Release kinetics By subhakanta Dhal

Presentation: Release Kinetics

Part-II By Subhakanta Dhal Alkem reaserch center, Mumbai Mail [email protected]

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1. To study prediction of in vitro release.

2. To study prediction release kinetics of excipients .

3. To support data of IVIVC.

4. Study helps in pharmacokinetic model.

5. To correlate pharmacokinetic parameter.

6. To study mechanism of enzyme as well as receptor

kinetics.

7. To study acclerated stability kinetic model.

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Objective of Kinetics

Release Rates : IR, SR, CR

Release Profiles : Dissolution Models

Release Times : Rapid onset, Delayed Release etc

Release Sites : One or More Sites of GI Tract

Design of Release Controlling Formulation

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Dissolution Rate

Modified Noyes and Whitney Equation:

Diffusion Rate Constant = D

Surface Area = S

Volume of the Dissolution Media = v

Thickness of the Saturated Layer = h

Concentration of the API at Saturation = Cs

Dissolution Rate Constant = k

Concentration of the Bulk Solution = Ct

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Cross Section of Drug Release

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Drug Release Mechanisms

• Wetting of the system’s surface with water.

• Water penetration into the device (e.g., via pores and/or through continuous polymeric networks).

• Phase transitions of (polymeric) excipients (e.g., glassy-to rubbery-phase transitions).

• Drug and Excipient dissolution.

• Hindrance of rapid and complete drug and Excipient dissolution due to limited solubility and/or dissolution rates under the given conditions.

• Drug and/or Excipient degradation.

• Dissolution and/or precipitation of degradation products.

• Creation of water-filled pores.

• Pore closing due to polymer swelling.

• Creation of significant hydrostatic pressure within the delivery system, e.g. in the case of coated dosage forms.

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• Creation of cracks within release rate limiting membranes.

• Creation of acidic or basic microenvironments within the dosage forms

due to degradation products.

• Changes in the rate of drug and/or Excipient degradation rate due to

changes in the microenvironmental pH.

• Physical drug-Excipient interactions (e.g., ion–ion attraction/repulsion

and Van der Waals forces), which might significantly vary with time and

position due to changes in the microenvironmental conditions, such as

the pH, presence of counter ions and ionic strength.

• Changes in drug and/or Excipient solubility due to altered micro

environmental conditions (e.g., pH, ionic strength, etc.).

• Diffusion of drugs and/or excipients out of the dosage form with

potentially time- and/or position-dependent diffusion coefficients.

Drug Release Mechanisms Cont…..

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The Mechanistic Realistic Theories

.

A mechanistic realistic mathematical model is based on equations that

describe real phenomena, e.g. mass transport by diffusion, dissolution of

drug and/or Excipient particles, and/or the transition of a polymer from

the glassy to the rubbery .

These equations form the basis of the mathematical theory,Often partial

differential equations are involved.

If the amount of drug released or release rate can be separated from all

other variables and parameters on one side of the equation, the solution

is called explicit and the effects of the considered formulation and

processing parameters can be (more or less) directly be seen. if it is not

possible to separate the amount/rate of drug release from the other

variables and parameters, only a so-called implicit solution can be derived,

and the effects of the formulation and processing parameters is often less

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The Mechanistic Realistic Theories

.

Based on the physical or chemical characteristics of polymer, drug

release mechanism from a polymer matrix can be categorized in

accordance to three main processes (systems).

Drug diffusion from the non-degraded polymer (diffusion-controlled

system).

Enhanced drug diffusion due to polymer swelling (swelling-

controlled system).

Drug release due to polymer degradation and erosion (erosion-

controlled system).

Drug release may be due to dissolution based.

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Diffusion - Controlled System

The boundary conditions are influenced by the mass transfer process

at the surface and the volume of the surrounding system. Based on

these conditions, there are three main cases which are commonly

considered

For diffusion-controlled drug release profile is obtained by solving

Fick's second law of diffusion subject to appropriate boundary

conditions.

For one-dimensional drug release from a Drug system, the second

Flick's law of diffusion is where D and C are the diffusion coefficient

and drug concentration in the polymer matrix.

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Diffusion - Controlled System Cont.…

The mass transfer resistance at the surface is negligible and the surrounding

release medium is infinitely large (perfect sink condition), implying that the

concentration on the surface of the matrix (Cs) is constant

(Cs=K .Cb=constant at r=R). Here, Cb is the drug concentration in

surrounding bulk medium and K is the drug partition coefficient between the

matrix and bulk medium.

