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Mathematical modeling of drug release from Eudragit RS-based delivery systems
J. DRUG DEL. SCI. TECH., 20 (2) 127-133 2010
Mathematical modeling of drug release from Eudragit RS-based delivery systems B. Glaessl1, 2, F. Siepmann1, I. Tucker2, T. Rades2, J.Siepmann1* 1
College of Pharmacy, JE 2491, University Lille-Nord de France, 3, rue du Professeur-Laguesse, 59006 Lille, France 2 New Zealand’s National School of Pharmacy, University of Otago, 18 Frederick Street, Dunedin, New Zealand *Correspondence: [email protected]
Various types of tartaric acid, metoprolol free base and metoprolol tartrate containing Eudragit RS-based films were prepared and physicochemically characterized. In particular, the water uptake and compound release kinetics were monitored upon exposure to 0.1 M HCl, phosphate buffer pH 7.4 and distilled water. Appropriate analytical solutions of Fick’s second law of diffusion, considering the given initial and boundary conditions, were used to elucidate the underlying mass transport mechanisms. Furthermore, the apparent diffusion coefficients of water, tartaric acid, metoprolol free base and metoprolol tartrate in the different Eudragit RS-based networks were determined. Importantly, the diffusivity of metoprolol tartrate and metoprolol free base significantly increased with increasing initial drug content, illustrating the strong plasticizing capacity of these compounds for the polymer. In contrast to Eudragit RL-based films, metoprolol free base precipitation occurred only at higher initial drug loadings, due to the lower water uptake resulting from the lower contents of quaternary ammonium groups. Interestingly, negatively charged tartrate ions diffused out more rapidly from metoprolol tartrate containing films than positively charged metoprolol ions, indicating that the lower molecular weight over-compensates the attractive ionic interactions with the positively charged macromolecules. Key words: Mathematical modeling – Eudragit RS – Controlled release – Drug polymer interactions – Diffusion.
Eudragit RS is frequently used as a matrix former or coating material in time-controlled drug delivery systems [1, 2]. It is a poly(acrylic acid) derivative [poly(ethylacrylate-methylmethacrylate-trimethylammonioethylmethacrylate chloride) 1:2:0.1], the structure of which is shown in Figure 1. In contrast to Eudragit RL, it contains only half the amount of quaternary ammonium groups [3]. Due to the presence of the permanent positive charges of these quaternary ammonium groups, the underlying drug release mechanisms from these types of dosage forms may be complex [4-7]. For instance, ionic drug-polymer interactions might occur [8-10] and strongly affect the resulting drug release patterns. Furthermore, drugs (charged or otherwise) might act as plasticizers for Eudragit RS [11, 12]. Thus, the initial drug loading of the system potentially affects the resulting polymer chain mobility and, consequently, drug release. In addition, the type of ions present in the surrounding bulk fluid (and diffusing into the system during drug release) might have a significant impact on the drug-polymer interactions in the dosage form. For instance, such ions can compete with negatively charged drug ions to interact with the positively charged quaternary ammonium groups and, thus, alter the relative importance of the involved physicochemical processes controlling drug release. Due to the considerable potential complexity of the system, the underlying mass transport phenomena in Eudragit RS-based devices are generally not well understood (despite the great practical importance of this type of dosage forms). Thus, system optimization is often based on time- and cost-intensive series of trial-and-error experiments. In order to get deeper insight into the physicochemical processes involved in the control of drug release from a particular type of dosage form, the latter first needs to be characterized as thoroughly as possible [13-15]. Then, based on the experimental results, mechanistic realistic mathematical theories should be developed/identified, which allow for a quantitative description of the occurring mass transport steps [16]. Importantly, all decisive phenomena must be taken into account in the model, whereas mass transport steps of negligible importance should not be considered in order to keep the theory as simple as possible otherwise too many system-specific parameters need to be determined. Once such a model is established/identified, it can be fitted to different types of experimental results, for instance water uptake
and drug release kinetics. Based on these calculations device specific parameters, including for example the diffusion coefficient of water and drug within the polymeric network, may be determined. Having determined these values, the relative importance of the respective mass transport steps may be estimated. Furthermore, the effects of different formulation parameters on these system-specific parameters may be quantified and thus the observed (often rather complex) relationships with the resulting drug release kinetics better understood. Previously, different types of tartaric acid, metoprolol free base and metoprolol tartrate containing Eudragit RL- and Eudragit RSsystems were prepared and physicochemically characterized in the dry state [17]. However, the presence of water can significantly affect the resulting system properties, water acting for instance as a strong plasticizer for many polymers [12]. Also, Eudragit RL-based films were studied in the wet state [7]. However, Eudragit RS contains only half the amount of quaternary ammonium groups and it is well known that drug release from Eudragit RS based dosage forms is much slower than from the Eudragit RL containing analogues [18]. It was the aim of this study to: (i) prepare and physicochemically characterize tartaric acid, metoprolol free base and metoprolol tartrate containing Eudragit RS films, in particular regarding their water uptake and compound release kinetics under various conditions, and (ii) to identify appropriate mechanistic realistic mathematical theories that result in a quantitative description of the observed mass transport processes in order to achieve deeper insight into this type of controlled drug delivery system.
I. Materials and methods 1. Materials
The following chemicals were used as received: tartaric acid (Acros Organics, Halluin, France), metoprolol tartrate (Novartis, Barleben, Germany) and Eudragit RS PO [poly(ethylacrylate-methylmethacrylate-trimethylammonioethylmethacrylate chloride) 1:2:0.1, Evonik Roehm, Darmstadt, Germany]. The free metoprolol base was obtained from metoprolol succinate (Novartis, Barleben, Germany) by first dissolving the salt in a sodium hydroxide solution, and subsequent extraction with dichloromethane, followed by drying with water-free 127
J. DRUG DEL. SCI. TECH., 20 (2) 127-133 2010
Mathematical modeling of drug release from Eudragit RS-based delivery systems B. Glaessl, F. Siepmann, I. Tucker, T. Rades, J. Siepmann
All experiments were conducted in triplicate. In order to quantify the observed water uptake kinetics of the thin films, the following analytical solution of Fick’s second law of diffusion was used, considering the given initial and boundary conditions (homogeneous film composition, negligible edge effects and excess amount of water at both surfaces of the films) [19]: ∞ ( 2n + 1) ⋅ π Mt 8 =1− ∑ ⋅ exp − ⋅D ⋅t 2 2 M∞ + ⋅ π 4⋅ L2 ( 2 n 1 ) n =0
(
2
2
)
Eq. 2
Here, Mt and M∞ denote the absolute cumulative amounts of water taken up at time t and t = ∞, respectively; D represents the apparent diffusion coefficient of water within the system and L the half-thickness of the film.
4. In vitro release from thin, polymeric films
The release of tartaric acid, metoprolol free base and metoprolol tartrate from thin Eudragit RS films was measured by placing film pieces into plastic flasks filled with pre-heated release medium [0.1 M HCl, phosphate buffer pH 7.4 (USP 30) or distilled water], followed by horizontal shaking for 8 h (37 °C, 80 rpm, GFL 3033) (n = 3). At pre-determined time points, samples of 3 mL were withdrawn and replaced with fresh, pre-heated medium. The respective compound was detected UV-spectrophotometrically (UV-1650; Shimadzu, Champssur-Marne, France) (λ = 212.0/204.3/220.0, 274.7/275.0/274.7, and 274.7/274.7/274.7 nm for tartaric acid/metoprolol free base/metoprolol tartrate in 0.1 M HCl, phosphate buffer pH 7.4 and distilled water, respectively), except for: (i) tartaric acid release in distilled water, and (ii) simultaneous and separate detection of metoprolol and tartrate release from metoprolol tartrate-containing films. In these two cases, the following HPLC techniques were applied: - tartaric acid release in water was quantified by isocratic HPLC analysis (HPLC ProStar 230, Varian, Paris, France), equipped with a ProStar 230 pump (Varian), an autosampler Prostar 410 (Varian) and an UV-Vis detector Prostar 325 (Varian). The reverse-phase column (Synergi 4u Hydro-RP 80A, 250 × 4.6 mm, Phenomenex, Auckland, New Zealand) was kept at 30 °C. The flow rate of the mobile phase [20 mM potassium phosphate buffer pH 2.9 (Phenomenex)] was 0.7 mL/min. Fifty-microlitre samples were injected and the drug detected at λ = 220 nm. Data was analyzed using the Galaxie software (Varian). Tartaric acid standard solutions containing 50, 100, 150, 200, 300, and 400 µg/mL were used for calibration (linear standard curve in the range of 50 to 400 µg/mL, correlation coefficient R2 = 1.00). Intra-day and inter-day variability as well as assay precision and accuracy were satisfactory; - metoprolol and tartrate species were simultaneously and separately detected using a newly developed method using an Agilent 1200 HPLC apparatus (Agilent Technologies, Waldbronn, Germany). The reversephase column (Synergi 4u Hydro-RP 80A, 250 × 4.6mm, Phenomenex) was kept at 30 °C. The mobile phase was a mixture of phosphate buffer pH 2.9 (Phenomenex) and acetonitrile. The blend ratios and flow rates were as follows: 0-6 min: 100:0 at 0.7 mL/min; 6-10 min: 15:85 at 1.5 mL/min; 10-15 min: 100:0 at 1.5 mL/min. Fifty-microlitre samples (adjusted to pH 2.5 with orthophosphoric acid) were automatically injected. Tartrate species were detected UV-spectrophometrically at λ = 220 nm during the first 6 min, metoprolol species were detected UV-spectrophotometrically at λ = 230 nm afterwards. Data was collected, integrated and analyzed using the Agilent Technologies software. Figure 2 shows the chromatogram of an aqueous metoprolol tartrate solution (500 µg/mL). The first peak at a retention time of 4.4 min represents the (more hydrophilic) tartrate species, the second peak at a retention time of 9.7 min represents the (more hydrophobic) metoprolol species. Metoprolol tartrate standard solutions containing 150, 300, 500, 700, and 1,000 µg/mL were used for calibration (linearity from 150 to 1,000 µg/mL, correlation coefficient R2 = 1.000 for both spe-
Figure 1 - Chemical structures of tartaric acid, metoprolol free base, metoprolol tartrate and Eudragit RS.
