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MODELLING & COMPARISON OF
DISSOLUTION PROFILES
BY MAHENDRA PRATAP SWAIN
Regd. No.: PHDPH100102019
BIRLA INSTITUTE OF TECHNOLOGY, MESRA, RANCHI
CONTENT IN
β€’ INTRODUCTION
β€’ DRUG DISSOLUTION PROCESS
β€’ DISSOLUTION PROFILES COMPARISON
β€’ DISSOLUTION MODELS/METHODS TO COMPARE DISSOLUTION PROFILE WITH
PROPER CLASSIFICATION & EXPLANATIONS
β€’ CONCLUSION
26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI
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INTRODUCTION
β€’ DEFINITION:
β€’ It is a graphical represents in terms of (Concentration Vs Time) of complete release of
API from a dosages form in a appropriate selected dissolution medium, i.e., in short it
is the measure of the release of API form a dosage from with respect to time
β€’ Rate of dissolution:
Amount of drug substance that goes in the solution per unit time under standardise
condition of liquid pH, solvent, temperature.
By kinetic model, dissolved amount of drug (Q) is a function of test time β€˜t’
𝑄 = 𝑓(𝑑)
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INTRODUCTION (CONT..)
β€’ The kind of drug, its polymorphic form, crystallinity, particle size, solubility &
amount in the pharmaceutical dosage form can influence the release kinetics
(Salomon & Doelker, 1980; El-Arini & Leuenberger, 1995)
β€’ A water soluble Drug = in Matrix = By Diffusion
β€’ Low Water soluble Drug = in Matrix = Self Erosion of Matrix
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DRUG DISSOLUTION PROCESS
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Tablet Granules Small Particles
Drug in
Solution
Very
Limited
Dissolution
Limited
Dissolution
Best
Dissolution
Disintegration Disintegration
WHY DISSOLUTION STUDY..??
β€’ OBJECTIVES:
β€’ To study the release of drug in desired amount from dosage form.
β€’ To study the uniformity of drug release from dosage form of different batches.
β€’ To show that drug release is equivalent to those batches proven to be bioavailable and
clinically effective.
β€’ To demonstrating equivalence after change in formulation of the Drug Product or
preparation of Pharmaceutically equivalent product
β€’ To Development a Bioequivalent product
β€’ To optimize dosage formula by comparing the dissolution profile of various formulas of
same API or to get chemically equivalent products.
β€’ To achieve desired dissolution profile w.r.t. condition & time in IR, MR formulations
β€’ To develop IVIV correlation which help to reduce Cost, Speed Up Product development &
reduce need of preform costly bioavailability human volunteer studies
β€’ To stabilize final dissolution specification for Regulatory filling
β€’ To Dissolution profiles od SUPAC (Scale-Up-Post-Approval-Changes) Product.
26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI
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DISSOLUTION MODELS/METHODS :
A. GRAPHICAL METHOD
B. STATISTICAL METHOD
a. t-student’s Test
I. Single Time
II. Multiple time Point
b. ANOVA
c. MANOVA
C. MATHEMATICAL MODELS DEPENDANTS
METHOD
a. Zero Order Kinetics Model
b. First Order Kinetics Model
c. Weibull Model
d. Higuchi Model
e. Hixon-Crowell model
f. Korsmeyer- Peppas Model
g. Baker- Lansodale Model
h. Hopfenberg Model
D. RELEASE PROFILE COMPARISION OR
MODEL INDEPENDENT METHOD
a. Ratio test
b. Pair-wise procedures
I. Similarity Factor (f2)
II. Difference Factor (f1)
E. OTHER RELEASE PARAMETER
a. Release time (tx%)
b. Sampling Time
c. Dissolution efficiency (DE)
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A. GRAPHICAL METHOD
β€’ In this method we plot graph of Time Vs Concentration(Drug) in the OGD or body
fluid simulation dissolution medium or biological fluid
β€’ Shape of two curve is compared for comparison of dissolution pattern & the
concentration of drug at each point is compared for extent of dissolution
β€’ If two or more curves are overlapping then the dissolution profile is comparable
β€’ If difference is small then it is accepted but higher differences indicate that the
dissolution profile is not comparable
β€’ m
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A
B
100%
0%
Concentration
Time
A
B
100%
0%
Concentration
Time
A
B
100%
0%
Concentration
Time
A
B
100%
0%
Concentration
Time
1 2 3 4
B. STATISTICAL METHOD
β€’ This also called statistical analysis, mainly included;
β€’ SINGLE TIME POINT DISSOLUTION
I. t-Students' Test
II. ANOVA
β€’ MULTIPLE TIME POINT DISSOLUTION
I. MANOVA
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STUDENT’S T-TEST
β€’ STUDENT’S T-TEST:
β€’ This have some tests like,
β€’ One sample t-Test
β€’ Paired t-Test
β€’ Unpaired t-Test
β€’ The equation for β€œt” is;
𝑑 = 𝑋 βˆ’ πœ‡ Γ· 𝑆 Γ· 𝑁
Where,
X = Sample Mean
N = Sample Size
S = Sample Standard Deviation (SSD)
Β΅ = Population Standard Deviation (PSD)
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ANOVA
β€’ This test is generally applied to different groups of data. Here we compare the variance of
different group of data & predict weather the data are comparable or not.
β€’ Minimum three sets of data are required. Here first we have to find the variance within
each individual group and than compare them with each other.
β€’ Step to perform ANOVA:
β€’ There are five steps,
1. Calculate the total sum of the squares of variance(SST)
𝑆𝑆𝑇 = 𝑋𝑖𝑗2 βˆ’
𝑇2
𝑁
Where, Xij = Shows the Observation
T2/N = Correction Factor (CF)
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ANOVA(CONT..)
2. Calculate the variance b/w the samples(SSC)
𝑆𝑆𝐢 =
𝐢𝑗2
β„Ž
βˆ’
𝑇2
𝑁
Where, Cj = sum of jth column
h = No of rows
3. Calculate the variance within the samples
𝑆𝑆𝐸 = 𝑆𝑆𝑇 βˆ’ 𝑆𝑆𝐢
4. Calculate the F-Ratio
𝐹𝑐 = 𝑆𝑆𝐢
π‘˜ βˆ’ 1 Γ· 𝑆𝑆𝐸
𝑁 βˆ’ π‘˜
k-1 = Degree of Freedom
5. Compare Fc Calculated with the FT (Tabulated Value)
If Fc<FT, accepted H0.
If H0 is accepted it can be concluded that the difference is not significance and hence could have
arisen due to fluctuation of random sampling.
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ANOVA(CONT..)
All the information about the analysis of variance is summarized in the following ANOVA
table:
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Sources of
Variation
Sum of
square (SS)
Degree of
Freedom (d.f.)
Mean Square
(M.S.)
