Evaluation of the 3D fractal dimension as a marker of structural brain complexity in multiple-acquisition MRI

Fractal analysis, i.e. the estimation of an object's fractal dimension (FD) as a marker of its morphometric complexity, has attracted increasing interest as a versatile tool for the analysis of structural neuroimaging data in both health and disease. However, a number of important methodological questions regarding fractal analysis in magnetic resonance images have so far remained unaddressed. This includes the stability of the FD over repeated within-subject measurements, i.e. the susceptibility of fractal analysis to noise, a formal assessment of its sampling distribution, and the impact of image acquisition and processing parameters. Importantly, fractal analysis has not yet been explored in detail in T2 contrast images. To address these issues, we analyzed structural images from the recently published MASSIVE data set (Multiple Acquisitions for Standardization of Structural Imaging Validation and Evaluation). We conduct a fine-grained stratification of image parameters, leading to 32 distinct analysis groups as a combination of image contrast, spatial resolution, segmentation procedures, tissue type, and image complexity. We estimate 3D tissue models based on the thus obtained input volumes and compute the FDs as the box-counting regression on these models. Furthermore, we present a detailed deviation analysis including resampling methods, composite normality assessment, outlier detection, and multivariate comparisons to establish the susceptibility of the FD to noise. We find that in both T1 and T2 contrasts, the FD of gray matter (GM) segmentations was generally higher than in white matter volumes (WM). FDs in both image contrasts were sampled in comparable range and showed similar responses to processing parameters, e.g. as regards the effects of binary vs. partial volume segmentation and a decrease in FD by image skeletization. Lower spatial resolution invariably resulted in decreased FDs in unskeletized images, while the response depended on the segmentation procedure in image skeletons. Furthermore, in multiple measurements, the FD can be assumed to be sampled from an underlying normal distribution. We tested different options for a sensible within-group deviation criterion and found that outlier detection by Grubbs testing and a 2 standard-deviation interval around the sample mean performed very well in this regard. Even with the more conservative threshold, the overall robustness of the FD to noise was well above 90 %. Most deviations were found in T1-weighted images, and binarized image skeletons were most susceptible to deviations. Importantly, our analysis was able to detect sample-wise deviation clusters, and we identify image registration as a source of noise in fractal analysis. Interestingly, registration-induced deviations were limited to T1-weighted images, lending even further support for the usefulness of T2 contrast in fractal analysis. In conclusion, we provide detailed evidence for the stability of the FD as a marker of structural brain complexity and its parameter-dependent characteristics in magnetic resonance images and thus contribute to the development of fractal analysis as a scientifically and clinically useful neuroimaging tool.