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. 2020 Apr 15;15:91. doi: 10.1186/s13023-020-01369-w

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© The Author(s) 2020

Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.

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Fig. 2 — Schematic illustration of the algorithms used to calculate tortuosity metrics as described by Bullitt et al. Distance Metric (DM) provides a ratio between the actual path length of a meandering curve (L, blue centerline) and the linear distance (D, green straight line segment) between the endpoints (a). Inflection count metric (ICM) is calculated by counting the inflection points, so those points where the curve changes from convex to concave (highlighted as yellow dots in the picture). The number of inflection points (N) is normalized by multiplying it by the DM (b). Sum of angles metric (SOAM) is assessed by subdividing the arterial centerline into small segments (T_1-3, white arrows) and summing the in-plane (IP_k) and torsional angles (TP_k) between these segments (c)