Fundamentals of modified release formulations

FUNDAMENTALS OF MODIFIED
RELEASE FORMULATIONS
Dr. Basavraj K. Nanjwade M. Pharm., Ph. D
Professor of Pharmaceutics
Department of Pharmaceutics
KLE University College of Pharmacy
BELGAUM – 590010, Karnataka, INDIA
1

CONTENTS:
Diffusion controlled
Dissolution controlled
Erosion controlled and hybrid system in drug
delivery
Mathematical models
Design and optimization of release rates based
desired pharmacokinetic profile 2

DIFFUSION CONTROLLED
In these type of system the rate controlling step is not dissolution rate
but the diffusion of dissolved drug through a polymeric barrier.
 Since the diffusional path length increases with time as the insoluble
matrix is gradually depleted by the drug and the release of drug is
never zero order.
 This system are broadly classified into two categories reservoir system
and monolithic system.
3

DIFFUSION CONTROLLED
 There are following type of diffusion controlled system
1. Reservoir devices
2. Matrix devices
1. Reservoir devices:-
 Drug will partition in to the membrane and exchange with fluid
surrounding the particle or tablet.
 The water soluble polymer material encases a core of drug.
 Additional drug will enter the membrane, diffuse to the
periphery and exchange with the surrounding media. 4

RESERVOIR DIFFUSION CONTROLLED
SYSTEM
 These systems are hollow in which core of drug is surrounded in
water insoluble polymer membrane.
 Coating or microencapsulation technique are
used to apply polymer.
 The permeability of membrane depend on thickness
of the coat/concentration of coating solution & on the nature of
polymer, ethyl cellulose and polyvinyl acetate are the commonly
used polymer in such devices.
5

RESERVOIR DIFFUSION CONTROLLED
SYSTEM
 The mechanism of drug release across the membrane
involves partitioning into the membrane with subsequent
release into the surrounding fluid by diffusion.
 The rate of drug release from the reservoir system can be
explained by Fick ’s Law of diffusion as per the following
equation.
dm/dt = DSK(ΔC)/l
6

dm/dt = DSK(ΔC)/l
Where,
S = is the active diffusion area.
D = is the diffusion coefficient of the drug across the coating
membrane.
l = is the diffusional path length (thickness of polymer coat)
ΔC = is the concentration difference across l.
K = is the partition coefficient of the drug between polymer
and the external medium.
7

METHODS TO DEVELOP THE RESERVOIR
DEVICES
There are 2 processes used to apply insoluble polymeric materials
to enclose drug containing core in tablets.
Press coating & Air suspension techniques
 Microencapsulation process is commonly used.
 In most cases drug is incorporated in coating film as well as in
the microcapsule.
 Care should be taken during placement into tablet or capsule
dosage forms to minimize fragmentation or fusion of the particle
both effects will alter release characteristics. 8

2. MATRIX DIFFUSION CONTROLLED SYSTEM
 In these system the drug is dispersed in insoluble matrix of rigid
non swellable hydrophobic materials or swellable hydrophilic
substances.
 Insoluble plastics such as PVC and fatty materials like stearic
acid, beeswax etc are the material used for rigid matrix.
 The drug is generally kneaded within the solution of plastic
material such as PVC in an organic solvent and granulated. The
wax drug matrix is prepared by dispersing the drug in molten fat
followed by congealing.
9

MATRIX DIFFUSION CONTROLLED SYSTEM
10

• The equation describing drug release for this system is given
by T. Higuchi.
Q=[Dἐ /T (La-ἐCs)Cs t]1/2
Q = weight in gram of drug release/unit surface area
D = diffusion coefficient
Cs = solubility of drug in the release medium
ἐ = Porosity of matrix
T = tourtuosity of matrix
A = Concentration of drug in the tablet express as g/ml
11

 Assumptions made in the previous equations :
A pseudo-steady state is maintained during release .
A>>Cs , i.e. , excess solute is present .
C=0 in solution at all times ( perfect sink ) .
Drug particles are much smaller than those in the matrix .
The diffusion coefficient remains constant .
No interaction between the drug and the matrix occurs .
12

