Crystallized and fluid intelligence are predicted by microstructure of specific white‐matter tracts

Abstract Studies of the neural basis of intelligence have focused on comparing brain imaging variables with global scales instead of the cognitive domains integrating these scales or quotients. Here, the relation between mean tract‐based fractional anisotropy (mTBFA) and intelligence indices was explored. Deterministic tractography was performed using a regions of interest approach for 10 white‐matter fascicles along which the mTBFA was calculated. The study sample included 83 healthy individuals from the second wave of the Cuban Human Brain Mapping Project, whose WAIS‐III intelligence quotients and indices were obtained. Inspired by the “Watershed model” of intelligence, we employed a regularized hierarchical Multiple Indicator, Multiple Causes model (MIMIC), to assess the association of mTBFA with intelligence scores, as mediated by latent variables summarizing the indices. Regularized MIMIC, used due to the limited sample size, selected relevant mTBFA by means of an elastic net penalty and achieved good fits to the data. Two latent variables were necessary to describe the indices: Fluid intelligence (Perceptual Organization and Processing Speed indices) and Crystallized Intelligence (Verbal Comprehension and Working Memory indices). Regularized MIMIC revealed effects of the forceps minor tract on crystallized intelligence and of the superior longitudinal fasciculus on fluid intelligence. The model also detected the significant effect of age on both latent variables.

