Novel Model for the Description of the Controlled Release of 5

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Novel Model for the Description of the Controlled Release of 5‑Fluorouracil from PLGA and PLA Foamed Scaffolds Impregnated in Supercritical CO2 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: Porous biodegradable polymeric foams loaded with drugs have potential applications in tissue engineering and sustained delivery systems. A single-step process using supercritical CO2 as a foaming and carrier agent was used for the impregnation of 5-fluorouracil in polylactide and poly(lactide-co-glycolide) probes. The release of 5-fluorouracil from the probes for 24 h at 37 °C and pH 7.4 was followed by measurement of the amount of drug released to the media and a change of the probe’s weight. In order to gain further insight into the drug-release mechanisms, a mathematical model (not previously described in the literature) is proposed to quantitatively describe the process of drug release. Our model considers that the release process goes through three different steps controlled first by external diffusion, second by internal mass transfer, and third by polymer degradation. The theoretical curves agreed fairly well with the experimental drug-release profiles.

1. INTRODUCTION Biodegradable aliphatic polyesters derived from lactic and glycolic acids (homopolymers and copolymers) are widely used in medical and pharmaceutical applications.1−3 These polymers, poly(D,L-lactide) (PLA) and poly(D,L-lactide-co-glycolide) (PLGA), respectively, are employed because of their biodegradation into lactic and glycolic acid, relatively harmless to the growing cells and which are removed from the body by normal metabolic pathways,4,5 and their use in other in vivo applications, such as resorbable sutures, has been approved by the Food and Drug Administration.6 Porous scaffolds with an open-pore structure are also desirable in many tissue engineering applications in order to maximize cell seeding, attachment, growth, extracellular matrix production, vascularization, and tissue growth.7 Concretely, porous PLGA foams have been used for the regeneration of various tissues and organs including bone7,8 and liver.9 These foams are susceptible to loading with small molecules, making them suitable for many therapeutic applications.10,11 Supercritical CO2 is an interesting way to produce impregnated polyester foams in a one-step process because of its porogenic character, with the advantage of a lack of residual solvent in the products.12,13 Because polymer scaffolds degrade, no synthetic polymer remains in the final engineered tissue. The degradation rate of the scaffold should either be similar to or slower than the rate of tissue formation. As a consequence, for these kinds of applications (tissue regeneration and drug release), it is important to understand the degradation profile of a given polymer scaffold. PLA and PLGA have been known to degrade by simple hydrolysis of the ester bonds, and the kinetics of this process is affected by the polymer composition, molecular weight, environmental conditions, drug loading (DL), or pore size.14−18 However, most of the studies in the literature were performed utilizing nonporous PLGA samples and, subse© XXXX American Chemical Society

quently, the degradation of highly porous PLA and PLGA foams is an interesting source of study. However, in vitro drug release from a polymer foam is not only caused by degradation of the polymer because the early time points of the release profile are due to diffusion of the charged drug from the polymer matrix into the release medium, and depending on the duration of the experiment, it could suppose the majority of the contribution.14,19 In view of the foregoing details, the main objectives of this work are as follows: (i) to develop a mathematical model in order to describe the release profile of a model anticancer drug, 5-fluorouracil (5-Fu), previously impregnated into different polymer foams (process influenced by foam characteristics such as the DL, pore size, or polymer composition) [the model includes the specific solubility of 5-Fu in the external aqueous medium, external and internal mass transfer, and polymer degradation] and (ii) to analyze the effect of the model parameters on the response curves.

2. MATERIALS AND METHODS 2.1. Materials. Poly(D,L-lactide) [PLA; Mn = 28000 g/mol as a polystyrene-equivalent molecular weight value measured using gel permeation chromatography (GPC)] and poly(D,Llactide-co-glycolide) [PLGA; 74% D,L-lactide/26% glycolide, Mn = 18000 g/mol as a polystyrene-equivalent molecular weight value measured using GPC] were synthesized previously as described by Mazarro et al.20 using D,L-lactide (3,6-dimethyl1,4-dioxane-2,5-dione; Purac Biochem BV, Gorinchem, The Netherlands) and glycolide (1,4-dioxane-2,5-dione; Purac Special Issue: Alirio Rodrigues Festschrift Received: November 28, 2013 Revised: January 31, 2014 Accepted: January 31, 2014