 The release of highly water soluble drug can be sustained by
using swellable matrix systems.
 Hydrophilic gums may be of natural origin (Guar gum,
tragacanth), semi synthetic (HPMC, CMC, Xanthan gum) or
synthetic (poly acryl amides) are the material generally used
for such matrices.
 In the solvent such as alcohol the gum and drug are
granulated together and compressed into tablet.
13

 The mechanism of drug release from this system involves
initial dehydration of hydrogel followed by absorption of
water and desorption of drug via swelling controlled
diffusion mechanism.
 As the gum swells and the drug diffuses out of it, the
swollen mass devoid of drug appear transparent or glass like
and so the system is sometimes called as glassy hydrogel.
14

Advantages and Disadvantages of Matrix and
Reservoir system
Matrix system Reservoir system
Suitable for both non- Degradable reservoir systems
degradable and degradable system. may be difficult to design
No danger of ‘dose dumping’ Rupture can result in dangerous
in case of rupture. Dose dumping.
Achievement of ‘zero order’ Achievement of zero order
release is difficult. release is easy.
15

DISSOLUTION CONTROLLED RELEASE
 These system are easiest to design.
 The drug with slow dissolution rate is inherently sustained.
E.g. Griseofulvin, Digoxin and Saliyclamide & they act as
natural prolonged release products.
16

 Aluminum aspirin and ferrous sulfate produce slow
dissolving form when it comes in contact with GI fluids.
 Drugs having high aqueous solubility & dissolution rate
E.g. Pentoxifylline steroid undergo transformation into less
soluble polymorphs during dissolution in absorption pool.
17

 The basic principle of dissolution control is as follows: If the
dissolution process is diffusion layer controlled where the rate
of diffusion from the solid surface through a unstirred liquid
film to the bulk solution is rate limiting, the flux ‘J’ is given by
J= -D(dc/dx)
Where,
D = Diffusion coefficient.
Dc/ dx = Concentration gradient between the solid surface and
bulk of solution.
18

 In terms of flow rate of material (dm/dt) through unit area (A), the
flux can be given as
J = (1/A) dm/dt
 For the system with linear concentration gradient and thickness of the
diffusion layer ‘h’
dc/ dx = (Cb - Cs)
 Where Cs represents the concentration at the solid surface and Cb is
the bulk solution concentration. A combined equation for rate of
material is given as
dm/dt = - (DA/h) (Cb - Cs) = kA (Cs - Cb)
Where, k is intrinsic dissolution rate constant.
19

Dissolution controlled release products are divided
in two classes:
1) Encapsulation dissolution control.
2) Matrix dissolution control.
1. Encapsulation/Coating dissolution controlled system
(Reservoir Devices):
 Encapsulation involves coating of individual particles, or
granules of drug with the slowly dissolving material.
 The particles obtained after coating can be compressed
directly into tablets as in spacetabs or placed in capsules as
in the spansule products.
20

Encapsulation/Coating dissolution controlled
system (Reservoir Devices):
 As the time required for dissolution of coat is a function of
its thickness and the aqueous solubility of the polymer one
can obtain the coated particles of varying thickness in the
range of 1- 200 micron.
21

 By using one of several microencapsulation techniques the
drug particles are coated or encapsulated with slowly
dissolving materials like cellulose, PEGs, olymethacrylates,
waxes etc.
Two methods of preparation are employed :
1. Seed or granule coating
2. Microencapsulation
22

Seed or Granule Coated Products :
Procedure:
 Non pareil seeds are coated with drug
 This followed with by a coat of slowly dissolving material such as
carbohydrate sugars & cellulose , PEG , polymeric material & wax.
 Coated granules can be placed in a capsule for administration.
E.g. amobarbital & dextroamphetamine sulfate
Microencapsulation :
• This method can be used to encase liquids , solids , or gases.
E.g. aspirin & potassium chloride
• Advantage of this method is that sustained drug release can be
achieved with taste abatement & better GI tolerability.
23

MICROENCAPSULATION PROCESSES
PROCESSES TYPES OF MATERIALS FOR
COATING
COASERVATION/ PHASE
SEPARATION
WATER –SOLUBLE POLYMER
INTERFACIAL
POLYMERIZATION
WATER-INSOLUBLE &WATER
SOLUBLE MONOMER
ELECTOSTATIC METHOD OPPOSITELY CHARGED
AEROSOLS
PRECIPITATION WATER OR SOLVENT-SOLUBLE
POLYMER
HOT MELT LOW MOLECULAR WEIGHT
LIPIDS
SALTING OUT WATER-SOLUBLE POLYMERS
SOLVENT EVAPORATION SOLVENT-SOLUBLE POLYMERS
24

