Presented by;

Aakash N S

M Pharm I Year

Department of Pharmaceutics

College of Pharmacy,

Madras Medical College.

MYPHARMAGUIDE.COM 1

Consolidation :

An increase in the mechanical strength of the material resulting

from particle to particle interactions.

Compaction = Compression + Consolidation

KINETIC MODELS STUDY:

1.MODEL DEPENDENT METHOD

▪ Zero order

▪ First order

▪ Hixson- Crowell law

▪ Korsemeyer – Peppas model

2. MODEL INDEPENDENT METHOD

(Pair wise procedure)

▪ f1 and f2 comparisons

MYPHARMAGUIDE.COM 2

DIFFUSION

Diffusion is a process of migration of solute molecules from a

region of high concentration to a region of low concentration

and is brought about by random molecular motion.

The passage of solute molecules through a barrier may occur by

▪ Simple molecular diffusion (permeation) or

▪ By movement through pores and channels

MYPHARMAGUIDE.COM 3

FICK’s FIRST LAW OF DIFFUSION:

Fick’s first law states that the quantity of solute dq diffusing

through a unit cross section “S” of a barrier in time dt (unit time)

is termed as flux ,J and is represented as

J = dq/S.dt … 1

Flux is the rate of transfer of solute molecules per unit area of

surface. The flux in turn is proportional to the concentration

gradient dc/dx in the barrier area

J= -D (dc/dx) … 2

c= concentration

x= distance of movement perpendicular to the surface of the barrier

D= diffusion coefficient

MYPHARMAGUIDE.COM 4

Combining both equations,

dq= -D.S(dc/dx).dt

The negative sign indicates that diffusion takes place in the

direction of decreasing concentration.

D is also affected by temperature, pressure, solvent properties

and chemical nature of diffusing solute.

FICK’s SECOND LAW OF DIFFUSION:

The second law is derived from first law by disregarding the

dependent variable dq and it emphasizes the rate of change of

concentration at a definite location.

dc/dt= D. d2c/dx2

MYPHARMAGUIDE.COM 5

Fick’s second law states that the change in concentration with

time at a particular region is proportional to the change in the

concentration gradient at that location in the system.

TIME LAG:

This is the time required for a diffusant to establish a uniform

concentration gradient within the membrane that separates the

donor and receptor compartments, represented by tl

This is given by equation,

tl = h2/6D

h= membrane thickness

D= diffusion coefficient

tl= time lag

MYPHARMAGUIDE.COM 6

Steady State

› . Consider the diffusant originally dissolved in a solvent in the left-hand

compartment of the chamber shown in Figure.

› Solvent alone is placed on the right-hand side of the barrier, and the solute

or penetrant diffuses through the central barrier from solution to solvent side

(donor to receptor compartment).

› In diffusion experiments, the solution in the receptor compartment is

constantly removed and replaced with fresh solvent to keep the

concentration at a low level. This is referred to as ―sink conditions,‖ the left

compartment being the source and the right compartment the sink.

MYPHARMAGUIDE.COM 7

MYPHARMAGUIDE.COM 8

› Originally, the diffusant concentration will fall in the left compartment and

rise in the right compartment until the system comes to equilibrium, based

on the rate of removal of diffusant from the sink and the nature of the

barrier.

› When the system has been in existence a sufficient time, the concentration

of diffusant in the solutions at the left and right of the barrier becomes

constant with respect to time but obviously not the same in the two

compartments.

› Then, within each diffusional slice perpendicular to the direction of flow, the

rate of change of concentration, dC/dt, will be zero, and by Fick’s second

law.

MYPHARMAGUIDE.COM 9

PERMEABILITY COEFFICIENT:

This shows the rate of permeation of drug molecules/ solute

across the semi-permeable membrane

BURST EFFECT:

› In many of the controlled release formulations, immediately

upon placement in the release medium, an initial large bolus of

drug is released before the release rate reaches a stable profile.

› This phenomenon is known as “burst effect”.

› Initial state of drug release into receptor side is at a higher rate

than the steady-state release rate

MYPHARMAGUIDE.COM 10

FACTORS AFFECTING DIFFUSION

▪ Size

▪ Shape

▪ Concentration

▪ Temperature

▪ Charge

▪ Lipid solubility

SIZE:

Small molecules can slip by the polar heads of the

phospholipids and through the membrane to the other side.