sodium sulfate. For further water elimination, the obtained oily liquid was dried at 80 °C in a rotary evaporator (Rotavapor R110, Buechi, Flawil, Switzerland) connected to a vacuum pump. The yellowish liquid was cooled down to 4-7 °C, inducing crystallization of the free base in the form of white crystals, which were subsequently gently ground with a mortar and pestle. The chemical structures of tartaric acid, metoprolol free base, metoprolol tartrate as well as Eudragit RS are shown in Figure 1.
2. Film preparation
Thin Eudragit RS films were prepared with a casting knife (Multicator 411, Erichsen, Hemer, Germany) and a PTFE plate from ethanolic polymer solutions, optionally containing tartaric acid, metoprolol free base or metoprolol tartrate (0 to 20.0 % w/w, based on the polymer mass). The films were dried for 3 d at room temperature, followed by 1 d at 50 °C. The thickness of the films was measured using a thickness gauge (Minitest 600, Erichsen).
3. Water uptake of thin, polymeric films
Thin Eudragit RS films (optionally containing tartaric acid, metoprolol free base or metoprolol tartrate) were cut into pieces of approximately 4 cm × 4 cm, which were placed into plastic flasks filled with pre-heated release medium [0.1 M HCl, phosphate buffer pH 7.4 (USP 30) or distilled water], followed by horizontal shaking for 8 h (37 °C, 80 rpm; GFL 3033, Gesellschaft fuer Labortechnik, Burgwedel, Germany). The films were weighed before exposure to the media [dry weight (t = 0), mdry]. At pre-determined time points, the films were withdrawn from the media, carefully dried from adhesive water and accurately weighed [wet weight (t)]. The water uptake (t) (%) at time t was calculated as follows: water uptake (t) (%) = [(mwet (t) - mdry)/mdry] . 100 (%)
Eq. 1 128
Mathematical modeling of drug release from Eudragit RS-based delivery systems B. Glaessl, F. Siepmann, I. Tucker, T. Rades, J. Siepmann
J. DRUG DEL. SCI. TECH., 20 (2) 127-133 2010
proportionality constant is called the mass transfer coefficient in the boundary layer, h. As the thickness of the boundary layer essentially depends on the rate of stirring, h is a function of the stirring rate. This boundary condition is mathematically expressed as: t > 0
Eq. 5
- D · |�c/�x|x=±L = h · (csur - c∞)
This initial value problem (Equations 3 to 5) can be solved using a Laplace transformation, leading to [20, 21]: ∞ Mt β2 2⋅G 2 =1− ∑ 2 ⋅ exp − n2 ⋅ D ⋅ t 2 2 M∞ L n =1 β n ⋅ ( β n + G + G )
(
)
Eq. 6
where the bn values are the positive roots of: Figure 2 - Chromatogram of an aqueous metoprolol tartrate solution, showing well separated peaks of tartrate species (retention time = 4.4 min) and metoprolol species (retention time = 9.7 min).
Eq. 7
G = (L · h)/D
Eq. 8
with:
cies). Intra-day variability was determined by five repeated analyses of quality control samples on the same day, and inter-day variability by repeated analyses on five consecutive days. A new calibration curve was used on each day. Assay precision was assessed by the percent relative standard deviation (% RSD) and accuracy was calculated as estimated concentration (percentage of the nominal concentration). The intra-day and inter-day precision (% RSD between 0.1 and 3.7) and accuracy (100.8 to 108.1 %) was satisfactory for both species: tartrate and metoprolol.
Here, Mt and M∞ are the cumulative amounts of tartaric acid, metoprolol free base or metoprolol tartrate released at time t and t = ∞, respectively; G denotes a dimensionless constant. The diffusion coefficient of the compound D was determined by fitting Equations 6 to 8 to experimentally measured in vitro release kinetics.
II. Results and discussion 1. Water uptake kinetics
The symbols in Figure 3 show the experimentally determined water uptake kinetics of thin Eudragit RS films initially containing 0, 5, 10, 15, or 20 % tartaric acid, metoprolol free base or metoprolol tartrate (as indicated) upon exposure to 0.1 M HCl, phosphate buffer pH 7.4 and distilled water (left, middle and right column) at 37 °C. Clearly, the extent of water uptake significantly increased in the following ranking order: films containing metoprolol free base (middle row) > films containing metoprolol tartrate (bottom row) > films containing
5. Mathematical modeling of compound release
The apparent diffusion coefficients of tartaric acid, metoprolol free base and metoprolol tartrate within the polymeric systems were determined by fitting an appropriate analytical solution of Fick’s second law of diffusion to the experimentally determined release kinetics from thin films, in which the compounds were molecularly dispersed (monolithic solutions). As the surface of the films was very large compared to their thickness, edge effects were negligible and the mathematical analysis could be restricted to one dimension. Hence, the release kinetics may be described by Fick’s second law of diffusion in a plane sheet [19]: �c/�t = D · (�2c/�x2)
b · tan b = G
Eq. 3
where c denotes the concentration of the compound within the polymeric system, as a function of the time t and position x. The initial condition for this partial differential equation is as follows, expressing the fact that the compound is uniformly distributed throughout the film at the beginning of the experiment: t = 0
c = cini
-L≤ x ≤+L
Eq. 4
Here, cini represents the initial compound concentration in the system, L is the half-thickness of the film. The concentration of the compound far away from the surface of the film is assumed to be constant and approximated to be equal to zero because the release medium is well stirred and perfect sink conditions are maintained throughout the experiments. Adjacent to the surface of the films an unstirred liquid layer is considered (even in well-agitated systems thin unstirred layers exist, leading to an additional mass transfer resistance). As there is no accumulation of any compound on the surface of the films, the rates at which they are transported to the surface by diffusion through the films are always equal to the rates at which they leave the films. These rates, per unit area, are proportional to the differences of the actual concentrations on the surface, csur, and the concentrations required to maintain equilibrium with the surrounding environment, c∞. The
Figure 3 - Water uptake kinetics of thin Eudragit RS films containing 0 % (closed squares), 5 % (open diamonds), 10 % (closed triangles), 15 % (open squares) or 20 % (closed diamonds) tartaric acid, metoprolol free base or metoprolol tartrate (as indicated) upon exposure to 0.1 M HCl, phosphate buffer pH 7.4 or distilled water (left, middle and right column) at 37 °C. The symbols indicate the experimentally determined results, the curves the fitted theory (Equation 2). Note the different scaling of the y-axes. 129
J. DRUG DEL. SCI. TECH., 20 (2) 127-133 2010
Mathematical modeling of drug release from Eudragit RS-based delivery systems B. Glaessl, F. Siepmann, I. Tucker, T. Rades, J. Siepmann
tartaric acid (top row) (note the different scaling of the y-axes). This may be attributed to the differences in the plasticizing efficiency of these compounds for Eudragit RS, as recently described in the dry state [17]. Metoprolol free base is likely to interact with the polymer backbone, whereas in the case of metoprolol tartrate ionic interactions with the quaternary ammonium groups also occur. The observed ranking order also agrees very well with that observed for Eudragit RL-based films upon exposure to 0.1 M HCl, phosphate buffer pH 7.4 and distilled water, respectively [7]. In contrast to Eudragit RL, Eudragit RS contains only half the number of quaternary ammonium groups. The partially observed shrinking of metoprolol tartrate and metoprolol free base containing films may be attributed to the leaching of these compounds out into the release medium (Figure 4). This results in reduced plasticization and, thus, decreasing mechanical flexibility of the polymeric network. Consequently, water is squeezed out into the surrounding bulk fluid. This phenomenon is more pronounced in the case of metoprolol tartrate containing films than in the case of metoprolol free base containing systems (in the observation period) because metoprolol tartrate is released more rapidly than metoprolol free base (Figure 4). The curves in Figure 3 show the theoretically calculated water uptake kinetics of Eudragit RS-based films upon exposure to 0.1 M HCl, phosphate buffer pH 7.4 and distilled water, respectively. The mathematical model (Equation 2) is based on Fick’s second law of diffusion and considers that: (i) the film structure is initially homogeneous, (ii) edge effects are negligible (large surface area of the films compared to their thickness) and (iii) excess amounts of water are present on the surfaces throughout the experiments. In the case of shrinking films, the observed relative maxima of the water contents were used as M∞ values in Equation 2. Good agreement between this theory and the experimental results was obtained