Tortuosity and other vessel attributes for arterioles and venules of the human cerebral cortex.

Despite its demonstrated potential in the diagnosis and/or staging of disease, especially in oncology, tortuosity has not received a formal and unambiguous clinical definition yet. Using idealized three-dimensional vessel models (wavy helices) with known characteristics, we first demonstrate that, among various possible tortuosity indices, the standard deviation of the curvature Ksd best satisfies i) scale invariance and ii) positive monotonic response with respect to the amplitude and frequency of vessel oscillations. Ksd can thus be considered as a robust measure of tortuosity. On the contrary, indices previously considered as tortuosity metrics, such as the distance factor metrics (DFM), are highly scale dependent and inappropriate for that purpose. The tortuosity and other vessel attributes (curvature, length-to-diameter ratio (LDR),…) of more than 15,000 cortical vessels are subsequently studied, establishing their statistical properties as a function of the vessel nature (arterioles versus venules) or topological order (hierarchical position). In particular, arterioles have a higher LDR than venules, but the two kinds of vessels have the same mean curvature and tortuosity. Moreover, the lower the order of the vessels, i.e. the nearer to the capillary network, the more curved and tortuous they are. These results provide an essential reference both for diagnosis and for a future large reconstruction of the cerebral microvascular network.