The document discusses various kinetic models that can be used to describe drug release from pharmaceutical formulations, including zero-order, first-order, Higuchi, Korsmeyer-Peppas, Hixson-Crowell, Weibull, Baker-Lonsdale, Hopfenberg, Gompertz, and sequential layer models. It provides the key equations and applications of each model, with graphics to analyze drug release over time. The models can help optimize drug release kinetics, predict effects of design parameters on release rates, and improve therapeutic efficacy and safety.

1. Presented By:
Ghate Ritesh Santosh
(M.Pharm SEM-IInd
)
Dept. of Pharmaceutics
R. C. Patel Institute of Pharmaceutical Education and
Research, shirpur.
1
May 22, 2017

2. Introduction
Objective
kinetic Models and it’s Applications
Conclusion
References
2May 22, 2017

3.  Drug release is the process by which a drug leaves a drug product
and is subjected to absorption, distribution, metabolism and
excretion (ADME), eventually becoming available for
pharmacological action.
 In order to ensure a desired effect, there must be an appropriate
rate of drug release and then proper absorption of active agents.
 Drug release is described in several ways like Immediate release,
controlled release, etc.
3May 22, 2017

4. Objective
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Optimization of the release kinetic.
 Prediction of the effect of design parameters viz. shape,
size and composition on the overall drug release rate.
 To improve therapeutic efficacy and safety of these drug.
 Prediction of drug diffusion behavior through polymers.

5. 5
kinetic Models
1.Zero order kinetic model
2. First order kinetic model
3. Higuchi model
4. Korsmeyer-peppas model (The power law)
5.Hixson –crowell model
6.Weibull model
7. Baker –Lonsdale model
8. Hopfenberg model
9. Gompertz model
10.Sequential layer model
May 22, 2017

6. 1. Zero Order Kinetic Model
“Zero order describes the system where the release rate of
drug is independent of its concentration.”
C= C0-K0 t
Where,
C = Amount of drug release
C0 = Initial amount of drug in solution
K0= Zero order rate constant
t = time
Graph- cumulative amount of drug released versus time
Applications
This relationship can be applied to describe the drug dissolution of
drug from several types of modified release Pharmaceutical dosage
form e.g. osmotic system 6May 22, 2017

7. May 22, 2017 7
2. First order kinetic model
dC/dt = -KC
Where,
K = first order rate constant
From eq. It is clear that a first-order process is the one whose rate is
directly proportional to the concentration of drug undergoing
reaction i.e. greater the concentration, faster the reaction.
Graph- log cumulative % of drug remaining vs. time
Applications
This relationship can be use to describe the drug dissolved in
Pharmaceutical dosage forms like those contained water soluble drugs
in porous matrices.

8. 3. Higuchi Model-
Higuchi proposed this model in 1961 to describe the drug
release from matrix system.
Hypotheses :
(i) initial drug concentration in the matrix is much higher than
drug solubility
(iii) drug particles are much smaller than system thickness
(iv) matrix swelling and dissolution are negligible
(v) In the release environment perfect sink conditions are
maintained.
The basic equation of Higuchi model is…..
C= [D (2qt-Cs) Cst] 1/2
8May 22, 2017

9. Where,
C=total amount of drug release per unit area of matrix[mg/cm2
]
D=diffusion coefficient
qt=total amount of drug in a unit volume of matrix [mg/cm3
]
Cs=solubility of drug[mg/cm3
]
t=time
Graph- cumulative % drug release vs. square root of time.
Applications
By using this model dissolution of drug from several modified
release dosage forms like some transdermal system and matrix
tablet with water soluble drugs are studied.
9May 22, 2017

10. May 22, 2017 10
4. Korsmeyer-Peppas Model (The Power law)
A simple relationship which described drug release from a
polymeric system equation was derived by Korsmeyer et al. in
1983.
Mt / M∞ = Ktn
Where,
Mt / M∞ = drug released at time ‘t’
k = release rate constant
n = release exponent

11. May 22, 2017 11
Release
mechanism
model
Geometry Release
exponent
(n)
Time in
function of n
Fickian diffusion
Anomalous
transport
Case I transport
Super Case II
transport
Planar (thin films)
Cylinders
Spheres
Planar (thin films)
Cylinders
Spheres
Planar (thin films)
Cylinders
Spheres
Planar (thin films)
Cylinders
Spheres
0.50
0.45
0.43
0.50<n<1.0
0.45<n<0.89
0.43<n<0.85
1.0
0.89
0.85
n>1
n>0.89
n>0.85
t0.50
t0.45
t0.43
t0.50<n<1.0
t0.45<n<0.89
t0.43<n<0.85
t(a
)
t0.89
t0.85
tn>1
tn>0.89
tn>0.85
The n value is used to characterize different release mechanism
of drug for cylindrical shaped matrices as described in Table
below:

12. Following assumptions were made in this model…….
This equation is applicable to small values of ‘t’ and the
portion of release curve, where Mt / M∞<0.6 should only use to
determine the exponent ‘n’
The ratio of system length to thickness should be at least 10.
Graph- log cumulative % drug release versus log time.
Application
This model has been used frequently to describe the drug
release from several modified release dosage forms.
12May 22, 2017

13. 5. Hixson-Crowell Model-
Hixson and Crowell (1931) recognizing that the particle regular
area is proportional to the cubic root of its volume.
It describes the drug releases by dissolution, with the changes in
surface area and diameter of the particles or tablets.
C0
1/3
-Ct
1/3
= Kt
Where,
Ct=amount of drug released in time ‘t’.
C0=initial amount of drug in the tablet.
K=rate constant
Graph- cube root of the initial conc. - cube root of % remaining
versus time(hr)
Application
The Hixson–Crowell equation applies to tablets, considering that
dissolution occurs in planes parallel to the surface of the active
agent. 16May 22, 2017

14. 6. Weibull Model-
The accumulated fraction of the drug ‘M’ in solution at time ‘t’ is
given by Weibull equation:
M = M0 [1-e (t-T)b
]
Where,
M = amount of drug dissolved
M0 = total amount of drug released
T= lag time
a = a scale parameter that describes the time dependence
b= shape of the dissolution curve
Graph- Log of dissolved amt Vs log time.
Applications
The Weibull model is more useful for comparing the release
profiles of matrix type drug delivery.
14May 22, 2017
a

15. 7. Baker-Lonsdale Model-
This model was modified form of Higuchi model, developed by
Baker and Lonsdale (1974).
It described the drug release from spherical matrix.
f1= 3/2[1-(1-Ct/C∞)2/3
] Ct/C∞=kt
Where,
Ct= drug release amount at time ‘t’.
C∞= amount of drug release
K= release constant
Graph- d(Ct/C∞)/dt with respect to root of time inverse.
Applications
This model used to linearization of release data from several
formulations of microcapsules.
15May 22, 2017

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8. Hopfenberg Model-
Hopfenberg developed a mathematical model to correlate the drug
release from surface eroding polymers so long as the surface area
remains constant during the degradation process. The cumulative
fraction of released drug at time ‘t’ was described as…
Ct/C∞= 1-[1-K0t/CL a]n
Where,
K0=zero order rate constant
CL=initial drug loading
a=system half thickness (i.e. radius for a sphere or cylinder.)
n=exponent
Graph- Ct/C∞Vs Time.
Applications
This model is useful for identification of drug release mechanism
from the oily- spheres.

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9. Gompertz Model-
The in vitro dissolution profile is often described.
C(t) = Cmax exp [-αeβ logt
]
Where,
C(t)= % dissolved at time ‘t’ divided by 100.
Cmax= maximum dissolution.
α= undissolved proportion at time ‘t’=1
β = dissolution rate per unit time
Applications
This model is useful for compare the release profile of the drugs
having good solubility and intermediate release rate.

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10. Sequential layer Model
Sequential layer model is used to determine the swelling and release
behavior from hydrophilic matrix tablet and to elucidate the effect of
the device geometry on the drug release pattern.
Model is performed in a computational grid and modified structure of
the grid is required for numerical analysis
In this model, tablet system is considered as a certain amount of
single layers penetrated by the water.
Here, it is considered that layer by layer swelling is takes place, in
which the swelling of first layer is occurred followed by neighboring
inner layer.
The polymer under goes a loss in molecular weight which is
characterized by the constant dissolution rate constant ‘k’.

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Applications
This model is useful for prediction of release behavior from tablet
containing hydrophilic matrix and also useful for determination of
shape and dimensions of the tablet.

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Conclusion-
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 drug or 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 existing
product as well as the development of new products.

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References
1.Shaikh H.K., Kshirsagar R.V. and Patil S.G., 2015.
Mathematical models for drug release characterization: a
review World J Pharm Pharmacent Sci, 4, pp.324-338.
2. Bruschi, M.L. (2015) ‘Mathematical models of drug release’,
in Strategies to Modify the Drug Release from Pharmaceutical
Systems. Elsevier BV, pp. 63–86.
3. Costa, P. and Lobo, J.M.S., 2001. Modeling and comparison
of dissolution profiles. European Journal of Pharmaceutical
Sciences, 13, pp.123-133.

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4. Singhvi, G. and Singh, M., 2011. Review: in-vitro drug release
characterization models. Int J Pharm Stud Res, 2(1), pp.77-84.
5. Ramteke, K.H., Dighe, P.A., Kharat, A.R. and Patil, S.V., 2014.
Mathematical models of drug dissolution: a review. Sch. Acad. J.
Pharm, 3(5), pp.388-396.
6. Brahmankar, D.M. And Jaiswal, S.B. (1995) Biopharmaceutics
And Pharmacokinetics A Treatise. Second Edition, Vallabh
Prakashan, Delhi-110033, pp.242.

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