Validation of a Mathematical Model for the Description of Hydrophilic

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Validation of a Mathematical Model for the Description of Hydrophilic and Hydrophobic Drug Delivery from Biodegradable Foams: Experimental and Comparison Using Indomethacin as Released Drug Leticia I. Cabezas, Ignacio Gracia, Antonio de Lucas, and Juan F. Rodríguez* Department of Chemical Engineering, Institute of Chemical and Environmental Technology, University of Castilla-La Mancha, Ciudad Real, 13071, Spain ABSTRACT: In drug delivery systems, mathematical modeling plays an important role in elucidating the release mechanisms, the potential applications of a determinate system matrix−drug, or the design of new delivery systems. In this work, we have modeled porous biodegradable foams based on polylactide (PLA) and poly(lactide-co-glycolide) (PLGA) impregnated with a hydrophobic drug (indomethacin) through a single-step process using supercritical CO2 as foaming agent. The modeling of indomethacin in vitro release was based on a previous model developed to describe accurately the process of release of a hydrophilic drug and consisting of three simpler and more comprehensible stages: external and internal mass transfer as well polymer degradation. It has been modified considering the low aqueous solubility of indomethacin and the variations in the mechanism produced, consequently improving its physical signification. Finally, the solubility of different drugs impregnated and their response in the release profiles were evaluated. nitis, or ankylosing spondylitis,19 but it is also a hydrophobic molecule with very low aqueous solubility.20 Consequently, there is much interest in being able to improve its solubility by increasing surface area of the drug within a polymeric matrix, since hydrophobic drugs have been found to be associated with problems of extremely slow release when encapsulated in dense microparticles or disks21 which results in an inefficient dose. Moreover, the delivery that takes place in dense particles, only due to bulk degradation of the polymer, is slower than in porous composites. Because of the advantages of controlled drug release, such as the providing of sustained concentrations of drug in blood, these kinds of systems have proliferated in their real application, which needs a previous theoretical study and prediction of their behavior. The first approximation of mathematical modeling was achieved by Peppas,22 whose well-known general equation (based on the semiempirical Korsmeyer23 model) distinguished between Fickian and non-Fickan models. This model has been widely applied, and it has provided the basis for many other mathematical models, nowadays based on the mechanism of delivery24 (dissolution, diffusion, osmotic, or ion exchange), separately or combined, or adapted especially to the type of polymer and drug impregnated (hydrophilic or hydrophobic). In a previous study,25 , we produced poly(D,L-lactide-coglycolide) (PLGA) and polylactide (PLA) foams impregnated with IDMC using supercritical fluid technology. The resulting probes reached drug loadings (DL) up to 15−20% (according to a commonly accepted value reported in literature26). These

1. INTRODUCTION Supercritical fluids technology (specifically supercritical CO2) results an interesting alternative to process polymeric materials, especially for foaming and impregnation, due to the lack of residual solvent in the products1−4 and its excellent nonsolvating porogenic character, plasticizing amorphous polymers (concretely polyesters1,5) and acting as a carrier for the drug into polymer matrix. The resulting foamed composites can be applied in tissue engineering as cellular scaffolds6,7 and, in the case of using certain degradable polymers for the solid matrix together with an active ingredient, as drug delivery systems.8−10 At this point, polymer foams that show an open cell structure play an important role in the tissue regeneration and controlled release processes because they allow a better exchange of mass transfer and the maximization of the cellular seeding and growth.11 Homo- and copolymers based on lactic and glycolic acid (or their corresponding cyclic dimers lactide and glycolide, respectively) are being widely used for these kinds of pharmaceutical applications12−14 because of their biodegradability and full biocompatibility with human organism. One point to take into account is the regulation of the degradation rate of the copolymer by varying the ratio of its comonomers.15,16 The drug release from PLGA and PLA foams is not only due to their degradation (although it is necessary to understand their degradation profile because this step contributes to the global delivery process), but the diffusion of the drug entrapped into the polymer matrix plays an important role depending on the extension of the experiments.17,18 Indomethacin (IDMC) is a nonsteroidal anti-inflammatory drug with a high relevance in the treatment of disorders like rheumatoid arthritis, osteoarthritis, pericarditis, bursitis, tendi© 2014 American Chemical Society