in most cases (at least) at early time points (curves and symbols in Figure 3). This indicates that diffusion (with apparently constant diffusivities) is the dominant mass transport mechanism in these cases. The observed zero order water uptake kinetics at early time points in the case of Eudragit RS films initially containing 10-20 % metoprolol free base upon exposure to phosphate buffer pH 7.4 indicate that one or more other physicochemical phenomena are of major importance (e.g., polymer chain relaxation). Based on the calculations (curves) shown in Figure 3, the apparent diffusion coefficients of water in the various types of Eudragit RSbased films upon exposure to 0.1 M HCl, phosphate buffer pH 7.4 and distilled water could be determined. The respective D-values are represented by the filled squares in Figure 5. For reasons of comparison, also the water diffusivities determined in thin Eudragit RL-based films (containing twice as many quaternary ammonium groups as Eudragit RS) are included in Figure 5 (open squares). Clearly, in all cases, the mobility of water within the polymeric networks is much higher in Eudragit RL-based systems compared to Eudragit RS-based films. This may be attributed to the higher amount of positively charged quaternary ammonium groups, rendering the macromolecular networks more hydrophilic. Thus, the extent of the water uptake is increased. This has been confirmed experimentally: the results obtained with Eudragit RS-based films are shown in Figure 3, those obtained with Eudragit RL have been reported in Glaessl et al. [7]. Because water acts as a plasticizer for these polymers, the resulting diffusion coefficients are also higher in Eudragit RL than in Eudragit RS, irrespective of the type of bulk fluid and incorporated compound (Figure 5). Interestingly, the observed dependencies of the water diffusivity on the: (i) initial content of tartaric acid, metoprolol free base and metoprolol tartrate, (ii) type of incorporated compound and (iii) type of release medium are very similar for Eudragit RS- and Eudragit RL-based films (filled versus open squares in Figure 5). This clearly indicates that the underlying physicochemical phenomena are not fundamentally different. In the case of tartaric acid and metoprolol
Figure 4 - Release kinetics of tartaric acid, metoprolol free base and metoprolol tartrate from thin Eudragit RS films initially containing 5 % (open diamonds), 10 % (closed triangles), 15 % (open squares), 20 % (closed diamonds), 25 % (open triangles), or 30 % (closed squares) of this compound upon exposure to 0.1 M HCl, phosphate buffer pH 7.4 or distilled water (left, middle and right column) at 37 °C. The symbols indicate the experimentally determined results, the curves the fitted theory (Equations 6 to 8).
Figure 5 - Apparent diffusion coefficient of water in thin Eudragit RS films (filled squares, solid curves) and (for reasons of comparison) in Eudragit RL films (open squares, dotted curves), initially containing 0, 5, 10, 15, or 20 % tartaric acid, metoprolol free base or metoprolol tartrate (as indicated) upon exposure to 0.1 M HCl, phosphate buffer pH 7.4 or distilled water (left, middle and right column) at 37 °C. The values in Eudragit RS films were determined by fitting Equation 2 to the experimentally measured water uptake kinetics shown in Figure 3. The diffusion coefficients in Eudragit RL films are reproduced from [7].
tartrate containing films, the water diffusion coefficient generally increases with increasing initial content of these compounds, irrespective of the type of bulk fluid (top and bottom rows in Figure 5). This may be explained by the plasticizing effects of these compounds on the two types of poly(acrylic acid) derivatives. In contrast, in the case of metoprolol free base, the water diffusivity: (i) first increases, and then decreases with increasing initial drug content upon exposure 130
Mathematical modeling of drug release from Eudragit RS-based delivery systems B. Glaessl, F. Siepmann, I. Tucker, T. Rades, J. Siepmann
to 0.1 M HCl, (ii) decreases/remains about constant with increasing initial drug content upon exposure to phosphate buffer pH 7.4, and (iii) monotonically increases with increasing initial drug content upon exposure to distilled water, irrespective of the type of Eudragit. The observed increase in water diffusivity with increasing initial metoprolol free base content may be explained by the plasticizing activity of this compound (via interactions with the polymer backbone). The partially observed decrease/leveling off in/of the diffusion coefficient with increasing initial metoprolol free base content might be attributable to the precipitation of this compound in the hydrated polymeric films (confirmed by visual observation). Thus, with increasing metoprolol free base content, the absolute amount of dissolved plasticizer does not increase, while the films become more and more hydrophobic, containing more and more precipitated free base. As metoprolol free base is better soluble in 0.1 M HCl than in phosphate buffer pH 7.4 [7], this precipitation effect occurs at lower initial drug contents in phosphate buffer pH 7.4 compared to 0.1 M HCl. However, it is yet unclear why this phenomenon is not observed in the investigated concentration range upon exposure to distilled water. Possibly, the creation of meta-stable, supersaturated drug solutions is involved.
J. DRUG DEL. SCI. TECH., 20 (2) 127-133 2010
Figure 6 - Apparent diffusion coefficient of tartaric acid, metoprolol free base and metoprolol tartrate in thin Eudragit RS (filled squares, solid curves) and (for reasons of comparison) Eudragit RL films (open squares, dotted curves) initially containing 5, 10, 15, 20, 25 or 30 % of this compound (as indicated) upon exposure to 0.1 M HCl, phosphate buffer pH 7.4, or distilled water (left, middle and right column) at 37 °C. The values in Eudragit RS films were determined by fitting Equations 6 to 8 to the experimentally measured release kinetics shown in Figure 4. The diffusion coefficients in Eudragit RL films are reproduced from [7].
2. Compound release kinetics
Figure 4 shows the experimentally determined (symbols) release of tartaric acid, metoprolol free base and metoprolol tartrate from thin Eudragit RS-based films upon exposure to 0.1 M HCl, phosphate buffer pH 7.4 and distilled water (left, middle and right column), respectively. The curves in Figure 4 indicate the theoretically calculated release kinetics of these compounds, assuming that diffusion through the polymeric networks with constant diffusivities is the release rate controlling mass transport step. The applied mathematical model (Equations 6 to 8) is based on Fick’s second law and considers that: (i) the compound is initially (before exposure to the bulk fluids, t = 0) homogeneously distributed throughout the system, (ii) edge effects are negligible (large surface area compared to the film thickness), (iii) the compounds are dissolved within the polymeric matrix (molecular distribution), (iv) perfect sink conditions are maintained throughout the experiments and (v) the presence of the liquid unstirred boundary layers on both sides of the films offer an additional mass transfer resistance for compound release, which can be characterized by the so-called mass transfer coefficient, h. As shown in Figure 4, good agreement between theory (curves) and experiment (symbols) was obtained in most cases, indicating that compound diffusion (with apparently constant diffusivity) is the dominant underlying mass transport mechanism. Interestingly, in these cases the dimensionless number G (Equation 8) was very high (> 100), indicating that the mass transfer resistance due to diffusion through the liquid unstirred boundary layers at the surfaces of the films is very low compared to the mass transfer resistance due to diffusion within the polymeric networks [22]. To account for arbitrary variations in the film thickness (all experiments were conducted in triplicate), the compound release kinetics shown in Figure 4 are normalized to this parameter (“time/thickness2” is plotted on the x-axes). Based on these calculations, the apparent diffusion coefficients of tartaric acid, metoprolol free base and metoprolol tartrate within the investigated Eudragit RS films could be determined upon exposure to 0.1 M HCl, phosphate buffer pH 7.4 and distilled water (filled squares in Figure 6). For reasons of comparison, the compound diffusivities in Eudragit RL films of analogous composition are also shown in the diagrams (open squares). Clearly, the apparent diffusivities are much higher in Eudragit RL-based films compared to Eudragit RS-based systems, irrespective of the type of compound and type of release medium. This may be explained by the higher hydrophilicity of Eudragit RL compared to Eudragit RS (containing twice as many quaternary ammonium groups), resulting in increased water uptake and, thus, more mobile macromolecular networks (as explained above).