2. Matrix (or Monolith)/ Embedded dissolution
controlled system.
 Since the drug is homogeneously dispersed throughout a rate
controlling medium matrix system are also called monoliths.
 The waxes used for such system are beeswax, carnauba wax,
hydrogenated castor oil etc.
 These waxes control the drug dissolution by controlling the rate
of dissolution fluid penetration into the matrix by altering the
porosity of tablet, decreasing its wettability or by itself dissolved
at a slower rate. 25

Matrix (or Monolith)/ Embedded dissolution
controlled system.
 The dispersion of drug wax is prepared by dispersing the drug in
the molten wax followed by congealing and granulating the
same.
 The process, compression parameters and size of particles
formed determine the release rate from this system. The drug
release is often first order from such matrices.
26

Matrix (or Monolith)/ Embedded dissolution
controlled system.
27

MARKETED FORMULATIONS
Dosage form Nature of chemical
entity
Release
mechanism
Company
Geomatrix Multilayered
tablets
- Dissolution Skye
pharmaceuticals,p
lc., (USA).
Reduced irritation
system
Capsules - Dissolution DepoMed, Inc.
Dimatrix
(Diffusion
consulted matrix
system)
Tablets - Dosage form Biovail
corporation
international,
IDDAS (Intestinal
Protective Drug
Absorption)
system
Tablets Hydrophillic
compounds
Diffusion Elan corporation
Multipor Tablets - Diffusion Ethical
Holding,plc.,
(UK).
PPDS (Pellatized
Pulsatile Delivery
Pellets (tablets) - Diffusion Andrx
pharmaceuticals.28

SMHS (Solubility
Modulating
Hydrogel System)
Tablets - Diffusion Andrx
pharmaceuticals
SPDS (Stablized
Pellets Delivery
System)
Pellets Unstable drugs Diffusion Andrx
pharmaceuticals
RingCap Matrix tablets - Diffusion Alker
MODAS (Multi
porous oral drug
absorption system)
Tablets Tablets Diffusion and
dissolution
Elan corporation,
(Ireland).
PRODAS
(Programmable
Oral Drug
Absorption
System)
Encapsulated
minitablets
Hydrophilic
molecules
Diffusion and
Dissolution
Elan corporation
SODAS
(Spheroidal Oral
Drug Absorption
System)
Beads (capsules
tablets)
Diffusion and
Dissolution
Elan corporation.
MARKETED FORMULATIONS
29

EROSION CONTROLLED DRUG DELIVERY
SYSTEM
 Erosion is defined as the disintegration of the polymer/ wax
matrix, as a result of degradation and is characterized by
material loss from the polymer generally in the physical state.
 Polymer or wax degradation or hydrolysis is brought by
enzyme, pH change or due to osmotic pressure or hydrodynamic
pressure that causes fragmentation.
 Erosion is effected by external stimuli, such systems can be
classified under stimuli activated drug delivery system. 30

SYSTEM
 It is classified on the type of stimuli:
1. Physical e.g. (osmotic pressure)
2. Chemical e.g.(pH)
3. Biological e.g. (enzyme)
 Examples of erodible matrices include hydrophobic
materials ethyl cellulose and waxes.
 Depending on the erosion mechanism, polymer or waxes
undergo either surface erosion or bulk erosion
31

SYSTEM
a) SURFACE EROSION:
 It occurs from the surface layers of the device only.
 It results in gradual decrease in the size of the device while
the bulk phase remain un-degraded.
 There is a difference in erosion rate between the surface
and centre of matrix, the process is also called as
heterogeneous erosion.
 Surface erosion occurs when water penetration is
restricted to device surface. 32

SYSTEM
b) BULK EROSION:
 it occurs throughout the polymer bulk and the process is
thus called as homogenous erosion.
 Bulk erosion occurs when the water is readily able to
penetrate the matrix of the device.
34