Received: Revised: Accepted: Published: 8866

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where wi and wd are initial foam weight and dried foam weight, respectively. The homogeneity of all the samples was previously demonstrated by measuring drug loading, weight, and pore size of all the spherical samples, obtaining analogous results for all of them 2.3. In Vitro Drug Release: Theoretical Mechanism. Several authors28−30 have described different approaches for the physical analysis of mechanism which follows the release of a drug from biodegradable substrates. Concretely, the model developed by Rothstein and co-workers31,32 shows a similar conceiving in its building. The most common pattern consists of the next three steps:18 (i) Step I: initial burst of drug into the liquid medium. Its magnitude depends on the solubility of drug in water, since the drug concentration together with its higher or lower hydrophilic character represents the driving force in the mass transfer process. Graphically, this zone of the curve can be suitably approximated to a straight line. At this early time no appreciable polymer weight loss is detected. (ii) Step II: The diffusion of the drug through the narrow or tortuous pores controls the mass transfer process. Graphically, changes in the slope of the curve are observed. (iii) Step III: The entrapped drug without mobility or enough time to be released during the previous steps is liberated when PBS penetrates into the polymer network and hydrolyzes the polymer into soluble oligomers and monomers. Drug is released progressively until complete polymer solubilization. This step is more or less important in the release process in function of its duration (reaching the maximum drug release in the case of total degradation of the polymeric carrier). In our case, the duration of the experiments was 24 h, insufficient time to achieve the complete degradation of PLGA or PLA. Figure 1 shows a typical drug delivery profile composed of these three steps. It is possible to appreciate the different shapes of the release curve depending on the character of drug: hydrophilic (Figure 1a) or hydrophobic (Figure 1b). 2.4. Mathematical Modeling. A mathematical model adapted to the low aqueous solubility of IDMC has been proposed to fit the experimental data assigning a full physical meaning according to the mechanisms previously described. To achieve this and taking into account the slow and sustained release during all the experiments, we have evaluated the feasibility of a mathematical model previously developed for a hydrophilic drug.18 We also have made some changes in it to accomplish its suitable application. The model comprises three different equations, one for each step of the physical mechanism. The application range of each one along an experiment is shown in Table 1 together with the concrete denomination of initial and final times (these values are an approximation taking into account the shapes of the different experimental release profiles and the final time of one stage concurs with the initial time of the next one). At any time we assumed that the drug is homogeneously distributed in the foam25 and therefore homogeneously released. The discontinuous character of this model is due to our purpose of maintaining the accurate mathematical description of the process, avoiding the mathematical model to evolve

impregnated porous foams can be implanted after surgical treatments or prosthesis fixing and release IDMC to reduce the subsequent inflammation even at the same time they help in the tissue reconstruction (depending on the treatment). In this work we have studied the in vitro release of IDMC impregnated into PLGA and PLA foams and the concrete objectives are the following: (i) to develop a mathematical model to describe the release profile of IDMC from biodegradable foams, including external and internal mass transfer and polymer degradation; (ii) to study the effect of the model parameters on the response curves; (iii) to analyze the experimental release profiles and their fit using the model; (iv) to compare the experimental profiles of hydrophilic and hydrophobic drugs in experimental profiles and their impact in the mathematical model; (v) to evaluate how the foams characteristics influence in the drug delivery process.

2. MATERIALS AND METHODS 2.1. Materials. Poly(D,L-lactide), PLA (Mn = 28 000 g/mol as polystyrene-equivalent molecular weight value measured using GPC), and poly(D,L-lactide-co-glycolide), PLGA, (74% D,L-lactide, 26% glycolide, Mn = 18 000 g/mol as polystyreneequivalent molecular weight value measured using GPC), were synthesized previously as described by Cabezas et al.27 using D,L-lactide (3,6-dimethyl-1,4-dioxane-2,5-dione; Purac Biochem bv, The Netherlands) and glycolide (1,4-dioxane-2,5-dione; Purac Biochem bv, The Netherlands) both with a purity higher than 99.5%. Indomethacin, IDMC (2-{1-[(4-chlorophenyl)carbonyl]-5-methoxy-2-methyl-1H-indol-3-yl}acetic acid) [CAS 53-86-1] (99.8% purity), was purchased from Fagron (Spain). The phosphate buffered saline (PBS) used as medium in release experiments was prepared using the following reagents: sodium chloride (NaCl), potassium chloride (KCl), disodium hydrogen phosphate (Na 2HPO 3), and monopotassium phosphate (KH2PO4) (99% purity all of them), which were purchased from Panreac (Spain). 2.2. Impregnation of IDMC, Polymer Foaming, and in Vitro Release Experiments. PLA and PLGA foams were synthesized and impregnated with IDMC using a single-step process and in supercritical medium. Equipment, experimental conditions, foam description, and properties are clearly explained in a previous work.25 For in vitro release experiments, IDMC-polymer foam samples of 10 mg, cut in a spherical shape and accurately weighed, were suspended in 80 mL of phosphate buffered saline (PBS, pH 7.4, 1 M) and placed in glass flasks stirred at 100 rpm placed in a shaking water bath at 37 °C. A metal mesh inside the flasks and immersed in the PBS provided perfect sink conditions in every case. A 10 mL sample of PBS was periodically removed, and the amount of IDMC was analyzed by UV spectrophotometry (Shimadzu UV-1603, Germany) at 320.2 nm. To keep a constant volume, 10 mL of fresh PBS was periodically added after each sampling until the end of the experiment (t = 24 h). All experiments were carried out in triplicate. Release profiles were built representing the cumulative release percentage of IDMC versus time. Mass loss was determined gravimetrically: dried foam weight initially and after in vitro degradation tests were measured. Mass loss (%) was calculated by following eq 1: mass loss (%) =

