Derivation of an Analytical Solution to a Reaction-Diffusion Model for Autocatalytic Degradation and Erosion in Polymer Microspheres

Experimental and mathematical approaches for drug delivery for the treatment of wet age-related macular degeneration

Several chronic eye diseases affect the posterior segment of the eye. Among them age-related macular degeneration can cause vision loss if left untreated and is one of the leading causes of visual impairment in the world. Most treatments are based on intravitreally injected therapeutics that inhibit the action of vascular endothelial growth factor. However, due to the need for monthly injections, this method is associated with poor patient compliance. To address this problem, numerous drug delivery systems (DDSs) have been developed. This review covers a selection of particulate systems, non-stimuli responsive hydrogels, implants, and composite systems that have been developed in the last few decades. Depending on the type of DDS, polymer material, and preparation method, different mechanical properties and drug release profiles can be achieved. Furthermore, DDS development can be optimized by implementing mathematical modeling of both drug release and pharmacokinetic aspects. Several existing mathematical models for diffusion-controlled, swelling-controlled, and erosion-controlled drug delivery from polymeric systems are summarized. Compartmental and physiologically based models for ocular drug transport and pharmacokinetics that have studied drug concentration profiles after intravitreal delivery or release from a DDS are also reviewed. The coupling of drug release models with ocular pharmacokinetic models can lead to obtaining much more efficient DDSs for the treatment of age-related macular degeneration and other diseases of the posterior segment of the eye.

The Effect of Polymer Blends on the In Vitro Release/Degradation and Pharmacokinetics of Moxidectin-Loaded PLGA Microspheres

To investigate the effect of polymer blends on the in vitro release/degradation and pharmacokinetics of moxidectin-loaded PLGA microspheres (MOX-MS), four formulations (F1, F2, F3 and F4) were prepared using the O/W emulsion solvent evaporation method by blending high (75/25, 75 kDa) and low (50/50, 23 kDa) molecular weight PLGA with different ratios. The addition of low-molecular-weight PLGA did not change the release mechanism of microspheres, but sped up the drug release of microspheres and drastically shortened the lag phase. The in vitro degradation results show that the release of microspheres consisted of a combination of pore diffusion and erosion, and especially autocatalysis played an important role in this process. Furthermore, an accelerated release method was also developed to reduce the period for drug release testing within one month. The pharmacokinetic results demonstrated that MOX-MS could be released for at least 60 days with only a slight blood drug concentration fluctuation. In particular, F3 displayed the highest AUC and plasma concentration (AUC0-t = 596.53 ng/mL·d, Cave (day 30-day 60) = 8.84 ng/mL), making it the optimal formulation. Overall, these results indicate that using polymer blends could easily adjust hydrophobic drug release from microspheres and notably reduce the lag phase of microspheres.

Interrelation between swelling, mechanical constraints and reaction-diffusion processes in molecular responsive hydrogels

The net swelling dynamics in molecular responsive hydrogels can be viewed as an integrated effect of discernible processes involving transport of actuating species, reaction with network components like destabilization of physical crosslinks or cleavage of network strands and concomitant network relaxation. Here, we describe a finite element modeling approach coupling these interdependent, underlying processes in hydrogels including oligonucleotide duplexes as physical crosslinks that can be destabilized by a particular molecule. These molecular responsive hydrogels based on acrylamide including either DNA or oligomorpholinos (MO), a DNA analogue, as functional elements can be made with various content of dsDNA or dsMO supported cross-links. The dsDNA or dsMO integrated in the hydrogel can be fabricated with ssDNA designed to competitively displace the connectivity of the dsDNA supported crosslinks, and similar for the MO hydrogels. The overall processes can be framed in a diffusion-reaction scheme. This process is dependent on the concentration of the diffusing species, their diffusion coefficients and their location. Thus, the reaction taking place in particular molecular responsive hydrogels is coupled with the deformations due to swelling and mechanical constraints undergone by the gel. Numerical examples show the importance of coupling reaction-diffusion with mechanical deformations for such gels. Finally, our model is compared to swelling experiments of hemi-spheroidal molecular responsive hydrogels bound to an optical fiber. Parameters of the reaction-diffusion model were obtained by fitting the model to reported experimental data where molecular stimuli designed with different molecular parameters for the competitive displacement reaction were employed in the swelling experiments.

