# Discriminative Dissolution Method Using the Open-Loop Configuration of the USP IV Apparatus to Compare Dissolution Profiles of Metoprolol Tartrate Immediate-Release Tablets: Use of Kinetic Parameters

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^{2}

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## Abstract

**:**

_{max}, AUC

_{0}

^{∞}, AUC

_{0}

^{Cmax,}and T

_{max}(kinetic parameters) of the generic/reference drugs, whereby generic drugs “C” and “D” presented the highest probability of similarity since their 90% confidence intervals were included, or they were very close to the acceptance interval (80.00–125.00%). These results were consistent with the f

_{2}, bootstrap f

_{2,}and dissolution efficiency approaches (independent models). In conclusion, the proposed comparison method can be an important tool to establish similarity in dissolution profiles and to facilitate the development/selection of new formulations and positively ensure bioequivalence in clinical studies.

## 1. Introduction

_{2}) when the variability of the dissolution profiles complies with what is established in the guidelines [10]. However, when the variability in the dissolution profiles is high, there is no single comparison method, since the EMA prefers to use the bootstrap f

_{2}approach and the FDA establishes the use of multivariate methods and dependent models, that is, still the comparison methods have not been homologated [1,11].

## 2. Materials and Methods

#### 2.1. Materials

^{®}100 (“A”, Novartis Farmacéutica, Mexico City, Mexico, Lot N0059) as the reference drug and four generic drugs: Kenaprol

^{®}(“B”, Laboratorios Kener, Mexico City, Mexico, lot M07410); Proken

^{®}(“C”, Laboratorios Kendrick, Mexico City, Mexico, lot OJS957); Nipresol

^{®}(“D”, Bruluart, Mexico City, México, lot 01052); and Metobest

^{®}(“E”, Laboratorios Best, Mexico City, Mexico, lot 1009042). All medications were purchased at a local pharmacy. Metoprolol tartrate reference standard was purchased from the United States Pharmacopeia (99.7% on the as is basis, catalog no. 1441301, USP, St. Rockville, MD, USA). Hydrochloric acid (HCl) at 36.5–38.0% was purchased from JT Baker (JT Baker, by Fisher Scientific GmbH, Schwerte, Germany).

#### 2.2. Dissolution Profile Studies

#### 2.2.1. Test 1: Selection of Dissolution Media

^{®}(Merck Millipore Ltd., Carrigtwohill, Ireland), and analyzed spectrophotometrically at 273 nm (UV-Vis Varian Cary 1E Spectrophotometer, Santa Clara, CA, USA) from a method previously validated by standard additions. The accumulated percentages of the dissolved drug were reported, considering the correction of the volume of the dissolution medium at each sampling time.

#### 2.2.2. Test 2: Dissolution Profiles in Apparatus II USP

^{®}(Merck Millipore Ltd., Carrigtwohill, Ireland), and analyzed spectrophotometrically at 273 nm (Varian Cary 1E UV-Vis spectrophotometer, Santa Clara, CA, USA) in order to determine the amount of metoprolol tartrate dissolved at each sampling time. Corrections in the amount of dissolved metoprolol tartrate were made according to the volume setting at each sampling time.

#### 2.2.3. Test 3: Dissolution Profiles in Apparatus IV USP (Open-Loop Configuration)

^{®}glass microfiber filter (GF/D, Millipore-Sigma, St. Louis, MI, USA). The dissolution medium also comprised degassed simulated gastric fluid (without enzyme) at 37 °C, which was pumped at a flow rate of 8 mL/min. The dissolution apparatus was used in an open-loop configuration, considering 12 tablets for each product evaluated. Dissolution samples were collected manually every minute for 8 min, then every 2 min until reaching 20 min of accumulated dissolution, and subsequently, every 5 min until completing 40 min. Samples were filtered through 0.45 μm Nylon Acrodiscs

^{®}(Merck Millipore Ltd., Carrigtwohill, Ireland) and analyzed spectrophotometrically at 273 nm (Varian Cary 1E UV-Vis spectrophotometer, Santa Clara, CA, USA), under the same conditions as in tests 1 and 2.

#### 2.3. Similarity Evaluation

_{1}), the similarity factor (f

_{2}), the derivation of the 95% confidence interval for f

_{2}based on bootstrap (bootstrap f

_{2}), analysis of variance (ANOVA), and the dissolution efficiency (DE), as well as independent multivariate methods such as multivariate statistical distance (MSD) and time series approaches, were considered. In the case of the dependent models, the dissolution profiles were fitted to different mathematical models, but only the parameters of the best model were compared by MSD to determine similarity as recommended by the FDA guidelines [15]. Finally, the non-accumulated profiles obtained in the apparatus IV USP were the only ones that were subject to comparison from an independent model based on the calculation of kinetic parameters. All calculations were performed in both Microsoft™ Excel and Statgraphics Centurion XV (2007; Statistical Graphics Co., Rockville, MD, USA).

#### 2.3.1. f_{1}, f_{2,} and Bootstrap f_{2} Approaches

_{1}and f

_{2}were calculated considering the average values from the first sampling time to a maximum sampling time after one of the drugs (reference or generics) has reached 85% dissolved metoprolol tartrate. While a calculated value of f

_{1}in the range of 0 to 15 suggests the similarity of the dissolution profiles between the drugs (Reference and generic), values of f

_{2}greater than 50 (50–100) also suggest the similarity of the two profiles [1,16,17].

_{1}and f

_{2}:

_{t}and T

_{t}are the mean dissolution values of the reference drug and generic drug, respectively, at time t.

_{2}bootstrap approach, the dissolution profile data sets were created by random sampling of individual dissolution rates at each time point in the original data, considering the criteria established above for f

_{2}. The number of randomly obtained dissolution profiles was set at 10,000, which was sufficient to stabilize the results. The similarity of the dissolution profiles was established considering the calculation of the 5th quartile of the f

_{2}distribution, which must be greater than 50.

