Evaluation of the Release Kinetics of a Pharmacologically Active Substance from Model Intra-Articular Implants Replacing the Cruciate Ligaments of the Knee

Implants are readily applied as a convenient method of therapy. There is great interest in the prolonged release of active substances from implants. The objective of this work was to evaluate the dissolution kinetics of steroidal anti-inflammatory preparation (SAP) released from novel implants, and to test the influence of the technology on SAP release kinetics. The proposed long-acting preparations may overcome difficulties resulting from repeated injections and often visits to ambulatory clinic, as the stabilizing function of the artificial ligament would be enriched with pharmacological activity. The potential advantages provided by the new coatings of knee implants include the continuous, sustained, and prolonged release of an active substance. The study was carried out using a modified United States Pharmacopoeia (USP) apparatus 4. The amount of SAP was measured spectroscopically. It was revealed that the transport of the drug was mainly a diffusion process. The drug release kinetics was analyzed using zero-, first-, and second-order kinetics as well as Korsmeyer-Peppas, Higuchi, and Hixon-Crowell models. The highest values of the release rate constants were k0 = (7.49 ± 0.05) × 10−5 mg × min−1, k1 = (6.93 ± 0.05) × 10−6 min−1, and k2 = (7.70 ± 0.05) × 10−7 mg−1 × min−1 as calculated according to zero-, first-, and second-order kinetics equations, respectively. The values of the rate constants obtained for the slowest process were k0 = (3.63 ± 0.06) × 10−5 mg × min−1, k1 = (2.50 ± 0.03) × 10−6 min−1, and k2 = (2.80 ± 0.03) × 10−7 mg−1 × min−1. They may suggest the possibility of sustained release of betamethasone from the system. Due to the statistical analysis, differences were observed between most of the studied implants. Incubation, temperature, time of stabilization of layers, and the method of SAP deposition on the matrix affected the drug release.


