# Influence of Hydrophilic Polymers on theβ Factor in Weibull Equation Applied to the Release Kinetics of a Biologically Active Complex ofAesculus hippocastanum

Authors: Justyna Kobryń; Sandra Sowa; Monika Gasztych; Andrzej Dryś; Witold Musiał
Journal: International Journal of Polymer Science
 (2017)

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## Abstract

Triterpenoid saponins complex of biological origin, escin, exhibits significant clinical activity in chronic venous insufficiency, skin inflammation, epidermal abrasions, allergic dermatitis, and acute impact injuries, especially in topical application. The aim of the study is the comparison of various hydrogel formulations, as carriers for a horse chestnut seed extract (EH). Methylcellulose (MC), two polyacrylic acid derivatives (PA1 and PA2), and polyacrylate crosspolymer 11 (PC-11) were employed. The release rates of EH were examined and a comparison with the Weibull model equation was performed. Application of MC as the carrier in the hydrogel preparation resulted in fast release rate of EH, whereas in the case of the hydrogel composed with PC-11 the release was rather prolonged. Applied Weibull function adhered best to the experimental data. Due to the evaluated shape parameterβ, in the Weibull equation, the systems under study released the active compound according to the Fickian diffusion.


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## Body

## 1. Introduction

The horse chestnut (Aesculus hippocastanum) seed extract (extractum hippocastani, EH) is a biological source of escin and its derivatives. Various substances are included in the composition of EH: triterpenoid saponins, flavonoids, tannins, coumarins, vitamins C and B, essential oils, and other substances [1, 2]. The extract is used in numerous preparations both internally and externally in patients suffering from chronic venous insufficiency and other inflammatory states of the veins, lower leg varicose veins, hemorrhoids, the treatment of burns, frostbite, skin inflammation, and epidermal abrasion [3]. The main active component of EH is escin. The molecule consists of protoescigenin with carbohydrate and acyl groups (see Figure 1). It occurs as a mixture of triterpenoid saponins, which exist in two forms, α and β, characterized by different melting point, specific rotation, water solubility, and hemolytic index. β-Escin is the main active component and at temperature of 100°C is converted to the α-escin, and consequently the hydroxide groups at C21, C22, and C28 migrate [4]. The saponins of β-escin from the EH contain mainly escin Ia, 24%, escin Ib, 17%, escin IIa, 13.5%, escin IIb, 6%, and escin IIIa, 1.5% [5].Figure 1
The schematic model ofβ-escin molecule.β-Escin is an antagonist to 5-HT and histamine and meliorates entry of ions into channels, raising venous tension. However, the mechanisms of escin activity have not yet been shown [6, 7]. According to recent study, escin induces apoptosis and may decrease pancreatic cancer cell survival, suppressing the NF-κB signal transduction pathway. This phenomenon may result in the sensitization of pancreatic cancer cells to chemotherapeutics agents [8]. Antifungal properties of escin were described; however, results are limited and need to be developed [9]. Escin has high potential of application. Numerous pharmaceutical and cosmetic products containing EH or escin alone are available on the market; however, there is a shortage of kinetic data connected with the release rate of escin from different formulations. The ionic effect between the escin and the functional groups of the polymeric carriers may be utilized for the prolongation of the activity of escin on the skin surface or directly beneath it. There are several biocompatible, biodegradable, and hydrophilic polymers, which are recognized as good carriers for various active compounds [10]. The applied polymers, as drug carriers, may affect the escin release; thus the selection of a suitable polymeric carrier is essential for controlling the release rate. In the present study, the evaluation of escin release from the hydrogel formulations was performed according to selected kinetic models, that is, zero-order kinetics, first-order kinetics, second-order kinetics, and the Weibull equation. In the zero-order kinetics reaction, the rate is constant and independent of concentration, whereas in first-order kinetics, the process depends on the concentration. The second-order kinetics expands the dependency on the concentrations of two substrates. The mathematical Weibull model enabled the comparison of release profiles of various formulations, using the distribution function, with shape and scale parameters [11]. The present study presents release patterns of formulations with EH, which contain methylcellulose (MC), polyacrylic acid derivatives (PA1 and PA2), and polyacrylate crosspolymer 11 (PC-11) (Figure 2).Figure 2
Schematic representation of applied hydrophilic polymers with various functional groups: (a) methylcellulose (MC), (b) polyacrylic acid derivatives (PA1 and PA2), and (c) polyacrylate crosspolymer 11 (PC-11).
(a) (b) (c)The aim of the study is to compare the release rate constants of escin, amongst the formulations containing various hydrophilic polymers, applying various kinetic models, including the Weibull model with the specificβ factor.


