Efficient estimation of 3-dimensional centerlines of inner carotid arteries and their curvature functions by free knot regression splines

This work stems from the need for accurate estimation of the curvature function of an artery, that emerged within ANEURISK Project, a research program that aims at investigating the role of vascular morphology and hemodynamics on the pathogenesis of cerebral aneurysms. We develop here a regression technique that exploits free knot splines in a novel setting, to estimate 3-dimensional curves, and their derivatives. We thoroughly compare this technique to a classical regression method, local polynomial smoothing, showing that 3-dimensional free knot regression splines yield more accurate and efficient estimates.