# WikiJournal Preprints/Antidepressant Mirtazapine Solid dispersions with Characterization and Formulation Development by 3² Factorial Design

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This article is an unpublished pre-print undergoing public peer review organised by the WikiJournal of Medicine.
First submitted: 25 Nov 2022 Reviewer comments
QID: Q115626598
Suggested (provisional) preprint citation format: Taraka Ramarao Challa; Pravallika Kottakota. "Antidepressant Mirtazapine Solid dispersions with Characterization and Formulation Development by 3² Factorial Design". WikiJournal Preprints. Wikidata Q115626598.
License: This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction, provided the original author and source are credited
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## Article information

Authors: Taraka Ramarao Challa  , Pravallika Kottakota
* ↑ Department of Pharmaceutical Technology, Sri Venkateswara College of Pharmacy, Etchrela, Srikakulam, Andhra Pradesh- 532410, India
* ↑ tarak.pharm60@gmail.com

## Abstract

Background: The purpose of this study was to examine how to improve the solubility of the poorly soluble drug mirtazapine by preparing six weight ratios of solid dispersions with different amounts of the pure drug (M1), drug: HPMC E5 (1:2), HPMC (1:2, 1:4), and drug: PVP k30 (1:1, 1:3). In comparison to pure drug release of 75.21% in 60 minutes, solid dispersions released medication in 8 to 10 minutes. The two independent components, X1 and X2, have good to exceptional flow characteristics and are suited for direct compression. X1 is a ratio of the solid dispersion equivalent (drug: PVP K30: HPMC) and X2 is a super disintegrant (Sodium starch glycolate).
Methods: Using Design Expert software, the analysis of variance (ANOVA), 3D surface plots, counterplots, optimization, and desirability were performed. Fourier-transform infrared spectroscopy is used to investigate drug-excipient compatibility. In the comparative studies, tablets (Mirtaz 30) with an improved tablet formulation were used (F2).
Findings: The values of f1 and f2 were determined to be 9.616 and 76.758, respectively; the dissolution profiles of the optimized formulation (F2) and the commercial tablet are the same. The optimized formula had a greater desirability concern (0.6271), indicating that the formulation was suitable. The model's predictability and validity were shown by the experimental values matching the expected values.
Conclusion: Comparative pharmacokinetics involve commercial medicine and optimized tablets.

## Introduction

Mirtazapine (mtz) is an antidepressant with slightly less a1-adrenoceptor-blocking activity, which increases the release of both noradrenalin and serotonin. It belongs to the biopharmaceutical classification system (BCS) Class II drug because of its low solubility and high permeability, chemical structure is shown in Figure 1.
According to current research, mtz meets the requirements of a prospective solid oral dosage form for local administration of a rapid dissolving film when placed in the oral cavity, quickly gets hydrated, binds to the site of application, and subsequently disintegrates to release the drug. In the sublimation technique, different concentrations of Explotab coupled with camphor were shown to have good drug release at 10 mg of Explotab; however, drug release is slowed above 10 mg. The mtz-loaded niosomes were then incorporated into an in situ gel base containing poloxamer 407 and carbopol 934, which was used to overcome the limitations of the pure drug by maintaining therapeutically effective drug concentration for a longer period, reducing drug administration frequency and increasing drug bioavailability by directly delivering the drug to the brain. The orally disintegrating tablets containing crospovidone, Lycoat, SSG, dehydrated banana powder, and Plantago ovata were created with a variety of natural and synthetic super disintegrants to boost mirtazapine oral bioavailability. The super disintegrant concentration was raised, and the time it took for tablets to dissolve decreased. To increase the solubility and oral bioavailability of the medicine mirtazapine and to provide taste-masked medication, self-emulsifying drug delivery devices have been created. In the coacervation process with Eudragit E-100, researchers utilized mirtazapine in vitro taste masking granules. The creation and assessment of solid lipid nanoparticles (SLNs) loaded with mirtazapine as a topical medication delivery method for the treatment of pruritus. The mirtazapine bioadhesive controlled-release dosage form is made using the controlled-release agents carbopol 934P and HPMC K4M.
The recently reported achievements in formulation research were made thanks to the utilization of HPMC and PVPK30 The reports on numerous carriers effectively employed. The release rates of the tablets and PVP-HPMC SDs, which PVP helped increase, and the stability of the SDS, which HPMC E5 helped maintain, all disintegrated, demonstrating the synergistic action of PVPs and HPMC E5. The poorly soluble medicines albendazole, danazol, and felodipine were co-ground with polyvinylpyrrolidone, hydroxypropyl methylcellulose, and sodium lauryl sulfate. The matrix is evenly distributed with the water-soluble drug addition of PVP to the HPMC drug release profiles. The norfloxacin solubilization was accelerated by HPMC addition up to 5% (w/w); inhibition of norfloxacin solubilization by HPMC addition above 5% (w/w). They looked into creating a ternary compound with hydroxypropyl to increase the solubility of modafinil in water. A novel hydroxypropyl methylcellulose (HPMC) solid dispersion (SD) system was created with sodium lauryl sulfate (SLS) as drug release promoters to speed up the release rate and oral absorption of tacrolimus. The various statistically experimental designs are in vitro and in vivo and are reported and optimization. Using a general multilevel factorial design, the primary and interaction effects of independent variables were optimized and assessed.
The purpose of this study was to improve the dissolution of the drug mirtazapine, which is poorly soluble, to examine six proportions of solid dispersion with pure drug (M1). The weight ratios of the drug: HPMC E5 (1:2) (M2), HPMC (1:2, 1:4) (M3, M4), and PVP k30 (1:1, 1:3) (M5, M6) were created. The 3$^2$ factorial design is one of the two independent components X1 and X2 is the ratio of solid dispersion equivalent (drug: PVP K30: HPMC) and super disintegrant. Utilizing Design Expert software, the analysis of variance (ANOVA), 3D surface plots, counterplots, optimization, and desirability were performed.

