Application of design mixture and desirability function in the optimization of pharmaco-technical parameters of macrogols-based suppositories

The objective of this work is to (i) study the effect of variations in the proportions of four Macrogols on the pharmaco-technical characteristics of suppositories, (ii) de ine the optimal formula for a suppository with immediate effect; maximum disintegration and a minimum of hardness as de ined in the EuropeanPharmacopoeia. The lattice designmixture has beenproposed as an optimization technique, the formulation factors are presented by the proportions of PEG400 (X1), PEG600 (X2), PEG4000 (X3) andPEG6000 (X4) and the response variables are (i) the disintegration time (Y1) (ii) the hardness (Y2). The second-degree empirical model was postulated to model the variations of the two response variables using the least-squares method. The selected model explained about 67% and 84% of the variation for Y1 and Y2, respectively. All four factors had signi icant effects on the properties of the suppository. Interactions negatively affected both responses. The numerical desirability method gave the following optimal formula: PEG400 (28.71334 %); PEG600 (24.23773%), PEG4000 (35.00944%) andPEG6000 (12.03949%) for a disintegration of 25.839 (+/-2.3) min and hardness =2147.321 (+/50) g.


INTRODUCTION
The modern pharmaceutical industry has different routes of administration and pharmaceutical forms in order to deliver the active ingredients to the site of action (Ummadi, 2013;Shargel et al., 2015;Loyd et al., 2013;Yvonne and V'iain, 2015). Among these routes, the oral route is the most commonly used, with the use of tablet and capsule forms in particular (Shargel et al., 2015;Loyd et al., 2013;Sachdeva et al., 2013). Next to it are the topical, parenteral, and rectal pathways (Yvonne and V'iain, 2015; Sachdeva et al., 2013). The latter is one of the oldest routes of administration (Shargel et al., 2015;Loyd et al., 2013;Touitou and Barry, 2006) and can be considered a good alternative to the oral route for children in an emergency with loss of consciousness, elderly subjects and in case of vomiting (Yvonne and V'iain, 2015;Jannin et al., 2014). Recent studies have shown that this pathway is equivalent to others (Loyd et al., 2013;Touitou and Barry, 2006;Jannin et al., 2014).
Suppositories are the main representatives of this pathway with a renewed interest in the use of Macrogols (Yvonne and V'iain, 2015;Jannin et al., 2014;Raymond et al., 2006). This polymer approved by the United States Food and Drug Administration (UFDA) is popular because of its safe use and well-established safety pro ile (D'souza and Shegokar, 2016;Ham and Buckheit, 2017a). For the development of controlled release suppositories based on Polys Ethylene Glycol (Yvonne and V'iain, 2015;Jannin et al., 2014;Berkó, 2002), it is important to design an optimal formulation (based on the proportions of different PEGs) with a reasonable time of action; the shortest possible or longest possible depending on whether the immediate or prolonged effect is sought (Yvonne and V'iain, 2015;Ham and Buckheit, 2017a;Ela et al., 2016), and a better bioavailability (Jannin et al., 2014;Ham and Buckheit, 2017a).
Nowadays, most of the experimentation in the development of Macrogol suppository formulations is done randomly without being able to discuss the contribution of each internal component at the formula level; these are generally empirical formulations (Ela et al., 2016), without proceeding to optimization (Ham and Buckheit, 2017b). The formulation involves taking into account the complexity of systems in which physicochemical phenomena are involved for all stages of the drug's life (Yvonne and V'iain, 2015;Jannin et al., 2014). As such, the development of suppositories has focused on improving the existing conventional design to improve active ingredient delivery.
Our study aims to understand the effect of different individual Macrogols on the bio pharmacy and pharmacokinetics of suppositories, develop predictive models of their pharmaco-technical characteristics as a function of PEG proportions and estimate by absolute desirability functions the optimal formulas based on their Physico-chemical characteristics, for immediate effect, before adding additives such as surfactants and cyclo-dextrins.