HYBRID SYSTEM IN DRUG DELIVERY
 They are also called as membrane cum matrix drug delivery
system.
 These systems are those where the drug in matrix of release-
retarding material is further coated with a release
controlling polymer membrane.
 It combines constant release kinetics of reservoir system
with mechanical robustness of matrix system. 35

SYSTEM
 Degradation by erosion normally takes place in devices that are
prepared from soluble polymers.
 In such instances, the device erodes as water is absorbed into the
systems causing the polymer chains to hydrate, swell, and ultimately
dissolved away from the dosage form.
 Degradation can also result from chemical changes to the polymer
including cleavage of covalent bonds, ionization and protonation
either along the polymer backbone or on pendent side chains.
36

MATHEMATICAL MODELS
 There are various mathematical models
1) Zero order kinetics
2) First order kinetics
3) Weibull model
4) Higuchi model
5) Hixson Crowell model
6) Korsmeyer Peppas model
7) Baker- Lonsdale model
8) Hopfenberg model
37

ZERO ORDER KINETICS
 This model is used for dosage forms that do not
disaggregate and release the drug slowly (assuming that
area does not change and no equilibrium conditions are
obtained).
 It can be represented by the following equation:
Wo - Wt = Kt
39

Wo - Wt = Kt
Where W is the initial amount of drug in the pharmaceutical
dosage form, W is the amount of drug in the pharmaceutical
dosage form at time t and K is a proportionality constant.
Dividing this equation by W0 and simplifying.
ft= kot
Where ft = 1-(Wt –W0) and f represents the fraction of drug
dissolved in time t and k0 the apparent dissolution rate
constant or zero order release constant. 40

FIRST ORDER KINETICS
 This model is applied for dissolution studies, and also
describe the absorption and elimination of some drugs.
ln Qt = ln Q0 + Kt
Qt = Drug amounts remaining to be released at time t
Q0 = Drug amounts remaining to be released at zero hr
Kt = First order release constant.
A graph of drug release versus time will be linear.
41

WEIBULL MODEL
 A general empirical equation adopted by Weibull was used
to describe the release process.
 Erodible matrix formulations follow this model.
M = 1- e[-(t-Ti)b/a
42

HIGUCHI MODEL
 Diffusion matrix formulations follow this model.
 This model is used to study the release of water soluble and
low soluble drugs incorporated in semisolid and / or solid
matrixes.
 It is denoted by the following equation
ft = KHt1/2
ft = fraction of drug released at time t
KH = Higuchi release rate constant
t = time 43

HIXSON – CROWELL MODEL
 Erodible matrix systems follow this model.
 When this model is used, it is assumed that release rate is
limited by the drug particles dissolution rate, and not by the
diffusion that may occur through polymeric matrix.
 It is represented by the following equation
Wo1/3 – Wt1/3= Kst
44

HIXSON – CROWELL MODEL
Wo1/3 – Wt1/3= Kst
Where,
Wo = initial amount of drug present in the matrix.
Wt = amount of drug released in time t.
Ks = release rate constant.
45

KORSMEYER- PEPPA’S MODEL
 Swellable polymer devices follow this model.
 This model is generally used to analyze the release of
pharmaceutical polymeric dosage forms, when the release
mechanism is not well known or when more than one type
of release phenomena could be involved.
 It is denoted by the following equation.
Mt/M∞ = Ktn
46

KORSMEYER- PEPPA’S MODEL
Mt/M∞ = Ktn
Where,
Mt = amount released at time t
M∞= amount released at infinite time
K = release rate constant
n = release exponents
47

BAKER- LANSDALE MODEL
 This model is suitable for microcapsules or microspheres.
 It describes the drug controlled release from a spherical
matrix.
ft = 3/2[1-(1-Mt/M∞)2/3] – Mt/M∞= Kt
Where,
Ft = fraction of drug released at time t
M∞ = amount released at infinite time
48

HOPFENBERG MODEL
 This model was used for the release of drugs from surface-
eroding devices with several geometries.
 This equation describes drug release from slabs, spheres and
infinite cylinders displaying heterogeneous erosion.
 It is given by the following the equation.
Mt/M∞ 1 – [1-k1t(t-l)]n
49

HOPFENBERG MODEL
M∞ = amount released at infinite time
K = rate constant
Mt/M∞ 1 – [1-k1t(t-l)]n
50

