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Neuroimage. Author manuscript; available in PMC 2011 June 1.

Published in final edited form as:

Published online 2010 March 4. doi: 10.1016/j.neuroimage.2010.02.072

PMCID: PMC2856800

NIHMSID: NIHMS186018

Michael Wahl,^{1,}^{2} Yi-Ou Li,^{1} Joshua Ng,^{1} Sara C. LaHue,^{1} Shelly R. Cooper,^{1} Elliott H. Sherr,^{2} and Pratik Mukherjee^{1,}^{3,}^{*}

The publisher's final edited version of this article is available at Neuroimage

See other articles in PMC that cite the published article.

The purpose of this study is to investigate whether specific patterns of correlation exist in diffusion tensor imaging (DTI) parameters across white matter tracts in the normal human brain, and whether the relative strengths of these putative microstructural correlations might reflect phylogenetic and functional similarities between tracts. We performed quantitative DTI fiber tracking on 44 healthy adult volunteers to obtain tract-based measures of mean diffusivity (MD), fractional anisotropy (FA), axial diffusivity (AD), and radial diffusivity (RD) from four homologous pairs of neocortical association pathways (arcuate fasciculi, inferior fronto-occipital fasciculi, inferior longitudinal fasciculi, and uncinate fasciculi bilaterally), a homologous pair of limbic association pathways (left and right dorsal cingulum bundles), and a homologous pair of cortical-subcortical projection pathways (left and right corticospinal tracts). From the resulting inter-tract correlation matrices, we show that there are statistically significant correlations of DTI parameters between tracts, and that there are statistically significant variations among these inter-tract correlations. Furthermore, we observe that many, but by no means all, of the strongest correlations were between homologous tracts in the left and right hemispheres. Even among homologous pairs of tracts, there were wide variations in the degree of coupling. Finally, we generate a data-driven hierarchical clustering of the fiber pathways based on pairwise FA correlations to demonstrate that the neocortical association pathways tended to group separately from the limbic pathways at trend-level statistical significance, and that the projection pathways of the left and right corticospinal tracts comprise the most distant outgroup with high confidence (p<0.01). Hence, specific patterns of microstructural correlation exist between tracts and may reflect phylogenetic and functional similarities between tracts. The study of these microstructural relationships between white matter pathways might aid research on the genetic basis and on the behavioral effects of axonal connectivity, as well as provide a revealing new perspective with which to investigate neurological and psychiatric disorders.

Since its introduction over 15 years ago, diffusion tensor imaging (DTI) has enabled the noninvasive assessment of the microstructural organization of human white matter pathways in health and disease (Basser & Pierpaoli, 1994; Pierpaoli et al., 1996). With the more recent advent of quantitative DTI fiber tractography (Conturo et al., 1999; Mori et al., 1999; Basser et al., 2000), it is now possible to reproducibly measure DTI parameters such as mean diffusivity, (MD), fractional anisotropy (FA), axial diffusivity (AD), and radial diffusivity (RD) over the three-dimensional course of many white matter tracts (Wakana et al., 2007). Measurements of DTI parameters from regions of interest within white matter as well as from entire tracts have been shown to correlate with cognitive and other behavioral performance, often with specific microstructure-function relationships in particular white matter tracts (Klingberg et al., 2000; Beaulieu et al., 2005; Tuch et al., 2005; Niogi & McCandliss 2006; Niogi et al., 2008b; Zahr et al., 2009). Decreases in the microstructural integrity of white matter pathways have been found for many neurologic and psychiatric disorders, often correlating with clinical and neurocognitive deficits in these patients (Klingberg et al., 2000; Niogi & McCandliss 2006; Niogi et al., 2008b).

While there has been rapid growth in the understanding of how the microstructural organization of specific white matter pathways correlates with behavior, to our knowledge there has not been a systematic examination of whether quantitative DTI parameters of different tracts co-vary with each other across individuals. The assumption implicit in many DTI studies is that a particular metric such as FA is independent across white matter tracts; hence, each pathway is analyzed separately with respect to its contribution to cognitive ability. Conversely, different tracts may be treated as if they were equivalent, such as when measurements in homologous tracts of the left and right hemispheres are averaged or when the contralateral tract is used as a control for the homologous tract ipsilateral to the pathology in clinical studies of disorders presumed to be unilateral. But the precise degree to which microstructural covariances exist between tracts is largely unknown. Several prior studies have reported hemispheric asymmetries in homologous pairs of fiber pathways using DTI in healthy adults (Gong et al., 2005; Powell et al., 2006; Rodrigo et al., 2007), in the developing human brain (Bonekamp et al., 2007; Wilde et al., 2009), and in the aging human brain (Li et al., 2009; Yasmin et al., 2009), but these studies have focused on group differences in the mean value of DTI parameters rather than on assessing their correlation.

