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92 | P a g e International Standard Serial Number (ISSN): 2319-8141

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International Journal of Universal Pharmacy and Bio Sciences 3(3): May-June 2014

INTERNATIONAL JOURNAL OF UNIVERSAL

PHARMACY AND BIO SCIENCES IMPACT FACTOR 1.89***

ICV 5.13*** Pharmaceutical Sciences REVIEW ARTICLE……!!!

KINETIC MODELING OF DRUG RELEASE FROM TOPICAL GEL

Phaldesai Saiesh *, A.R Shabaraya, Shripathy D, Leyana Soman.

Department of Pharmaceutics, Srinivas College of Pharmacy, Valachil,

Mangalore, Karnataka.

KEYWORDS:

Mathematical design,

Quantitative analysis,

mathematical modeling.

For Correspondence:

Phaldesai Saiesh *

Address:

Department of

Pharmaceutics, Srinivas

College of Pharmacy,

Valachil, Mangalore,

Karnataka.

Email:

saieshphaldesai12@gmai

l.com

ABSTRACT

In this paper we review the mathematical models used to

determine the kinetics of drug release from drug delivery

systems. The quantitative analysis of the values obtained in

dissolution/release rates is easier when mathematical formulae

are used to describe the process. The mathematical modeling can

ultimately help to optimize the design of a therapeutic device to

yield information on the efficacy of various release models. Also

explained with example of gel formulation.



INTRODUCTION:

In topical drug delivery, drug loaded formulation is applied on skin directly to treat cutaneous manifestations

of a general disease. Topical route avoids first pass effects, gastro-intestinal irritation, metabolic degradation

associated with oral administration of drug, less greasy nature and ease in its removal from skin. To bypass

these disadvantages, gel formulations have been proposed as topical drug delivery system. When

dispersed in an appropriate solvent, gelling agents merge or entangle to form a three-dimensional colloidal

network structure, which limits fluid flow by entrapment and immobilization of solvent molecules [1]. At

present, the most common form of delivery of drugs is the oral route. While this has the notable

advantage of easy administration, it also has significant drawbacks namely poor bioavailability due to

hepatic metabolism (first pass) and the tendency to produce rapid blood level spikes leading to a need for

high and /or frequent dosing, which can be both cost prohibitive and inconvenient. The success of

transdermal delivery depends on the ability of the drug to permeate the skin in sufficient quantities to

achieve its desired therapeutic effects. The skin is very effective as a selective penetration barrier.

Percutaneous absorption involves the passage of the drug molecule from the skin surface into the stratum

corneum under the influence of a concentration gradient and its subsequent diffusion through the stratum

corneum and underlying epidermis through the dermis and into the blood circulation. The skin behaves as

a passive barrier to the penetrating molecule. The stratum corneum provides the greatest resistance to

penetration and it is the rate-limiting step in percutaneous absorption [2] .the use of mathematical

modeling turns out to be very useful as this approach enables, in the best case, the prediction of release

kinetics before the release systems are realized. More often, it allows the measurement of some important

physical parameters, such as the drug diffusion coefficient and resorting to model fitting on experimental

release data. Thus, mathematical modeling, whose development requires the comprehension of all the

phenomena affecting drug release kinetics [3], has a very important value in the process optimization of

such formulation. The model can be simply thought as a mathematical metaphor of some aspects of

reality that, in this case, identifies with the ensemble of phenomena ruling release kinetics [4]. For this

generality, mathematical modeling is widely employed in different disciplines such as genetics, medicine,

psychology, biology, economy and obviously engineering and technology.