Variance
Ration of F
Variance
Ration of F
SSC k-1 𝑀𝑆𝐢
= 𝑆𝑆𝐢
π‘˜ βˆ’ 1
Within the
sample
SSE N-k 𝑀𝑆𝐢
= 𝑆𝑆𝐸
𝑁 βˆ’ π‘˜
Total SST N-1
MSC = Mean Sum of Square b/w samples
MSE = Mean Sum of Square within samples
MANOVA
β€’ MANOVA = Multivariate Analysis of Variance
β€’ This is generally applied to different groups of date.
β€’ Here we compared the variance of different groups of data & predict weather the
data are comparable or Not
β€’ Minimum Three sets of data are required. Here first we have to find the variance
within each individual group & then compare with each other
β€’ It generally calculated with software after calculating ANOVA by wilk’s Lambda
equation;
β€’ Wilk’s Lambda =
E
H+E
β€’ E = error some of square and cross production matrix
β€’ H = hypothesis sum of square and cross production matrix
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C. MATHEMATICAL MODEL
DEPENDANT METHODS
β€’ For quantitative interpretation of values
obtained as dissolution assays is easier
to using following mathematical
models/Equations, which describe the
release profile which further relate to all
types dosage forms. Like;
a. ZERO ORDER KINETICS MODEL
b. FIRST ORDER KINETICS MODEL
c. SECOND ORDER KINETICS MODEL
d. WEIBULL MODEL
e. HIGUCHI MODEL
f. HIXON-CROWELL MODEL
g. KORSMEYER- PEPPAS MODEL
h. BAKER- LANSODALE MODEL
i. HOPFENBERG MODEL
j. QUADRATIC MODEL
k. LOGISTIC MODEL
l. GOMPERTZ MODEL
m. HOPFENBERG MODEL
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ZERO ORDER KINETICS MODEL
β€’ Zero Order API release contributes drug release from dosage for that is independent of amount of
drug in delivery system (i.e. constant drug release)
β€’ Drug Release Rate is independent of Concentration
β€’ Graphically we will get always of a Straight line within %CDR Vs Time
β€’ Equation:
π‘Š0 βˆ’ π‘Šπ‘‘ = 𝐾𝑑
Where,
W0 = Initial amount of drug in dosage form
Wt = Amount of drug in the dosage form at time β€œt”
K = Proportionality t
β€’ This Equation can written as,
𝑄𝑑 = 𝑄0 + 𝐾0 𝑑
Where,
Qt = The amount of drug dissolved in time t
Q0 = Initial amount of drug in the solution
K0 = Zero Order Constant (Mostly it is considered as ZERO)
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100%
0%
Cumulative%ofDrug
Release
Time in Hrs.
ZERO ORDER KINETICS MODEL
(CONT..)β€’ This release is achieved by making;
β€’ Reservoir Diffusion System
β€’ Osmotically Controlled Devices
β€’ EXAMPLES WHERE IT IS APPLIED:
β€’ Transdermal DDS
β€’ Implantable Depot.
β€’ Oral Control Release
β€’ Matrix Tablet with low solubility drug
β€’ Suspension
β€’ Oral osmotic pressure
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FIRST ORDER KINETICS MODEL
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β€’ Used to describe absorption and/or elimination of some drugs, although it is difficult to
conceptualise this mechanism in a theoretical basis.
β€’ The dissolution phenomenon of a solid-particle in a liquid media implies a surface action & seen by
Noyes-Whitney Equation:
𝑑𝐢
𝑑𝑑
= 𝐾 𝐢𝑠 βˆ’ 𝐢
β€’ Where,
dC/dt = Dissolution Rate
Cs = Solubility at Max/ Saturation or Concentration of drug at stagnant layer
C = Drug concentration in Bulk of solution in time t
β€’ At Sink condition = dissolution rate limiting step for in-vitro study absorption = dissolution rate
limiting step for in-vitro study, so this equation will be,
𝑑𝐢
𝑑𝑑
= 𝐾 𝐢𝑠 = πΆπ‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘
β€’ So it becomes , 𝑄𝑑 = 𝑄0. π‘’βˆ’πΎπ‘‘
Where,
Qt = Drug dissolved in time t
Q0 = Initial drug concentration
K = Constant at time t
FIRST ORDER KINETICS MODEL
(CONT..)
β€’ USED IN GENERALLY MOSTLY;
β€’ Water soluble drugs in porous matrix
β€’ Low Water soluble drug in porous matrix
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WEIBULL MODEL
β€’ This equation can be successfully applied to almost all kinds of dissolution curves
by preceding equation;
log βˆ’ln(1 βˆ’ π‘š) = 𝑏 Γ— log(𝑑 βˆ’ 𝑑𝑖) βˆ’ log π‘Ž
Where,
β€’ m = cumulated fraction of drug in solution at time t
β€’ a = time scale parameter or time scale of process, it can be replaced by more informative
dissolution time (td) or ordinate value in graph, a can be calculated by formula; π‘Ž = 𝑇𝑑
𝑏
,
Where Td is time necessary to dissolve or release 63.2% of drug from dosage.
β€’ Ti = Location parameter or lag time before onset of dissolution or release process & it is
mostly zero
β€’ b = shape parameter or slop of line in graph
If b = 0 then Curve as either exponential
If b > 1 then sigmoid shape with upward curvature followed by a turning point
If b < 1 then parabolic with higher initial slop & after that consistent with exponential
26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI
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WEIBULL MODEL (CONT..)
β€’ USED FOR,
β€’ Almost all type of dissolution curve
β€’ CRITICISM:
β€’ There is not any kinetic fundamental and could only describe, but does not adequately
characterize, the dissolution kinetic properties of the drug
β€’ There is not any single parameter related with the intrinsic dissolution rate of drug
β€’ It is of limited use for establishing in in-vivo/ in-vitro correlation
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HIGUCHI MODEL
β€’ Higuchi proposed this model in 1961 to describe the drug release from matrix
system
β€’ It is assume that these system are neither surface coated nor that their matrices
undergo a significant alteration in the presence of water.
β€’ Equation:
𝑓𝑑 = 𝑄 = 𝐴 𝐷 2𝐢 βˆ’ 𝐢𝑠 𝐢𝑠. 𝑇
β€’ Where,
β€’ Q = Amount of drug release in time t per unit area A
β€’ C = Initial drug Concentration
β€’ Cs = Drug solubility in Matrix media
β€’ D = Diffusivity of the drug molecules
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HIGUCHI MODEL (CONT..)
β€’ IT IS DEVELOPED TO STUDY THE RELEASE OF
β€’ Diffusion Matrix system:
β€’ Homogenous matrices of Suspension from ointment base
β€’ Planar or spherical system having a granular heterogenous matrix
β€’ Water soluble drugs incorporated in semi-solid or solid matrix
β€’ Low water soluble drug incorporated in semi-solid or solid matrix
β€’ Too accordance with other all types dissolution from other pharmaceutical dosage forms
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HIXON-CROWELL MODEL
β€’ To evaluate the drug release with change in the surface area and the diameter of
the particles/ tablets
β€’ The rate of dissolution depends on the surface of solvent
so THE LARGE IS AREA THE FASTER IS DISSOLUTION.
