269248 - PowerPoint Presentation

Slide1

THEORIES AND MECHANISMS OF

DISSOLUTION TESTING

By

D.Narender

M.pharmacy 1

st

Semester

DEPARTMENT OF PHARMACEUTICS

UNIVERSITY COLLEGE OF PHARMACEUTICAL SCIENCES

KAKATIYA UNIVERSITYSlide2

OUT LINE

Definitions

Theories of Dissolution

Mechanisms of drug release

Wagner theory

Zero order release

First order release

Hixon -Crowel model

Higuchi model

Peppas model

Weibull model

ConclusionSlide3

Definitions:

Dissolution:

Dissolution is defined as a process in which a solid substance solubilizes in a given solvent i.e. mass transfer from solid surface to the liquid

phase

.

Dissolution rate:

Dissolution rate is defined as the amount of solute dissolved in a given solvent under standard conditions of temperature, pH, solvent composition and constant solid surface area.

It is a dynamic process

The rate of dissolution of drug substance is determined by the rate at which solvent-solute forces of attraction overcome the cohesive forces present in solid

Slide4

Drug Dissolution ProcessSlide5

THEORIES OF DISSOLUTION

:

3 Theories

1)

Diffusion layer model / Film theory2) Danckwert’s model (penetration or surface renewal theory)3) Interfacial barrier model (double barrier or limited solvation theory)Diffusion layer modelAssumes that there is a stagnant layer or diffusion layer which is saturated with the drug at the solid –liquid interface.From this stagnant layer, diffusion of soluble solute occurs to the bulk of the solution. Slide6

S

Film boundary

bulk solution

Stagnant layer

Cs

c

Diffusion layer model

Here ,the dissolution is diffusion controlled where the solvent-solute interaction is fast when compared with the transport of solute into bulk of solution

Once the solute molecules pass the liquid film-bulk film interface rapid mixing occurs and concentration gradient is destroyed. The rate of solute movement and therefore the dissolution rate are determined entirely by the Brownian motion diffusion of molecules in liquid film.Slide7

The rate of dissolution when the process is diffusion controlled is given by noyes-whitney equation

Equation:

dC/dt =D.A.Kw/o (Cs –Cb)\ v.h

dC/dt = dissolution rate of the drug.

D = diffusion coefficient of the drug.A = surface area of the dissolving solidKw/o = water/oil partition coefficient of drugV = volume of dissolution mediumh = thickness of stagnant layerCs–Cb = concentration gradient of diffusion of drugLimitation : Assumes that surface area of the dissolving solid remains constant during dissolution which is practically not possible.To account for particle size ,Hixson and Crowell cube root law was developed Equation: w01/3 – w1/3 = k .tW=mass of drug remaining to be dissolvedat time tK=dissolution rate constant w0 =original mass of the drug.Slide8

2)

Danckwert model:

Did not approve the existence of stagnant layer as said by diffusion layer theory

Instead, said that turbulence existed in dissolution medium near solid –liquid interface. Due to agitation, mass of eddies or packets reach the solid –liquid interface and absorb the solute and carry to bulk of solution

since solvent molecules are exposed to new solid surface each time, the theory is called surface renewal theory

Equation:

V.dC/dT= dm/dt = A ( Cs-Cb). (ү.D)1/2m=mass of solid dissolvedҮ = rate of surface renewal.Slide9

S

Film boundary

Bulk solution

C

s

C

Stagnant layer

In this model it is assumed that the reaction at solid surface is not instantaneous i.e. the reaction at solid surface and its diffusion across the interface is slower than diffusion across liquid film.

therefore the rate of solubility of solid in liquid film becomes the rate limiting than the diffusion of dissolved molecules

equation :

dm/dt = Ki (Cs – C )

K = effective interfacial transport rate

constant

3) Interfacial layer modelSlide10

Biopharmaceutical Classification System

High Solubility

(Dose Vol. NMT 250 mL)

Low Solubility

(Dose Vol. >250 mL)