An interesting strand of these studies, one that we will follow in this article, suggests links of white-matter microstructural properties (such as fractional anisotropy or FA) to cognitive informationprocessing speed and thus to the neural foundation of general intelligence (Penke et al., 2012). FA quantifies the dispersion of water molecules, and it is constrained by the organization of white-matter structures. While sometimes interpreted as a measure of white-matter integrity, FA is a very complex and indirect measure with various limitations, and its relationship to white-matter health is not yet fully understood (Bender, Prindle, Brandmaier, & Raz, 2016;Jones, Knösche, & Turner, 2013). Nevertheless, FA is widely used, as it has been shown to be associated with individual differences in a range of cognitive domains, especially in old age (Madden et al., 2009). As an example, there are significant correlations between water diffusion parameters and intelligence across the life span, from childhood (Deary et al., 2010) to old adulthood (Charlton et al., 2006;Deary et al., 2006). Other studies have provided evidence that all measures of information-processing speed, as well as a general speed factor composed from these tests (g-speed), were significantly associated with FA (Kuznetsova et al., 2015).
Many of these studies suffer from three main shortcomings: 1. The relation of neuroimaging with intelligence measures is usually based on simple correlations. While useful in exploratory analyses, they do not provide information about causal pathways that require more complex multivariate analyses. Specific statistical methods for causal analysis must be used.
2. There is an inconsistent exploration of cognitive domains. Some studies rely on specially designed cognitive scales, then summarized to reflect a single latent variable. Even when widely available scales, such as the Wechsler Adult Intelligence Scale (WAIS) (Wechsler, Sierra, & Blanca, 2003), are used, they are often also reduced to a single score, such as the general or "g" factor (Spearman, 1904), or "fluid intelligence" using different procedures.
It is better to explore the individual indices of the WAIS, those related to performance intelligence: Perceptual Organization c. FA averages along tracts obtained from each subject's DWI in native space (mTBFA-individual).
We now review the solution to these three issues and analyze recent papers which dealt with them.
Regarding the first problem about statistical issues, appropriate multivariate methods to determine causal pathways are now emerging. Specifically, the Structural Equation Modeling (SEM) framework has proven to be particularly useful (Bollen & Hoyle, 2012). These models estimate a set of regression equations which may be interpreted in terms of a directed Bayesian network in which the variables studied are considered as nodes of a graph with each valid regression equation a directed edge. This graph fulfills a Markov property that can be explained as follows: If variable A is connected to B and B to C, and there is no other direct or indirect path from A to C, B "totally mediates" the influence of A on C. In other words, B "screens off" A from C. Under appropriate conditions (Pearl, 2000), the resulting graphs allow some inference about mechanistic causal relations. For a discussion of these concepts in brain networks, see Valdes-Sosa, Roebroeck, Daunizeau, and Friston (2011). A particularly useful type of SEM is the Multiple Indicator, Multiple Causes (MIMIC) introduced by Jöreskog and Goldberger (2006) in which latent variables are introduced as mediators between two sets of observed variables. This framework was leveraged by Kievit et al. (2012Kievit et al. ( , 2016 and Kievit, Fuhrmann, Borgeest, Simpson-Kent, and Henson (2018) to provide an SEM specification for the study of the relation of FA with intelligence, work that is worth summarizing in the next paragraph.
In Kievit et al. (2012), a MIMIC model was estimated with the following three levels to the data of 80 subjects: (a) Voxel-based region of interest (ROI) measures for four FA (VBFA) tracts and 4 Gy matter, (b) a single g (WAIS) latent variable, (c) the four WAIS indices (WM, VC, PO, and PS). This model was applied and showed a good fit but considered only a single cognitive domain based on a sample with a limited age range (18-29 years) and a limited small number of FA measures that were not actually tract based.
The former study was followed by a seminal paper by Kievit et al. (2016) that embodied statistically the "watershed model" proposed by Cannon and Keller (2006) within the MIMIC framework. That model postulated that multiple causes act through latent variables (endophenotypes) to produce the observable phenotypes. This MIMIC/ watershed model was fit to a cross-sectional sample of 555 subjects aged from 18 to 87 years of age (Cam-CAN; Shafto et al., 2014). The model comprised four levels, the first level consisting of 10 mBTFAatlas measures (Table 1). The second level was six speed of processing (CAM/CAN). The third level was a unique latent variable identified with "fluid intelligence" (FI-CAM/CAM). Hereon we will identify psychometric scales and latent variable by the initials of the study. Finally, the last level consisted of the four subtests of fluid intelligence of Cattell's Culture Fair, Scale 2, Form A (Cattell, 1971). This model was built up by a successive exploration of increasingly more complex models verified with confirmatory factor analyses. The overall model gave an excellent fit to such a large sample, verifying the use of the MIMIC approach. Note that age was not included as an explicit variable at level one.
Subsequent to the Kievit et al. (2016) proposal of the watershed model for intelligence regularized regression methods were integrated into SEM/MIMIC modeling (Jacobucci, Brandmaier, & Kievit, 2019).
Regularization (Zou & Hastie, 2005) imposes restrictions on the relations between coefficients allowing the exploration of large sets of variables with built-in selection of those that are relevant. This model was used to study subjects from the UK Biobank (Kievit et al., 2018) in a longitudinal study with three waves, with 185,317, 9,719, and 870 subjects, respectively. As acknowledged by the authors, the cognitive domains explored were limited by the UK Biobank design with a conflation of fluid and crystal intelligence items. Interestingly, a three-level MIMIC model was integrated with a longitudinal one to analyze individual variable trajectories. This time, a three-level model was assumed: 1. Fifteen mTBFA individual for a set that includes those described in Table 1; 2. Coefficients of the age regression (two latent variables); 3. Fluid intelligence scores (FI-UK Biobank).
In this very large longitudinal study, the use of MIMIC models is once more validated, the effect of aging is discussed, and the use of personalized (mTBFA-individual) and not atlas-based FA measures was introduced. As the authors state, the "suboptimal task design" restricted the exploration of cognitive interpretation. Besides, findings from the same group (Kievit et al., 2018) showed a weak but significant negative association between age and fluid intelligence.
Our study reported here will attempt to fill in some of the gaps of previous studies. We will take advantage of one of the rare population-based studies based in a country in Latin America: the second wave of the Cuban Human Brain Mapping Project (CHBMP; Hernandez-Gonzalez et al., 2011). This cross-sectional study evaluated more than 95% of a random sample of 2,109 subjects with medical, cognitive, and neuroimaging studies (T1, T2, DWI, electroencephalogram (EEG)) to yield a final group of 240 "functionally healthy" subjects, of which 83 (aged 18-69 years) were used in this study. Not only does this allow us to reexamine some of the unanswered questions from previous studies but also to construct an MIMIC (watershed model) that integrates previous approaches by the following: 1. Exploring a wider range of cognitive domains namely, the four WAIS indices for intelligence as in Kievit et al. (2012).
2. Partitioning for the first time, the variance of these indices among the optimal number of latent variables.
3. Using individualized average FA tract-based measures of whitematter microstructure as in Kievit et al. (2018).  Center. The recruitment procedure did not involve any kind of reward, but only feedback about the results and participants were included in the study after accepting and signing the informed consent.

| Assessments
Each participant underwent an interview and medical examination with specialists in Neurology and Psychiatry, in order to rule out chronic diseases (e.g., addictions, including smoking) or any disorders of the nervous system that would invalidate their participation in the study. Neurological examination was performed following the proce-  The raw measures were scored according to the official normative data included in the printed version of WAIS-III. However, to avoid culture bias, they were subsequently standardized with information from the Cuban sample to produce scores of the specific performance, adjusted for age for our population.