The mass transfer resistance at the surface is finite and the surrounding

volume is in perfect sink condition, implying that the concentration of the

surrounding system is constant, but the convective mass transfer coefficient

(h) will determine the surface concentration.

The surrounding system is a well-stirred finite volume. This implies that the

concentration of the surrounding system changes with time. The surface

resistance may or may not be negligible.

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Schematic illustration of cross-section of drug-system of (a) reservoir system,

(b) dissolved drug system, and(c) dispersed drug system. In reservoir system,

drug is confined by a spherical shell of outer radius R and inner radius Ri;

therefore, the drug must diffuse through a polymer layer of thickness (R−Ri).

In dissolved drug system, drug is dissolved uniformly at loading concentration

C0 in the polymeric matrix. In dispersed drug system, the radius of inner

interface between “core” (non-diffusing) and matrix (diffusing) regions, r′(t),

shrinks with time. The “core” region is assumed to be at drug loading

concentration C0.

Based on the Above figure region where the drug diffusion primarily takes place, the

diffusion-controlled system can be further categorized to reservoir and matrix systems.

Reservoir Systems

The reservoir system consists of a drug reservoir surrounded by the polymer matrix shell.

The reservoir model is the simplest model of a solute of drug released from a sphere

It assumes that drug is confined by a spherical shell of outer radius R and inner radius Ri;

thus, the drug must diffuse through a layer of thickness (R−Ri).

Matrix System In matrix system, the drug is incorporated in the polymer matrix in either dissolved or dispersed condition. Mathematical models for matrix systems are often valid for drug devices developed based on no biodegradable polymers. In these models, the drug is commonly assumed to be uniformly distributed inside the non- biodegradable polymer matrix. There are two possible cases, which are (i) the initial drug loading is lower than the solubility of the drug inside the polymer matrix (C0bCs), which implies a dissolved drug system, and (ii) the initial drug loading is higher than the solubility of the drug inside the polymer matrix (C0NCs), which implies a dispersed drug system.


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Swelling - Controlled Systems

The idea of using a swelling polymer is to provide more control over the release of drug, especially when its diffusivity in polymer is very low.

For this purpose, a swell able is commonly made using a hydrophilic polymer so that water is able to imbibe into the polymer matrix and cause polymer disentanglement..

The imbibing water into the polymer matrix decreases the polymer concentration and changes the level of polymer disentanglement.

The polymer matrix disentanglement also leads to matrix swelling that results in the rubbery (gel layer) region, in which there is an “enhanced diffusion” where drug mobility increases.

The polymer will also dissolve at the interface when the entanglement is weak since polymer concentration is very low.

Thus, in this system, the deviation from Fickian model is observe when the drug release is not only controlled by the diffusion of the drug inside the matrix, but also by the polymer matrix disentanglement and dissolution process.

For swelling-controlled system, the hydrophilic polymer is susceptible to swelling as water tends to penetrate and relax the polymer matrix. In this case, the composition of the hydrophilic polymer will determine the extent of swelling.

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Typical Hydrophilic Polymers-Hydroxypropyl Methylcellulose (HPMC), Poly

(hydroxyethyl Methacrylate) or Pol (HEMA), and Poly (Vinyl Alcohol) (PVA).

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Swelling - Controlled Systems Cont...

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Lee and Peppas Model

The swelling occurs to achieve thermodynamics equilibrium when water penetrates cross linked region inside the polymer matrix due to a water concentration gradient.

As water penetrates and swelling takes place, a transformation of polymer from a glassy to rubbery state occurs and the dimension of the matrix increases.

This change of state basically creates a gel layer of rubbery region for the drug to diffuse, in which the drug diffusivity increases substantially.

Therefore, during the swelling, two different states, namely the glassy core and gel layer (rubbery), exist in the polymer matrix.

Here, the concept of two moving fronts, namely the glassy– rubbery front (R) and the rubbery–solvent front (S), is introduced. Initially during swelling, front R moves inwards, whereas front S moves outward. When the polymer at interface S reaches its thermodynamic equilibrium with the surrounding medium, interface S will start dissolving and, therefore, front S moves inwards.