## Materials and Methods

Materials
Mirtazapine, A Gift sample from New land PVT.ltd Hyderabad, PVP K 30 (Polyvinyl pyrrolidine): Purchased sample from Loba Chemie PVT ltd. Mumbai India, HPMC E5 (Hydroxy propyl methyl cellulose): Purchased sample from Otto Chemie PVT ltd. Mumbai, India, Super tab 11sd: Gift sample from IMDC Private Limited, Mumbai, Sodium starch glycolate (extra pure): purchased from Loba Chemie.Pvt. Ltd. Mumbai, Talc fine powder extra pure (talcum powder): Purchased sample from Loba Chemie Pvt ltd Mumbai India, Magnesium stearate: Purchased sample from Loba Chemie Pvt ltd Mumbai India, Acetone: Purchased sample from Thermo fisher scientific, Dichloro methane: Emplura Merck life science Pvt ltd. Mumbai, India.
Preparation of Solid dispersions by Solvent Evaporation method
The solvent evaporation was used to make solid dispersion of mirtazapine pure drug (M1) with varied weight ratios of polymers such as HPMC (1:2) (M2), HPMC (1:2)(M3), 1:4(M4), and PVP k30 (1:1 (M5),1:3(M6). To perform the surface modification, a precisely weighed amount of the drug and polymer was introduced to the triturate well in the motor and pestle. The solution of acetone and dichloromethane (1:4) was then added drop by drop. The product was sieved through # 22 sieves after the solvent was removed using a hot air oven at 50–60 degrees Celsius. The sample was then kept in desiccators at room temperature for subsequent analysis.
Preparation of tablets
The tablets were made utilizing the direct compression approach, which was based on an experimental design that used a 3$^2$-factorial design, as indicated in Tables.1. The solid dispersion comprises varying weighted ratios of the medication equivalent to 30mg. The independent variable X1 with different weight ratios of the drug: PVP K30: HPMC (higher level) (+) (30:30:7.5) (mg), medium level (0) (30:30:3.75) (mg), and low level (-) (30:30:2.5) (mg). To create a dry blending, combine with Super tab 11SD and other excipients. Talc and magnesium stearate were combined, and the independent variable X2 with higher (+) (8.5%), medium (-) (4.5%), and lower (-) (2.7%) sodium starch glycolate (super disintegrate) was added. The mixture of materials was compressed into a tablet using a single-punch tablet machine.
Evaluation of the tablets
All tablets prepared were evaluated for the Content of active ingredients, Hardness, Friability, Disintegration time, and Dissolution rate.
Content of active ingredient
The five tablets were properly weighed and ground. The tablet powder equivalent to 30mg of mirtazapine was extracted with 6–10 ml of methanol and then heated in a boiling test. A pH 6.8 phosphate buffer was used to dilute the methanolic extract to 100 ml, and the drug content was then assessed using a UV spectrophotometric method.
Hardness
Monsanto uses a hardness tester to determine the tablet's hardness.
Friability
Friability was measured using a Labindia tablet friability tester (FT 1020).
Disintegration time
The Labindia Tablet Distentegrating Tester was used to determine the disintegration time (DT 1000).
Dissolution study
A USP Type II (Paddle method) dissolution test instrument (Labindia, DS 8000) was used to measure the dissolution rate of mirtazapine and its tablet formulation. Throughout the inquiry, phosphate buffer pH6.8 was used as the dissolution fluid, and the stirrer speed was set at 50 rpm. Various time intervals, including 10, 20, 30, 40, 50, and 60 minutes, were used to collect each test sample (5 ml). The samples were evaluated at a wavelength of 246nm with a UV-Visible Spectrophotometer (ELICO Double beam SL 210). A new fluid was added after each sample of the evaporating liquid was taken out. Each created tablet was repeated three times for its rate of dissolution.
