Release kinetics By subhakanta Dhal

Presentation: Release Kinetics
Part-II
By
Subhakanta Dhal
Alkem reaserch center, Mumbai
Mail id-sdhal82@gmail.com
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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
direct.
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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
tim e(in m in)
w01/3-w1/3
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
%cdr
%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)
LOGMt/Minf
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
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Comparison of Dissolution Data

Release kinetics By subhakanta Dhal

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