A quantitative index for the measurement of the tortuosity of blood vessels

We propose a novel index for quantitating arterial tortuosity, based on second differences of the coordinates of the vessel midline. The index is independent of the magnification of the image and of sampling frequency. We have demonstrated its validity as an indicator of changes in morphology using simulated shapes. It is superior to two other putative indices based on vessel elongation and the variance of differences in the vessel midline coordinates, presented previously in the literature. The proposed index is easily generalised to three dimensions, allowing a true three-dimensional tortuosity index to be calculated from biplane angiograms or serial tomographic slices. It has a number of clinical applications. Preliminary data, using 82 aortograms from radiographic archives, showed a significant correlation between the tortuosity of the abdominal aorta and subject age (r=0.684, P<0.001). For this group, increased tortuosity was especially evident for subjects above 40 yr of age.