Drug Excipient Compatibility studies
The Fourier Infrared Spectroscopy (FTIR) spectra of samples were obtained on a Bruker ALPHA II FTIR system (Bruker OPTIK GmbH, Rudolf-Plank-Str, Germany) by using Kbr disc method (2mg sample in 300mg of Kbr) the scanning range was 4000-600 cm-$^1$ and the resolution was 1cm-$^1$.
Model Independent Approach
A basic model-independent method uses a difference factor (f$_1$) and a similarity factor to evaluate dissolution profiles (f$_2$). The percent difference between the two curves at each time point is determined by the difference factor, which measures the relative error between the two curves. We can investigate the superimposed dissolution profiles for f$_1$ values between 0 and 15. The similarity between the two dissolution profiles is indicated by the f$_2$ values between 50 and 100.
The Comparative studies marketed tablets (Mirtaz 30 mg) with optimized tablet formulation F2 with marketed tablets manufactured by Sun pharma laboratories ltd , Batch no: EMX0192, Manufacturing date: 01/2020, Expiry date: 12/2022.
Mean Dissolution Time (MDT)
Model-independent techniques come in several forms, including ratio tests and pair-wise processes. The ratio tests are relationships between variables collected simultaneously from the release assays of the reference formulation and the test product. They can range from a straight percent dissolved drug (%) to a ratio of mean dissolution time (MDT).
Dissolution efficiency (DE)
As a result of the expanding interest in medication availability, in vitro dissolution testing has become typical for several dosage formulations. Comparing the amount of time it takes for various amounts of active medication to be released into solution is the most typical method of assessment. The amount of drug still in solution after a specific amount of time is utilized for comparison. Dissolution Efficiency can take on a wide range of values depending on the periods chosen. To account for the bulk of the dissolving pattern, this should ideally be larger than 90% of the formulation, although, with slowly released drugs, this isn't always attainable.
High-performance liquid chromatography (HPLC) Method
The concentration in plasma samples was eluted using a mobile phase utilizing the HPLC method (Waters Alliance HPLC System, Model: e2695) at 290 nm with an Inertsil ODS (150x4.6 mm) at a flow rate of 1.0 mL/min. The mobile phase was composed of acetonitrile and 20 mM ammonium acetate buffer, pH 4.5, in a 60:40 volume ratio (35:65 percent v/v). The internal standard retention durations for mirtazapine and carbamazepine were 6.9766 minutes and 10.791 minutes, respectively.
Pharmacokinetics
18 male Wistar rats (250–300 g) were used in this study. The in vivo experimental methods were approved by the institutional animal ethics committee. The rats (n = 6) were split into three groups of six and fed a constant diet. At regular intervals, heparinized syringes were used to extract 0.3 mL of blood from each cannulated rat's right femoral artery and emptied into heparinized microtubes. Each blood sample was spun at 8000 rpm for 10 minutes to separate the plasma. The samples were then examined using the recommended HPLC method.
Data Analysis
Data were analyzed using a first-order and zero-order kinetics model. Using Design Expert software, dissolution parameters such as PD 10 (percent drug dissolved in 10 minutes), DE 10 (dissolution efficiency), and DE 30 (dissolution efficiency) are subjected to ANOVA (analysis of variance), 3D Surface plots, Counter plots, Desirability, and other statistical parameters.

