PRESENTATION ON KINETICS OF DRUG RELEASE

FROM THEORY OF MASS TRANSFER

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Presented by Vikas Aggarwal M.Pharm (Ist sem)Pharmaceutics

Matrix Type Also called as Monolith dissolution

controlled system.

Controlled dissolution by: 1.Altering porosity of tablet. 2.Decreasing its wettebility. 3.Dissolving at slower rate.

First order drug release.

Drug release determined by dissolution rate of polymer.

Examples: Dimetane extencaps, Dimetapp extentabs.

Soluble drug

Slowly dissolving matrix

Encapsulation Called as Coating dissolution

controlled system.

Dissolution rate of coat depends upon stability & thickness of coating.

Masks colour,odour,taste,minimising GI irritation.

One of the microencapsulation method is used.

Examples: Ornade spansules,

Chlortrimeton Repetabs

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Soluble drug

Slowly dissolving or erodible coat

Diffusion

Major process for absorption.

No energy required.

Drug molecules diffuse from a region of higher concentration to lower concentration until equilibrium is attainded.

Directly proportional to the concentration gradient across the membrane.

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Matrix Diffusion Types

Rigid Matrix Diffusion Materials used are insoluble plastics such as PVP & fatty acids.Swellable Matrix Diffusion

1. Also called as Glassy hydrogels.Popular for sustaining the release of highly water soluble drugs. 2. Materials used are hydrophilic gums. Examples : Natural- Guar gum,Tragacanth. Semisynthetic -HPMC,CMC,Xanthum gum. Synthetic -Polyacrilamides. Examples: Glucotrol XL, Procardia XL

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Matrix system

Rate controlling step:

Diffusion of dissolved drug in matrix.

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Higuchi Equation

Q = DE/T (2A.E Cs)Cs.t)1/2

Where , Q=amt of drug release per unit surface area at time t. D=diffusion coefficient of drug in the release medium. E=porosity of matrix. Cs=solubility of drug in release medium. T=tortuosity of matrix. A=concentration of drug present in matrix per unit volume.

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Reservoir System

Also called as Laminated matrix device. Hollow system containing an inner core surrounded in water

insoluble membrane. Polymer can be applied by coating or micro encapsulation. Rate controlling mechanism - partitioning into membrane with

subsequent release into surrounding fluid by diffusion. Commonly used polymers - HPC, ethyl cellulose & polyvinyl

acetate. Examples: Nico-400, Nitro-Bid

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Reservoir System Rate controlling steps :

Polymeric content in coating, thickness of coating, hardness of microcapsule.

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Dissolution & Diffusion Controlled Release system

Drug encased in a partially soluble membrane.

Pores are created due to dissolution of parts of membrane.

It permits entry of aqueous medium into core & drug dissolution.

Diffusion of dissolved drug out of system.

Ex- Ethyl cellulose & PVP mixture dissolves in water & create pores of insoluble ethyl cellulose membrane.

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Insoluble membrane

Pore created by dissolution of soluble fraction of membrane

Entry of dissolution fluid

Drug diffusion

FACTORS INFLUENCING DRUG RELEASE1. Permeation-Depends on crystallinity,nature of

polymer,its degree of polymerization,presence of fillers and plasticizers,matrix properties like thickness,porosity,diffusion layer etc.

2. Diffusion-diffusion coefficient 3. Partition coeffficient-imp. when matrix contains drug

dissolved in polymer.4. Solubility-imp when drug is not dissolved in polymer

matrix,rather dispersed.5. Pharmaceutical manipulations-porosity,compression

pressure,coat thickness,plasticizer conc., polarity of coating materials etc.

1. Permeation-It is the process whereby drug is transported through one or more polymeric membranes.FICK’S FIRST LAWJ=dM/dt=-DA(dC/dX)where J=Flux i.e. permeation of drug through membrane of an I unit area( 1 sq.cm)dM/dt=Amt of drug permeating w.r.t definite interval of time.D=Diffusion coefficientA=Diffusion areadX=Diffusion layer thicknessdC/dX=conc gradientPermeability of a drug across the barrier is directly proportional to area and conc. gradient and inversely proportional to the thickness of membrane.

J=-D(dC/dX)This is the one dimensional form of fick’s first law.As long as we are at steady state,solutions to Fick’s first law provides a completely adequate description of the diffusional process.

When a drop of dye is placed in a beaker of water at constant temp,the dye tends to diffuse throughout the water,eventually giving the solution a uniform colour.Dye molecules can be viewed as being in a state of continual random motion.As such,each molecule can move in any direction with equal probability.The reason that molecules diffuse away from their source is that there are more dye molecules at the source than in the bulk solution.Therefore more molecules can move away from the source than towards the source.