Very large molecules like proteins cannot diffuse across the

membrane at all.

MYPHARMAGUIDE.COM 11

SHAPE:

– Glucose is able to get into cells much faster than other sugars.

– Made by facilitated diffusion.

– A carrier protein specific for glucose combines with it on the outer

surface, closes around it and then opens to the inside of the cell where the

glucose is released.

– The carrier then returns to its original shape and is ready to transport

another glucose molecule.

CONCENTRATION:

– The greater the concentration gradient between the outside and inside of

the membrane the greater the rate of diffusion.

– If the concentration of oxygen outside the cell increases then it will

diffuse more quickly into the cell

MYPHARMAGUIDE.COM 12

TEMPERATURE:

– Increase in temperature causes all molecule to move faster.

– Diffusion is a passive movement of molecules, so quicker molecule

movement translates into quicker diffusion.

CHARGE:

– Ions or molecules with a charge cannot pass through the lipid bi-layer by

diffusion.

– Other mechanisms involving protein carriers and ATP energy are

required.

Ex: Na+-K+ ATPase Pump.

LIPID SOLUBILITY:

– Lipid soluble molecules can move through the lipid bi-layer.

– These molecules are other lipids.

Ex: Steroid hormones like Testosterone, Oestrogen.

MYPHARMAGUIDE.COM 13

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.

Dissolution is the rate determining step for hydrophobic, poorly

aqueous soluble drugs

E.g. Griseofulvin, Spironolactone

MYPHARMAGUIDE.COM 14

The rate of dissolution is given by Noyes and Whitney:

dC / dt = k(Cs – Cb)

This equation was based on Fick’s Second Law of diffusion

Where,

dC/dt = Dissolution rate of the drug

k = Dissolution rate constant

Cs = Concentration of drug in stagnant layer

Cb = Concentration of drug in the bulk of the solution at time t

MYPHARMAGUIDE.COM 15

MYPHARMAGUIDE.COM 16

MYPHARMAGUIDE.COM 17

FACTORS AFFECTING DISSOLUTION

› Effect of agitation

› Effect of dissolution fluid

› Influence of pH of dissolution fluid

› Effect of surface tension of the dissolution medium

› Effect of viscosity of the dissolution medium

› Effect of the presence of unreactive and reactive additives in the

dissolution medium

› Volume of dissolution medium and sink conditions

› De-aeration of the dissolution medium

› Effect of temperature of the dissolution medium

MYPHARMAGUIDE.COM 18

▪ EFFECT OF AGITATION:

– The relationship between the intensity of agitation and the rate of

dissolution varies considerably to the type of agitation used, degree of

laminar and turbulent flow in the system, shape and design of the stirrer

and the physicochemical properties of the solid.

– For the basket method(100rpm) is utilized while for the paddle method

(50-75rpm) is recommended.

▪ EFFECT OF DISSOLUTION FLUID:

– Selection of proper medium for dissolution testing depends largely on the

physicochemical properties of the drug.

MYPHARMAGUIDE.COM 19

▪ INFLUENCE OF pH OF DISSOLUTION FLUID:

– Change in pH exert greatest effect in drug solubility.

– For weak acids dissolution rate increases with increase in pH

– For weak bases dissolution rate increases with decrease in pH

– Tablets containing active ingredients, whose solubility are independent of

pH, dissolution rate does not vary significantly with change of pH of

dissolution medium unless they contain certain excipients that are

influenced by pH

– Tablets that are formulated with CO2 producing compounds (NaHCO3,

CaCO3) tend to have slightly faster dissolution rate in acid medium than

in water.

MYPHARMAGUIDE.COM 20

▪ EFFECT OF SURFACE TENSION OF THE

DISSOLUTION MEDIUM:

➢ According to the diffusion film theory, dissolution of the drug is

governed by the interplay between

I. Release of the drug from solid surface and

II. Its transfer throughout the bulk of the dissolution medium

➢ If the drug is hydrophobic the dissolution rate is influenced primarily

by the process of release, 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.

MYPHARMAGUIDE.COM 21

➢ Addition of surfactant below CMC can increase significantly the

dissolution rate because of better penetration of the solvent into the tablet

resulting in greater availability of the drug surface.

▪ EFFECT OF VISCOSITY OF THE DISSOLUTION

MEDIUM:

If the interaction at the interfaces occurs much faster than the rate of

transport, such as in case of diffusion controlled dissolution processes, it

would be expected that the dissolution rate decreases with an increase in

viscosity.

