Let S N be an immersed horizontal surface in a 3dimensional graph manifold. We show that the fundamental group of the surface S is quadratically distorted whenever the surface is virtually embedded (i.e., separable) and is exponentially distorted when the surface is not virtually embedded.

A polyol method was used to obtain ultrasmall ZnO nanoparticles (NPs) doped with iron ions and coated with a low molecular weight fucoidan in order to perform in vivo MR and ex vivo fluorescence imaging of athrothrombosis. During the synthesis, the early elimination of water by azeotropic distillation with toluene allowed us to produce NPs which size, determined by XRD and TEM, decreased from 7 nm to 4 nm with the increase of iron/zinc ratios from 0.05 to 0.50 respectively. For the highest iron content (NP-0.50) NPs were evidenced as a mixture of nanocrystals made of wurtzite and cubic phase with a molar ratio of 2.57:1, although it was not possible to distinguish one from the other by TEM. NP-0.50 were superparamagnetic and exhibited a large emission spectrum at 470 nm when excited at 370 nm. After surface functionalization of NP-0.50 with fucoidan (fuco-0.50), the hydrodynamic size in the physiological medium was 162.0 ± 0.4 nm, with a corresponding negative zeta potential of −48.7 ± 0.4 mV, respectively. The coating was evidenced by FT-IR spectra and thermogravimetric analysis. Aqueous suspensions of fuco-0.50 revealed high transverse proton relaxivities (T2) with an r2 value of 173.5 mM−1 s−1 (300 K, 7.0 T) and remained stable for more than 3 months in water or in phosphate buffer saline without evolution of the hydrodynamic size and size distribution. No cytotoxic effect was observed on human endothelial cells up to 48 h with these NPs at a dose of 0.1 mg/mL. After injection into a rat model of atherothrombosis, MR imaging allowed the localization of diseased areas and the subsequent fluorescence imaging of thrombus on tissue slices.