Raw materials
Four types of Macrogols were selected in this study for the preparation (formulation) of suppositories; PEG 400 D, PEG 600 D, PEG 4000 D and PEG 6000 D (Shanghai Yayu Biomedical Shanghai, China). The four Macrogols are characterized by different Physico-chemical properties: molecular weight, melting temperature and hydroxyl number, hence the interest of the association to have hard, but not brittle suppositories (D'souza and Shegokar, 2016;Raymond et al., 2006). The characteristics of the suppository, including the rate and speed of dissolution, are directly in luenced by the exact combination and composition of Macrogols (Yvonne and V'iain, 2015;Ham and Buckheit, 2017a;Berkó, 2002).

Design of experiment (DOE)
Emerging research on suppository development includes the use of experimental designs to better understand the effect of different individual excipients on the dissolution and pharmacokinetics of suppositories and to optimize their composition.
The simplex design mixing design was used in this study (Sahin et al., 2016;Cafaggi et al., 2003) to statistically optimize suppository formulation parameters for maximum delay and disaggregation. It delimits an experimental domain in the form of a regular tetrahedron without upper or lower limits of its four components (Satish and ., 2012). The factors studied were Macrogol 400 (X 1 ), Macrogol 600 (X 2 ), Macrogol 4000 (X 3 ) and Macrogol 6000 (X 4 ) (Wang et al., 2010). For each formula, the sum of the proportions of the four components is 100% (Sahin et al., 2016;Wang et al., 2010;Dabbas et al., 2003). Table A summarizes the proportions of the 4 components and the responses recorded for the 15 trials (Wang et al., 2010).

Preparation of suppositories: fusion method
A mixture 20 g of four Macrogols; taking into account the losses when illing the metal molds (suficient quantity for 6 suppositories), was prepared, the weight of the suppositories was designed to reach about 3 g for each unit by manually feeding the six cells of the metal molds with stainless steel (Yvonne and V'iain, 2015;Jannin et al., 2014).
For each test, the required quantities of PEGs were loaded into a stainless-steel capsule, then heated to 42 C • (Yvonne and V'iain, 2015; Raymond et al., 2006), mixed until the mixture was homogeneous and cooled to a temperature below 40 C • . The liquid mixture obtained was poured into the metal mold previously lubricated by petroleum jelly oil and then allowed to cool in the refrigerator for a few minutes. Once cooled and de-molded, the suppositories were stored in vials until later use (Ela et al., 2016). Table 1 show the hardness and disintegration time of the prepared suppositories, 15 tests with two replicates.

Determination of Mechanical Strength (Hardness)
This test was performed with the Erweka AR 400 hardness tester (Erweka, Langen, Germany). The suppository was placed in the holding device with the tip up and the test chamber was then closed with a glass plate. The temperature inside the test chamber was maintained at 25 • C by means of circulating Legend : X 1 = Macrogol 400, X 2 = Macrogol 600, X 3 = Macrogol 4000 and X 4 = Macrogol 6000g/mol water from the thermostat connected to the tester. An initial load (600 g) was applied and at regular one-minute intervals, a 200 g disc was added until the suppository was crushed. The mass required to crush the suppository was then calculated as the sum of the initial charge and the added masses until the suppository collapsed (Yvonne and V'iain, 2015; Nürnberg, 1986;Onyeji et al., 1999;Hasian, 2015).

Determination of the disintegration time
The test was performed in a 6.8 pH buffer solution at 37 • C (+/-0.5) using the U.S.P tablet disintegration apparatus (SOTAX DT 3, Heusenstamm, Germany). The disintegration time was recorded as soon as the suppositories placed in the basket were completely dissolved. (Loyd et al., 2013;Belniak et al., 2017;Onyeji et al., 1999;Hargoli et al., 2013).

