A new model of resorbable device degradation and drug release: Transient 1-dimension diffusional model

A reaction-diffusion framework for hydrolytic degradation of amorphous polymers based on a discrete chain scission model

Hydrolytic degradation of polymers involves the scission of long chain molecules, leading to molecular weight reduction and mass loss. The precise degradation response however depends on the scission probability of individual bonds along the polymer backbone. In particular, bonds near the chain ends are considered to be more susceptible to hydrolysis than inner bonds. In this paper, we incorporate a discrete chain scission model that can handle arbitrary bond scission probabilities within a continuum reaction-diffusion framework. Overall hydrolysis kinetics (including autocatalysis) is described independently of the chain scission model. By decoupling the description of the chain scission mechanism from kinetics, our framework enables the identification of the chain scission mechanism from molecular weight reduction and mass loss curves commonly reported in experimental degradation studies. We further propose a reduced continuum model which is better suited for large-scale simulations while retaining the predictive capability of the full discrete-continuum model. The model capability is illustrated in representative case studies based on experimental data from the literature for different materials and geometries. STATEMENT OF SIGNIFICANCE: Many models have been proposed to predict the evolution of molecular weight and mass loss in biodegradable polymers undergoing hydrolytic degradation. However, existing models remain limited in their ability to describe the degradation mechanism, autocatalytic kinetics and short chains diffusion simultaneously. Moreover, existing models often rely on empirical relations and a large number of fitting parameters. Here, we propose a conceptually simple discrete-continuum mathematical framework with a small number of parameters which all have a clear physical meaning. Model calibration against experimental data is simplified, and further provides insights into the degradation mechanisms at play, namely random scission, chain-end scission, or a combination of both. The framework can serve as a basis for future generalisations, including a description of evolving crystallinity, or other degradation mechanisms, such as thermal oxidation or photo-degradation.

Modeling the release of food bioactive ingredients from carriers/nanocarriers by the empirical, semiempirical, and mechanistic models

The encapsulation process has been utilized in the field of food technology to enhance the technofunctional properties of food products and the delivery of nutraceutical ingredients via food into the human body. The latter application is very similar to drug delivery systems. The inherent sophisticated nature of release mechanisms requires the utilization of mathematical equations and statistics to predict the release behavior during the time. The science of mathematical modeling of controlled release has gained a tremendous advancement in drug delivery in recent years. Many of these modeling methods could be transferred to food. In order to develop and design enhanced food controlled/targeted bioactive release systems, understanding of the underlying physiological and chemical processes, mechanisms, and principles of release and applying the knowledge gained in the pharmaceutical field to food products is a big challenge. Ideally, by using an appropriate mathematical model, the formulation parameters could be predicted to achieve a specific release behavior. So, designing new products could be optimized. Many papers are dealing with encapsulation approaches and evaluation of the impact of process and the utilized system on release characteristics of encapsulated food bioactives, but still, there is no deep insight into the mathematical release modeling of encapsulated food materials. In this study, information gained from the pharmaceutical field is collected and discussed to investigate the probable application in the food industry.

A model of polymer degradation and erosion for finite element analysis of bioresorbable implants

Finite element analysis is a powerful tool for the design of bioresorbable medical implants made of aliphatic polyesters such as bioresorbable vascular scaffolds. However polymer erosion has been traditionally modelled using empirical rules rather than differential equations. The rule-based models are difficult to implement in a finite element analysis. Consequently, these models have been limited to simple geometries such as plates or spheres. This paper presents a set of differential equations that govern the hydrolytic chain scission and bulk erosion of bioresorbable implants where polymer erosion is modelled using a differential equation instead of empirical rules. These differential equations can be conveniently solved using a commercial finite element package to calculate the molecular weight and mass loss as functions of time for bioresorbable implant made of aliphatic polyesters. A case study of Absorb bioresorbable vascular scaffolds (BVSs) is presented using data obtained from the literature, where 98 Absorb BVSs were implanted in 40 porcine coronary arteries. It is demonstrated that the finite element model can fit the data of both molecular weight and mass loss as functions of time to an accuracy of approximately 5%. The finite element model and the back-calculated model parameters can be used to design future implants that degrade in a controlled pattern with required mechanical performance.