Fundamentals of kinetics of drug release

Noyes-Whitney Rule:-

The fundamental principle for evaluation of the kinetics of drug release was offered by Noyes and

Whitney in 1897 as the equation (10):



dM/dt = KS (Cs-Ct) (1)

where M, is the mass transferred with respect to time t, by dissolution from the solid particle of

instantaneous surface, S, under the effect of the prevailing concentration driving force (Cs ñ Ct), where

Ct is the concentration at time t and Cs is the equilibrium solubility of the solute at the experimental

temperature. The rate of dissolution dM/dt is the amount dissolved per unit area per unit time and for

most solids can be expressed in units of g ×cm-2

×s-1

When Ct is less than 15% of the saturated solubility Cs, Ct has a negligible influence on the dissolution

rate of the solid. Under such circumstances, the dissolution of the solid is said to be occurring under sink

conditions. In general, the surface area, S is not constant except when the quantity of material present

exceeds the saturation solubility, or initially, when only small quantities of drug have dissolved.

Model dependent methods

Model dependent methods are based on different mathematical functions, which describe the dissolution

profile. Once a suitable function has been selected, the dissolution profiles are evaluated depending on

the derived model parameters. In order to determine the suitable drug release kinetic model describing the

dissolution profile, the nonlinear regression module of Statistical 5.0 was used.

In non-linear regression analysis the Quasi-Newton and Simplex methods minimized the least squares

[5,6]. The model dependent approaches included zero order, first order, Higuchi, Hixson-Crowell,

Korsmeyer-Peppas, Baker-Lonsdale, Weibull, Hopfenberg, Gompertz and regression models [7,8].

Zero-order model

Drug dissolution from dosage forms that do not disaggregate and release the drug slowly can be

represented by the equation:

Q0- Qt = K0t (3)

Rearrangement of equation (3) yields:

Qt = Q0 + K0t (4)

where Qt is the amount of drug dissolved in time t, Q0 is the initial amount of drug in the solution (most

times, Q0 = 0) and K0 is the zero order release constant expressed in units of concentration/time.

To study the release kinetics, data obtained from in vitro drug release studies were plotted as

cumulative amount of drug released versus time [9,10].

Application: This relationship can be used to describe the drug dissolution of several types of

modified release pharmaceutical dosage forms, as in the case of some transdermal systems, as well as

matrix tablets with low soluble drugs in coated forms, osmotic systems, etc. [11,12].



First order model

This model has also been used to describe absorption and/or elimination of some drugs, although it is

difficult to conceptualize this mechanism on a theoretical basis. The release of the drug which followed

first order kinetics can be expressed by the equation:

dC/dt = -Kc (5)

where K is first order rate constant expressed in units of time-1

Equation (5) can be expressed as:

log C = log C0 - Kt / 2.303 (6)

where C0 is the initial concentration of drug, k is the first order rate constant, and t is the time [13]. The

data obtained are plotted as log cumulative percentage of drug remaining vs. time which would yield a

straight line with a slope of -K/2.303.

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 [14,15].

Higuchi model

The first example of a mathematical model aimed to describe drug release from a matrix system was

proposed by Huguchi in 1961 [16]. Initially conceived for planar systems, it was then extended to

different geometrics and porous systems [17]. This model is based on the hypotheses that (i) initial drug

concentration in the matrix is much higher than drug solubility; (ii) drug diffusion takes place only in one

dimension (edge effect must be negligible); (iii) drug particles are much smaller than system thickness;

(iv) matrix swelling and dissolution are negligible; (v) drug diffusivity is constant; and (vi) perfect sink

conditions are always attained in the release environment. Accordingly, model expression is given by the

equation:

ft = Q = A √D(2C - Cs) CsT

where Q is the amount of drug released in time t per unit area A, C is the drug initial concentration, Cs is

the drug solubility in the matrix media and D is the diffusivity of the drug molecules (diffusion

coefficient) in the matrix substance. This relation is valid during all the time, except when the total

depletion of the drug in the therapeutic system is achieved. To study the dissolution from a planar

heterogeneous matrix system, where the drug concentration in the matrix is lower than its solubility and

the release occurs through pores in the matrix, the expression is given by equation (8)



RESULTS AND DISCUSSION

In this work initially gels containing the antifungal agent was subjected to the invitro diffusion method

using the franz diffusion cell. Based on the results obtained on the basis of the release pattern shown

during the diffusion the best formulations were selected as F7, F2, F11, F8. Where in F7 showed the

quality result. The selected best formulations were subjected to the mathematical kinetical model study to

find out the mechanism of release.