β€’ Both scientist recognized that Particle regular area is proportional to the cubic root
of its volume, so describe a equation for easier,
𝑀0
1
3 βˆ’ 𝑀
1
3 = 𝐾 Γ— 𝑑
Where,
M0 =Original mass of API Particles
K = Cubic root dissolution rate constant
M = Mass of the API at the time β€˜t’
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HIXON-CROWELL MODEL (CONT..)
β€’ APPLICABLE FOR
β€’ Polymeric matrix system
β€’ Erodible Matrix Formulations
Note: when this model is, it is assumed that the release rate is limited by the drug
particles dissolution rate and not by the diffusion that might occur through the
polymeric matrix.
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BAKER- LANSODALE MODEL
β€’ In 1974 Baker- Lonsdale developed the model from Higuchi model and given
equation;
3
2
1 βˆ’ 1 βˆ’
𝑀𝑑
π‘€βˆž
2
3
βˆ’
𝑀𝑑
π‘€βˆž
=
3. 𝐷 π‘š. 𝐢 π‘šπ‘ 
π‘Ÿ0
2. 𝐢0
t
Where,
β€’ Mt = Drug Release at time t
β€’ M∞ = Drug Release at infinite time
β€’ Dm = Diffusion coefficient
β€’ Cms = Drug solubility in matrix
β€’ R0 = Radius of spherical matrix
β€’ C0 = Initial concentration at matrix
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BAKER- LANSODALE MODEL
(CONT..)
β€’ THIS EQUATION HAS BEEN USED TO
β€’ Linearization of release data of Microcapsules
β€’ Linearization of release data of Microspheres
β€’ Matrix system formulations
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HOPFENBERG MODEL
β€’ Model explain rate limiting step of drug release is erosion of matrix itself
β€’ Time dependant diffusional resistance internal or external to eroding matrix do not
influence it. Or simply called as Modified Las time, it calculated by following
equation,
𝑀𝑑
π‘€βˆž
= 1 βˆ’ 1 βˆ’
𝐾0 𝑑
𝐢0 π‘Ž0
𝑛
Where,
β€’ Mt = Drug dissolved in time t
β€’ M∞ = Drug dissolved in infinite time
β€’ Mm /M∞ = Fraction of drug dissolved
β€’ a0 = Initial Radius of sphere or cylinder or half thickness for a slab
β€’ C0 = Initial concentration at matrix
β€’ n = 1, 2, 3 for a slab, cylinder, and sphere respectively
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HOPFENBERG MODEL (CONT..)
β€’ CALCULATION OF DRUG RELEASE FROM SURFACE ERODING DEVICE WITH
DIFFERENT GEOMETRIC, LIKE
β€’ Slab
β€’ Sphere
β€’ Infinite cylinder display heterogenous erosion
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KORSMEYER- PEPPAS MODEL
β€’ The simple relationship which describe the drug release from the polymeric system
equation was derived by Korsmeyer et. al. in 1983
β€’ It is used to describe the first 60% release of drug from dosage form
β€’ Equation:
𝑀𝑑
π‘€βˆž
= π‘Žπ‘‘ 𝑛
+ 𝑏
β€’ Where,
β€’ Mt/M∞ = Fraction of drug release at time β€œt”
β€’ a = constant incorporating structure or geometrical characteristics of drug dosage form
β€’ n = Release Exponent
β€’ n value is used to characterize the drug release for cylindrical matrices and the n
value characterize the release mechanism of drug as described.
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KORSMEYER- PEPPAS MODEL
(CONT..)
β€’ n value is used to characterize the drug release for cylindrical matrices and the n
value characterize the release mechanism of drug as described;
β€’ n is estimated as linear regression of Log (mt/m) Vs Log T
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100%
0%
Log%ofdrugrelease
Log time in Hrs.
Release exponents(n) Indications or drug
transport mechanism
Rate as a function of
time
Less than 0.45 (<0.45) Quasi fickian -
0.45 Fickian Diffusion T-0.5
0.45 < n < 0.89 Non Fickian diffusion tn-1
0.89 to 1 Zero Order Non fickian case 2 Zero order release
More than 1 (>1) Non Fickian super case
2
tn-1
KORSMEYER- PEPPAS MODEL
(CONT..)
β€’ USED IN;
β€’ Could be predicted the best model for the release of drug from the dosage form
β€’ Different Pharmaceutical Modified release dosage forms
β€’ Polymeric system formulations
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D. RELEASE PROFILE COMPARISION
OR MODEL INDEPENDENT
METHODβ€’ Model independent Method can be further differentiated to
β€’ RATIO TEST
β€’ Ratio of Area Under the Curve (AUC)
β€’ Mean Dissolution Time(MDT)
β€’ PAIR-WISE PROCEDURES
β€’ F1 = Difference Factor
β€’ f2 = Similarity Factor
β€’ ΞΎ1 = Rescigno index or bioequivalence index
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RATIO TEST
β€’ Parameters from release assay of reference & test at same point(Tx%).
β€’ Taken Ratio of AUC of both reference & Test Product
Or
β€’ Ratio of Mean Dissolution Time (MDT)
𝑀𝐷𝑇 =
𝑗=1
𝑛
βˆ†π‘€π‘— 𝑑𝑗
𝑗=1
𝑛
βˆ†π‘€π‘—
Where,
j = sample No
n = No. of sample time
tj = Midpoint b/w tj & T(j-1)
βˆ†Mj = Drug dissolved
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PAIR WISE PROCEDURE
β€’ Pair wise procedure includes
β€’ F1 VALUE: DIFFERENCE FACTOR
β€’ F2 VALUE: SIMILARITY FACTOR
β€’ RESCIGNO INDEX OR BIOEQUIVALENCE INDEX (ΞΎ1 & ΞΎ2 )
β€’ These F1 & F2 equations described by Moore & Flamner and ΞΎ1 & ΞΎ2 by Rescigno.
β€’ Both F1 & F2 equations are endorsed by FDA as acceptable method for dissolution
profile comparison
β€’ They are used to study the comparison of dissolution profiles of the two dosage
forms.
β€’ It can be calculated using Excel or various readymade software (E.g.:
PhEq_bootstrap) and Rescigno index too calculated by Software.
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DIFFERENCE FACTOR (F1)
β€’ It calculate % difference b/w two curves at each time point & measure relative error b/w two
curves.
β€’ F1 equation is sum of absolute values of vertical distance b/w reference (Rt) & Test (Tt) mean
% release values i.e. (Rt-Tt) at each dissolution points.
β€’ The f1- Value is equal to zero to zero when the test and reference profiles are identical &
increase as the profile
β€’ Equation
𝑓1 =
𝑑=1
𝑛
𝑅𝑑 βˆ’ 𝑇𝑑
𝑑=1
𝑛
𝑅𝑑
Γ— 100
Where,
Rt = Reference Dissolution Value
n = No of dissolution time points
Tt = Test dissolution value
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SIMILARITY FACTOR (F2)
β€’ f2 equation is logarithmic transformation of average squared vertical distance b/w
reference & test mean dissolution values at each time point, multiplied by an
approximate weighting i.e. Wt(Rt-Tt).