## Results and Discussion

The aim of the present study work optimizes mirtazapine formulation by 3$^2$ factorial designs. The two independent factors such as X1 and X2 were tested to 3 level factorial design with different levels and an experimental trial to perform nine possible combinations were shown in Table.1.
Table. 1: Formula as per 3$^2$ factorial designs
| Formulation | X$_1$ | X$_2$ |
| F1 | + | + |
| F2 | + | 0 |
| F3 | + | _ |
| F4 | 0 | + |
| F5 | 0 | 0 |
| F6 | 0 | _ |
| F7 | _ | + |
| F8 | _ | 0 |
| F9 | _ | _ |
Different solid dispersions' dissolution behavior
The six weight ratios of a pure drug (M1), drug: HPMC E5 (1:2) (M2), HPMC (1:2, 1:4) (M3, M4), and drug: PVP k30 (1:1, 1:3) (M5, M6) solid dispersion were created, and dissolution was assessed using the dissolution profile. Under phosphate buffer pH 6.8, the in vitro performance of solid dispersions up to drug-polymer ratios of Drug: HPMC (1:2) (M2) and Drug: PVP K30 (1:1) (M5) was judged well. Both solid dispersions extend the release of mirtazapine to more than 10 minutes, whereas Drug: PVP K30 (1:1) provides 100% release in less than 8 minutes. In comparison to pure medicine, 75.210 percent of the substance is released in 60 minutes. The behavior of the dissolution In comparison to a pure medicine, 75.210 percent of the substance is released in 60 minutes. Figure 2 depicts the dissolving behavior of pure drug with various carriers HPMC E5 (1:2, 1:4), HPMC (1:2), and Drug: PVP K30 (1:1, 1:3). The dissolution of prepared solid dispersions was shown in Figure 2.
Flowability and compressibility
The angle of repose, bulk density, tapped density, Hausner's ratio, and Carr's index was used to determine the flow parameters of the preparation blend. The bulk density ranges from 0.240 to 0.378 gm/cc, tapped density from 0.356 to 0.450 gm/cc, the angle of repose from 10 to 16, Carr's index from 10 to 17, and Hauser's ratio from 1 to 1.25. The above characteristics of the preparation blend show good to excellent flow qualities and are appropriate for direct compression, Table.2 depicts the flow properties.
Table 2. Flow Properties of prepared blend
| S/n | Formulations | Bulk density (gr/cc) | True density (gr/cc) | Angle of repose | Carr’s Index | Hausner’s ratio |
| 1 | F1 | 0.310 | 0.356 | 12.167 | 10.86 | 0.870 |
| 2 | F2 | 0.345 | 0.450 | 11.321 | 14.21 | 0.766 |
| 3 | F3 | 0.313 | 0.410 | 13.03 | 12.43 | 0.7603 |
| 4 | F4 | 0.240 | 0.357 | 13.807 | 15.81 | 0.672 |
| 5 | F5 | 0.372 | 0.415 | 12.372 | 17.84 | 0.896 |
| 6 | F6 | 0.301 | 0.396 | 14.731 | 16.18 | 0.760 |
| 7 | F7 | 0.357 | 0.423 | 11.911 | 12.63 | 0.843 |
| 8 | F8 | 0.378 | 0.411 | 10.781 | 10.51 | 0.919 |
| 9 | F9 | 0.363 | 0.378 | 15.263 | 13.26 | 0.960 |
Drug excipient compatibilities
Figure 3 and Figure 4 show mirtazapine's FTIR spectrum, which shows characteristic peaks at 3709 cm$^{-1}$, 3647 cm$^{-1}$, 3615cm$^{-1}$ (due to N-H stretch), 3218cm$^{-1}$, 2935cm$^{-1}$, 2840cm$^{-1}$, 2796cm$^{-1}$ (due to C-H stretch), 2362cm$^{-1}$ (due to C-C stretch), 1572cm$^{-1}$ (due to N-H bending), 1427 cm$^{-1}$, Pure drug FTIR spectrum with various excipients PVP K30, HPMC, and SSG all have same peaks. Because the FTIR spectra of pure drugs and combinations with diverse excipients were identical, no chemical interactions were found.
Tablet properties
The physical properties of all tablet formulations are shown in Table.3
Table 3. Physical properties of Mirtazapine tablet formulation F1-F9
| S/n | Formulation | Hardness (Kg/cm$^2$) | Friability (%) | Disintegration time(min.sec) | Drug content (%) |
| 1 | F1 | 4.5 | 0.1956 | 9 .9 | 98.1 |
| 2 | F2 | 4.1 | 0.2652 | 5. 30 | 99.3 |
| 3 | F3 | 4.3 | 0.1643 | 7. 33 | 97.9 |
| 4 | F4 | 4.0 | 0.8412 | 7. 40 | 98.57 |
| 5 | F5 | 4.4 | 0.1892 | 4. 2 | 99.3 |
| 6 | F6 | 4.2 | 0.3215 | 6. 28 | 98.187 |
| 7 | F7 | 4.1 | 0.4281 | 11.29 | 99.130 |
| 8 | F8 | 4.5 | 0.3654 | 6. 4 | 98.319 |
| 9 | F9 | 4.0 | 0.2010 | 3.12 | 98.187 |
Hardness
The hardness of all the tablets was found to be between 4 and 4.5 kg/cm2, with the highest hardness in (F8), indicating that the increase in hardness was related to the binding capabilities of mirtazapine tablets.