Introduction
The optimal mechanical properties of musculoskeletal joints are ensured by cartilage and synovial fluid. The failure of these tissues as a result of various arthritis forms leads to the development Sodium hydroxide and anhydrous potassium dihydrogen phosphate were delivered from Chempur (Poland, PiekaryŚląskie, Poland). All chemicals were pharmaceutical grade and used without further purification. Phosphate buffer solution, pH 7.4, was prepared according to the European Pharmacopoeia [28]. SAP was diluted in phosphate buffer solution and effected in the concentration of the drug ca. 0.03624 mg/mL. The UV-Vis spectrum (Jasco V-530, Tokyo, Japan) of the substance was recorded from 200 to 900 nm, with a scanning speed of 500 nm per min at room temperature. The characteristic absorption band was observed at 240 nm. At this wavelength, the absorbance of 5 various concentrations of SAP ranging from 0.00604-0.01812 mg/mL were read to prepare the calibration curve. The composition of SAP was: betamethasone sodium phosphate and betamethasone dipropionate, disodium phosphate dehydrate, disodium phosphate anhydrous, sodium chloride, disodium edetate, polysorbate 80, benzyl alcohol, methyl parahydroxybenzoate, propyl parahydroxybenzoate, sodium carboxymethylcellulose, macrogol, hydrochloric acid. The measured spectrum of SAP is presented in Graphical abstract. Based on literature data the observed band at 240 nm has been assigned to both betamethasone sodium phosphate and betamethasone dipropionate [28][29][30]. No additional peaks in the wavelength range 200-900 nm at the used conditions were observed. This observation suggested that excipients do not present signal in the above-mentioned region. The spectrum of the same mixture stored for 24 h was the same as the spectrum of fresh mixture. It indicated the lack of disturbances from any decomposition products. Unlike conventional dosage forms, there is a lack of standard pharmacopoeial or other regulatory tests dedicated for parenteral, controlled-release drug products in the form of implanted ligaments. In particular, a method for the in vitro release of a drug from implants was not found. Burgess et al. [31], and Siewert et al. [32] proposed combined methods or their modification for the study of the in vitro dissolution of a drug from novel or special formulations. The validation of USP apparatus 4 used for the in vitro drug release study from microspheres revealed that the dissolution of the drug was not affected by the flow rate in the assessed flow range, the number of microspheres, or the cell size. However, slight changes in the temperature affected the differences in drug dissolution profiles [33].
In the present work, the release study was carried out using a modified USP apparatus 4-the flow-through cell equipment (Laboratory Glass Apparatus, Inc., Berkeley, CA, USA). The acceptor fluid used in the experiment was phosphate buffer solution, pH 7.4 (USP 32), at temperature of 37 • C. The temperature was controlled using a thermostat (Prüfgeräte-Werk, B2 E10, Medingen, Germany). The drug content in the samples was determined by UV measurements (JASCO V-530, Tokyo, Japan), reading the absorbance every 2 min at a wavelength of 240 nm. A flow rate of 5 mL/min was established by employing a peristaltic pump (PS-16 Sipper Pump, PG Instruments Limited, Leicestershire, UK), and the rotation speed of the fluid was 100 rpm (magnetic stirrer, 2 mag magnetic emotion, Munich, Germany). Each experiment was conducted in triplicate. The schematic representation for the release apparatus is presented in Figure 1. dissolution of a drug from novel or special formulations. The validation of USP apparatus 4 used for the in vitro drug release study from microspheres revealed that the dissolution of the drug was not affected by the flow rate in the assessed flow range, the number of microspheres, or the cell size. However, slight changes in the temperature affected the differences in drug dissolution profiles [33].
In the present work, the release study was carried out using a modified USP apparatus 4-the flow-through cell equipment (Laboratory Glass Apparatus, Inc., Berkeley, CA, USA). The acceptor fluid used in the experiment was phosphate buffer solution, pH 7.4 (USP 32), at temperature of 37 °C. The temperature was controlled using a thermostat (Prüfgeräte-Werk, B2 E10, Medingen, Germany). The drug content in the samples was determined by UV measurements (JASCO V-530, Tokyo, Japan), reading the absorbance every 2 min at a wavelength of 240 nm. A flow rate of 5 mL/min was established by employing a peristaltic pump (PS-16 Sipper Pump, PG Instruments Limited, Leicestershire, UK), and the rotation speed of the fluid was 100 rpm (magnetic stirrer, 2 mag magnetic emotion, Munich, Germany). Each experiment was conducted in triplicate. The schematic representation for the release apparatus is presented in Figure 1. It was found that the drug release from implants depends on the test method as well as the media used in the experiment. Differences between the release profiles obtained using various dissolution tests were observed. These results suggest the necessity of knowledge about the underlying in vivo processes and the need to translate this research to the in vitro test systems [34].
The zero-order kinetics model is as follows: where mt is the amount of the drug released over time t, mb is the amount of the drug in solution before release (usually it is 0), and k0 is the zero-order release rate constant. The first-order kinetics model is as follows: where m0 is the amount of the drug in the formulation before dissolution, and k1 is the first-order release rate constant. The second-order kinetics model is as follows: where k2 is the second-order rate constant. The Korsmeyer-Peppas model [35,36,39] is as follows: It was found that the drug release from implants depends on the test method as well as the media used in the experiment. Differences between the release profiles obtained using various dissolution tests were observed. These results suggest the necessity of knowledge about the underlying in vivo processes and the need to translate this research to the in vitro test systems [34].
The zero-order kinetics model is as follows: where m t is the amount of the drug released over time t, m b is the amount of the drug in solution before release (usually it is 0), and k 0 is the zero-order release rate constant. The first-order kinetics model is as follows: where m 0 is the amount of the drug in the formulation before dissolution, and k 1 is the first-order release rate constant. The second-order kinetics model is as follows: where k 2 is the second-order rate constant. The Korsmeyer-Peppas model [35,36,39] is as follows: where m ∞ is the amount of the drug released after an infinitive time (in this research after 24 h), k K-P is the Korsmeyer-Peppas rate constant, and n is the parameter indicative of the drug release mechanism. The Higuchi model [37] is as follows: where k H is the Higuchi rate constant. The Hixon-Crowell model [38] is as follows: where m left is the amount of drug left in the formulation over time t, and k H-C is the Hixon-Crowell rate constant. Moreover, the difference factor, f 1 , was calculated to compare the dissolution profiles [40,41]: where n is the number of time points, R t is the dissolution value of the reference batch at a given time (t), and T t is the dissolution value of the test batch at time t. Linear regression analysis based on the least-squares regression method was employed to study the linearity of the kinetic models. Comparing the standard deviation (SD) and the correlation coefficient, R 2 , allowed us to choose the kinetic model that describes the observed processes well. Statistical analysis using analysis of variance (ANOVA) with Tukey's test and Student's t-test were used to assess the differences between the obtained release profiles. A statistically significant difference was indicated when p < 0.05 [42].