A

dx.doi.org/10.1021/ie404028t | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

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Biochem BV, Gorinchem, The Netherlands) both with a purity higher than 99.5%. 5-Fluorouracil [5-Fu; 5-fluoro-2,4(1H,3H)pyrimidinedione, CAS [51-21-8], 99.9% purity] was purchased from Fagron (Spain). The phosphate-buffered saline (PBS) used in release experiments was prepared using the following reagents: sodium chloride (NaCl), potassium chloride (KCl), disodium hydrogen phosphate (Na2HPO3), and monopotassium phosphate (KH2PO4) (99% purity for all of them), which were purchased from Panreac (Spain). 2.2. Impregnation of 5-Fu, Polymer Foaming, and in Vitro Release Experiments. PLA and PLGA foams were synthesized and impregnated with 5-Fu using supercritical fluids technology. Although the experimental setup, process conditions, and foam characteristics were widely explained in a previous work,13 we can remark that foams were produced using the “pressure quench” methodology in a high-pressure atmosphere of CO2 using a stainless steel cylinder of 300 mL equipped with a magnetic stirrer and an electric heating coat. Polymer and drug (0.4 and 0.1 g, respectively) were placed in the vessel before the pressurization step and foaming and impregnation process (carried out for 60 min at 180 bar and 40 °C). Finally, the experimental setup was depressurized, and the impregnated porous devices (with an approximately average diameter of 20 mm and a height of 10 mm) were collected. 5Fu was impregnated molecularly into the polymeric chains. Regarding in vitro release experiments, an approximately 10 mg sample of 5-Fu polymer foam, cut into a spherical shape and accurately weighed, was suspended in 80 mL of PBS (pH 7.4, 1 M), placed in the middle of a 100 mL flask, stirred at 100 rpm, and incubated in a shaking water bath at 37 °C. The homogeneity of all samples was previously checked by measuring the DL, weight, and pore size and obtaining analogous results for all of them. A 10 mL solution was periodically removed, and the amount of 5-Fu was analyzed by UV spectrophotometry (Shimadzu UV-1603, Germany) at 266.5 nm. In order to maintain the original PBS volume and pH value, 10 mL of fresh PBS was periodically added until the end of the experiment (t = 24 h). Release profiles were calculated in terms of the cumulative release percentage of 5-Fu with the incubation time. Each experiment was carried out in triplicate. Mass loss was determined gravimetrically: the individual foam weight initially and the dried foam weight after in vitro degradation were measured. Mass loss (%) was calculated using eq 1 w − wd mass loss (%) = i × 100 wi (1)

Figure 1. In vitro cumulative release profile of 5-Fu from PLGA- and PLA-based foams in PBS at pH 7.4. Relationship between the curve and three-stage release process.

(ii) Once the most-accessible drug has been released, diffusion of the drug from the bead matrix through the polymer chain network controls the mass-transfer process. Graphically, a drastic change in the shape of the release profile is observed. (iii) Finally, the drug that has been entrapped in the polymer network without mobility or enough time to be released can be liberated when water hydrolyzes the polymer into soluble oligomeric and monomeric products. The drug is released progressively because of polymer degradation until complete polymer solubilization. This part of the release experiments is more or less important in the function of their duration (reaching maximum drug release in the case of total degradation of the polymeric carrier). In our case, the experimental duration was 24 h, insufficient time to achieve complete dissolution of PLGA or PLA. For this reason, the percentage of drug released through this process represents only around 15% of the total amount of drug released to the medium. Figure 2 shows a diagram in which these three different steps in the release process from impregnated foams is represented schematically. 2.4. Mathematical Modeling. A mathematical model adapted to each of these three patterns has been developed to fit the experimental data, achieving full physical significance according to the release mechanisms previously described. This mathematical model is composed of widely used physical laws, but it has still not been previously described in the literature entirely from this particular point of view. In order to facilitate an understanding of the successive equations applied in the model and how they run along the different stages of the process, the specific denominations of the time variable are presented in Table 1. Also, the different initial and final values for each stage are summed up. These values are a quite realistic approximation, taking into account the shapes of the different experimental release profiles, and the final moment of each stage is considered to be the initial instant of the next one. 2.4.1. Release of the Most Accessible Drug. As has been explained in the hypothesis on which the physical model proposed is supported, an initial very quick release of the most accessible drug occurs. With this in mind, these first moments of the release can be physically viewed as the direct dissolution of a bead of pure drug in water, and this process will only be

