Finite element analysis of bioresorbable polymers using a thermo-mechanical co-simulation model

Abstract

Event Abstract Back to Event Finite element analysis of bioresorbable polymers using a thermo-mechanical co-simulation model Rosa Shine1, Caoimhe A. Sweeney1, Nicola Kelly1 and Peter E. Mchugh1 1 College of Engineering and Informatics, National University of Ireland Galway, Center for Biomechanics Research, Dept of Biomedical Engineering, Ireland Introduction: The recent surge in the use of bioresorbable polymers in vascular stent applications is due to their attractive biodegradable natures. Such materials, i.e. poly-L-lactide (PLLA), yield stents which gradually dissolve in-vivo, once the initial scaffolding period has passed. PLLA breaks down through hydrolytic degradation, when water enters the material and causes scission of the polymer chains into monomer products, which are naturally metabolized, leading to a loss of molecular weight. Our objective is to develop a novel computational model that captures the physical aspects of the degradation and also examines its effects on the mechanical performance of a bioresrobable PLLA scaffold. Methods: The physically-based model developed by Wang et al. (2008)[1] describes the degradation of polyesters through changes in the ester bond and monomer concentrations. In a novel approach, the governing equations of this physical model are implemented into the finite-element package Abaqus/Standard (DS SIMULIA,USA), using a thermal analogy to model the degradation of PLLA. A correlation between key events of degradation, hydrolysis of the ester bonds and diffusion of the monomers , with the transfer of heat and temperature in a physical system is established. Correspondence between degradation and thermal parameters is shown in Table 1[5]. The mechanical behavior of PLLA is described using the strain energy function proposed by Knowles(1977)[2] for a hyperelastic incompressible material; W = μ/2b { [(1+b/n(I1 - 3)]n-1} + 1/D1(J-1)2, where μ is the shear modulus, D1 governs compressibility and b and n are softening parameters. The elasticity tensor for this model has previously been derived and implemented into finite-element code by Suchocki et al. (2011)[3]. User material subroutines (UMATHT,UMAT) were applied to a cylindrical part (3mm OD; 2.8mm ID; Length=12mm) to assign the degradation parameters (Table. 1) and mechanical properties (E=3.5GPa;ν= 0.475;b=n=1)[4]. Displacement boundary conditions were applied and the monomer concentration was set to zero at a free surface, representing immediate diffusion of the monomers (Fig. 1). Coupled temperature-displacement elements were used in the mesh and a pressure load of 2atm was applied to the inner surface. Results: Fig. 2 shows the results for the PLLA cylinder, for a 6 month period. The maximum principal stress reaches its highest value at the inner surface of the cylinder (Fig. 2(a)). The ester bond concentration decreases from its initial value, to 970mol/m3 on the outer surface, whereas the monomer concentration increases on this surface. Discussion: This analysis shows it is possible to simulate the degradation and mechanical loading of a bioresorbable polymeric cylinder using finite-element techniques. Stress is generated in the cylinder at the location of the applied loading pressure. The decrease in the ester bond concentration can be attributed to hydrolysis of the polymer chains, controlled by the equations of the physically-based model, which also govern the diffusion of the monomer products. Since this coupled model provides a novel insight into the degradation of bioresorbable polymers, its further development (for example, enhancements to allow investigation of the interactions between in-vivo mechanical loading and degradation rates) and experimental validation would allow for more accurate examination of bioresorbable polymeric stents. This work was funded in part by an NUI Galway, College of Engineering and Informatics, Postgraduate Research Scholarship and a Travelling Studentship in Mechanical & Biomedical Engineering, from the National University of Ireland; The authors also wish to acknowledge the SFI/HEA Irish Centre for High-End Computing (ICHEC) for the provision of computational facilities and support