OPTIMIZATION TECHNIQUES IN
PHARMACEUTICAL FORMULATION
AND PROCESSING
51

CONTENTS
 CONCEPT OF OPTIMIZATION
 OPTIMIZATION PARAMETERS
 CLASSICAL OPTIMIZATION
 STATISTICAL DESIGN
 DESIGN OF EXPERIMENT
 OPTIMIZATION METHODS
52

INTRODUCTION
 The term Optimize is defined as “to make perfect”.
 It is used in pharmacy relative to formulation and processing
 Involved in formulating drug products in various forms
 It is the process of finding the best way of using the existing
resources while taking in to the account of all the factors that
influences decisions in any experiment
53

 In development projects , one generally experiments by a
series of logical steps, carefully controlling the variables &
changing one at a time, until a satisfactory system is
obtained
 It is not a screening technique.
 Optimization tech provide both depth of understanding &
ability to explore & defend range for formulation &
processing factors.
INTRODUCTION
54

OPTIMIZATION PARAMETERS
optimization parameters
Problem types variable
Constrained unconstrained dependent independent
55

VARIABLES
Independent Dependent
Formulating processing
Variables Variables
56

 Independent variables or primary variables :
Formulations and process variables are directly
under control of the formulator. These includes
ingredients
 Dependent or secondary variables :
These are the responses of the in progress material
or the resulting drug delivery system. It is the result of
independent variables
VARIABLES
57

 Relationship between independent variables and response
defines response surface.
 Representing >2 becomes graphically impossible
 Higher the variables , higher are the complications hence it
is to optimize each & everyone.
VARIABLES
58

 Response surface representing the relationship between the
independent variables X1 and X2 and the dependent variable
Y.
VARIABLES
59

CLASSIC OPTIMIZATION
 It involves application of calculus to basic problem for
maximum/minimum function.
 Applications:
i. Problems that are not too complex
ii. They do not involve more than two variables
 For more than two variables graphical representation is
impossible.
 It is possible mathematically.
60

GRAPH REPRESENTING THE RELATION
BETWEEN THE RESPONSE VARIABLE AND
INDEPENDENT VARIABLE
61

 Using calculus the graph obtained can be solved.
Y = f (x)
 When the relation for the response y is given as the function of two
independent variables,X1 &X2
Y = f(X1 , X2)
The above function is represented by contour plots on which the axes
represents the independent variables X1& X2
CLASSIC OPTIMIZATION
62

STATISTICAL DESIGN
 These Techniques are divided in to two types.
 Experimentation continues as optimization proceeds
 It is represented by evolutionary operations(EVOP) and
simplex methods.
 Experimentation is completed before optimization takes
place.
 It is represented by classic mathematical & search
methods.
63

 There are two possible approaches
 Theoretical approach- If theoretical equation is known , no
experimentation is necessary.
 Empirical or experimental approach – With single
independent variable formulator experiments at several
levels.
STATISTICAL DESIGN
64

 The relationship with single independent variable can be obtained by
simple regression analysis or by least squares method.
 The relationship with more than one important variable can be
obtained by statistical design of experiment and multi linear
regression analysis.
 Most widely used experimental plan is factorial design.
STATISTICAL DESIGN
65

TERMS USED
 FACTOR: It is an assigned variable such as concentration ,
Temperature etc..,
 Quantitative: Numerical factor assigned to it
Ex; Concentration- 1%, 2%,3% etc..
 Qualitative: Which are not numerical
Ex; Polymer grade, humidity condition etc
 LEVELS: Levels of a factor are the values or designations
assigned to the factor
FACTOR LEVELS
Temperature 300 , 500
Concentration 1%, 2%
66

 RESPONSE: It is an outcome of the experiment.
 It is the effect to evaluate.
 Ex: Disintegration time etc..,
 EFFECT: It is the change in response caused by varying the levels
 It gives the relationship between various factors & levels
 INTERACTION: It gives the overall effect of two or more variables
Ex: Combined effect of lubricant and glidant on hardness of the tablet
TERMS USED
67

 Optimization by means of an experimental design may be helpful in
shortening the experimenting time.
 The design of experiments is a structured , organized method used to
determine the relationship between the factors affecting a process and
the output of that process.
 Statistical DOE refers to the process of planning the experiment in
such a way that appropriate data can be collected and analyzed
statistically.
TERMS USED
68