where wi and wd are the initial and dried foam weights, respectively. 2.3. In Vitro Drug-Release Kinetics: Theoretical Mechanism. Several authors21−23 have described different approaches for the physical treatment of the controlled release of drug from biocompatible substrates. They follow the next pattern (Figure 1): (i) There is an initial burst of drug release in which the most accessible drug (impregnated on the surface or in larger pores), in direct contact with the medium, is released as a function of the solubility of the drug in water. Consequently, the gradient in the drug concentration represents the driving force in the mass-transfer process in which the external mass-transfer coefficient (kext) is the most characteristic parameter. Also, no appreciable weight loss and no soluble monomer product are formed at this early time. B



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Figure 2. Scheme of the process of drug release and its three different steps from a porous biodegradable polymeric carrier.

chosen model equation was given by Crank25 and solved considering the following initial and boundary conditions based on the experimental results and setup used for the experiments): int (i) At t = text f = t0 , the remaining drug is homogeneously distributed throughout the spherical foams.13 (ii) The initial drug concentration is below the solubility of the drug (which is also known as molecular dispersion or monolithic solution). In the literature,26 it was found that the 5Fu solubility in PBS is 20 g/L at 37 °C, so the driving force is very high at any time during the entire experiment and the approximation of “infinite dilution” will be accepted (perfect sink conditions are provided throughout the experiment). (iii) The rate at which the drug leaves the device is always equal to the rate at which the drug is brought to the surface by internal diffusion (no drug accumulation at the surface). Taking into account all of this, the total amount of diffusing substance entering or leaving the sphere is given25 by eq 3:

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

t0

tf

first second third

text 0 (0 h) tint 0 (2 h) tdeg 0 (5 h)

text f (0−2 h) tint f (2−5 h) tdeg (5−∞ h) f

controlled by the concentration gradient, and the equation based on a “thin film diffusion model” (eq 2) may be applied24 to describe the rate of release in this part of the process because it only takes into account the drug mass: 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. A linear plot of −ln(1 − F) versus t, whereby F has zero intercepts, would suggest that the kinetics of the adsorption process is controlled by diffusion through the liquid film surrounding the drug. Experimentally, the linear tendency was observed in all experiments until an experimental time of approximately 2 h. Consequently, this first pattern of the release profile was modeling using this diffusion equation. 2.4.2. Release of the Most Inaccessible Drug. Once the most accessible drug is released, a second step of the process controlled by the internal diffusion of the drug impregnated into the polymer network takes control of the release process. This slow transport of the solute molecules through the polymer network corresponds to the second zone of the curves. In the simplest version, this intraporous diffusion is well described by “Fick’s second law of diffusion”.25 As stated before, 5-Fu-impregnated probes can be considered for a practical approximation spherical in shape, and so the mathematical analysis has been based on this geometry. The

Mt 6 =1− 2 M∞ π

∞

∑ n=1

⎛ n 2π 2 ⎞ 1 ⎜ exp − 2 Dt ⎟ n2 ⎝ R0 ⎠

(3)

where R0 is the characteristic length of the spherical foam radius (0.2 cm) and D represents the apparent diffusion coefficient considering a homogeneous particle (the existence of “micropores” would not affect the convenience of using this equation). It was checked that an increase in the stirring rate of the experimental systems did not produce a significant variation of the rate of drug release. So, the stirring rate employed is high enough to consider that the mass-transfer rate is not appreciably affected by diffusion in the film. 2.4.3. Degradation of the Foam Substrate and Release of the Remaining Drug. Once the greater part of the drug is liberated, it seems that the release of the remaining drug is directly associated with degradation of the polymer substrate. The progressive degradation of the foam produces direct liberation of the drug molecules that are located at this radial position of the bead. A drug molecule can be at a certain radial position because it has moved from the inside by diffusion or C