Importantly, the general tendencies observed with Eudragit RS-based films were similar to those observed with Eudragit RL-based films: The diffusion coefficient of metoprolol tartrate significantly increased with increasing initial drug content, irrespective of the type of release medium (bottom row in Figure 6). This may be explained by the strong plasticizing activity of this compound. Furthermore, the mobility of tartaric acid (overall) slightly increased with increasing initial content of this compound (tartaric acid acting as a moderate plasticizer for these polymers) (top row in Figure 6). Also, in the case of metoprolol free base (middle row) drug precipitation occurred upon water penetration at higher initial drug contents and, thus, did not allow for the application of the described mathematical theory (Equations 6 to 8), which does not take this phenomenon into account. However, this precipitation effect occurred at higher initial drug contents in Eudragit RS-based films compared to Eudragit RL-based systems (confirmed by visual observation). This is due to the higher water uptake of Eudragit RL films, rendering the polymeric networks more hydrophilic. Importantly, the plasticizing activity of metoprolol free base on Eudragit RS becomes clearly visible until precipitation occurs: The apparent drug diffusivity increased with increasing initial metoprolol free base loading (Figure 6). In the case of metoprolol tartrate release from thin polymeric films, the amount of drug released into 0.1 M HCl, phosphate buffer pH 7.4 and distilled water was detected UV-spectrophotometrically at λ = 274.7/274.7/274.7 nm. Importantly, the measured absorptions were caused by the metoprolol species, and not by the tartrate species. Thus, strictly speaking it was not “metoprolol tartrate” release but “metoprolol” release that was measured. As metoprolol is the bioactive compound, this simplification is often applied. However, in order to be able to distinguish between tartrate and metoprolol species release from metoprolol tartrate loaded films, the amounts of these compounds in the bulk fluid were also determined by HPLC analysis, as described in section “2.4. In vitro release from thin, polymeric films”. Figure 7 shows as an example the release of the tartrate species and metoprolol species into phosphate buffer pH 7.4 from thin Eudragit RS films initially containing 10 or 20 % metoprolol tartrate (squares 131
J. DRUG DEL. SCI. TECH., 20 (2) 127-133 2010
Mathematical modeling of drug release from Eudragit RS-based delivery systems B. Glaessl, F. Siepmann, I. Tucker, T. Rades, J. Siepmann
The obtained new insight into the mass transport phenomena occurring in Eudragit RS-based drug delivery systems can help to facilitate the optimization of this type of pharmaceutical dosage form. The importance of drug-polymer interactions is often not well understood, leading to unexpected effects of formulation parameters on drug release. A more comprehensive mechanistic understanding of these systems can be highly valuable.
References 1. 2. 3. Figure 7 - Simultaneous release of tartrate and metoprolol species from metoprolol tartrate loaded Eudragit RS films in phosphate buffer pH 7.4 with an initial drug content of 10 and 20 %. Filled symbols: tartrate species, open symbols: metoprolol species, squares: 10 % loading, diamonds: 20 % loading. The symbols indicate the experimentally determined results, the curves the fitted theory (Equations 6 to 8).
4.
5.
and diamonds, respectively). Tartrate species release is indicated by filled symbols, whereas metoprolol release is indicated by open symbols. Clearly, the release of the tartrate species is much faster than that of the metoprolol species, irrespective of the initial drug loading. This is interesting, because at pH 7.4, the tartrate species are likely to be de-protonated and, thus, negatively charged (pKa1 = 2.98). Consequently, they can be expected to be attracted by the positively charged quaternary ammonium groups of the polymeric network. It has previously been reported that such attractive ionic interactions can significantly slow down drug release [23]. In the present case, such attractive ionic interactions seem to be overcompensated by the difference in the molecular weight of tartrate versus the metoprolol ions (MW = 149.1 vs. 268.4 Da) (also the metoprolol species can be expected to be mainly in the ionized form at pH 7.4, pKa = 9.7). Comparing the squares (10 % initial drug loading) and diamonds (20 % initial drug loading) in Figure 7, it becomes obvious that compound release from the Eudragit RS films is much faster at higher initial metoprolol tartrate contents, irrespective of the diffusing species. This confirms the significant plasticizing effect of this drug on this polymer. Fitting Equations 6 to 8 to the experimentally determined release kinetics of the tartrate and metoprolol species led to good agreement between theory (curves) and experiments (symbols), as shown in Figure 7. Thus, diffusion (with apparently constant diffusivities) is the dominant mass transfer step controlling compound release from these systems, irrespective of the type of diffusing species and initial drug loading. Based on these calculations, the following apparent diffusion coefficients could be determined: tartrate species at 10 % initial drug loading: D = 2.3 (± 0.3) · 10-8 cm2/s, metoprolol species at 10 % initial drug loading: D = 0.5 (± 0.0) · 10-8 cm²/s, tartrate species at 20 % initial drug loading: D = 5.3 (± 0.2) · 10-8 cm²/s, metoprolol species at 20 % initial drug loading: D = 2.3 (± 0.2) · 10-8 cm²/s. These values confirm the above described plasticizing effects of metoprolol tartrate for Eudragit RS as well as the overcompensation of the attractive interactions between the negatively charged tartrate ions and positively charged quaternary ammonium groups by the higher molecular weight of the metoprolol ions.
6.
7. 8.
9. 10. 11. 12.
13. 14. 15. 16.
17.
*
132
McGinity J.W. (Ed.) - Aqueous Polymeric Coating for Pharmaceutical Dosage Forms. - Marcel Dekker, New York, 1989. Wagner K.G., McGinity J.W. - Influence of chloride ion exchange on the permeability and drug release of Eudragit RS 30 D films. - J. Control. Rel., 82, 385-397, 2002. Evonik Roehm, Product Specification, Info 7.7/E, Specifications and test methods for Eudragit RL 100 and Eudragit RL PO, Eudragit RS 100 and Eudragit RS PO, Evonik Roehm GmbH, Pharma Polymers, 2007. Soltero R., Krailler R., Czeisler J. - The effects of pH, ionic concentration and ionic species of dissolution media on the release rates of quinidine gluconate sustained release dosage forms. - Drug Dev. Ind. Pharm., 17, 113-140, 1991. Narisawa S., Nagata M., Hirakawa Y., Kobayashi M., Yoshino H. - An organic acid-induced sigmoidal release system for oral controlled-release preparations. 2. permeability enhancement of Eudragit RS coating led by the physicochemical interactions with organic acid. - J. Pharm. Sci., 85, 184-188, 1996. Beckert T.E., Lynenskjold E., Petereit H.-U. - Anionic influences on the permeability of Eudragit RS. - Proceedings of the 24th International Symposium on Controlled Release of Bioactive Materials, Stockholm, 16-19 June 1997, CRS Ed., Vol. 24, p. 1031. Glaessl B., Siepmann F., Tucker I., Siepmann J., Rades T. Deeper insight into the drug release mechanisms in Eudragit RL-based delivery systems. - Submitted. Ravishankar H., Patil P., Samel A., Petereit H.-U., Lizio R., IyerChavan J. - Modulated release metoprolol succinate formulation based on ionic interactions: in vivo proof of concept. - J. Control. Rel., 111, 65-72, 2006. Siepmann F., Le Brun V., Siepmann J. - Drugs acting as plasticizers in polymeric systems: A quantitative treatment. - J. Control. Rel., 115, 298-306, 2006. Kaur K., Kim K. - Studies of chitosan/organic acid/Eudragit RS/ RL-coated system for colonic delivery. - Int. J. Pharm., 366, 140-148, 2009. Wu C., McGinity J.W. - Non-traditional plasticization of polymeric films. - Int. J. Pharm., 177, 15-27, 1999. Lecomte F., Siepmann J., Walther M., Macrae R.J., Bodmeier R. - Polymer blends used for the coating of multiparticulates: Comparison of aqueous and organic coating techniques. - Pharm. Res., 21, 882-890, 2004. Siepmann J., Goepferich A. - Mathematical modeling of bioerodible, polymeric drug delivery systems. - Adv. Drug Del. Rev., 48, 229-247, 2001. Siepmann J., Peppas N.A. - Modeling of drug release from delivery systems based on hydroxypropyl methylcellulose (HPMC). - Adv. Drug Del. Rev., 48, 139-157, 2001. Siepmann J., Siepmann F. - Mathematical modeling of drug delivery. - Int. J. Pharm., 364, 328-343, 2008. Siepmann J., Siepmann F., Florence A.T. - Local controlled drug delivery to the brain: Mathematical modeling of the underlying mass transport mechanisms. - Int. J. Pharm., 314, 101-119, 2006. Glaessl B., Siepmann F., Tucker I., Siepmann J., Rades T. Characterization of quaternary polymethacrylate films containing tartaric acid, metoprolol free base or metoprolol tartrate. - Eur. J. Pharm. Biopharm., 73, 366-372, 2009.
Mathematical modeling of drug release from Eudragit RS-based delivery systems B. Glaessl, F. Siepmann, I. Tucker, T. Rades, J. Siepmann
18.
19. 20. 21. 22.
23.
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Acknowledgements
Azarmi S., Farid J., Nokhodchi A., Bahari-Saravi S.M., Valizadeh H. - Thermal treating as a tool for sustained release of indomethacin from Eudragit RS and RL matrices. - Int. J. Pharm., 246, 171-177, 2002. Crank J. (Ed.) - The Mathematics of Diffusion. - 2nd ed., Clarendon Press, Oxford, 1975. Carslaw H., Jaeger J. (Eds.) - Conduction of Heat in Solids. Clarendon Press, Oxford, 1959. Vergnaud J. (Ed.) - Controlled Drug Release of Oral Dosage Forms. - Ellis Horwood, Chichester, 1993. Siepmann J., Lecomte F., Bobmeier R. - Diffusion-controlled drug delivery systems: Calculation of the required composition to achieve desired release profiles. - J. Control. Rel., 60, 379389, 1999. Klose D., Siepmann F., Elkharraz K., Siepmann J. - PLGA-based drug delivery systems: importance of the type of drug and device geometry. - Int. J. Pharm., 354, 95-103, 2008.
