# Assessment of the Inter-Batch Variability of Microstructure Parameters in Topical Semisolids and Impact on the Demonstration of Equivalence

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

## 1. Introduction

_{R}), elastic and viscous moduli (G’ and G″), or loss tangent (tan δ). To conclude equivalence of these microstructure characteristics, the 90% confidence interval (CI) of the difference between means of both formulations should not be more than 10% from the reference product mean, assuming normal distribution of data. According to this draft guideline, equivalence has to be concluded for all rheological parameters that define the microstructure of the product. Neither the parameters that define the microstructure of semisolid pharmaceuticals, nor the acceptance limits that ensure equivalence in those parameters have so far been defined in the literature. Moreover, since all the rheological parameters mentioned above are not included as routine analysis when delivering new batches, the inter-batch variability has not been characterized. When evaluating rheological parameters, inter-batch variability can be due to multiple factors, such as excipient or formulation manufacturing, storage conditions and aging of the formulation.

## 2. Materials and Methods

#### 2.1. Drug Products

#### 2.2. Rheological Analysis

^{®}RheoStress

^{®}1 (Thermo Fisher Scientific, Karlsruhe, Germany) connected to a Haake K10 thermostatic bath, using the RheoWin 4.0 software. After 600 s relaxation time, all measurements (10 batches; 12 replicates per batch) were done at 25 °C using the serrated parallel plates (35 mm diameter, 1 mm gap). All rheological parameters were calculated using the Kaleidagraph 4.03 software (Synergy Software, Reading, PA, USA). The following rheological measurements were performed.

#### 2.2.1. Hysteresis Loops

^{−1}and 100 s

^{−1}in a stepped ramp (20 steps in logarithmic distribution; 10 s per step).

^{−1}for 60 s (measuring 10 timepoints).

^{−1}to 1 s

^{−1}in stepped ramp (20 steps in logarithmic distribution; 10 s per step).

_{A}) and the downward (S

_{D}) curves were calculated by numerical integration, the difference between them being the thixotropic area (S

_{T}). The relative thixotropic area (S

_{R}) [5] is useful in order to compare different samples:

#### 2.2.2. Flow Curves

_{0}is the zero-shear viscosity, $\dot{\gamma}$

_{c}is critical shear rate, and s the shear thinning index. Viscosity corresponding to 100 s

^{−1}was also calculated from the curve fits obtained.

_{0}) was estimated on the double log scaled rheograms η = f (σ) from the point where the straight line corresponding to the viscosity plateau intersects the tangent line to the fall in viscosity [7].

#### 2.2.3. Viscoelastic Properties from Oscillatory Tests

#### 2.3. Spreadability Measurements

#### 2.4. Parametric Comparison

#### 2.4.1. Comparison of 1 Batch vs. 1 Batch

#### 2.4.2. Comparison of 5 Batches vs. 5 Batches

#### 2.4.3. Comparison of Median of 5 Batches vs. Median of 5 Batches

#### 2.5. Non-Parametric Comparison

## 3. Results and Discussion

_{R}), yield stress (σ

_{0}), zero shear viscosity (η

_{0}), viscosity al 100 s

^{−1}(η

_{100}), loss tangent (tan δ), calculated elastic and viscous moduli at 1 Hz (${G}_{1}^{\prime}$ and ${G}_{1}^{\u2033}$, respectively), the parameters m’ and m″ of the fit, and spreadability (Table 1). Raw data are shown in Table S1.

_{0}), relate to the area occupied when applying weight on the formulation. This area is obtained through spreadability measurements, which are simple routine tests for semisolid preparations informing about the spreadability of a formulation when applied on skin, while the other two parameters mentioned correspond to a more rigorous analysis of flow properties. The internal structure of formulations and their viscoelastic properties is given by the determination of storage and loss moduli (G’ and G″) and their dependence with frequency oscillation. In the here tested formulation, elastic behaviour clearly predominated over viscous (G’ > G″) and both moduli varied with frequency, as characterized by their slopes (i.e., m’ and m″) in double logarithmic scale.

_{100}, tan δ, m’, m″ and spreadability showed an inter-batch CV ≤ 5.7%. The contribution to the total variability of each parameter was similar in terms of inter- and intra-batch variability.

_{R}, σ

_{0}, η

_{0}, tan δ nor m’ follow a normal distribution. Those physical parameters not following a normal distribution would not qualify for comparison according to the EMA draft guideline [4].

_{100}), the number of successful comparisons was 100% if the number of batches compared was 5 either comparing mean values or the median batch.

