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. 2017 Oct 5;7:12727. doi: 10.1038/s41598-017-13097-6

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© The Author(s) 2017

Open Access This 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 license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license 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 license, visit http://creativecommons.org/licenses/by/4.0/.

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Algorithm to quantify image volume distortion. (a) Co-register via a 3-D translation transform the two volumes to be assessed (e.g. DWI and T2W) leaving the resulting volumes interpolated to the same coordinate space. (b) For each slice, align volume sections so that their centroids are coincident recording the translation T _s(slice) necessary to achieve this. (c) Calculate the local radial distortion vector d(slice, ϕ) at the surface of each volume section using cylindrical polar coordinates. Also calculate the resultant distortion vector d _res(slice, ϕ) = d(slice, ϕ) + T _s(slice). (d) Express total distortion at surface as a root-mean-square value d_rms for both d and d _res. (e) Show the results graphically as a colour-coded 3-D surface distortion map together with a ‘tree’ of slice centroid translations.