The authors are grateful for the support of this work by the Nord-Pasde-Calais Regional Council (Interdisciplinary Research Center on Drug Products, PRIM: “Pôle de recherche interdisciplinaire pour le médicament”).
Manuscript Received 27 July 2009, accepted for publication 21 December 2009.
133
Mathematical modeling of drug release from Eudragit RS-based delivery systems B. Glaessl1, 2, F. Siepmann1, I. Tucker2, T. Rades2, J.Siepmann1* 1
College of Pharmacy, JE 2491, University Lille-Nord de France, 3, rue du Professeur-Laguesse, 59006 Lille, France 2 New Zealand’s National School of Pharmacy, University of Otago, 18 Frederick Street, Dunedin, New Zealand *Correspondence: [email protected]
Various types of tartaric acid, metoprolol free base and metoprolol tartrate containing Eudragit RS-based films were prepared and physicochemically characterized. In particular, the water uptake and compound release kinetics were monitored upon exposure to 0.1 M HCl, phosphate buffer pH 7.4 and distilled water. Appropriate analytical solutions of Fick’s second law of diffusion, considering the given initial and boundary conditions, were used to elucidate the underlying mass transport mechanisms. Furthermore, the apparent diffusion coefficients of water, tartaric acid, metoprolol free base and metoprolol tartrate in the different Eudragit RS-based networks were determined. Importantly, the diffusivity of metoprolol tartrate and metoprolol free base significantly increased with increasing initial drug content, illustrating the strong plasticizing capacity of these compounds for the polymer. In contrast to Eudragit RL-based films, metoprolol free base precipitation occurred only at higher initial drug loadings, due to the lower water uptake resulting from the lower contents of quaternary ammonium groups. Interestingly, negatively charged tartrate ions diffused out more rapidly from metoprolol tartrate containing films than positively charged metoprolol ions, indicating that the lower molecular weight over-compensates the attractive ionic interactions with the positively charged macromolecules. Key words: Mathematical modeling – Eudragit RS – Controlled release – Drug polymer interactions – Diffusion.
Eudragit RS is frequently used as a matrix former or coating material in time-controlled drug delivery systems [1, 2]. It is a poly(acrylic acid) derivative [poly(ethylacrylate-methylmethacrylate-trimethylammonioethylmethacrylate chloride) 1:2:0.1], the structure of which is shown in Figure 1. In contrast to Eudragit RL, it contains only half the amount of quaternary ammonium groups [3]. Due to the presence of the permanent positive charges of these quaternary ammonium groups, the underlying drug release mechanisms from these types of dosage forms may be complex [4-7]. For instance, ionic drug-polymer interactions might occur [8-10] and strongly affect the resulting drug release patterns. Furthermore, drugs (charged or otherwise) might act as plasticizers for Eudragit RS [11, 12]. Thus, the initial drug loading of the system potentially affects the resulting polymer chain mobility and, consequently, drug release. In addition, the type of ions present in the surrounding bulk fluid (and diffusing into the system during drug release) might have a significant impact on the drug-polymer interactions in the dosage form. For instance, such ions can compete with negatively charged drug ions to interact with the positively charged quaternary ammonium groups and, thus, alter the relative importance of the involved physicochemical processes controlling drug release. Due to the considerable potential complexity of the system, the underlying mass transport phenomena in Eudragit RS-based devices are generally not well understood (despite the great practical importance of this type of dosage forms). Thus, system optimization is often based on time- and cost-intensive series of trial-and-error experiments. In order to get deeper insight into the physicochemical processes involved in the control of drug release from a particular type of dosage form, the latter first needs to be characterized as thoroughly as possible [13-15]. Then, based on the experimental results, mechanistic realistic mathematical theories should be developed/identified, which allow for a quantitative description of the occurring mass transport steps [16]. Importantly, all decisive phenomena must be taken into account in the model, whereas mass transport steps of negligible importance should not be considered in order to keep the theory as simple as possible otherwise too many system-specific parameters need to be determined. Once such a model is established/identified, it can be fitted to different types of experimental results, for instance water uptake
and drug release kinetics. Based on these calculations device specific parameters, including for example the diffusion coefficient of water and drug within the polymeric network, may be determined. Having determined these values, the relative importance of the respective mass transport steps may be estimated. Furthermore, the effects of different formulation parameters on these system-specific parameters may be quantified and thus the observed (often rather complex) relationships with the resulting drug release kinetics better understood. Previously, different types of tartaric acid, metoprolol free base and metoprolol tartrate containing Eudragit RL- and Eudragit RSsystems were prepared and physicochemically characterized in the dry state [17]. However, the presence of water can significantly affect the resulting system properties, water acting for instance as a strong plasticizer for many polymers [12]. Also, Eudragit RL-based films were studied in the wet state [7]. However, Eudragit RS contains only half the amount of quaternary ammonium groups and it is well known that drug release from Eudragit RS based dosage forms is much slower than from the Eudragit RL containing analogues [18]. It was the aim of this study to: (i) prepare and physicochemically characterize tartaric acid, metoprolol free base and metoprolol tartrate containing Eudragit RS films, in particular regarding their water uptake and compound release kinetics under various conditions, and (ii) to identify appropriate mechanistic realistic mathematical theories that result in a quantitative description of the observed mass transport processes in order to achieve deeper insight into this type of controlled drug delivery system.
I. Materials and methods 1. Materials
The following chemicals were used as received: tartaric acid (Acros Organics, Halluin, France), metoprolol tartrate (Novartis, Barleben, Germany) and Eudragit RS PO [poly(ethylacrylate-methylmethacrylate-trimethylammonioethylmethacrylate chloride) 1:2:0.1, Evonik Roehm, Darmstadt, Germany]. The free metoprolol base was obtained from metoprolol succinate (Novartis, Barleben, Germany) by first dissolving the salt in a sodium hydroxide solution, and subsequent extraction with dichloromethane, followed by drying with water-free 127
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Mathematical modeling of drug release from Eudragit RS-based delivery systems B. Glaessl, F. Siepmann, I. Tucker, T. Rades, J. Siepmann
All experiments were conducted in triplicate. In order to quantify the observed water uptake kinetics of the thin films, the following analytical solution of Fick’s second law of diffusion was used, considering the given initial and boundary conditions (homogeneous film composition, negligible edge effects and excess amount of water at both surfaces of the films) [19]: ∞ ( 2n + 1) ⋅ π Mt 8 =1− ∑ ⋅ exp − ⋅D ⋅t 2 2 M∞ + ⋅ π 4⋅ L2 ( 2 n 1 ) n =0
(
2
2
)
Eq. 2
Here, Mt and M∞ denote the absolute cumulative amounts of water taken up at time t and t = ∞, respectively; D represents the apparent diffusion coefficient of water within the system and L the half-thickness of the film.
4. In vitro release from thin, polymeric films
The release of tartaric acid, metoprolol free base and metoprolol tartrate from thin Eudragit RS films was measured by placing film pieces into plastic flasks filled with pre-heated release medium [0.1 M HCl, phosphate buffer pH 7.4 (USP 30) or distilled water], followed by horizontal shaking for 8 h (37 °C, 80 rpm, GFL 3033) (n = 3). At pre-determined time points, samples of 3 mL were withdrawn and replaced with fresh, pre-heated medium. The respective compound was detected UV-spectrophotometrically (UV-1650; Shimadzu, Champssur-Marne, France) (λ = 212.0/204.3/220.0, 274.7/275.0/274.7, and 274.7/274.7/274.7 nm for tartaric acid/metoprolol free base/metoprolol tartrate in 0.1 M HCl, phosphate buffer pH 7.4 and distilled water, respectively), except for: (i) tartaric acid release in distilled water, and (ii) simultaneous and separate detection of metoprolol and tartrate release from metoprolol tartrate-containing films. In these two cases, the following HPLC techniques were applied: - tartaric acid release in water was quantified by isocratic HPLC analysis (HPLC ProStar 230, Varian, Paris, France), equipped with a ProStar 230 pump (Varian), an autosampler Prostar 410 (Varian) and an UV-Vis detector Prostar 325 (Varian). The reverse-phase column (Synergi 4u Hydro-RP 80A, 250 × 4.6 mm, Phenomenex, Auckland, New Zealand) was kept at 30 °C. The flow rate of the mobile phase [20 mM potassium phosphate buffer pH 2.9 (Phenomenex)] was 0.7 mL/min. Fifty-microlitre samples were injected and the drug detected at λ = 220 nm. Data was analyzed using the Galaxie software (Varian). Tartaric acid standard solutions containing 50, 100, 150, 200, 300, and 400 µg/mL were used for calibration (linear standard curve in the range of 50 to 400 µg/mL, correlation coefficient R2 = 1.00). Intra-day and inter-day variability as well as assay precision and accuracy were satisfactory; - metoprolol and tartrate species were simultaneously and separately detected using a newly developed method using an Agilent 1200 HPLC apparatus (Agilent Technologies, Waldbronn, Germany). The reversephase column (Synergi 4u Hydro-RP 80A, 250 × 4.6mm, Phenomenex) was kept at 30 °C. The mobile phase was a mixture of phosphate buffer pH 2.9 (Phenomenex) and acetonitrile. The blend ratios and flow rates were as follows: 0-6 min: 100:0 at 0.7 mL/min; 6-10 min: 15:85 at 1.5 mL/min; 10-15 min: 100:0 at 1.5 mL/min. Fifty-microlitre samples (adjusted to pH 2.5 with orthophosphoric acid) were automatically injected. Tartrate species were detected UV-spectrophometrically at λ = 220 nm during the first 6 min, metoprolol species were detected UV-spectrophotometrically at λ = 230 nm afterwards. Data was collected, integrated and analyzed using the Agilent Technologies software. Figure 2 shows the chromatogram of an aqueous metoprolol tartrate solution (500 µg/mL). The first peak at a retention time of 4.4 min represents the (more hydrophilic) tartrate species, the second peak at a retention time of 9.7 min represents the (more hydrophobic) metoprolol species. Metoprolol tartrate standard solutions containing 150, 300, 500, 700, and 1,000 µg/mL were used for calibration (linearity from 150 to 1,000 µg/mL, correlation coefficient R2 = 1.000 for both spe-
Figure 1 - Chemical structures of tartaric acid, metoprolol free base, metoprolol tartrate and Eudragit RS.