_{R}, σ

_{0}, η

_{0}, ${G}_{1}^{\prime}$ and ${G}_{1}^{\u2033}$) the equivalence between batches of the same reference product could not be concluded in more than 80% of comparisons, by any of the comparison methods. Thus, according to the EMA draft guideline these batches of same reference formulation would not be considered equivalent in half of the physical parameters evaluated [4], despite the fact that more than the minimum required number of batches (five instead of only three) were tested. Since the equivalence criterion seems to be inappropriate when inter-batch variability is large, the acceptance range could be widened under these circumstances.

_{R}, which with 79% successful comparisons was very close of being considered equivalent.

_{0}) with a total CV of 11.8% (and an inter-batch CV of 9.6%) (Table 1) and a theoretical difference between batches of zero (batches of the same reference product). Therefore, a sample size calculation taking into account inter-batch variability would be necessary to ensure that the experiments have the desired power. In the absence of proper sample size calculations, pharmaceutical companies might be tempted to conduct pilot experiments to select those batches that behave similarly, before performing a formal comparison for regulatory submission, which could be considered data manipulation.

_{100}), equivalence could only be concluded with the “5 vs. 5″ comparison method, the probability distributions of the geometric means of the “1 vs. 1″ comparison method being notably wider (Figure 2 and Figure 3). For rheological parameters with total CV > 10% (S

_{R}, σ

_{0}, η

_{0}, ${G}_{1}^{\prime}$ and ${G}_{1}^{\u2033}$), equivalence could not be concluded by neither the “1 vs. 1″, nor the “5 vs. 5″ method.

_{max}in pharmacokinetic bioequivalence studies [18] and it is also proposed by other authors for the comparison of some in vitro parameters [19].

