Participants in the S259 sample

Two hundred fifty-nine participants (138 males) between 18 and 40 years of age (M = 24.31, SD = 4.41) took part in the study. Since this is the first study to investigate the microstructural correlates of intelligence using NODDI, it was not possible to estimate the necessary sample size a priori based on existing literature. Instead, we collected data from a reasonably large sample and computed the achieved power post hoc using G*Power56. The analysis was based on the multiple regression model reported for sample S259 (Table 1) (f2 = 0.16, α = 0.05, 10 predictors, 259 participants) and yielded a power of 0.99, thereby indicating sufficient sample size. Two hundred thirty-five participants were right-handed and the remaining 24 participants were left-handed as measured by the Edinburgh Handedness Inventory57. This ratio is representative of the human population58. All participants had normal or corrected-to-normal vision and hearing. They were either paid for their participation or received course credit. All participants were naive to the purpose of the study and had no former experience with the administered intelligence test. Participants had no history of psychiatric or neurological disorders and matched the standard inclusion criteria for fMRI examinations. Each participant completed the matrix-reasoning test and neuroimaging measurement described below. All behavioral and neuroimaging variables used for analyses on the whole-brain level were normally distributed according to a Kolmogorov–Smirnov test. All data were checked for extreme outliers as defined by Tukey’s fences59 (observations three interquartile ranges below the first or above the third quartile, respectively), but none were found. Thus, no observations were excluded. The study was approved by the local ethics committee of the Faculty of Psychology at Ruhr-University Bochum. All participants gave their written informed consent and were treated in accordance with the declaration of Helsinki.

Participants in the S498 sample

For the purpose of validating the results obtained from sample S259, recruited at Ruhr-University Bochum, we downloaded additional data provided by the Human Connectome Project, namely, the “S500 plus MEG2” release25. This set includes 506 participants with data suitable for our analyses. We excluded eight participants because of extreme outliers being detected in their behavioral or neuroimaging data59. Thus, all of the reported analyses were performed on data from 498 participants (202 males) between 22 and 36 years of age (M = 29.16, SD = 3.48). Again, we performed a post hoc analysis using G*Power56 in order to compute the achieved power. Based on the multiple regression model reported for sample S498 (Supplementary Table 4) (f2 = 0.09, α = 0.05, 10 predictors, 498 participants), the analysis resulted in a power of 0.99 and indicated sufficient sample size. As with sample S259, all neuroimaging variables used for analyses on the whole-brain level were normally distributed according to a Kolmogorov–Smirnov test. The PMAT24 test scores did not follow a normal distribution but were slightly skewed to the left. For the sake of comparability, sample S498 was analyzed in the same way as sample S259.

Acquisition of behavioral data in the S259 sample

The acquisition of behavioral data was conducted in a group setting of up to six participants, seated at individual tables, in a quiet and well-lit room. Intelligence was measured with a German matrix-reasoning test called BOMAT21, which is widely used in neuroscientific research60,61,62. The test examines non-verbal mental abilities that contribute to intelligence and is similar to Raven’s Advanced Progressive Matrices9. We conducted the “advanced short version” of the BOMAT, which has the advantage of high discriminatory power in samples with generally high intellectual abilities, thus avoiding possible ceiling effects60. The BOMAT inventory comprises two parallel test forms (A and B) with 29 matrix-reasoning items each. Participants had to complete only one of the two test forms, which were randomly assigned. Split-half reliability of the BOMAT is 0.89, Cronbach’s α is 0.92, and parallel-forms reliability between A and B is 0.8621. Additionally, convergent and predictive validity are given for both BOMAT test forms since they are strongly correlated with other intelligence inventories (r = 0.59), tests of perceptual speed (r = 0.51), and German high school GPA (r = −0.35)21. The recent norming sample consists of about 2100 individuals with an age range between 18–60 years and equal sex representation.