sodium sulfate. For further water elimination, the obtained oily liquid was dried at 80 °C in a rotary evaporator (Rotavapor R110, Buechi, Flawil, Switzerland) connected to a vacuum pump. The yellowish liquid was cooled down to 4-7 °C, inducing crystallization of the free base in the form of white crystals, which were subsequently gently ground with a mortar and pestle. The chemical structures of tartaric acid, metoprolol free base, metoprolol tartrate as well as Eudragit RS are shown in Figure 1.
2. Film preparation
Thin Eudragit RS films were prepared with a casting knife (Multicator 411, Erichsen, Hemer, Germany) and a PTFE plate from ethanolic polymer solutions, optionally containing tartaric acid, metoprolol free base or metoprolol tartrate (0 to 20.0 % w/w, based on the polymer mass). The films were dried for 3 d at room temperature, followed by 1 d at 50 °C. The thickness of the films was measured using a thickness gauge (Minitest 600, Erichsen).
3. Water uptake of thin, polymeric films
Thin Eudragit RS films (optionally containing tartaric acid, metoprolol free base or metoprolol tartrate) were cut into pieces of approximately 4 cm × 4 cm, which were placed into plastic flasks filled with pre-heated release medium [0.1 M HCl, phosphate buffer pH 7.4 (USP 30) or distilled water], followed by horizontal shaking for 8 h (37 °C, 80 rpm; GFL 3033, Gesellschaft fuer Labortechnik, Burgwedel, Germany). The films were weighed before exposure to the media [dry weight (t = 0), mdry]. At pre-determined time points, the films were withdrawn from the media, carefully dried from adhesive water and accurately weighed [wet weight (t)]. The water uptake (t) (%) at time t was calculated as follows: water uptake (t) (%) = [(mwet (t) - mdry)/mdry] . 100 (%)
Eq. 1 128
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proportionality constant is called the mass transfer coefficient in the boundary layer, h. As the thickness of the boundary layer essentially depends on the rate of stirring, h is a function of the stirring rate. This boundary condition is mathematically expressed as: t > 0
Eq. 5
- D · |�c/�x|x=±L = h · (csur - c∞)
This initial value problem (Equations 3 to 5) can be solved using a Laplace transformation, leading to [20, 21]: ∞ Mt β2 2⋅G 2 =1− ∑ 2 ⋅ exp − n2 ⋅ D ⋅ t 2 2 M∞ L n =1 β n ⋅ ( β n + G + G )
(
)
Eq. 6
where the bn values are the positive roots of: Figure 2 - Chromatogram of an aqueous metoprolol tartrate solution, showing well separated peaks of tartrate species (retention time = 4.4 min) and metoprolol species (retention time = 9.7 min).
Eq. 7
G = (L · h)/D
Eq. 8
with:
cies). Intra-day variability was determined by five repeated analyses of quality control samples on the same day, and inter-day variability by repeated analyses on five consecutive days. A new calibration curve was used on each day. Assay precision was assessed by the percent relative standard deviation (% RSD) and accuracy was calculated as estimated concentration (percentage of the nominal concentration). The intra-day and inter-day precision (% RSD between 0.1 and 3.7) and accuracy (100.8 to 108.1 %) was satisfactory for both species: tartrate and metoprolol.
Here, Mt and M∞ are the cumulative amounts of tartaric acid, metoprolol free base or metoprolol tartrate released at time t and t = ∞, respectively; G denotes a dimensionless constant. The diffusion coefficient of the compound D was determined by fitting Equations 6 to 8 to experimentally measured in vitro release kinetics.
II. Results and discussion 1. Water uptake kinetics
The symbols in Figure 3 show the experimentally determined water uptake kinetics of thin Eudragit RS films initially containing 0, 5, 10, 15, or 20 % tartaric acid, metoprolol free base or metoprolol tartrate (as indicated) upon exposure to 0.1 M HCl, phosphate buffer pH 7.4 and distilled water (left, middle and right column) at 37 °C. Clearly, the extent of water uptake significantly increased in the following ranking order: films containing metoprolol free base (middle row) > films containing metoprolol tartrate (bottom row) > films containing
5. Mathematical modeling of compound release
The apparent diffusion coefficients of tartaric acid, metoprolol free base and metoprolol tartrate within the polymeric systems were determined by fitting an appropriate analytical solution of Fick’s second law of diffusion to the experimentally determined release kinetics from thin films, in which the compounds were molecularly dispersed (monolithic solutions). As the surface of the films was very large compared to their thickness, edge effects were negligible and the mathematical analysis could be restricted to one dimension. Hence, the release kinetics may be described by Fick’s second law of diffusion in a plane sheet [19]: �c/�t = D · (�2c/�x2)
b · tan b = G
Eq. 3
where c denotes the concentration of the compound within the polymeric system, as a function of the time t and position x. The initial condition for this partial differential equation is as follows, expressing the fact that the compound is uniformly distributed throughout the film at the beginning of the experiment: t = 0
c = cini
-L≤ x ≤+L
Eq. 4
Here, cini represents the initial compound concentration in the system, L is the half-thickness of the film. The concentration of the compound far away from the surface of the film is assumed to be constant and approximated to be equal to zero because the release medium is well stirred and perfect sink conditions are maintained throughout the experiments. Adjacent to the surface of the films an unstirred liquid layer is considered (even in well-agitated systems thin unstirred layers exist, leading to an additional mass transfer resistance). As there is no accumulation of any compound on the surface of the films, the rates at which they are transported to the surface by diffusion through the films are always equal to the rates at which they leave the films. These rates, per unit area, are proportional to the differences of the actual concentrations on the surface, csur, and the concentrations required to maintain equilibrium with the surrounding environment, c∞. The
Figure 3 - Water uptake kinetics of thin Eudragit RS films containing 0 % (closed squares), 5 % (open diamonds), 10 % (closed triangles), 15 % (open squares) or 20 % (closed diamonds) tartaric acid, metoprolol free base or metoprolol tartrate (as indicated) upon exposure to 0.1 M HCl, phosphate buffer pH 7.4 or distilled water (left, middle and right column) at 37 °C. The symbols indicate the experimentally determined results, the curves the fitted theory (Equation 2). Note the different scaling of the y-axes. 129
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Mathematical modeling of drug release from Eudragit RS-based delivery systems B. Glaessl, F. Siepmann, I. Tucker, T. Rades, J. Siepmann
tartaric acid (top row) (note the different scaling of the y-axes). This may be attributed to the differences in the plasticizing efficiency of these compounds for Eudragit RS, as recently described in the dry state [17]. Metoprolol free base is likely to interact with the polymer backbone, whereas in the case of metoprolol tartrate ionic interactions with the quaternary ammonium groups also occur. The observed ranking order also agrees very well with that observed for Eudragit RL-based films upon exposure to 0.1 M HCl, phosphate buffer pH 7.4 and distilled water, respectively [7]. In contrast to Eudragit RL, Eudragit RS contains only half the number of quaternary ammonium groups. The partially observed shrinking of metoprolol tartrate and metoprolol free base containing films may be attributed to the leaching of these compounds out into the release medium (Figure 4). This results in reduced plasticization and, thus, decreasing mechanical flexibility of the polymeric network. Consequently, water is squeezed out into the surrounding bulk fluid. This phenomenon is more pronounced in the case of metoprolol tartrate containing films than in the case of metoprolol free base containing systems (in the observation period) because metoprolol tartrate is released more rapidly than metoprolol free base (Figure 4). The curves in Figure 3 show the theoretically calculated water uptake kinetics of Eudragit RS-based films upon exposure to 0.1 M HCl, phosphate buffer pH 7.4 and distilled water, respectively. The mathematical model (Equation 2) is based on Fick’s second law of diffusion and considers that: (i) the film structure is initially homogeneous, (ii) edge effects are negligible (large surface area of the films compared to their thickness) and (iii) excess amounts of water are present on the surfaces throughout the experiments. In the case of shrinking films, the observed relative maxima of the water contents were used as M∞ values in Equation 2. Good agreement between this theory and the experimental results was obtained in most cases (at least) at early time points (curves