Both fronts will move inwards until the front R diminishes as the glassy core disappears. Subsequently at later time, only the rubbery region is present and dissolution at interface S eventually controls the shrinking process

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Schematic illustration of one-dimensional swelling process due to solvent diffusion and

polymer dissolution as proposed by Lee (a) initial thickness of the carrier, (b) early-time

swelling when there are increasing position of the rubbery/solvent interface (S) and

decreasing position of the glassy/rubbery interface (R), (c) late-time swelling when

there are decreases of both interface S and R positions, and (d) final dissolution process

when the slab only comprises rubbery region with the decrease of interface S .


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THE erosion kinetics can be altered by modifying copolymer composition or the

degree of crystallinIty as crystalline and amorphous polymers erode at different rates.

It is important to distinguish the two different terms commonly used in describing the

polymer erosion phenomena, namely degradation and erosion.

In a simplistic point of view, degradation refers to the polymer chain/bond

cleavage/scission reaction (chemical process), whereas the erosion designates the loss of

polymer material in either monomers or oligomers (chemical and physical process).

The erosion may consist of several chemical and physical steps, including degradation.

Since erosion is a more general term to capture the overall mechanism of the bio

erodible system, this section will mainly utilize the term erosion.

The term of degradation will still be used when specific degradation processes, e.g.

polymer backbone cleavage and autocatalytic process, are involved in the model.

Gel permeation chromatography (GPC) can be used to monitor the polymer molecular

weight changes during the drug release and erosion.

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Erosion - Controlled Systems

Erosion - Controlled Systems Cont…

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There are two ideal scenarios for polymer erosion, namely surface (heterogeneous) and

bulk (homogeneous) erosions

In bulk erosion, the system has a constant diameter size and external fluid is allowed to

penetrate into the during which erosion of the polymer occurs.

On the other hand, in surface erosion, the system has an evolving shrinking diameter as

the erosion of the polymer takes place at the external matrix boundary.

surface erosion polymer-- (1,3-bis-p-carboxyphenoxypropane-co-sebacic acid) (p(CPP-

SA)) and poly(1,6-bis-p-carboxyphenoxyhexane- co-sebacic acid) (p(CPH-SA)).

Bulk erosion polymer-- poly(lactic acid) (PLA), poly(lacticco- glycolic acid) (PLGA),

and poly(ε caprolactone)( PCL).

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Release Kinetics

Release Kinetics: Data obtained from in-vitro release studies were fitted to various kinetics

models to find out the mechanism of drug release Kinetics models used for in-

vitro drug release from are

Zero order release kinetic model

First order release kinetic model [1897]

Hixon-crowell model[1931]

Higuichi model [T. Higuichi 1963 & W. I Higuichi 1967]

Kosysmer-peppes model.

Other Model- Weibull model, Hopfenberg model, Gompertz, sequential

layer, Empirical models, reciprocal powered time model

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Zero Order Kinetics

According to this model, under standard condition of temperature and agitation, the dissolution medium, the dissolution rate model can be described by the equation. DQ/dt=K0 Or, in an integrated form q= K0t Where, q = Amount of drug released per unit surface area K0 = Zero order release rate constant T= Time A plot ‘q’ vs. t’ gives a straight line.

CONDITION Drug dissolution from pharmaceutical dosage forms that do not disaggregate and release the drug slowly (assuming that area does not change and no equilibrium conditions are obtained).

APPLICATION modified release pharmaceutical as in the case of some transdermal systems as well as matrix tablets with low soluble drugs, coated forms, osmotic systems, etc. for prolonged action.

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First Order Release Kinetics (Noyes Whitney’s Equation)

According to Noyes Whitney, under standard condition of agitation and temperature, the

dissolution rate process for solids can be described by the equation.

Dq/dt = K1 (Cs –Ct)

Under sink condition, i.e. when Ct<0. 15Cs, the equation becomes,

Dq/dt = K1Cs

Or, in an integrated form

In q0/q = K1t

Where, q= Amount of drug release per unit surface area

K1 = first order release rate constant

Q0 = Initial amount

Cs = saturation solubility

Ct = Concentration at time‘t’

A plot of log % remaining to be released vs. ‘time’ gives a straight line with a negative

slope.