MYPHARMAGUIDE.COM 22

▪ EFFECT OF PRESENCE OF UNREACTIVE AND REACTIVE

ADDITIVES IN THE DISSOLUTION MEDIUM:

– EXAMPLE: When neutral ionic compounds like sodium chloride and

sodium sulphate or non-ionic organic compounds like dextrose if added

to the dissolution medium, the dissolution of benzoic acid was linearly

dependent upon its solubility in particular solvent.

– When certain buffers or bases were added to the aqueous solvent, an

increase in the dissolution rate was observed.

MYPHARMAGUIDE.COM 23

▪ DEAERATION OF THE DISSOLUTION MEDIUM:

➢ Presence of dissolved air or other gases in the dissolution medium may

influence the dissolution rate of certain formulations and lead to variable

and unreliable results.

➢ Example: The dissolved air in distilled water could lower its pH

➢ The air bubbles that circulate can affect the hydrodynamic flow pattern

generated by the stirring mechanism.

➢ The air bubbles on solid surface of tablet can lead to reduction in the

specific gravity and thus there is a minimum chance of being wetted

efficiently.

MYPHARMAGUIDE.COM 24

▪ EFFECT OF TEMPERATURE OF THE DISSOLUTION MEDIUM:

➢ Drug solubility is temperature dependent.

➢ Generally the temperature of 37±0.5ºC is maintained during dissolution

determination of oral dosage forms and suppositories.

➢ For topical preparations as low as 30ºC and 25ºC have been used.

MYPHARMAGUIDE.COM 25

PHARMACOKINETICS

❖Pharmacokinetics is the study of the kinetics of drug absorption,

distribution, metabolism and elimination and their relationship

with the pharmacological, therapeutic or toxicological response

in man and animals.

❖Pharmacokinetics describe what the body does to the drug, as

opposed to pharmacodynamics which describe what the drug

does to the body.

MYPHARMAGUIDE.COM 26

PARAMETERS THAT WILL BE ESTIMATED :

1.Absorption

➢Bioavailability (Cmax, tmax, AUC)

➢Absorption rate constant (Ka)

➢Salt factor

2.Distribution

➢Volume of distribution ( Vd)

➢Distribution equilibrium

➢Distribution rate constant

3.Elimination

➢Clearance

➢Half-life

➢1st order, 0 order and mixed order kinetics

➢Elimination rate constant (Kel), Ku, Km MYPHARMAGUIDE.COM 27

Bioavailability :

› Bioavailability is the fraction of administered drug that reaches the systemic

circulation.

› Bioavailability is expressed as the fraction of administered drug that gains

access to the systemic circulation in a chemically unchanged form.

› For example, if 100 mg of a drug are administered orally and 70 mg of this

drug are absorbed unchanged, the bioavailability is 0.7 or 70 percent.

MYPHARMAGUIDE.COM 28

MYPHARMAGUIDE.COM 29

Absorption rate (Ka)

➢The rate of drug absorption can be zero order, first order, pseudo zero order, pseudo first

order, etc.

➢ Generally for I.R dosage form Ka is first order because of physical nature of drug

diffusion.

➢ For I.V. infusion and certain controlled-release drug products, Ka will be zero-order rate

constant.

➢Ka determined by:

1. Method of residuals

2. Flip-Flop method of Ka and KE

3. Wagner – Nelson Method

4. Loo – Riegelman method

MYPHARMAGUIDE.COM 30

Salt factor (S)

➢Drug is administered as a salt

➢Proportion of the parent drug contained in the salt (weight/weight basis)

➢Dose of salt = Dose of drug req. (D) / Salt factor (S)

➢Aminophylline → Theophylline + ethylenediamine salt

➢D=400 mg; S=0.8 ( 1 gm of aminophylline is equivalent to 800 mg of

theophylline)

➢Aminophylline reqd. → 500 mg

MYPHARMAGUIDE.COM 31

Volume of Distribution (Vd) :

➢ It is defined as the volume in which the amount of drug would need to be uniformly

distributed to produce the observed blood concentration.

EQUATION:

➢The units for Volume of Distribution are typically reported in (ml or liter)/kg body weight.

