The proper diffrence between dissolution and dissolution rate and detailed description of dissolution model with application

1. Dissolution
Model
Presented by- Rajdeepa Kundu(JISU/2022/0198)
Batch-M.Pharm 1st year Pharmaceutics
Under the guidance of – Dr Tapan Kumar Shaw
(Associate professor of JIS university)

2. Dissolution
• According to the IUPAC,the term
“dissolution” is defined as “The mixing of
two phases with the formation of one new
homogeneous phase (i.e. the solution).”
• The “dissolution rate” of a drug in a
liquid is generally defined as the change in
the concentration of dissolved drug
(individualized drug
molecules/ions/atoms), dc, in the time
interval dt:
• dissolution rate = dc/ dt

3. 5 major steps involved in the dissolution of solid
drug particles in a well-stirred aqueous medium
• The surface of the drug particle is wetted with water.
• (b) Solid-state bonds in the drug particle are broken down (e.g. attractive
electrostatic forces in a drug crystal consisting of cations and anions).
• (c) Individualized drug molecules/ions/atoms are surrounded by a shell of water
molecules (“solvation”). (d) The individualized drug molecules/ions/atoms diffuse from
the surface of the drug particle through the liquid, unstirred boundary layer surrounding
the system into the well-stirred bulk fluid. It has to be pointed out that even in
thoroughly stirred aqueous liquids thin unstirred boundary layers exist directly at the
surfaces of the drug particles (due to adhesional forces). The thickness of these
boundary layers is a function of the degree of agitation.
• (e) If the surrounding bulk fluid is well-stirred, the drug molecules/ions/atoms are
transported by convection in the liquid, which is not part of the unstirred boundary
layer: The mass flow created by stirring assures rapid movement of water and

4. Modeling of dissolution profiles
A water-soluble drug incorporated in a matrix is
mainly released by diffusion, while for a low
water-soluble drug the self-erosion of the matrix
will be the principal release mechanism.
• To accomplish these studies the cumulative
profiles of the dissolved drug are more
commonly used.
• To compare dissolution profiles between two
drug products model dependent (curve fitting),
statistic analysis and model independent
methods can be used.
Mathematical models:
• Zero order kinetics
• First-order kinetics
• Weibull model
• Higuchi model
• Hixson–Crowell model
• Korsmeyer–Peppas model
• Baker–Lonsdale model
• Hopfenberg model
• Other release parameters

5. Zero-order
kinetics
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) can be
represented by the following equation.
The pharmaceutical dosage forms following this profiles release the
same amount of drug by unit of time and it is the ideal method of
drug release in order to achieve a pharmacological prolonged
action.
• W0 – Wt = Kt , where W0 is the initial amount of drug in the
pharmaceutical dosage form, Wt is the amount of drug dissolved at
time t and K is a proportionality constant.
Applications: This relation can be used to describe the drug
dissolution of several types of modified release pharmaceutical
dosage forms, as in the case of some transdermal systems, as
well as matrix tablets with low soluble drugs, coated forms,
osmotic systems, etc

6. First-order
kinetics
This model was first proposed by Gibaldi and Feldman (1967) and
later by Wagner (1969).
The dissolution phenomena of a solid particle in a liquid media
implies a surface action, as can be seen by Noyes–Whitney
Equation: dC/dt = K(Cs –C),where C is the concentration of the
solute in time t, Cs is the solubility and K is a first order
proportionality constant.
This equation was altered by Brunner et al. (1900), to incorporate
the value of the solid area accessible to dissolution, S, getting:
dC/dt = K1 S(Cs-C), Where, k1 is a new proportionality constant.
Using the Fick first law, it is possible to establish the following
relation ,for the constant k1 = D/Vh , where D is the solute diffusion
coefficient in the dissolution media, V is the liquid dissolution
volume and h is the width of the diffusion layer.

7. Continue…
Hixson and Crowell adapted the Noyes–Whitney equation in the following manner:
dW/dt = kS(Cs-C), where W is the amount of solute in solution at time t, dW/dt is the
passage rate of the solute into solution in time t and K is a constant.
This last equation is obtained from the Noyes–Whitney equation by multiplying both
terms of equation by V and making K equal to k V. Comparing these terms, the following
relation is obtained: • K= D/h
In this manner, Hixson and Crowell equation can be written as:dW/ dt = KS/V (VCs-W) =
k (VCs-W),Where k = k1S.
If one pharmaceutical dosage form with constant area is studied in ideal conditions (sink
conditions), it is possible to use this last equation that, after integration, will become: W =
VCs (1 – e -kt) .This equation can be transformed, applying decimal logarithms in both
terms, into: Log (VCs- W) = log VCs- (kt/2.303), The data obtained are plotted as log
cumulative percentage of drug remaining vs. time which would yield a straight line with a
slope of-K/2.303
Applications: This relationship can be used to describe drug dissolution in
pharmaceutical dosage forms such as those containing water-soluble drugs in porous
matrices.