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Chang, R.-K.; Raw, A.; Lionberger, R.; Yu, L. Generic Development of Topical Dermatologic Products, Part II: Quality by Design for Topical Semisolid Products. AAPS J.
**2013**, 15, 674–683. [Google Scholar] [CrossRef] [PubMed][Green Version] - Baynes, R.; Riviere, J.; Franz, T.; Monteiro-Riviere, N.; Lehman, P.; Peyrou, M.; Toutain, P.-L. Challenges obtaining a biowaiver for topical veterinary dosage forms. J. Vet. Pharmacol. Ther.
**2012**, 35, 103–114. [Google Scholar] [CrossRef] [PubMed] - Pershing, L.K.; Nelson, J.L.; Corlett, J.L.; Shrivastava, S.P.; Hare, D.B.; Shah, V.P. Assessment of dermatopharmacokinetic approach in the bioequivalence determination of topical tretinoin gel products. J. Am. Acad. Dermatol.
**2003**, 48, 740–751. [Google Scholar] [CrossRef] [PubMed] - Committee for Medicinal Products for Human Use (CHMP). Draft guideline on quality and equivalence of topical product. CHMP/QWP/708282/2018. 2018. Available online: https://www.ema.europa.eu/en/documents/scientific-guideline/draft-guideline-quality-equivalence-topical-products_en.pdf (accessed on 18 October 2018).
- Dolz, M.; Hernández, M.J.; Pellicer, J.; Delegido, J. Shear Stress Synergism Index and Relative Thixotropic Area. J. Pharm. Sci.
**1995**, 84, 728–732. [Google Scholar] [CrossRef] [PubMed] - Mezger, T.G. The Rheology Handbook: For Users of Rotational and Oscillatory Rheometers, 4th ed.; Vincentz Network: Hannover, Germany, 2014; ISBN 978-3-87870-174-3. [Google Scholar]
- Picó, J.A.; Peris, J.; Sánchez, A.; Hernández, M.J.; Nacher, A.; Diez-Sales, O. A comparative rheological study of several dentifrices trademarks. In The multidisciplinary science of rheology. Towards a healthy and sustainable development; GER: Valencia, Spain, 2017; pp. 164–168. [Google Scholar]
- Sanz, T.; Salvador, A.; Hernández, M.J. Creep–Recovery and Oscillatory Rheology of Flour-Based Systems. In Advances in Food Rheology and Applications; Elsevier: Amsterdam, The Netherlands, 2017; pp. 277–295. ISBN 978-0-08-100431-9. [Google Scholar]
- Bonate, P.L. Appendix: Computer Intensive Statistical Methods. In Pharmacokinetic-Pharmacodynamic Modeling and Simulation; Springer: New York, NY, USA, 2016; pp. 353–363. [Google Scholar]
- Shapiro, S.S.; Wilk, M.B. An Analysis of Variance Test for Normality (Complete Samples). Biometrika
**1965**, 52, 591–611. [Google Scholar] [CrossRef] - Royston, J.P. An Extension of Shapiro and Wilk’s W Test for Normality to Large Samples. J. R. Stat. Soc. Ser. C Appl. Stat.
**1982**, 31, 115–124. [Google Scholar] [CrossRef] - Committee For Medicinal Products For Human Use (CHMP). Guideline on the requirements for clinical documentation for orally inhaled products (OIP) including the requirements for demonstration of therapeutic equivalence between two inhaled products for use in the treatment of asthma and chronic obstructive pulmonary disease (COPD) in adults and for use in the treatment of asthma in children and adolescents. CPMP/EWP/4151/00 Rev. 1. 2009. Available online: https://www.ema.europa.eu/en/documents/scientific-guideline/guideline-requirements-clinical-documentation-orally-inhaled-products-oip-including-requirements_en.pdf (accessed on 22 January 2009).
- Questions and Answers of the Pharmacokinetic Working Party. 3.4 Evaluation of orally inhaled medicinal products: Can I scale acceptance limits (for Cmax and perhaps AUC) to allow for variability in reference product for fine particle dose? January 2015. Available online: https://www.ema.europa.eu/en/human-regulatory/research-development/scientific-guidelines/clinical-pharmacology-pharmacokinetics/clinical-pharmacology-pharmacokinetics-questions-answers (accessed on 23 September 2019).
- Davit, B.M.; Stier, E.; Jiang, X.; Anand, O. Expectations of the US-FDA regarding dissolution data in generic drug regulatory submissions. Biopharma. Asia
**2013**, 2, 14–21. [Google Scholar] - Mould, D.R.; Upton, R.N. Basic Concepts in Population Modeling, Simulation, and Model-Based Drug Development—Part 2: Introduction to Pharmacokinetic Modeling Methods. CPT Pharmacomet. Syst. Pharmacol.
**2013**, 2, e38. [Google Scholar] [CrossRef] [PubMed] - Gobburu, J.V.S.; Lawrence, J. Application of Resampling Techniques to Estimate Exact Significance Levels for Covariate Selection During Nonlinear Mixed Effects Model Building: Some Inferences. Pharm. Res.
**2002**, 19, 92–98. [Google Scholar] [CrossRef] [PubMed] - Mangas-Sanjuan, V.; Pastor, J.M.; Rengelshausen, J.; Bursi, R.; Troconiz, I.F. Population pharmacokinetic/pharmacodynamic modelling of the effects of axomadol and its O-demethyl metabolite on pupil diameter and nociception in healthy subjects. Br. J. Clin. Pharmacol.
**2016**, 82, 92–107. [Google Scholar] [CrossRef] [PubMed] - Committee For Medicinal Products For Human Use (CHMP). Guideline on the investigation of bioequivalence. CPMP/EWP/QWP/1401/98 Rev 1/Corr **. 2010. Available online: https://www.ema.europa.eu/en/investigation-bioequivalence (accessed on 29 January 2010).
- Kryscio, D.R.; Sathe, P.M.; Lionberger, R.; Yu, L.; Bell, M.A.; Jay, M.; Hilt, J.Z. Spreadability Measurements to Assess Structural Equivalence (Q3) of Topical Formulations—A Technical Note. AAPS Pharm. Sci. Tech.
**2008**, 9, 84–86. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**Experimental distribution of each batch (coloured) and overall distribution (black) stratified by the rheological parameters considered. The p value of the Shapiro–Wilk test assesses the normality of the overall distribution. S

_{R}, relative thixotropic area; σ

_{0}, yield stress; η

_{0}, zero-shear viscosity; η

_{100}, viscosity at 100 s

^{−1}; tan δ, loss tangent at 1 Hz; ${G}_{1}^{\prime}$, calculated elastic modulus; ${G}_{1}^{\u2033}$, calculated viscous modulus; m’ and m″ are the parameters obtained when fitting G’ and G’’, respectively, versus frequency; AUC, area under the surface versus weight curve.