and symbols in Figure 3). This indicates that diffusion (with apparently constant diffusivities) is the dominant mass transport mechanism in these cases. The observed zero order water uptake kinetics at early time points in the case of Eudragit RS films initially containing 10-20 % metoprolol free base upon exposure to phosphate buffer pH 7.4 indicate that one or more other physicochemical phenomena are of major importance (e.g., polymer chain relaxation). Based on the calculations (curves) shown in Figure 3, the apparent diffusion coefficients of water in the various types of Eudragit RSbased films upon exposure to 0.1 M HCl, phosphate buffer pH 7.4 and distilled water could be determined. The respective D-values are represented by the filled squares in Figure 5. For reasons of comparison, also the water diffusivities determined in thin Eudragit RL-based films (containing twice as many quaternary ammonium groups as Eudragit RS) are included in Figure 5 (open squares). Clearly, in all cases, the mobility of water within the polymeric networks is much higher in Eudragit RL-based systems compared to Eudragit RS-based films. This may be attributed to the higher amount of positively charged quaternary ammonium groups, rendering the macromolecular networks more hydrophilic. Thus, the extent of the water uptake is increased. This has been confirmed experimentally: the results obtained with Eudragit RS-based films are shown in Figure 3, those obtained with Eudragit RL have been reported in Glaessl et al. [7]. Because water acts as a plasticizer for these polymers, the resulting diffusion coefficients are also higher in Eudragit RL than in Eudragit RS, irrespective of the type of bulk fluid and incorporated compound (Figure 5). Interestingly, the observed dependencies of the water diffusivity on the: (i) initial content of tartaric acid, metoprolol free base and metoprolol tartrate, (ii) type of incorporated compound and (iii) type of release medium are very similar for Eudragit RS- and Eudragit RL-based films (filled versus open squares in Figure 5). This clearly indicates that the underlying physicochemical phenomena are not fundamentally different. In the case of tartaric acid and metoprolol
Figure 4 - Release kinetics of tartaric acid, metoprolol free base and metoprolol tartrate from thin Eudragit RS films initially containing 5 % (open diamonds), 10 % (closed triangles), 15 % (open squares), 20 % (closed diamonds), 25 % (open triangles), or 30 % (closed squares) of this compound upon exposure to 0.1 M HCl, phosphate buffer pH 7.4 or distilled water (left, middle and right column) at 37 °C. The symbols indicate the experimentally determined results, the curves the fitted theory (Equations 6 to 8).
Figure 5 - Apparent diffusion coefficient of water in thin Eudragit RS films (filled squares, solid curves) and (for reasons of comparison) in Eudragit RL films (open squares, dotted curves), initially containing 0, 5, 10, 15, or 20 % tartaric acid, metoprolol free base or metoprolol tartrate (as indicated) upon exposure to 0.1 M HCl, phosphate buffer pH 7.4 or distilled water (left, middle and right column) at 37 °C. The values in Eudragit RS films were determined by fitting Equation 2 to the experimentally measured water uptake kinetics shown in Figure 3. The diffusion coefficients in Eudragit RL films are reproduced from [7].
tartrate containing films, the water diffusion coefficient generally increases with increasing initial content of these compounds, irrespective of the type of bulk fluid (top and bottom rows in Figure 5). This may be explained by the plasticizing effects of these compounds on the two types of poly(acrylic acid) derivatives. In contrast, in the case of metoprolol free base, the water diffusivity: (i) first increases, and then decreases with increasing initial drug content upon exposure 130
Mathematical modeling of drug release from Eudragit RS-based delivery systems B. Glaessl, F. Siepmann, I. Tucker, T. Rades, J. Siepmann
to 0.1 M HCl, (ii) decreases/remains about constant with increasing initial drug content upon exposure to phosphate buffer pH 7.4, and (iii) monotonically increases with increasing initial drug content upon exposure to distilled water, irrespective of the type of Eudragit. The observed increase in water diffusivity with increasing initial metoprolol free base content may be explained by the plasticizing activity of this compound (via interactions with the polymer backbone). The partially observed decrease/leveling off in/of the diffusion coefficient with increasing initial metoprolol free base content might be attributable to the precipitation of this compound in the hydrated polymeric films (confirmed by visual observation). Thus, with increasing metoprolol free base content, the absolute amount of dissolved plasticizer does not increase, while the films become more and more hydrophobic, containing more and more precipitated free base. As metoprolol free base is better soluble in 0.1 M HCl than in phosphate buffer pH 7.4 [7], this precipitation effect occurs at lower initial drug contents in phosphate buffer pH 7.4 compared to 0.1 M HCl. However, it is yet unclear why this phenomenon is not observed in the investigated concentration range upon exposure to distilled water. Possibly, the creation of meta-stable, supersaturated drug solutions is involved.
J. DRUG DEL. SCI. TECH., 20 (2) 127-133 2010
Figure 6 - Apparent diffusion coefficient of tartaric acid, metoprolol free base and metoprolol tartrate in thin Eudragit RS (filled squares, solid curves) and (for reasons of comparison) Eudragit RL films (open squares, dotted curves) initially containing 5, 10, 15, 20, 25 or 30 % of this compound (as indicated) upon exposure to 0.1 M HCl, phosphate buffer pH 7.4, or distilled water (left, middle and right column) at 37 °C. The values in Eudragit RS films were determined by fitting Equations 6 to 8 to the experimentally measured release kinetics shown in Figure 4. The diffusion coefficients in Eudragit RL films are reproduced from [7].
2. Compound release kinetics
Figure 4 shows the experimentally determined (symbols) release of tartaric acid, metoprolol free base and metoprolol tartrate from thin Eudragit RS-based films upon exposure to 0.1 M HCl, phosphate buffer pH 7.4 and distilled water (left, middle and right column), respectively. The curves in Figure 4 indicate the theoretically calculated release kinetics of these compounds, assuming that diffusion through the polymeric networks with constant diffusivities is the release rate controlling mass transport step. The applied mathematical model (Equations 6 to 8) is based on Fick’s second law and considers that: (i) the compound is initially (before exposure to the bulk fluids, t = 0) homogeneously distributed throughout the system, (ii) edge effects are negligible (large surface area compared to the film thickness), (iii) the compounds are dissolved within the polymeric matrix (molecular distribution), (iv) perfect sink conditions are maintained throughout the experiments and (v) the presence of the liquid unstirred boundary layers on both sides of the films offer an additional mass transfer resistance for compound release, which can be characterized by the so-called mass transfer coefficient, h. As shown in Figure 4, good agreement between theory (curves) and experiment (symbols) was obtained in most cases, indicating that compound diffusion (with apparently constant diffusivity) is the dominant underlying mass transport mechanism. Interestingly, in these cases the dimensionless number G (Equation 8) was very high (> 100), indicating that the mass transfer resistance due to diffusion through the liquid unstirred boundary layers at the surfaces of the films is very low compared to the mass transfer resistance due to diffusion within the polymeric networks [22]. To account for arbitrary variations in the film thickness (all experiments were conducted in triplicate), the compound release kinetics shown in Figure 4 are normalized to this parameter (“time/thickness2” is plotted on the x-axes). Based on these calculations, the apparent diffusion coefficients of tartaric acid, metoprolol free base and metoprolol tartrate within the investigated Eudragit RS films could be determined upon exposure to 0.1 M HCl, phosphate buffer pH 7.4 and distilled water (filled squares in Figure 6). For reasons of comparison, the compound diffusivities in Eudragit RL films of analogous composition are also shown in the diagrams (open squares). Clearly, the apparent diffusivities are much higher in Eudragit RL-based films compared to Eudragit RS-based systems, irrespective of the type of compound and type of release medium. This may be explained by the higher hydrophilicity of Eudragit RL compared to Eudragit RS (containing twice as many quaternary ammonium groups), resulting in increased water uptake and, thus, more mobile macromolecular networks (as explained above).