High Permeability

(Fract. Abs. NLT 90%)

CLASS

І

e.g. Propranolol metoprolol

CLASS II

e.g. piroxicam, naproxen

Low Permeability

(Fract. Abs. <90%)

CLASS III

e.g. ranitidine cimetidine

CLASS IV

e.g. furosemide hydrochlorothiazide

 Slide11

Mechanisms of dissolution

Wagner theory

Wagner interpreted the percent dissolved time plots derived from the in vitro testing of regular tablets and capsules.

this concept relates to the apparent first order kinetics under sink conditions to the fact that a percent dissolved value at time t may be equivalent to the percent surface area generated at same time.

Wagner utilized the following mathematical method to desribe his theory for the dissolution kinetics of conventional tablets and capsules assuming that surface area available for dissolution decreases exponentially with time according to the equation; S = S0 e-ks ( t-to) --------------------------------> 1Where So is the surface area at time to. Slide12

But we know that

dW/dt = K.S.Cs ------------------------(2)

Substitution for S from equation (1) ,we get

dW/dt = K.Cs.So.e

-ks(t-to) ------------------------(3)Integration of above equation gives w= w0+K/ks Cs So [1-e-ks(t-to)] ------------------------(4)If it is assumed that W∞ is the amount in solution at infinite time and M= K/ks.Cs.So,thenW∞ = Wo+M and W∞-W = M e-ks(t-to) -------------------(5)Applying log to both sides ,we get, log (W∞ - W) = log M – ks/2.303( t – to) ------------(6)Where W∞ - w is the amount of undissolved drug.Slide13
Slide14

Zero order release:

Zero order refers to the process of constant drug release from a drug delivery device such as oral osmotic tablets,transdermal systems,matrix tablets with low soluble drugs

constant refers to the same amount of drug is released per unit time.

drug release from pharmaceutical dosage forms that donot disaggregate and release the drug slowly can be represented by the following equation

W0 – Wt = K .t ------------------- 1 W0 = initial amount of drug in the dosage form.Wt = amount of drug in the pharmaceutical dosage form at time tK = proportionality constant. Dividing this equation by W0 and simplifying ft = K0 .t where ft = 1-(Wt/W0)Ft = fraction of drug dissolved in time t and Ko the zero order release constnat.A graphic of the drug dissolved fraction versus time will be linear. Slide15

Applications:

Zero order kinetic model can be used to describe the drug dissolution of several types of modified release pharmaceutical dosage forms, as in case of some trans dermal systems ,as well as matrix tablets with low soluble drugs, coated forms ,osmotic systems etc

.Slide16

First order release:

If the amount of drug Q is decreasing at a rate that is proportional to he amount of drug Q remaining ,then the rate of release of drug Q is expressed as

dQ/dt = -k.Q -----------------1

Where k is the first order rate constant.

Integration of above equation gives,

ln Q = -kt + ln Q0 ---------------- 2The above equation is aslo expressed as Q = Q0 e-kt ------------------------ 3Because ln=2.3 log, equation (2) becomes log Q = log Q0 + kt/2.303 ---------------------(4)This is the first order equationA graphic of the logarithm of released amount of drug versus time will be linear.Slide17

Inference

The pharmaceutical dosage forms following this model, such as those drugs containing water soluble drugs in porous matrices, release the drug in a way that is proportional to the amount of drug remaining in its interior.

This model has been also used to describe absorption and elimination of drugs.Slide18
Slide19

Higuchi’s mechanism.

Higuchi developed an equation for the release of drug from an ointment base and applied it to diffusion of solid drugs dispersed in homogenous and granular matrix devices.

Higuchi pointed out that to develop mathematical relationship for the release of drugs from matrix tablets, two systems are considered.

first, when the drug particles are dispersed in homogeneous uniform matrix, which acts as diffusional mechanism

b) When the drug particles are incorporated in granular matrix and released by leaching action of penetrating solvent.Slide20

Higuchi demonstrated that during the initial release phase from a spherical system until approximately 50% of drug content in vehicle has been released,the square root of time behaviour is dominating and then it depends on design of sustaine release system.