wi − wd × 100 wi

(1) 8867

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ln(1 − F ) = −kextt

(2)

where F is the fractional attainment of equilibrium (it corresponds to Mt/M∞, where Mt and M∞ denote the absolute cumulative amounts of drug released at any time t and at infinity, respectively) and kext is the external mass transfer coefficient. Experimentally, the linear tendency was observed in all experiments from the beginning (t0ext) until an experimental time (tfext) of approximately 1 h. Consequently, this first pattern of the release profile was modeled using this diffusion equation. 2.4.2. Step II. This step is controlled by the internal diffusion of IDMC impregnated into the most tortuous or narrow pores. This intraporous slow transport of the solute molecules through the pores can be described in a simple way by “Fick’s second law of diffusion”.34 Following the same assumptions, initial and boundary conditions as in the analysis of a hydrophilic drug,18 the total amount of diffusing substance entering or leaving the sphere is given28 by eq 3: Mt 6 =1− 2 M∞ π

Table 1. Specific Denominations of the Variable t (Initial and Final Time, Respectively) and Their Numerical Values for the Three Stages of the Model t0

tf

t0ext (0 h) t0int (1 h) t0deg (5 h)

tfext (1 h) tfint (5 h) tfdeg (∞ hours)

n=1

⎛ n 2π 2 ⎞ 1 exp⎜ − 2 Dt ⎟ 2 n ⎝ R0 ⎠

(3)

where R0 is the characteristic length of spherical foam radius (0.2 cm) and D represents the apparent diffusion coefficient considering the homogeneous particle (the existence of “micropores” would not affect the convenience of using this equation). 2.4.3. Step III. Once the immediate effects of external and internal mass transfer have taken place in the process of IDMC release, the process of separation of polymeric chains and their degradation play an important role in the liberation of the drug molecules that are located in a certain radial position inside the bead. Although it is known that in general terms, depending on the drug impregnated in the biodegradable device, the process of hydrolysis of the biopolymer can change, it is also known that in short-term experiments (less than 24 h) it will be very difficult to appreciate significant changes in the degradation profiles. Moreover, we must take into account that the majority of impregnated drugs are released by external or internal diffusion due to its hydrophilic character.35 In this step, the main difference with respect to a hydrophilic drug is the fact that the majority of drug has not been released yet. Consequently, at this point of the experiments the effect of polymer degradation must be combined together with the external diffusion of IDMC throughout the new channels created by the relaxation of polymer network and chains hydrolysis. In the case of hydrophilic drugs some release by conventional diffusion can be also taking place in this period, but we consider that it is negligible compared with that produced by the polymer degradation. An easy way to describe the bead degradation is to use the “shrinking core model” (SCM) described by Levenspiel36 and shown in eq 4. It assumes a first-order kinetics analogous to the pseudo-first-order kinetics of the degradation of PLA or PLGA:37,38

Figure 1. Typical in vitro cumulative release profile in PBS pH 7.4 from PLGA and PLA-based foams impregnated with (a) hydrophilic drug and (b) hydrophobic drug.

1st step 2nd step 3rd step

∞

∑

freely just for the best fitting. In that case, the slowest part of the release process (the degradation) would determine the fitting and only the parameter for that part will be accurate while the diffusional parameters would have little significance. Consequently, as the release process experimentally is not a process continuously controlled by the same effect, the model has to incorporate changes (discontinuities) in the phenomena description between the different experimental zones. The only one difference between continuous or discontinuous models in this case consists of the selection of preset duration of each step. This selection depends, of course, on the observation and can be related to the material properties like the type of polymer or the impregnated drug. 2.4.1. Step I. The initial very quick IDMC release can be physically assimilated as the direct dissolution of a particle of pure drug in water. This process is only controlled by the diffusion in the film, and an equation based on a “thin film diffusion model” (eq 2) may be applied33 to describe the rate of release in this part of the process:

⎛ M f ⎞1/3 kdegr ⎜ ⎟ =1− R0 ⎝ M0 ⎠

(4)

where M0 and Mf represent the mass (foam together with drug) at the beginning of the final part of the release curve (tfinf = t0deg = 5 h) and at the end of the experiment, respectively, R0 is the 8868

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Figure 2. Cumulative IDMC release profiles using PLGA foams synthesized in different experimental conditions (indicated in the figure). Symbols show the experimental data, and curves are the theoretical values. Dotted line represents the simplified model (only eq 4 for the step III), and solid line represents the corrected model (eqs 3 and 4 for step III).

initial radius of the spherical foam (0.2 cm), and kdegr is the pseudo-first-order kinetics constant of degradation for the PLGA or PLA foam. Comparing the experimental IDMC mass released to the liquid medium and the polymer weight loss to the DL of each foam (to quantify theoretically the drug discharged by degradation), there is not a good agreement, since experimental values were higher than the theoretical ones. For that reason, the experimental release profiles have been modeled using not only the simplification but the contribution of both effects: degradation and external diffusion. Taking into account all the previous information, the following global model parameters are identified: (i) External mass transfer coefficient (kext): step I.