Modulation of protein release from penta-block copolymer microspheres

Releasing a protein according to a zero-order profile without protein denaturation during the polymeric microparticle degradation process is very challenging. The aim of the current study was to develop protein-loaded microspheres with new PLGA based penta-block copolymers for a linear sustained protein release. Lysozyme was chosen as model protein and 40 µm microspheres were prepared using the solid-in-oil-in-water solvent extraction/evaporation process. Two types of PLGA-P188-PLGA penta-block copolymers were synthetized with two PLGA-segments molecular weight (20 kDa or 40 kDa). The resulting microspheres (50P20-MS and 50P40-MS) had the same size, an encapsulation efficiency around 50-60% but different porosities. Their protein release profiles were complementary: linear but non complete for 50P40-MS, non linear but complete for 50P20-MS. Two strategies, polymer blending and microsphere mixing, were considered to match the release to the desired profile. The (1:1) microsphere mixture was successful. It induced a bi-phasic release with a moderate initial burst (around 13%) followed by a nearly complete linear release for 8 weeks. This study highlighted the potential of this penta-block polymer where the PEO block mass ratio influence clearly the Tg and consequently the microsphere structure and the release behavior at 37 °C. The (1:1) mixture was a starting point but could be finely tuned to control the protein release.

Toehold Length of Target ssDNA Affects Its Reaction-Diffusion Behavior in DNA-Responsive DNA-co-Acrylamide Hydrogels

In the present study, we expand on the understanding of hydrogels with embedded deoxyribonucleic acid (DNA) cross-links, from the overall swelling to characterization of processes that precede the swelling. The hydrogels respond to target DNA strands because of a toehold-mediated strand displacement reaction in which the target strand binds to and opens the dsDNA cross-link. The spatiotemporal evolution of the diffusing target ssDNA was determined using confocal laser scanning microscopy (CLSM). The concentration profiles revealed diverse partitioning of the target DNA inside the hydrogel as compared with the immersing solution: excluding a nonbinding DNA, while accumulating a binding target. The data show that a longer toehold results in faster cross-link opening but reduced diffusion of the target, thus resulting in only a moderate increase in the overall swelling rate. The parameters obtained by fitting the data using a reaction-diffusion model were discussed in view of the molecular parameters of the target ssDNA and hydrogels.

Morpholino Target Molecular Properties Affect the Swelling Process of Oligomorpholino-Functionalized Responsive Hydrogels

Responsive hydrogels featuring DNA as a functional unit are attracting increasing interest due to combination of versatility and numerous applications. The possibility to use nucleic acid analogues opens for further customization of the hydrogels. In the present work, the commonly employed DNA oligonucleotides in DNA-co-acrylamide responsive hydrogels are replaced by Morpholino oligonucleotides. The uncharged backbone of this nucleic acid analogue makes it less susceptible to possible enzymatic degradation. In this work we address fundamental issues related to key processes in the hydrogel response; such as partitioning of the free oligonucleotides and the strand displacement process. The hydrogels were prepared at the end of optical fibers for interferometric size monitoring and imaged using confocal laser scanning microscopy of the fluorescently labeled free oligonucleotides to observe their apparent diffusion and accumulation within the hydrogels. Morpholino-based hydrogels' response to Morpholino targets was compared to DNA hydrogels' response to DNA targets of the same base-pair sequence. Non-binding targets were observed to be less depleted in Morpholino hydrogels than in DNA hydrogels, due to their electroneutrality, resulting in faster kinetics for Morpholinos. The electroneutrality, however, also led to the total swelling response of the Morpholino hydrogels being smaller than that of DNA, since their lack of charges eliminates swelling resulting from the influx of counter-ions upon oligonucleotide binding. We have shown that employing nucleic acid analogues instead of DNA in hydrogels has a profound effect on the hydrogel response.

Reaction-Multi Diffusion Model for Nutrient Release and Autocatalytic Degradation of PLA-Coated Controlled-Release Fertilizer

A mathematical model for the reaction-diffusion equation is developed to describe the nutrient release profiles and degradation of poly(lactic acid) (PLA)-coated controlled-release fertilizer. A multi-diffusion model that consists of coupled partial differential equations is used to study the diffusion and chemical reaction (autocatalytic degradation) simultaneously. The model is solved using an analytical-numerical method. Firstly, the model equation is transformed using the Laplace transformation as the Laplace transform cannot be inverted analytically. Numerical inversion of the Laplace transform is used by employing the Zakian method. The solution is useful in predicting the nutrient release profiles at various diffusivity, concentration of extraction medium, and reaction rates. It also helps in explaining the transformation of autocatalytic concentration in the coating material for various reaction rates, times of reaction, and reaction-multi diffusion. The solution is also applicable to the other biodegradable polymer-coated controlled-release fertilizers.