TYPES OF EXPERIMENTAL DESIGN
 Completely randomized designs
 Randomized block designs
 Factorial designs
 Full
 Fractional
 Response surface designs
 Central composite designs
 Box-Behnken designs
 Adding centre points
 Three level full factorial designs
69

 Completely randomised Designs
 These experiments compares the values of a response variable based
on different levels of that primary factor.
 For example ,if there are 3 levels of the primary factor with each level
to be run 2 times then there are 6 factorial possible run sequences.
 Randomised block designs
 For this there is one factor or variable that is of primary interest.
 To control non-significant factor, an important technique called
blocking can be used to reduce or eliminate the contribution of these
factors to experimental error.
TYPES OF EXPERIMENTAL DESIGN
70

 Full: used for small set of factors
 Fractional: used to examine multiple factors efficiently with fewer
runs than corresponding full factorial design
 Types of fractional factorial designs
 Homogenous fractional
 Mixed level fractional
 Box-Hunter
 Plackett-Burman
 Taguchi
 Latin square
FACTORIAL DESIGN
71

 Homogenous fractional
 Useful when large number of factors must be screened.
 Mixed level fractional
 Useful when variety of factors need to be evaluated for main
effects and higher level interactions can be assumed to be
negligible.
 Box-hunter
 Fractional designs with factors of more than two levels can be
specified as homogenous fractional or mixed level fractional.
FACTORIAL DESIGN
72

PLACKETT-BURMAN
 It is a popular class of screening design.
 These designs are very efficient screening designs when only the
main effects are of interest.
 These are useful for detecting large main effects economically
,assuming all interactions are negligible when compared with
important main effects.
 Used to investigate n-1 variables in n experiments proposing
experimental designs for more than seven factors and especially
for n*4 experiments.
73

 TAGUCHI:
 It allows estimation of main effects while minimizing variance.
 LATIN SQUARE:
 They are special case of fractional factorial design where there is
one treatment factor of interest and two or more blocking
factors.
FACTORIAL DESIGN
74

RESPONSE SURFACE DESIGNS
 This model has quadratic form
 Designs for fitting these types of models are known as response
surface designs.
 If defects and yield are the outputs and the goal is to minimize
defects and maximize yield
γ =β0 + β1X1 + β2X2 +….β11X1
2 + β22X2
2
75

 Two most common designs generally used in this response surface
modeling are :
 Central composite designs
 Box-Behnken designs
 Box-Wilson central composite Design
 This type contains an embedded factorial or fractional factorial design
with centre points that is augmented with the group of ‘star points’.
 These always contains twice as many star points as there are factors in
the design.
76

 The star points represent new extreme value (low & high) for each factor in
the design.
 To picture central composite design, it must imagined that there are several
factors that can vary between low and high values.
 Central composite designs are of three types
 Circumscribed designs-Cube points at the corners of the unit cube ,star
points along the axes at or outside the cube and centre point at origin
 Inscribed designs-Star points take the value of +1 & -1 and cube points lie
in the interior of the cube
 Faced –star points on the faces of the cube.
77

BOX-BEHNKEN DESIGN
 They do not contain embedded factorial or fractional
factorial design.
 Box-Behnken designs use just three levels of each factor.
 These designs for three factors with circled point appearing
at the origin and possibly repeated for several runs.
78

Three-level full factorial designs
 It is written as 3k factorial design.
 It means that k factors are considered each at 3 levels.
 These are usually referred to as low, intermediate & high
values.
 These values are usually expressed as 0, 1 & 2
 The third level for a continuous factor facilitates
investigation of a quadratic relationship between the
response and each of the factors.
79

FACTORIAL DESIGN
 These are the designs of choice for simultaneous determination
of the effects of several factors & their interactions.
 They are used in experiments where the effects of different
factors or conditions on experimental results are to be elucidated.
 Two types
 Full factorial- Used for small set of factors
 Fractional factorial- for optimizing more number of factors
80

LEVELS OF FACTORS IN THIS FACTORIAL DESIGN
FACTOR
LOWLEVEL(mg)
HIGH LEVEL(mg)
A:stearate 0.5 1.5
B:Drug 60.0 120.0
C:starch 30.0 50.0
81

