Research Paper
Modelling the degradation and elastic properties of poly(lactic-co-glycolic acid) films and regular open-cell tissue engineering scaffolds

https://doi.org/10.1016/j.jmbbm.2015.08.030Get rights and content

Highlights

  • A coupled molecular weight degradation and mechanical properties model is developed

  • The coupled model captures the experimentally observed degradation of PLGA films

  • Degradation is shown to be homogenous or autocatalytic depending on scaffold size

  • Autocatalysis is caused by diffusion-limited build-up of monomers inside scaffolds

Abstract

Scaffolding plays a critical rule in tissue engineering and an appropriate degradation rate and sufficient mechanical integrity are required during degradation and healing of tissue. This paper presents a computational investigation of the molecular weight degradation and the mechanical performance of poly(lactic-co-glycolic acid) (PLGA) films and tissue engineering scaffolds. A reaction-diffusion model which predicts the degradation behaviour is coupled with an entropy-based mechanical model which relates Young׳s modulus and the molecular weight. The model parameters are determined based on experimental data for in-vitro degradation of a PLGA film. Microstructural models of three different scaffold architectures are used to investigate the degradation and mechanical behaviour of each scaffold. Although the architecture of the scaffold does not have a significant influence on the degradation rate, it determines the initial stiffness of the scaffold. It is revealed that the size of the scaffold strut controls the degradation rate and the mechanical collapse. A critical length scale due to competition between diffusion of degradation products and autocatalytic degradation is determined to be in the range 2–100 μm. Below this range, slower homogenous degradation occurs; however, for larger samples monomers are trapped inside the sample and faster autocatalytic degradation occurs.

Introduction

It is well known that scaffolding plays a critical role in tissue engineering. Biodegradable polymers have been used widely to provide a three-dimensional structure that facilitates tissue regeneration and wound healing (Cheng et al., 2013, Harada et al., 2014, Ren et al., 2005, Uematsu et al., 2005). The degradation process of biodegradable polyesters such as poly(lactic-co-glycolic acid) (PLGA) is based on a hydrolytic reaction. Diffusion of water causes hydrolysis of the ester bonds in the polymer chains, leading to the generation of water soluble oligomers. Consequently, the molecular weight of the polymer decreases. The degradation products diffuse into the surrounding medium, which results in a mass loss for the polymer (Pamula and Menaszek, 2008, Shirazi et al., 2014, Vey et al., 2012).

Diffusion of the degradation products may occur more slowly in a large-sized sample due to the greater diffusion length (Dunne et al., 2000, Grayson et al., 2005, Grizzi et al., 1995, Lu et al., 1999, Witt and Kissel, 2001). This leads to accumulation of degradation products inside the polymer matrix, which are able to catalyse hydrolysis of the other ester bonds and consequently accelerates the degradation process. This phenomenon is called autocatalysis. Therefore, due to the autocatalytic effect the large PLGA samples undergo a heterogeneous degradation with a degradation rate which is greater at the centre than at the surface.

In order to support tissue formation, the scaffold should retain sufficient stability during degradation. A clear understanding of the evolution of the mechanical properties of PLGA scaffolds during degradation is required. Towards this, computational modelling offers an efficient framework to understand the behaviour of biodegradable implants. Many models have been proposed to describe the degradation of biodegradable polymers (Sackett and Narasimhan, 2011) including PLGA (Ford Versypt et al., 2013). Reaction-diffusion models have been applied to a range of aliphatic polyesters. Among these models, the ones which account for the autocatalytic effect are the most comprehensive, as autocatalysis plays a strong role in the degradation mechanism (Chen et al., 2011, Ford Versypt et al., 2013, Wang et al., 2008).