(ii) Effective diffusion coefficient (DII and DIII): step II and step III in corrected model. (iii) Pseudo-first-order kinetics constant of polymer degradation (kdegr): step III. Equations 2 and 4 were solved by simple linearization, and eq 3 was solved using 50 terms of the summation (n) and minimizing the summation of the deviations in absolute value between theoretical and experimental values with MS Excel “solver” tool. The results of the model simulation using different values for each parameter are fully shown in a previous study.18 8869

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Figure 3. Cumulative IDMC release profiles using PLA foams synthesized in different experimental conditions (indicated in the figure). Symbols show the experimental data, and curves are the theoretical values. Dotted line represents the simplified model (only eq 4 for the step III), and solid line represents the corrected model (eqs 3 and 4 for step III).

3. RESULTS AND DISCUSSION Once verified that the theoretical curves followed the expected trend, the experimental curves were fitted using the simplified and the corrected model. The differences in the fitting of experimental data by both models were evaluated as well as the variation in these release profiles with respect to curves produced by hydrophilic drugs.18 Finally, the profile of drug release of each probe was analyzed in terms of the foams feature, treating to relate some aspects of kinetic behavior of the foams with their different synthesis conditions.25 3.1. Release of Hydrophobic IDMC versus Hydrophilic Profiles. Basically, the main differences consist of the magnitude of the initial burst, which is much larger for

hydrophilic drugs, since the release profile of hydrophobic drugs at early times is very slow because of their low aqueous solubility in water and the concentration gradient, driving force, will remain low. In general, the burst defines an approximate line with large slope in which the external mass transfer coefficient (kext) is the most characteristic parameter.18 The diffusivity within the polymer matrix is also affected by the drug chemical character,39 and consequently, hydrophilic profiles undergo a slope change after the burst in contrast to hydrophobic ones which maintain a sustained release in time. In both cases the effective diffusion coefficient (DII) is the parameter that describes this step. 8870

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Table 2. Summary of Characteristics of Foams and Their Resultant Model Parameters run Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure

polymer 2a 2b 2c 2d 2e 2f 3a 3b 3c 3d 3e 3f

PLGA PLGA PLGA PLGA PLGA PLGA PLA PLA PLA PLA PLA PLA

DL (%) 12.42 16.71 13.63 4.2 2.96 16.8 15.28 16.71 16.86 6.35 7.6 21.67

Dp (μm)a 146.43 ± 23 172.92 ± 30 221.76 ± 57 61.57 ± 7 79.88 ± 12 104.57 ± 16 241.85 ± 51 288.43 ± 54 408.99 ± 98 198.67 ± 27 210.35 ± 31 216.96 ± 36

kext (h−1) 0.0125 0.0405 0.0203 0.0071 0.0043 0.0711 0.0508 0.0406 0.0582 0.0190 0.0143 0.0769

DII (cm2/s)b 5.38 2.58 5.66 2.35 2.26 6.36 3.20 2.65 4.15 7.25 6.96 6.61

× × × × × × × × × × × ×

−10

10 10−9 10−10 10−10 10−10 10−9 10−9 10−9 10−9 10−10 10−10 10−9

DIII (cm2/s)c 4.01 1.91 6.08 2.11 1.69 2.31 1.60 1.35 1.42 4.79 2.86 3.28

× × × × × × × × × × × ×

10−10 10−9 10−10 10−10 10−10 10−9 10−9 10−9 10−9 10−10 10−10 10−9

kdegr (cm) 1.03 1.34 2.70 1.14 7.41 1.06 1.97 1.41 7.19 7.32 3.55 3.22

× × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−4 10−3 10−3 10−3 10−4 10−4 10−4 10−3

a

Mean pore size and standard deviation. bAverage value calculated using the obtained values from 1 to 5 h (step II). cAverage value calculated using the obtained values from 5 to 24 h (step III).