EXAMPLE OF FULL FACTORIAL
EXPERIMENT
Factor
combination
stearate drug starch Response
Thickness
Cm*103
(1) _ _ _ 475
a + _ _ 487
b _ + _ 421
ab + + _ 426
c _ _ + 525
ac + _ + 546
bc _ + + 472
abc + + + 522
82

 Calculation of main effect of A (stearate)
 The main effect for factor A is
 {-(1)+a-b+ab-c+ac-bc+abc] 10-3
 Main effect of A =
=
= 0.022 cm
4
a + ab + ac + abc
4
_ (1) + b + c + bc
4
[487 + 426 + 456 + 522 – (475 + 421 + 525 + 472)] 10-3
EXAMPLE OF FULL FACTORIAL
EXPERIMENT
83

GENERAL OPTIMIZATION
 By the relationships are generated from experimental data ,
resulting equations are on the basis of optimization.
 These equation defines response surface for the system
under investigation.
 After collection of all the runs and calculated responses
,calculation of regression coefficient is initiated.
 Analysis of variance (ANOVA) presents the sum of the
squares used to estimate the factor main effects.
84

FLOW CHART FOR OPTIMIZATION
85

APPLIED OPTIMIZATION METHODS
 Evolutionary operations
 Simplex method
 Lagrangian method
 Search method
 Canonical analysis
86

EVOLUTIONARY OPERATIONS (EVOP)
 It is a method of experimental optimization.
 Technique is well suited to production situations.
 Small changes in the formulation or process are
made (i.e. repeats the experiment so many times)
& statistically analyzed whether it is improved.
 It continues until no further changes takes place
i.e., it has reached optimum-the peak
87

 Applied mostly to TABLETS.
 Production procedure is optimized by careful
planning and constant repetition
 It is impractical and expensive to use.
 It is not a substitute for good laboratory scale
investigation
EVOLUTIONARY OPERATIONS (EVOP)
88

SIMPLEX METHOD
 It is an experimental method applied for
pharmaceutical systems.
 Technique has wider appeal in analytical method other
than formulation and processing.
 Simplex is a geometric figure that has one more point
than the no. of factors.
 It is represented by triangle.
 It is determined by comparing the magnitude of the
responses after each successive calculation
89

GRAPH REPRESENTING THE SIMPLEX MOVEMENTS TO THE
OPTIMUM CONDITIONS
90

 The two independent variables show pump speeds for the two
reagents required in the analysis reaction.
 Initial simplex is represented by lowest triangle.
 The vertices represents spectrophotometric response.
 The strategy is to move towards a better response by moving
away from worst response.
 Applied to optimize CAPSULES, DIRECT COMPRESSION
TABLET (acetaminophen), liquid systems (physical stability)
SIMPLEX METHOD
91

LAGRANGIAN METHOD
 It represents mathematical techniques.
 It is an extension of classic method.
 It is applied to a pharmaceutical formulation and processing.
 This technique follows the second type of statistical design.
 Limited to 2 variables - disadvantage
92

STEPS INVOLVED
 Determine objective formulation
 Determine constraints.
 Change inequality constraints to equality constraints.
 Form the Lagrange function F
 Partially differentiate the lagrange function for each variable
& set derivatives equal to zero.
 Solve the set of simultaneous equations.
 Substitute the resulting values in objective functions 93

 Optimization of a tablet.
 phenyl propranolol (active ingredient)- kept constant
 X1 – disintegrate (corn starch)
 X2 – lubricant (stearic acid)
 X1 & X2 are independent variables.
 Dependent variables include tablet hardness, friability
,volume, in-vitro release rate etc.,
STEPS INVOLVED (EXAMPLE)
94

 Polynomial models relating the response variables to independents
were generated by a backward stepwise regression analysis program.
 Y= B0+B1X1+B2X2+B3 X1
2
+B4 X2
2
+B+5 X1 X2 +B6 X1X2
+ B7X1
2
+B8X1
2
X2
2
Y – response
Bi – regression coefficient for various terms containing the levels of
the independent variables.
X – independent variables
STEPS INVOLVED (EXAMPLE)
95

