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Similarity factor, higuchi plot, peppas plot

This document summarizes various mathematical models used to analyze drug release kinetics from pharmaceutical dosage forms. It discusses the Higuchi, Korsmeyer-Peppas, and difference factor (f1) and similarity factor (f2) models. The Higuchi model describes drug release from a matrix based on square root of time. The Korsmeyer-Peppas model characterizes drug release mechanisms based on the release exponent n value. The f1 and f2 factors are used to compare dissolution profiles between two drug products.

Education◦
Prepared By:- Garje Mahesh Arjun Roll No.: 04 M. Pharm Sem-1 (Pharmaceutics) Guide:- Prof. A.W. Ambekar M. Pharm Dept. of Pharmaceutics Dr. Vithalrao Vikhe Patil Foundation's College of Pharmacy Vilad Ghat, Ahmednagar
Introduction Dissolution:- The process in which a solid drug substance solubilises in given solvent i.e. mass transfer from solid surface to liquid phase. Rate of dissolution:- Amount of drug substance that goes in the solution per unit time under standardised condition of liquid pH , solvent, temperature. 1
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To study the release of drug in desired amount from dosage form. To study the uniformity of drug release from dosage form of different batches. To show that drug release is equivalent to those batches proven to be bioavailable and clinically effective. 33
1. Model independent method:- F1 and f2 comparison 2. Graphical method 3. Statistical method 4. Zero order kinetic model 5. 1st order kinetic model 6. Higuchi model 7. Hixson- Crowell model 8. Korsmeyar Peppas model 4
Difference factor f1 and similarity factor f2  These equations described by Moore and Flamner  Both equations are endorsed by FDA as acceptable method for dissolution profile comparison.  f1 value – difference factor  f2 value – similarity factor  They are used to study the comparison of dissolution profiles of the two dosage form.  It can be calculated using Excel or various readymade software's (E.g. PhEq_bootstrap) 5
 It calculate % difference between two curves at each time point & measure relative error between two curves.  f1 equation is sum of absolute values of vertical distance between reference(Rt) and test(Tt) mean % release values i.e. (Rt-Tt) at each dissolution point.  Equation:- Where, Rt:-Reference dissolution value, N:- No. of dissolution time point Tt:- Test dissolution value 66
 f2 equation is logarithmic transformation of average squared vertical distance between reference and test mean dissolution values at each time point, multiplied by an approximate weighting i.e. Wt(Rt-Tt)  Equation:- Where, Rt-Reference dissolution value, n- No. of dissolution time point Tt- Test dissolution value Wt- Optional weighting factor 7
1. If both the test and reference product show ≥ 85% dissolution within 15 minutes,  the profiles are considered to be similar  No calculations are required 2.f1 value(difference Factor):-  if f1=0 to 15 3. f2 value (similarity factor):-  If f2 ≥ 50 , the profiles are regarded similar. 8
Additional Requirements  At least 12 unit should used .  Same test conditions should maintained.  Dissolution time points for Immediate Release products like 15,30,45,60 min  For sustained release 1, 2, 3, 5, and 8 hrs until at least 85% of drug is released.  Only one measurement should considered after 85% dissolution of drug.  SD: ≤ 20% at early time point & ≤ 10% at later time points 99
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 45 0 0 60 0 0 Sum Of (Rt-Tt)=40 Sum of (Rt-Tt)2=400 Sum of Rt=280 Difference Factor f1= 14 Similarity Factor f2=50 No of time points: 04 Insert No of points where both products ≥85 % Rt= Cumulative % dissolved of reference product at time t Tt= Cumulative % dissolved of Test product at time t Example: 1010
In 1961 Higuchi developed mathematical model for study of release of drug from its matrix.  Initial drug concentration in matrix is much higher.  As drug is released distance for diffusion is progressively increases.  Drug is leached out polymer matrix by entrance of surrounding medium.  In release environment perfect sink is maintained. 1111
 The Equation Of Higuchi model: Q= [D(2A-Cs)Cs×t]1/2 or Q=(2ADCst)1/2 By differentiating above equan we get, dQ/dt=(ADCs/2t)1/2 The Drug release from granular matrix is given by Where, dQ/dt – rate of drug release Cs- Solubility of drug in matrix A- Total Concentration of drug in matrix D- Diffusion Coefficient t- Time, ε -porosity of matrix, τ-Tortuosity 1212
Example  Problem:- 1.What is amount of drug per unit area released from tablet matrix at time t= 120 ? Total concentration in homogeneous matrix A is 0.02 g/cm3. Solubility Cs is 1.0×10-3 g/cm3 in polymer. Diffusion coefficient d at 250c is 360×10-6 cm2/min.  Solution:- we have equation Q= (2ADCst)1/2 = [ 2 (0.02 g/cm3) (360×10-6 cm2/min) (1×10-3 g/cm3) (120 min) ]1/2 Q= 1.3 × 10-3 g/cm2 1313
 Problem.2: What is instantaneous rate of release of drug occurring at 120 min?  Solution:- We have equation, dQ/dt = (ADCs/2t)1/2 =[ (0.02)(360×10-6)(1.0×10-3)/ 2×120]1/2 = 5.5×10-6 gcm-2min-1 1414
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 / M∞ = k. tn  Mt / M∞ = 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 15 15
 The n value characterises different releases from matrix and specify release mechanisms as shown below  To study release kinetic data obtained plotted as log cumulative % drug release versus time.  Application: To study modified release dosage form and release phenomenon of drug. Release Exponent (n) Drug transport mechanism 0.5 Fickian diffusion 0.5<n=0.89 Non Fickian transport 0.89 Case II transport Higher than 0.89 Super case II transport 1616
References  Sinko PJ, Singh Y , “Martin’s Physical Pharmacy and Pharmaceutical Sciences”, Fifth edition, Lippincott Williams and Wilkins , p. 344 to 346.  Lachman L, Lieberman HA, “Theory And Practice Of Industrial Pharmacy” Fourth Edition, Reprint 1991, Varghese Publishing House; p. 205, 206, 207.  Bramhankar DM, Jaiswal SB , “Biopharmaceutics and Pharmacokinetics-A Treatise”, Third Edition, Reprint 2016, Vallabh Prakashan; p.334-336, 434-437. 17
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