The purpose of this study is to investigate whether specific patterns of correlation exist in DTI parameters across white matter tracts in the normal adult human brain, and whether the strength of these putative correlations might reflect phylogenetic and functional similarities between tracts. To this end, we examined tract-based measures of MD, FA, AD, and RD from four pairs of neocortical association pathways (arcuate fasciculi, inferior fronto-occipital fasciculi, inferior longitudinal fasciculi, and uncinate fasciculi bilaterally), a pair of limbic association pathways (bilateral dorsal cingulum bundle), and a pair of cortical-subcortical projection pathways (bilateral corticospinal tract), following the tract terminology of Mori et al. (2005). From the resulting inter-tract correlation matrices, we investigate whether there are statistically significant correlations of DTI parameters between tracts, and whether there are statistically significant variations among these inter-tract correlations. We specifically examine if correlations between homologous pairs of tracts always exceed those between non-homologous tracts. Finally, we perform a data-driven hierarchical clustering analysis of pairwise DTI correlations to group tracts based on their microstructural relatedness, using the results to test the hypothesis that microstructural correlations reflect phylogenetic and functional similarities between white matter pathways.

The inclusion criteria for subjects in this study were healthy volunteers ages 20–50 years. Exclusion criteria included any history of chronic medical illness, neurological or psychiatric disorder, including substance abuse, as well as any contraindications to MR imaging including pregnancy. Any brain morphological abnormalities found on structural MR imaging also constituted an exclusion criterion. Written informed consent was obtained from all participants in accordance with protocols approved by the institutional review board of the University of California, San Francisco. There were a total of 44 subjects (mean age 30.8 ± 7.8 years, 24 men and 20 women, 35 right-handed and 9 left-handed) enrolled who met all inclusion and exclusion criteria.

Magnetic resonance imaging was acquired on a 3T Signa EXCITE scanner (GE Healthcare, Waukesha, WI) equipped with an 8-channel phased-array head coil. Whole-brain DTI was performed with a multislice single-shot spin echo echoplanar pulse sequence (TE=63 ms, TR=14 s) using 55 diffusion-encoding directions, isotropically distributed over the surface of a sphere with electrostatic repulsion, acquired at *b* = 1000 s/mm^{2}, 1 acquisition with *b* = 0 s/mm^{2}, 72 interleaved axial slices oriented along the anterior commissure - posterior commissure (AC-PC) line, 1.8-mm slice thickness with no gap between slices, a 128×128 matrix and a field of view (FOV) of 230 mm. To reduce echoplanar image distortion, parallel imaging was employed using the Array Spatial Sensitivity Encoding Technique (ASSET) with an acceleration factor of 2. Total acquisition time was 13.07 minutes. The signal-to-noise ratio (SNR) was in the range of 18–33 on the *b* = 0 s/mm^{2} images, as calculated using the difference method that has been shown by Dietrich et al. (2007) to be the most accurate for parallel imaging acquisitions. Higher SNR was found in superficial regions and lower SNR in deeper regions of the brain, reflecting variations in sensitivity of the multichannel phased array head coil.

High-resolution structural 3T MR imaging was performed using an axial 3D inversion recovery fast spoiled gradient-recalled echo (FSPGR) T1-weighted sequence (TE=1.5 ms, TR=6.3 ms, TI=400 ms, flip angle of 15 degrees) with 230 mm FOV, 156 1.0-mm contiguous partitions at a 256×256 matrix.