| Magnetic resonance imaging acquisition protocol
A Siemens 1.5 T Magnetom Symphony system with a standard birdcage head coil for signal transmission/reception (Siemens, Erlangen, Germany) was used to acquire images, including a high-resolution T1-weighted anatomical image and a standard diffusion sequence.
The T1-weighted structural image (1 × 1 × 1 mm resolution) was acquired with the following parameters: echo time ( In order to correct the distortions caused by magnetic field inhomogeneities in the series of diffusion-weighted images, phase and magnitude maps were obtained. The parameters used were voxel size of 3.5 mm, ET 1 = 7.71 ms, ET 2 = 12.47 ms, and RT = 672 ms. The Diffusion Tensor Imaging images were movement, eddy-current, and distortion corrected. Using the magnitude and phase images and the unwarping functionality (Anderson, 2001), the effects of the principal inhomogeneities of magnetic fields were corrected. Later, the diffusion tensor and the FA were determined in each voxel (Pierpaoli & Basser, 1996).

| Fiber tracking computation
Computation of the diffusion tensor and fiber tracking was performed using DTI&FiberTools v.3.0 (www.uniklinik-reiburg.de/mr/live/ arbeitsgruppen/diffusion_en.html; Kreher, Hennig, & Il'yasov, 2006) and implemented in Matlab (The MathWorks, 2014). According to the formulation of Basser, Mattiello, and LeBihan (1994), and by diagonalizing the diffusion tensor for each voxel, the toolbox generates as output six components of a diffusion tensor, three eigenvectors that characterize the direction of diffusion, and three eigenvalues that characterize the magnitude of the diffusion in the corresponding eigenvector calculated (Basser et al., 1994).
Three-dimensional reconstruction of the tracts was performed using the deterministic tractography method Fiber Assignment by Continuous Tracking algorithm and a brute-force reconstruction approach (Mori, Crain, Chacko, & Van Zijl, 1999). to generate the coordinates of all fibers in the brain from which the tract trajectory is reconstructed after drawing an ROI in a userdefined region of the brain.

| Definition of tract-based fractional anisotropy (mTBFA)
A multiple ROIs approach was used for the reconstruction of the tracts of interest because it has been shown that the two-ROI and brute-force approaches could effectively reduce the sensitivity to the noise and ROI placement (Huang, Zhang, van Zijl, & Mori, 2004). The fiber tracking was performed on every voxel of the brain, and fibers that penetrated the previously defined ROIs were assigned to the specific tracts associated with each pair of ROIs.
Definition of ROIs for studied tracts was made by replicating a set of predefined ROI by Mori et al. (2002) that was employed successfully in subsequent work (Góngora, Domínguez, & Bobes, 2016;Mori et al., 2008;Wakana et al., 2007;Wakana, Jiang, Nagae-Poetscher, Van Zijl, & Mori, 2004). The following procedure replicated the methodology published by Góngora et al. (2016). These ROIs were drawn using the program MRIcron (http://www.mricron.com) on a reference anatomical image with a spatial resolution of 1 × 1 × 1 mm 3 in stereotactic space of the Montreal Neurological Institute (Evans et al., 1993). The ROIs were then transformed to each individual brain space automatically using the SPM toolbox functionalities (Friston, Ashburner, Kiebel, Nichols, & Penny, 2007). In this routine, the highresolution anatomical T1 image was realigned to the standard position on the AC-PC plane and normalized using the procedures of SPM.
The unnormalized T1 was rigidly co-registered with the b0 image using a mutual information cost function (Collignon et al., 1995). The ROIs were defined for the following tracts defined in Table 1. The resulting path of these tracts was visually inspected and corrected in cases where necessary by the exclusion of fibers that did not belong anatomically to tracts. The mean tract-based FA (mTBFA) was obtained as an estimate of the average along each tract, which resulted from the superposition of the specific coordinates for each tract on the corresponding maps of FA. For the statistical analysis, this parameter was averaged between the corresponding bilateral tracts.

| Statistical analysis
In the present study, we first used the MIMIC model to determine the number of latent variables necessary to explain the four indices of WAIS-III. For this purpose, we first fitted a single latent g (WAIS-III) model as in Kievit et al. (2012) as a composite of PO and PS, and VC and WM. Subsequently, a two-latent variable model was fitted to these same indices corresponding to verbal and performance intelligence scales.
Subsequently, the sample was fitted with a modification of the watershed model proposed by Kievit et al. (2016). In our model, anatomical variables (mTBFA) affect the two intelligence latent variables that in turn mediate the WAIS-III indices. Age is also included as affecting the latent variables as in Kievit et al. (2018). Exploratory analysis regarding possible confounds (gender, handedness, and educational level) in the estimations was performed but without relevant effects in the estimations and will not be further considered in this article.
Estimates may be imprecise when using maximum likelihood estimation with large numbers of variables and a limited sample size. We therefore used the regularized SEM model (Jacobucci et al., 2019) implemented in the cv_regsem function (regsem package in R) The final model is shown as that selected by the regularized SEM package.