TABLET FORMULATIONS
Formulation
no,.
Drug Dicalcium
phosphate
Starch Stearic acid
1 50 326 4(1%) 20(5%)
2 50 246 84(21%) 20
3 50 166 164(41%) 20
4 50 246 4 100(25%)
5 50 166 84 100
6 50 86 164 100
7 50 166 4 180(45%)
96

 Constrained optimization problem is to locate the levels of stearic
acid (x1) and starch (x2).
 This minimize the time of in-vitro release(y2),average tablet
volume(y4), average friability (y3)
 To apply the lagrangian method, problem must be expressed
mathematically as follows
Y2 = f2(X1,X2) - in vitro release
Y3 = f3(X1,X2) < 2.72-Friability
Y4 = f4(x1,x2) < 0.422-avg tab.vol
LAGRANGIAN METHOD
97

CONTOUR PLOT FOR TABLET HARDNESS
98

CONTOUR PLOT FOR TABLET
DISSOLUTION(T50%)
99

GRAPH OBTAINED BY SUPER IMPOSITION OF
TABLET HARDNESS & DISSOLUTION
100

CONTOUR PLOT FOR TABLET FRIABILITY
101

SEARCH METHOD
 It is defined by appropriate equations.
 It do not require continuity or differentiability of function.
 It is applied to pharmaceutical system
 For optimization 2 major steps are used
 Feasibility search - used to locate set of response constraints
that are just at the limit of possibility.
 Grid search – experimental range is divided in to grid of
specific size & methodically searched
102

STEPS INVOLVED IN SEARCH METHOD
 Select a system
 Select variables
 Perform experiments and test product
 Submit data for statistical and regression analysis
 Set specifications for feasibility program
 Select constraints for grid search
 Evaluate grid search printout
103

EXAMPLE
Tablet formulation
Independent variables Dependent variables
X1 Diluent ratio Y1 Disintegration time
X2 compressional force Y2 Hardness
X3 Disintegrant level Y3 Dissolution
X4 Binder level Y4 Friability
X5 Lubricant level Y5 weight uniformity
104

 Five independent variables dictates total of 32
experiments.
 This design is known as five-factor,orthagonal,central
,composite , second order design.
 First 16 formulations represent a half-factorial design for
five factors at two levels .
 The two levels represented by +1 & -1, analogous to high
& low values in any two level factorial.
SEARCH METHOD
105

TRANSLATION OF STATISTICAL DESIGN IN TO PHYSICAL UNITS
Experimental conditions
Factor -1.54eu -1 eu Base0 +1 eu +1.54eu
X1=
ca.phos/lactose
24.5/55.5 30/50 40/40 50/30 55.5/24.5
X2= compression
pressure( 0.5 ton)
0.25 0.5 1 1.5 1.75
X3 = corn starch
disintegrant
2.5 3 4 5 5.5
X4 = Granulating
gelatin(0.5mg)
0.2 0.5 1 1.5 1.8
X5 = mg.stearate
(0.5mg)
0.2 0.5 1 1.5 1.8
106

 Again formulations were prepared and are measured.
 Then the data is subjected to statistical analysis followed by
multiple regression analysis.
 The equation used in this design is second order
polynomial.
 y = a0+a1x1+…+a5x5+a11x1
2
+…+a55x2
5+a12x1x2
+a13x1x3+a45 x4x5
SEARCH METHOD
107

 A multivariant statistical technique called principle
component analysis (PCA) is used to select the best
formulation.
 PCA utilizes variance-covariance matrix for the
responses involved to determine their interrelationship.
SEARCH METHOD
108

PLOT FOR A SINGLE VARIABLE
109

ADVANTAGES OF SEARCH METHOD
 It takes five independent variables in to account.
 Persons unfamiliar with mathematics of optimization &
with no previous computer experience could carryout an
optimization study.
112

CANONICALANALYSIS
 It is a technique used to reduce a second order
regression equation.
 This allows immediate interpretation of the
regression equation by including the linear and
interaction terms in constant term.
113

 It is used to reduce second order regression equation to an
equation consisting of a constant and squared terms as
follows.
 It was described as an efficient method to explore an
empherical response.
Y = Y0 +λ1W1
2 + λ2W2
2 +..
CANONICALANALYSIS
114

Thank you
E-mail: bknanjwade@yahoo.co.in
Cell No:00919742431000
115

Fundamentals of modified release formulations

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