➢The volume of distribution is given by the following equation:

➢ If 100 mg of drug X is administered intravenously and the plasma concentration is

determined to be 5 mg/L just after the dose is given, calculate volume of distribution-

20L

MYPHARMAGUIDE.COM 32

› The volume of distribution(vd), also known as apparent volume of

distribution, is used to quantify the distribution of a medication between

plasma and the rest of the body after oral or parenteral dosing.

➢How the drug binds in the blood or serum compared to the binding in

tissues is also an important determinate of the Vd for a drug.

➢Reflects the extent to which it is present in extra vascular tissues and

not in the plasma.

➢For example, Warfarin has such a small volume of distribution is that it is

highly bound to serum albumin so that the free fraction of drug in the blood

(fB) is very small.

MYPHARMAGUIDE.COM 33

Distribution equilibrium

➢Rate of transfer of drug from blood to various organs & tissues = Rate of transfer of

drug from various tissues & organs back into the blood

➢Rapid distribution → Rate of transfer of drug from blood to all organs & tissues &

vice-versa have become equal instantaneously following administration (intra/extra

vascular) of the dose of a drug.

Distribution rate constant (kT)

➢Measure of how rapidly drug would leave tissue if the arterial concentration were to

drop to zero.

➢Fractional rate of drug distribution from an organ to blood

MYPHARMAGUIDE.COM 34

Clearance :

➢The definition of clearance is the volume of serum or blood completely

cleared of the drug per unit time.

➢ it determines the maintenance dose

➢Extraction Ratio (ER) : The ability of an organ to remove or extract the

drug from the blood or serum

ER = (Cin − Cout)/Cin

MYPHARMAGUIDE.COM 35

MYPHARMAGUIDE.COM 36

➢Overall drug elimination from the body (Ku + Km)

➢Ku – Excretion rate constant

➢Km – Metabolic rate constant

➢If drug completely metabolized Kel = Km

➢ If drug removed in unchanged form Kel = Ku

› FOR, Zero order rate of elimination is constant irrespective of plasma

concentration:

› Er = KE.

MYPHARMAGUIDE.COM 37

HALF-LIFE :

› The biological half-life or elimination half life of a substance is the

time it takes for a substance (drug, radioactive nuclide, or other) to

lose half of its pharmacologic, physiologic, or radiologic activity.

EQUATION:

t1/2 = 0.693/Ke

Where Ke = Elimination rate constant

This equation holds true for first order kinetics.

➢ t1/2 = 0.693*Vd/ CLT

MYPHARMAGUIDE.COM 38

Peak Plasma concentration (Cmax)

➢The point of maximum concentration of drug in plasma is called as the 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.

➢The peak level depends uponƒdose administered, ƒrate of absorption and ƒrate

of elimination.

➢The peak represents the point of time when absorption rate equals

elimination rate of drug.

MYPHARMAGUIDE.COM 39

➢The portion of curve to the left of peak represents absorption phase i.e

.when the rate of absorption is greater than the rate of elimination.

➢The section of curve to the right of peak generally represents elimination

phase i.e. when the rate of elimination exceeds rate of absorption .

➢Peak concentration is often related to the intensity of pharmacological

response and should ideally be above minimum effective

concentration(MEC) but less than the maximum safe concentration(MSC).

MYPHARMAGUIDE.COM 40

MYPHARMAGUIDE.COM 41

Time of Peak Concentration (tmax)

➢The time for drug to reach peak concentration in plasma(after extra

vascular administration) is called as the time of peak concentration.

➢It is expressed in hours and is useful in estimating the rate of absorption.

➢Onset time and onset of action are dependent upon tmax.

➢The parameter is of particular importance in assessing the efficacy of drug

used to treat acute conditions like pain and insomnia which can be treated

by a single dose.

MYPHARMAGUIDE.COM 42

MYPHARMAGUIDE.COM 43

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 * hours.

➢ It is the most important parameter in evaluating the

bioavailability of a drug from its dosage form as it represents the extent of absorption.

➢ AUC is also important for drugs that are administered repetitively for

the treatment of chronic conditions like asthma or epilepsy.

MYPHARMAGUIDE.COM 44

Methods to measure AUC

1. Planimeter → An instrument for mechanically measuring the area of plane figures

2. “Cut and weigh” method

3. Trapezoidal rule

– Linear method

– Logarithmic method

4. Integration method

5. Tai’s formula

MYPHARMAGUIDE.COM 45

HECKEL PLOT

HECKEL analysis is the most popular method of deforming reduction

under compression pressure.