A Systematic Experimental and Computational Analysis of Commercially Available Aliphatic Polyesters

Aliphatic polyesters, such as polylactic acid (PLA), polyglycolic acid (PGA), and their copolymer polylactic-co-glycolic acid (PLGA) have become an established choice in the biomedical field in a wide range of applications, from nanoparticles for local drug delivery to bone fixation screws, and, hence, in a huge spectrum of uses in different medical devices currently available on the market worldwide. The reason for their popularity lies in their combination of interesting peculiarities: in situ degradation, intrinsic biocompatibility (degradation products are recognized and metabolized), processability with standard industrial technologies, and tailorable properties. The knowledge of the degradation rate is an essential requirement for optimal device design when, e.g., fast adsorption time is required, or mechanical properties must be assured over a given time span. In this regard, experimental studies can be time- and money-consuming, due to the time scales (weeks–months) involved in the hydrolysis process. This work aims at providing to both industry and academia robust guidelines for optimal material choice through a systematic experimental and computational analysis of most commonly used PLGA formulations (selected from commercially available products), evaluating the degradation kinetics and its impact on polymer properties.

Industrial Development of a 3D-Printed Nutraceutical Delivery Platform in the Form of a Multicompartment HPC Capsule

Following recent advances in nutrigenomics and nutrigenetics, as well as in view of the increasing use of nutraceuticals in combination with drug treatments, considerable attention is being directed to the composition, bioefficacy, and release performance of dietary supplements. Moreover, the interest in the possibility of having such products tailored to meet specific needs is fast growing among costumers. To fulfill these emerging market trends, 3D-printed capsular devices originally intended for conveyance and administration of drugs were proposed for delivery of dietary supplements. Being composed of separate inner compartments, such a device could yield customized combinations of substances, relevant doses, and release kinetics. In particular, the aim of this work was to face early-stage industrial development of the processes involved in fabrication of nutraceutical capsules for oral pulsatile delivery. A pilot plant for extrusion of filaments based on pharmaceutical-grade polymers and intended for 3D printing was set up, and studies aimed at demonstrating feasibility of fused deposition modeling in 3D printing of capsule shells according to Current Good Manufacturing Practices for dietary supplements were undertaken. In this respect, the stability of the starting material after hot processing and of the resulting items was investigated, and compliance of elemental and microbiological contaminants, as well as of by-products, with internal specifications was assessed. Finally, operating charts highlighting critical process variables and parameters that would serve as indices of both intermediate and final product quality were developed.

Scaffolds as Structural Tools for Bone-Targeted Drug Delivery

Although bone has a high potential to regenerate itself after damage and injury, the efficacious repair of large bone defects resulting from resection, trauma or non-union fractures still requires the implantation of bone grafts. Materials science, in conjunction with biotechnology, can satisfy these needs by developing artificial bones, synthetic substitutes and organ implants. In particular, recent advances in materials science have provided several innovations, underlying the increasing importance of biomaterials in this field. To address the increasing need for improved bone substitutes, tissue engineering seeks to create synthetic, three-dimensional scaffolds made from organic or inorganic materials, incorporating drugs and growth factors, to induce new bone tissue formation. This review emphasizes recent progress in materials science that allows reliable scaffolds to be synthesized for targeted drug delivery in bone regeneration, also with respect to past directions no longer considered promising. A general overview concerning modeling approaches suitable for the discussed systems is also provided.

A Methodologic Approach for the Selection of Bio-Resorbable Polymers in the Development of Medical Devices: The Case of Poly(l-lactide-co-ε-caprolactone)

In the last decades bioresorbable and biodegradable polymers have gained a very good reputation both in research and in industry thanks to their unique characteristics. They are able to ensure high performance and biocompatibility, at the same time avoiding post-healing surgical interventions for device removal. In the medical device industry, it is widely known that product formulation and manufacturing need to follow specific procedures in order to ensure both the proper mechanical properties and desired degradation profile. Moreover, the sterilization method is crucial and its impact on physical properties is generally underestimated. In this work we focused our attention on the effect of different terminal sterilization methods on two commercially available poly(l-lactide-co-ε-caprolactone) with equivalent chemical composition (70% PLA and 30% PCL) and relatively similar initial molecular weights, but different chain arrangements and crystallinity. Results obtained show that crystallinity plays a key role in helping preserve the narrow distribution of chains and, as a consequence, defined physical properties. These statements can be used as guidelines for a better choice of the most adequate biodegradable polymers in the production of resorbable medical devices.