## 2. Materials and Methods

### 2.1. Materials

The hydrogels used in the release study were prepared from the following polymers: methylcellulose (MC, Sigma-Aldrich, Poznan, Poland), Carbopol 980 NF (PA1, Lubrizol, Wickliffe, USA) and polyacrylate crosspolymer 11 (PC-11, Aristoflex Velvet, Clariant, Muttenz, Switzerland). As a reference, a marketed dermatological gel, Venescin, containing EH and Carbopol 5984 (PA2), was used (WZZ Herbapol, Wroclaw, Poland). The composition of the prepared gels is presented in Table1. EH (7.08 g) was dissolved in 51.72 g (P1) or 52.02 g (P2, P3) of distilled water. In the case of formulation P1, the water of 80°C was applied. The mixtures were complemented by 1.20 g of MC or 0.90 g of PA1 or PC-11. 50.00 mg of 50% of NaOH was added to formulation P2. The formulations were conditioned in a refrigerator at 8°C for 48 hours and equilibrated to the experiment temperature before further evaluation.Table 1
The composition of the prepared gels comprising EH and different polymers.
Formulation Composition [%] EH MC PA1 PC-11 PA2 W P1 11.80 2.00 — — — 86.20 P2 11.80 — 1.50 — — 86.70 P3 11.80 — — 1.50 — 86.70 P4 11.80 — — — qs qs EH, extractum hippocastani; MC, methylcellulose; PA1, polyacrylic acid 980 NF; PA2, Carbopol 5984; PC-11, modified polyacrylic acid; W, water; qs, quantum satis: according to the declaration of the manufacturer.


### 2.2. Methods

The release study was performed using a synthetic membrane applied on the extraction cells. The release study was performed by using a paddle apparatus following the pharmacopoeial method, at 50 rpm. The weighed gel samples were placed in the extraction cells (Perspex, Pharma Test Apparatebau, Germany) and a dialysis tubing cellulose membrane with MWCO of ca. 14000 Da (Sigma-Aldrich, USA) was used for tapping. Drug Dissolution Tester ERWEKA GmbH DT 700 (Heusenstamm, Germany) was utilized in the experiment, with purified water as an acceptor fluid in a volume of 900 ml at 37°C. The experiments were conducted at 37°C, based on the contemporary studies of transdermal absorption using an artificial semipermeable membrane [12–15]. Three collateral measurements proceeded in extraction cells by sampling the acceptor fluid volume of 3 mL every 5, 10, 15, and 20 minutes for over 7 hours. Acceptor fluid was not supplemented. Analysis of taken samples was performed spectrophotometrically (UV/VIS Jasco V-530, Tokyo, Japan) at 265 nm, due to the standard curve according to the available bibliography; the wavelength was selected in accordance with the measured absorption spectrum of escin in aqueous solution [16]. Standard curve was based on three independent series of assessments, with six measurement points at concentrations between 59.00 and 236.00 μg/mL. Statistica software was used to perform statistical tests on the results. The obtained data were evaluated according to zero-order kinetics, first-order kinetics, and second-order kinetics models [17, 18], as well as applying the Weibull model (Table 2) [11].Table 2
Kinetic models applied for evaluation of obtained data.
Applied model General equation Parameters Zero-order Q t = Q 0 - K ( 0 ) t K ( 0 ) = Q 0 - Q t t t 0.5 = Q 0 2 K 0  1st-order Q t = Q 0 e - K ( I ) t K ( I ) = 1 t ln ⁡ Q 0 Q t t 0.5 = 0.693 K ( I )  2nd-order Q t - 1 = Q 0 - 1 + K ( I I ) t K ( I I ) = Q 0 - Q t Q 0 Q t 1 t t 0.5 = 1 K ( I I ) Q 0  Weibull Q t = ( 100 - Q 0 ) 1 - e - t / T d β β = log - t / T d ⁡ ln ⁡ 1 - Q t 100 - Q 0 Td=e-b/a K is rate constant, respectively, for zero-order kinetics (K(0)), 1st-order kinetics (K(I)), 2nd-order kinetics (K(II)), and Higuchi model (K(H)); t, time; t0.5, half release time; Q0, initial percentage of the released drug; Qt, percentage of the released drug after time t; Td, time after release of 63.2% of drug from the formulation; β, a shape parameter in the Weibull model; a, b, slope and intersection of the graph representing the release process.