Mechanism of the Drug Release
The transport of drugs from pharmaceutical systems involves various physical and chemical rules, what results in difficulties in ascribing proper mathematical model to the occurring processes. Zero-order kinetics may be used if the pharmaceutical dosage form does not disaggregate and release the drug slowly. First-order model may describe the early stage of dissolution of a poorly water-soluble drug embedded in water-soluble matrix. Higuchi equation is based on several assumptions: the initial concentration of the drug in the formulation is higher than the drug solubility; the drug spreads only in one dimension; the substance particle are smaller than the size of a carrier; swelling of the system and its dissolution is insignificant; the drug diffusivity does not change; sink condition are achieved. Hixon-Crowell model may be applied when the drug is released on parallel planes of the drug form surface, e.g., in the case of tablet, when the size reduces proportionally and the geometrical shape stay constant [43,44]. Siepmann and Peppas [39] observed that the geometry of the system, the amount of the drug as well as water-solubility of the drug can exclude some of the models. In the present work several equations were used to fit the experimental data to the theoretical curve. Zero-, first-, and second-order kinetics were employed to describe the release of SAP from all implants studied and the results are listed in Table 2. However, in the case of implants E, F, and G, it was hard to fit the release data to the Higuchi model. The Korsmeyer-Peppas model was unsuitable for describing the release of the drug from implant F, and the Hixon-Crowell model was inappropriate to reflect the dissolution of SAP from implants A and C. The values of the correlation coefficient R 2 indicate which kinetic model is appropriate for the release of the drug. Gouda et al. [43] obtained the value of R 2 between 0.933 and 0.9157, and discussed that the release kinetics do not perfectly follow the used model, although it is gently approaching. This observation suggests that the drug was transported from the studied systems in various ways. A regression coefficient value, R 2 , close to 1 indicated the model fitting the release mechanism. For implants A-D, the best kinetic model was the Higuchi equation, as the plots showed high linearity, with R 2 values in the range 0.9872-0.9962, suggesting mainly the diffusion process [45]. These results were consistent with results obtained from Korsmeyer-Peppas model analysis for systems A and C. According to this model, the drug was transported via Fickian diffusion when the value of the parameter n was below or equal to 0.5, while the n value between 0.5 and 1.0 indicated anomalous transport [35,39]. In the case of implants B and D, the n values were slightly above 0.5, namely, 0.582 ± 0.004 and 0.579 ± 0.005, suggesting a coupling of diffusion and erosion mechanisms, anomalous diffusion, and may indicate that betamethasone release from implants B and D was controlled by more than one process. However, Antesh et al. [46] obtained n values between 0.4225 and 0.7309 in their study and interpreted the observed transport of the active substance was controlled by diffusion. In the present work, fitting the data to the Higuchi equation together with n values slightly above 0.5, may suggest diffusion-controlled drug release. In the case of implant E, the n value was 0.46 ± 0.01, suggesting diffusion of the drug. However, the regression coefficient, R 2 , of implant E in the Korsmeyer-Peppas model has the lowest value (0.8113) in comparison to the R 2 value obtained for the rest of implants. The highest R 2 value in this kinetic model (0.9722) was obtained for the G system and corresponded to the highest n value (0.75 ± 0.01) among all implants studied. This value of n above 0.5, together with the non-adherence of the experimental data to the Higuchi model, may be regarded as an indicator of the anomalous transport of the drug. The data derived from the dissolution of betamethasone from implants F were unsuitable for analysis with the Higuchi and Korsmeyer-Peppas models.
The dissolution data were also plotted according to the Hixon-Crowell model. The possibility of describing the release of betamethasone from implants B and D-G using this model may indicate that the change in the surface area and in the diameter of particles during the dissolution process affected the drug release. The difficulties with describing the dissolution process of betamethasone from implants A and C, using the Hixon-Crowell equation, may indicate that changes of surface area and of diameter slightly influenced the release.
It could be concluded that diffusion was the dominant mechanism of betamethasone release from implants A-E. The temperature and time of stabilization of layers and the incubation of implants did not influence the mechanism of betamethasone transport. These results contrasted with results obtained for implants F-G. The release of the drug from these implants was best expressed by first-order kinetics, and betamethasone was transported via non-Fickian diffusion. This could be a result of more silica layers that contained the drug applied on polyester than in implants A-E (Table 1). SAP molecules must overcome the silica layers to reach the surface of the implant. This process was not simple diffusion, which was confirmed by the value of parameter n above 0.5 in the case of the G system. The release of betamethasone from implants B and D-G was connected to the change in the surface area and diameter of particles along with the progressive dissolution process.

