Computer aided design and finite element modeling to predict bulk mechanical properties of bone scaffolds using triply periodic minimal surfaces (progettazione assistita al calcolatore ed analisi con il metodo degli elementi finiti per predire il comportamento meccanico di scaffolds ossei creati con l'uso di superfici minime periodiche in tre direzioni)

The aim of Tissue Engineering is to develop biological substitutes that will restore lost morphological and functional features of diseased or damaged portions of organs. Recently computer-aided technology has received considerable attention in the area of tissue engineering and the advance of additive manufacture (AM) techniques has significantly improved control over the pore network architecture of tissue engineering scaffolds. To regenerate tissues more efficiently, an ideal scaffold should have appropriate porosity and pore structure. More sophisticated porous configurations with higher architectures of the pore network and scaffolding structures that mimic the intricate architecture and complexity of native organs and tissues are then required. This study adopts a macro-structural shape design approach to the production of open porous materials (Titanium foams), which utilizes spatial periodicity as a simple way to generate the models. From among various pore architectures which have been studied, this work simulated pore structure by triply-periodic minimal surfaces (TPMS) for the construction of tissue engineering scaffolds. TPMS are shown to be a versatile source of biomorphic scaffold design. A set of tissue scaffolds using the TPMS-based unit cell libraries was designed. TPMS-based Titanium foams were meant to be printed three dimensional with the relative predicted geometry, microstructure and consequently mechanical properties. Trough a finite element analysis (FEA) the mechanical properties of the designed scaffolds were determined in compression and analyzed in terms of their porosity and assemblies of unit cells. The purpose of this work was to investigate the mechanical performance of TPMS models trying to understand the best compromise between mechanical and geometrical requirements of the scaffolds. The intention was to predict the structural modulus in open porous materials via structural design of interconnected three-dimensional lattices, hence optimising geometrical properties. With the aid of FEA results, it is expected that the effective mechanical properties for the TPMS-based scaffold units can be used to design optimized scaffolds for tissue engineering applications. Regardless of the influence of fabrication method, it is desirable to calculate scaffold properties so that the effect of these properties on tissue regeneration may be better understood.

Synthesis and characterization of hydroxyapatite modified with (9r)-9-hydroxystearic acid

(9R)-9-hydroxystearic acid (9R-HSA) has been proven to have antitumoral activity because it is shown to inhibit histone deacetylase 1, an enzyme which activates DNA replication, and the (R)-enantiomer has been shown to be more active than the (S)-enantiomer both in vitro and by molecular docking. Hydroxyapatite is the main mineral component of bone and teeth and has been used for over 20 years in prostheses and their coating because it is biocompatible and bioactive. The goal of incorporating 9R-HSA into hydroxyapatite is to have a material that combines the bioactivity of HA with the antitumoral properties of 9R-HSA. In this work, 9R-HSA and its potassium salt were synthesized and the latter was also incorporated into hydroxyapatite. The content of (R)-9-hydroxystearate ion incorporated into the apatitic structure was shown to be a function of its concentration in solution and can reach values higher than 8.5%. (9R)-9-hydroxystearic acid modified hydroxyapatite was extensively characterized to determine the effect of the incorporation of the organic molecule. This incorporation does not significantly alter the unit cell but reduces the size of both the crystals as well as the coherent domains, mainly along the a-axis of hydroxyapatite. This is believed to be due to the coordination of the negatively charged carboxylate group to the calcium ions which are more exposed on the (100) face of the crystal, therefore limiting the growth mainly in this direction. Further analyses showed that the material becomes hydrophobic and more negatively charged with the addition of 9R-HSA but both of these properties reach a plateau at less than 5% wt of 9R-HSA.

Dispersion and energy relations in periodic chains and grids

In this study wave propagation, dispersion relations, and energy relations for linear elastic periodic systems are analyzed. In particular, the dispersion relations for monoatomic chain of infinite dimension are obtained analytically by writing the Block-type wave equation for a unit cell in order to capture the dynamic behavior for chains under prescribed vibration. By comparing the discretized model (mass-spring chain) with the solid bar system, the nonlinearity of the dispersion relation for chain indicates that the periodic lattice is dispersive in contrast to the continuous rod, which is non dispersive. Further investigations have been performed considering one-dimensional diatomic linear elastic mass-spring chain. The dispersion relations, energy velocity, and group velocity have been derived. At certain range of frequencies harmonic plane waves do not propagate in contrast with monoatomic chain. Also, since the diatomic chain considered is a linear elastic chain, both of the energy velocity and the group velocity are identical. As long as the linear elastic condition is considered the results show zero flux condition without residual energy. In addition, this paper shows that the diatomic chain dispersion relations are independent on the unit cell scheme. Finally, an extension for the study covers the dispersion and energy relations for 2D- grid system. The 2x2 grid system show a periodicity of the dispersion surface in the wavenumber domain. In addition, the symmetry of the surface can be exploited to identify an Irreducible Brillouin Zone (IBZ). Compact representations of the dispersion properties of multidimensional periodic systems are obtained by plotting frequency as the wave vector’s components vary along the boundary of the IBZ, which leads to a widely accepted and effective visualization of bandgaps and overall dispersion properties.