dissolution models

2. 2
Objectives:
 Dissolution science is not just a quality control tool.
Apart from that in present era dissolution data act as
surrogate marker for in-vivo bioavailability .
 Along with wide versatility of application to
pharmaceutical scientist it also form basis for setting
specification to allow the release of batch to market.
 Present seminar try’s to give a bird eye view of
various dissolution model’s which will be helpful in
predicting the drug release kinetics ( dissolution
kinetics.)

3. DISSOLUTION
Dissolution is a process in which a solid substance
solubilizes in a given solvent i.e. mass transfer from
the solid surface to the liquid phase
Rate of dissolution is the amount of drug substance
that goes in solution per unit time under standardized
conditions of liquid/solid interface, temperature and
solvent composition
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4. Why dissolution studies?
1. To show that the release of drug from the
tablet is close to 100%.
2. To show that the rate of drug release is
uniform batch to batch.
3. And to show that release is equivalent to
those batches proven to be bioavailable
and clinically effective.
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5. Factors affecting Drug Dissolution
Factors relating to the physicochemical
properties of drug.
i. Solubility
ii. Particle size and
effective surface area
of the drug
iii. Polymorphism and
amorphism
iv. Salt form of the drug-
Factors relating to the dosage forms.
i. Pharmaceutical excipients –
 Diluents
 Lubricants
 Binders
 Surfactants
 Colorants
 Disintegranting Agents
ii. Method of granulation –
 Wet granulation
 Direct compression
 Agglomerative phase of
communication (APOC)
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6. DISSOLUTION MODEL’s & IT’s NEED
 Dissolution Profile- It is graphical representation [in
terms of concentration vs. time] of complete release of
A.P.I. from a dosage form in an appropriate selected
dissolution medium.
i.e. in short it is the measure of the release of A.P.I
from a dosage form with respect to time.
 IT’s NEED
 To Develop invitro-invivo correlation which can
help to reduced costs, speed-up product
development and reduced the need of perform costly
bioavailability human volunteer studies.
 To stabilize final dissolution specification for
the pharmacological dosage form
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7. TYPES OF DISSOLUTION MODELS
1 • Diffusion layer model
2 • Danckwert’s MODEL
3 • Interfacial barrier model
4 • Zero-order model
5 • First-order model
6 • Higuchi model
7 • Korsmeyer-Peppas model
8 • Hixson-Crowell model
9 • Baker-Lonsdale model
10 • Weibull model 7

8. 1. DIFFUSION LAYER MODEL
 Formation of a thin film at the interface, called as stagnant
layer.
 2 steps are involved:
i. Interaction of solvent with drug surface to form a saturated
drug layer , called stagnant layer.
ii. Diffusion of drug molecules from stagnant layer into bulk of
the system.

