Modeling of dissolution data Presented by: NAKAT ANUP RAMESH 1st semester,

Guided By: Dr.A.R.Madgulakar Department Of Pharmaceutics, AISSMS COLLEGE OF PHARMACY,

PUNE1

Contents Introduction. Zero Order Drug release. First Order Drug release. Weibull model Higuchi model. Hixon - Crowell Cube Root model. Korsemeyer - Peppas equation. Baker - lonsdale model Hopfenberg model Similarity factor. Conclusion. References.

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Dissolution

Definition-

It is a process in which a solid substance solubilizes in a given solvent i.e. Mass transfer from the solid surface to the liquid phase.

Drug dissolution in an aqueous medium is an

important condition of systemic absorption.

Dissolution is the rate controlling step in the absorption of drug with low solubility.

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Zero Order release kineticsSame amount of drug is released per unit time.

Drug dissolution from pharmaceutical dosage form that do not disaggregate and release the drug slowly,

Can be given by following equation,

Q= Qo + Kot

Where,

Q =amount of drug released or dissolved.Qo=initial amount of drug in solution.Ko=zero order drug release constant .

Zero Order Drug Release

Topical drug delivery system.

Transdermal drug delivery system.

Implantable depot system.

Oral control release systems.

Oral osmotic tablets.

Matrix tablet with low solubility drug.6

Zero Order release kinetics

As initial amount of drug in solution is usually zero,

So equation becomes, Q= Kot Hence to represent

zero order drug release, Plot of % Cumulative drug Release Vs time is plotted.

Zero order drug release

0

1

2

3

4

5

6

0 0.2 0.4 0.6 0.8 1 1.2time in hr%

cum

ulat

ive

drug

rele

ase

time in hr

Linear (time in hr)

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• To obtain good correlation between in vitro- in vivo dissolution rate, In vitro is always carried out under sink condition.

This can be achieved by: Bathing the dissolving solid by fresh solvent

from time to time. Increasing the volume of dissolution fluid. Adding a Water miscible solvent such as alcohol

to the dissolution fluid. By adding selected adsorbents to remove the

dissolved drug.

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First Order Drug Release

Sustained release dosage form. Release rate depends on concentration of drug.Dissolution is said to be under nonsink condition. Release rate equation for first order kinetics can be given by,

Qt=Q0e-Kt

Or

In(Qt/Q0)=kt

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First Order Release Kinetics

Hence to illustrate relationship between drug release & time, plot of log of % drug remaining Vs time is plotted.

First order drug release

1.821.841.861.881.9

1.921.941.961.98

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0 1 2 3 4 5

time in hrlo

g of

%dr

ug re

mai

ning

log of %drugremaining

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If we plot a graph between conc. Of dissolved drug Vs. time is plotted.

Fist order dissolution and Zero order dissolution under sink and nonsink condition are compared

Dissolution rate under sink and nonsink condition

0

1020

30

4050

60

0 2 4 6

time in hr

conc

entra

tion

of

diss

olve

d dr

ug Zero orderdissolutionunder sinkcondition

First orderdissolutionunder non-sinkcondition

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Weibull Model • This model can successfully applied to all kinds of

dissolution curve.• This model express the accumulated fraction of the

drug m, in solution at time t,

Equation can be given by,

a- Scale parameter –define as time scale of process.Ti-location parameter-lag time before the onset o the

dissolution process.b- shape parameter-characterize the curve exponential (b=1) sigmoid, s-shape (b>1) parabolic with higher initial slope (b<1)

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Hence plot of, logarithm of the dissolved amount of drug Vs logarithm of time.

Weibull model

0

1

2

3

4

5

6

0 5 10

log of time

log

of d

isso

lved

am

ount

of

drug

Dissovledamount ofdrug

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Disadvantage: It does not characterize the dissolution kineticproperties of the drug. Not any single parameter related with dissolution

rate of drug

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Higuchi Equation• Explained release of water soluble & poorly water soluble

drug from variety of matrixes including semisolid & solid.

• Higuchi equation is mainly followed, when release of drug depend upon it’s diffusion.

• Equation can be given by,

Mt / M0 = kt1/2

Mt = amount of drug release in time t. M0 =Initial amount of drug release. t= time required.

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Hence plot of % cumulative drug released Vs square root of time is plotted.

Higuchi Equation

0

20

40

60

80

100

0 1 2 3

SQRT

% c

umul

ativ

e dr

ug

rele

ase % cumulative

drug release

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Higuchi Equation

Hixon –Crowell cube root law

• The geometric shape of the dosage form stays constant as dissolution is occurring then the dissolution occurs in plane that are parallel to the dosage form surface.

• The rate of dissolution is based on the cube root of the weight of the particle.

Equation can be given by,

M01/3-M1/3= kt

Where,M0=original mass of drug particles.M =mass of particle undissolved.t =time required.

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Hence plot of cube root of mass of drug dissolved Vs time is plotted.

Hixson-Crowel cube root law

0

1

2

3

4

5

0 2 4 6 8

time in hrcu

be ro

ot o

f mas

s of

dru

g di

ssol

ved

cube root of mass ofdrug dissolved

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Hixon –Crowell cube root law

Korsemeyer-Peppas equationModel for understanding release behavior of drug from hydrophilic matrix.