β€’ Equation:
𝑓2 = 50log10 1 +
1
𝑛
𝑑=1
𝑛
π‘Šπ‘‘(𝑅𝑑 βˆ’ 𝑇𝑑)2
βˆ’0.5
Γ— 100
Where,
Rt = Reference Dissolution Value
n = No of dissolution time points
Tt = Test dissolution value
Wt = Optional weighting Factor
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WHEN ARE DISSOLUTION PROFILE SIMILAR..??
β€’ If in both Test & Reference product shows dissolution more than or equal to 85% (β‰₯
85%) within 15min, then
β€’ Profiles are considered to be similar
β€’ No further calculations required
β€’ F1 value limit : 0% to 15%
β€’ F2 Value limit : β‰₯ 50%
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ADDITIONAL REQUIREMENTS FOR F1 & F2
β€’ At least 12 unit should used
β€’ Same test conditions should maintained
β€’ Dissolution time points for Immediate Release(IR) products like 5, 15,30, 60 min
β€’ For Sustained Release(SR) Products, 1, 2, 3, 5, 8 Hrs. etc. until at least 85% of drug is
released
β€’ Only one measurement should considered after 85% dissolution of drug
β€’ Standard Deviation (DV):
β€’ ≀20% at early time points
β€’ ≀10% at later time points
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EXAMPLE FOR F1 & F2
Time Rt Tt (Rt-Tt) (Rt-Tt)2
10 45 55 10 100
15 65 75 10 100
20 80 90 10 100
30 90 100 10 100
𝑅𝑑 = 280 𝑅𝑑 βˆ’ 𝑇𝑑 = 40 (𝑅𝑑 βˆ’ 𝑇𝑑)2
= 400
26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI
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By putting Data in Eq. we will get;
F1 =14
F2 =50
Insert No of points where both products β‰₯85%
Rt = Cumulative % dissolved of reference product at time t
Tt = Cumulative % dissolved of test product at time t
RESCIGNO INDEX
β€’ Also called as bioequivalence Index generally used in CR formulations
β€’ Used to measure dissimilarity b/w Reference & Test product based on PDC & time
β€’ Equation;
ξ𝑖 = 0
∞
𝑑 𝑅 𝑑 βˆ’ 𝑑 𝜏(𝑑) 𝑖 𝑑𝑑
0
∞
𝑑 𝑅 𝑑 + 𝑑 𝜏(𝑑) 𝑖 𝑑𝑑
1
𝑖
Where,
dR t = Reference Product Dissolved amount
dΟ„(t) = Test product dissolved at each sample time points
β€’ This Rescigno index always lies b/w 0 & 1 (0< ξ𝑖<1)
β€’ If ξ𝑖 = 0 then Two profiles are similar
β€’ If ξ𝑖 = 1 then either test or reference not release at all
26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI
41
E. OTHER RELEASE PARAMETER
I. RELEASE TIME (tX%) :
β€’ Time Necessary to release determine % of Drug
E.g.: 20% of drug in pre-planned time
II. SAMPLING TIME (AX%):
β€’ The amount of drug w.r.t. time tx%
E.g.: X amount of drug released in 20min
III. DISSOLUTION EFFICIENCY (DE):
β€’ The area under the dissolution curve upto a certain time t, expressed as % of area of
rectangle describe the 100% dissolution in the same time.
𝐷𝐸 % =
𝑆𝐴
𝑅
Γ— 100 β†’ 𝐷𝐸 % = 0
𝑑
π‘Œ. 𝑑𝑑
π‘Œ100. 𝑑
Γ— 100
Where,
β€’ SA = Shaded Area
β€’ R= Rectangle Area
26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI
42
SUMMARY
S. No. Model Name Graph to be Estimated Equation Application for
1 Zero Order Kinetic Model Cumulative Release Vs Time 𝑄𝑑 = 𝑄0 + 𝐾0 𝑑 TDDS, Coating, Osmotic System
2 First Order Kinetic Model Log Cumulative Release Vs Time 𝑄𝑑 = 𝑄0. π‘’βˆ’πΎπ‘‘ Water soluble & Low soluble drugs in
porous matrix
3 Second Order Kinetic Model Release amount Fraction to infinite time
Vs real time
𝑄𝑑
π‘„βˆž
= π‘„βˆž βˆ’ 𝑄𝑑 . 𝐾2 𝑑
NA
4 Weibull Model Log Cumulative Release Vs Log Time log βˆ’ln(1 βˆ’ π‘š)
= 𝑏 Γ— log(𝑑 βˆ’ 𝑑𝑖) βˆ’ log π‘Ž
Almost all type of dissolution curves
5 Higuchi Model % Cumulative Relase Vs (Time)1/2
𝑓𝑑 = 𝑄 = 𝐴 𝐷 2𝐢 βˆ’ 𝐢𝑠 𝐢𝑠. 𝑇 Diffusion Matrix formulation
6 Hixon – Crowell Model %CRt/CR∞ Vs (Time)1/2
𝑀0
1
3 βˆ’ 𝑀
1
3 = 𝐾 Γ— 𝑑 Erodible matrix formulation
7 Korsmeyer – Peppas model (Unreleased fraction)1/3 Vs Time 𝑀𝑑
π‘€βˆž
= π‘Žπ‘‘ 𝑛
+ 𝑏
MR Dosage forms
8 Baker – Lonsdale Model Mt/M∞ Vs Time
3
2
1 βˆ’ 1 βˆ’
𝑀𝑑
π‘€βˆž
2
3
βˆ’
𝑀𝑑
π‘€βˆž
=
3. 𝐷 π‘š. 𝐢 π‘šπ‘ 
π‘Ÿ0
2. 𝐢0
t
Microsphere, Microcapsules
9 Hopfenberg Mt/M∞ Vs Erosion Time 𝑀𝑑
π‘€βˆž
= 1 βˆ’ 1 βˆ’
𝐾0 𝑑
𝐢0 π‘Ž0
𝑛 Erosion matrix itself
10 Gompertz %dissolved Vs Max dissolution w.r.t. time 𝑄𝑑 = 𝐴. π‘’βˆ’π‘’βˆ’πΎ(π‘‘βˆ’π‘Œ) Comparing b/w good & intermediate
release
26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI
43
REFERENCE
β€’ Brahmankar D.M., Jaiswal S. B., 2013. Biopharmaceutics & Pharmacokinetics a
treatise, Vallabh Prakashan 32 ISBN 978-81-85731-47-6
β€’ Costa P., Lobo J.M.S., 2000. Modelling & Comparison of dissolution profiles, EJPS 12
(2001) 123-133
26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI
44
26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI
45
Thanking You..!!