**Figure 2.**Bootstrap analysis of rheological parameters - 1 reference batch versus 1 reference batch. 10,000 geometric mean ratios (light grey area) resulting from the bootstrap analysis of “1 reference batch versus 1 test batch″ for each rheological parameter. Data of 10 batches and 12 replicate each were used. Median (red line) and non-parametric 90% CI (blue lines) of the probability distribution. Dashed lines represent the acceptance limits for equivalence (90–111.11%) stated in the EMA guideline [4]. S

_{R}, relative thixotropic area; σ

_{0}, yield stress; η

_{0}, zero-shear viscosity; η

_{100}, viscosity at 100 s

^{−1}; tan δ, loss tangent;${G}_{1}^{\prime}$, calculated elastic modulus; ${G}_{1}^{\u2033}$, calculated viscous modulus; m’ and m″ are the parameters obtained when fitting G’ and G’’, respectively, versus frequency; AUC, area under the surface versus weight curve (spreadability).

**Figure 3.**Bootstrap analysis of rheological parameters – five reference batches versus five reference batches. 10,000 geometric mean ratios (light grey area) resulting from the bootstrap analysis of “5 reference batches versus five test batches″ for each rheological parameter. Data of 10 batches and 12 replicate each were used. Median (solid red line) and non-parametric 90% CI (solid blue lines) of the probability distribution. Dashed lines represent the acceptance limits for equivalence (90–111.11%) stated in the EMA guideline [4]. S

_{R}, relative thixotropic area; σ

_{0}, yield stress; η

_{0}, zero-shear viscosity; η

_{100}, viscosity at 100 s

^{−1}; tan δ, loss tangent at 1 Hz;${G}_{1}^{\prime}$, calculated elastic modulus; ${G}_{1}^{\u2033}$, calculated viscous modulus; m’ and m″ are the parameters obtained when fitting G’ and G’’, respectively, versus frequency; AUC, area under the surface versus weight curve (spreadability).

**Table 1.**Physical parameters (rheological properties and spreadability) of 10 batches (12 replicates each) of reference formulation.

Parameter | Mean | SD | Minimum | Maximum | Total CV (%) | Inter-Batch CV (%) | Intra-Batch CV | |
---|---|---|---|---|---|---|---|---|

Minimum | Maximum | |||||||

S_{R} (%) | 33.80 | 4.82 | 25.06 | 44.56 | 14.3 | 12.2 | 1.0 | 16.4 |

σ_{0} (Pa) | 519 | 57 | 369 | 647 | 11.0 | 10.6 | 1.6 | 6.8 |

η_{0} (Pa·s) | 630,067 | 74,229 | 488,890 | 839,980 | 11.8 | 9.6 | 3.6 | 10.1 |

η _{100} (Pa·s) | 9.63 | 0.67 | 8.05 | 11.40 | 7.0 | 5.7 | 2.0 | 9.3 |

tan δ | 0.700 | 0.020 | 0.651 | 0.737 | 2.9 | 2.7 | 0.8 | 2.0 |

${G}_{1}^{\prime}$ (Pa) | 53,255 | 7741 | 37,195 | 76,270 | 14.6 | 13.1 | 5.9 | 11.5 |

m′ | 0.369 | 0.010 | 0.334 | 0.394 | 2.6 | 1.9 | 1.3 | 2.7 |

${G}_{1}^{\u2033}$ (Pa) | 35,829 | 4723 | 26,149 | 49,457 | 13.2 | 11.7 | 5.2 | 10.6 |

m″ | 0.365 | 0.015 | 0.310 | 0.399 | 4.1 | 3.1 | 1.8 | 4.6 |

Spreadability (mm^{2}) | 342,224 | 15,438 | 292,922 | 379,991 | 4.5 | 3.7 | 1.7 | 4.9 |

_{R}, relative thixotropic area; σ

_{0}, yield stress; η

_{0}, zero-shear viscosity; η

_{100}, viscosity at 100 s

^{−1}; tan δ, loss tangent measured at 1 Hz; ${G}_{1}^{\prime}$, calculated elastic modulus; ${G}_{1}^{\u2033}$, calculated viscous modulus; m′ and m″ are the parameters obtained when fitting G′ and G″, respectively, versus frequency.

**Table 2.**Comparison of rheological parameters and spreadability. Number of ratios within the limits of equivalence (n) divided by total number of comparisons made (N).