From Ficks first law,

dM/S.dt = dQ/dt = D.Cs/ h --------------------------(1)

As the drug passes out of a homogeneous matrix. the boundary of drug( represented by the dashed vertical line), moves to the left by an infinitesimal distance, dh. The infinitesimal amount ,dQ, of the drug released because of this shift is given by

dQ = A.dh – ½ Cs dh -----------------------(2)

Substituting (2) in (1),we get D .Cs /h = (A – ½ Cs) dh/dt --------------------(3)Slide21

The steps for derivation as given by higuchi are ,

2A – Cs/2DCs

∫ h dh = ∫ dt ------------------ (4)

t = (2A –Cs) h2/4DCs +C -------------------------(5)The integration constant C,can be evaluated at t=0 at which h=0.giving. t = (2A – Cs)h2/4DCs --------------------------------(6) h = ( 4.D.Cs t / 2A – Cs)1/2 ------------------------------(7) The amount of drug depleted per unit area of matrix .Q at time t is obtained by integrating the equation (2) to yield, Q = h.A -1/2 h.Cs ---------------------------- (8)Substituting Q = (D.Cs.t / 2A – Cs)1/2 . (2A – Cs) orQ = [D(2A-Cs)Cs.t]1/2 ------------------------------------- (9)This is known as higuchi equation.Slide22

When the porosity and tortuosity of the matrix is concerned, the equation is modified as ; ( for heterogeneous type matrix)

Q = [D€/t( 2A - € Cs)Cs.t]1/2 -------------------------------- (10)

The instantaneous rate of release of a drug at time t is obtained by differentiating equation (10 ) to yield,

dQ / dt = ½ [ D(2 A – Cs)Cs/t]1/2 ------------------------ (11)

Ordinarily A is much greater that Cs and hence equation ( 9 ) reduces to Q = (2.A.D.Cs.t)1/2 --------------------------- (12)And hence equation ( 11) becomes . dQ/dt = (A.D.Cs/2t)1/2 ---------------------------- (13)Equation (12), indicates that the amount of drug released is proportional to square root of A , the total amount of drug in unit volume of matrix; D. the diffusion coefficient of the drug in matrix; Cs is the solubility of drug in polymeric matrix and t the time.Graph : graph is plotted between % drug release and square root of time.Slide23

Applications:

Higuchi describes the drug release as a diffusion process based on Ficks law, square root time dependent .

This model is useful for studying the release of water soluble and poorly soluble drugs from variety of matrices ,including solids and semi solids.Slide24

Hixon-crowell cube root law

Hixon Crowell cube root equation

for dissolution kinetics is based on assumption that:

Dissolution occurs normal to the surface of the solute particles

Agitation is uniform all over the exposed surfaces and there is no stagnation.

The particle of solute retains its geometric shapeThe particle (sphere) has a radius r and surface area 4Π r2Through dissolution the radius is reduced by dr and the infinitesimal volume of section lost is dV = 4Π r2 . dr ------------------(1)For N such particles,the volume loss is dV = 4N Π r2 dr ----------------------------(2)The surface of N particles is S = 4 N Π r2 -----------------------------(3)Now ,the infinitesimal weight change as represented by he noyes –whitney law ,equation is dW = k.S.Cs.dt ---------------------------(4)The drugs density is multiplied by the infinitesimal volume change Slide25

ρ

.dV, can be setequal to dW,

ρ

.dV = k.S.Cs.dt --------------------------- (5)

Equations (2) and (3) are substituted into equation (5) , to yield

-4 ρ N Π r2 . dr = 4 N Π r2 . K .Cs .dt -------------(6)Equation 6 is divided through by 4 N Π r2 to give - ρ . Dr = k Cs.dt -------------------------(7)Integration with r = ro at t= 0produces the expression r = ro – kCs .t/ ρ -----------------------------(8)