The friability test is important for determining the physical strength of tablets and ensuring that all manufactured formulations meet pharmacopeia criteria with a percentage weight loss of less than 1%.
3.5.3 All formulation tablets disintegrate within time, with disintegration times of F1 is 9 min. 9 seconds, F2 is 5 min. 30 seconds, F3 is 7 min.33 seconds, F4 is 7 min. 40 seconds, F5 is 4 min. 2 seconds, F6 is 6 min. 28 seconds, F7 is 11 min. 29 seconds, F8 is 6 min. 4 seconds, and F9 is 3 min. 12 seconds, respectively. The disintegration times of all produced tablets range from 3 min. 12 seconds to 9 min. 9 seconds. The F9 formulations, which contain low levels of X1 and X2, have a short disintegration time. Figure 5 depicts the influence of X1 and X2 concentrations on tablet disintegration time. A greater level of two polymers concentration and a lower level of two polymers concentration increased and decreased the disintegration time, respectively. The combination of high polymer concentrations X1 and X2 has a negative effect on tablet disintegration, requiring the creation of a thick barrier to prevent more disintegration medium penetration.
Active ingredient content
The medication concentration of all manufactured tablets is between 97 and 99 percent. According to IP, the above quality control criteria of the prepared tablets meet the standard specification of uncoated tablets.
In- vitro dissolution
Figure 6 and Figure 7 illustrate the in vitro dissolving profile of preparation tablets. In comparison to other formulations, the F2, and F4 formulation has a quick and maximal drug release of 100% at 50 minutes. The Drug: PVP K30: HPMC (30:30:7.5) mg and 11.25mg of SSG (Sodium Starch Glycolate) in the F2 formulation had a significantly superior dissolving performance. The F4 contains Drug: PVP K30: HPMC,(30:30:3.75)mg, and 8.5% of SSG. The F1 formulation has a medication release rate of 58 percent in 60 minutes. The F3 formulation has a medication release rate of 69 percent in 60 minutes, and 75 percent medication release in 60 minutes with the F5 formulation. The F6 formulation has a medication release rate of 66% in 60 minutes. The F7 formulation has a medication release rate of 84 percent in 60 minutes. The F8 formulation has a medication release rate of 75% in 60 minutes. The F9 formulation has a 60 minute medication release rate of 59 percent. The F1, F9 formulation results in less dissolving, which is used to reduce variability. The order of drug dissolution of various formulations is displayed in ascending order F2< F4<F7<F5< F8< F3<F6<F9<F1.
Model Dependent
The zero-order and first-order drug release kinetics were used. Table.4 shows the correlation coefficient (r-value). The correlation coefficient values in all situations were greater than first-order release kinetics rather than zero-order release kinetics. Table.4 shows the dissolution parameters PD$_{10}$, DE $_{30}$, DE$_{10}$, t $_{50}$, t $_{90}$, MDT, and Dissolution rate constant (K1).
Table 4. Dissolution parameters of prepared mirtazapine tablet formulation F1-F9
| Formulation | PD$_{10}$ (%) | DE$_{10}$ (%) | DE$_{30}$ (%) | t$_{50}$ (min) | t$_{90}$ (min) | K$_1$ (min$^{-1}$) | Correlation coefficient (r)Zero order | Correlation coefficient (r) First order | MDT |
| F1 | 38.24 | 19.12 | 28.58 | 56.5 | 80 | 0.0161 | 0.7763 | 0.7885 | 34.3240 |
| F2 | 86.76 | 43.25 | 74 | 5 | 20 | 0.0299 | 0.7272 | 0.9214 | 28.3005 |
| F3 | 37.73 | 18.86 | 25.28 | 49 | 70.1 | 0.0262 | 0.8842 | 0.888 | 37.0597 |
| F4 | 69.5 | 34.5 | 69.5 | 7 | 59 | 1.612 | 0.7724 | 0.8778 | 70.403 |
| F5 | 29.25 | 14.76 | 30.83 | 33.5 | 75.5 | 0.0156 | 0.9715 | 0.992 | 37.4833 |
| F6 | 28.42 | 14.71 | 33.45 | 26 | 75.5 | 0.0274 | 0.9239 | 0.9710 | 98.1907 |
| F7 | 38.6 | 19 | 46.5 | 13.5 | 76.5 | 0.075 | 0.7908 | 8815 | 35.900 |
| F8 | 35.16 | 17.58 | 35.63 | 18.5 | 49 | 0.0308 | 0.8159 | 0.9016 | 79.269 |
| F9 | 31.72 | 15.86 | 33.811 | 29.5 | 76 | 0.0105 | 0.8618 | 0.8858 | 35.978 |
Comparative Studies
The investigations compared the optimized Mirtazapine tablet formulation (F2) to the commercially available tablets (mirtz 30). The value of f1 was determined to be smaller than 15 (9.616), indicating that the two curves are identical. The f2 value was discovered to be more than 50 (76.758). As a result, the dissolution profiles of the optimized formulation F2 and the market tablet are close or identical.
