Presentation by

PAYAL H. PATIL (M.pharm, 2nd sem.)

Dept. of pharmaceuticsR.C.Patel Institute of Pharmaceutical Education

and Research, Shirpur.

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CONTENT Introduction. Zero Order Drug release. First Order Drug release. Hixon - Crowell Cube Root Law. Higuchi equation. Korsemeyer - Peppas equation. Peppas & Sahlin equation. Weibull equation. Release profile comparison. The advanced dissolution software Conclusion. References.

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DRUG RELEASE

• Definition- “It is a process by which a drug leaves a drug

product & is subjected to ADME & eventually becoming available for pharmacological action.”

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RELEASE KINETICS MODELS

• The mathematical models are used to evaluate the kinetics and mechanism of drug release from the dosage form.

• A model is used to express quantitative relationships.

• The model that best fits the release data is selected based on the correlation coefficient (r2) value in various models.

• The model that gives high ‘r2’ value is considered as the best fit of the release data.(considering r2 < or = 1)

• The equation for zero order release is Qt = Q0 + K0 t

where Q0 = Initial amount of drug released.

Qt = Cumulative amount of drug release at time ‘t’

K0 = Zero order release constant

t = Time in hours

• It describes the systems where the drug release rate is independent of concentration of the dissolved substance.

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• As initial amount of drug in solution is usually zero. Therefore , Q0 = zero So equation becomes, Q = Ko t • Hence to represent zero order drug release. Plot of % Cumulative drug Release Vs time is plotted which gives a straight line.

1. Topical drug delivery system.2. Transdermal drug delivery system.3. Implantable depot system.4. Oral control release systems.5. Oral osmotic tablets.6. Matrix tablet with low solubility drug.

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• The first order release equation is Log Qt = Log Q0- Kt /2.303 

where Q0 = Initial amount of drug

Qt = Cumulative amount of drug release at time ‘t’

K = First order release constant t = Time in hours• The drug release rate depends on its concentration.

• EXAMPLE: Sustained release dosage form.

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• A graph is plotted of the log % of drug remaining (to be released) Vs time ,which gives a straight line.

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• The Hixson - Crowell release equation is M0

1/3- Mt 1/3= kt

Where, M0 = Initial amount of drug released.

Mt = Amount of drug remained at time ‘t’

K = Hixson crowell release constant t = Time in hours.

• It describes the drug releases by dissolution & considers the surface area & geometric shape of dissolving entity.

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• A linear plot of the cube root of the initial drug amount minus the cube root of drug amount remaining Vs time(hours) for the dissolution data in accordance with the Hixson-crowell equation.

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• The Higuchi release equation is

Q = KHt1/2 OR Mt / M0 = kt1/2

where, Q = Cumulative amount of drug release at time ‘t’

KH = Higuchi constant

t = Time in hours• The Higuchi equation suggests that the drug release by

diffusion.• Explained release of water soluble & poorly water

soluble drug from variety of matrixes including semisolid & solid.

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• A graph is plotted between cumulative % of drug release Vs square root of time(hours) it gives a straight line.

• Korsmeyer – peppas equation is F = (Mt /M∞ ) = Ktn

where, F = Fraction of drug released at time ‘t’ Mt = Amount of drug released at time ‘t’ M∞ = Amount of drug release ‘∞’.

K = Constant related to structural & geometrical factors.

n = Diffusion or release exponent used for elucidation of drug release mechanism

t = Time in hours• Model for understanding release behavior of drug from

hydrophilic matrix. 14

• A graph is plotted between the log % of drug release Vs log time(hours) it gives a straight line.

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RELEASE EXPONE

NT (n)VALUE

DRUG RELEASE MECHANISM

RATE AS A FUNCTION OF TIME(dMt/dt)

<0.5 Quasi fickian diffusion t0.5

0.5 Fickian diffusion t0.5

0.5<n<1 Anomalous transport tn-1

1 Nonfickian case 2 transport Zero order release

n>1 Nonfickian Supercase 2 transport

tn-1

• ‘n’ is estimated from linear regression of Log(Mt/M∞) Vs log t.

TABLE: Release exponent & drug release mechanism.

• Peppas & Sahlin equation is mainly followed, when release of drug depends upon it’s diffusion as well as on relaxation of polymer.