8. Hixson–
Crowell
model
Drug powder that having uniformed size particles, Hixson and Crowell derived the
equation which expresses rate of dissolution based on cube root of weight of
particles and the radius of particle is not assumed to be constant.
This is expressed by the equation, M0 1/3 - Mt 1/3 = κ t ,Where, M0 is the initial
amount of drug in the pharmaceutical dosage form, Mt is remaining amount of drug
in the pharmaceutical dosage form at time ‘t’ and κ is proportionality constant.
To study the release kinetics, data obtained from in vitro drug release studies were
plotted as cube root of drug percentage remaining in matrix versus time
Applications: This applies to different pharmaceutical dosage forms such as
tablets, where the dissolution occurs in planes parallel to the drug surface if the
tablet dimensions diminish proportionally, in such a way that the initial geometrical
form keeps constant all the time.
Cube root law- The dissolution data are plotted in accordance with the
Hixson-Crowell cube root law, i.e. the cube root of the initial concentration
minus the cube root of per cent remained, as a function of time. The results
indicates that a linear relationship was obtained in all cases.

9. Higuchi model
This is the first mathematical model that describes drug release from a matrix system, proposed
by Higuchi in 1961.
This model is based on the different hypotheses that (1) Initial drug concentration in the matrix is
much higher than drug solubility, (2) Drug diffusion takes place only in one dimension (Edge
effect should be avoided), (3) Drug particles are much smaller than thickness of system, (4)
swelling of matrix and dissolution are less or negligible, (5) Drug diffusivity is constant, (6)
Perfect sink condition is always attained in the release environment.
Equation-ft = Q = √D(2C-Cs )Cs t , where Q is the amount of drug released in time t per unit
area, C is the drug initial concentration, Cs is the drug solubility in the matrix media and D is the
diffusivity of the drug molecules (diffusion constant) in the matrix substance.
Higuchi describes drug release as a diffusion process based in Fick’s law, square root time
dependent. The data obtained were plotted as cumulative percentage drug release versus
square root of time
Applications: This relationship can be used to describe the drug dissolution from several types
of modified-release pharmaceutical dosage forms, as in the case of some transdermal systems
and matrix tablets with water-soluble drugs.

10. Korsmeyer–
Peppas
model
Nicholas Peppas was the first to introduce this equation in the field of drug delivery
(Peppas, 1985).
Clearly, the classical Higuchi equation as well as the above-described short time
approximation of the exact solution of Fick’s second law for thin films with initial drug
concentrations, which are below drug solubility (monolithic solutions)
Frequently used and easy-to-apply model to describe drug release Peppas equation, or
power law: Mt/M∞= kt n , Here, Mt and M∞ are the absolute cumulative amount of drug
released at time t and infinite time, respectively; k is a constant incorporating structural and
geometric characteristics of the system, and n is the release exponent, which might be
indicative of the mechanism of drug release.
Used when a release exponent of 0.5 can serve as an indication for diffusion-controlled
assumptions drug release, but only if all these particular solutions are based on are
fulfilled, for example film geometry with negligible edge effects, time- and position-
independent diffusion coefficients in a non-swellable and insoluble matrix former
Applications: This equation has been used to the linearization of release data from
several formulations of microcapsules or microspheres.

12. Comparison of dissolution
profiles
The drug-release profiles can be analyzed using the f2 metrics
mathematical equation that compares drug-release curves.
• f2 metric is the similarity factor, and values of f2 between 50 and
100 suggest profile similarity. A value less than 50 represents a
significant difference and equates to a greater than 10% dissolved
difference between the two drug-release curves.
• Rt represents the reference profile, Tt represents the test profile
where (n) is the number of data points collected.
Equation:
Difference
factor(F1)
Similarity
factor(F2)
innference
0 100 Dissolution
profile are
similar
<=15 50 Similarity
or
equivalenc
e of 2
profile

13. Reference
Cartensen JT; Modeling and data treatment
in the pharmaceutical sciences. Technomic
Publishing Co. Inc., New York, Basel
1996
Ramteke KH, Dighe PA, Kharat AR, Patil
SV. Mathematical models of drug
dissolution: a review. Sch. Acad. J. Pharm.
2014 Jan;3(5):388-96.
2014

14. Thank you.