Data Analysis
The direct compression method was used to create 3$^2$ factorial designs. The expert design software (design expert version 13 stat-Ease Inc.com, USA). After fitting these data, the Design expert generated a viable model equation. For statistical optimization, the three responses Y1 (t$_{90}$), Y2 (t$_{50}$), and Y3 (MDT) were chosen and fitted to a specified model. Table 6 compares statistical parameters such as R$^2$, and PRESS, and provides an overview of statistical parameters. Design expert software was used to compute std.dev, Mean, C.V percent, Adj. R$^2$, Pred R$^2$, Adeq accuracy, BIC, AICc, -2 log-likelihood, F values, and P values. To calculate the value of t$_{90}$, t $_{50}$, and MDT, the dependent responses were measured. The polynomial equation three parameters t$_{90}$, t$_{50}$, and MDT, was applied as a mathematical modeling. Y= βₒ + β1 x1 + β2 x2 + β 1,1 x2 + β 1,2 x1 x 2 + β 2,2 x2 x2
Where Y= is the dependent variable, β0 is the mean response of 9 runs, and 1, 2 is the estimated coefficient for the associated factor X1, and each represents the average result of altering one component at a time from a low to a high value. When three elements change at the same time, the interaction time (X1.X1, X1.X2, and X2.X2) defeats the changes in the response.
t$_{90}$ responses (Y1): The t$_{90}$ analysis of variance and statistical parameters are shown in Table.5 and Table.6. The model equation can be used to describe the parameter are t$_{90}$ = + 57.68 + 4.36X1 + 2.60X 2 + 15.34 X1.X2 + 35.70 X1X2 – 8.722. X2. The positive sign for X1, and X2 shows that increasing the level of X1, and X2 higher drug release by 90 percent. The R$^2$ value of 0.5285 for t$_{90}$ indicates that the independent and dependent variables are well correlated. The analysis of variance was significance p< 0.0339 was determined. The 'F' value for t$_{90}$ was discovered to be of model 5.04, with independent variable X1= 9.91 and other statistical characteristics such as Adj.R$^2$ = 0.4237, PRESS =75.47, Adeq precision = 4.4809, BIC= 56.67, AICc= 58.22, - 2 log likelihood =49.22, Mean = 5.58, Std. DEV= 2.17, C.V%=38.96, Pred R square. =0.5285.
t$_{50}$(Y2): The t$_{50}$ analysis of variance and statistical parameters shown in Table.5 and Table.6, analysis of variance of the t$_{50}$ model yielded a statistically significant result of p< 0.04130. The model equation can determine the desirability of the parameter t50 (Y2) = +2.96003 - 0.293708.X1 - 0.084595 X2 + 0.017917. The negative sign for X1 and X2 implies that the level of X1 and X2 has decreased by t$_{50}$. The R$^2$ value of 0.6235 for t$_{50}$ indicates that the independent and dependent variables are well correlated. The 'F' value for t$_{50}$ was determined to be 4.42, with independent variables X1, 2.5, and X2, 4.31, as well as other statistical metrics like Std. DEV = 0.7554, Mean =3.14, and C.V percent =24.02, PRESS=10.27, -2log likelihood =22.46, Adj R-squared=0.4823, Pred R- squared=0.1529, Adeq precision=6.1794, BIC=32.40, AICc=36.17.
Table 5. Analysis of Variance (ANOVA) of Different Dependent Variables Y1, Y2 and Y3
Time Requires to 90% Drug Release (t$_{90}$) :
| Source | Sum of square | Df | Mean square | F value | P- value | Remarks |
| Model | 47.58 | 2 | 23.79 | 5.04 | 0.0339 | Significant |
| A- PVP K 30-HPMC | 9.91 | 1 | 9.91 | 1.95 | 0.1963 | |
| A$^2$ | 38.39 | 1 | 38.39 | 8.14 | 0.0190 | |
| Residual | 42.45 | 9 | 4.72 | | | |
| Cor total | 90.03 | 11 | | | | |
| Time Requires to 50% Drug Release ( t$_{50}$) |||||||
| Model | 7.56 | 3 | 2.52 | 4.42 | 0.0413 | Significant |
| A- PVP K 30-HPMC | 4.31 | 1 | 2.52 | 7.56 | 0.0251 | |
| B – SSG | 3.01 | 1 | 4.31 | 5.27 | 0.0508 | |
| C- Super tab 11 sd | 0.2379 | 1 | 3.01 | 0.4169 | 0.5366 | |
| Residual | 4.57 | 8 | 0.2379 | | | |
| Cor total | 12.31 | 1 | 0.5707 | | | |
| Mean Dissolution Time (MDT) |||||||
| Model | 94.88 | 3 | 31.63 | 53.98 | <0.0001 | Significant |
| A- PVP K 30-HPMC | 0.2205 | 1 | 0.2205 | 0.3760 | 0.5568 | |
| B – SSG | 5.33 | 1 | 5.33 | 9.09 | 0.0167 | |
| A$^2$ | 89.32 | 1 | 89.32 | 152.31 | <0.0001 | |
| Residual | 4.69 | 8 | 0.5865 | | | |
| Cor total | 99.57 | 11 | | | | |
Table 6. Statistical parameters of Dependent variables