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APPLICATION

The pharmaceutical dosage forms, such as those containing water-soluble

drugs in porous matrices release getting: the drug in a way that is

proportional to the amount of drug remaining in its interior . in such

way, that the amount of drug released by unit of time diminish.

First Order Release Kinetics (Noyes Whitney’s Equation) Cont….

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Hixson – Crowell Model Kinetics

As solid dissolved the surface area S changes with time. The Hixon Crowell cube root

equation for dissolution kinetics is based on the assumption that:

Dissolution occurs normal to the surface of soluble particles.

Agitation is on the overall exposed surface and there is no stagnation.

The particles of solute retain its geometric shape.

For a non- dispersed powder with spherical particles a bit mathematical derivation leads

to the kinetics equation.

W01/3 – W 1/3 = KHCt

Where, W0 = Initial weight of the particles.

W = weight of the particles at t

KHC = Hixon – Crowell release rate constant.

T = Time

A plot of W01/3 – W 1/3 vs. time gives a straight line with a negative slope since

W increases with time.

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Hixon-crowel equation

0

1

2

3

0 50 100

time(in min)

w01

/3-w

1/3

W01/3-

W1/3

APPLICATION When this model is used, it is assumed that the release rate is limited by the drug particles

dissolution rate and not by the diffusion that might occur through the polymeric matrix.

This model has been used to describe the release characterize profile keeping in mind the

diminishing surface of the drug for values for a particles during the dissolution

Hixson – Crowell Model Kinetics Cont…

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Higuichi Model Kinetics

For coated or matrix type dosage form, the dissolution medium enters the dosage

form in order for the drug to be released and diffused into the bulk solution.

In such conditions, often the dissolution follows the equation proposed by

Higuichi

Q = [ DE (2A – Ecs) Cs/t]0.5

Or, Q = KHG t 0.5

Where, Q = Amount of drug released per unit area of the dosage form.

D = diffusion Coefficient of the drug.

E = porosity of the matrix

T = Tortuousity of the matrix

Cs = Saturation solubility of the drug in the surrounding liquid.

K HG = Higuichi Release Rate Constant.

Fitness of the data into various kinetics modes were assessed by determining the

correlation coefficient, the constants, for respective models were also calculated

from slope.

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Higuchi-equation

0

50

100

0 5 10

sqrt

%cd

r

%cdr

APPLICATION

Higuchi describes drug release as a diffusion process based in the Fick’s law, square

root time dependant. This relation can be used to describe the drug dissolution

from several types of modified release pharmaceutical dosage forms, as in the case

of some transdermal and matrix tablets with water a soluble drugs

Higuichi Model Kinetics Cont….

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Koseymer-peppes model

The model explain that

Mt/Minf = ktn

Where Mt/Minf is a fraction of drug released at any time t;K is the release rate constant

incorporating the structural and geometric characteristics ; n is the diffusional exponent,

indicative of the release mechanism. (The value of n for a is <0.45 for Fickian release,

>0.45 and <0.89 for non-Fickian release, 0.89 for case II release, and >0.89 for super II

release) The values of K, n, and r (correlation co efficient), as obtained from the

dissolution data KOSEMEYER-PEPPS

-1.5

-1

-0.5

0

0 2 4

LOG(TIME)

LO

G M

t/M

inf

Series1

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Comparison of Dissolution Data

Dissimilarity Factor (f1) :

It was calculated in the comparison with reference or innovator product to

know the dissimilarity.

The dissimilarity factor (f1) should be always less than 10 (f1<10)

Rt - Tt

f1= ---------------× 100

Rt

Where

Rt = mean % dissolution of reference listed drug

Tt = mean % dissolution of our formulated product

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Similarity Factor (f2) : The similarity factor (f2) was defined as the ‘logarithmic reciprocal

square root transformation of one plus the mean squared difference in

percent dissolved between the test and the reference products’. This

was calculated to compare the test with reference release profiles.

The similarity factor (f2) should be always greater than 50 (f2>50).

The method is more adequate to compare dissolution profiles when

more than three or four dissolution time points are available and can

only be applied if average difference between Rt and Tt is less than 100.

If this difference is higher than 100, normalization of data is required.

1

f2= 50 × log10 × ------------------------------- × 100

1+ 1/n × (Rt – Tt) 2

Where n= no. of sampling point a

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Comparison of Dissolution Data

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Release kinetics By subhakanta Dhal

Health & Medicine