This document discusses model dependent approaches for drug release testing of controlled drug delivery systems. It provides an overview of various mathematical models that can be used to describe drug release kinetics, including zero-order, first-order, Higuchi, Korsmeyer-Peppas, Hixson-Crowell, Baker-Lonsdale, and Weibull models. It explains the equations and mechanisms of drug release for each model. The document also discusses how to select the best-fitting model by comparing the coefficient of determination and other statistical parameters between models. The overall aim is to predict drug release profiles and optimize controlled drug delivery system performance using appropriate kinetic models.

1. MODEL DEPENDENT APPROACH
FOR
DRUG RELEASE TESTING
OF
CONTROLLED DRUG DELIVERYSYSTEM
MANIPAL COLLEGE OF PHARMACEUTICAL SCIENCES
Submitted by
Neha Benedicta Fernandes
First Year M.Pharm (Pharmaceutics)
Under the guidance of
Dr. Vamshi Krishna T.
Associate Professor, Pharmaceutics
MCOPS, Manipal
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2. CONTENTS
2
Introduction
Model Dependent and Model Independent Approach
Various Approaches to Determine Drug Release
Model Dependent Approaches
Selection of the Best Model
Conclusion
References

3. Mathematical Model
• Empirical / Semi-empirical equation that describes the dependence of release in function of time
Importance
 To predict the drug release profile and optimize release kinetics
 To design new DDS based on general release expressions
 To predict physical parameters and the effect of design parameters and resort to model fitting on
experimental release data.
 To elucidate mass transport mechanism
 Accurate prediction of drug release profile and thereby improve the overall therapeutic efficacy and
safety of the drugs
INTRODUCTION
3

4. Model Dependent Approach
• Based on different mathematical functions, useful to describe the release profile.
• Once a suitable function has been selected, the dissolution profiles are evaluated depending on the
derived model parameters.
Model Independent Approach
• Recommended when the aim is to evaluate the similarities between dissolution/release behaviors
• Involves comparison of the dissolution profile using 2 factors, difference factor (𝒇𝟏) and
similarity factor ( 𝒇𝟐)
• ‘f’ factors are easier to apply and interpret; only one value is obtained to describe the closeness of
the two dissolution profiles.
Statistical Approach
4

5. Model Dependent
Approaches
Zero Order Model
First Order Model
Higuchi Model
Korsmeyer- Peppas Model
Hixson-Crowell Model
Baker- Lonsdale Model
Weibull Model
Hopfenberg Model
Gompertz Model
Sequential Layer Model
Model Independent
Approaches
Difference Factor (𝑓1)
Similarity Factor (𝑓2)
Statistical Approaches
Exploratory Data
Analysis Method
Repeated Measures
Design
Multivariate Approach
(MANOVA)
5
VARIOUSAPPROACHESTO DETERMINE DRUG RELEASE

6. • Dissolution rate is independent of the concentration of the drug undergoing reaction
• Applicable to dosage forms that do not disaggregate and release drug slowly
• The equation for zero order release is
Where,
𝑸𝟎 - Initial amount of drug at time t=0
𝑸𝒕 - Cumulative amount of drug released at time ‘t’
𝑲𝟎 - Zero order release constant (conc/time)
t - Time in hours
𝑸𝒕 = 𝑸𝟎 + 𝑲𝟎𝒕

7. Application
Describes drug dissolution of several types of modified release dosage forms -
• Transdermal systems
• Matrix tablets with low solubility drugs in coated forms, osmotic systems
• Certain classes of medicines intended for antibiotic delivery, heart and blood pressure maintenance, pain
control and antidepressants.
7
Plot of % CDR VS Time
Plot 1

8. • The drug release rate is directly proportional to the concentration of the drug administered
• The first order release equation is
log 𝑸𝒕 = log 𝑸𝟎 - Kt / 2.303
Where,
𝑸𝟎- Initial concentration of drug
𝑸𝒕- Percent of drug remaining at time ‘t’
K- First order release constant
t – Time in hours
8

9. Application:
• This relationship can be used to describe the drug dissolution in pharmaceutical dosage forms such as those
containing water soluble drugs in porous matrices
9
Log % CDR Vs Time
Plot 2

10. • First mathematical model which explains drug release from matrix system
• It describes the drug release as a diffusion process based on Fick’s Law and is square root time
dependent
• The Higuchi release equation is
Q=𝑲𝑯 . 𝒕𝟏/𝟐
Where,
Q – Cumulative amount of drug released at time ‘t’
𝑲𝑯- Higuchi constant
t - Time in hours

11. Application
• Applicable for some transdermal systems and matrix tablets with water soluble drugs.
11
Cumulative % CDR VS Square Root of Time
Plot 3

12. • It describes drug release from a polymeric system
• The Korsmeyer-Peppas equation is:
F= (
𝑴𝒕
𝑴
)= 𝑲𝒎𝒕𝒏
Where,
F - Fraction of drug released at time ‘t’
𝑴𝒕 - 𝐀𝐦𝐨𝐮𝐧𝐭 𝐨𝐟 𝐝𝐫𝐮𝐠 𝐫𝐞𝐥𝐞𝐚𝐬𝐞𝐝 𝐚𝐭 𝐭𝐢𝐦𝐞 ‘t’
M - Amount of drug in dosage form
𝑲𝒎 - 𝐊𝐢𝐧𝐞𝐭𝐢𝐜 𝐜𝐨𝐧𝐬𝐭𝐚𝐧𝐭
n - Diffusion or release exponent
t - Time in hours
• To find out the mechanism of drug release, first 60% drug release data is to be fitted in Korsmeyer-Peppas
model.