Equation can be given by,

Mt/M∞ = Ktn

Mt = amount of drug release in time t.M∞= amount of drug release in time ∞.k = constant related to structural & geometrical

factors.n = release exponent related to release mechanism

used for elucidation of drug release mechanism.20

Korsemeyer-Peppas equation

Hence plot of log cumulative % release Vs log time is plotted.

This plot explains the diffusion mechanism by which drug diffuses from dosage form.

n value indicates the release mechanism.

Korsmeyer-Peppas equationy = 1.176x + 1.1264

R2 = 0.9729

0

0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8

log of time

log

of %

cum

ulat

ive

drug

re

leas

e

log of % cumulative drugrelease

Linear (log of % cumulativedrug release)

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Korsemeyer-Peppas equation

n value Diffusion mechanism <0.5

Quasi fickian

0.5 Fickian 0.5<n<1 Anomalous

1 Non fickian case 2

n>1 Non fickian super case 2

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Baker-Lonsdale ModelDeveloped from the Higuchi model.

Describes the Drug controlled released from Spherical matrix.

Equation can be given by,

If matrix is heterogeneous

Matrix porosity can be describe by:

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Hence plot of left side of equation Vs. time is plotted.

Baker-Lonsdale model

00.5

11.5

22.5

33.5

44.5

5

0 1 2 3 4 5 6

time in hr

left

sid

e of

equ

atio

n

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Hopfenberg ModelThe release of drug from surface-eroding devise

with several geometries was analysed by Hopfenberg.

He describes the drug released from slabs, spheres, infinite cylinders showing heterogeneous erosion.

Mt-amount of drug dissolved in time t Ko-erosion rate constant. Co-initial conc. Of drug in matrix. ao-initial radius of sphere or cylinder. The value of n is 1,2,3 for slab , cylinder and and

sphere respectively.25

• Modified form of this model is developed in that the lag time (l)is placed in the beginning of the drug release from pharmaceutical dosage form.

• In the rate limiting step of drug release the matrix erosion is done. So this equation does not influence the matrix erosion.

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Of all these above mentioned models, the kinetic model that best fits the dissolution data was evaluated by comparing the correlation coefficient ( r ) values obtained in various models, the model that gave higher ‘r’ value is considered as best fit model.

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Other release parameter tx%, Sampling time and Dissolution efficiency are

the parameter used to characterise drug release and gives information of drug release.

tx%-time necessary to the release of a determined percentage of drug.

Sampling time-amount of drug dissolved in that time.

Dissolution efficiency-

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Release profile comparision

Method that compare the drug release

1)Statistical method. a) Single time point dissolution. b) Multiple time point dissolution.

2)Model Independent method. a) Ratio test procedure. b) Pair wise procedure.

3)Model dependent method.

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1)Statistical method.

The method is based on in the analysis of variance can be distinguished in one-way analysis of variance (ANOVA) and multivariate analysis of variance (MANOVA).

It is the difference between the means of two drug release data set in single time point dissolution or in multiple time point dissolution.

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2) Model independent method. a) Ratio test procedure- It is the relation between parameters obtain

from release assay of test of the reference formulation and the release assay of test product at same time.

b) Pair wise procedure- This includes: 1)Difference Factor. 2) Similarity factor.

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1)Difference factor. It is the percent error between two curves

over all time points, denoted by f1.

n-sampling number.Rj-% dissolved of the reference product.Tj-% dissolved of the test product.

The percent error is zero when test and reference profile are identical.

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2)Similarity factor- It is logarithmic transformation of the sum-

squared error difference between the test and reference product over all time points.

It is used to denote similarity between two profile, denoted by f2.

It is fits results between 0-100

This method is more adequate to dissolution profile comparisons when more than 3 or 4 dissolution time points are available.

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FDA has set a standard of f1 value between 0 to 15 & f2 value between 50 to 100 shows similarity of the dissolution profile.

To compare dissolution treatment effect the 12 individual dosage units should take.

Model independent method are very easy to apply.

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Conclusion

Hence this conclusion can be drawn that the in vitro drug release kinetics is necessary step to be done to study the drug release patterns from the dosage form.

The graphs obtained from kinetic data states the efficiency of drug release from the dosage

form.

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Martin’s physical pharmacy &pharmaceutical sciences, fifth edition, Patrick J. sinko,lippincott Williams & Wilkins publication,337-349.

Kinetic analysis of dissolution data of ambroxol hydrochloride sustained release matrix tablet,IJPS,sept-oct 2006,594-598.

Modeling and comparison of dissolution profiles

European Journal of Pharmaceutical Sciences 13 (2001) ,123-133

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References

References

Evaluation of mathematical models describing drug release from lipophilic matrices , journal of controlled release, august 2006,224-228.

Compaction properties, drug release kinetics and fronts movement studies from matrices combining mixtures of swellable and inert polymers, International Journal of Pharmaceutics, September 2007, 61–73.

www.dissolutiontech.com/DTresour/899art/dis sprofile.html

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ReferencesMathematical evaluation of in vitro release

profiles of hydroxypropylmethylcellulose matrix tablet

containing carbamazepine associated to b-cyclodextrin, European Journal of Pharmaceutics and Biopharmaceutics ,May 2004, 177–179.

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Thank you !!!

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