Analysis of the IQ measures
The application of the WAIS-III resulted in the estimation of a  we used these two latent factors identifying the verbal one with "crystallized intelligence" and the performance one with "fluid intelligence" according to Cattell (1963)), denoted in this article as CI and FI without any further clarification. The detailed breakdown of the contribution of the indices to latent factors is as follows. For FI, PO has an R 2 of 0.856 while PS: 0.408. For CI, the R 2 of VC is 0.756 and WM 0.483.

| MIMIC (watershed) model of integrated WM and cognitive measures
We fitted a regularized SEM/MIMIC/Watershed model with an elastic-net penalty (Jacobucci et al., 2019), introducing the following hierarchical levels: 1. The most upstream variables were the 10 major white-matter tract mTBFA, which were modeled as influencing only the two latent variables. Note that age was also added at this level as in Kievit et al. (2018). were identified: reasoning, spatial ability, memory, PS, and vocabulary (Salthouse, 2004), which are very closely related but not identical to the four independent indexes of the WAIS-III: PO or Reasoning (PO), PS, VC, and WM. Thus, the single-factor summarization of intelligence scales in Kievit et al. (2016, Kievit et al., 2018 lead to a misallocation of variance of the intelligence measures that will affect the full model. By contrast, here we leveraged the availability of the full WAIS-III recorded with DWI from the CHBMP. Our analysis showed that two latent factors, fluid intelligence or FI and crystalized intelligence or CI, provide better fits than a single general or g (WAIS) latent variable. This is in agreement with the observation of Kievit et al. (2016) who suggested that fitting more than one latent variable, with the exploration of more cognitive domains, would increase the explained variance of the models.
4.2 | Full MIMIC model relating white-matter microstructure to intelligence indexes, mediated by latent variables As mentioned before, the model produced by regsem is not accompanied by p values or confidence intervals, which may seem surprising. Jacobucci et al. (2019) point out that this type of model incurs acceptable bias when using regularization, but the more important aim is the holdout sample generalization, which is achieved by reducing variance and preferring models of a complexity that is afforded by the observed data. In this framework, the resulting edges left in the MIMIC model are important if they are simply not set to zero. This is the interpretation we will follow here.
The regularized MIMIC model indicated an age effect on both FI and CI. This points to the effectiveness of this method to unravel more subtle relations in a set of predictors since age was not significant in nonregularized versions of MIMIC models. This method of regularization is supported by previous studies that showed its ability to model the relation between cognitive performance and imaging metrics, taking a high-dimensional set of predictors and reducing this set to create a relatively parsimonious representation of key tracts previously implicated in specific tasks, for example, visual short-term memory performance (Jacobucci et al., 2019).
The regularized MIMIC model revealed two tracts that are connected directly to the latent variables. We describe these two paths of putative causation next.
One tract, Fmn is an interhemispheric tract whose fibers connect left and right frontal lobes through the genu of the corpus callosum (Mori, Wakana, Van Zijl, & Nagae-Poetscher, 2005), the enhanced anatomical connectivity of which may underlie the greater fluid reasoning, visuospatial WM, and creative capabilities appreciated in mathematically gifted children (Navas-Sánchez et al., 2014). The microstructural characteristics of interhemispheric connections have been positively correlated to some intelligence variables in females but negatively correlated in males (Tang et al., 2010).
In our model, the Fmn was connected to the CI latent variable, therefore also predicting performance in the WM and VC indices. In contradistinction, a positive association of the Fmn with the FI (Cam-CAN) has been reported by Kievit et al. (2016). This is not surprising since FI (Cam-CAN) in the words of the authors they are all subtests of a single cognitive domain (Cattell, 1971). Even more complicated is the comparison with results of the UK Biobank study (Kievit et al., 2018) since the latent variable is defined with a set of measures that have been suggested to be difficult to interpret (Lyall et al., 2016).
Our model also identified another white-matter tract as important, the SLF. The SLF is located over the cingulum running from the dorsal and medial parietal cortex to premotor and prefrontal cortices (Schmahmann et al., 2007). Specifically, it is on the superior lateral portion of the putamen forming a long arch that emits branches toward the temporal, parietal, and occipital lobes (Mori et al., 2005).
This tract connects the caudal part of the inferior parietal lobule and intraparietal sulcus, areas that are involved in visuospatial information processing. Also, their fibers get to the posterior prefrontal cortex, which is of great importance in perception and awareness (Petrides & Pandya, 2006;Schmahmann et al., 2007).  (Tang et al., 2010), at least for males in the left branch of the SLF.
This apparently counterintuitive result may be viewed as we stated in the introduction, due to the fact that FA is a highly complex measure that must be interpreted with caution (Jones et al., 2013).
Although it is true that FA is directly related to increased myelin thickness, parallelism, and packing of axons, it also depends on other factors such as barriers and obstacles imposed by microstructure, cell membranes, myelin sheaths, and microtubules (Beaulieu, 2002). It may decrease with larger axonal diameters due to an increase in the mobility of water in the intra-axonal compartment water mobility (Takahashi et al., 2002). Fiber crossings may be another factor influencing the observed values of FA. This may explain both positive and negative correlations of FA with reaction time as reported and discussed by Tuch et al. (2005). A deeper understanding of whitematter microstructural determinants of cognitive functions will require improved diffusion magnetic resonance imaging (MRI) technology and methods (Jelescu & Budde, 2017;Jones et al., 2013;Riffert, Schreiber, Anwander, & Knösche, 2014).
Interestingly, the effect of the SLF was restricted to FI while we were expecting some influence over CI. There are some reports of a relationship of this white-matter tract with the tests which composed CI. For example, a multiple sclerosis study by combining the Paced Visual Serial Addition Test with functional MRI-guided fiber tractography found the SLF was the main white-matter tract connecting areas active during this attention and WM task (Bonzano, Pardini, Mancardi, Pizzorno, & Roccatagliata, 2009). In addtition, Papagno et al. (2017) found that direct electrical stimulation of the SLF during awake surgery improves verbal short-term memory. This also supports the participation of the SLF in the so-called "phonological loop," which has been described as a crucial component for language acquisition (Papagno et al., 2017).