After non-brain tissue was removed using the Brain Extraction Tool (BET; http://www.fmrib.ox.ac.uk/analysis/research/bet/) with a fractional intensity threshold of 0.3 (Smith, 2002), the diffusion-weighted images were corrected for motion and eddy currents using FMRIB’s Linear Image Registration Tool (FLIRT; www.fmrib.ox.ac.uk/fsl/flirt) with 12-parameter linear image registration (Jenkinson et al., 2002). All diffusion-weighted images were registered to the unweighted b=0 s/mm^{2} image. Images were post-processed offline in DTIstudio v2.4 software (Jiang et al., 2006) using multivariate linear fitting to obtain maps of FA, MD, AD, RD, and directionally encoded color FA. Tractography was performed with Fiber Assignment by Continuous Tracking (Mori et al., 1999), using the brute-force method in which tracks were seeded from all voxels in the brain with an FA value larger than 0.3. Fibers were tracked while voxel FA values exceeded 0.2 and turning angles of the primary eigenvectors between neighboring voxels were less than 50^{0}. These fiber tracking parameters are similar to other recent quantitative DTI tractography studies of the normal adult brain (Reich et al., 2006; Rodrigo et al., 2007; Wakana et al., 2007; Danielian et al., 2009). Individual tracts were then selected by requiring fibers to pass through manually placed Regions of Interest (ROIs) on DTI color maps, according to protocols specific for each tract, as described by Wakana et al. (2007) and implemented in DTIstudio. Any anatomically implausible fibers were removed using exclusion ROIs, as also described by Wakana et al. (2007). Quantitative tract-based measurements of FA, MD, AD, and RD were obtained for six axonal pathways bilaterally, specifically the arcuate fasciculus (AF), dorsal cingulate bundle (CB), corticospinal tract (CST), inferior fronto-occipital fasciculus (IFO), inferior longitudinal fasciculus (ILF) and uncinate fasciculus (UF). Mid-sagittal projections of the three dimensional course of the left-sided tracts are illustrated in Figure 1. Our terminology differs from that of Wakana et al. (2007) in that they refer to the arcuate fasciculus as the “temporal component of the superior longitudinal fasciculus” and they refer to the dorsal cingulum as the “cingulum in the cingulate gyrus part”. Since spatial overlap of tracts would influence their microstructural correlation, the degree of overlap was quantified for each tract pair within the same hemisphere in 25 consecutive subjects as the percentage of shared voxels. This is calculated as follows: let V_{A} be the number of voxels contained within tract A, V_{B} be the number of voxels within tract B, and V_{AB} be the total number of voxels within tracts A and B where voxels contained within both tracts are counted only once. Then 100% × (V_{A} + V_{B} − V_{AB})/(V_{A} + V_{B}) represents the percentage of shared voxels between tracts A and B.

The distributions of FA values of each set of *p* = 12 tracts across the 44 subjects did not differ from normality using the Shapiro-Wilk test, except for FA of the left UF which showed a statistically significant deviation from normality (p < 0.05). However, MD values in 8 of the 12 tracts showed significant departures from normality (p < 0.05). There were no deviations from normality for AD values in any of the 12 tracts (p > 0.05), but the distribution of RD values differed significantly from Gaussian in 6 of the 12 tracts (p < 0.05). Hence, the nonparametric Spearman’s rank correlation coefficient *ρ* was used to measure all correlations. A correlation matrix was constructed for each of the 4 DTI parameters using pairwise correlation values between tracts. The correlation matrices are symmetric and have values of unity along the main diagonal that represent perfect correlation of each tract with itself. There are *p* * (*p* - 1)/2 = 66 unique nontrivial elements in each matrix, which correspond to the symmetric pairwise correlations of the DTI parameter in each of the 12 tracts with the 11 other tracts.

To determine if there are statistically significant correlations of FA, MD, AD, and RD between white matter tracts, the 4 correlation matrices were tested for equivalence to the identity matrix and for equal correlations using the following two procedures from Rencher (2002). Consider the correlation matrix of a *p* × *n* data matrix, with *n* random samples from a *p*-dimensional normal distribution. The first null hypothesis is that the correlation matrix is the identity matrix, i.e.,
${\text{H}}_{0}:\mathrm{\sum}=\left[\begin{array}{cccc}1& 0& \dots & 0\\ 0& 1& \dots & 0\\ \phantom{\rule{0.16667em}{0ex}}& \dots & \phantom{\rule{0.16667em}{0ex}}& \phantom{\rule{0.16667em}{0ex}}\\ 0& \dots & 0& 1\end{array}\right]$. The test statistic is a modified likelihood ratio,
${u}_{1}=\upsilon [ln\mid {\mathrm{\sum}}_{0}\mid -ln\mid \text{S}\mid +\phantom{\rule{0.16667em}{0ex}}tr(\text{S}{\mathrm{\sum}}_{0}^{-1})-p]$, where *υ* = *n* – 1 is the degrees of freedom of the test, Σ_{0} = I is the hypothesized correlation matrix, S is the calculated sample correlation matrix, and *tr*(·) is the trace of a matrix. If H_{0} is true, *u* is approximately distributed as
${\chi}^{2}[\frac{1}{2}p(p+1)]$, therefore, we reject the hypothesis if *u*_{I} is greater than
${\chi}^{2}[\alpha ,\frac{1}{2}p(p+1)]$. We use a significance level of α = 0.0125, which represents a Bonferroni correction for four comparisons from the typical significance threshold of α = 0.05.