Development of mathematical models
The variations of the two responses are modelled        according to the fractions of the four Macrogols using the mathematical quadratic model (Cornell, 2011;Tinsson, 2010) according to Equation (1), Where Y is the dependent variable (hardness or disintegration) and b1 b2 ...b3-4 are the parameters of the model to be estimated. The main effects (X1, X2, X3 and X4) represent the average result of modifying a factor. The interaction terms (X1X4, X2X3, X2X4, X2X4 and X3X4) show how the response changes when two or more factors are modi ied simultaneously (Cornell, 2011;Tinsson, 2010;Tabandeh and Erfan, 2013;Bello et al., 2011).
The selection of the most parsimonious model for each of the two response variables was carried out by the step-by-step method (Khusainova et al., 2016) by (Chodankar and Dev, 2016).
To determine whether the association between the response and each of the model terms is statistically signi icant, the p-value of the term is compared to the signi icance level (noted alpha or α) of 0.05 to assess the null hypothesis that there is no association between the term and the response.

Figure 5: The Three-Dimensional (3D) Response Surface Plot of Desirability at the Prediction
The model was selected on the basis of the adjusted determination coef icient (R2) and PRESS. The normality of the residues and the homo-scedasticity of the model were veri ied for the global model and reveri ied for the selected model (Patel et al., 2017;Preece and Cornell, 1982). A test for lack of model it was also performed to test the adequacy of the model (Tinsson, 2010;Tabandeh and Erfan, 2013;Tauler et al., 2009).

Optimization of multiple quality characteristics (desirability function)
The use of the notion of absolute desirability, introduced by Derringer and Suich (Sahin et al., 2016;Şimşek et al., 2013;Preece and Cornell, 1982;Pal and Gauri, 2018), makes it possible to optimize the choice of mixture parameters on the basis of the Physico-chemical characteristics of Macrogols. In this way; for each answer Yi(x), the desirability function di (Yi) varies between 0 and 1 di (Yi) = 0 representing a totally undesirable value of Yi and di (Yi) = 1 representing the desirable or ideal response value. The desirability (di) of a response variable (Yi) may increase or decrease with the increase of (Yi); under certain conditions, the relationship between di and Yi may be parabolic in nature. In the case of Y1, our objective is to minimize the response. The desirability function of Y1 is Equation (2), With Ui and Si, the upper and lower values observed for the response Y1.
In the case of Y 2, our objective is to target a minimum hardness value of 1800 to 2000 g knowing that the values of Y2 are between the target value (Ti) and the maximum value (Ui), the desirability function for Y2 (hardness) is given by the following Equation (3), With Ui and Ti, the desired upper and target values for the answer Y2 and Li ≤ Ti ≤ ≤ Ui.
The individual desirability are then combined to obtain the overall desirability D (Wu, 2004) as follows Equation (4),

RESULTS AND DISCUSSION
In Table 2, columns 2 to 5 represent the four control factors and their proportions and columns 6 and 7 correspond to the results of the two controls Y 1 and Y 2 .
The experimental results are analyzed by ANOVA (Analysis of Variance) procedures and the results are given in Table 3.

Statistical modeling
The experimental results are analyzed by ANOVA procedures (Analysis of Variance) and the results (the ANOVA table) are given as following. The coef icients with p ≤ α will be retained in the model equation. On the contrary, if p > α, the coef icient will not be retained in the model equation (see Table 3 below) (Preece and Cornell, 1982). The regression model equations obtained with NemrodW ® were given in the following Equation (5) and Equation (6), (Cornell, 2011).

Equation of Disintegration time (5)
All four factors had positive effects on the properties of the suppository. The interactions had a negative effect on both responses. The disintegration time equation suggests that X4 (PEG 6000) had a more dominant effect than X3 (PEG4000), X2 (PEG 600) and X1 (PEG 400) with an antagonistic effect between X1 and X4. Equation of hardness shows the importance of PEG low molecular weight 400, as well as the antagonism between X1 and X3 (Satish and ., 2012;Tabandeh and Erfan, 2013).
Table 4 (a) shows that the variables selected for the modeling of the response as a whole have a signi icant effect at a con idence level of 95% (F exp (9.14) = 6.2361) is higher than theoretical (F0.05 (9.14) = 2.65. So, the model allows a better it of the data.
Table 4 (c) shows that the variables selected for the modeling of the response as a whole have a signi icant effect at a con idence level of 95% (F exp (9.11) = 11.8265) is higher than theoretical (F0.05 (9.11) = 2.90). So, the model allows a better it of the data (Tauler et al., 2009). The selected model was signi icant with P < 0.05 (Sahin et al., 2016;Şimşek et al., 2013) and explained approximately 84% (R square (adjust) = 0.84) and 67% (R square (adjust) = 0.67) of the variation for suppository hardness and disintegration time respectively (Table 4 (b) and Table 4 (d)). Figure 1 represent the degree of reconciliation of the experimental data with the data predicted by the model. The model allowed a better adjustment of the data (Dabbas et al., 2003;Bello et al., 2011).

