  Following the recent discussion on the puzzling nature of the interactions in
the nanotubular system Na2V3O7, we present a detailed ab-initio microscopic
analysis of its electronic and magnetic properties. By means of a non-trivial
downfolding study we propose an effective model in terms of tubes of nine-site
rings with the geometry of a spin-diamond necklace with frustrated inter-ring
interactions. We show that this model provides a quantitative account of the
observed magnetic behavior.
