Consolidation parameters

RAJGAD DNYANPEETH’s COLLEGE
OF PHARMACY , BHOR
Presentation by :Yadav Pawankumar Hanamant
1st year M. Pharm (sem –l)
Dept. : Pharmaceutics
Guided by :Prof. M.T Deshmukh
Subject :Modern Pharmaceutics

CONTENTS:
•Diffusion Parameters
•Dissolution Parameters
•Pharmacokinetic Parameters
•Similarity Factors –f2 & f1
•Higuchi
•Peppas plot
•Zero order
•First order
•Hixson Crowell

Diffusion is a net movement of anything from a region of higher
concentration to a region of lower concentration. Diffusion is driven
by gradient in concentration.
Diffusion parameter Is mainly to determinate the parameters of
the coefficient function called the diffusion parameters.
• This is given by Higuchi.
𝑄 = 𝐾√𝑻
• Where Q is the amount of drug released in time ‘t’ per unit area,
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.
DIFFUSION PARAMETERS:

DISSOLUTION PARAMETERS:
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 surface tension of the dissolution
Medium
e)Effect of viscosity of the dissolution medium.
f)Effect of the presenceof unreactive and reactive
additives in the dissolution medium.

g)Volume of dissolution medium and sink
Conditions
h) Deaeration of the dissolution medium
i) Effect of temperature of the dissolution medium

PHARMACOKINETIC
PARAMETERS:
• Pharmacokinetics is defined as the kinetics of
drug absorption, distribution, metabolism, and
excretion and their relationship with
pharmacologic, therapeutic or toxicologic
response in mans and animals.

Plasma drug concentration-time profile:

• Three important pharmacokinetic
parameters:
1. Peak plasma concentration (Cmax)
2. Time of peak concentration (tmax)
3. Area under the curve (AUC)

• The point of maximum concentration of a drug in
plasma is called as peak and the concentration of drug at
peak is known as peak plasma concentration.
• It is also called as peak height concentration and
maximum drug concentration.
• Cmax is expressed in mcg/ml.
Peak plasma concentration(Cmax)

Time of peak concentration (tmax)
• The time for drug to reach peak concentration inplasma
( 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.
• The parameter is of particular importance in assessing
the efficacy of drugs used to treat acute conditions like
pain and insomnia.

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.
• It is important for the dugs that are administered
repetitively for the treatment of chronic conditions like
asthma or epilepsy.

• 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 (post change)

•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

HIGUCHI MODEL:
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.

• Accordingly, model expression is given by the
equation:
ft = Q = A √D(2C ñ 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 and
D is the diffusivity of the drug molecules
(diffusion coefficient) in the matrix substance.

•This relation is valid during all the time, except when the total
depletion of the drug in the therapeutic system is achieved.
•To study the dissolution from a planar heterogeneous matrix
system, where the drug concentration in the matrix is lower than
its solubility and the release occurs through pores in the matrix,
the expression is given by:
ft = Q = √ Dδ/Ţ (2C – δ Cs) Cs t ..
where D is the diffusion coefficient of the drug molecule in the
solvent,
δ is the porosity of the matrix,
τ is the tortuisity of the matrix and
Q, A, Cs and t have the meaning assigned above.

•Tortuisity is defined as the dimensions of radius and branching
of the pores and canals in the matrix.
•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.
•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.

PEPPAS PLOT:
•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 …….(12)
• where Mt / M∞ is a fraction of drug released
at time t,
•k is the release rate constant and
•n is the release exponent.

•The n value is used to characterize different release for
cylindrical shaped matrices.
•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.

ZERO ORDER:
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 (3) 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.

•To study the release kinetics, data obtained from
in vitro drug release studies were plotted as
cumulative amount of drug released versus time
•Application: This relationship 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 in coated
forms, osmotic
systems, etc.

FIRST ORDER MODEL:
This model has also been used to describe absorption and/or
elimination of some drugs, although it is difficult to conceptualize
this mechanism on a theoretical basis.
The release of the drug which followed first order kinetics can be
expressed by the equation:
-dC /dt = - Kc …
where K is first order rate constant expressed in units of time-1.
Equation above can be expressed as:
log C = log C0 - Kt / 2.303 …
where C0 is the initial concentration of drug,
k is the first order rate constant, and
t is the time.

•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.
•Application: This relationship can be used to describe
the drug dissolution in pharmaceutical dosage forms
such as those containing water-soluble drugs in porous
matrices.

HIXSON CROWELL:
•Hixson and Crowell (1931) recognized that the particles regular
area is proportional to the cube root of its volume.
•They derived the equation:
W0 1/3 - Wt 1/3 = κ t …
where W0 is the initial amount of drug in the pharmaceutical
dosage form,
Wt is the remaining amount of drug in the pharmaceutical
dosage form at time t and
κ (kappa) is a constant incorporating the
surface-volume relation.

•The equation describes the release from systems
where there is a change in surface area and
•diameter of particles or tablets.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.
•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.

Consolidation parameters

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