Measuring arterial tortuosity in the cerebrovascular system using Time-of-Flight MRI

The Circle of Willis (CW) is a critical cerebrovascular structure that supports collateral blood flow to maintain brain perfusion and compensate for eventual occlusions. Increased tortuosity of highrisk vessels within the CW has been implicated as a marker in the progression of cerebrovascular diseases especially in structures like the internal carotid artery (ICA). This is partly due to age-related plaque deposition or arterial stiffening. Producing reliable tortuosity measurements for vessels segmented from magnetic resonance (MR) time-of-flight (TOF) images requires precise curvature estimation, but existent methods struggle with noisy or sparse segmentation data. We introduce an open-source, end-to-end pipeline that uses unit-speed spline fitting for accurate curvature estimation, generating robust curvature-based tortuosity metrics for the ICA combined with an indicator of spline fit quality. We test this with theoretical data and apply this method to TOF data from 22 participants. We report that our metrics are able to capture tortuosity even under heightened noise constraints and discriminate different types of abnormal arterial coiling. We found that our ICA tortuosity measures correlate positively with age and ultrasound measured carotid artery intima media thickness. This ultimately has important translational implications for being able to reliably generate TOF tortuosity measures and estimate cerebrovascular disease burden. We provide open-source code in a GitHub repository.