Acquisition of behavioral data in the S498 sample

As with sample S259, intelligence was measured with a matrix-reasoning test, namely, the Penn Matrix Analysis Test (PMAT24)26. This instrument is included in the Computerized Neuropsychological Test Battery provided by the University of Pennsylvania (PennCNP). The PMAT24 is an abbreviated version of the Raven’s Progressive Matrices and includes 24 items of increasing difficulty. Each matrix pattern is made up of 2 × 2, 3 × 3, or 1 × 5 arrangements of squares with one of the squares missing. The participant must pick one of five response choices that best fits the missing square on the pattern. There is no time limit to the completion of the test, although the task discontinues if the participant makes five incorrect responses in a row. The PMAT24 has two test forms of which the Human Connectome Project only used one (form A) in order to assess intelligence.

Acquisition of imaging data in the S259 sample

All imaging data were acquired at the Bergmannsheil hospital in Bochum (Germany) using a Philips 3T Achieva scanner with a 32-channel head coil.

For the purpose of segmenting brain scans into gray and white matter segments as well as for the identification of anatomical landmarks, a T1-weighted high-resolution anatomical image was acquired (MP-RAGE, TR = 8179 ms, TE = 3.7 ms, flip angle = 8°, 220 slices, matrix size = 240 × 240, voxel size = 1 × 1 × 1 mm). The acquisition time of the anatomical image was 6 min.

For the analysis of NODDI coefficients, diffusion-weighted images were acquired using echo planar imaging (TR = 7652 ms, TE = 87 ms, flip angle = 90°, 60 slices, matrix size = 112 × 112, voxel size = 2 × 2 × 2 mm). Diffusion weighting was based on a multi-shell, high-angular-resolution scheme consisting of diffusion-weighted images for b-values of 1000, 1800, and 2500 s/mm2, respectively, applied along 20, 40, and 60 uniformly distributed directions. All diffusion directions within and between shells were generated orthogonal to each other using the MASSIVE toolbox63. Additionally, eight data sets with no diffusion weighting (b = 0 s/mm²) were acquired as an anatomical reference for motion correction and computation of NODDI coefficients. The acquisition time of the diffusion-weighted images was 18 min.

Acquisition of imaging data in the S498 sample

All imaging data included in sample S498 were acquired on a customized Siemens 3T Connectome Skyra scanner housed at Washington University in St. Louis using a standard 32-channel Siemens receive head coil. Anatomical and diffusion-weighted imaging were carried out on two separate days with a mock scanner practice preceding the anatomical imaging on the first day. The Human Connectome Project’s imaging hardware and protocols are documented elaborately in the reference manual for the “S500 plus MEG2” release.

A T1-weighted high-resolution anatomical image was acquired by means of an MP-RAGE sequence and the following parameters: TR = 2400 ms, TE = 2.14 ms, flip angle = 8°, matrix size = 224 × 224, voxel size = 0.7 × 0.7 × 0.7 mm. The acquisition time of the anatomical image was 7 min and 40 s.

The Human Connectome Project provides diffusion-weighted data suitable for the analysis of NODDI coefficients. The respective images were acquired using echo planar imaging and the following parameters: TR = 5520 ms, TE = 89.5 ms, flip angle = 78°, 111 slices, matrix size = 168 × 144, voxel size = 1.25 × 1.25 × 1.25 mm. The diffusion-weighted imaging session included six runs based on three different gradient tables once acquired in the right-left and left-right phase-encoding direction. The gradient tables included 90 diffusion weighting directions and six acquisitions with b = 0 s/mm² interspersed throughout each run. As with the data obtained for sample S259, diffusion weighting consisted of three shells, in this case b = 1000, 2000, and 3000 s/mm² interspersed with an approximately equal number of acquisitions on each shell within each run. Each of the six runs lasted approximately 9 min and 50 s, thereby, overall acquisition time amounted to about an hour.

