This document discusses various parameters used to characterize drug release from pharmaceutical formulations, including diffusion parameters described by Higuchi's equation, dissolution parameters like the effects of agitation and pH, and pharmacokinetic parameters like Cmax, Tmax, and AUC. It also covers models like the Heckel equation that can be applied to understand powder compaction and the Korsmeyer-Peppas model for characterizing drug release mechanisms.

1. Study of consolidation
parameters
Presented by
(Dr) Kahnu Charan Panigrahi
Asst. Professor, Research Scholar,
Roland Institute of Pharmaceutical Sciences,
(Affiliated to BPUT)
Web of Science Researcher ID: AAK-3095-2020

2. CONTENT:
 Diffusion parameters
 Dissolution parameters
 Pharmacokinetic parameters
 Heckel plot
 Similarity factors f1 and f2
 Higuchi and Peppas plot

3. DIFFUSIONPARAMETERS
• This is given by Higuchi.
𝑄= 𝐾𝑻
• Where Q is the amount of drug released in time‘t’ per
unitarea, K is higuchi constant. T is time in hr.
• Plot: The data obtained is to be plotted as cumulative
percentage drug release versus Square root of time.
• Application: modified release pharmaceutical dosage
forms, transdermal systems and matrix tablets with
water soluble drugs.

4. Dissolutionparameters
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.
Dissolution parameters
a) Effect of agitation
b) Effect of dissolution fluid
c) Influence of pH of dissolution fluid
d) Effect of temperature of the dissolution medium
e) Effect of surface tension of the dissolution medium
f) Effect of viscosity of the dissolution medium
g) Volume of dissolution medium and sink conditions

5. Effect ofagitation
• The relationship between the intensity of agitation and the
rate of dissolution varies considerably according to the type
of agitation used, degree of laminar and turbulent flow in
the system, the shape and design of the stirrer and the
physicochemical properties of the solid.
• For the basket method, 100 rpm usually is utilized, while for
the paddle procedure, a 50 –75 rpm is recommended.
Effect of dissolutionfluid
• Selection of proper medium for dissolution testing depends
largely on the physicochemical properties of the drug.
• It also depend on the in vivo conditions in the
gastrointestinal tract, especially pH, surface tension,
viscosity and sink conditions.

6. Influenceof pH of dissolution fluid
• For weak acids, the dissolution rate increases with
increasing pH, whereas, for weak bases, the dissolution
rate increases with decreasing pH.
• Therefore for acetylsalicylic acid (pKa=3.5) tablets and
capsules, the dissolution rate would be expected to increase
if the pH of the dissolution medium was higher than 3.
Effect of temperature ofthe dissolutionmedium
• Drug solubility is temperature dependent, therefore careful
temperature control during the dissolution process is extremely
important.
• Generally a temperature of 37°±0.5 is maintained during
dissolution determination of oral dosage forms and
suppositories.

7. Effectof surfacetensionof the dissolutionmedium
• According to the diffusion film theory, dissolution of the drug is
governed by two processes, the release of the drug from the solid
surface and its transfer throughout the bulk of the dissolution
medium.
• If the drug is hydrophobic the dissolution rate is influenced primarily
by the release processes, whereas, for hydrophilic drugs the transfer
process is more likely to be the rate limiting step.
• Incorporation of surface active agents in the dissolution medium,
is expected to enhance the dissolution rate of a poorly soluble
drug in solid dosage forms by reducing the interfacial tension and
micelle formation.

8. Effectof viscosityof thedissolution medium
• If the interaction at the interfaces, occurs much faster than the
rate of transport, such as in the case of diffusion controlled
dissolution processes, it would be expected that the dissolution
rate decreases with an increase in viscosity.
• The rate of dissolution of zinc in HCl solution containing
sucrose was inversely proportional to the viscosity of solution.
• The Einstein equation expresses the diffusion coefficient as a
function of viscosity, as can be seen from the following treatment.
𝐷= µ𝑘𝑇
µ = mobility (velocity at a force of one dyne)
k = boltzmann constant (1.38× 10
−16)
T = Absolute temperature

9. Volumeof dissolutionmedium and sinkconditions
• The proper volume of the dissolution medium depends
mainly
on the solubilty of the drug in the selected fluid.
• If the drug is poorly soluble in water, a relatively large
amount of fluid should be used if complete dissolution is
to be expected.
• In order to maintain the effect of the concentration
gradient and maintain sink conditions, the concentration
of the drug should not exceed 10 % of its maximum
solubility in the dissolution medium selected.

10. Hixson-Crowells cube rootlaw
• Hixson and Crowell described this
W0
1/ 3 −Wt
1/ 3 = Kt
Where W0 is the initial amount of drug
Wt is the remaining amount of drug at time t .
• Plot: Data is to be plotted as cube root of drug percentage
remaining in matrix versus time.
• Application: This expression applies to pharmaceutical dosage
form such as tablets, where the dissolution occurs in planes that
are parallel to the drug surface if the tablet dimensions diminish
proportionally in such a manner that the initial geometrical form
keeps constant all the time.

11. Pharmacokineticparameters
• Pharmacokinetics is defined as the kinetics of drug
absorption, distribution, metabolism, and excretion and
their relationship with pharmacologic, therapeutic or
toxicologic response.
• Three important pharmacokinetic parameters:
1. Peak plasma concentration (Cmax)
2. Time of peak concentration (tmax)
3. Area under the curve (AUC)

12. Plasma drugconcentration-time
profile

13. Peak plasma concentration(Cmax)
• The point of maximum concentration of a drug in plasma
is called as peak plasma concentration.
• Cmax is expressed in mcg/ml.
Time of peakconcentration (tmax)
• The time for drug to reach peak concentration in plasma (
after extravascular administration) is called the time of
peak concentration.
• It is expressed in hours. Onset time and onset of action is
dependent upon tmax.