Table 3. Summary of Diffusion Effective Coefficients of Various Biodegradable Devices for Highly Hydrophobic Drug Release polymer

drug

type of device

D (cm2/s)

ref

PLGA PLA PLA PLGA block copolymer styrene−isoprene−styrene PLGA PLGA PLA PLA PLA poly(ε-caprolactone)

IDMC IDMC IDMC IDMC IDMC lidocaine lidocaine lidocaine lidocaine paclitaxel paclitaxel

porous matrix porous matrix dense nanoparticles dense nanoparticles PSA matrices dense microparticles films dense nanoparticles dense nanoparticles dense microparticles films

17.5 × 10−10 30.1 × 10−10 2.25 × 10−12 (1.98−2.35) × 10−12 3.5 × 10−10 (14−106) × 10−12 19 × 10−12 (1.35−7.15) × 10−16 (7.7−7.9) × 10−16 (1.04−2.78) × 10−11 1.04 × 10−11

this work this work 44 44 45 43 43 46 47 42 48

Drug remaining is released because of polymer degradation. Diffusion is still taking place at this point of the delivery process; however, its effect is noticeable only if low quantity of drug has been released until now. For that reason, hydrophilic profiles can be suitably described only taking into account polymer degradation, since the majority of drug has been released in the previous two steps and diffusion is negligible. However, hydrophobic drugs require the contribution of both effects (diffusion and degradation) to characterize correctly the end of their profiles. Consequently we can assume that drugs like IDMC show profiles more or less linear17 during the steps II and III and their contribution is larger than in hydrophilic profiles.18 3.2. Model Fitting. Experimental points and both model curves are shown in Figure 2 (PLGA foams) and Figure 3 (PLA foams). The foams showed a variety of pore sizes and DL as a consequence of their synthesis and impregnation conditions.25 However, these different specifications did not result in significant changes of the IDMC release profiles, since the hydrophobic character of the drug produced flat profiles very similar between them. The pattern of the curves corresponded in all the cases with the general description presented in Figure 1b. Regarding the value of the model parameters previously defined, they are summarized in Table 2 together with the foams description. A good agreement between the experimental data and the mathematical model was achieved in such conditions. In general it has been observed that the model produces a small underestimation of the two first experimental data (step

I) but only for those experiments whose initial burst was relatively high followed by a drastic change in the trend (see Figures 2b, 2f, 3a, 3b, 3c, and 3e). This small variation could be due to other molecular interactions besides the delivery device polymer−drug affinity for the solvent, which can reasonably hinder the release event.40 However, the fitting is acceptably good and this phenomenon is due to the theoretical basis commented in section 2.4.1: the low driving force (IDMC concentration gradient between liquid medium and device) decreases rapidly because of the low aqueous solubility of IDMC in water, with a value41 of 0.23 g/mL (25 °C) with the first discharges of drug until the negligible effect of this mechanism. That explains the shorter range of this step, only 1 h from the beginning of the experiment in contrast with the 2 h of this model applied to hydrophilic drugs.18 Regarding to the intermediate step, based on external diffusion, the results are in very good agreement with the experimental data. It is not surprising that models based on Fick’s second law are widely used in literature by many authors28,42,43 to confer theoretical character facing other empirical models (i.e., the Peppas equation) due to its high capacity to describe this kind of processes. Table 3 shows a comparison between the average value for the effective diffusion coefficient, DII, obtained in the present work for both PLGA and PLA and some values reported in the literature. As can be observed, the obtained values are of magnitude 10−9−10−10 cm2/s and their orders of magnitude are in correspondence with other values of IDMC described in literature.44,45 Table 3 also summarizes D values corresponding to other hydrophobic drugs like lidocaine43,46,47 and paclitax8871

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el42,48 whose orders of magnitude are homogeneous for each substance but not between different drugs. It evident that the chemical nature of a low soluble drug, and consequently its grade of hydrophobicity, is determinant in the process of external diffusion over the geometry or the composition of the biodegradable device. By use of hydrophilic drugs, these aspects are less relevant than the morphology (porosity or particle diameter) of the device, since it can modify the value of D up to 5 orders of magnitude.18 Finally, the last part of the curves describes the delivery of the nonreleased drug, entrapped in the polymer matrix, because of the polymer degradation which allows the direct contact of the molecules of IDMC with the aqueous media. In consequence, diffusion is supposed to be as important as degradation in this part of the process.48 This is evident in Figure 2 and Figure 3 which show that the corrected model (cooperative effect of these both mechanisms) fitted much better the experimental data with respect to simplified model (only degradation mechanism) in any case. 3.3. Influence of Foam Characteristics in the Release Profiles. It is well-known that there are some aspects of the porous devices that affect the drug release: (i) DL: Generally the devices with higher value of DL show larger burst in their release profile.37,49 This is also applicable for hydrophobic drugs.41 (ii) Density (size and distribution of the pores): It determines the ratio between surface area and volume.49,50 (iii) Composition of the polymer foam: It is decisive in the rate of degradation of the polymer matrix, since in the case of the copolymer PLGA, it is possible to regulate its capacity of degradation just by varying the ratio lactide/ glycolide.15,16 Higher ratios of glycolide increase the hydrophilicity of the polymer that improves the penetration of water molecules between the polymer chains. However, because of the hydrophobicity of the IDMC which affects the entire delivery process,41 these effects are less clear than in the case of hydrophilic drugs.18 Even so, we can distinguish specially the effect of DL in the magnitude of the burst. Figures 2b, 2f, 3a, 3b, 3c, and 3f (corresponding to percentage DL values of 16.71, 16.8, 15.28, 16.71, 16.86, and 21.67, respectively, and according to Table 2) showed the higher values of kext. The effect of the polymer composition on the shape of the curve is not clearly appreciable in Figure 2 and Figure 3 because the experimental profile for step III is a consequence of a sum of effects, the known diffusion and degradation. This fact masks the influence of glycolide on the degradation process and its subsequent role in the shape of the curve. Nevertheless PLGA foams had slightly higher values of kdegr than in PLA foams, although in certain experiments the values are quite similar (see Table 2). What is clear is that the obtained kdegr values are in any case lower than those using hydrophilic drugs even using the same impregnation conditions and varying only the drug.4,18,25 Regarding the effect of porosity, it is necessary to make a more rigorous study in order to establish a clear tendency.