| Parameter | Y1 (t$_{90}$) | Y2 (t$_{50}$) | Y3 (MDT) |
| Std. DEV | 2.17 | 0.7554 | 0.7658 |
| Mean | 5.58 | 3.14 | 7.62 |
| C.V% | 38.96 | 24.02 | 10.06 |
| R$^2$ | 0.5285 | 0.6235 | 0.9529 |
| Adj R$^2$ | 0.4237 | 0.4823 | 0.9352 |
| Predicted R$^2$ | 0.1617 | 0.1529 | 0.8803 |
| Adeq precision | 4.4809 | 6.1794 | 17.1584 |
| PRESS | 75.47 | 10.27 | |
| -2 Log Likelihood | 49.22 | 22.46 | |
| BIC | 56.67 | 32.40 | |
| AICc | 58.22 | 36.17 | |
MDT (Y3): The MDT analysis of variance and statistical parameters shown in Table.5 and Table.6, analysis of the variance model that has a statistically significant result of p< 0.0001. The model equation can make the parameter MDT = -12.92110 + 9.19379.X1 + 0.1112599 X2 - 0.926019.X1.X2. The positive indication for X1 and X2 suggests that the levels of X1 and X2 are rising, indicating growth in MDT. The ANOVA was significance level was set at P <0.0001. The MDT's 'F' was discovered to be of model 53.98, with independent variable X1= 0.2205 and other statistical metrics such as Adj.R$^2$ = 0.9352, Adeq accuracy = 17.1584, and AIC 58.22, Mean = 7.62, Std. DEV= 0.7658, C.V%=10.06, Pred R$^2$ =0.8803. The contour and 3D response surface as a function of two factors at a time, with all other parameters, held constant, are more useful in analyzing the individual and interaction effects of three elements shown in Figures 8-17 show the contour and response surface plots, as well as the normal plot of residual, desirability, and optimize plots of all formulation components.
Optimization
The optimized formula had a greater desirability concern (0.6271), indicating that the formulation was suitable. The goal was to make t $_{90}$ (Y1) minimal, t50 (Y2) was chosen as the target while MDT (Y3) was chosen as the target. Table.7 shows the composition of the optimum formulation based on two independent variables for optimizing following the goals of replies using a desirability function, where X1 are Drug: PVPK30:HPMC (30:30:3.75) mg and X2 is 4.5 percent of SSG. Table.7 shows that the in vitro percentage drug release t$_{90}$ was found to be 36.7 minutes, t$_{50}$ was found to be 10 minutes and MDT was found to be 37.9 for observed and close agreement with model prediction. For each answer, the relative error percent between anticipated and experimental values was determined, and the results were -0.0763%, -0.032016%, and -0.0300791% respectively. The experimental values matched the anticipated values, demonstrating the model's predictability and validity. The optimized formulation yielded t$_{90}$ was 36.72 min and t$_{50}$ was 10 min and MDT 37.9 respectively. The optimal formulation's drug release follows a first-order kinetic model. The optimal formulation's drug release follows a first-order kinetic model. The percentage prediction error was used to compare the predicted value to the experimental value to measure the prediction's validity and accuracy.
Table 7. Comparison of Predicted and Experimental response for Optimized formulation
| Parameter | | | |
| Independent Variables | X1 | X2 | |
| Composition | HPMC (7.5%) | SSG (4.5%) | |
| Response | T $_{90}$ | T$_{50}$ | MDT |
| Predicted value | 35.545 | 9.237 | 36.760 |
| Experimental value | 36.72 | 10 | 37.90 |
| Predicted error (%) | -0.032016 | - 0.0763 | -0.0300791 |
Pharmacokinetics
Figure 18 shows a comparison of the plasma concentration-time curves for mirtazapine-marketed and optimized tablets. Table 8 shows the pharmacokinetic parameters for the formulations. In mirtazapine and optimized tablets, the C$_{max}$ was 17.78 1.230 (µg/ml) and 20.76 2.12 (µg/ml), respectively. The mirtazapine (AUC)$_{0-∞}$ concentration and optimized tablets were 145.20 3.800 (µg/ mL).h and 163.50 6.23 (µg/ mL).h, respectively. The mirtazapine-marketed and optimized tablets, on the other hand, had T$_{max}$ of 0.518h and 0.4897h, respectively.
Table.8 Pharmacokinetic parameters
| Parameter | Mirtazepine(Marketed) | Optimized Tablets |
| t$_{max}$ (h) | 0.518 | 0.4897 |
| C$_{max}$(μg/mL) | 17.78 ± 1.230 | 20.76 ± 2.12 |
| Vd (L/kg) | 0.12 ± 0.04 | 0.15 ± 0.03 |
| t$_{1/2}$ (h) * | 3.06 ± 0.13 | 5.72 ± 0.43 |
| Kel (h−$^1$)* | 0.164 ± 0.0200 | 0.0513 ± 0.01 |
| AUC (0-∞) (μg·h/mL) * | 145.20 ± 3.800 | 163.50 ± 6.23 |