13. Release exponent (n) Drug transport mechanism
n< 0.45 Quasi Fickian
0.45 Fickian diffusion
0.45<n<0.89 Anomalous (Non-Fickian) diffusion
0.89 Case-2 Relaxation/ Case-II Transport
n> 0.89 Super case 2 transport
• ‘n’ is estimated from linear regression of log ( 𝑀𝑡
𝑀) versus log t
• ‘n’ value is used to characterize different release for cylindrical shaped matrices
• Anomalous diffusion or Non- Fickian diffusion refers to the combination of both diffusion
and erosion controlled rate release
• Case-2 relaxation or super case-2 transport refers to the erosion of the polymeric chain
13
Table 1

14. Log % Drug ReleaseVs LogTime in Hours
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Application:
• This model has been used frequently to describe the drug release from several modified release dosage
forms.
Plot 4

15. HIXSON-CROWELL MODEL
• The model describe the release of dose from system ,where there is change in surface area and
diameter of particle or tablet
• The equation is
𝑾𝟎
𝟏/𝟑
-𝑾𝒕
𝟏/𝟑
= K× t
Where,
𝑾𝟎 – Initial amount of drug in the pharmaceutical dosage form
𝑾𝒕 - Remaining amount of drug in the pharmaceutical dosage form at time ‘t’
κ (kappa) - Constant, incorporating the surface-volume relation
t - Time in hours
• Drug release is limited by dissolution velocity and not by diffusion
15

16. 3
𝑄0-3
𝑄𝑡
Application
• This equation is used for interpretation of dissolution data of conventional dosage form, dispersible dosage form
or immediate release dosage form, where the dissolution occurs in planes that are parallel to the drug surface
if the tablet dimensions diminish proportionally, but with maintenance of the geometrical characteristics..
16
𝟑
𝑸𝟎 -𝟑
𝑸𝒕 VS Time
Plot 5

17. • This model was developed by Baker and Lonsdale (1974) from the Higuchi model
• It described the drug release from spherical matrices according to the equation:
𝒇𝒕=
𝟑
𝟐
[1- (1-
𝑴𝒕
𝑴∞
)𝟐/𝟑
] -
𝑴𝒕
𝑴∞
= kt
Where,
𝒇𝒕 -fraction of drug released at time t
𝑴𝒕 - amount of drug released at time t
𝑴∞ -amount of drug released at an infinite time
k -release constant which corresponds to the slope of the graph
t - Time in hours
BAKER- LONSDALE MODEL
17

18. Application
• This equation has been used for the linearization of release data from several microparticle
formulations (microcapsules or microspheres).
18
3/2[1-(1-Q)𝟐/𝟑] - Q VS Time
Plot 6

19. 19
1
• Calculate the coefficient of determination (𝑹𝟐
), to assess the fit of the
model
2
• This method is used when the parameters of the model equation are
similar
3
• When the parameters of the comparing equation is increased; an adjusted
coefficient of determination (𝑅2 𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑) is calculated.
4
• The best model is the one which have the highest adjusted coefficient of
determination.
5
• Similarly, other statistical methods like correlation coefficient (R),
ANOVA and MANOVA are used for the comparison and selection of the
suitable models
How to select the Best Model?
𝑹𝒂𝒅𝒋𝒖𝒔𝒕𝒆𝒅
𝟐
=1-
𝒏−𝟏
𝒏−𝒑
(1-𝑹𝟐
)
n - number of dissolution
data points
p - number of parameters in
the model

20. CONCLUSION
• The kinetic models are derived from the theoretical analysis of the occurring process.
• In most of the cases the theoretical concept does not exist and some empirical equations have proved
to be more appropriate.
• The kinetic model is an important cursor for prediction and elucidation of the exact behavior of the
drug or the drug release profile from a specific drug delivery system
• The model can definitely ensure batch to batch uniformity and the success of the intended therapy
with the expected quality, safety and efficacy of the product.
• It can also significantly facilitate the optimization of the existing product as well as the development of
new products
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21. REFERENCES
 Hina Kouser Shaikh, R. V. Kshirsagar, S. G. Patil; Mathematical models for Drug Release
Characterization: a review; World Journal of Pharmacy and Pharmaceutical Sciences; 2015; 4:324-338.
 Gautam Singhavi, Review: In vitro drug release characterization models, International Journal of
Pharmaceutical Studies and Research, January 2011; 2: 77-84.
 Paulo Costa, Modeling and comparison of dissolution profile, European journal of Pharmaceutical
sciences, 2001; 13: 123-133.
 Mathematical Models of Drug Release. Strategies to Modify the Drug Release from Pharmaceutical
Systems, 63-86.
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22. QUESTIONS??
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