and adapted. Also, the differences observed in the delivery profile between hydrophilic and hydrophobic drugs have been discussed. The influence of the foam characteristics (DL, pore size, and polymer composition) affecting the response of the system has been analyzed. Typical model parameters (kext, DII, DIII, and kdegr) have been obtained using a theoretical model made up of three different equations describing the main mechanisms of drug release in each part. Concretely, the value of diffusion coefficient (DII) resulted in the same order of magnitude of other porous PLGA/PLA devices impregnated with IDMC and previously reported in literature and was lower than the resultant of an analogous process using a hydrophilic drug. In the last step of the process it was necessary to include an additional diffusional contribution to the term of polymer degradation with respect to the starting model in order to improve the fitting and the physical signification of the model. This three-step mathematical model, divided by simple mechanisms, is useful to describe a complex process such as the release of a hydrophobic drug from biodegradable polymeric foams used as drug carriers. In spite of its simplicity, it achieved a good agreement with experimental data.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +34 926295300, extension 6345. Fax: +34 926295256. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from JCCM Project PCI08-0122 is gratefully acknowledged.

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REFERENCES

(1) Reverchon, E.; Cardea, S. Production of controlled polymeric foams by supercritical CO2. J. Supercrit. Fluids 2007, 40, 144. (2) Duarte, A. R. C.; Mano, J. F.; Reis, R. L. Supercritical fluids in biomedical and tissue engineering applications: a review. Int. Mater. Rev. 2009, 54, 214. (3) Temtem, M.; Casimiro, T.; Mano, J. F.; Aguiar-Ricardo, A. Preparation of membranes with polysulfone/polycaprolactone blends using a high pressure cell specially designed for a CO2-assisted phase inversion. J. Supercrit. Fluids 2008, 43, 542. (4) Cabezas, L. I.; Gracia, I.; García, M. T.; de Lucas, A.; Rodríguez, J. F. Production of biodegradable scaffolds impregnated with 5fluorouracil in supercritical CO2. J. Supercrit. Fluids 2013, 80, 1. (5) Howdle, S. M.; Watson, M. S.; Whitaker, M.; JVladimir, K. P.; Davies, M. C.; Mandel, F. S.; Wang, J. D.; Shakesheff, K. M. Supercritical fluid mixing: preparation of thermally sensitive polymer composites containing bioactive materials. Chem. Commun. 2001, 1, 109. (6) Tayton, E.; Purcell, M.; Aarvold, A.; Smith, J. O.; Briscoe, A.; Kanczler, J. M.; Shakesheff, K. M.; Howdle, S. M.; Dunlop, D. G.; Oreffo, R. O. C. A comparison of polymer and polymer-hydroxyapatite composite tissue engineered scaffolds for use in bone regeneration. An in vitro and in vivo study. J. Biomed. Mater. Res., Part A 2013, DOI: 10.1002/jbm.a.34926. (7) Karimi, M.; Heuchel, M.; Weigel, T.; Schossig, M.; Hofmann, D.; Lendlein, A. Formation and size distribution of pore in poly(εcaprolactone) foams prepared by pressure quenching using supercritical CO2. J. Supercrit. Fluids 2012, 61, 175. (8) Duarte, A. R. C.; Mano, J. F.; Reis, R. L. Preparation of chitosan scaffolds loaded with dexamethasone for tissue engineering

4. CONCLUSION In order to describe the mechanism of release of a hydrophobic drug (IDMC) from PLGA and PLA foams for in vitro systems, a mathematical model previously developed has been evaluated 8872

