Complexity analysis of cortical surface detects changes in future Alzheimer's disease converters

Abstract

Alzheimer's disease (AD) is a neurological disorder that creates neurodegenerative changes at several structural and functional levels in human brain tissue. The fractal dimension (FD) is a quantitative parameter that characterizes the morphometric variability of the human brain. In this study, we investigate spherical harmonic-based FD (SHFD), thickness, and local gyrification index (LGI) to assess whether they identify cortical surface abnormalities toward the conversion to AD. We study 33 AD patients, 122 mild cognitive impairment (MCI) patients (50 MCI converters and 29 MCI nonconverters), and 32 healthy controls (HC). SHFD, thickness, and LGI methodology allowed us to perform not only global level but also local level assessments in each cortical surface vertex. First, we found that global SHFD decreased in AD and future MCI converters compared to HC, and in MCI converters compared to MCI nonconverters. Second, we found that local white matter SHFD was reduced in AD compared to HC and MCI mainly in medial temporal lobe. Third, local white-matter SHFD was significantly reduced in MCI converters compared to MCI nonconverters in distributed areas, including the medial frontal lobe. Thickness and LGI metrics presented a reduction in AD compared to HC. Thickness was significantly reduced in MCI converters compared to healthy controls in entorhinal cortex and lateral temporal. In summary, SHFD was the only surface measure showing differences between MCI individuals that will convert or remain stable in the next 4 years. We suggest that SHFD may be an optimal complement to thickness loss analysis in monitoring longitudinal changes in preclinical and clinical stages of AD. Hum Brain Mapp 38:5905-5918, 2017. © 2017 Wiley Periodicals, Inc.

Keywords: Alzheimer's disease; fractal dimension; gyrification index; mild cognitive impairment; spherical harmonics; thickness.

Figure 1

3D visualization of a T1‐weighted volumetric image (A). Surfaces and maps obtained from image A through the FreeSurfer pipeline: pial surface with overlapped tessellation (B); white surface (C); thickness map (D); and local gyrification index (LGI) map (E). The original cortical surface of a right hemisphere as was obtained from FreeSurfer and the reconstructed surfaces obtained with SPHARM for the SH functions with degree l ranging from 1 to 60 (F). [Color figure can be viewed at http://wileyonlinelibrary.com]

Figure 2

(A) Global SHFD computation as the slope of the regression line of the log–log plot of surface area versus degree l of the reconstruction. Surface areas of reconstructions were normalized by the original surface area. The linear approximation shown in red corresponds to reconstructions with degrees l from 11 to 29. (B) Local SHFD computation for a vertex as the slope of the regression line of the log–log plot of average area versus degree l of the reconstruction. Average areas for the vertex in each reconstruction were normalized by the original average area for that vertex. The linear approximation shown in red corresponds to reconstructions with degrees l from 21 to 40. (D) Local SHFD map of the pial surface shown in Figure 1. (C) Local SHFD map of the white surface shown in Figure 1. [Color figure can be viewed at http://wileyonlinelibrary.com]

Figure 3

Boxplot with differences between groups for each hemisphere in Global SHFD ‐ white (A), Global SHFD ‐ pial (B), average thickness (C), and average LGI (D). P values correspond to ANCOVA analyzes with age as covariate. Only P values below 0.05 are displayed. [Color figure can be viewed at http://wileyonlinelibrary.com]

Figure 4

Vertex‐wise comparisons of white‐matter SHFD, thickness, and local gyrification index between Alzheimer's disease and elderly healthy control groups in inflated surface. Statistical analysis was controlled for age. Results were corrected for multiple comparisons using false discovery rating with q rate of 0.05. Uncorrected results are also displayed in the second row for references purposes. The color bars show the logarithmic scale of P values (−log 10). [Color figure can be viewed at http://wileyonlinelibrary.com]

Figure 5

Vertex‐wise comparisons of white‐matter SHFD, thickness, and local gyrification index between Alzheimer's disease and mild cognitive impairment groups in inflated surface. Statistical analysis was controlled for age. Results were corrected for multiple comparisons using false discovery rating with q rate of 0.05. Uncorrected results are also displayed in the second row for reference purposes. The color bars show the logarithmic scale of P values (−log 10). [Color figure can be viewed at http://wileyonlinelibrary.com]

Figure 6

Vertex‐wise comparisons between mild cognitive impairment converters and mild cognitive impairment nonconverters groups for white‐matter SHFD (A), and vertex‐wise comparisons between mild cognitive impairment converters and elderly healthy control groups for thickness in inflated surface (B). Statistical analysis was controlled for age. Results were corrected for multiple comparisons using false discovery rating with q rate of 0.05. Uncorrected results are also displayed in the second row for reference purposes. The color bars show the logarithmic scale of P values (−log 10). [Color figure can be viewed at http://wileyonlinelibrary.com]

Figure 7

Vertex‐wise partial correlations, with age as nuisance covariate, between cortical measures and MMSE for AD plus MCI. Results were corrected for multiple comparisons using false discovery rating with q rate of 0.05. The color bars show the logarithmic scale of P values (−log 10). [Color figure can be viewed at http://wileyonlinelibrary.com]