#### 2.3.2. ANOVA-Based Method

_{1}− y

_{2}is the difference in the means of drug dissolved in the generic and reference drugs at each sampling time; df: degree of freedom; MSE: mean square of the error; and n

_{1}and n

_{2}: number of samples of each drug.

#### 2.3.3. Dissolution Efficiency

_{t}is the percentage dissolved at time t, %D

_{max}is the maximum percentage dissolved at the final time T, and AUC

_{0–T}is the area under the curve from zero to T. The DE obtained from each of the individual tablets of both the reference drug and the generic drugs were compared by ANOVA and using 90% confidence intervals for the ratio of the means (log-transformed). The similarity criterion was based on the maximum limits of differences between the profiles (±10%), the same criterion as for the ANOVA-based method.

#### 2.3.4. Multivariate Statistical Distance (MSD)

^{2}statistic (global similarity) and considering their 90% confidence intervals for each sampling time (local similarity) [22]. In this case, to declare the similarity between the dissolution profiles, the 90% confidence intervals of Hotelling’s T

^{2}at each sampling time had to be included in the acceptance limit of ±10% [23]. The comparison of the dissolution profiles by this method was performed considering a point after one of the drugs (reference or generic) reached 85% dissolved, that is, the same criteria as for f

_{2}.

#### 2.3.5. Time Series Approach

_{L}) and upper (δ

_{U}) equivalence limit based on the Q value (% drug dissolved in a determined time “t”) applicable to the drug according to the monographs established in the pharmacopeias, in this case, Q = 75%. If the ratio of the mean dissolution rates was within the bioequivalence limit (δ

_{L}, δ

_{U}), then the dissolution profiles could be said to be similar. To evaluate the local similarity, the construction of confidence intervals for the relative dissolution ratios at each sampling moment was considered, and the same criteria were used to establish similarity between the profiles as for the global similarity.

#### 2.3.6. Dependent Model: Fit to Mathematical Models

^{2}) and the lowest Akaike information criterion (AIC) [28]. The comparison of the dissolution profiles obtained in both dissolution apparatus considering these methods consisted in the estimation of the 90% confidence region limits of their α (scale factor) and β (shape factor) parameters (log-transformed) and the region of similarity, which considered 2 standard deviations (2 STD) for the reference product, that is, approximately 95% confidence [15,19,27]. Dissolution profiles were considered similar if the 90% confidence region limits for each model parameter were included in the region of similarity [11].

#### 2.3.7. Kinetic Parameters: Non-Cumulative Dissolution Profiles

_{max}), time to reach maximum concentration (T

_{max}), area under the curve extrapolated from time zero to infinity (AUC

_{0}

^{∞}), and area under the curve from time zero to C

_{max}(AUC

_{0}

^{Cmax}) were determined from non-cumulative dissolution profiles obtained in the USP IV dissolution apparatus (open-loop configuration). C

_{max}and T

_{max}were determined directly from the non- accumulated dissolution profiles. Meanwhile, AUC was calculated using the linear trapezoidal method (linear up and down) [29]. To determine the equivalence of the dissolution profiles of the reference drug with the generic drugs, 90% confidence intervals were constructed considering the % ratio of the geometric means (generic/reference) of the kinetic parameters (C

_{max}, AUC

_{0}

^{∞}, AUC

_{0}

^{Cmax,}and T

_{max}) with the help of the Statgraphics XVI centurion software (Statpoint Technologies INC., Warrenton, VA, USA). If the confidence intervals in both drugs (reference and generic) were between 80.00% and 125.00%, the drugs were considered equivalent [16].

## 3. Results and Discussion

#### 3.1. Selection of Dissolution Media (Test 1)

_{max}= 1.63 ± 0.47 h) [38]. This T

_{max}value indicates that the dissolution process is carried out rapidly in the stomach and immediately after gastric emptying the absorption process begins [39,40,41], that is, a dissolution medium of phosphate buffer pH = 6.8 was not representative.

#### 3.2. Dissolution Profiles Obtained in the USP II Apparatus (Test 2)

#### 3.3. Dissolution Profiles Obtained in the USP IV Apparatus (Test 3)

#### 3.4. Similarity Evaluation

#### 3.4.1. f_{1}, f_{2}, and Bootstrap f_{2} Approaches

_{2}) approach, a relatively simple method that is vital for regulatory authorities as it requires very little statistical consideration in terms of dissolution data and calculations [17,46]. However, the rules and criteria associated with the application of this dissolution profile comparison method are not globally harmonized, but an f

_{2}greater than 50 indicates that there is less than a 10% difference between the compared dissolution profiles. Another method of dissolution profile comparison established only by FDA guidelines is the difference factor (f

_{1}), which suggests a similarity between dissolution profiles when presenting values between 0 and 15 [17,47]. Both methods are used to compare dissolution profiles with low variability.

_{1}and f

_{2}is shown in Table 2. In general, the f

_{2}values were lower in dissolution profiles obtained in the USP IV apparatus compared to those of the USP II apparatus, except for the generic drug “D” since the f

_{2}value in the USP IV apparatus was slightly higher compared to that in the USP II apparatus. In this sense, while in the USP II apparatus the generic drug “B” was the only one that did not meet the criteria established for f

_{2}(42.76), in the USP IV apparatus, generic drugs “B” and “E” presented f

_{2}values of 36.58 and 46.46, respectively. In contrast, f

_{1}values were higher in the dissolution profiles obtained in the USP IV apparatus, and even generic drugs B, C, and E did not meet the similarity criteria. In the case of the dissolution profiles obtained in the USP II apparatus, generic drug B was the only one that did not meet the similarity criteria (f

_{1}= 30.65). This trend can again be supported since the USP IV apparatus presented a greater discriminative capacity to determine differences between dissolution profiles, which makes it an attractive dissolution apparatus for the development/selection of formulations and thus positively ensure clinical bioequivalence studies [7,48]. However, because the dissolution profiles of the reference drug “A” and the generic drugs “B” and “E” were of high variability, the comparison of profiles by the f

_{1}and f

_{2}approaches to establish similarity was not appropriate since their ability to identify real differences is limited [21].

