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 - Pharmacokinetics

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AUC

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 Models – Analysis

I.v. bolus injection – Calculation of AUC

and AUMCGrcp

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Noncompartment Models – Analysis

I.v. bolus injection - AUC Grcp

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Noncompartment Models – Analysis

I.v. bolus injection - AUMC Grcp

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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 Grcp

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Noncompartment Models – PK Parameters

Oral product - AUMC Grcp

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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

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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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