For your attention

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Modelling & comparison of dissolution profiles by Paulo Costa

  • 1. MODELLING & COMPARISON OF DISSOLUTION PROFILES BY MAHENDRA PRATAP SWAIN Regd. No.: PHDPH100102019 BIRLA INSTITUTE OF TECHNOLOGY, MESRA, RANCHI
  • 2. CONTENT IN β€’ INTRODUCTION β€’ DRUG DISSOLUTION PROCESS β€’ DISSOLUTION PROFILES COMPARISON β€’ DISSOLUTION MODELS/METHODS TO COMPARE DISSOLUTION PROFILE WITH PROPER CLASSIFICATION & EXPLANATIONS β€’ CONCLUSION 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 2
  • 3. INTRODUCTION β€’ DEFINITION: β€’ It is a graphical represents in terms of (Concentration Vs Time) of complete release of API from a dosages form in a appropriate selected dissolution medium, i.e., in short it is the measure of the release of API form a dosage from with respect to time β€’ Rate of dissolution: Amount of drug substance that goes in the solution per unit time under standardise condition of liquid pH, solvent, temperature. By kinetic model, dissolved amount of drug (Q) is a function of test time β€˜t’ 𝑄 = 𝑓(𝑑) 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 3
  • 4. INTRODUCTION (CONT..) β€’ The kind of drug, its polymorphic form, crystallinity, particle size, solubility & amount in the pharmaceutical dosage form can influence the release kinetics (Salomon & Doelker, 1980; El-Arini & Leuenberger, 1995) β€’ A water soluble Drug = in Matrix = By Diffusion β€’ Low Water soluble Drug = in Matrix = Self Erosion of Matrix 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 4
  • 5. DRUG DISSOLUTION PROCESS 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 5 Tablet Granules Small Particles Drug in Solution Very Limited Dissolution Limited Dissolution Best Dissolution Disintegration Disintegration
  • 6. WHY DISSOLUTION STUDY..?? β€’ OBJECTIVES: β€’ To study the release of drug in desired amount from dosage form. β€’ To study the uniformity of drug release from dosage form of different batches. β€’ To show that drug release is equivalent to those batches proven to be bioavailable and clinically effective. β€’ To demonstrating equivalence after change in formulation of the Drug Product or preparation of Pharmaceutically equivalent product β€’ To Development a Bioequivalent product β€’ To optimize dosage formula by comparing the dissolution profile of various formulas of same API or to get chemically equivalent products. β€’ To achieve desired dissolution profile w.r.t. condition & time in IR, MR formulations β€’ To develop IVIV correlation which help to reduce Cost, Speed Up Product development & reduce need of preform costly bioavailability human volunteer studies β€’ To stabilize final dissolution specification for Regulatory filling β€’ To Dissolution profiles od SUPAC (Scale-Up-Post-Approval-Changes) Product. 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 6
  • 7. DISSOLUTION MODELS/METHODS : A. GRAPHICAL METHOD B. STATISTICAL METHOD a. t-student’s Test I. Single Time II. Multiple time Point b. ANOVA c. MANOVA C. MATHEMATICAL MODELS DEPENDANTS METHOD a. Zero Order Kinetics Model b. First Order Kinetics Model c. Weibull Model d. Higuchi Model e. Hixon-Crowell model f. Korsmeyer- Peppas Model g. Baker- Lansodale Model h. Hopfenberg Model D. RELEASE PROFILE COMPARISION OR MODEL INDEPENDENT METHOD a. Ratio test b. Pair-wise procedures I. Similarity Factor (f2) II. Difference Factor (f1) E. OTHER RELEASE PARAMETER a. Release time (tx%) b. Sampling Time c. Dissolution efficiency (DE) 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 7
  • 8. A. GRAPHICAL METHOD β€’ In this method we plot graph of Time Vs Concentration(Drug) in the OGD or body fluid simulation dissolution medium or biological fluid β€’ Shape of two curve is compared for comparison of dissolution pattern & the concentration of drug at each point is compared for extent of dissolution β€’ If two or more curves are overlapping then the dissolution profile is comparable β€’ If difference is small then it is accepted but higher differences indicate that the dissolution profile is not comparable β€’ m 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 8 A B 100% 0% Concentration Time A B 100% 0% Concentration Time A B 100% 0% Concentration Time A B 100% 0% Concentration Time 1 2 3 4
  • 9. B. STATISTICAL METHOD β€’ This also called statistical analysis, mainly included; β€’ SINGLE TIME POINT DISSOLUTION I. t-Students' Test II. ANOVA β€’ MULTIPLE TIME POINT DISSOLUTION I. MANOVA 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 9
  • 10. STUDENT’S T-TEST β€’ STUDENT’S T-TEST: β€’ This have some tests like, β€’ One sample t-Test β€’ Paired t-Test β€’ Unpaired t-Test β€’ The equation for β€œt” is; 𝑑 = 𝑋 βˆ’ πœ‡ Γ· 𝑆 Γ· 𝑁 Where, X = Sample Mean N = Sample Size S = Sample Standard Deviation (SSD) Β΅ = Population Standard Deviation (PSD) 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 10
  • 11. ANOVA β€’ This test is generally applied to different groups of data. Here we compare the variance of different group of data & predict weather the data are comparable or not. β€’ Minimum three sets of data are required. Here first we have to find the variance within each individual group and than compare them with each other. β€’ Step to perform ANOVA: β€’ There are five steps, 1. Calculate the total sum of the squares of variance(SST) 𝑆𝑆𝑇 = 𝑋𝑖𝑗2 βˆ’ 𝑇2 𝑁 Where, Xij = Shows the Observation T2/N = Correction Factor (CF) 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 11
  • 12. ANOVA(CONT..) 2. Calculate the variance b/w the samples(SSC) 𝑆𝑆𝐢 = 𝐢𝑗2 β„Ž βˆ’ 𝑇2 𝑁 Where, Cj = sum of jth column h = No of rows 3. Calculate the variance within the samples 𝑆𝑆𝐸 = 𝑆𝑆𝑇 βˆ’ 𝑆𝑆𝐢 4. Calculate the F-Ratio 𝐹𝑐 = 𝑆𝑆𝐢 π‘˜ βˆ’ 1 Γ· 𝑆𝑆𝐸 𝑁 βˆ’ π‘˜ k-1 = Degree of Freedom 5. Compare Fc Calculated with the FT (Tabulated Value) If Fc<FT, accepted H0. If H0 is accepted it can be concluded that the difference is not significance and hence could have arisen due to fluctuation of random sampling. 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 12