_{2}based on quantiles of resampling distributions, which contrasts with what is established in the FDA guidelines, since these suggest the use of multivariate methods, specifically the calculation of the multivariate statistical distance (MSD) [1]. In accordance with the above, it has been described that the f

_{2}bootstrap method offers several advantages since its interpretation is the same as f

_{2}and, moreover, it is more sensitive to detecting differences in dissolution profiles than multivariate methods based on the 90% confidence region of the Mahalanobis distance (MD) [49]. Table 2 shows that the bootstrap f

_{2}values for the comparison of dissolution profiles were slightly lower than those of f

_{2}in both dissolution apparatus, but the same trend was maintained in terms of similarity, that is, the dissolution profiles of generic drug B obtained in the USP II apparatus, and the dissolution profiles of generic drugs B and E obtained in the USP IV apparatus were not similar.

#### 3.4.2. ANOVA-Based Method

_{1}, f

_{2,}and bootstrap f

_{2}. These results were due to the fact that the ANOVA-based method is more sensitive than other comparison methods since it detects differences between the dissolution profiles in terms of level and shape [50,51,52]. Furthermore, it has been described that this dissolution profile comparison method violates the underlying assumption of independence because it does not consider the correlation between the dissolution data over time, and therefore it is not recommended [53]. However, its interest applies to immediate-release systems when it is required to compare a single point in dissolution to study its repeatability and reproducibility considering the different sources of variation that can affect the test [51,53].

#### 3.4.3. Dissolution Efficiency

_{1}, f

_{2,}and bootstrap f

_{2}approaches. Instead, in the dissolution profiles obtained in the USP IV apparatus, which were characterized by high variability (reference drug “A” and generic drugs “B” and “E”), generic drug D was the only similar one, which is consistent with the f

_{1}approach and to a certain extent with the f

_{2}and bootstrap f

_{2}approaches since generic drug “C” is at the limit of being able to be considered similar with the DE approach (88.93–91.47%), but it is also in the limit of being considered not similar by the f

_{2}(53.78) and bootstrap f

_{2}(50.81) approaches. In this sense, DE can be a good method for comparing dissolution profiles with both low and high variability.

#### 3.4.4. Multivariate Statistical Distance (MSD)

^{2}test should be used [53]. Considering these assumptions, when comparing the dissolution profiles of the reference drug with the generic drugs obtained in both dissolution apparatus, Hotelling’s T

^{2}test was used to establish similarity since the variance–covariance matrices were not symmetrical in any of the cases according to a chi-square test performed (p < 0.05). Table 5 shows the results of local similarity for the comparison of dissolution profiles obtained in the USP II apparatus (low variability). The only profile that met the similarity criteria was generic drug “C” since the 90% confidence intervals of Hotelling’s T

^{2}at each sampling point were included in the acceptance limit of ±10%. Meanwhile, in the comparison of dissolution profiles obtained in the USP IV apparatus (high variability), none of the generic drugs presented similarity (Table 6) given that at least one of the 90% confidence intervals of Hotelling’s T

^{2}were outside the acceptance limit of ±10%. These results are consistent with those of the ANOVA-based comparison method. Although it has been described that multivariate methods such as MSD are less discriminative and sensitive than the calculation of f

_{2}[21] and that even a crossover in the dissolution profiles could have important implications in the similarity (non-discriminative, low specificity, and positive predictive value due to false positives) [10], these limitations can be solved to some extent if the comparison of dissolution profiles by this method is performed considering a point after reaching 85% dissolved, as described in the FDA and EMA guidelines for the calculation of f

_{2}since the method becomes more sensitive to detect differences, and thus the dissolution profiles obtained in USP II and IV apparatuses were analyzed up to 25 min and 40 min of dissolution, respectively. However, the bootstrap f

_{2}method is considered a better alternative to dissolution profiles with high variability [49,57].

#### 3.4.5. Time Series Approach

#### 3.4.6. Dependent Models: Fit to Mathematical Models

^{2}) and the lowest values in the Akaike information criterion (AIC); that is, the release of the API is a function of time and the process takes place at a constant rate independent of API concentration [62]. In addition, their release mechanisms were adjusted to super case-II transports since their diffusion exponents “n” were greater than 0.89 in the Korsmeyer–Peppas model, so the API diffusion process in the non-swellable matrix was very fast [63,64]. On the contrary, the dissolution profiles of the generic drugs “B” and “C” obtained in both dissolution apparatuses were adjusted to the Hixson–Crowell model (Table 8), and therefore the drug release was limited by the dissolution velocity and not by diffusion. However, as the diffusion coefficient “n” was less than 0.89 in the case of the dissolution profiles obtained in the USP II apparatus, the drug release mechanism through generic drugs “B” and “C” is governed by diffusion and swelling [63].

^{2}and lowest AIC. The fit results were logical as the Weibull model has been reported to be the most flexible model for describing a wide variety of shapes compared to the other dependent models with two parameters [66]. Table 9 and Table 10 show the similarity results in the dissolution profiles obtained in USP II and IV apparatuses, respectively, through the comparison of the α and β parameters of the Weibull model. However, none of the dissolution profiles were similar, regardless of the dissolution apparatus used since in all cases the 90% confidence region limits of model parameters were outside the region of similarity. These results can be attributed to the multivariate method used, since as previously mentioned, these types of methods are less discriminative and more sensitive, although a potential danger has also been described for the model parameters since they can be biased or not be estimable if the sampling points are not chosen properly [66]. However, to minimize this last point, the comparison of the dissolution profiles obtained in the USP II and IV apparatuses were compared up to 25 min and 40 min, respectively. In short, these dependent models can be used more in the comparison of intra-batch dissolution profiles when there are minimal changes at the formulation level [27].