## 2.1. Materials

The hydrogels used in the release study were prepared from the following polymers: methylcellulose (MC, Sigma-Aldrich, Poznan, Poland), Carbopol 980 NF (PA1, Lubrizol, Wickliffe, USA) and polyacrylate crosspolymer 11 (PC-11, Aristoflex Velvet, Clariant, Muttenz, Switzerland). As a reference, a marketed dermatological gel, Venescin, containing EH and Carbopol 5984 (PA2), was used (WZZ Herbapol, Wroclaw, Poland). The composition of the prepared gels is presented in Table1. EH (7.08 g) was dissolved in 51.72 g (P1) or 52.02 g (P2, P3) of distilled water. In the case of formulation P1, the water of 80°C was applied. The mixtures were complemented by 1.20 g of MC or 0.90 g of PA1 or PC-11. 50.00 mg of 50% of NaOH was added to formulation P2. The formulations were conditioned in a refrigerator at 8°C for 48 hours and equilibrated to the experiment temperature before further evaluation.Table 1
The composition of the prepared gels comprising EH and different polymers.
Formulation Composition [%] EH MC PA1 PC-11 PA2 W P1 11.80 2.00 — — — 86.20 P2 11.80 — 1.50 — — 86.70 P3 11.80 — — 1.50 — 86.70 P4 11.80 — — — qs qs EH, extractum hippocastani; MC, methylcellulose; PA1, polyacrylic acid 980 NF; PA2, Carbopol 5984; PC-11, modified polyacrylic acid; W, water; qs, quantum satis: according to the declaration of the manufacturer.


## 2.2. Methods

The release study was performed using a synthetic membrane applied on the extraction cells. The release study was performed by using a paddle apparatus following the pharmacopoeial method, at 50 rpm. The weighed gel samples were placed in the extraction cells (Perspex, Pharma Test Apparatebau, Germany) and a dialysis tubing cellulose membrane with MWCO of ca. 14000 Da (Sigma-Aldrich, USA) was used for tapping. Drug Dissolution Tester ERWEKA GmbH DT 700 (Heusenstamm, Germany) was utilized in the experiment, with purified water as an acceptor fluid in a volume of 900 ml at 37°C. The experiments were conducted at 37°C, based on the contemporary studies of transdermal absorption using an artificial semipermeable membrane [12–15]. Three collateral measurements proceeded in extraction cells by sampling the acceptor fluid volume of 3 mL every 5, 10, 15, and 20 minutes for over 7 hours. Acceptor fluid was not supplemented. Analysis of taken samples was performed spectrophotometrically (UV/VIS Jasco V-530, Tokyo, Japan) at 265 nm, due to the standard curve according to the available bibliography; the wavelength was selected in accordance with the measured absorption spectrum of escin in aqueous solution [16]. Standard curve was based on three independent series of assessments, with six measurement points at concentrations between 59.00 and 236.00 μg/mL. Statistica software was used to perform statistical tests on the results. The obtained data were evaluated according to zero-order kinetics, first-order kinetics, and second-order kinetics models [17, 18], as well as applying the Weibull model (Table 2) [11].Table 2
Kinetic models applied for evaluation of obtained data.
Applied model General equation Parameters Zero-order Q t = Q 0 - K ( 0 ) t K ( 0 ) = Q 0 - Q t t t 0.5 = Q 0 2 K 0  1st-order Q t = Q 0 e - K ( I ) t K ( I ) = 1 t ln ⁡ Q 0 Q t t 0.5 = 0.693 K ( I )  2nd-order Q t - 1 = Q 0 - 1 + K ( I I ) t K ( I I ) = Q 0 - Q t Q 0 Q t 1 t t 0.5 = 1 K ( I I ) Q 0  Weibull Q t = ( 100 - Q 0 ) 1 - e - t / T d β β = log - t / T d ⁡ ln ⁡ 1 - Q t 100 - Q 0 Td=e-b/a K is rate constant, respectively, for zero-order kinetics (K(0)), 1st-order kinetics (K(I)), 2nd-order kinetics (K(II)), and Higuchi model (K(H)); t, time; t0.5, half release time; Q0, initial percentage of the released drug; Qt, percentage of the released drug after time t; Td, time after release of 63.2% of drug from the formulation; β, a shape parameter in the Weibull model; a, b, slope and intersection of the graph representing the release process.


