Improving blood vessel tortuosity measurements via highly sampled numerical integration of the Frenet-Serret equations*

Measures of vascular tortuosity, how curved and twisted a vessel is, are associated with a variety of vascular diseases. Consequently, accurate measurements of vessel tortuosity are greatly needed yet have proven problematic. Some researchers do not measure it at all, and others' results have been mismeasured, null, or contradictory. We present a new method that ensures accurate measurement of vessel tortuosity from medical image data that relies on numerical integration of the Frenet-Serret equations. By reconstructing vessel coordinates from tortuosity measurements, our approach identifies a minimally-sufficient sampling rate based on vessel radius. This work further identifies a key failing in current practices of filtering asymptotic measurements, and also highlights inconsistencies bewteen existing tortuosity metrics. We demonstrate the utility of our method on published data for a range of healthy human vessels including: cerebral and coronary vascular networks and individual carotid, abdominal, renal and illiac arteries. Preliminary application to disease data will also be discussed.