#### 3.4.7. Independent Model Comparison for Non-Accumulated Data (USP IV Apparatus)

_{max}, AUC

_{0}

^{∞}, AUC

_{0}

^{Cmax}and T

_{max}) obtained from non-accumulated dissolution profiles was proposed to establish similarities, as is undertaken for bioequivalence studies, following the FDA and EMA guidelines [16,67]. The results in Table 11 show that the generic drugs “B” and “E” presented the highest and lowest C

_{max}, respectively, compared to the reference drug “A”. Regarding the T

_{max}in which C

_{max}was reached, the generic drug “C” presented the smaller value (6.00 min), followed by the generic drug “B” (6.42 min) when compared to the reference drug “A” (7.25 min). In contrast, the generic drugs “D” and “E” showed the highest T

_{max}, 8.00 min and 10.33 min, respectively. Furthermore, although the AUC

_{0}

^{∞}did not show differences between the drugs, the AUC

_{0}

^{Cmax}of the generic drugs “B”, “D”, and “E” was higher compared to that of the reference drug “A”. Instead, the generic drug “C” had a lower AUC

_{0}

^{Cmax}in comparison with the reference drug “A”.

_{max}, AUC

_{0}

^{∞}, AUC

_{0}

^{Cmax,}and T

_{max}, but only AUC

_{0}

^{Cmax}and C

_{max}(in this order) were considered to establish similarity between the dissolution profiles, as long as their confidence intervals were within the acceptance interval of 80.00 to 125.00% [4,68], in the case of immediate-release drugs. Table 11 also shows the % ratio of the geometric means of the kinetic parameters (C

_{max}, AUC

_{0}

^{∞}, AUC

_{0}

^{Cmax}, and T

_{max}) with their respective 90% confidence intervals. The % ratio of the geometric means of AUC

_{0}

^{Cmax}and C

_{max}for the generic drug “C” (C/A, AUC

_{0}

^{Cmax}: 85.04–93.95% and C

_{max}: 75.25–81.97%) and “D” (D/A, AUC

_{0}

^{Cmax}: 125.12–136.84% and C

_{max}: 79.71–87.05%) were the ones that came closest to the acceptance interval (80.00 to 125.00%), so the probability that they are similar with the reference drug “A” is high and is also supported by the values of f

_{2}and bootstrap f

_{2}since in both drugs it was greater than 50 and, in addition, it is related to the method of DE since generic drug “D” was considered similar and generic drug C was very close to being considered similar in the dissolution profiles obtained in the USP IV apparatus. In the case of the generic drug “E”, while the interval of the % ratio of the geometric means of AUC

_{0}

^{Cmax}(105.88–131.03) was slightly above those of acceptance, the interval of the % ratio of the geometric means of C

_{max}(64.41–72.59%) was the lowest. Finally, the intervals of the % ratio of the geometric means of AUC

_{0}

^{Cmax}and C

_{max}for the generic drug “B” (B/A, AUC

_{0}

^{Cmax}: 148.03–192.01% and C

_{max}: 143.01–166.46%) were very high. Therefore, the probability of similarity of generic drugs “B” and “E” with the reference drug “A” is supported by the fact that in both cases the values of f

_{2}and bootstrap f

_{2}were less than 50 and the DE method considered them not similar. In this sense, the analysis of kinetic parameters from non-cumulative dissolution profiles can be an excellent option to determine if the compared drugs are similar since the dissolution profiles obtained in the USP IV apparatus using the open-loop configuration are more uniform and discriminative compared to those of the USP I and II apparatuses [4,69]. Therefore, the USP IV apparatus in the open-loop configuration can be an excellent tool to ensure similarity in dissolution profiles during the drug development stage, as well as to detect variations at the formulation level when there are minor changes and evaluate the variability per dosage unit (process control).

## 4. Conclusions

_{max}, AUC

_{0}

^{∞}, AUC

_{0}

^{Cmax}and T

_{max}), a method that resembles the comparison of pharmacokinetic parameters obtained in bioequivalence studies, was proposed and was found to be consistent with the f

_{2}, bootstrap f

_{2,}and DE approaches, since from these, similarity was established in the generic drugs “C” and “D” and not similarity in the generic drugs “B” and “E”. Therefore, this type of comparison method can be an important tool to facilitate the development/selection of new formulations and positively ensure clinical bioequivalence studies. Therefore, the proposed comparison method can be an important tool to establish similarity in dissolution profiles and to facilitate the development/selection of new formulations and positively ensure bioequivalence in clinical studies. Furthermore, it is a method that does not require complex calculations such as those required by multivariate methods and special conditions of analysis to avoid overestimating the results.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Dissolution profiles of metoprolol tartrate 100 mg immediate-release tablets in simulated gastric fluid (without enzymes) and phosphate buffer pH 6.8 using the USP dissolution apparatus II (Paddle) at 50 rpm and 37 °C. The results are expressed as mean ± SD (n = 6).

**Figure 2.**Cumulative dissolution profiles of reference drug “A” (Lopresor 100) and generic drugs “B”, “C”, “D”, and “E” obtained using the USP II apparatus. The results are expressed as mean ± SD (n = 12).

**Figure 3.**Cumulative dissolution profiles of reference drug “A” (Lopresor 100) and generic drugs “B”, “C”, “D”, and “E” obtained using the USP IV apparatus. The results are expressed as mean ± SD (n = 12).

**Figure 4.**Non-cumulative dissolution profiles of reference drug “A” (Lopresor 100) and generic drugs “B”, “C”, “D”, and “E” obtained using the USP IV apparatus. The results are expressed as mean ± SD (n = 12).