Powder packing with increasing compression load is normally

attributed to particles rearrangement, elastic and plastic deformation and

particle fragmentation.

It is analogous to 1st order reaction, where the pores in the mass are the

reactant i.e.,

Log 1/E = Ky (P)+ Kr

Ky = Material dependent constant

Kr = Initial repacking stage

Ky α 1/S

S = Yield strength

MYPHARMAGUIDE.COM 46

› HECKEL proposed equation to study the effect of applied pressure on

density or relative density.

› It states that, powder compression follow first order kinetics.

› Inter-particular pores= Reactant

› Densification of powder bed= Product

› Rate dependent on concentration of one product

› When more is the reactant more is the product densification

ln (1/1-D) = kP + A

D=Relative density

P=Pressure applied

A=Die filling and particle rearrangement before deformation

k=Measure of plasticity

MYPHARMAGUIDE.COM 47

Relative density= Density of powder

True density of material

D=1 {when no pores left after compression}

D=0.3 or 0.1 {30% or 10% of volume of tablet consists of

Pores [porosity]}

Porosity(E) = 1-D

MYPHARMAGUIDE.COM 48

APPLICATIONS:

› Information of k helps in selection of binder in tablet formation

› Crushing strength of tablet can be correlated with the value of k

› Larger k value indicate the harder tablets. This Knowledge used to select

binder during designing of tablet.

TYPES OF MATERIALS ON THE BASIS OF HECKEL PLOT

1. Type A

2. Type B

3. Type C

MYPHARMAGUIDE.COM 49

MYPHARMAGUIDE.COM 50

CASE STUDY : FOMULATION DEVELOPMENT OF PARACETAMOL

TABLET USING NATURAL PLANT BASED EXCIPIENT AS

BINDER

› Compressibility of granules was evaluated by HECKEL equation

› The tablets were formulated under different pressures applied to constant

density was 20-100kg/cm2

› The tablets were stored in airtight container for 24 hours to enable elastic

recovery and hardening

› Studied by HECKEL equation

› From intercept A, relative density DA can be calculated by following

equation

DA = 1-e-A

MYPHARMAGUIDE.COM 51

› Relative density DB is calculated by equation,

DB = DA – D0

› The values of D0 , which represents the degree of initial packing in

the die as a result of die filling.

› Formulations containing PVP K-30 and acacia showed higher value

than the formulation containing mango gum.

› The DB value represents the phase of particles rearrangement in the

early stages of compression.

› DB values tend to indicate the extent of fragmentation of granules/

particles, although fragmentation can occur concurrently with plastic

and elastic deformation of constituent particles.

› DB values decreased with increase in binder concentration and thus the

acacia and PVP K-30 showed higher value than mango gum

MYPHARMAGUIDE.COM 52

The values of DA , which represent total degree of packing achieved at

zero and low pressure also decreased with an increase in the binder

concentration.

Formulations containing mango gum showed lower value.

From the above studies it showed that mango gum deforms plastically faster

during compression than the standard binders.

MYPHARMAGUIDE.COM 53

MYPHARMAGUIDE.COM 54

Korsmeyer’s-Peppa’s model

› A simple relationship which described drug release from a polymeric system

equation was derived by Korsmeyer-Peppa in 1983

› To understand the mechanism of drug release and to compare the release

profile differences among these matrix formulations ,the percent drug released

time versus time were fitted using this equation

› Mt/Ma = ktn

› Mt / Ma= percent drug released at time t

› K= constant incorporating structural and geometrical characteristics of the

sustained release device.

› n =exponential which characterizes mechanism of drug release

MYPHARMAGUIDE.COM 55

MYPHARMAGUIDE.COM 56

SIMILARITY FACTOR (f2)

Similarity factor (f2) as defined by FDA is,

› Logarithmic reciprocal square root transformation of sum of

squared error and is measurement of the Similarity in the

percentage (%) dissolution between two curves.

n= No. of time points

Rt= %dissolved of reference product

Tt= %dissolved of test product

MYPHARMAGUIDE.COM 57

DIFFERENCE FACTOR (f1)

› 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.

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)

MYPHARMAGUIDE.COM 58

STEPS INVOLVED:

› This model- independent method is most suitable for the dissolution

profile comparison when 3-4 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 above formulas.

› 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 sameness or equivalence of the 2 curves.