Validation of the model (Validation of model)
The linear correlation coef icient is a statistical parameter used to de ine the linear relationship between the predicted and actual value, indicating the reliability and stability of the response surface. The linear correlation coef icient results for time disintegration (0.894), while for the hardness, it is quite low (0.695). The reliability of these results was con irmed by the corresponding residual plot between the run number and internally studentized residuals for various response variables, as shown in Figure 2 (Cornell, 2011;Preece and Cornell, 1982).
Based on the completely randomized analysis, the dispersion of residues studied internally was not off the line, from bottom to top, indicating that most of the points are within limits (at the level of con idence 95%). Our results indicate that NemrodW ® has successfully estimated the response surface showing the relationship between the composition and the characteristics of the suppositories (Cornell, 2011).
From these data, it can be said that the model is adequate and allows for better data adjustment (Cornell, 2011;Bello et al., 2011).

Determination of the optimal formula by maximizing the multi-response desirability
At this stage, and in Table 5, the target of our responses is guided by the speci ications of the sup-pository.
The effect of four Macrogols on the pharmacotechnical characteristics of the suppository is shown in Figure 3. (Bello et al., 2011;Preece and Cornell, 1982).
The formulations generally use both categories of Macrogols, for compensatory purposes, mixed in various proportions as required to obtain a inished product of satisfactory hardness and dissolution time (Raymond et al., 2006;Berkó, 2002;Kellaway and Marriott, 1975). Different PEG ratios of low and high molecular weight can be used to alter the time to disintegrate the hardness of the suppository (Raymond et al., 2006;Kellaway and Marriott, 1975;Chatterjee et al., 2014). Figure 4 shows the iso-résponses curves of the different combinations of Macrogol for both responses each taken alone. The PEG 6000, which has a higher molecular weight, will be tougher than the PEG 4000, but both can break and delay disintegration, whereas the addition of PEG 400 and 600 makes the suppositories hard, elastic and In view of drug incompatibilities, it is advantageous to minimize the proportions of low molecular weight PEGs because they have higher OH-values (Kellaway and Marriott, 1975;Chatterjee et al., 2014;Duangjit et al., 2014). Figure 5 shows the three-dimensional representation (3D) of the response surface of the desirability of the suppository. (Shivakumar et al., 2007;Kumar et al., 2016). The opportunity of the prediction was 91.20%. To evaluate the accuracy of the optimal formulation predicted by NemrodW ® , the optimal formulation was prepared and studied experimentally. The ideal characteristics estimated by the software and the experimental characteristics measured are shown in Table 5. The results showed that the optimal characteristics demonstrated by the experiment were more or less close to the estimated predicted values. The reliability of this study was judged by the calculation of the bias (See Table 7) (Duangjit et al., 2014).

CONCLUSIONS
The study showed that the proportions of different Macrogols have a signi icant in luence on the disintegration time and hardness of suppositories. The reduction in disintegration time has compromised the hardness of suppository, a key parameter for measuring the performance of these pharmaceutical forms. It can be attributed to an increase in the proportion of low molecular weight Macrogols and a decrease in the proportion of high molecular weight Macrogol, which allows for an improvement in biopharmaceuticals while maintaining the minimum hardness required by regulation. Finally, in addition to the composition in excipients, other factors should be studied in the presence of an active ingredient to control its release from the mass of Macrogol; namely its solubility in the mass of excipients, additives (TA and Cyclodextrin) and Physicochemical interactions PA-excipients.