Model | Equation |
---|---|

Zero-order | ${\mathrm{Q}}_{\mathrm{t}}={\mathrm{Q}}_{0}+{\mathrm{K}}_{0}\mathrm{t}$ |

First-order | ${\mathrm{In}\mathrm{Q}}_{\mathrm{t}}={\mathrm{In}\mathrm{Q}}_{0}-{\mathrm{K}}_{1}\mathrm{t}$ |

Higuchi | ${\mathrm{Q}}_{\mathrm{t}}={\mathrm{K}}_{\mathrm{H}}\cdot \sqrt{\mathrm{t}}$ |

Hixon–Crowell | ${\mathrm{Q}}_{0}^{1/3}-{\mathrm{Q}}_{\mathrm{t}}^{1/3}={\mathrm{K}}_{\mathrm{s}}\cdot \mathrm{t}$ |

Korsmeyer–Peppas | ${\mathrm{Q}}_{\mathrm{t}}/{\mathrm{Q}}_{\infty}={\mathrm{K}}_{\mathrm{k}}\cdot {\mathrm{t}}^{\mathrm{n}}$ |

Weibull | ${\mathrm{Q}}_{\mathrm{t}}={\mathrm{Q}}_{\mathrm{max}}\cdot \left\{1-\mathrm{exp}\left[-\mathrm{a}\cdot {\left(\mathrm{t}\right)}^{\mathrm{b}}\right]\right\}$ |

Gompertz | ${\mathrm{Q}}_{\mathrm{t}}={\mathrm{Q}}_{\mathrm{max}}\cdot \mathrm{exp}\left\{-\mathrm{a}\cdot \mathrm{exp}\left[-\mathrm{b}\cdot \mathrm{log}\left(\mathrm{t}\right)\right]\right\}$ |

Logistic | ${\mathrm{Q}}_{\mathrm{t}}={\mathrm{Q}}_{\mathrm{max}}\cdot \left\{\frac{\mathrm{exp}\left[\mathrm{a}+\mathrm{b}\cdot \mathrm{log}\left(\mathrm{t}\right)\right]}{1+\mathrm{exp}\left[\mathrm{a}+\mathrm{b}\cdot \mathrm{log}\left(\mathrm{t}\right)\right]}\right\}$ |

_{t}: amount of drug release in time t; Q

_{0}: initial amount of drug in the tablet; Q

_{t}/Q

_{∞}: fraction of drug release at time t; Q

_{max}: maximum dissolved at the final time; k

_{0}, k

_{1}, k

_{H}, k

_{k}, k

_{s}: release rate constants; n: release exponent; and a and b: parameters of the models.

**Table 2.**Comparison of the difference factors (f

_{1}), similarity factors (f

_{2}), and bootstrap f

_{2}of the dissolution profiles obtained in apparatus II and IV USP of the generic drugs with the reference drug “A” (Lopresor 100).

Drug | Difference Factor (f_{1}) | Similarity Factor (f_{2}) | Bootstrap f_{2} | |||
---|---|---|---|---|---|---|

USP Dissolution Apparatus | ||||||

II | IV | II | IV | II | IV | |

Generic Drug “B” | 30.65 * | 58.78 | 42.76 | 36.58 | 39.84 | 34.60 |

Generic Drug “C” | 8.13 | 18.32 | 64.60 | 53.78 | 59.96 | 50.81 |

Generic Drug “D” | 9.89 | 10.99 | 60.39 | 65.30 | 55.25 | 61.05 |

Generic Drug “E” | 10.40 | 26.99 | 59.47 | 46.46 | 54.76 | 44.09 |

**Table 3.**Comparisons of dissolution profiles of generic drugs with reference drug “A” (Lopresor 100) obtained in the USP II and IV apparatus using ANOVA-based statistical analysis

^{1}.

Drug | USP II Apparatus | USP IV Apparatus | ||||
---|---|---|---|---|---|---|

Two-Factor p Value | 95% CI | Decision | Two-Factor p Value | 95% CI | Decision | |

Generic Drug “B” | <0.01 | Significant differences at 4–16 min | Non-similar | <0.01 | Significant differences at 4–20 min | Non-similar |

Generic Drug “C” | 0.10 | No significant differences | Similar | <0.01 | Significant differences at 16–35 min | Non-similar |

Generic Drug “D” | <0.01 | Significant differences at 16 min | Non-similar | <0.01 | Significant differences at 35 and 30 min | Non-similar |

Generic Drug “E” | <0.01 | Significant differences at 16 and 20 min | Non-similar | <0.01 | Significant differences at 10 and 35 min | Non-similar |

^{1}p value represents the interaction between drug and time (D × T).

**Table 4.**Comparison of dissolution profiles obtained in the USP II and IV apparatus by 90% confidence intervals for the mean ratio of dissolution efficiency (DE %) between the generic drugs with respect to the reference drug “A” (Lopresor 100) (G/R).

Drug | USP II Apparatus | USP IV Apparatus | ||
---|---|---|---|---|

DE % 90% CI for Mean Ratio G/R | Decision ^{1} | DE % 90% CI for Mean Ratio G/R | Decision | |

Generic Drug “B” | 117.91 114.68–121.24 | Non-similar | 117.71 115.39–120.07 | Non-similar |

Generic Drug “C” | 106.58 103.57–109.67 | Similar | 90.19 88.93–91.47 | Non-similar |

Generic Drug “D” | 95.72 93.02–98.51 | Similar | 94.54 92.92–96.20 | Similar |

Generic Drug “E” | 98.56 95.88–101.31 | Similar | 83.40 82.07–84.76 | Non-similar |

^{1}Similarity decision between the profiles (generic/reference) was made considering a maximum difference of ±10%, that is, considering a similarity interval between 90.0% and 110.0%.