Dissolution Study
The kinetic release parameters and regression coefficients calculated from various kinetic models, such as zero-, first-, and second-order kinetics, as well as the Higuchi [37], Korsmeyer-Peppas [35,36,39] and Hixon-Crowell [38] models, are listed in Table 2. Exemplary fitting of release models to experimental data obtained from the dissolution of SAP from implant B is shown in Figure 2. In Figure 2a, the application of zero-order kinetics is presented. This model describes the drug release rate from pharmaceutical dosage forms independent of the drug concentration in contrast to the first-order kinetics, where the rate was concentration dependent, meaning the greater the concentration, the faster the process. The first-order model is illustrated in Figure 2b. The second-order kinetics, when the rate depends on the concentration of the drug in the second power, is presented in Figure 2c. The comparison of the rate constants derived employing zero-order, first-order, and second-order kinetics for all implants studied is attached in Figure 3. It should be noted that the highest value of the rate constant was achieved for implant F, and the lowest value was obtained for implant C, reflecting the release rates for F and C, respectively. According to these observations, implant C was able to prolong and control betamethasone release. Based on zero-order kinetics that describe the release of SAP from implant C well, the half-release time is 133,064 ± 1881 min, which corresponds to a period of approximately three months (92 days). The half-release time in implant F, calculated using first-order kinetics, which expressed the release of SAP well, was 102,166 ± 763 min, corresponding to a period of approximately 72 days. It is worth mentioning that both implants C and F were incubated, suggesting that this process does not influence the kinetics of SAP release from these implants. The difference in kinetic parameters may be attributed to the temperature and time of the silica layer stabilization. Moreover, these discrepancies may occur due to the methods of SAP application on the polymeric system. Comparing the kinetic parameters obtained from tested models (Table 2, Figure 3), the values were different for each implant. For the evaluation of in vitro release differences, a simple model-independent approach, based on the calculation of a difference factor f1 [41,42], was employed. The results of the calculations are listed in Table 3. The differences in the release studies of the drug were noticed in each instance, with f1 values below 15. These results demonstrated the inconsistency in the release of SAP from all implants studied, except for comparisons of systems: E and D, B and G, A and F. In these comparisons, the differences were not observed.
In general, it could be concluded that the incubation, the method of SAP deposition and the temperature and time of silica layer stabilization influence the kinetics of drug release.

Statistical Analysis
To confirm the differences in the release of SAP from the implants tested, statistical analysis by ANOVA, together with Tukey's test, was performed [41]. The obtained value of F was 245 and was higher than the critical value of F = 2.22. The SAP dissolution profiles were significantly different. All The half-release time in implant F, calculated using first-order kinetics, which expressed the release of SAP well, was 102,166 ± 763 min, corresponding to a period of approximately 72 days. It is worth mentioning that both implants C and F were incubated, suggesting that this process does not influence the kinetics of SAP release from these implants. The difference in kinetic parameters may be attributed to the temperature and time of the silica layer stabilization. Moreover, these discrepancies may occur due to the methods of SAP application on the polymeric system. Comparing the kinetic parameters obtained from tested models (Table 2, Figure 3), the values were different for each implant.
For the evaluation of in vitro release differences, a simple model-independent approach, based on the calculation of a difference factor f 1 [41,42], was employed. The results of the calculations are listed in Table 3. The differences in the release studies of the drug were noticed in each instance, with f 1 values below 15. These results demonstrated the inconsistency in the release of SAP from all implants studied, except for comparisons of systems: E and D, B and G, A and F. In these comparisons, the differences were not observed.
In general, it could be concluded that the incubation, the method of SAP deposition and the temperature and time of silica layer stabilization influence the kinetics of drug release.

Statistical Analysis
To confirm the differences in the release of SAP from the implants tested, statistical analysis by ANOVA, together with Tukey's test, was performed [41]. The obtained value of F was 245 and was higher than the critical value of F = 2.22. The SAP dissolution profiles were significantly different. All possible pairs of SAP dissolution profiles were compared using Tukey's test to determine exactly where are the differences, which indicated that specific groups compared with each other were different. The calculated value of the honest significant difference was 0.032. The data coming from comparisons of the individual groups were collected in Table 4 and were predominantly higher than 0.032. Table 4. The values of near-infrared (NIR)-test Tukey. There were significant differences between the SAP dissolution profiles from all implants tested, apart from E and G, as well as A and F. Only in these two cases the value of NIR was below 0.032. These results are consistent with the results obtained from Student's t-test analysis. According to the data presented in Table 5, differences in dissolution profiles exist between all dissolution profiles of SAP, except two pairs: E and G, as well as A and F. In these cases, the value of t is lower than the critical value of 1.96, reflecting statistical similarity of the release profiles.

Conclusions
In conclusion, diffusion was the dominant mechanism of betamethasone release from implants A-E. The temperature and time of stabilization of the layers as well as incubation of implants did not change the transport mechanism of betamethasone. In the case of implants F-G, the drug dissolution was expressed by first-order kinetics, and betamethasone was transported via non-Fickian diffusion. The dissolution of the drug from the assessed implants could be described by zero-, first-, and second-order kinetic equations. The release rate constants obtained from these models had the highest value for implants F and the lowest value for implants C. This model-independent analysis confirmed the variability of the release of the drug in most cases between the different implants.