Analysis of imaging data in the S259 sample

We used published surface-based methods in FreeSurfer (http://surfer.nmr.mgh.harvard.edu, version 5.3.0) to reconstruct the cortical surfaces of the T1-weighted images. The details of this procedure have been described elsewhere22,23. The automated reconstruction steps included skull stripping, gray and white matter segmentation, as well as reconstruction and inflation of the cortical surface. After preprocessing, each individual segmentation was quality controlled slice by slice and inaccuracies for the automated steps were corrected by manual editing if necessary. The automated brain segmentation yielded an estimate of the overall cortical volume (VOL Cortex ) and the overall white matter volume (VOL WM ). For the purpose of analyzing our data with regard to structure–function relationships on the level of single brain regions, we utilized the Human Connectome Project’s multi-modal parcellation (HCPMMP)37. This parcellation scheme delineates 180 cortical brain regions per hemisphere and is based on the cortical architecture, function, connectivity, and topography from 210 healthy individuals. The original data provided by the HCP were converted to annotation files matching the standard cortical surface in FreeSurfer called fsaverage. This fsaverage parcellation was transformed to each participant’s individual cortical surface and converted to volumetric masks. In a final step, the two segments delineating the overall cortex and white matter as well as the 360 masks representing single cortical brain regions yielded by the HCPMMP were linearly transformed into the native space of the diffusion-weighted images (Fig. 1, left box). The transformed regions served as anatomical landmarks from which NODDI coefficients were extracted (Fig. 1, right box).

Diffusion images were preprocessed using FDT (FMRIB’s Diffusion Toolbox) as implemented in FSL version 5.0.7. Preprocessing steps included a correction for eddy currents and head motion using the eddy_correct tool. Subsequently, gradient directions were corrected to account for any reorientations in the eddy_correct output. NODDI coefficients were computed using the AMICO toolbox24. The AMICO approach is based on a convex optimization procedure that converts the non-linear fitting into a linear optimization problem24. This reduces processing time dramatically64. Data analysis with NODDI can be applied to cortical regions as well as white matter structures. However, it is necessary to optimize the NODDI model for the purpose of analyzing gray matter structures since different types of brain tissue may vary considerably with regard to their intrinsic free diffusivity18,65,66. Because of this, we adjusted the AMICO toolbox and changed its respective parameter for intrinsic free diffusivity to 1.1 × 10−3 mm2/s for analyzing gray matter structures and utilized the toolbox’ default setting of 1.7 × 10−3 mm2/s for the analysis of white matter. The NODDI technique is based on a two-level approach and features a three-compartment model distinguishing intra-neurite, extra-neurite, and CSF environments. First, the diffusion signal obtained by the multi-shell high-angular-resolution imaging protocol is used to determine the proportion of free moving water within each voxel15,16,17,24,67. This ratio is termed isotropic volume fraction and reflects the amount of isotropic diffusion with gaussian properties likely to be found in the CSF of gray (ISO Cortex ) and white matter (ISO WM ) regions. Second, the remaining portion of the diffusion signal is attributed to either intra-neurite environments or extra-neurite environments15,16,17. The proportion of intra-neurite environments is quantified as the intra-neurite volume fraction (INVF). INVF represents the amount of stick-like or cylindrically symmetric diffusion that is created when water molecules are restricted by the membranes of neurites. In white matter structures this kind of diffusion (INVF WM ) is likely to resemble the proportion of axons. In gray matter regions (INVF Cortex ) it serves as an indicator of dendrites and axons forming the neuropil. Extra-neurite environments are characterized by hindered diffusion and are usually occupied by various types of glial cells in white matter structures and both neurons and glial cells in gray matter regions15,16,17.

Neurite orientation dispersion is a tortuosity measure coupling the intra-neurite space and the extra-neurite space, resulting in alignment or dispersion of axons in white matter (ODI WM ) or axons and dendrites in gray matter (ODI Cortex )17,67. Examples of INVF, ODI, and ISO coefficient maps from a representative individual are illustrated in Fig. 1, right box. As described above, the cortical and white matter regions defined for the T1-weighted anatomical scans were transformed into the native space of the diffusion-weighted images to compute NODDI coefficients for areas across the whole brain.