  • 13. ANOVA(CONT..) All the information about the analysis of variance is summarized in the following ANOVA table: 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 13 Sources of Variation Sum of square (SS) Degree of Freedom (d.f.) Mean Square (M.S.) Variance Ration of F Variance Ration of F SSC k-1 𝑀𝑆𝐢 = 𝑆𝑆𝐢 π‘˜ βˆ’ 1 Within the sample SSE N-k 𝑀𝑆𝐢 = 𝑆𝑆𝐸 𝑁 βˆ’ π‘˜ Total SST N-1 MSC = Mean Sum of Square b/w samples MSE = Mean Sum of Square within samples
  • 14. MANOVA β€’ MANOVA = Multivariate Analysis of Variance β€’ This is generally applied to different groups of date. β€’ Here we compared the variance of different groups of data & predict weather the data are comparable or Not β€’ Minimum Three sets of data are required. Here first we have to find the variance within each individual group & then compare with each other β€’ It generally calculated with software after calculating ANOVA by wilk’s Lambda equation; β€’ Wilk’s Lambda = E H+E β€’ E = error some of square and cross production matrix β€’ H = hypothesis sum of square and cross production matrix 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 14
  • 15. C. MATHEMATICAL MODEL DEPENDANT METHODS β€’ For quantitative interpretation of values obtained as dissolution assays is easier to using following mathematical models/Equations, which describe the release profile which further relate to all types dosage forms. Like; a. ZERO ORDER KINETICS MODEL b. FIRST ORDER KINETICS MODEL c. SECOND ORDER KINETICS MODEL d. WEIBULL MODEL e. HIGUCHI MODEL f. HIXON-CROWELL MODEL g. KORSMEYER- PEPPAS MODEL h. BAKER- LANSODALE MODEL i. HOPFENBERG MODEL j. QUADRATIC MODEL k. LOGISTIC MODEL l. GOMPERTZ MODEL m. HOPFENBERG MODEL 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 15
  • 16. ZERO ORDER KINETICS MODEL β€’ Zero Order API release contributes drug release from dosage for that is independent of amount of drug in delivery system (i.e. constant drug release) β€’ Drug Release Rate is independent of Concentration β€’ Graphically we will get always of a Straight line within %CDR Vs Time β€’ Equation: π‘Š0 βˆ’ π‘Šπ‘‘ = 𝐾𝑑 Where, W0 = Initial amount of drug in dosage form Wt = Amount of drug in the dosage form at time β€œt” K = Proportionality t β€’ This Equation can written as, 𝑄𝑑 = 𝑄0 + 𝐾0 𝑑 Where, Qt = The amount of drug dissolved in time t Q0 = Initial amount of drug in the solution K0 = Zero Order Constant (Mostly it is considered as ZERO) 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 16 100% 0% Cumulative%ofDrug Release Time in Hrs.
  • 17. ZERO ORDER KINETICS MODEL (CONT..)β€’ This release is achieved by making; β€’ Reservoir Diffusion System β€’ Osmotically Controlled Devices β€’ EXAMPLES WHERE IT IS APPLIED: β€’ Transdermal DDS β€’ Implantable Depot. β€’ Oral Control Release β€’ Matrix Tablet with low solubility drug β€’ Suspension β€’ Oral osmotic pressure 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 17
  • 18. FIRST ORDER KINETICS MODEL 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 18 β€’ Used to describe absorption and/or elimination of some drugs, although it is difficult to conceptualise this mechanism in a theoretical basis. β€’ The dissolution phenomenon of a solid-particle in a liquid media implies a surface action & seen by Noyes-Whitney Equation: 𝑑𝐢 𝑑𝑑 = 𝐾 𝐢𝑠 βˆ’ 𝐢 β€’ Where, dC/dt = Dissolution Rate Cs = Solubility at Max/ Saturation or Concentration of drug at stagnant layer C = Drug concentration in Bulk of solution in time t β€’ At Sink condition = dissolution rate limiting step for in-vitro study absorption = dissolution rate limiting step for in-vitro study, so this equation will be, 𝑑𝐢 𝑑𝑑 = 𝐾 𝐢𝑠 = πΆπ‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘ β€’ So it becomes , 𝑄𝑑 = 𝑄0. π‘’βˆ’πΎπ‘‘ Where, Qt = Drug dissolved in time t Q0 = Initial drug concentration K = Constant at time t
  • 19. FIRST ORDER KINETICS MODEL (CONT..) β€’ USED IN GENERALLY MOSTLY; β€’ Water soluble drugs in porous matrix β€’ Low Water soluble drug in porous matrix 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 19
  • 20. WEIBULL MODEL β€’ This equation can be successfully applied to almost all kinds of dissolution curves by preceding equation; log βˆ’ln(1 βˆ’ π‘š) = 𝑏 Γ— log(𝑑 βˆ’ 𝑑𝑖) βˆ’ log π‘Ž Where, β€’ m = cumulated fraction of drug in solution at time t β€’ a = time scale parameter or time scale of process, it can be replaced by more informative dissolution time (td) or ordinate value in graph, a can be calculated by formula; π‘Ž = 𝑇𝑑 𝑏 , Where Td is time necessary to dissolve or release 63.2% of drug from dosage. β€’ Ti = Location parameter or lag time before onset of dissolution or release process & it is mostly zero β€’ b = shape parameter or slop of line in graph If b = 0 then Curve as either exponential If b > 1 then sigmoid shape with upward curvature followed by a turning point If b < 1 then parabolic with higher initial slop & after that consistent with exponential 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 20
  • 21. WEIBULL MODEL (CONT..) β€’ USED FOR, β€’ Almost all type of dissolution curve β€’ CRITICISM: β€’ There is not any kinetic fundamental and could only describe, but does not adequately characterize, the dissolution kinetic properties of the drug β€’ There is not any single parameter related with the intrinsic dissolution rate of drug β€’ It is of limited use for establishing in in-vivo/ in-vitro correlation 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 21
