Robust measures of three-dimensional vascular tortuosity based on the minimum curvature of approximating polynomial spline fits to the vessel mid-line

Abstract

The clinical recognition of abnormal vascular tortuosity is important in the diagnosis of many diseases. This paper presents a novel approach to the quantification of vascular tortuosity, using robust metrics based on unit speed parameterizations of three-dimensional (3D) curvature. The use of approximating polynomial spline-fitting obviates the need for arbitrary filtering of mid-line data which is necessary with other tortuosity indices. The metrics were tested using both two-dimensional and three-dimensional synthesized images that mimicked clinically significant pathologies: two of the three metrics were scale invariant, additive, and produced tortuosity values tailored to be independent of the resolution of the imaging system. Our methodology is designed to explicitly handle the challenge of noisy data, and is largely tolerant of the inaccuracies in the mid-line extraction. While all the proposed metrics are sensitive to gently curved vessels, the rms curvature of the smoothest path was more effective in recognizing abnormalities involving high-frequency coiling such as occurs in malignant tumors. We have also indicated how values from two projection images, such as acquired in biplane angiography, can be combined to give an accurate approximation of the 3D value of this metric. Our proposed methodology is well-suited to automated detection and measurement, which are a prerequisite for clinical implementation.

Measurement of retinal vascular tortuosity and its application to retinal pathologies

“…We previously defined tortuosity metrics, M and K [15], in terms of a unit speed vector-valued function, f. For d [ {2, 3,4,…} let f: [a, b] ? R d be a vector-valued function such that f, f 0 and f 00 are continuous.…”

“…We previously defined robust metrics employing unit speed parameterization for quantifying vascular tortuosity in terms of three-dimensional (3-D) curvature, using approximate polynomial spline fitting to ''data balls'' centred along the mid-line axis of the vessel [15]. The method circumvents the arbitrary filtering of mid-line data needed with other methods to minimize digitization errors.…”

Methods for digital analysis of human vascular system. Literature review

“…При многих сосудистых за-болеваниях одним из признаков заболевания является изменение извилистости сосудов. Автоматическая оценка извилистости сосудов является мощным инст-рументом для раннего диагностирования заболевания сосудов [176,177]. В работах Hiroki et al [149] и Spangler et al [178] говорится, что такие заболевания, как гипертония, диабет и многие аутоиммунные забо-левания вызывают увеличение извилистости сосудов.…”

Quantification and classification of retinal vessel tortuosity

“…Lately, computer-aided image analysis of the retina was developed for the measurement of tortuosity and width of retinal veins and arteries using simulated vessels 18 . Robust metrics employing unit speed parametrization for quantifying vascular tortuosity in terms of 3-D curvature is also defined 19 . In previous work, we have defined and evaluated methods for automatic measurement of retinal vessel tortuosity in infant retinal images using PCA 20 and combination of inflection count and curvature of improved chain code 21 , and curvature based on chain code rules 22 .…”