Identification of inflection points and filtering torsion spikes in digitally reconstructed vessels improves tortuosity estimates of cardiovascular data

Measures of arterial and blood vessel tortuosity (e.g. curvature and torsion) are strongly linked with a suite of cardiovascular diseases. Examples include: broad “C”- and “S”- shaped vessels associated with hypertension and atherosclerosis; tight clustering associated arteriovenous malformations; and helical coiling associated with malignant tumors. Current methods of measuring vessel torsion are error prone when encountering inflection points. Using the Frenet-Serret Theorem of Curves, estimates of torsion exhibit singular behavior at inflection points due to the vanishing second- and third-order derivatives of the blood vessel position vector. We present numerical methods for solving the Frenet-Serret system of equations to identify inflection points and filter spikes in torsion estimates. We apply this method to real blood vessel data from the human torso, head, and brain and demonstrate order of magnitude reductions in estimates of the maximum torsion. We discuss further implications for other common tortuosity metrics (e.g. sum of all angles), and applications toward classification methods for disease diagnostics.