  • 22. HIGUCHI MODEL β€’ Higuchi proposed this model in 1961 to describe the drug release from matrix system β€’ It is assume that these system are neither surface coated nor that their matrices undergo a significant alteration in the presence of water. β€’ Equation: 𝑓𝑑 = 𝑄 = 𝐴 𝐷 2𝐢 βˆ’ 𝐢𝑠 𝐢𝑠. 𝑇 β€’ Where, β€’ Q = Amount of drug release in time t per unit area A β€’ C = Initial drug Concentration β€’ Cs = Drug solubility in Matrix media β€’ D = Diffusivity of the drug molecules 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 22
  • 23. HIGUCHI MODEL (CONT..) β€’ IT IS DEVELOPED TO STUDY THE RELEASE OF β€’ Diffusion Matrix system: β€’ Homogenous matrices of Suspension from ointment base β€’ Planar or spherical system having a granular heterogenous matrix β€’ Water soluble drugs incorporated in semi-solid or solid matrix β€’ Low water soluble drug incorporated in semi-solid or solid matrix β€’ Too accordance with other all types dissolution from other pharmaceutical dosage forms 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 23
  • 24. HIXON-CROWELL MODEL β€’ To evaluate the drug release with change in the surface area and the diameter of the particles/ tablets β€’ The rate of dissolution depends on the surface of solvent so THE LARGE IS AREA THE FASTER IS DISSOLUTION. β€’ Both scientist recognized that Particle regular area is proportional to the cubic root of its volume, so describe a equation for easier, 𝑀0 1 3 βˆ’ 𝑀 1 3 = 𝐾 Γ— 𝑑 Where, M0 =Original mass of API Particles K = Cubic root dissolution rate constant M = Mass of the API at the time β€˜t’ 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 24
  • 25. HIXON-CROWELL MODEL (CONT..) β€’ APPLICABLE FOR β€’ Polymeric matrix system β€’ Erodible Matrix Formulations Note: when this model is, it is assumed that the release rate is limited by the drug particles dissolution rate and not by the diffusion that might occur through the polymeric matrix. 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 25
  • 26. BAKER- LANSODALE MODEL β€’ In 1974 Baker- Lonsdale developed the model from Higuchi model and given equation; 3 2 1 βˆ’ 1 βˆ’ 𝑀𝑑 π‘€βˆž 2 3 βˆ’ 𝑀𝑑 π‘€βˆž = 3. 𝐷 π‘š. 𝐢 π‘šπ‘  π‘Ÿ0 2. 𝐢0 t Where, β€’ Mt = Drug Release at time t β€’ M∞ = Drug Release at infinite time β€’ Dm = Diffusion coefficient β€’ Cms = Drug solubility in matrix β€’ R0 = Radius of spherical matrix β€’ C0 = Initial concentration at matrix 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 26
  • 27. BAKER- LANSODALE MODEL (CONT..) β€’ THIS EQUATION HAS BEEN USED TO β€’ Linearization of release data of Microcapsules β€’ Linearization of release data of Microspheres β€’ Matrix system formulations 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 27
  • 28. HOPFENBERG MODEL β€’ Model explain rate limiting step of drug release is erosion of matrix itself β€’ Time dependant diffusional resistance internal or external to eroding matrix do not influence it. Or simply called as Modified Las time, it calculated by following equation, 𝑀𝑑 π‘€βˆž = 1 βˆ’ 1 βˆ’ 𝐾0 𝑑 𝐢0 π‘Ž0 𝑛 Where, β€’ Mt = Drug dissolved in time t β€’ M∞ = Drug dissolved in infinite time β€’ Mm /M∞ = Fraction of drug dissolved β€’ a0 = Initial Radius of sphere or cylinder or half thickness for a slab β€’ C0 = Initial concentration at matrix β€’ n = 1, 2, 3 for a slab, cylinder, and sphere respectively 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 28
  • 29. HOPFENBERG MODEL (CONT..) β€’ CALCULATION OF DRUG RELEASE FROM SURFACE ERODING DEVICE WITH DIFFERENT GEOMETRIC, LIKE β€’ Slab β€’ Sphere β€’ Infinite cylinder display heterogenous erosion 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 29
  • 30. KORSMEYER- PEPPAS MODEL β€’ The simple relationship which describe the drug release from the polymeric system equation was derived by Korsmeyer et. al. in 1983 β€’ It is used to describe the first 60% release of drug from dosage form β€’ Equation: 𝑀𝑑 π‘€βˆž = π‘Žπ‘‘ 𝑛 + 𝑏 β€’ Where, β€’ Mt/M∞ = Fraction of drug release at time β€œt” β€’ a = constant incorporating structure or geometrical characteristics of drug dosage form β€’ n = Release Exponent β€’ n value is used to characterize the drug release for cylindrical matrices and the n value characterize the release mechanism of drug as described. 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 30
  • 31. KORSMEYER- PEPPAS MODEL (CONT..) β€’ n value is used to characterize the drug release for cylindrical matrices and the n value characterize the release mechanism of drug as described; β€’ n is estimated as linear regression of Log (mt/m) Vs Log T 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 31 100% 0% Log%ofdrugrelease Log time in Hrs. Release exponents(n) Indications or drug transport mechanism Rate as a function of time Less than 0.45 (<0.45) Quasi fickian - 0.45 Fickian Diffusion T-0.5 0.45 < n < 0.89 Non Fickian diffusion tn-1 0.89 to 1 Zero Order Non fickian case 2 Zero order release More than 1 (>1) Non Fickian super case 2 tn-1
  • 32. KORSMEYER- PEPPAS MODEL (CONT..) β€’ USED IN; β€’ Could be predicted the best model for the release of drug from the dosage form β€’ Different Pharmaceutical Modified release dosage forms β€’ Polymeric system formulations 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 32
  • 33. D. RELEASE PROFILE COMPARISION OR MODEL INDEPENDENT METHODβ€’ Model independent Method can be further differentiated to β€’ RATIO TEST β€’ Ratio of Area Under the Curve (AUC) β€’ Mean Dissolution Time(MDT) β€’ PAIR-WISE PROCEDURES β€’ F1 = Difference Factor β€’ f2 = Similarity Factor β€’ ΞΎ1 = Rescigno index or bioequivalence index 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 33
  • 34. RATIO TEST β€’ Parameters from release assay of reference & test at same point(Tx%). β€’ Taken Ratio of AUC of both reference & Test Product Or β€’ Ratio of Mean Dissolution Time (MDT) 𝑀𝐷𝑇 = 𝑗=1 𝑛 βˆ†π‘€π‘— 𝑑𝑗 𝑗=1 𝑛 βˆ†π‘€π‘— Where, j = sample No n = No. of sample time tj = Midpoint b/w tj & T(j-1) βˆ†Mj = Drug dissolved 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 34