CONCLUSION

From the above work it was concluded that formulation F7,F11 showed higuchis release, F8 showed

Krosmeyer – peppas. Which was taken based on the r2 value. Hence the formulation F7 which was

considered to be the best formulation showed the release mechanism having Higuchis Models.

ACKNOWLEDGEMENTS

We are thankful to Srinivas college of Pharmacy for providing the opportunity to carry out our research

work successfully. I heartly thank Prof Dr AR Shabaraya for providing us Kind support all the time

throughout the work.

TABLES

Tab.No.1 Composition of Gel

Constituents

F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12

ECONAZOLE

NITRATE

( mg )

150 150 150 150 150 150 150 150 150 150 150 150

SODIUM ALGINATE

( gm)

1 - - 0.5 0.25 0.75 - - - 0.5 0.25 0.75

HPMC K4M

(gm)

- 1 - 0.5 0.75 0.25 0.5 0.25 0.75 - - -

CARBOPOL

(gm)

- - 1 - - - 0.5 0.75 0.25 0.5 0.75 0.25

TRIETHANOLAMINE 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23

DMSO

( mg )

2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2

METHYL PARABIN

( mg )

15 15 15 15 15 15 15 15 15 15 15 15

WATER UPTO

100GMS



Tab.No.2 Kinetic release of gel containing EN + HPMC ( 0.5 )+ CARBOPOL (0.5) F7

Time -

mins

Log

Time

SQRT

Time Concentration

Amount

release

%

Cumula

Release

Log %

Release

% Drug

remaining

Log %

Drug

remaining

0 0 0 0 0 0 100 0

5 0.699 2.236 1.125 10.125 13.35 1.125 86.65 1.938

15 1.176 3.873 1.729 15.561 19.9 1.2989 80.1 1.904

30 1.477 5.477 2.364 21.276 23.88 1.3780 76.12 1.881

45 1.653 6.708 3.158 28.422 32.28 1.5089 67.72 1.831

60 1.778 7.746 3.974 35.766 38.07 1.5806 61.93 1.792

90 1.954 9.487 5.421 48.789 45.87 1.6615 54.13 1.733

120 2.079 10.954 6.875 61.875 56.18 1.7496 43.82 1.642

150 2.176 12.247 7.621 68.589 79.56 1.9007 20.44 1.310

180 2.255 13.416 7.845 70.605 88.56 1.9472 11.44 1.058

210 2.322 14.491 8.741 78.669 91.2 1.9600 8.8 0.944

240 2.380 15.492 9.334 84.006 98.24 1.9923 1.76 0.246



Tab.No.3 Kinetic release of gel containing EN + HPMC ( 0.25 )+ CARBOPOL (0.75) F8

