Dissolution Analyses: Comparison of Profiles Using f2 Analysis Calculation

A dosage form is the form in which a drug is produced and dispensed; for example, tablet, capsule or suspension. The rate and extent to which the amount of drug substance dissolved over a period of time is called dissolution. Dissolution testing is the primary pharmaceutical test that is designed to probe the performance of dosage forms.  The dissolution method developed is compared with the innovator’s reference product to evaluate the release pattern and establish the method comparison for estimating the drug release. The purpose of this article is to provide some insight into the comparison of dissolution profiles using f2 analyses.

Dissolution profile comparison: Why is it so important?

Under appropriate test conditions, a dissolution profile can characterize the product more precisely than a single point dissolution test. It has extensive applications throughout the product development process and FDA has been requesting it for post-approval changes. It establishes a comparison between batches of pre-change and post-change (e.g. formulation change or manufacturing site change) and helps assure similarity in product performance.

Guidance for industry

The model developed by Moore and Flanner is used to compare the dissolution profile using two factors, f1 and f2 (1) following the FDA guidance for comparing the dissolution profiles (2, 3). A profile comparison is not necessary for products that are rapidly dissolving (i.e., more than 85% in 15 minutes or less).

The difference factor (f1) calculates the percent (%) difference between the two curves at each time point and is a measurement of the relative error between the two curves.

The similarity factor (f2) is a logarithmic reciprocal square root transformation of the sum of squared error and is a measurement of the similarity in the percent (%) dissolution between the two curves.

Statistical calculations

Where n = number of time points, R_t = % Active Pharmaceutical Ingredient (API) dissolved of reference product at time point x, T_t = % API dissolved of test product at time point x.

Data structure and steps to follow:

1. This model-independent method is most suitable for the dissolution profile comparison when three to four or more dissolution time points are available.
2. Determine the dissolution profile of two products (12 units each) of the test (post-change) and reference (pre-change) products.
3. Using the mean dissolution values from both curves at each time interval, calculate the difference factor (f1) and similarity factor (f2) using the above equations.
4. 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 two curves and, thus, of the performance of the test (post-change) and reference (pre-change) products.
5. In dissolution profile comparisons, especially to assure similarity in product performance, the regulatory interest is in knowing how similar the two curves are, and to have a measure which is more sensitive to large differences at any particular time point. For this reason, the f2 comparison has been the focus in agency guidance and used to make a decision.

Some recommendations:

1. The dissolution measurements of the test and reference batches should be made under exactly the same conditions.
2. The dissolution time points for both the profiles should be the same (e.g. 15, 30, 45, 60 minutes).
3. The reference batch used should be the most recently manufactured pre-change product.
4. Only one measurement should be considered after 85% dissolution of both the products (when applicable).
5. To allow use of mean data, the percent coefficient of variation (% CV) at the earlier time points (e.g. 15 minutes) should not be more than 20%, and at other time points should not be more than 10%.
6. The mean dissolution values for reference can be derived either from last pre-change batch or the last two or more consecutively manufactured pre-change batches.

 Example of a study design

As per the method, twelve chewable (n=12) were analyzed for each lot (Normal and Test). The dissolution measurements of the two profile comparisons were made under the same test conditions (e.g. temperature). The sampling time intervals for both the profiles were similar (15, 30, 45, 60 and 90 minutes).  The data, calculations and profile plot is presented below.

Table1: Data

Table 2: Calculations

Figure 1: Dissolution profile plot

Observations:

All the time points until 90 minutes were used in the f2 calculation since more than 85% dissolution mean was seen for both the formulations by 60 minutes. For both the profiles, the % CV at the earlier point (e.g. 15 minutes) was not more than 20% and at other time points was not more than 10%. The calculated f1 value was equal to 2 and f2 value was equal to 85 (f2 values greater than 50 ensure sameness or equivalence of the two curves).

Conclusion

The normal and the test change dissolution profiles for chewable were similar as f2 was 85.

References

1. W.Moore and H.H.Flanner, Mathematical Comparison of curves with an emphasis on in vitro dissolution profiles. Pharm. Tech. 20(6): 64-74, 1996.
2. Guidance for Industry: Dissolution Testing of Immediate Release Solid Oral Dosage Forms U.S. Department of Health and Human Services Food and Drug Administration Center for Drug Evaluation and Research (CDER) August 1997.
3. Guidance for Industry: Waiver of In Vivo Bioavailability and Bioequivalence Studies for Immediate-Release Solid Oral Dosage Forms Based on a Biopharmaceutics Classification System. Draft Guidance May 2015