MYPHARMAGUIDE.COM 59

CONDITIONS INVOLVED:

› The dissolution measurements of the test and reference batches should be

made under exactly the same conditions.

› The dissolution time points for both the profiles should be the same (ex:

15,30,45,60 minutes)

› The reference product used should be the most recently manufactured pre-

change product.

› Only one measurement should be considered after 85% dissolution of both

the products

› To allow use of mean data, the %coefficient variation (%cv) at the earlier

time points (ex: 15 minutes)should not be more than 20% and at other time

points should not be more than 10%

MYPHARMAGUIDE.COM 60

%Coefficient of variation (%CV)

It is the Standard deviation (s)divided by mean times(m) 100%

%CV = (s/m) 100%

› The mean dissolution values for reference can be derived either from last pre-

change batch or the last 2 or more consecutively manufactured pre-change

batches.

OBJECTIVES:

› To develop, in-vitro in-vivo correlation which can help to reduce costs, speed-

up product development and reduce the need to perform costly bioavailability

human volunteer studies

› Establish the similarity of pharmaceutical dosage forms, for which

composition, manufacture site, scale of manufacture, manufacture process and/

or equipment may have changed within defined limits.

MYPHARMAGUIDE.COM 61

HIGUCHI MODEL

Higuchi proposed this model in 1961 to describe the drug release

from matrix system.

HYPOTHESIS:

› Initial drug concentration in the matrix is much higher than drug solubility.

› Drug diffusion takes place only in one dimension (edge effect should be

avoided)

› Drug particles are much smaller the system thickness.

› Matrix swelling and dissolution are less or negligible.

› Drug diffusivity is constant.

› In the release environment perfect sink conditions are maintained.

MYPHARMAGUIDE.COM 62

Higuchi model is given by the equation,

C= [D (2qt-Cs) Cst]

½

C= Total amount of drug release per unit area of matrix (mg/cm2)

D= Diffusion coefficient

qt= Total amount of drug in a unit volume of matrix (mg/cm3)

Cs = Solubility of drug (mg/cm3)

t= Time

APPLICATIONS:

▪ By using this model dissolution of drug from several modified release dosage forms like

some trans-dermal system and matrix tablet with water soluble drugs are studied.

▪ Also used for study of poorly soluble drugs from variety of matrices including solids and

semisolids.

MYPHARMAGUIDE.COM 63

Here the value of

r2 for carbidopa is 0.9931 and

levodopa is 0.9916

This implies that the release of drug from

matrix as a square root of time

dependent process and diffusion

controlled.

The r2 value is the correlation coefficient.

[Strong positive correlation = 1

Strong negative correlation = -1

No correlation = 0

Thus for the above example the is nearest

to and shows the best fit of correlation.

MYPHARMAGUIDE.COM 64

Standard deviation :

› Standard deviation is a statistic that measures the dispersion of a

dataset relative to its mean.

MYPHARMAGUIDE.COM 65

STEPS INVOLVED:

▪ Calculate mean

▪ Write a table that subtracts mean from each observed value

▪ Square each of the differences

▪ Add this column

▪ Divide by n-1 where n is the number of items in the sample. This is

the variance.

▪ To get Standard Deviation we take the square root of variance

TYPES:

Low Standard Deviation-indicates that the data points tend to

be very close to the mean.

High Standard Deviation -indicates that the data is spread out

over a large range of values.

MYPHARMAGUIDE.COM 66

MYPHARMAGUIDE.COM 67

Level of significance :

1. A Formal statistical procedure for comparing observed data with

a hypothesis (predicted data)

2.The results of a significance test are expressed in a probability that

measures how well the data and claim agree.

STEPS INVOLVED :

1.State the null and alternate hypothesis

2.Calculate the test statistics

3.Find the P-value

4.Compare P-value with alpha value and decide whether the null

hypothesis should be accepted or rejected.

MYPHARMAGUIDE.COM 68

Example :

experiment on size reduction for solubility enhancement.

HYPOTHESIS : Size reduction can cause 5% increase in solubility

enhancement

NULL HYPOTHESIS ALTERNATE HYPOTHESIS

Size reduction will not cause 5% Size reduction will cause 5% increase in

Increase in solubility solubility

The aim of the researcher is to prove the hypothesis by

rejecting the null hypothesis

MYPHARMAGUIDE.COM 69

Calculation of Test statistic:

data from the experiment

Before size reduction – Solubility :100

After size reduction- Solubility: 108

Standard deviation -16

Sample size N -16

It was found to be 2

MYPHARMAGUIDE.COM 70

› P Value :

It represents the probability of getting this specific sample mean

score if it is actually no different from the population mean.