**Table 5.**Multivariate analysis based on 90% confidence intervals for each sampling time of the reference drug “A” (Lopresor 100)/generic drug profiles obtained in the USP II apparatus using Hotelling’s T

^{2}statistic (local similarity).

Sampling Time (min) | 90% Confidence Intervals (90% CI) | |||
---|---|---|---|---|

USP II Apparatus | ||||

Generic Drug B | Generic Drug C | Generic Drug D | Generic Drug E | |

2 | [5.65, 8.23] | [7.13, 9.03] | [−0.73, 1.23] | [1.02, 3.16] |

4 | [12.44, 14.81] | [7.16, 9.24] | [1.41, 3.64] | [−0.07, 2.96] |

6 | [12.74, 15.80] | [4.60, 7.91] | [−3.42, 0.20] | [−3.83, 0.34] |

8 | [14.42, 18.35] | [3.46, 7.26] | [−5.18, −1.29] | [−5.67, −0.58] |

10 | [13.94, 18.52] | [1.21, 6.42] | [−8.09, −4.11] | [−7.82, −1.82] |

12 | [13.65, 18.20] | [−0.03, 6.82] | [−6.70, −3.12] | [−9.15, −3,62] |

14 | [11.82, 16.93] | [−2.65, 4.11] | [−10.29, −5.73] | [−10.37, −4.16] |

16 | [8.83, 13.19] | [−4.01, 1.52] | [−12.91, −7.70] | [−12.55, −7.03] |

18 | [6.80, 10.45] | [−4.21, 0.57] | [−10.54, −5.12] | [−11.77, −4.42] |

20 | [1.99, 4.99] | [−6.50, −2.19] | [−10.56, −5.11] | [−13.81, −7.25] |

25 | [−2.56, 0.95] | [−5.50, −1.41] | [−5.68, −1.79] | [−9.55, −5.53] |

Conclusion | Non-similar | Similar | Non-similar | Non-similar |

**Table 6.**Multivariate analysis based on 90% confidence intervals for each sampling time of the reference drug “A” (Lopresor 100)/generic drug profiles obtained in the USP IV apparatus using Hotelling’s T

^{2}statistic (local similarity).

Sampling Time (min) | 90% Confidence Intervals (90% CI) | |||
---|---|---|---|---|

USP IV Apparatus | ||||

Generic Drug B | Generic Drug C | Generic Drug D | Generic Drug E | |

1 | [1.66, 2.24] | [0.67, 1.05] | [0.75, 1.09] | [0.33, 068] |

2 | [4.15, 5.35] | [1.90, 2.49] | [1.95, 2.49] | [0.51,1.16] |

3 | [6.61, 8.62] | [2.35, 3.39] | [2.54, 3.45] | [−0.17, 1.01] |

4 | [9.38, 12.08] | [2.28, 3.78] | [2.53, 3.77] | [−1.19, 0.43] |

5 | [12.01, 15.24] | [1.96, 3.47] | [2.11, 3.42] | [−2.52, −0.75] |

6 | [14.38, 18.38] | [1.25, 2.86] | [1.33, 2.78] | [−4.27, −2.25] |

7 | [16.27, 21.05] | [−0.01, 1.76] | 0.28, 1.92] | [−6.28, −3.90] |

8 | [18.08, 23.58] | [−1.33, 0.63] | [−0.43, 1.45] | [−8.02, −5.21] |

10 | [20.70, 27.41] | [−4.03, −1.68] | [−1.92, 0.44] | [−11.00, −7.51] |

12 | [22.05, 30.09] | [−6.65, −3.87] | [−3.29, −046] | [−13.41, −9.41] |

14 | [21.88, 30.81] | [−9.50, −6.17] | [−4.76, −057] | [−15.97, −11.39] |

16 | [20.66, 29.09] | [−12.11, −8.34] | [−6.28, −2.93] | [−18.28, −13.44] |

18 | [18.27, 26.07] | [−14.63, −10.50] | [−7.99, −4.37] | [−20.47, −15.37] |

20 | [13.77, 21.26] | [−17.07, −12.57] | [−9.88, −6.02] | [−22.68, −17.27] |

25 | [2.06, 9.49] | [−23.87, −17.56] | [−15.86, −10.73] | [−27.94, −21.25] |

30 | [−0.72, 6.25] | [−19.95, −13.46] | [−11.69, −6.39] | [−22.10, −15.81] |

35 | [−1.73, 5.04] | [−14.47, −8.15] | [−7.06, −2.26] | [−14.20, −8.02] |

40 | [−2.14, 4.67] | [−9.10, −2.56] | [−4.70, 0.43] | [−7.97, −2.26] |

Decision | Non-similar | No-similar | Non-similar | Non-similar |

**Table 7.**Comparison of dissolution profiles obtained in the USP II and IV apparatus by a time series approach considering 95% confidence intervals for global and local similarities.

Drug | USP II Apparatus | USP IV Apparatus | ||||
---|---|---|---|---|---|---|

95% CI (Global Similarity) | 95% CI (Local Similarity) | Decision | 95% CI (Global Similarity) | 95% CI (Local Similarity) | Decision | |

Generic Drug “B” | 123.01–144.84 | Significant differences before 18 min | Non-similar | 157.67–215.20 | Significant differences at all times of the profile | Non-similar |

Generic Drug “C” | 108.50–126.72 | Significant differences before 12 min | Non-similar | 97.10–129.22 | Non-similar | |

Generic Drug “D” | 82.11–107.90 | Significant differences at 4 min and between 8–20 min | Non-similar | 103.95–133.50 | Non-similar | |

Generic Drug “E” | 73.50–119.10 | Significant differences at all times, except at 6 min | Non-similar | 63.57–116.63 | Non-similar | |

Limit of similarity: 87.50–114.29% ^{1} |

^{1}Limit of similarity calculated considering that the metoprolol tartrate monograph at USP establishes a Q = 75%.