Importantly, the general tendencies observed with Eudragit RS-based films were similar to those observed with Eudragit RL-based films: The diffusion coefficient of metoprolol tartrate significantly increased with increasing initial drug content, irrespective of the type of release medium (bottom row in Figure 6). This may be explained by the strong plasticizing activity of this compound. Furthermore, the mobility of tartaric acid (overall) slightly increased with increasing initial content of this compound (tartaric acid acting as a moderate plasticizer for these polymers) (top row in Figure 6). Also, in the case of metoprolol free base (middle row) drug precipitation occurred upon water penetration at higher initial drug contents and, thus, did not allow for the application of the described mathematical theory (Equations 6 to 8), which does not take this phenomenon into account. However, this precipitation effect occurred at higher initial drug contents in Eudragit RS-based films compared to Eudragit RL-based systems (confirmed by visual observation). This is due to the higher water uptake of Eudragit RL films, rendering the polymeric networks more hydrophilic. Importantly, the plasticizing activity of metoprolol free base on Eudragit RS becomes clearly visible until precipitation occurs: The apparent drug diffusivity increased with increasing initial metoprolol free base loading (Figure 6). In the case of metoprolol tartrate release from thin polymeric films, the amount of drug released into 0.1 M HCl, phosphate buffer pH 7.4 and distilled water was detected UV-spectrophotometrically at λ = 274.7/274.7/274.7 nm. Importantly, the measured absorptions were caused by the metoprolol species, and not by the tartrate species. Thus, strictly speaking it was not “metoprolol tartrate” release but “metoprolol” release that was measured. As metoprolol is the bioactive compound, this simplification is often applied. However, in order to be able to distinguish between tartrate and metoprolol species release from metoprolol tartrate loaded films, the amounts of these compounds in the bulk fluid were also determined by HPLC analysis, as described in section “2.4. In vitro release from thin, polymeric films”. Figure 7 shows as an example the release of the tartrate species and metoprolol species into phosphate buffer pH 7.4 from thin Eudragit RS films initially containing 10 or 20 % metoprolol tartrate (squares 131
J. DRUG DEL. SCI. TECH., 20 (2) 127-133 2010
Mathematical modeling of drug release from Eudragit RS-based delivery systems B. Glaessl, F. Siepmann, I. Tucker, T. Rades, J. Siepmann
The obtained new insight into the mass transport phenomena occurring in Eudragit RS-based drug delivery systems can help to facilitate the optimization of this type of pharmaceutical dosage form. The importance of drug-polymer interactions is often not well understood, leading to unexpected effects of formulation parameters on drug release. A more comprehensive mechanistic understanding of these systems can be highly valuable.
References 1. 2. 3. Figure 7 - Simultaneous release of tartrate and metoprolol species from metoprolol tartrate loaded Eudragit RS films in phosphate buffer pH 7.4 with an initial drug content of 10 and 20 %. Filled symbols: tartrate species, open symbols: metoprolol species, squares: 10 % loading, diamonds: 20 % loading. The symbols indicate the experimentally determined results, the curves the fitted theory (Equations 6 to 8).
4.
5.
and diamonds, respectively). Tartrate species release is indicated by filled symbols, whereas metoprolol release is indicated by open symbols. Clearly, the release of the tartrate species is much faster than that of the metoprolol species, irrespective of the initial drug loading. This is interesting, because at pH 7.4, the tartrate species are likely to be de-protonated and, thus, negatively charged (pKa1 = 2.98). Consequently, they can be expected to be attracted by the positively charged quaternary ammonium groups of the polymeric network. It has previously been reported that such attractive ionic interactions can significantly slow down drug release [23]. In the present case, such attractive ionic interactions seem to be overcompensated by the difference in the molecular weight of tartrate versus the metoprolol ions (MW = 149.1 vs. 268.4 Da) (also the metoprolol species can be expected to be mainly in the ionized form at pH 7.4, pKa = 9.7). Comparing the squares (10 % initial drug loading) and diamonds (20 % initial drug loading) in Figure 7, it becomes obvious that compound release from the Eudragit RS films is much faster at higher initial metoprolol tartrate contents, irrespective of the diffusing species. This confirms the significant plasticizing effect of this drug on this polymer. Fitting Equations 6 to 8 to the experimentally determined release kinetics of the tartrate and metoprolol species led to good agreement between theory (curves) and experiments (symbols), as shown in Figure 7. Thus, diffusion (with apparently constant diffusivities) is the dominant mass transfer step controlling compound release from these systems, irrespective of the type of diffusing species and initial drug loading. Based on these calculations, the following apparent diffusion coefficients could be determined: tartrate species at 10 % initial drug loading: D = 2.3 (± 0.3) · 10-8 cm2/s, metoprolol species at 10 % initial drug loading: D = 0.5 (± 0.0) · 10-8 cm²/s, tartrate species at 20 % initial drug loading: D = 5.3 (± 0.2) · 10-8 cm²/s, metoprolol species at 20 % initial drug loading: D = 2.3 (± 0.2) · 10-8 cm²/s. These values confirm the above described plasticizing effects of metoprolol tartrate for Eudragit RS as well as the overcompensation of the attractive interactions between the negatively charged tartrate ions and positively charged quaternary ammonium groups by the higher molecular weight of the metoprolol ions.
6.
7. 8.
9. 10. 11. 12.
13. 14. 15. 16.
17.
*
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McGinity J.W. (Ed.) - Aqueous Polymeric Coating for Pharmaceutical Dosage Forms. - Marcel Dekker, New York, 1989. Wagner K.G., McGinity J.W. - Influence of chloride ion exchange on the permeability and drug release of Eudragit RS 30 D films. - J. Control. Rel., 82, 385-397, 2002. Evonik Roehm, Product Specification, Info 7.7/E, Specifications and test methods for Eudragit RL 100 and Eudragit RL PO, Eudragit RS 100 and Eudragit RS PO, Evonik Roehm GmbH, Pharma Polymers, 2007. Soltero R., Krailler R., Czeisler J. - The effects of pH, ionic concentration and ionic species of dissolution media on the release rates of quinidine gluconate sustained release dosage forms. - Drug Dev. Ind. Pharm., 17, 113-140, 1991. Narisawa S., Nagata M., Hirakawa Y., Kobayashi M., Yoshino H. - An organic acid-induced sigmoidal release system for oral controlled-release preparations. 2. permeability enhancement of Eudragit RS coating led by the physicochemical interactions with organic acid. - J. Pharm. Sci., 85, 184-188, 1996. Beckert T.E., Lynenskjold E., Petereit H.-U. - Anionic influences on the permeability of Eudragit RS. - Proceedings of the 24th International Symposium on Controlled Release of Bioactive Materials, Stockholm, 16-19 June 1997, CRS Ed., Vol. 24, p. 1031. Glaessl B., Siepmann F., Tucker I., Siepmann J., Rades T. Deeper insight into the drug release mechanisms in Eudragit RL-based delivery systems. - Submitted. Ravishankar H., Patil P., Samel A., Petereit H.-U., Lizio R., IyerChavan J. - Modulated release metoprolol succinate formulation based on ionic interactions: in vivo proof of concept. - J. Control. Rel., 111, 65-72, 2006. Siepmann F., Le Brun V., Siepmann J. - Drugs acting as plasticizers in polymeric systems: A quantitative treatment. - J. Control. Rel., 115, 298-306, 2006. Kaur K., Kim K. - Studies of chitosan/organic acid/Eudragit RS/ RL-coated system for colonic delivery. - Int. J. Pharm., 366, 140-148, 2009. Wu C., McGinity J.W. - Non-traditional plasticization of polymeric films. - Int. J. Pharm., 177, 15-27, 1999. Lecomte F., Siepmann J., Walther M., Macrae R.J., Bodmeier R. - Polymer blends used for the coating of multiparticulates: Comparison of aqueous and organic coating techniques. - Pharm. Res., 21, 882-890, 2004. Siepmann J., Goepferich A. - Mathematical modeling of bioerodible, polymeric drug delivery systems. - Adv. Drug Del. Rev., 48, 229-247, 2001. Siepmann J., Peppas N.A. - Modeling of drug release from delivery systems based on hydroxypropyl methylcellulose (HPMC). - Adv. Drug Del. Rev., 48, 139-157, 2001. Siepmann J., Siepmann F. - Mathematical modeling of drug delivery. - Int. J. Pharm., 364, 328-343, 2008. Siepmann J., Siepmann F., Florence A.T. - Local controlled drug delivery to the brain: Mathematical modeling of the underlying mass transport mechanisms. - Int. J. Pharm., 314, 101-119, 2006. Glaessl B., Siepmann F., Tucker I., Siepmann J., Rades T. Characterization of quaternary polymethacrylate films containing tartaric acid, metoprolol free base or metoprolol tartrate. - Eur. J. Pharm. Biopharm., 73, 366-372, 2009.
Mathematical modeling of drug release from Eudragit RS-based delivery systems B. Glaessl, F. Siepmann, I. Tucker, T. Rades, J. Siepmann
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19. 20. 21. 22.
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J. DRUG DEL. SCI. TECH., 20 (2) 127-133 2010
Acknowledgements
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The authors are grateful for the support of this work by the Nord-Pasde-Calais Regional Council (Interdisciplinary Research Center on Drug Products, PRIM: “Pôle de recherche interdisciplinaire pour le médicament”).
Manuscript Received 27 July 2009, accepted for publication 21 December 2009.
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