When the P-value is very small the research can strongly evidence

that null hypothesis is false.

› α- value : 0.05 or 5%

› P value > α :accept the null hypothesis

› P value <= α :reject the null hypothesis

MYPHARMAGUIDE.COM 71

ANOVA (Analysis of Variance) :

• ANOVA measures two sources of variation in the data and compares their relative sizes

o Variation BETWEEN groups— for each data value look at the difference between its

group mean and the overall mean

( )2

xi − x

o Variation WITHIN groups — for each data value look at the difference between that

value and the mean of its group

( )2xij − xi

MYPHARMAGUIDE.COM 72

Examples of obvious confounding :

› (1) a clinical study in which patients are allowed to take various concomitant

drugs other than the test drug that affect the condition being treated and

› (2) a comparison of a new tablet formulation to the former formulation for

dissolution, with the tablets prepared on two different tablet presses, one

formulation on each press.

Differences in the performance of the presses (pressure, for example) can

contribute to differences in dissolution in addition to differences due to

formulation changes.

ANOVA does

Consider an experiment to assess the effects of lubricating agent and

disintegrating agent on the dissolution of a tablet.

MYPHARMAGUIDE.COM 73

› The final analysis of variance would separate the effects of these factors by

computing that part of the total variation attributable to the lubricating and

disintegration agents isolated from that variation due to experimental error.

This separation serves as a basis for testing statistical hypotheses.

CONDITIONS USED :

➢ In two sample situation

➢ In paired set-up

➢ In repeated measures, when the same subject is measured at different time

points such as after 5 minutes, 15 minutes, 30 minutes, 60 minutes etc,.

➢ Removing the effect of a covariate

➢ Regression.

MYPHARMAGUIDE.COM 74

› The ANOVA F-statistic is a ratio of the Between Group Variation divided by

the Within Group Variation:

𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝒗𝒂𝒓𝒊𝒂𝒕𝒊𝒐𝒏 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 𝒕𝒉𝒆 𝒈𝒓𝒐𝒖𝒑𝒔 𝑴𝑺𝑮

F = =

𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝒗𝒂𝒓𝒊𝒂𝒕𝒊𝒐𝒏 𝒘𝒊𝒕𝒉𝒊𝒏 𝒕𝒉𝒆 𝒈𝒓𝒐𝒖𝒑𝒔 𝑴𝑺𝑬

➢MSG is the estimated average variation between the groups means

➢ MSE is the estimated average variation within the groups

➢If the computed F ratio is less than 1, the means are not significantly

different. If the F ratio is greater than 1, an F table should be used to

determine if the ratio is sufficiently large to declare significance.

MYPHARMAGUIDE.COM 75

A large F is evidence against H0, since it indicates that there is more

difference between groups than within groups.

Different types of ANOVA ;

› One-way ANOVA

› Two-way Analysis of Variance

› Mixed design ANOVAs

MYPHARMAGUIDE.COM 76

One-way ANOVA :

One factor with more than 2 levels

Eg: Change of blood pressure in preclinical study comparing two drugs and

control.

Two-way Analysis of Variance (Randomized Blocks) :

The two-way model is an extension of the paired t test in which more than two

groups or treatments are compared.

Eg: Stability of five batches of tablets using threeM YkPHiAnRdMAsG UoIDfE .pCOaMckaging materi7a7l.

Mixed design ANOVAs

Some factors independent, others related

Application :

1. If a pharma company, has 3 different medications for treating ulcers by

using ANOVA , we can determine the effectiveness of treating them.

can compare which medication works better for treatment and can choose

the best one.

2. In Pharma company, QA officer collects four samples groups (A,B,C,D)

each of 6 tablets to measure the hardness of the tablet.

Observation :

P-value is 0.004 (From ANOVA Table) which is less than our alpha value

0.05

MYPHARMAGUIDE.COM 78

› Means are significantly different from each other.

› On interval plot we can see the mean differences between each other.

3. Evaluation of bio-equivalence studies.

MYPHARMAGUIDE.COM 79

Chi square test :

› Most commonly used non-parametric statistics

› Used when data is represented in frequencies or proportions

› Useful in discrete data

› Any continuous data can be converted to categorical data and the statistics can

be used

› The chi-square test statistic can be used to evaluate whether there is an

association between the rows and columns in a contingency table.