The radius of spherical particles can be replaced by the weight of N particles by using the relationship of volume of sphere

W = N

ρ

(

Π

/6)d

3

----------------------------(9)

Taking cube root of the equation (9) yield,

W

1/3 = [ N ρ(Π/6)]1/3. d. ----------------------------(10) The diameter d from equation (10) ,is substituted for 2r into equation 8 to give Slide26

W

0

1/3

- W

1/3

=k t ------------------(11)Where k = [ N ρ(Π/6)]1/3.2 k Cs/ρ.Wo is the original weight of drug particles .Equation (11) is known as Hixson- Crowell cube root law ,and k is the cube root dissolution rate constant.Futher dividing euation (11) by w01/3 and simplifying,we get ( 1 – ft )1/3 = k t Where ft = 1-(w/w0) and it represents the drug dissolved fraction at time tAnd k is release constant.Slide27

Korsmeyer and peppas model

Also called as

power law

To understand the mechanism of drug release and to compare the release profile differences among these matrix formulations ,the percent drug released time versus time were fitted using this equation

Mt / M∞ = k. tn Mt / M∞ = percent drug released at time t K= constant incorporating structural and geometrical characteristics of the sustained release device. n =exponential which characterizes mechanism of drug release Slide28

Exponent

n

slab

Cylinder

Sphere

DR mechanism

0.5

0.5 <

n

< 1.0

1.0

0.45

0.45 <

n

< 0.89

0.89

0.43

0.43 <

n

< 0.85

0.85

Fickian diffusion

Anomalous transport

Case-II transport

Exponent

n

of the power law and drug release mechanism

from polymeric controlled delivery systems of different geometrySlide29

Applications:

This equation can be applied to any kind of delivery system

This model is generally used to analyze the release of pharmaceutical dosage forms, when the release mechanisms is not well known or when more than one type of release phenomena could be involved.Slide30

Weibull Model

It expresses the accumulated fraction of the drug in solution at time by following equation:

m = 1- exp [-(t –T

i

)

b /a ] m = accumulated fraction of the drug at time t a = scale parameter

Ti = location parameter ( represents lag time before the onset of dissolution or release process and in most cases will be zero ) b = shape parameter.The equation may be rearranged into: log[ -ln(1-m)]= b log ( t-Ti )- log agraph: -ln(1-m) vs t gives linear relation and the slope is equal to shape parameter Slide31

CONCLUSION

The Quantitative interpretation of the values obtained in dissolution assays is easier using mathematical equations which describe the release profile in function of some parameters related with the pharmaceutical dosage forms.

The release models with the major appliance and the best describing drug release phenomena are in general ,the Higuchi model, Zero order model and Korsmeyer- Peppas model. the Higuchi and Zero order models represent two limit cases in the transport and drug release phenomena and the Korsmeyer-Peppas model can be a decision parameter between these two models

while the Higuchi model has a larger application in polymeric systems, the zero order model becomes ideal to describe coated dosage forms or membrane controlled dosage forms.Slide32

References

1

) Remington's “The science and practice of pharmacy” 21

st

edition page no 672-685.

2) “A Text book of Applied Bio pharmaceutics and pharmacokinetics”, by Leon Shargel,andrew , 4 th edition ,page no 131-195.3) “Text book of Bio pharmaceutics and pharmacokinetics” ,by V.Venkateshwarlu page no.32-55.4) Text book of Bio pharmaceutics and pharmacokinetics, by Brahmankar.page no.15-48.5) Text book of Dissolution ,Bio availability and Bio equivalence, by hammed m.abdoue.page no 337-354.6) Pharmaceutical Dissolution Testing ,by Umesh .V. Banakar, pg.no 1-100,pg no 200- 3507) Text book of Martins, physical pharmacy and pharmaceutical sciences. page no 337-354.8)Encyclopedia of pharmaceutical technology, by James Swarbrick, James C.Boylan volume 4 page no 121-1269) European Journal of Pharmaceutical sciences 13 (2001) page no.123 – 133.