A number of models have been presented to predict the mechanical properties of degradable polymers (Hayman et al., 2014, Soares et al., 2010, Vieira et al., 2014, Vieira et al., 2011, Wang et al., 2010). A model was developed by Vieira et al. (2014) based on the relationship between fracture strength and molecular weight for thermoplastic polymers to predict the mechanical properties of PLA–PCL fibres during degradation. Since this model is based on an empirical equation, the model parameters must be determined experimentally for each material and during degradation. Also, in this model, the hydrolytic degradation rate is assumed constant, which is a significant simplification for highly heterogeneous degradation as autocatalysis has a significant effect on degradation.

The model of Soares et al. (2010) relates the degradation rate to the mechanical deformation in order to determine the mechanical properties of poly(L-lactide) (PLLA) fibres loaded under uniaxial extension. The degradation behaviour is determined from a thermodynamic analysis of the degradation process and as degradation proceeds the material loses its ability to store energy.

Despite the fact that the degradation of PLGA polymers results in a quick decrease in the polymer molecular weight, Young׳s modulus does not decrease until the number of polymer chains reaches a critical molecular weight (Shirazi et al., 2014). Wang et al. (2010) proposed a model for amorphous biodegradable polymers, based on the relationship between Young׳s modulus and the number of polymer chains. This model is physically motivated by the hydrolytic random scission of the polymer chains. The model assumes that the number of polymer chains above a critical molecular weight determines Young׳s modulus as chain scissions occur. This model successfully predicted the experimental observed degradation of PLLA films.

Motivated by recent developments, an integrated modelling framework based on the work of Wang et al., 2010, Wang et al., 2008 was developed in the current study to predict the degradation of biodegradable polymers and, in particular, PLGA. The first objective of this study was to develop a computational framework that links both of the key physical processes: the reduction in molecular weight over time during degradation; and the relationship between Young׳s modulus and molecular weight (and polymer chain length). The second objective was to calibrate the models based on the experimental data for in-vitro degradation of a PLGA film. The third objective was to predict the molecular weight and the reduction in Young׳s modulus for PLGA films of different thicknesses and also for a range of PLGA scaffolds. The effect of strut size and architecture of the scaffold on the degradation rate and the mechanical performance were investigated.

Section snippets

Methods

This section is organised as follows: an overview of the phenomenological degradation model of Wang et al. (2010), which predicts the changes in the molecular weight distribution during degradation, is presented (hereafter referred to as the molecular weight model); the entropy spring model which relates Young׳s modulus to the molecular weight distribution is described (hereafter referred to as the mechanical properties model); the coupling of these two models is then described; and finally we

Model calibration

The parameters of the molecular weight model (k1, k2, and D0) and the mechanical properties model (Nchains, Rscissions, and Mncrit) were calibrated to fit the experimental data obtained by Shirazi et al. (2014) which described the reduction in the molecular weight and the Young׳s modulus for a PLGA (50:50) film (with a thickness of 250 μm) degraded in a phosphate buffer solution, pH 7.4 at 37 °C.

Fig. 3 (A–C) compares the M¯n experimental data with different combinations of parameters for the

Discussion

The current study presents a computational investigation of the molecular weight degradation and the mechanical performance of PLGA films and tissue engineering scaffolds. We developed a computational framework to couple a reaction-diffusion model that captures changes in molecular weight distribution during degradation to a polymer chain model that captures the relationship between the molecular weight distribution and the mechanical properties. The model framework was calibrated based on

Conclusion

This study used a numerical model that couples changes in molecular weight caused by degradation to the mechanical properties of PLGA. The predictions presented here show that heterogeneous degradation occurs in PLGA when the length scale of the PLGA sample results in a diffusion limited regime where autocatalysis is the dominant degradation mechanism. Consequently, scaffolds with thicker struts demonstrate a higher degradation rate due to stronger autocatalysis and they collapse more rapidly.

Acknowledgements

Funding support was provided by the Structured PhD Programme in Biomedical Engineering and Regenerative Medicine (BMERM). Funded under the Programme for Research in Third-Level Institutions (PRTLI) Cycle 5 (Strand 2) and co-funded under the European Regional Development Fund (ERDF).

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