Comparison Method | 1 Batch vs. 1 Batch | 5 Batches vs. 5 Batches | Median Batch within 5 Batches vs. Median Batch within 5 Batches | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Acceptance Range | 10% | 15% | 20% | 25% | 30% | 10% | 15% | 20% | 25% | 10% | 15% | 20% | 25% |

Parameter | |||||||||||||

S_{R} (%) | 7/45 (16%) | 17/45 (38%) | 27/45 (60%) | 36/45 (80%) | 43/45 (96%) | 66/126 (52%) | 100/126 (79%) | 124/126 (98%) | 126/126 (100%) | 54/126 (43%) | 60/126 (48%) | 105/126 (83%) | 126/126 (100%) |

σ_{0} (Pa) | 17/45 (38%) | 26/45 (58%) | 34/45 (76%) | 39/45 (87%) | 42/45 (93%) | 83/126 (66%) | 120/126 (95%) | 126/126 (100%) | 126/126 (100%) | 90/126 (71%) | 111/126 (88%) | 126/126 (100%) | 126/126 (100%) |

η _{0} (Pa·s) | 10/45 (22%) | 25/45 (56%) | 36/45 (80%) | 41/45 (91%) | 45/45 (100%) | 96/126 (76%) | 124/126 (98%) | 126/126 (100%) | 126/126 (100%) | 0/126 (0%) | 102/126 (81%) | 117/126 (93%) | 126/126 (100%) |

η _{100} (Pa·s) | 33/45 (73%) | 39/45 (87%) | 44/45 (98%) | 45/45 (100%) | 45/45 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) |

tan δ | 45/45 (100%) | 45/45 (100%) | 45/45 (100%) | 45/45 (100%) | 45/45 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) |

${G}_{1}^{\prime}$ (Pa) | 7/45 (16%) | 19/45 (42%)) | 25/45 (56%) | 34/45 (76%) | 42/43 (93%) | 65/126 (52%) | 108/126 (86%) | 124/126 (98%) | 126/126 (100%) | 36/126 (29%) | 78/126 (62%) | 84/126 (67%) | 126/126 (100%) |

m’ | 45/45 (100%) | 45/45 (100%) | 45/45 (100%) | 45/45 (100%) | 45/45 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) |

${G}_{1}^{\u2033}$ (Pa) | 7/45 (16%) | 20/45 (44%) | 31/45 (69%) | 39/45 (87%) | 43/45 (96%) | 76/126 (60%) | 117/126 (93%) | 126/126 (100%) | 126/126 (100%) | 36/126 (29%) | 84/126 (67%) | 126/126 (100%) | 126/126 (100%) |

m″ | 45/45 (100%) | 45/45 (100%) | 45/45 (100%) | 45/45 (100%) | 45/45 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) |

Spreadability (mm^{2}) | 41/45 (91%) | 45/45 (100%) | 45/45 (100%) | 45/45 (100%) | 45/45 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) | 126/126 (100%) |

**bold**identify the lowest acceptance range that concludes equivalence ≥ 80% of comparisons. S

_{R}, relative thixotropic area; σ

_{0}, yield stress; η

_{0}, zero-shear viscosity; η

_{100}, viscosity at 100 s

^{−1}; tan δ, loss tangent at 1 Hz; ${G}_{1}^{\prime}$, calculated elastic modulus; ${G}_{1}^{\u2033}$, calculated viscous modulus; m′ and m″ are the parameters obtained when fitting G′ and G″, respectively, versus frequency.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mangas-Sanjuán, V.; Pleguezuelos-Villa, M.; Merino-Sanjuán, M.; Hernández, M.J.; Nácher, A.; García-Arieta, A.; Peris, D.; Hidalgo, I.; Soler, L.; Sallan, M.;
et al. Assessment of the Inter-Batch Variability of Microstructure Parameters in Topical Semisolids and Impact on the Demonstration of Equivalence. *Pharmaceutics* **2019**, *11*, 503.
https://doi.org/10.3390/pharmaceutics11100503

**AMA Style**

Mangas-Sanjuán V, Pleguezuelos-Villa M, Merino-Sanjuán M, Hernández MJ, Nácher A, García-Arieta A, Peris D, Hidalgo I, Soler L, Sallan M,
et al. Assessment of the Inter-Batch Variability of Microstructure Parameters in Topical Semisolids and Impact on the Demonstration of Equivalence. *Pharmaceutics*. 2019; 11(10):503.
https://doi.org/10.3390/pharmaceutics11100503

**Chicago/Turabian Style**

Mangas-Sanjuán, Víctor, María Pleguezuelos-Villa, Matilde Merino-Sanjuán, Mª Jesús Hernández, Amparo Nácher, Alfredo García-Arieta, Daniel Peris, Irene Hidalgo, Lluís Soler, Marta Sallan,
and et al. 2019. "Assessment of the Inter-Batch Variability of Microstructure Parameters in Topical Semisolids and Impact on the Demonstration of Equivalence" *Pharmaceutics* 11, no. 10: 503.
https://doi.org/10.3390/pharmaceutics11100503