› More specifically, this statistic can be used to determine whether there is any

difference between the study groups in the proportions of the risk factor of

interest. Chi-square test and the logic of hypothesis testing were developed by

Karl Pearson.

MYPHARMAGUIDE.COM 80

MYPHARMAGUIDE.COM 81

MYPHARMAGUIDE.COM 82

Students t Test:

› Pharmaceutical Company, they manufacture lakhs of tablets per day – in

such case, it is difficult to know the population parameters like mean and

standard deviation. So we apply sample t-tests.

Types of t-test

› There are various types of t-test namely

-one sample t-test,

-two sample t-test and

-paired sample t-tests.

MYPHARMAGUIDE.COM 83

› One Sample t-test

› We use one sample t-test when we have one

sample group.

› By doing so, we would be able to find

whether the mean is significantly different or

not with regards to our target specification.

› For e.g. in a Pharmaceutical Company, QA

officer collects samples of 12 tablets to

measure the dissolution rate of a drug. Here,

we can find whether the mean of a dissolution

rate is significant to our target dissolution rate

or not (target = 365 C).

MYPHARMAGUIDE.COM 84

› Ho=Target mean value, x bar=Sample

mean value

› Since our p-value is 0.019 which is less

than our alpha value of 0.05, we can

conclude that the mean of the dissolution

rate is significantly different than the target

value.

MYPHARMAGUIDE.COM 85

› Two Sample t-test

› We use two sample t-test when we have

two independent sample groups. By doing

so, we would be able to find whether the

means are significantly different or not.

And we would be able to compare which

one is good.

› For e.g. in a Pharmaceutical Company, QA

officer collects a two sample groups (A

and B) each of 12 tablets to measure the

dissolution rate of a drug. We can compare

which of these types have a better

dissolution rate and hence we able to

choose the best one.

MYPHARMAGUIDE.COM 86

› Since our p-value is 0.3 which is greater

than our alpha value of 0.05, we can

conclude that the mean of the dissolution

rate is not significantly different. But there

is a difference in the variance part

(individual value plot).

MYPHARMAGUIDE.COM 87

Paired Sample t-test

› We use paired sample t-test when we have two dependent sample data of the

same subject i.e. to measure the effect on a particular group before and after

the treatment.

› For e.g. during a Clinical Trial, we choose 20 patients and measure their

weight before the drug treatment.

› And again, after the two months, we again measure their weight. By doing

so, we can check whether the drug is effective or not. Here we will have two

sets of data

› It is also called a dependent sample t-test. Here the patient’s weight is

dependent on drug treatment.

MYPHARMAGUIDE.COM 88

Since our p-value is 0.007 which is less than alpha value of 0.05, we can

conclude there is a significant difference between the treatments.

We can visualize the differences whether the drug is effective or not based on

their weights.

MYPHARMAGUIDE.COM 89

References :

1.Biopharmaceutics & Pharmacokinetics –a treatise by D M

Brahmankar, Sunil B. Jaiswal.

2.Textbook of Biopharmaceutics & pharmacokinetics –concept and

application by C.V.S.Subramaniyam.

3.Biopharmaceutics and pharmacokinetics by J.S. Kulkarni, A.P.

Pawar.

4. Martin’s Physical Pharmacy and Pharmaceutical sciences 6th

Edition.

5.Applied Biopharmaceutics and Pharmacokinetics by Leon Shargel,

PhD, RPh and Andrew B.C. Yu, PhD, RPh 7th edition.

MYPHARMAGUIDE.COM 90

6..Lachmann Libermann, “The theory and practice of industrial

pharmacy”

7. https://qsutra.com/anova-in-pharmaceutical-and-healthcare/

8. https://qsutra.com/t-tests-in-pharmaceutical-industry/

9.Anoop Kumar Singh, “Formulation development of Paracetamol

tablet using natural plant based excipient as a binder”

10.Himankar Baishya et al., “Application of mathematical models

in drug release kinetics of Carbidopa and Levodopa ER tablets:

Journal of developing drugs 2017; 6(2): p(1-8)

11.Pharmaceutical Statistics : Clinical Practice & Application by

Stanford Balton.

MYPHARMAGUIDE.COM 91

MYPHARMAGUIDE.COM 92