9. 1. DIFFUSION LAYER MODEL (contd…)
Using Fick’s law, Noyes-Whitney equation for DIFFUSION LAYER
MODEL is as follows
Where,
 dC/dt = dissolution rate of the drug.
 D = diffusion coefficient of the drug.
 A = surface area of the dissolving solid
 Kw/o = water/oil partition coefficient of drug
 V = volume of dissolution medium
 h = thickness of stagnant layer
 Cs–Cb = concentration gradient of diffusion of drug
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10. 2. DANCKWERT’s MODEL
The Danckwert’s model is expressed by following equation:
Where,
• m=mass of solid dissolved
• ү = rate of surface renewal.
 Danckwert’s model assumes that turbulence in the dissolution
medium exists at solid –liquid interface.
 The agitated fluid consists of macroscopic masses of
eddies(packets of solvent molecules)which keep continuously
moving in arandom fashion and touch the surface of solid
particle.
 The solid-liquid contact (interface) results in diffusion of drug
into packets wherein drug loaded packets move into the bulk of
solution.
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11. 2. DANCKWERT’s MODEL (contd…)
 In agitated fluid drug loaded packets are continuously replaced by
fresh packets due to which drug conc at solid liquid interface
never reaches saturation concentration.
 Since the solvent packets continuously replace the surface of the
solid , it is called as SATURATION RENEWAL THEORY
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12. 3. INTERFACIAL BARRIER MODEL
 Interfacial barrier model considers drug dissolution as crystal
dissolution wherein solids get hydrated initially and is not
instantaneous
 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
 When considering the dissolution of the crystal will have a different
interfacial barrier given by following equation,
G = ki (Cs – Cb)
 Where,
 G = dissolution per unit area
 Ki = effective interfacial transport constant
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13. 4. 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
Rearrangement of equation yields:
Qt = Q0 + K0t
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.
The release rate
is independent
of concentration
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14. 5. First-order model
This model is used to describe absorption and/or elimination of
some drugs. The release of the drug which followed first order
kinetics can be expressed by the equation:
LOG CUM.%DRUG
REMAINING
dC/dt = -Kc
TIME
The plot between Time (hrs) vs log cumulative % of drug remaining
to be release gives straight line.
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15. 6. HIGUCHI MODEL
 Higuchi developed models to study the release of water
soluble and low soluble drugs incorporated in semisolid
and solid matrices.
 To study the dissolution from a planar system having a
homogeneous matrix the relation obtained was;
A = [D (2C – Cs)Cs × t]1/2
Where,
 A is the amount of drug released in time ‘t’ per unit
area,
 D is the diffusivity of drug molecules in the matrix
substance
 C is the initial drug concentration,
 Cs is the drug solubility in the matrix media
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16. 6. HIGUCHI MODEL (contd…)
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.
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17. 7. Hixson-Crowell model
 Hixon-Crowell recognized that the particle regular area is
proportional to the cubic root of its volume, and hence desired
an equation as
1/3- M1/3 = K × t
Mo
where, Mo = original mass of particles
K = cube-root dissolution rate constant
M = mass of the A.P.I at the time ‘t’
APPLICATIONS:
 To evaluate the drug release with changes in the surface area
and the diameter of the particles /tablets
 The rate of dissolution depends on the surface of solvent - the
larger is area the faster is dissolution.
 It describes the drug releases by dissolution, with the changes
in surface area and diameter of the particles or tablets.
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18. 7. Hixson-Crowell model (contd…)
 The plotted graph will be linear if the following conditions
are fulfilled:-
 The equilibrium conditions are not reached and
 The geometrical shape of the pharmaceutical dosage form
diminishes proportionally over time.
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19. 8. Korsmeyer-Peppas model
 The KORSEMEYAR AND PEPPAS empirical expression relates the
function of time for diffusion controlled mechanism.
 It is given by the equation :
Mt / Ma = Ktn
where,
 Mt / Ma is fraction of drug released
 t = time
 K=constant includes structural and geometrical characteristics
of the dosage form
 n= release component which is indicative of drug release
mechanism
where , n is diffusion exponent.
i. If n= 1 , the release is zero order .
ii. n = 0.5 the release is best described by the Fickian diffusion
iii. 0.5 < n < 1 then release is through Anomalous diffusion
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20. 10.Korsmeyer-Peppas model (contd…)
Application:
 This equation has been used to the linearization of release data
from several formulations of microcapsules or microspheres
 Use to analyze the release of p’ceutical polymeric dosage form.
 When the release mechanism is not known or when more than
one type of release phenomena could be involved.
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21. 9.Baker-Lonsdale model
 This model was developed by Baker and Lonsdale (1974) from the
Higuchi model and described the drug release from spherical
matrices according to the equation
F= 3/2 [1-(1-At/A∞)2/3]-At/A∞
= (3DmCms) / (r02C0) X t
Where,
 At is the amount of drug released at time’t’
 A∞ is the amount of drug released at an infinite time,
 Dm is the diffusion coefficient,
 Cms is the drug solubility in the matrix,
 ro is the radius of the spherical matrix
 Co is the initial concentration of the drug in the matrix
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22. 10. Weibull model
Weibull model is generally applied to drug dissolution or
release from pharmaceutical dosage forms. The accumulated
fraction of the drug M in solution at time t is given by Weibull
equation:
M = M0[1-e-(t-T/a)b]
Where,
 m = % dissolved at time ‘t’
 a = scale parameter which defines time scale of the
dissolution process
 T1 = location parameters which represents lag period
before the actual onset of dissolution process (in most of
the cases T1 = 0)
 b = shape parameter which quantitatively defines the curve
Application:
The Weibull model is more useful for comparing the release
profiles of matrix type drug delivery
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23. 1) Remington's “The science and practice of pharmacy” 21st
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) European Journal of Pharmaceutical sciences 13 (2001)
page no.123 – 133.
6) Mathematical models of dissolution- Master’s thesis by
Jakub ˘ Cupera May 4, 2009 Masarykova Univerzita
7) Vinod P. Shah The role of dissolution testing in the
regulation of pharmaceuticals: The FDA perspective,
Taylor and Francis Group 2005 page no.81-95.
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References

24. CONCLUSION
 The Quantitative interpretation of the values
obtained n 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.
 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.
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