Clinical validation of three-dimensional tortuosity metrics based on the minimum curvature of approximating polynomial splines

The clinical recognition of abnormal vascular tortuosity is important in the diagnosis of many diseases. Metrics based on three-dimensional (3D) curvature, using approximating polynomial spline-fitting to “data balls” centered along the mid-line of the vessel, minimize digitization errors and give tortuosity values largely independent of the resolution of the imaging system. We applied two of these metrics to a number of clinical vascular systems, using both 2D and 3D datasets. Using abdominal aortograms of low tortuosity, we established their validity by their strong correlation with the ranking of an expert panel of three vascular surgeons. The values of the Spearman rank correlation coefficient between our rankings, using a data ball radius of one-quarter of the local vessel radius, and the average ranking of the expert panel were 0.96 (with a 95% confidence interval of [0.91, 0.99]) for the mean curvature and 0.98 ([0.94, 0.99]) for the root-mean-square (RMS) curvature. These confidence intervals indicate that our automated analysis is producing rankings whose reliability is similar to that of a human expert, and is significantly better than that achieved with existing algorithms. The metrics provided good discrimination between vessels of different tortuosity for both 2D and 3D datasets, and produced values sufficiently discriminating to assess the relative utility of arteries for endoluminal repair of aneurysms.