Finite element analysis of an accordion-like honeycomb scaffold for cardiac tissue engineering

Optimizing the function of tissue engineered cardiac muscle is becoming more feasible with the development of microfabricated scaffolds amenable to mathematical modeling. In the current study, the elastic behavior of a recently developed poly(glycerol sebacate) (PGS) accordion-like honeycomb (ALH) scaffold [Engelmayr et al., 2008. Nature Materials 7 (12), 1003–1010] was analyzed. Specifically, 2D finite element (FE) models of the ALH unit cell (periodic boundary conditions) and tessellations (kinematic uniform boundary conditions) were utilized to determine a representative volume element (RVE) and to retrospectively predict the elastic effective stiffnesses. An RVE of 90 ALH unit cells (≃3.18×4.03mm) was found, indicating that previous experimental uni-axial test samples were mechanically representative. For ALH scaffolds microfabricated from PGS cured 7.5 h at 160 °C, FE predicted effective stiffnesses in the two orthogonal material directions (0.081±0.012 and 0.033±0.005 MPa) matched published experimental data (0.083±0.004 and 0.031±0.002 MPa) within 2.4% and 6.4%. Of potential use as a design criterion, model predicted global strain amplifications were lower in ALH (0.54 and 0.34) versus   rectangular honeycomb (1.19 and 0.74) scaffolds, appearing to be inversely correlated with previously measured strains-to-failure. Important in matching the anisotropic mechanical properties of native cardiac muscle, FE predicted ALH scaffolds with 50μm wide PGS struts to be maximally anisotropic. The FE model will thus be useful in designing future variants of the ALH pore geometry that simultaneously provide proper cardiac anisotropy and reduced stiffness to enhance heart cell-mediated contractility.