# Comparison of dissolution profiles using f1 and f2 factors

The primary constraint for comparison of two products or formulations or dosage forms is the in vitro dissolution profile. For comparison of in vitro dissolution profiles, similarity and difference factors are emphasized by US FDA.

Similarity Factor (f2)1, 2, 3:

As the name specifies, it stresses on the comparison of closeness of two comparative formulations.Generally similarity factor in the range of 50-100 is acceptable according to US FDA. It can be computated using the formula

f2= 50xlog {[1+ (1/n) S t=1n (Rt-Tt) 2] -0.5 x100}........(1)

where, n is the number of dissolution sample times,

Rt and Tt are the individual or mean percent dissolved at each time point, t, for the reference and test dissolution profiles, respectively.

The similarity factor should be between 0 and 100. It is 100 when two comparative groups of reference and test are identical and approaches 0 as the dissimilarity increases.

Difference Factor (f1)1, 2:

Difference factor focuses on the difference in percent dissolved between reference and test at various time intervals. It can be mathematically computed by using

f1= {[S t=1n |Rt-Tt|] / [S t=1n Rt]} x100................(2)

Therefore the factors directly compare the difference between percent drug dissolved per unit time for a test and a reference product.

US FDA included the f1, f2 factors in various guidance documents and stated different criterias for dissolution profile comparison as 4, 5

1. The dissolution profiles can be compared only when number of dissolution units used are equal to or greater than 12. The similarity factor should be computed from the average mean dissolution data of 12 units. The mean data for comparison can be used only if the coefficient of variation at the first time point is NMT 20%, and NLT 10% at the rest of time intervals.

2. For accurate calculation of similarity factor, statistical approach of establishment of confidence intervals, to determine whether the reference and test are statistically significant or not may be used.

3. The dissolution conditions should be identical for both reference and test products (example the strength of dosage form, test time intervals, temperature, rpm, total test time etc).

4. The literature also states to consider only one time after 85% dissolution of product, since f2 values are sensitive to number of dissolution time points.

5. For rapid dissolving products, that may dissolve 85% in 15 minutes, comparison of dissolution profiles is not mandatory.

6. Similarity factor of 50-100 ensures sameness of two products

7. Difference factor of 0-15 ensures minor difference between two products.

Prior to in vivo study, comparison of in vitro dissolution profiles using similarity and difference factors may be the promising surrogate.

References:

1. Yuksel N, Kanik AE, Baykara T, Comparison of in vitro dissolution profiles by ANOVA-based, model-dependent and -independent methods, Int J Pharm, 209, 2000, 57-67.

2. Costa P & Jose MSL, Modeling and comparison of dissolution profiles, Eur J Pharm Sci, 13, 2001, 123-133.

3. Ocana J, Frutos G & Sanchez O P, Using the similarity factor f2 in practice: A critical revision and suggestions for its standard error estimation, Chemometrics and Intelligent Laboratory Systems, 99, 2009, 49-56.

4. Costa P, An alternative method to the evaluation of similarity factor in dissolution testing, Int J Pharm, 220, 2001, 77-83.

5. O Hara T, Dunne A, Butler J & Devane J, A review of methods used to compare dissolution profile data, Pharmaceutical Science & Technology Today, 1(5), 1998, 214-223.

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Abbreviations:

NMT - Not more than

NLT - Not less than

 Author: TK Indira Indu Roy is post graduate in pharmacy and working as Research Officer, Formulation-IPR Department at Mylan Laboratories Limited (A subsidiary of Mylan Inc) . G Profile : https://plus.google.com/105328821168414118220/about

### Quite a brief summary of the

Quite a brief summary of the similarity and dissimilarity factors. Thank you for sharing.

Regards, Niklesh Rao V

### Simple and short.....

Dear Indira, It was a gud presentation.Thanq for the info. Regards

ABHIGNA.P.V.

### Why f1 factor

Dear Indira, nice information. Can u you explanation for the range why F1 factor value 0-15 is accepatble. can we increase this range for any special formulation e.g. 0-20 or other? If you optimise any two formulation and u seen for 1st f1 is 12 and f2 is 80, other f1 is 6 and f2 is 55. which formulation you accept or select for further development? Regards,

### Dear amol sir

Thank you for your comment. Well coming to the queries, 1) f1 factor is difference factor, so it indicates the statistical difference between percent mean dissolved at various time intervals. So, the guidance documents stated that the mean data for comparison can be used only if the coefficient of variation at the first time point is NMT 20%, and NLT 10% at the rest of time intervals. So, statistically when the range is calculated, the resultant value is 0-15. So, if the range is increased then, the confidence limits have to be increased which may lead to increased error calculations and intern the difference between comparative groups. Therefore, the limits are established according to the guidance documents. 2) Yes if we optimize any two formulations resulting in values you specified, i would definitely select both the formulations, as both of them are within the limits. Beacuse in the first formulation though difference is high and similarity is high. Where as in second formulation difference is small and similarity is within the limits. So, best way would be selecting the two formulations for further studies like invivo. The one that gives the best bioavailability in in vivo might be selected as appropriate at the end (It is not mandatory that formulations with high similarity factor in vitro should result in high bioavailability in in vivo. Alternative way is to select the second formulation for further development (since it gives a small difference between reference and test).Its intern the in vivo studies that decides finally. The formulation that gives more bioavailability should be considered as the best formulation with f1 and f2 factors within limits. One more thing i would like to share with you sir. I was informed from the F-R&D scientists that maximum f2 factor that might be obtained would be within 80-85. They said that it would be really difficult to obtain the similarity higher than 85. You are most welcome for further discussion sir.

T.K. Indira. http://www.pharmainfo.net/tkindira

-- "Our greatest glory is not in never falling, but in rising every time we fall..." Team 'Char'minar.

### YA that what I expect

Dear Indira, Good explanation! I know it very difficult to obtain higher than 80-85% similarity factor. because I also experience when we r comparing with reference/innovator with our formulation, we also able to get 75% it is real diffucult to go beyond that. That what formulation is easy but proper formulation is not so.... Regards,

### Good knowledge for initial stage

Dear indira mam, i would realy appreciate u for this. it gives very good overview of f1 and f2 factor for those who wants a quick knowledge

Dulichand