Analysis of imaging data in the S498 sample

The analyses of anatomical and diffusion-weighted data from sample S498 were carried out in the same way as described for sample S259. The only differences in analyses were found in their preprocessing. For example, the Human Connectome Project utilizes a combination of the FSL tools topup and eddy in order to correct for eddy currents, head motion, and EPI distortions simultaneously. These tools represent an updated version of the eddy_correct tool used for the S259 sample and make use of the fact that one-half of the HCP’s diffusion-weighted data was acquired in the right-left phase-encoding direction and the other half in the left-right phase-encoding direction. The HCP’s preprocessing pipelines for anatomical and diffusion-weighted data are detailed in the reference manual for the “S500 plus MEG2” release as well as in Glasser, Sotiropoulos68.

Matching single brain regions against the P-FIT model

Subsequent to the analysis of structure–function relationships on the level of single brain regions, all brain regions showing statistically significant associations between NODDI coefficients and intelligence were matched against the P-FIT model6,19. To this end we employed a cortical parcellation based on Brodmann areas69, which is included as annotation files named “lh.PALS_B12_Brodmann” and “rh.PALS_B12_Brodmann” in FreeSurfer. By using FreeSurfer’s aparc2aseg tool, both files were converted to a volumetric segmentation matching the cortex of the fsaverage standard brain. The same was done to the HCPMMP annotation file. By means of an in-house Matlab program, each brain region included in the HCPMMP was assigned to one of the Brodmann areas. This was done by comparing each voxel within a HCPMMP region to its corresponding voxel from the Brodmann segmentation. The Brodmann area showing the largest overlap with the respective HCPMMP region was identified in terms of number of matching voxels. In the original version proposed by Jung and Haier6, the P-FIT features a network of 14 Brodmann areas. In an updated version by Basten et al.19 the network’s composition was confirmed, but also extended to five additional Brodmann areas. If our partial correlation analyses yielded a statistically significant brain region that was assigned to one of these 19 Brodmann areas, it was considered to belong to the P-FIT model.

Statistical analysis

Statistical analyses were carried out using Matlab, version 7.14.0.739 (R2012a, The MathWorks Inc., Natick, MA) and SPSS version 20 (SPSS Inc., Chicago, IL). For all analyses, linear parametric methods were used. Testing was two-tailed with an α-level of 0.05, which was FDR corrected for multiple comparisons using the Benjamini–Hochberg method70 when conducting correlation analyses on the level of single brain regions.

We examined structure–function relationships on a whole-brain level by computing partial correlation coefficients reflecting the associations between intelligence and the structural brain properties included in this study. Age and sex were used as controlling variables. We followed a similar but more stringent approach for our analyses on the level of single brain regions. As described above, the parcellation scheme provided by the Human Connectome Project37 yielded 180 cortical regions per hemisphere. NODDI coefficients and volume measures from homotopic regions were averaged across both hemispheres, resulting in 180 mean values for INVF Cortex , ODI Cortex , ISO Cortex , and VOL Cortex , respectively. The associations between INVF Cortex and intelligence as well as ODI Cortex and intelligence were analyzed by means of partial correlations, controlling for age and sex, and the remaining cortical brain properties, while correcting for multiple comparisons using the Benjamini–Hochberg method70.

To examine the structure–function relationships with regard to the unique contribution of each brain property included in the correlation analyses, we computed a multiple regression analysis using SPSS. Intelligence was treated as the dependent variable and INVF Cortex , INVF WM , ODI Cortex , ODI WM , ISO Cortex , ISO WM , VOL Cortex , VOL WM , age, and sex as predictors.

Code availability

The Matlab code that was used to compute the overlap between statistically significant brain regions and those included in the P-FIT model is available from the corresponding author upon reasonable request.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request. The data used for sample S498 are part of the “S500 plus MEG2” release provided by the Human Connectome Project and can be accessed via its ConnectomeDB platform (https://db.humanconnectome.org/).