• Equation can be given by, Mt / M∞ = Kdt

m+Krt

2m

Where, Kd= Diffusion constant Kr= Relaxation constant m = Purely fickian diffusion exponent for device of any geometrical shape,which exhibit controlled release.

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PEPPAS-SAHLIN MODEL

• A graph is plotted between the cumulative % of drug release Vs time(hours) it gives a straight line.

• Exponential function widely used for analysis & characterization of drug dissolution process from different dosage forms.• Equation can be given by, m = 1 – exp [-(t – Ti )b / a ]

Taking log on Both Sides, Log [-ln (1-m)] = b log (t-Ti) - log a

Here, m = accumulated fraction, a = time scale process, Ti = lag time ( generally zero),

b = shape factor, t = time. 19

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• A graph is plotted between the Log of drug released Vs log time.

Mathematical evaluation of in vitro release profiles of HPMC matrix tablet containing carbamazepine

associated to β-cyclodextrin.TABLE: r2 value of different formulations.

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DISSOLUTION MODELS

COMPLEX MIXTURE PHYSICAL

MIXTURE

Spray dried

Freeze dried

Zero order 0.963 0.979 0.998

First order 0.993 0.987 0.988

Higuchi 0.997 0.999 0.987

Weibull 0.999 0.994 0.997

DIFFERENT METHODS:1)Model dependent methods - All this models.

2)Model Independent methods -a)Difference(dissimilarity) factor(f1):

Calculates % difference between two curves at each time point & is measurement of the relative error between

two curves, value between 0 to 15.

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b) Similarity factor(f2): Calculates similarity in the % dissolution between two curves & it is a logarithmic reciprocal square root transformation of the sum of squared error, value between 50 to 100.

Here, R & T = Dissolution measurements at n time points of the reference and test, respectively. n = no. of time points. t = Time

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PROCEDURE SET BY FDA FOR DISSOLUTION PROFILE COMPARISON:• At least 12 units of reference & test product used.• Use mean dissolution values from both curves at each time interval to calculate f1 & f2 .• Measurement should be carried out under same test conditions.• f1 & f2 values are sensitive to number of dissolution time points.• For rapidly dissolving products comparison is not necessary.• For curves to be considered similar, f1 values should be close to 0 & f2 close to 100.

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Mathematical evaluation of in vitro release profiles of HPMC matrix tablet containing carbamazepine associated to β-cyclodextrin.

TABLE: f1 & f2 values for each comparison.

a The first f1 Value is obtained when the first formulation

on the left column is set as reference.

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COMPARISONS f1a (0-15) f2(50-100)

SD × FD 5.5 OR 5.8 74.0

SD × PM 28.4 OR 39.6 36.8

FD × PM 25.2 OR 33.8 40.4

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THE ADVANCED DISSOLUTION SOFTWARE

• PCP DISSOLUTION SOFTWARE• Win SOTAX (for automatic disso apparatus)

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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.

Brahmankar D.M. & Jaiswal S.B. , Biopharmaceutics and pharmacokinetics-A treatise, 5thed,Vallabh prakashan, New delhi, 325-350.

Mathiowitz E., Encyclopedia of controlled drug delivery, 1sted,Vol. І & II, A wiley interscience publication, 70, 921-935.

Sinko P. J., Martin’s physical pharmacy & pharmaceutical sciences, 5thed, Lippincott williams & wilkins, 337-349.

Subramanyam C.V.S, Textbook of physical pharmaceutics, 2nd ed, Vallabh prakashan, New delhi, 216-218, 344-345.

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REFERENCES

Mathematical evaluation of in vitro release profiles of HPMC matrix tablet containing carbamazepine

associated to β-cyclodextrin, European Journal of Pharmaceutics & Biopharmaceutics ,May 2004, 177–179.

Mathematical modeling of drug delivery, International Journal of Pharmaceutics, 2008, 328-343. A simple equation for the description of solute release. III. Coupling of diffusion & relaxation , International Journal of Pharmaceutics, June 1989,169-172. Chein Y.W., Novel drug delivery systems, 2nded, Vol 50, Marcel & dekker, Newyork, 130-139. Remington’s The science & practice of pharmacy, 21st ed, Vol 1, Lippincott william & wilkins, 687

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