14. Area under the curve(AUC)
• It represents the total integrated area under the plasma
level-time profile and expresses the total amount of drug
that comes into the systemic circulation after its
administration.
• AUC is expressed in mcg/ml X hrs.

15. DIFFERENCE FACTOR (f1) & SIMILARITY FACTOR(f2)
The difference factor (f1) as defined by FDA
calculates the % difference between 2 curves at each
time point and is a measurement of the relative error
between 2 curves.
where, n = number of time points
Rt = % dissolved at time t of reference product (pre change)
Tt = % dissolved at time t of test product (postchange)
3
0
/7

16.  The similarity factor (f2) as defined by FDA is logarithmic
reciprocal square root transformation of sum of squared
error and is a measurement of the similarity in the
percentage (%) dissolution between the two curves
3
1
/7

17. Data structure and steps to follow:
• This model-independent method is most suitable for the
dissolution profile comparison when three to four or more
dissolution time points are available.
• Determine the dissolution profile of two products (12 units each) of
the test (post-change) and reference (pre-change) products.
• Using the mean dissolution values from both curves at each time
interval, calculate the difference factor (f1) and similarity factor (f2)
using the above equations.
• For curves to be considered similar, f1 values should be close to 0,
and f2 values should be close to 100. Generally, f1 values up to 15
(0-15) and f2 values greater than 50 (50-100) ensure equivalence of
the two curves.

18. Heckel Equation
The heckel analysis is a most popular method of
deforming reduction under compression pressure
Powder packing with increasing compression load is
normally attributed to particles rearrangement , elastic &
plastic deformation & particle fragmentation.
It is analogous to first order reaction ,where the pores in
the mass are the reactant , that is:
Log 1/E= Ky . P + Kr
Where….. Ky =material dependent constant
inversely proportional to its yield strength ‘s’
Kr=initial repacking stage hence E0

19. The applied compressional force F & the movement of
the punches during compression cycle & applied
pressure P ,porosity E.
For a cylindrical tablets
P=4F/л. D2
Where… D is the tablet diameter
similarly E can be calculated by
E=100.(1-4w/ρt .л.D2.H)
Where…w is the weight of the tableting mass ,
ρt is its true density ,
H is the thickness of the tablets.

20. Heckel Plots
Heckel plot is density v/s applied pressure
Follows first order kinetics
As porosity increases compression force also increases
Thus the Heckel’s plot allows for the interpretation of the
mechanism of bonding.
Materials that are comparatively soft & that readily
undergo plastic deformation retain different degree of
porosity , depending upon the initial packing in the die.
This in turn is influenced by the size distribution, shape
etc of the original particles.
Ex: sodium chloride (shown by Type a in graph)

21. Harder material with higher yield pressure values usually
undergo compression by fragmentation first , to provide a
denser packing.
Ex: Lactose, sucrose ( shown in Type b in graph).
Type-a plots exhibits higher slop (Ky) then type-b, because
type-a materials have lower yield stress.
Type-b plots exhibits lower slop because brittle, hard
materials are more difficult to compress.

22. Higuchi Model
The first example of a mathematical model aimed to describe drug release
from a matrix system was proposed by Huguchi in 1961.
This model is based on the hypotheses that
(i) initial drug concentration in the matrix is much higher than drug solubility;
(ii) drug diffusion takes place only in one dimension (edge effect must be
negligible);
(iii) drug particles are much smaller than system thickness;
(iv) matrix swelling and dissolution are negligible;
(v) drug diffusivity is constant; and
(vi) perfect sink conditions are always attained in the release environment.

23. • Accordingly, model expression is given by the equation:
ft = Q = A √D(2C - Cs) Cs t
Where Q is the amount of drug released in time t per unit area A,
C is the drug initial concentration,
Cs is the drug solubility in the matrix media
D is the diffusivity of the drug molecules (diffusion coefficient) in the
matrix substance.
•In a general way it is possible to simplify the Higuchi model as
(generally known as the simplified Higuchi model):
f t = Q = KH X t1/2
where, KH is the Higuchi dissolution constant

24. •The data obtained were plotted as cumulative percentage drug
release versus square root of time .
•Application: 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

25. Korsmeyer-Peppas model
• Korsmeyer et al. (1983) derived a simple relationship which
described drug release from a polymeric system equation.
• To find out the mechanism of drug release, first 60% drug
release data were fitted in Korsmeyer-Peppas model.
Mt / M∞ = Ktn
where Mt / M∞ is a fraction of drug released at time t,
k is the release rate constant
and n is the release exponent.
• In this model, the value of n characterizes the release
mechanism of drug.

26. •For the case of cylindrical tablets, 0.45 ≤ n corresponds to a Fickian
diffusion mechanism, 0.45 < n < 0.89 to non-Fickian transport, n =
0.89 to Case II (relaxational) transport, and n > 0.89 to super case II
transport .
•To find out the exponent of n the portion of the release curve, where
Mt / M∞ < 0.6 should only be used.
•To study the release kinetics, data obtained from in vitro drug
release studies were plotted as log cumulative percentage drug
release versus log time.

27. Thank You