsEg: comparison of furosemide dosage forms
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Noncompartment Models – PK Parameters Steady State Plasma Drug
ConcentrationThe C1ss is a function of the effective
rate
of dosing and total body clearance of the
drug in a patient
In multiple dosage regimen
RoC1
ss = Cl
When absorption follows zero order
In continuous infusion
AUCss
Cavss =
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Noncompartment Models – PK Parameters Steady State Plasma Drug
ConcentrationAverage plasma drug concentration at steady
state, Cavss F x dosing rate
Cav
ss = ClIf 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 StateTime 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 GrcpCVS
Noncompartment Models – PK Parameters Predicting the Time to Steady StateIn 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)Grcp
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Noncompartment Models – PK Parameters
Bioavailability (F) of a dosage form
AUCoral Div
Absolute bioavailability, F = AUCiv Doral
Bioavailability
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 Grcp
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Noncompartment Models – PK Parameters
Fraction of a drug metabolized, fm, is equal
to ratio of zero moments of the metabolite,
administered the drug to the metabolite
directly
Fraction of Drug Metabolised, fm
AUCx1
Fraction metabolized, fm = AUC1
AUCx1 = AUC of metabolite, when drug
is
administered by i.v. bolus injection,
zero to infinity time, g.h/mlAUC1 = AUC of metabolite, when metabolite
is administered by i.v. bolus injection,
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Noncompartment Models – PK Parameters
Metabolite is administered in equimolar i.v.
dose
Fraction of Drug Metabolised, fm
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