In first case amt. in core changes but conc remains same inside upto a particular time and undergoes dilution so that dC becomes constt.So when concentrations are changing with time,as in the case of above experiment,we may know dC/dX at the beginning of experiment,but the mass flow will continually be changing the conc. gradient.Therefore it is necessary to introduce time as a variable.Eqn then becomes-

This equation is called Fick’s 2nd law of diffusion.Interpretation from the equation-Rate of change in conc. in volume element is proportional to area of change of conc. gradient in that region of field. Diffusion coefficient(D) is a measure of rate of drug movt.

J=[dC/dt]x=D[d²C/dX²]ᵼ

FACTORS INFLUENCING DIFFUSIVITY Temperature-Diffusion is a dynamic process.Movt of a

molecule in a particular build of matrix will take place based on enthalpy of system.As the temp. is increased,D value increases.At higher temp.,there will be a higher flux rate.

As per Arrhenius equation - Or lnD=lnD₀‒Ed⁄RTD₀=temp independent frequency factor i.e. all molecules

are at rest at 0⁰KEd=Energy of activation for polymer diffusion Molecular wt.-As molecular weight and mol. Volume

related to each other directly,because density is constt.As molecular wt increases,there will be more amt of resistance to movt.

D=Dₒe¯ᴱᵈ/ᴿᵀ

D α (1/Mol. Wt)⅓

Factors continued……… Radius of particles .Particles are assumed to be

spherical,small and electrically neutral.We can find out the diameter of particles and its diffusivity in any particular media.

where Na=Avogadro’s no(no. of particles in any particular system)

As radius increases ,diffusion decreases.Ƞ=viscosity.As viscosity increases diffusion

decreases

D=RT/Na(6πƞ)r

4 Drug solubility As diffusion depends on conc gradient, drug solubility in penetrant becomes important and then drug release becomes dissolution dependent for sparingly soluble drugs . This can be expressed by Noyes –Whitney eqn

Where dC/dt = Amt of drug release per unit time K= dissolution rate constant Cs= Saturation solubility in solvent C = Conc in solvent at time t.K= DsA/VlbTherefore Noyes- Whitney Eqn becomes

where Ds=diffusion coeff. in solventV=vol of soln.

dC/dt= DsA/Vlb (Cs-C)

dC/dt= K(Cs-C)

Time

Am

t re

leasi

ng

DRUG DIFFUSION THROUGH MICROPARTICLESWhen drug diffusion through

microparticles/microcapsules is concerned,drug transport involves dissolution of permeating drug in polymer and diffusion across the membrane.

J=(DKA.ΔC/lm)ΔC=conc difference on either side of membranelm=membrane thicknessK=partition coefficient of drug towards polymerDK=permeability coefficient(imaginary)DK/lm=permeability when lm is not knownD/lm=permeability constant(actual)In case of nanoparticles of size 100 nm say and coat

thickness about 2nm or < 1nm,lm is insignificant,so DK/lm=DK only

Si-Nang and Carler eqn for drug release from microcapsulesdC/dt= [DsAK/Vlm]Where A= internal surface area of coating.K= Porosity and tortuosity.

Mechanisms/ Mathematical models of drug release

1. First order ln Xt = ln Xo+Kt (Release proportional to

amount of drug remaining )Systems that follow the model – Water soluble

drugs in porus metrix

2 Zero order Ft= Kot (Release independent of drug conc)Eg : Osmotic Systems, Transdermal systems 3 Higuchi eqn. Ft= Kн t½Eg :Diffusion matrix formulations4 Khanna et al modified Noyes Whitney

eqn. or Hixson and Crowell’s cubic root low of

dissolution W0⅓-Wt⅓= KaᵼWhere Wo = Original mass of drugWt= mass of drug remaining to dissolve at time t.aᵼ = surface wt fraction at time t

5 Korsmeyer-Peppas eqn. Mᵼ/Mₒ = KtᵈWhere Mᵼ/Mₒ fraction mass of drug released at time t.Eg Hydrating sytems, Eroding systems where D is not

constant, thereby giving anomalous diffusion .For Non-Fickian or anomalous diffusion m>0.5, which is

usually found in swellable systems

APPLICATIONS OF DRUG RELEASE DATA

1. Quality control 2. Understanding physiochemical aspects of drug

delivery system.3. Understanding the release mechanisms.4. Predict behaviour of system in vivo.

However there are difficulties in modelling drug release data as there is great diversity in the physical form of microcapsules/microparticles with respect to size,shape,arrangement of core and coat,properties of core like difffusivity,partition coeffficient,properties of coat like porosity,thickness,crystallinity,inertness etc.

Brahmankar D.M., Jaiswal Sunil B. “Biopharmaceutics and Pharmacokinetics A Treatise Pg 408, 409,432.Robinson Joseph R., Lee Vincent H.L. “Controlled drug delivery Fundamentals and Applications Pg 97, 101, 105.Chien Yie W. “Novel Drug Delivery systems” Pg 45,47,58,62,64,67.

REFERENCES