MicroCT/Micromechanics-Based Finite Element Models and Quasi-Static Unloading Tests Deliver Consistent Values for Young's Modulus of Rapid-Prototyped Polymer-Ceramic Tissue Engineering Scaffold

Abstract

A 71 volume-% macroporous tissue engineering scaffold made of poly-l-lactide (PLLA) with 10 mass-% of pseudo-spherical tri-calcium phosphate (TCP) inclusions (exhibiting diameters in the range of several nanometers) was microCT-scanned. The corresponding stack of images was converted into regular Finite Element (FE) models consisting of around 100,000 to 1,000,000 finite elements. Therefore, the attenuation-related, voxel-specific grey values were converted into TCP-contents, and the latter, together with nanoindentation tests,entered a homogenization scheme of the Mori-Tanaka type, as to deliver voxel-specific (and hence, finite element-specific) elastic properties. These FE models were uniaxially loaded, giving access to the macroscopic Young's modulus of the entire scaffold, amounting to EFE=142.86±2.68MPa. The reliability of the FE simulations was shown through comparison with results from quasi-static unloading tests on the same scaffold sample, delivering an experimental value of the longitudinal Young's modulus, Eunl=125.85±19.33MPa. The uniaxial test simulations also provided access to Poisson's ratios in the transverse material directions, which turned out to be quasi-cubic, and amounted, on average, to 0.0638±0.0136. This is much smaller than the Poisson's ratio of the solid phase made up of PLLA-TCP, which amounted to 0.44. This indicates that on the microscopic level, the pores are, on average, much more deformed, than the solid phase made of PLLA-TCP. Namely, significant (micro)deformation of the latter is restricted to the junctions between the rapid-prototyped beams making up the scaffold.