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directly because it could not move previously because it was entangled by the polymer chains. So, the physical picture of this part is that the mass of drug discharged in this final part of the experiments is entirely related to polymer degradation; that is, because we consider that the drug is homogeneously distributed in the polymer probe, the release of the drug is directly and proportionally related with polymer degradation. Of course, some release by conventional diffusion can also be taking place in this period, but we consider that to be negligible compared to that produced by polymer degradation. This period is considered to go from tdeg 0 = 5 h approximately up to the end. Consequently, when the mass loss of each probe is quantified and their individual DLs are known, it is possible to determine the theoretical drug released to the medium and compare it to the experimental results. For this purpose, we keep assuming that the drug is homogeneously distributed in the foam and therefore homogeneously released together with the polymer dissolved. An easy way to describe this situation is to use the “shrinking core model” (SCM),27 shown in eq 4, because it assumes a first-order kinetics analogous to the pseudo-first-order kinetics of the degradation of PLA or PLGA:16,17,28,29 ⎛ M f ⎞1/3 kdegr ⎜ ⎟ =1− R0 ⎝ M0 ⎠

Figure 3. Theoretical cumulative release profiles calculated from the thin film diffusion model (eq 2). Influence of the external masstransfer coefficient, kext.

(4)

where M0 and Mf represent the mass (foam together with drug) deg at the beginning of the final part of the release curve (tinf f = t0 = 5 h) and at the end of the experiment, respectively, R0 is the initial radius of the spherical foam (0.2 cm), and kdegr is the pseudo-first-order kinetic constant of degradation for the PLGA or PLA foam. It is possible to estimate Mf at the end of the experiment in two different ways that agreed fairly well, with each one corresponding to both sides of the mass balance (eq 5): M f = M i − M1drug − M 2drug − M3drug − M3polymer

Figure 4. Theoretical cumulative release profiles calculated from Fick’s second law of diffusion integrated considering spherical geometry (eq 3). Influence of the apparent diffusion coefficient, D (kext = 0.3 h−1 for t = 0 − 2 h; R0 = 0.2 cm; n = 6).

(5)

where Mf is previously defined and measured by direct weighting, Mi is the known mass of the sample at the beginning of the experiment (approximately 10 mg) in which the percentage of polymer and drug is known through the value drug drug of DL, Mdrug are the mass of drug released 1 , M2 , and M3 during the first, second, and third steps of the process and is the mass of measured by UV spectrophotometry, and Mpolymer 3 polymer degraded during the last stage of the experiment. In addition, this mass balance satisfied M0 = Mi − Mdrug − Mdrug 1 2 . Taking into account all the previous information, global model parameters are as follows: (i) Zone I: external mass-transfer coefficient (kext). (ii) Zone II: effective diffusion coefficient (D). (iii) Zone III: pseudo-first-order kinetic constant of polymer degradation (kdegr). The model equations consisting of eqs 2 and 4 were solved by simple linearization, and eq 3 was solved using six terms of the summation (n) and minimizing the summation of the deviations in absolute value between the theoretical and experimental values with the MS Excel “solver” tool.30

Figure 5. Theoretical cumulative release profiles calculated from the SCM (eq 4). Influence of the pseudo-first-order kinetic constant of degradation, kdegr (kext = 0.3 h−1 for t = 0−2 h; D = 3 × 10−7 cm2/s for t = 2−5 h; R0 = 0.2 cm).

3. RESULTS AND DISCUSSION Once the model was developed, the coherence of the results obtained only over a theoretical basis was checked using standard values to verify whether the theoretical curves obtained follow the same trend as the experimental ones.

Once the previous issue was confirmed, the experimental curves were fitted using the proposed model. Finally, the profile of drug release of each probe was analyzed in terms of the foam feature, treating to relate the different kinetic behaviors of each material with its different synthesis conditions.13 D



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Figure 6. Cumulative 5-Fu 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 calculated using eqs 2−4 for zones I−III, respectively (marked in the figure).

3.1. Simulation Results. Prior to analysis of the goodnessof-fit of our model, we ran it using different values for its parameters, not to show their well-known evolution over the fractional attainment of equilibrium but to join the specific shape of the resultant curves with the concrete values taken by these parameters in order to facilitate subsequent analysis of the experimental profiles. Thus, theoretical cumulative release profiles are shown in Figures 3−5, which correspond with the concrete analysis of zones I−III, respectively. Chosen values of kext and D of 0.3 h−1 and 3 × 10−7 cm2/s, respectively (necessary for construction of the latter parts of the curve), respond to a simple criterion of fixing the average values to properly describing all of the experimental profiles. As expected, for the higher kext value, the burst is more pronounced, which means that the drug is initially more rapidly