**Table 8.**Parameters of the mathematical models and descriptive statistics of regression for the dissolution data.

Model | Statistics ^{1} | USP II Apparatus | USP IV Apparatus | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Reference “A” | Generic “B” | Generic “C” | Generic “D” | Generic “E” | Reference “A” | Generic “B” | Generic “C” | Generic “D” | Generic “E” | ||

Zero-order | r^{2} | 0.9922 | 0.9166 | 0.9502 | 0.9898 | 0.9929 | 0.9749 | 0.9657 | 0.9919 | 0.9953 | 0.9883 |

k_{0} (%Dis ∗ min^{−1}) | 4.9024 | 5.9298 | 5.0479 | 4.4087 | 4.4161 | 3.3844 | 4.9917 | 2.8718 | 3.1668 | 2.4538 | |

MSE | 5.8329 | 63.9021 | 28.3103 | 5.4318 | 3.7852 | 14.3348 | 32.9669 | 1.8453 | 1.9696 | 3.1387 | |

AIC | 36.2512 | 57.9025 | 50.2955 | 33.8004 | 31.2852 | 74.3746 | 85.3320 | 48.9331 | 46.5559 | 53.3278 | |

First-order | r^{2} | 0.9286 | 0.9612 | 0.9777 | 0.9602 | 96.3200 | 0.9144 | 0.9403 | 0.9842 | 0.9654 | 0.9583 |

k_{1} (min^{−1}) | 0.0770 | 0.1136 | 0.0844 | 0.0660 | 0.0663 | 0.0447 | 0.0827 | 0.0370 | 0.0417 | 0.0300 | |

MSE | 53.1229 | 31.1351 | 13.0971 | 22.6939 | 20.2464 | 48.8620 | 58.3842 | 5.1922 | 14.4517 | 11.2917 | |

AIC | 56.4263 | 50.4021 | 42.4009 | 47.7845 | 47.2864 | 91.9112 | 92.9871 | 58.6913 | 74.7632 | 71.5421 | |

Higuchi | r^{2} | 0.8133 | 0.9128 | 0.9075 | 0.8409 | 0.8451 | 0.7250 | 0.8315 | 0.8205 | 0.7920 | 0.7554 |

k_{H} (%Dis ∗ min^{−1/2}) | 17.1046 | 21.0966 | 17.9065 | 15.4558 | 15.4901 | 11.5370 | 0.1756 | 10.0318 | 10.9832 | 8.4341 | |

MSE | 138.6870 | 67.5427 | 51.8659 | 88.2738 | 83.5642 | 155.4990 | 156.9909 | 56.9645 | 85.8074 | 65.9340 | |

AIC | 65.0834 | 58.3930 | 56.1195 | 60.8167 | 60.4724 | 108.4083 | 108.3192 | 94.2654 | 100.1338 | 96.4672 | |

Hixson–Crowell | r^{2} | 0.9621 | 0.9908 | 0.9942 | 0.9814 | 0.9848 | 0.9377 | 0.9688 | 0.9940 | 0.9800 | 0.9704 |

k_{s} (%Dis ∗ min^{−1/3}) | 0.0223 | 0.0313 | 0.0240 | 0.0194 | 0.0194 | 0.0137 | 0.0239 | 0.0114 | 0.0127 | 0.0094 | |

MSE | 28.1260 | 7.5387 | 3.4102 | 10.7124 | 8.4516 | 35.5652 | 30.6325 | 2.6745 | 8.3986 | 7.9981 | |

AIC | 50.6311 | 36.0721 | 30.1136 | 40.2526 | 38.9975 | 87.3931 | 83.4847 | 45.8812 | 67.0090 | 66.6547 | |

Korsmeyer–Peppas | r^{2} | 0.9933 | 0.9847 | 0.9961 | 0.9945 | 0.9974 | 0.9936 | 0.9746 | 0.9954 | 0.9963 | 0.9975 |

k_{k} (%Dis ∗ min^{−n}) | 5.0637 | 11.8948 | 9.1967 | 5.3606 | 5.4351 | 1.8844 | 6.6770 | 3.1345 | 2.8404 | 1.6715 | |

n | 0.9920 | 0.7322 | 0.7703 | 0.9264 | 0.9217 | 1.2229 | 0.8935 | 0.9679 | 1.0423 | 1.1469 | |

MSE | 5.6997 | 13.8821 | 2.6908 | 3.5050 | 1.6278 | 3.9871 | 26.6685 | 1.5489 | 1.6252 | 0.7375 | |

AIC | 36.9205 | 43.8078 | 27.3260 | 28.0736 | 24.7320 | 56.6951 | 83.1922 | 44.7129 | 44.7520 | 30.4641 |

^{1}Coefficient of determination (r

^{2}); constants of the dependent models (k

_{0}, k

_{1}, k

_{H}, k

_{s}, k

_{k}); diffusion exponent (n); mean square error (MSE) and Akaike information criterion (AIC).

**Table 9.**Comparison of the fit parameters of the Weibull model for the dissolution profiles between the reference drug “A” (Lopresor 100) and the generic drugs obtained in the USP II apparatus through multivariate confidence regions.

Weibull Parameters | Ln Differences | USP II Apparatus | |||
---|---|---|---|---|---|

Generic Drug “B” | Generic Drug “C” | Generic Drug “D” | Generic Drug “E” | ||

$\alpha $ ^{1} | 90% CI | −0.125 to −0.090 | 0.403 to 0.454 | 0.078 to 0.184 | 0.157 to 0.248 |

2 STD Similarity region ^{3} | −0.045–0.045 | ||||

$\beta $ ^{2} | 90% CI | −0.189 to −0.072 | −0.122 to −0.107 | −0.071 to −0.037 | −0.077 to −0.055 |

2 STD Similarity region | −0.008–0.008 | ||||

Decision | Non-similar | Non-similar | Non-similar | Non-similar |

^{1}α: scale factor,

^{2}β: shape factor and

^{3}2 STD is approximately 95% confidence.

