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. 2021 Dec 1;11:23202. doi: 10.1038/s41598-021-02495-6

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© The Author(s) 2021

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 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/.

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Computing lacunarity and fractal dimension (FD) and testing the statistical significance of these against patient survival data. (A) As an example, lacunarity and FD are computed on each slice of T1Gd necrosis segmentations. The median of these values is stored, giving one value of lacunarity and FD for each patient. We do the same for T1Gd enhancement with necrosis, and T2/FLAIR edematous regions. (B) Individual median values are collated into a cohort analysis. Each median value that does not split the cohort into groups of less than 10% of the cohort size is then tested as a cutoff to distinguish either overall survival or progression free survival. A log-rank test provides a significance value for each potential cutoff and a log-rank statistic is calculated alongside a separate significance threshold that accounts for multiple comparisons. The maximal log-rank statistic is chosen as this maximally distinguishes the two groups. This is carried out for lacunarity and FD, across necrosis, enhancement with necrosis, and edema regions.