released (Figure 3); the higher the D value is, the more noticeable the curvature results in zone II (Figure 4), and if kdegr has high values, proportionally the drug release would also be high (Figure 5). 3.2. Model Fitting. Once the coherence of the results of the mathematical model had been confirmed and it was demonstrated that the physical mechanisms that lead to the process can be described properly, the experimental 5-Fu cumulative release profiles obtained in the in vitro study were fitted with the model. The experimental points and model curves are shown in Figures 6 (from 5-Fu impregnated in PLGA foams) and 7 (PLA foams). The biodegradable probes used were based on PLGA or PLA, and they showed a variety of pore sizes and DLs as a consequence of their synthesis and impregnation conditions.13 These different specifications resulted in the release of 5-Fu profiles with some small changes E



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Figure 7. Cumulative 5-Fu 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 calculated using eqs 2−4 for zones I−III, respectively (marked in the figure).

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

6a 6b 6c 6d 6e 6f 7a 7b 7c 7d 7e 7f

polymer

DL (%)

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

8.31 13.19 14.98 5.52 6.62 16.88 5.38 13.74 14.59 9.76 13.86 15.30

Dp (μm)a 117.23 182.04 341.98 58.35 80.36 101.96 237.41 355.68 363.35 101.08 144.20 202.58

± ± ± ± ± ± ± ± ± ± ± ±

20 31 87 6 13 15 49 84 89 17 21 34

kext (h−1) 0.264 0.3896 0.3192 0.3783 0.4535 0.304 0.244 0.4348 0.5594 0.5528 0.342 0.6581

D (cm2/s)b 7.92 1.59 1.05 1.38 2.61 1.01 8.76 1.64 2.81 2.65 1.64 3.66

× × × × × × × × × × × ×

10−8 10−7 10−7 10−7 10−7 10−7 10−8 10−7 10−7 10−7 10−7 10−7

kdegr (cm) 8.27 4.08 7.12 1.13 1.58 5.34 4.92 5.13 6.19 4.78 3.39 5.27

× × × × × × × × × × × ×

10−3 10−3 10−3 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3

Mean pore size and standard deviation (in micrometers). bAverage value calculated using the obtained values from times of 2−5 h.

F



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full review of the different modeling of release processes, the process of fitting or mathematical calculus of these reported values of diffusion has not been minutely analyzed, and this summary is shown only for informative purposes; for that reason, only the order of magnitude has been taken into account in the location of our result. As can be observed, the present values are on the order of magnitude of 10−7 cm2/s, around 5 times the majority of those reported using PLGA and PLA biodegradable carriers.35−37 The main reason is because of the common use of dense microparticles as biodegradable carriers for drug release instead of porous devices. The latter are widely used as scaffolds for tissue regeneration but not as widespread as drug carriers. However, drug diffusion coefficients of porous devices29,38 are on the same order of magnitude as the resulting ones in this study. Therefore, PLGA and PLA foams are suitable devices for the release of hydrophobic drugs because they facilitate the in vitro and in vivo diffusion of the drug.19 3.3. Influence of Foam Characteristics in the Release Results. After a careful look at the different release profiles shown in Figures 6 and 7, it is possible to establish consistent relationships between the shape of the curves and the characteristics of the impregnated foams. According to the literature,14,17,39 the release rate of 5-Fu increases with an increase of the 5-Fu loading amount in the polymeric foams. This rapid release rate (burst) is related with the DL value of the foam. The burst in the first stage is faster in Figure 7c,f (high slope of the profile) for high values of DL and slower in Figures 6a and 7a (low slope of the first profile). The density of the foams is related to the size of the pores and also has an influence in the rate of release because it determines the ratio between the surface area and volume,14,18,40 and the differences in the shape of the curve in the second stage (as shown in Figure 4) are related with that. Nevertheless, on the basis of only our experimental results, it is not possible to establish a general rule without comparison with the general tendencies and diffusion values reported in the literature. It would be necessary to make a rigorous study of the porosity and distribution of the pore size and its relationship with the rate of release of molecules with different sizes and substrate affinities. Finally, the composition of the polymer foam is the most important factor determining the rate of degradation of a delivery matrix. According to the literature,41,42 the copolymer PLGA has a useful advantage over the homopolymer PLA, consisting of its capacity to regulate its degradation rate by just varying the ratio lactide/glycolide (L/G). Moreover, the presence of glycolide in the polymer increases its degradation rate14,16,40 because a higher content of glycolide makes the polymer more hydrophilic than PLA and increases more pronounced polymer swelling because of the best penetration of water molecules between the polymer chains.19 Regarding the degradation process, it must be noticed that the composition of the polymer only plays a role in the final part of the release curves (zone III), so PLGA foams show more sloping lines in contrast to the horizontal lines shown by PLA. Although the duration of the experiments did not make a larger extension of the degradation reaction possible, this effect is clearly shown in Figures 6a,d,e (PLGA foams) and 7b,d,e (PLA foams). Furthermore, quantitatively the different slope of the third stage is manifested in the higher values of kdegr that PLGA exhibit versus PLA.

