A comparison of quantitative measures of arterial tortuosity using sine wave simulations and 3D wire models

This paper discusses the quantitative measurement of arterial tortuosity. The measures described are a tortuosity coefficient, TC, based on the second derivative of the vessel midline and the distance factor, DF, defined as L/D - 1, where L is the vessel length and D is the straight line distance between the vessel end points. A tortuosity scale derived from sine wave simulations was used to determine the ability of these two measures to quantify tortuosity. The tortuosity coefficient was demonstrated to be an appropriate measure whilst the distance factor was found to be a measure of vessel elongation rather than tortuosity. A tomographic method of deriving three-dimensional measures of TC and DF is described using a wire model. The x, y coordinates along the length of the wire were obtained from CT slices and the three-dimensional values calculated as the geometric mean of the TC and DF values measured in the x and y directions. Rotation of the wire through 90 degrees demonstrated that the three-dimensional derivations of TC and DF were independent of the orientation of the wire.