## 3. Results

The initial amount of EH in the evaluated formulations is given in Table1. Due to the course of the plot in Figure 3(a), the largest quantity of EH was released from formulation P1, based on the MC. There was 44.43% of released EH from the MC preparation after 420 min. Comparable amount of EH, that is, 44.03%, was released from the reference formulation P4 after 420 min of the process. Intermediate value of EH, 34.23%, after the same time, was released from the preparation P2 containing the PA1 polymer. The lowest amount of released EH was observed in the case of formulation P3, containing PC-11; only 30.48% of EH was released after 420 min. According to Figure 2(a), the release processes did not follow the linear course of the zero-order kinetics function. The release rate constants of the extreme formulations P3 and P1 were 6.72·10-2%·min−1 and 9.50·10-2%·min−1, respectively. The calculations executed in compliance with first-order kinetics revealed low adherence of the results to the model (Figure 3(b)); the release rate constants were in the range of 8.19·10-4 min−1 to 1.29·10-3 min−1. Analyzed formulations exhibited the best match for the second-order kinetics equation, as it is seen in Figure 3(c). The range of the release rate constants in boundary formulations P3 and P1 was between 1.00·10-5 min−1·%−1and 1.80·10-5 min−1·%−1. In comparison, as it is seen in Figure 3(d), the formulation P2 exhibited the best fit to the Weibull model. Additionally, calculated values of a shape parameter β were between 0.6426 and 0.6764 in preparations P3 and P1, respectively, as depicted in Figure 4. The constants and regression coefficients are shown in Table 3. The range of the regression coefficients from 0.95224 to 0.99840 indicated the best matching for second-order kinetics equation and departing from zero-order process model for all formulations. According to the Weibull model, the range of regression coefficients was 0.99134–0.99801.Table 3
The parameters determined in the course of release kinetics evaluation of gel formulations P1, P2, P3, and P4.
Parameter Kinetics model BF Zero-order 1st-order 2nd-order Weibull K ( 0 ) [%⋅min−1] SD K ( I ) [ m i n - 1 ] SD K ( I I ) [min−1⋅%−1] SD β[-] SD Formulation type: P1 (MC formulation) Constant 9.50 ⋅ 10 - 2 6.59 ⋅ 10 - 3 1.29 ⋅ 10 - 3 1.23 ⋅ 10 - 4 1.80 ⋅ 10 - 5 2.26 ⋅ 10 - 6 6.76 ⋅ 10 - 1 3.01 ⋅ 10 - 2 II r 2 0.96380 0.01246 0.98490 0.00791 0.99500 0.00216 0.99584 0.00327  Formulation type: P2 (PA1 formulation) Constant 7.42 · 10 - 2 3.89 · 10 - 3 9.30 · 10 - 4 5.38 ⋅ 10 - 5 1.18 ⋅ 10 - 5 7.58 ⋅ 10 - 7 6.47 ⋅ 10 - 1 3.75 ⋅ 10 - 2 II r 2 0.95712 0.00802 0.97493 0.00657 0.98776 0.00464 0.99801 0.00063  Formulation type: P3 (PC-11 formulation) Constant 6.72 ⋅ 10 - 2 1.73  ·  10 - 3 8.19 ⋅ 10 - 4 2.27 ⋅ 10 - 5 1.00 ⋅ 10 - 5 3.11 ⋅ 10 - 7 6.43 ⋅ 10 - 1 2.46 ⋅ 10 - 2 II r 2 0.95224 0.00464 0.96941 0.00356 0.98286 0.00256 0.99632 0.00129  Formulation type: P4 (PA2, reference formulation) Constant 9.25 ⋅ 10 - 2 3.25 ⋅ 10 - 3 1.25 ⋅ 10 - 3 4.79 ⋅ 10 - 5 1.73 ⋅ 10 - 5 7.75 ⋅ 10 - 7 6.70 ⋅ 10 - 1 3.71 ⋅ 10 - 2 II r 2 0.97479 0.00131 0.99155 0.00110 0.99840 0.00027 0.99134 0.00516 K represents release rates for respective models: zero-order kinetics (K(0)), 1st-order kinetics (K(I)), and 2nd-order kinetics (K(II)); β, a shape parameter in Weibull model; r2, correlation coefficient for the regression fit describing the course of the release as the first-order process; MC, methylcellulose; PA1, polyacrylic acid derivative Carbopol 980P NF; PC-11, modified polyacrylic acid; PA2, polyacrylic acid derivative Carbopol 5984.Figure 3
Presentation of release kinetics of EH from various hydrophilic gels according to specified release models. (a) Zero-order kinetics, (b) first-order kinetics, (c) second-order kinetics, and (d) Weibull model. ○, MC;△, PA1; ●, PC-11; ▲, reference gel, PA2; n=6; Θ, ln [−ln(1 − (released percent/100%))].
(a) (b) (c) (d)Figure 4
Courses of EH release in Weibull model applied for formulation: (a) MC, (b) PA1, (c) PC-11, and (d) PA2.
(a) (b) (c) (d)Figure5 presents the half-release times for the kinetics models and 63.2%-release time for the Weibull model for all formulations. The range of half-release time in the zero-order model was 5.28·102 min to 7.44·102 min for formulations P1 and P3, respectively. For the first-order kinetics, the maximal half-release time of EH was 8.47·102 min and the minimal half-release time was 5.39·102 min. For the second-order equation, the half-release times range was between 5.64·102 min and 9.96·102 min. The Weibull model showed the shortest release time (63.2% of EH) after 9.49·102 min and the longest after 19.47·102 min. The plots (Figure 5) exhibited the fastest release of EH for the zero-order kinetics model and the slowest release for the Weibull model.Figure 5
Histograms of half-release times and 63.2%-release time of EH for various hydrogels prepared with the use of MC (P1), PA1 (P2), PC-11 (P3), and PA2 (P4), evaluated according to the kinetics models: (a) zero-order kinetic equation, (b) first-order kinetic equation, (c) second-order kinetic equation, and (d) Weibull model; the Y-bar represents SD;n=6.
(a) (b) (c) (d)