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applications using supercritical fluid technology. Eur. Polym. J. 2009, 45, 141. (9) Porta, G. D.; Campardelli, R.; Falco, N.; Reverchon, E. PLGA microdevices for retinoids sustained release produced by supercritical emulsion extraction: Continuous versus batch operation layouts. J. Pharm. Sci. 2011, 100, 4357. (10) Yoganathan, R.; Mammucari, R.; Foster, N. R. Impregnation of ibuprofen into polycaprolactone using supercritical carbon dioxide. J. Phys.: Conf. Ser. 2010, 215, 1. (11) Ishaug, S. L.; Crane, G. M.; Miller, M. J.; Yasko, A. W.; Yaszemski, M. J.; Mikos, A. G. Bone formation by three-dimensional stromal osteoblast culture in biodegradable polymer scaffolds. J. Biomed. Mater. Res. 1997, 36, 17. (12) Singh, L.; Kumar, V.; Ratner, B. D. Generation of porous microcellular 85/15 poly(D,L-lactide-co-glycolide) foams for biomedical applications. Biomaterials 2004, 25, 2611. (13) Anderson, J. M.; Shive, M. S. Biodegradation and biocompatibility of PLA and PLGA microspheres. Adv. Drug Delivery Rev. 2012, 64, 72. (14) Ignatius, A. A.; Claes, L. E. In vitro biocompatibility of bioresorbable polymers: poly(L,DL-lactide) and poly(L-lactide-coglycolide). Biomaterials 1996, 17, 831. (15) Miller, R. A.; Brady, J. M.; Cutright, D. E. Degradations rates of oral resorbable implants (polylactates and polyglycolates): rate modification with changes in PLA/PGA copolymer ratios. J. Biomed. Mater. Res., Part A 1977, 11, 711. (16) Nakamura, T.; Hitomi, S.; Watanabe, S.; Shimizu, Y.; Jamshidi, K.; Hyon, S. H.; Ikada, Y. Bioabsorption of polylactides with different molecular properties. J. Biomed. Mater. Res., Part A 1989, 23, 1115. (17) Lee, L. Y.; Ranganath, S. H.; Fu, Y.; Zheng, J. L.; Lee, H. S.; Wang, C.-H.; Smith, K. A. Paclitaxel release from micro-porous PLGA disks. Chem. Eng. Sci. 2009, 64, 4341. (18) Cabezas, L. I.; Gracia, I.; de Lucas, A.; Rodríguez, J. F. Novel model for the description of the controlled release of 5-fluorouracil from PLGA and PLA foamed scaffolds impregnated in supercritical CO2. Ind. Eng. Chem. Res. 2014, DOI: 10.1021/ie404028t. (19) Rusu, D.; Cimpoiu, C.; Hodisan, T. The control over the new obtaining procedeum of indomethacin. J. Pharm. Biomed. Anal. 1998, 17, 409. (20) Longhemard, P.; Bilou, M. J.; Guyot-Hermann, A. M.; Guyot, J. C. Ground and native crystals: comparison of compression capacity and dissolution rate. Int. J. Pharm. 1998, 170, 51. (21) Wang, J.; Ng, C. W.; Win, K. Y.; Shoemakers, P.; Lee, T. K.; Feng, S. S.; Wang, C. H. Release of paclitaxel from polylactide-coglycolide (PLGA) microparticles and discs under irradiation. J. Microencapsulation 2003, 20, 317. (22) Peppas, N. A. Analysis of Fickian and non-Fickian drug release from polymers. Pharm. Acta Helv. 1985, 60, 110. (23) Korsmeyer, R. W.; Gurny, R.; Doelker, E. M.; Buri, P.; Peppas, N. A. Mechanism of solute release from porous hydrophilic polymers. Int. J. Pharm. 1983, 15, 25. (24) Wen, H., Park, K., Eds. Oral Controlled Release Formulation Design and Drug Delivery: Theory to Practice; Wiley: Hoboken, NJ, 2010. (25) Cabezas, L. I.; Fernández, V.; Mazarro, R.; Gracia, I.; de Lucas, A.; Rodríguez, J. F. Production of biodegradable porous scaffolds impregnated with indomethacin in supercritical CO2. J. Supercrit. Fluids 2012, 63, 155. (26) Kang, Y.; Wu, J.; Yin, G.; Huang, Z.; Yao, Y.; Liao, X.; Chen, A.; Pu, X.; Liao, L. Preparation, characterization and in vitro cytotoxicity of indomethacin-loaded PLLA/PLGA microparticles using supercritical CO2 technique. Eur. J. Pharm. Biopharm. 2008, 70, 85. (27) Cabezas, L. I.; Mazarro, R.; Gracia, I.; de Lucas, A.; Rodríguez, J. F. Optimizing the bulk copolymerization of D,L-lactide and glycolide by response surface methodology. eXPRESS Polym. Lett. 2013, 7, 886. (28) Siepmann, J.; Faisant, N.; Benoit, J.-P. A new mathematical model quantifying drug release from bioerodible microparticles using Monte Carlo simulations. Pharm. Res. 2002, 19, 1885.

