pharmacokinetic & pharmacodynamic (pk and pd)models of controlled release system

7/30/2019 pharmacokinetic & pharmacodynamic (pk and pd)models of controlled release system

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Pradeep Kumar

M.pharm(pharmaceutics)

Dept. of pharmaceutics

[email protected]


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CONTENT

Introduction

Pharmacokinetic models Pharmacodynamic models

Conclusion

References


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Controlled release:

The term controlled release is associated with therapeutic

agents that may be automatically delivered at predetermined ratesover long period of time.

The main Goals are :

To reduce the frequency of dosing

To increase the effectiveness of the drug by localizing it

To reduce the dose requiredTo provide uniform drug delivery


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PHARMACOKINETIC MODELS FOR CONTROLLED DRUG DELIVERY

Several models have been proposed to explain thepharmacokinetic behavior of controlled drug deliverysystems.

Models of time course profile of absorption andelimination

Loo-Riegelman and Wagner-Nelson model

Model independent pharmacokinetic analysis


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MODELS OF TIME COURSE PROFILE OF ABSORPTION AND ELIMINATION

Based upon either zero order or first order rate constantsfor absorption and elimination.

Zero order absorption followed by first order elimination.

Slow first order absorption followed by first order elimination.

Rapid first order absorption of part of those, then release andabsorption of the reminder dose over an extended period of timeby zero order kinetic process followed by first order eliminationprocess.

Rapid first order absorption of part of those ,then release andabsorption of the reminder dose over an extended period of timeby slow first order kinetic process followed by first order eliminationprocess.


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ASSUMPTIONS:

The elimination of the drug follows first orderprocess

The rate of distribution is governed by the rateof drug absorption

All kinetic process, except for drug absorption,are linear.


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ZERO ORDER ABSORPTION FOLLOWED BY FIRST ORDER

ELIMINATION

Fk0C = (1 e-Ke

T)Vd ke

kO = zero order drug absorption rate constant

Zero order release systems are ideal controlled delivery

formulations.


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First Order Absorption Followed by First Order Elimination

The concentration of the drug after single dose administrationfrom sustained release product following first order releasekinetics can be given by,

FDka

C1 = (e-ket - e-kat)Vd (kake)

When ka< ke flip-flop phenomenon is observed.

Repeated dosing of first order release formulation generallyobserves, lower C max and longer TMAX in comparison toconventional release formulation


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Rapid first order absorption of a part of dose, then release and

absorption of the reminder dose over an extended period of

time by zero order kinetic process followed by first order

elimination process

The release of the drug from dosage forms occur in two

ways :The intial dose is released for immediate availability to

be absorbed by first order process and the remaining fraction is

absorbed at constant rate i.e ., a slow zero order process which

results in zero order absorption over a prolonged period time

FDIk0 Fk0C = (e-ke

t- e

-ka

t) + (e-ket)

V(ka - ke) Vdke


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With this model, both the rate of decline ofdrug levels from the fast release component andthe rate increase in level due to slow zero orderrelease component are controlled by drugelimination rate constant.

Cont


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Rapid first order absorption of part of those ,thenrelease and absorption of the reminder dose over an

extended period of time by slow first order kinetic

process followed by first order elimination process This type of .formulation also contain two portions- one to describe

Rapid first order absorption and the other for slow first order

absorption.

FDIkaC= (e-ket -e-kat) +

Vd(kake)

FDMkr (e-ket -e-krt)

Vd(krke)


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Models of time course profile of absorption and elimination

Limitations:

The absorption rate for sustained release products maybe slower the after conventional dosage form ,it may bemixed or combined first and zero order processtherefore can not be precisely described by a singlemodel dependent equation


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Loo-Riegelman Model

This model states that the amount of drug absorbed atany given time is equal the sum of the amount of drugpresent in central comportment and peripheralcomportment and of the amount eliminated by all routes.

The only assumption with this model is the drugpharmacokinetic can be described by at least twocompartment model.

To use this model a drug must be given by the i.v. route asreference.

(XA)T/(XA) = CT+ke 0T Cdt + (XP)T/VC/ke0

T Cdt


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Two approximations can be made from kineticequation using Loo-Riegelman model:

If a plot of percent unabsorbed [100(1-(XA)(XA)] versustime on semi logarithmic

plot yields a straight line, it is suggestiveof a apparent 1st order absorption kinetics.

If a plot of percent unabsorbed [100(1-(XA)(XA)] versustime on a rectilinear plot yield a straight line, it is

suggestive of an apparent zero order absorptionkinetics.

Cont


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Wagner-Nelson method

Wagner-Nelson model is restricted to drugs, which follow one-compartment open-model characteristics and in a way demonstratethe actual disposition of drugs after i.v. administration.

This method has the advantage of not needing results from an i.v.reference standard.

This model is usually not recommended for the analysis of data after

oral administration of controlled delivery, which follow multi-compartmental disposition characteristics.


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The Wagner-Nelson model is given as follows;

(XA)T/(XA)=CT + Ke 0TCdt/ Ke 0Cdt

For many drugs, which are given as SR formulations andhave a rapid distribution phase relative to drug

absorption, the Wagner- Nelson model can provide areasonable basis for the estimation of absorptionparameters.


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Model independent pharmacokinetic analysisThe model independent disposition of the drug from a

sustained release formulation is applicable in thesituation when the drug is eliminated following linearformulation.

By using statistical moment theory, one can calculate

MRT after administration of standard and sustainedrelease formulation.

MRT is defined as the mean time for the intact drugmolecule through the body tissue and involves acomposite of all kinetic process including release fromthe dosage form drug absorption in to the body anddrug disposition.


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The MRT can be used in comparative to evaluate the in vivoperformance of sustained release dosage form.

Longer the MRT the more sustained or prolong is the

absorption of the drug assuming a constant elimination rateconstant.

MAT is more relevant in assessing the absorption process thanMRT.

The longer the MAT the more sustained or prolonged is theabsorption of the drug.

Cont


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MAT parameter can be used in calculation of apparentabsorption rate constant in the case of first orderabsorption process and absorption time (T) in the case of

zero order absorption process.

MAT= 1/Ka

MAT= T/2

Cont


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Pharmacodynamic Models

Fixed effect model:

The drug concentration can be related to a pharmacological effectwhich is either observed or not.

The major draw back of fixed effect model is inability to relate a rangeof drug concentration to broad range of pharmacological effect.

Linear model:

The most fundamental model directly linking drug concentration andeffect.

E= P.C

E= P.C + EO

The parameter P estimated from E-EOversus C

E= P. log C + EO


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Conclusion Pharmacokinetic and pharmacodynamic models help

in understanding the various parameters involved withcontrolled release systems.

They also help in designing specific requirementsrequired for drug molecules to be formulated ascontrolled release systems, there by enhancing better

opportunities for the development of controlledrelease systems in future.


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References

Controlled drug release, conceptsand advances,by S.P.Vyas & Roop K.Khar.

Controlled drug delivery, fundamentals &

applications,by Joseph R.Robinson, Vincent.H.L.Lee. Encyclopedia of pharmaceutical technology, by

James.Swarbrick

Applied Biopharmaceutics & pharmacokinetics,

by Leon Shargel. www.sciencedirect.com
http://www.sciencedirect.com/http://www.sciencedirect.com/


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pharmacokinetic & pharmacodynamic (pk and pd)models of controlled release system