Semi-automatic measurements and description of the geometry of vascular tree based on Bézier spline curves: application to cerebral arteries

Abstract

BackgroundThe geometry of the vessels is easy to assess in novel 3D studies. It has significant influence on flow patterns and this way the evolution of vascular pathologies such as aneurysms and atherosclerosis. It is essential to develop robust system for vascular anatomy measurement and digital description allowing for assessment of big numbers of vessels.MethodsA semiautomatic, robust, integrated method for vascular anatomy measurements and mathematical description are presented. Bezier splines of 6th degree and continuity of C3 was proposed and distribution of control points was dependent on local radius. Due to main interest of our institution, the system was primarily used for the assessment of the geometry of the intracranial arteries, especially the first Medial Cerebral Artery division.Results1359 synthetic figures were generated: 381 torus and 978 spirals. Experimental verification of the proposed methodology was conducted on 400 Middle Cerebral Artery divisions.ConclusionsIn difference to other described solution all proposed methodology steps were integrated allows analysis of variability of geometrical parameters among big number of Medial Cerebral Artery bifurcations using single application. This allows for determination of significant trends in the parameters variability with age and in contrary almost no differences between men and women.

Age‐ and gender‐dependent variability in the geometry of middle cerebral artery bifurcations

“…All planned measurements were performed and data stored using dedicated software to increase precision and avoid most human‐dependent errors (3D Reconstructor; Żyłkowski et al, 2018).…”

“…We assumed that both will be calculated over the course of the division bend, which contains the point of split of the CLs leading from the trunk into the two branches. In mathematical terms, the bend was defined as part of a curve containing the division point and extending between the two minima of the curvature (Żyłkowski et al, 2018).…”

“…The fitting algorithm was a 3D extension of the 2D algorithm postulated by Pastva (1998). CL smoothing was an additional result of this transformation (Żyłkowski et al, 2018).…”

“…All developed tools and algorithms were described in our previous work concerning tools for the analysis of vascular geometry (Żyłkowski et al, 2018), and only key features will be presented in this study.…”

“…A detailed analysis of the algorithms used is presented in our previous study (Żyłkowski et al, 2018). In this section, we present the results of additionally performed validation on artificial models and real‐life CTA studies.…”