(29) Ramchandani, M.; Robinson, D. In vitro and in vivo release of ciprofloxacin from PLGA 50:50 implants. J. Controlled Release 1998, 54, 167. (30) Amann, L. C.; Gandal, M. J.; Lin, R.; Liang, Y.; Siegel, S. J. In vitro−in vivo correlations of scalable PLGA-risperidone implants for the treatment of schizophrenia. Pharm. Res. 2010, 27, 1730. (31) Rothstein, S. N.; Federspiel, W. J.; Little, S. R. A simple model framework for the prediction of controlled release from bulk eroding polymer matrices. J. Mater. Chem. 2008, 18, 1873. (32) Rothstein, S. N.; Federspiel, W. J.; Little, S. R. A unified mathematical model for the prediction of controlled release from surface and bulk eroding polymer matrices. Biomaterials 2009, 30, 1657. (33) Boyd, G. E.; Adamson, A. M.; Myers, L. S. The exchange adsorption of ions from aqueous solutions by organic zeolites. II: Kinetics. J. Am. Chem. Soc. 1947, 69, 2836. (34) Crank, J. The Mathematics of Diffusion; Clarendon Press: Oxford, U.K., 1956. (35) Siegel, S. J.; Kahn, J. B.; Metzger, K.; Winey, K. I.; Werner, K.; Dan, N. Effect of drug type on the degradation rate of PLGA matrices. Eur. J. Pharm. Biopharm. 2006, 64, 287−293. (36) Levenspiel, O. The Chemical Reactor Omnibook; Reverté: Barcelona, Spain, 2002. (37) Lee, J. S.; Chae, G. S.; Kim, M. S.; Cho, S. H.; Lee, H. B.; Khang, G. Degradation behaviour in vitro for poly(D,L-lactide-co-glycolide) as drug carrier. Bio-Med. Mater. Eng. 2004, 14, 185. (38) Wu, X. S.; Wang, N. Synthesis, characterization, biodegradation, and drug delivery application of biodegradable lactic/glycolic acid polymers. Part II: Biodegradation. J. Biomater. Sci., Polym. Ed. 2001, 12, 21. (39) Arifin, D. Y.; Lee, L. Y.; Wang, C.-H. Mathematical modeling and simulation of drug release from microspheres: Implications to drug delivery systems. Adv. Drug Delivery Rev. 2006, 58, 1274. (40) Kasimova, A. O.; Pavan, G. M.; Danani, A.; Mondon, K.; Cristiani, A.; Scapozza, L.; Gurny, R.; Möller, M. Validation of a novel molecular dynamics simulation approach for lipophilic drug incorporation into polymer micelles. J. Phys. Chem. B 2012, 116, 4338. (41) Kiortsis, S.; Kachrimanis, K.; Broussali, Th.; Malamataris, S. Drug release from tableted wet granulations comprising cellulosic (HPMC o HPC) and hydrophobic component. Eur. J. Pharm. Biopharm. 2005, 59, 73. (42) Liggins, R. T.; Burt, H. M. Paclitaxel loaded poly(L-lactic acid) microspheres: properties of microspheres made with low molecular weight polymers. Int. J. Pharm. 2001, 222, 19. (43) Klose, D.; Siepmann, F.; Elkharraz, K.; Siepmann, J. PLGAbased drug delivery systems: importance of the type of drug and device geometry. Int. J. Pharm. 2008, 354, 95. (44) Liu, H.; Finn, N.; Yates, M. Z. Encapsulation and sustained release of a model drug, indomethacin, using CO2-based microencapsulation. Langmuir 2005, 21, 379. (45) Hayashi, T.; Yamazaki, T.; Yamaguchi, Y.; Yamaguchi, Y.; Sugibayashi, K.; Morimoto, Y. Release kinetics of indomethacin from pressure sensitive adhesive matrices. J. Controlled Release 1997, 43, 213. (46) Polakovic, M.; Görner, T.; Gref, R.; Dellacherie, E. Lidocaine loaded biodegradable nanospheres II: Modelling of drug release. J. Controlled Release 1999, 60, 169. (47) Rouzes, C.; Leonard, M.; Durand, A.; Dellacherie, E. Influence of polymeric surfactants on the properties of drug-loaded PLA nanospheres. Colloids Surf., B 2003, 32, 125. (48) Lao, L. L.; Venkatraman, S. S.; Peppas, N. A. Modeling of drug release from biodegradable polymer blends. Eur. J. Pharm. Biopharm. 2008, 70, 796. (49) Makadia, H. K.; Siegel, S. J. Poly lactic-co-glycolic acid (PLGA) as biodegradable controlled drug delivery carrier. Polymers 2011, 3, 1377. (50) Braunecker, J.; Baba, M.; Milroy, G. E.; Cameron, R. E. The effects of molecular weight and porosity on the degradation and drug release form polyglycolide. Int. J. Pharm. 2004, 282, 19. 8873

dx.doi.org/10.1021/ie500760m | Ind. Eng. Chem. Res. 2014, 53, 8866−8873