Clinical applications of three-dimensional tortuosity metrics

The measurement of abnormal vascular tortuosity is important in the diagnosis of many diseases. Metrics based on three-dimensional (3-D) curvature, using approximate 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. In order to establish their clinical validity we applied them to a number of clinical vascular systems, using both 2-D (standard angiograms and retinal images) and 3-D datasets (from computed tomography angiography (CTA) and magnetic resonance angiography (MRA)). Using the abdominal aortograms we found that the metrics correlated well with the ranking of an expert panel of three vascular surgeons. Both the mean curvature and the root-mean square curvature provided good discrimination between vessels of different tortuosity: and using a data ball size of one-quarter of the local vessel radius in the spline fitting gave consistent results. Tortuous retinal vessels resulting from retinitis or diabetes, but not from vasculitis, could be distinguished from normal vessels. Tortuosity values based on 3-D data sets gave higher values than their 2-D projections, and could easily be implemented in automatic measurement. They produced values sufficiently discriminating to assess the relative utility of arteries for endoluminal repair of aneurysms.