## Conclusion

The present research optimizes mirtazapine formulation by 3$^2$ factorial designs successfully designed and developed. The solid dispersions were compared to pure drugs with various carries significantly enhanced dissolution. The prepared blend exhibits excellent to good flow properties and is suitable for the direct compression method. The FTIR spectrum of pure drug with various excipients PVP K30, HPMC, and SSG exhibit characteristics peaks the FTIR spectrum of pure drug with various mixtures of excipients are similar it indicates no chemical interaction between the drug and excipients. The quality control parameters of the prepared tablets fulfill the official specification of uncoated tablets as per IP. The F2 formulation containing 7.5% HPMC, SSG (Sodium starch glycolate) 4.5% as significantly better dissolution, and the F4 formulation containing 3.75% HPMC, 8.5% SSG as significantly better dissolution performance. The increasing orders of drug dissolution of various formulations are F2 < F4 < F7 < F5 < F8 < F3 < F6 < F9 < F1. In all the cases correlation coefficient (r) values were higher first-order rather than zero-order release kinetics. The comparison with optimized formulation (F2) and market tablets (Mertz 30) are similar or identical dissolution profiles. The ANOVA of (analysis of variance) t$_{90,}$ t$_{50}$, and MDT are models with statistically significant p< 0.0001. The statistical optimization that fulfills all the dissolution parameters was carried out on the prepared optimized formulation to verify the theoretical prediction. The optimized formulation gave t$_{90}$ is 36.72 min, t$_{50}$ is 10 min and MDT is 37.90 respectively. The drug release from the optimized formulation follows the first-order kinetic model. The pharmacokinetics are identical in both pure drug and optimized formulation.

## Additional information
### Acknowledgements

The authors are thankful to Sri Venkateswara College of Pharmacy for providing the research facilities, Seshu, Kodati from IMCD Pvt.Ltd, Mumbai provided the gift samples of SuperTab-11 SD, G.Srinivasarao, and FTIR sampling was provided by Obvez Lab, Hyderabad, PV. Bhaskar, while GSK.Pvt. Ltd helped in the design of the expert software support.

### Competing interests

The Authors all declared a conflict of no interest.

### Authors Contribution

The contribution were in the following order; Concept (Dr.Ch.Tarakaramarao), Design (K.Pavallika), Supervision (Tarakaramarao.Ch), Materials (Seshu. Kodati), Data Collection and Processing (Pravallika. K), Analysis, and Interpretation (Dr.Ch.TarakaRamarao), Literature Search (K.Pravallika), Writing (K.Pravallika), and Critical Reviews (Takaramarao.Ch).