Table 3. Summary of Diffusion Coefficients for PLGA and PLA as Drug-Release Carriers polymer

impregnated substance

type of device

D (cm2/s) −7

1.41 × 10

reference

PLA

5-Fu

porous matrix

2.21 × 10

PLGA PLGA PLGA

porous disk porous matrix porous matrix

10−7−10−8 7.2 × 10−7 5.9 × 10−7

PLGA

5-Fu ovoalbumin bovine serum albumin (BSA) 5-Fu

this work this work 34 39 39

4.7 × 10−13

33

PLGA

lidocaine lidocaine

PLGA

ibuprofen

PLGA

BSA

PLA

thymol

4.6 × 10−14−2 × 10−12 (14−104) × 10−12 (16−106) × 10−12 (3−24) × 10−12 1.39 × 10−11

35

PLGA

PLA

p-cymene

dense microparticles dense microparticles dense microparticles dense microparticles dense microparticles dense microparticles dense microparticles

5.21 × 10−13

38

PLGA

5-Fu

porous matrix

−7

36 36 37 38

between them, although all of the patterns of the curves corresponded in all cases with the general description presented in Figure 1. Regarding the calculations of the typical model parameters previously defined, the resulting values are summarized in Table 2 together with the foam description. A good fitting between the experimental data and mathematical model was achieved in such conditions. In general, an underestimation of the thin film equation in zone I was observed with an average relative percentage error of around 13%. In general, it has been observed that the model produces a small overestimation of the experimental data in zone III. This may be caused by no consideration of the porous nature of the foams that are viewed as homogeneous particles or their different compositions because they both play a decisive role in the polymer degradation process, as will be analyzed in the following section. Nevertheless, the short duration of the experiments and the consequent low grade of degradation motivated an almost imperceptible error at the end of the profiles. The total degradation of the foams depends mainly on their composition but also on the concrete porous structure of the concrete foam; each one would show a different dissolution time. Supposing that they show a constant dissolution rate noninfluenced by the changes in their molecular weight, upon extrapolation of the experimental data, the complete polymer dissolution and drug release would take from 5 days (corresponding to kdegr = 1.13 × 10−2 cm) to 16 days (corresponding to kdegr = 3.39 × 10−3 cm). Finally, for the intermediate step (zone II), the results are in very good agreement with the experimental data. In general, models based on Fick’s second law have often been used in the literature31−34 as equations more theoretical than the widely used empirical models (i.e., the well-known Peppas equation) because its high capacity to describe these kinds of diffusion processes. Table 3 shows a comparison between the average value for the apparent diffusion coefficient obtained for both PLGA and PLA in the present work and some values reported in the literature. Because the aim of this paper is very far from being a G



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4. CONCLUSION A mathematical model for analyzing the 5-Fu release from PLGA and PLA foams for in vitro systems has been developed. The influence of the foam characteristics (DL, pore size, and polymer composition) affecting the response of the system has been discussed. Typical model parameters (kext, D, and kdegr) have been obtained using a theoretical model composed of three different equations describing the main release processes found. Concretely, the value of diffusion coefficient (D) resulted in the same order of magnitude as that of other porous PLGA/ PLA devices previously reported in the literature and was higher than that to the dense microparticles. This mathematical method divided by zones can therefore be useful to describe the release of a hydrophilic drug such as 5-Fu from biodegradable polymeric foams used as drug carriers and achieving a good agreement with the experimental data.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +34 926295300 ext. 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

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Novel Model for the Description of the Controlled Release of 5

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