**Table 10.**Comparison of the fit parameters of the Weibull model for the dissolution profiles between the reference drug “A” (Lopresor 100) and the generic drugs obtained in the USP IV apparatus through multivariate confidence regions.

Weibull Parameters | Ln Differences | USP IV Apparatus | |||
---|---|---|---|---|---|

Generic Drug “B” | Generic Drug “C” | Generic Drug “D” | Generic Drug “E” | ||

$\alpha $ ^{1} | 90% CI | 0.484 to −0.654 | 0.374 to 0.521 | 0.333 to 0.461 | 0.164 to 0.319 |

2 STD Similarity region ^{3} | −0.093–0.0933 | ||||

$\beta $ ^{2} | 90% CI | −0.084 to −0.048 | −0.147 to −0.114 | −0.118 to −0.092 | −0.117 to −0.085 |

2 STD Similarity region | −0.019–0.019 | ||||

Decision | Non-similar | Non-similar | Non-similar | Non-similar |

^{1}α: scale factor,

^{2}β: shape factor and

^{3}2 STD is approximately 95% confidence.

**Table 11.**Kinetic parameters of dissolution profiles obtained in the USP IV apparatus and their 90% confidence intervals (CI) of the ratio of geometric means (generic/reference).

Parameter | Geometric Mean ± SE | Geometric Point Estimate Ratio | |||||||
---|---|---|---|---|---|---|---|---|---|

(90% CI) | (90% CI) | ||||||||

Reference (A) | Generic (B) | Generic (C) | Generic (D) | Generic (E) | B/A | C/A | D/A | E/A | |

C_{max} (µg/mL) | 565.21 ± 13.39 | 869.69 ± 31.73 | 441.77 ± 4.16 | 468.73 ± 6.65 | 384.54 ± 7.95 | 153.29 | 78.36 | 83.10 | 68.09 |

(541.17–589.26) | (812.72–926.67) | (434.30–449.25) | (456.78–480.68) | (370.27–398.81) | (142.55–164.84) | (74.91–81.98) | (79.23–87.15) | (64.48–71.89) | |

AUC_{0}^{∞}(µg·min/mL) | 12,507.10 ± 189.35 | 12,580.20 ± 135.68 | 12,507.20 ± 151.82 | 12,234.30 ± 157.75 | 12,352.10 ± 115.31 | 101.57 | 99.19 | 97.86 | 98.84 |

(12,167.10–12,847.10) | (12,336.50–12,823.90) | (12,234.50–12,779.80) | (11,951.00–12,517.60) | (12,145.00–12,559.20) | (98.61–104.63) | (96.12–102.36) | (97.61–98.11) | (95.21–102.62) | |

AUC_{0}^{Cmax}(µg·min/mL) | 2203.29 ± 57.32 | 3857.76 ± 185.18 | 1966.84 ± 20.74 | 2864.59 ± 22.51 | 2896.96 ± 188.61 | 173.57 | 89.52 | 131.09 | 128.99 |

(2099.41–2307.18) | (3525.20–4190.33) | (1929.58–2004.09) | (2824.16–2905.02) | (2558.25–3235.68) | (157.88–190.82) | (85.11–94.17) | (124.82–137.68) | (114.23–145.67) | |

T_{max}(min) | 7.25 ± 0.25 | 6.42 ± 0.19 | 6.00 ± 0.00 | 8.00 ± 0.00 | 10.33 ± 0.54 | 88.57 | 83.20 | 110.94 | 141.17 |

(6.80–7.70) | (6.07–6.76) | (6.00–6.00) | (8.00–8.00) | (9.36–11.31) | (82.53–95.06) | (78.88–87.77) | (105.17–117.02) | (127.35–156.49) |

_{max}: maximum concentration, T

_{max}: time to reach maximum concentration, AUC

_{0}

^{∞}: area under the curve extrapolated from time zero to infinity, and AUC

_{0}

^{Cmax}: area under the curve from time zero to C

_{max}.

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## Share and Cite

**MDPI and ACS Style**

Solis-Cruz, B.; Hernandez-Patlan, D.; Morales Hipólito, E.A.; Tellez-Isaias, G.; Alcántara Pineda, A.; López-Arellano, R.
Discriminative Dissolution Method Using the Open-Loop Configuration of the USP IV Apparatus to Compare Dissolution Profiles of Metoprolol Tartrate Immediate-Release Tablets: Use of Kinetic Parameters. *Pharmaceutics* **2023**, *15*, 2191.
https://doi.org/10.3390/pharmaceutics15092191

**AMA Style**

Solis-Cruz B, Hernandez-Patlan D, Morales Hipólito EA, Tellez-Isaias G, Alcántara Pineda A, López-Arellano R.
Discriminative Dissolution Method Using the Open-Loop Configuration of the USP IV Apparatus to Compare Dissolution Profiles of Metoprolol Tartrate Immediate-Release Tablets: Use of Kinetic Parameters. *Pharmaceutics*. 2023; 15(9):2191.
https://doi.org/10.3390/pharmaceutics15092191

**Chicago/Turabian Style**

Solis-Cruz, Bruno, Daniel Hernandez-Patlan, Elvia A. Morales Hipólito, Guillermo Tellez-Isaias, Alejandro Alcántara Pineda, and Raquel López-Arellano.
2023. "Discriminative Dissolution Method Using the Open-Loop Configuration of the USP IV Apparatus to Compare Dissolution Profiles of Metoprolol Tartrate Immediate-Release Tablets: Use of Kinetic Parameters" *Pharmaceutics* 15, no. 9: 2191.
https://doi.org/10.3390/pharmaceutics15092191