Novel magnetic iron oxide nanoparticles coated with poly(ethylene imine)-g-poly(ethylene glycol) for potential biomedical application: synthesis, stability, cytotoxicity and MR imaging

Magnetic iron oxide nanoparticles have found application as contrast agents for magnetic resonance imaging (MRI) and as switchable drug delivery vehicles. Their stabilization as colloidal carriers remains a challenge. The potential of poly(ethylene imine)-g-poly(ethylene glycol) (PEGPEI) as stabilizer for iron oxide (γ-Fe₂O₃) nanoparticles was studied in comparison to branched poly(ethylene imine) (PEI). Carrier systems consisting of γ-Fe₂O₃-PEI and γ-Fe₂O₃-PEGPEI were prepared and characterized regarding their physicochemical properties including magnetic resonance relaxometry. Colloidal stability of the formulations was tested in several media and cytotoxic effects in adenocarcinomic epithelial cells were investigated. Synthesized γ-Fe₂O₃ cores showed superparamagnetism and high degree of crystallinity. Diameters of polymer-coated nanoparticles γ-Fe₂O₃-PEI and γ-Fe₂O₃-PEGPEI were found to be 38.7 ± 1.0 nm and 40.4 ± 1.6 nm, respectively. No aggregation tendency was observable for γ-Fe₂O₃-PEGPEI over 12 h even in high ionic strength media. Furthermore, IC₅₀ values were significantly increased by more than 10-fold when compared to γ-Fe₂O₃-PEI. Formulations exhibited r₂ relaxivities of high numerical value, namely around 160 mM⁻¹ s⁻¹. In summary, novel carrier systems composed of γ-Fe₂O₃-PEGPEI meet key quality requirements rendering them promising for biomedical applications, e.g. as MRI contrast agents.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes

We introduce and analyze hp-version discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems in three-dimensional polyhedral domains. To resolve possible corner-, edge- and corner-edge singularities, we consider hexahedral meshes that are geometrically and anisotropically refined toward the corresponding neighborhoods. Similarly, the local polynomial degrees are increased linearly and possibly anisotropically away from singularities. We design interior penalty hp-dG methods and prove that they are well-defined for problems with singular solutions and stable under the proposed hp-refinements. We establish (abstract) error bounds that will allow us to prove exponential rates of convergence in the second part of this work.