  • 35. PAIR WISE PROCEDURE β€’ Pair wise procedure includes β€’ F1 VALUE: DIFFERENCE FACTOR β€’ F2 VALUE: SIMILARITY FACTOR β€’ RESCIGNO INDEX OR BIOEQUIVALENCE INDEX (ΞΎ1 & ΞΎ2 ) β€’ These F1 & F2 equations described by Moore & Flamner and ΞΎ1 & ΞΎ2 by Rescigno. β€’ Both F1 & F2 equations are endorsed by FDA as acceptable method for dissolution profile comparison β€’ They are used to study the comparison of dissolution profiles of the two dosage forms. β€’ It can be calculated using Excel or various readymade software (E.g.: PhEq_bootstrap) and Rescigno index too calculated by Software. 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 35
  • 36. DIFFERENCE FACTOR (F1) β€’ It calculate % difference b/w two curves at each time point & measure relative error b/w two curves. β€’ F1 equation is sum of absolute values of vertical distance b/w reference (Rt) & Test (Tt) mean % release values i.e. (Rt-Tt) at each dissolution points. β€’ The f1- Value is equal to zero to zero when the test and reference profiles are identical & increase as the profile β€’ Equation 𝑓1 = 𝑑=1 𝑛 𝑅𝑑 βˆ’ 𝑇𝑑 𝑑=1 𝑛 𝑅𝑑 Γ— 100 Where, Rt = Reference Dissolution Value n = No of dissolution time points Tt = Test dissolution value 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 36
  • 37. SIMILARITY FACTOR (F2) β€’ f2 equation is logarithmic transformation of average squared vertical distance b/w reference & test mean dissolution values at each time point, multiplied by an approximate weighting i.e. Wt(Rt-Tt). β€’ Equation: 𝑓2 = 50log10 1 + 1 𝑛 𝑑=1 𝑛 π‘Šπ‘‘(𝑅𝑑 βˆ’ 𝑇𝑑)2 βˆ’0.5 Γ— 100 Where, Rt = Reference Dissolution Value n = No of dissolution time points Tt = Test dissolution value Wt = Optional weighting Factor 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 37
  • 38. WHEN ARE DISSOLUTION PROFILE SIMILAR..?? β€’ If in both Test & Reference product shows dissolution more than or equal to 85% (β‰₯ 85%) within 15min, then β€’ Profiles are considered to be similar β€’ No further calculations required β€’ F1 value limit : 0% to 15% β€’ F2 Value limit : β‰₯ 50% 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 38
  • 39. ADDITIONAL REQUIREMENTS FOR F1 & F2 β€’ At least 12 unit should used β€’ Same test conditions should maintained β€’ Dissolution time points for Immediate Release(IR) products like 5, 15,30, 60 min β€’ For Sustained Release(SR) Products, 1, 2, 3, 5, 8 Hrs. etc. until at least 85% of drug is released β€’ Only one measurement should considered after 85% dissolution of drug β€’ Standard Deviation (DV): β€’ ≀20% at early time points β€’ ≀10% at later time points 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 39
  • 40. EXAMPLE FOR F1 & F2 Time Rt Tt (Rt-Tt) (Rt-Tt)2 10 45 55 10 100 15 65 75 10 100 20 80 90 10 100 30 90 100 10 100 𝑅𝑑 = 280 𝑅𝑑 βˆ’ 𝑇𝑑 = 40 (𝑅𝑑 βˆ’ 𝑇𝑑)2 = 400 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 40 By putting Data in Eq. we will get; F1 =14 F2 =50 Insert No of points where both products β‰₯85% Rt = Cumulative % dissolved of reference product at time t Tt = Cumulative % dissolved of test product at time t
  • 41. RESCIGNO INDEX β€’ Also called as bioequivalence Index generally used in CR formulations β€’ Used to measure dissimilarity b/w Reference & Test product based on PDC & time β€’ Equation; ξ𝑖 = 0 ∞ 𝑑 𝑅 𝑑 βˆ’ 𝑑 𝜏(𝑑) 𝑖 𝑑𝑑 0 ∞ 𝑑 𝑅 𝑑 + 𝑑 𝜏(𝑑) 𝑖 𝑑𝑑 1 𝑖 Where, dR t = Reference Product Dissolved amount dΟ„(t) = Test product dissolved at each sample time points β€’ This Rescigno index always lies b/w 0 & 1 (0< ξ𝑖<1) β€’ If ξ𝑖 = 0 then Two profiles are similar β€’ If ξ𝑖 = 1 then either test or reference not release at all 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 41
  • 42. E. OTHER RELEASE PARAMETER I. RELEASE TIME (tX%) : β€’ Time Necessary to release determine % of Drug E.g.: 20% of drug in pre-planned time II. SAMPLING TIME (AX%): β€’ The amount of drug w.r.t. time tx% E.g.: X amount of drug released in 20min III. DISSOLUTION EFFICIENCY (DE): β€’ The area under the dissolution curve upto a certain time t, expressed as % of area of rectangle describe the 100% dissolution in the same time. 𝐷𝐸 % = 𝑆𝐴 𝑅 Γ— 100 β†’ 𝐷𝐸 % = 0 𝑑 π‘Œ. 𝑑𝑑 π‘Œ100. 𝑑 Γ— 100 Where, β€’ SA = Shaded Area β€’ R= Rectangle Area 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 42
  • 43. SUMMARY S. No. Model Name Graph to be Estimated Equation Application for 1 Zero Order Kinetic Model Cumulative Release Vs Time 𝑄𝑑 = 𝑄0 + 𝐾0 𝑑 TDDS, Coating, Osmotic System 2 First Order Kinetic Model Log Cumulative Release Vs Time 𝑄𝑑 = 𝑄0. π‘’βˆ’πΎπ‘‘ Water soluble & Low soluble drugs in porous matrix 3 Second Order Kinetic Model Release amount Fraction to infinite time Vs real time 𝑄𝑑 π‘„βˆž = π‘„βˆž βˆ’ 𝑄𝑑 . 𝐾2 𝑑 NA 4 Weibull Model Log Cumulative Release Vs Log Time log βˆ’ln(1 βˆ’ π‘š) = 𝑏 Γ— log(𝑑 βˆ’ 𝑑𝑖) βˆ’ log π‘Ž Almost all type of dissolution curves 5 Higuchi Model % Cumulative Relase Vs (Time)1/2 𝑓𝑑 = 𝑄 = 𝐴 𝐷 2𝐢 βˆ’ 𝐢𝑠 𝐢𝑠. 𝑇 Diffusion Matrix formulation 6 Hixon – Crowell Model %CRt/CR∞ Vs (Time)1/2 𝑀0 1 3 βˆ’ 𝑀 1 3 = 𝐾 Γ— 𝑑 Erodible matrix formulation 7 Korsmeyer – Peppas model (Unreleased fraction)1/3 Vs Time 𝑀𝑑 π‘€βˆž = π‘Žπ‘‘ 𝑛 + 𝑏 MR Dosage forms 8 Baker – Lonsdale Model Mt/M∞ Vs Time 3 2 1 βˆ’ 1 βˆ’ 𝑀𝑑 π‘€βˆž 2 3 βˆ’ 𝑀𝑑 π‘€βˆž = 3. 𝐷 π‘š. 𝐢 π‘šπ‘  π‘Ÿ0 2. 𝐢0 t Microsphere, Microcapsules 9 Hopfenberg Mt/M∞ Vs Erosion Time 𝑀𝑑 π‘€βˆž = 1 βˆ’ 1 βˆ’ 𝐾0 𝑑 𝐢0 π‘Ž0 𝑛 Erosion matrix itself 10 Gompertz %dissolved Vs Max dissolution w.r.t. time 𝑄𝑑 = 𝐴. π‘’βˆ’π‘’βˆ’πΎ(π‘‘βˆ’π‘Œ) Comparing b/w good & intermediate release 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 43
  • 44. REFERENCE β€’ Brahmankar D.M., Jaiswal S. B., 2013. Biopharmaceutics & Pharmacokinetics a treatise, Vallabh Prakashan 32 ISBN 978-81-85731-47-6 β€’ Costa P., Lobo J.M.S., 2000. Modelling & Comparison of dissolution profiles, EJPS 12 (2001) 123-133 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 44
  • 45. 26-09-2019Mahendra Pratap Swain, PHDPD100102019, BIT-MESRA, RANCHI 45 Thanking You..!! For your attention