Time

-

mins

Log

Time

SQRT

Time Concentration

Amount

release

% Cumula

Release

Log %

Release

% Drug

remaining

Log %

Drug

remaining

0 0 0 0 0 0 100 0

5 0.699 2.236 1.125 10.125 13.03921569 1.115 86.96078 1.939

15 1.176 3.873 1.729 15.561 19.62543992 1.2928 80.37456 1.905

30 1.477 5.477 2.364 21.276 22.64203117 1.3549 77.35797 1.889

60 1.778 7.746 3.158 28.422 28.82101559 1.4597 71.17898 1.852

90 1.954 9.487 3.974 35.766 37.83308195 1.5779 62.16692 1.794

120 2.079 10.954 5.421 48.789 45.84213172 1.6613 54.15787 1.734

150 2.176 12.247 6.875 61.875 57.05882353 1.7563 42.94118 1.633

180 2.255 13.416 7.621 68.589 73.57466063 1.8667 26.42534 1.422

210 2.322 14.491 7.845 70.605 89.41176471 1.9105 18.63248 1.270

240 2.380 15.492 8.741 78.669 96.95324284 1.9514 10.58824 1.025



Tab.No.4 Kinetic release of gel containing EN +SA (0.25) + CARBOPOL (0.75) F11

Time

Log

Time

SQRT

Time Concentration

Amount

release

%

Cumula

Release

Log %

Release

% Drug

remaining

Log %

Drug

remaining

0 0 0 0 0 100 0

5 0.699 2.236 1.125 10.125 13.88386 1.143 86.11614 1.935

15 1.176 3.873 1.729 15.561 20.19356 1.3052 79.80644 1.902

30 1.477 5.477 2.364 21.276 24.18552 1.3836 75.81448 1.880

60 1.778 7.746 3.158 28.422 28.58723 1.4562 71.41277 1.854

90 1.954 9.487 3.974 35.766 40.37959 1.6062 59.62041 1.775

120 2.079 10.954 5.421 48.789 47.02614 1.6723 52.97386 1.724

150 2.176 12.247 6.875 61.875 53.95928 1.7321 46.04072 1.663

180 2.255 13.416 7.621 68.589 72.637 1.8612 27.363 1.437

210 2.322 14.491 7.845 70.605 85.65862 1.9328 14.34138 1.157

240 2.380 15.492 8.741 78.669 96.7194 1.9671 7.302665 0.863



Tab.No.5 Kinetic release of gel containing EN + HPMC F7

Time

(mins)

Log

Time

SQRT

Time Concentration

Amount

release

%

Cumulative

Release

Log %

Release

% Drug

remaining

Log %

Drug

remaining

0 0 0 0 0 0 100 0

5 0.699 2.236 1.125 10.125 13.09 1.117 86.91 1.939

15 1.176 3.873 1.729 15.561 18.83 1.2749 81.17 1.909

30 1.477 5.477 2.364 21.276 22.23 1.3469 77.77 1.891

45 1.653 6.708 3.158 28.422 27.6 1.4409 72.4 1.860

60 1.778 7.746 3.974 35.766 39.94 1.6014 60.06 1.779

90 1.954 9.487 5.421 48.789 45.94 1.6622 54.06 1.733

120 2.079 10.954 6.875 61.875 54.36 1.7353 45.64 1.659

150 2.176 12.247 7.621 68.589 61.99 1.7923 38.01 1.580

180 2.255 13.416 7.845 70.605 81.75 1.9125 18.25 1.261

210 2.322 14.491 8.741 78.669 88.79 1.9484 11.21 1.050

240 2.380 15.492 9.334 84.006 96.83 1.9860 3.17 0.501



Tab.No.6 Regression analysis (r2) of release data based on best curve-fitting method

FIGURES

Fig.No.1 Zero Order Plots of selected gels

0

20

40

60

80

100

120

0 50 100 150 200 250 300

F2

F7

F8

F11

Formulation

code

Zero order

First order

Highuchi

Korsmeyer-

peppas

Best fit

release

mechan

ism n

r2

n r2

n r2

n r2

F2 0.373278

0.9799

-0.005

0.8701

29.24 0.9619

1.18 0.9547

Zero

order

F7 0.395111

0.9714

-0.006

0.8869

31.152 0.9730

1.19 0.9605

Highuchi

F8 0.339889

0.9806

-0.003

0.9179

20.724 0.9416

1.80 0.9916 Korsmeyer-

peppas

F11 0.346294

0.9747

-0.004

0.8721

29.24 0.9946

1.81 0.9916

Highuchi



Fig.No.2 First Order Plots of selected gels

Fig.No.3 Korsemeyer-Peppas Plot of selected gels.

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250 300

F2

F7

F8

F11

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2 2.5

F2

F7

F8

F11



Fig.No.4 Higuchi’s plots of selected gels.

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