Polymer degradation and drug delivery in PLGA-based drug-polymer applications: A review of experiments and theories

Poly (lactic-co-glycolic acid) (PLGA) copolymers have been broadly used in controlled drug release applications. Because these polymers are biodegradable, they provide an attractive option for drug delivery vehicles. There are a variety of material, processing, and physiological factors that impact the degradation rates of PLGA polymers and concurrent drug release kinetics. This work is intended to provide a comprehensive and collective review of the physicochemical and physiological factors that dictate the degradation behavior of PLGA polymers and drug release from contemporary PLGA-based drug-polymer products. In conjunction with the existing experimental results, analytical and numerical theories developed to predict drug release from PLGA-based polymers are summarized and correlated with the experimental observations. © 2016 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 105B: 1692-1716, 2017.

A mechanistic model for drug release in PLGA biodegradable stent coatings coupled with polymer degradation and erosion

Biodegradable poly(d,l-lactic-co-glycolic acid) (PLGA) coating for applications in drug-eluting stents has been receiving increasing interest as a result of its unique properties compared with biodurable polymers in delivering drug for reducing stents-related side effects. In this work, a mathematical model for describing the PLGA degradation and erosion and coupled drug release from PLGA stent coating is developed and validated. An analytical expression is derived for PLGA mass loss that predicts multiple experimental studies in the literature. An analytical model for the change of the number-average degree of polymerization [or molecular weight (MW)] is also derived. The drug transport model incorporates simultaneous drug diffusion through both the polymer solid and the liquid-filled pores in the coating, where an effective drug diffusivity model is derived taking into account factors including polymer MW change, stent coating porosity change, and drug partitioning between solid and aqueous phases. The model is used to describe in vitro sirolimus release from PLGA stent coating, and demonstrates the significance of simultaneous sirolimus release via diffusion through both polymer solid and pore space. The proposed model is compared to existing drug transport models, and the impact of model parameters, limitations and possible extensions of the model are also discussed.

Impact of polymer structure and composition on fully resorbable endovascular scaffold performance

Fully erodible endovascular scaffolds are being increasingly considered for the treatment of obstructive arterial disease owing to their potential to mitigate long-term risks associated with permanent alternatives. While complete scaffold erosion facilitates vessel healing, generation and release of material degradation by-products from candidate materials such as poly-L-lactide (PLLA) may elicit local inflammatory responses that limit implant efficacy. We developed a computational framework to quantify how the compositional and structural parameters of PLLA-based fully erodible endovascular scaffolds affect degradation kinetics, erosion kinetics and the transient accumulation of material by-products within the arterial wall. Parametric studies reveal that, while some material properties have similar effects on these critical processes, others induce qualitatively opposing responses. For example, scaffold degradation is only mildly responsive to changes in either PLLA polydispersity or the initial degree of crystallinity, while the erosion kinetics is comparatively sensitive to crystallinity. Moreover, lactide doping can effectively tune both scaffold degradation and erosion, but a concomitant increase in local by-product accumulation raises concerns about implant safety. Optimized erodible endovascular scaffolds must precisely balance therapeutic function and biological response over the implant lifetime, where compositional and structural parameters will have differential effects on implant performance.

Mathematical modeling of drug delivery from autocatalytically degradable PLGA microspheres--a review

PLGA microspheres are widely studied for controlled release drug delivery applications, and many models have been proposed to describe PLGA degradation and erosion and drug release from the bulk polymer. Autocatalysis is known to have a complex role in the dynamics of PLGA erosion and drug transport and can lead to size-dependent heterogeneities in otherwise uniformly bulk-eroding polymer microspheres. The aim of this review is to highlight mechanistic, mathematical models for drug release from PLGA microspheres that specifically address interactions between phenomena generally attributed to autocatalytic hydrolysis and mass transfer limitation effects. Predictions of drug release profiles by mechanistic models are useful for understanding mechanisms and designing drug release particles.

Assessment of material by-product fate from bioresorbable vascular scaffolds

Fully bioresorbable vascular scaffolds (BVS) are attractive platforms for the treatment of ischemic artery disease owing to their intrinsic ability to uncage the treated vessel after the initial scaffolding phase, thereby allowing for the physiological conditioning that is essential to cellular function and vessel healing. Although scaffold erosion confers distinct advantages over permanent endovascular devices, high transient by-product concentrations within the arterial wall could induce inflammatory and immune responses. To better understand these risks, we developed in this study an integrated computational model that characterizes the bulk degradation and by-product fate for a representative BVS composed of poly(L-lactide) (PLLA). Parametric studies were conducted to evaluate the relative impact of PLLA degradation rate, arterial remodeling, and metabolic activity on the local lactic acid (LA) concentration within arterial tissue. The model predicts that both tissue remodeling and PLLA degradation kinetics jointly modulate LA fate and suggests that a synchrony of these processes could minimize transient concentrations within local tissue. Furthermore, simulations indicate that LA metabolism is a relatively poor tissue clearance mechanism compared to convective and diffusive transport processes. Mechanistic understanding of factors governing by-product fate may provide further insights on clinical outcome and facilitate development of future generation scaffolds.