| Limitations and future work
Several limitations should be noted in the present research which pertain to study design, measures of brain organization, and statistical methodology. We detail them here and point out that the next wave of the CHBMP will take them into consideration.
The sample is relatively small with data gathered cross-sectionally. A larger sample is foreseen for the third wave of the CHBMP, and collaborative studies with other Latin American countries are being organized. A major difficulty to perform combined analyses with other databases from the United States or Europe is the lack of harmonization of their cognitive studies. There are also the following problems related to measures of brain organization: 1. Even when the trajectories obtained agreed with neuro-anatomic descriptions derived from postmortem and other in vivo tractography studies (Carpenter & Sutin, 1983;Góngora et al., 2016;Mori et al., 2002;Nieuwenhuys, Voogd, & Van Huijzen, 2007;Wakana et al., 2007), the existence of inaccuracies due to partial volume effects, noise, and crossing fibers involve the visualized pathways do not necessarily reflect brain connectivity since individual axons could be merging and blanching at any point along the bundle (Wakana et al., 2007).

2.
A further limitation is related to the quality of DWI images gathered in the second wave of the CHBMP: a. Only 12 diffusion-sensitizing gradient directions were recorded (too sparse to allow higher order diffusion models); b. Also, only limited voxel size was possible (2 × 2 × 3) that could affect the robustness to noise, partial volume effect, and crossing fiber regions. These limitations were due to the technology available in 2004 in Cuba, which has been since then modernized.

The fiber tracking algorithm (Fiber Assignment by Continuous
Tracking) employed is highly susceptible to errors in the orientation of the principal eigenvector, due both to noise and to instances where the direction of the underlying tract anatomy is ambiguous, for example, assessment of voxels where fiber bundles cross, diverge, or converge. Improved algorithms now exist and will be used in the future.
4. The only measure of brain organization analyzed is FA, which as we have discussed previously is not very specific. Improved measures of white-matter microstructure are to be preferred (Riffert et al., 2014)

| CONCLUSIONS
The present work was inspired by the watershed model of Kievit et al. to this domain, something that seems to have been overlooked in many studies. In fact, we believe that a wide range of cognitive functions could be explored, something apparently not yet envisaged in the current large brain projects.

ACKNOWLEDGMENT
The authors would like to thank the support from the National Natural Ceballos, Nancy Iglesias Pozo, and Geraldine Tudela. Note that this is a representative list of researchers involved in the two waves of the project.

CONFLICT OF INTERESTS
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.