## 4. Discussion

The most adhering kinetic models were ascribed to the respective assessed samples of hydrogels, according to the high correlation coefficients. The most appropriate model for all the samples studied was the second-order kinetics model (vide data presented in Table3). The less fitting kinetics belong to the zero-order kinetics model. In the case of second-order kinetics, the change of concentration of two substrates influences the process rate. MC was applied in the P1 hydrogel. The methyl groups in MC are substituted by hydroxyl groups at C2, C3, and/or C6 of glucose (see Figure 2(a)). This molecule is nonionic and has an amphiphilic character. It is water-soluble and organo-soluble, depending on the number of substitutions and distribution of the methoxy groups [19]. Degrees of substitution larger than 1.3 and a heterogeneous distribution of the methyl groups facilitate hydrophobic interactions of the polymer [20]. There are few recent studies based on a MC as a drug carrier [12, 13]. The highest quantity of model active compound (calcium dobesilate, CD) was released from the hydrogel based on a hydroxypropyl methylcellulose (HPMC), 82% after 250 min, and similarly in the case of MC and PC-11 the gels released around 81% after 250 min [13]. Comparatively, in another study, 51% of CD was released from HPMC gel, and 68% was released from MC-based hydrogel. For the PC-11-based preparation, the largest amount of CD was released, that is, 88%, after 250 minutes [12]. However, it must be stressed that the porcine ear skin was utilized in the second study as a way of active components transport. The variability between release rates of active substances in our studies might depend on their structure and properties. EH mostly contains a complex of escin with free carboxyl groups, which might interact with cations. Because of complex character of escin, few interactions have been examined [21]. PA1 and PA2 were used in hydrophilic gels in preparations P2 and P4, respectively. Polyacrylic acid derivatives are anionic polymers, which have the ability to create complexes with cationic residues of other compounds [22]. The bulky structural form of PA1 and PA2, as a net of polyalkene polyether, may immure the EH components and interrupt the active compounds diffusion [23]. Formulation P3 consisted of cationic polymer which may interact with anionic compounds into complexes. Additionally, ammonium groups enable binding of carboxyl groups, for example. Moreover, a cross-structure of the PC-11 may influence the release rate of diffusing components [23].The release rates, as presented in Table3, were between 6.72·10-2%·min−1 and 9.50·10-2%·min−1 for the zero-order kinetics, between 8.19·10-4 min−1 and 1.29·10-3 min−1 for the first-order kinetics, and between 1.00·10-5 min−1·%−1 and 1.80·10-5 min−1·%−1 for the second-order kinetics. The highest values of release rate were observed in the case of formulation with MC (P1), and the lowest one was in the case of the preparation with PC-11 (P3). The detailed insight into the variability of the processes was confirmed by the half-release time values presented in Figure 5. The amphiphilic properties of MC may positively influence the solubility of the assessed active complex. On the other hand, ammonium groups of PC-11 may bond to the carboxyl groups of escin (see Figure 6). The ability of ionic cross-linking with other polymers groups was indicated in the case of chitosan hydrogel structure by Berger et al. [24].Figure 6
The scheme of possibility of ionic binding ammonium group of polymer with the carboxyl group of escin.According to the Weibull model, the range of a shape parameterβ was 0.6426–0.6764 (see Figure 4). The dependency between β value and the release mechanism of substances has been established by several authors. Fickian diffusion was estimated for processes with β ≤ 0.75. In β range between 0.75 and 1.0, the Fickian diffusion is combined with case II transport. For β value more than 1.0, the complex mechanism of drug transport has been reported [25]. Monte Carlo simulation techniques were used for the evaluation of drug release via Fickian diffusion, applying Euclidean matrix. Kosmidis et al. pointed to the Weibull function as a general form appropriate for drug release studies [26]. Similarly, Papadopoulou et al. proved a successful use of the Weibull model in drug release, based on the formulations of diltiazem and diclofenac [25]. Moreover, in the present study, the Weibull equation gave better adherence of processed data, compared to the standard kinetics model equations, with the exception of PA2 system. The good adherence of release data to the Weibull model was confirmed in previously reported studies [25, 26].


## 5. Conclusions

Application of the nonionic polymer, MC, as a carrier in the hydrogel preparation results in a fast release rate of EH. The release pattern of EH from the hydrogel, composed of PC-11, results in a rather prolonged release. This may be ascribed to the presence of the carboxylic groups interacting with the active compound. The Weibull function adheres best to the experimental data. Due to the evaluated shape parameterβ, the studied systems released the active compound according to the Fickian diffusion.



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