Modeling of diffusion controlled drug delivery

Mathematical modeling of drug release can be very helpful to speed up product development and to better understand the mechanisms controlling drug release from advanced delivery systems. Ideally, in silico simulations can quantitatively predict the impact of formulation and processing parameters on the resulting drug release kinetics. The aim of this article is to give an overview on the current state of the art of modeling drug release from delivery systems, which are predominantly controlled by diffusional mass transport. The inner structure of the device, the ratio "initial drug concentration:drug solubility" as well as the device geometry determine which type of mathematical equation must be applied. A straightforward "road map" is given, explaining how to identify the appropriate equation for a particular type of drug delivery system. The respective equations for a broad range of devices are indicated, including reservoir and matrix systems, exhibiting or not an initial excess of drug and the geometry of slabs, spheres and cylinders. The assumptions the models are based on as well as their limitations are pointed out. Practical examples illustrate the usefulness of mathematical modeling of diffusion controlled drug delivery. Due to the advances in information technology the importance of in silico optimization of advanced drug delivery systems can be expected to significantly increase in the future.

Characterization and degradation behavior of agar-carbomer based hydrogels for drug delivery applications: solute effect

In this study hydrogels synthesized from agarose and carbomer 974P macromers were selected for their potential application in spinal cord injury (SCI) repair strategies following their ability to carry cells and drugs. Indeed, in drug delivery applications, one of the most important issues to be addressed concerns hydrogel ability to provide a finely controlled delivery of loaded drugs, together with a coherent degradation kinetic. Nevertheless, solute effects on drug delivery system are often neglected in the large body of literature, focusing only on the characterization of unloaded matrices. For this reason, in this work, hydrogels were loaded with a chromophoric salt able to mimic, in terms of steric hindrance, many steroids commonly used in SCI repair, and its effects were investigated both from a structural and a rheological point of view, considering the pH-sensitivity of the material. Additionally, degradation chemistry was assessed by means of infrared bond response (FT-IR) and mass loss.

Modeling material-degradation-induced elastic property of tissue engineering scaffolds

The mechanical properties of tissue engineering scaffolds play a critical role in the success of repairing damaged tissues/organs. Determining the mechanical properties has proven to be a challenging task as these properties are not constant but depend upon time as the scaffold degrades. In this study, the modeling of the time-dependent mechanical properties of a scaffold is performed based on the concept of finite element model updating. This modeling approach contains three steps: (1) development of a finite element model for the effective mechanical properties of the scaffold, (2) parametrizing the finite element model by selecting parameters associated with the scaffold microstructure and/or material properties, which vary with scaffold degradation, and (3) identifying selected parameters as functions of time based on measurements from the tests on the scaffold mechanical properties as they degrade. To validate the developed model, scaffolds were made from the biocompatible polymer polycaprolactone (PCL) mixed with hydroxylapatite (HA) nanoparticles and their mechanical properties were examined in terms of the Young modulus. Based on the bulk degradation exhibited by the PCL/HA scaffold, the molecular weight was selected for model updating. With the identified molecular weight, the finite element model developed was effective for predicting the time-dependent mechanical properties of PCL/HA scaffolds during degradation.

Analysis of degradation data of poly(l-lactide-co-l,d-lactide) and poly(l-lactide) obtained at elevated and physiological temperatures using mathematical models

The degradation of resorbable polymeric devices often takes months to years. Accelerated testing at elevated temperatures is an attractive but controversial technique. The purposes of this paper include: (a) to provide a summary of the mathematical models required to analyse accelerated degradation data and to indicate the pitfalls of using these models; (b) to improve the model previously developed by Han and Pan; (c) to provide a simple version of the model of Han and Pan with an analytical solution that is convenient to use; (d) to demonstrate the application of the improved model in two different poly(lactic acid) systems. It is shown that the simple analytical relations between molecular weight and degradation time widely used in the literature can lead to inadequate conclusions. In more general situations the rate equations are only part of a complete degradation model. Together with previous works in the literature, our study calls for care in using the accelerated testing technique.