The second null hypothesis is that the correlation matrix has homogeneous structure, i.e.,
${\text{H}}_{0}:\mathrm{\sum}=\left[\begin{array}{cccc}1& \rho & \dots & \rho \\ \rho & 1& \dots & \rho \\ \phantom{\rule{0.16667em}{0ex}}& \dots & \phantom{\rule{0.16667em}{0ex}}& \phantom{\rule{0.16667em}{0ex}}\\ \rho & \dots & \rho & 1\end{array}\right]$, where *ρ*>0 is the common correlation coefficient among all variables. The test statistic is a likelihood ratio,
${u}_{\text{H}}=\frac{\mid \text{S}\mid}{{({s}^{2})}^{p}{(1-r)}^{p-1}[1+(p-1)r]}$ where S is the calculated sample correlation matrix, *s*^{2} = 1 is the variance of each variable due to variance normalization, and
$r=\frac{1}{p(p-1)}{\displaystyle \sum _{j\ne k}}{s}_{jk}$ is the estimated common correlation coefficient *ρ* If H_{0} is true, a modified test statistic
${u}_{\text{H}}^{\prime}=-\left[\upsilon -\frac{p{(p+1)}^{2}(2p-3)}{6(p-1)({p}^{2}+p-4)}\right]ln{u}_{\text{H}}$ is approximately distributed according to
${\chi}^{2}[\frac{1}{2}p(p+1)-2]$, similarly, we reject the hypothesis if
${u}_{\text{H}}^{\prime}$ is greater than
${\chi}^{2}[\alpha ,\frac{1}{2}p(p+1)-2]$ with α = 0.0125, which represents a Bonferroni correction for four 2 comparisons from the typical significance threshold of α = 0.05.

Finally, after establishing that the pairwise inter-tract correlations are significantly different from zero and also significantly different from each other, hierarchical clustering methods were used to characterize the patterns of inter-tract correlation in each matrix. The quantity 1 - *ρ*, where *ρ* is the Spearman’s rank correlation coefficient, was used as the measure of distance or “dissimilarity” between white matter tracts for the purpose of clustering. Hierarchical clustering employed the hclust function in R version 2.9.2 (http://sekhon.berkeley.edu/stats/html/hclust.html). This function proceeds by iterative agglomeration of the white matter tracts into successively larger groups based on the distance measure. The results are viewed as a dendrogram, which illustrates the fusions made at each successive stage of agglomeration. Average distance linkage was employed as the method of agglomeration. Average distance linkage defines the distance between groups as the average of distances between all pairs of objects, where each pair is made up of one object from each group. To characterize the uncertainty of the linkages in these dendrograms of correlational distances, a multiscale bootstrap was applied to the clustering with 100,000 repetitions of the analysis, using the pvclust function in R (Suzuki & Shimodaira, 2006). The multiscale bootstrap yields an approximately unbiased p-value for each linkage in hierarchical clustering (Shimodaira 2002; Shimodaira 2004), and its application to hierarchical clustering of correlational distances has been previously demonstrated (http://research.stowers-institute.org/efg/R/Visualization/cor-cluster/index.htm). This uncertainty is expressed as a percentage confidence level. For the purpose of this study, a 95% confidence level, corresponding to an approximately unbiased p-value of 0.05, was chosen as the threshold for statistical significance for the grouping of tracts. At 100,000 bootstrap repetitions, the standard error for estimation of the percentage confidence level for each cluster was less than 0.05%. For clusters with confidence levels greater than 90%, this standard error was less than 0.002%.

Structural MR images of all subjects were interpreted by a board-certified neuroradiologist as being free of any morphological abnormalities of the brain. DTI tractography was successfully performed for all 12 white matter pathways in all 44 subjects, with the exception of the right arcuate fasciculus in four subjects. The means and standard deviations for the FA, MD, AD, and RD values for each tract are provided in Table 1. Left hemispheric tracts tended to have greater FA than their right hemispheric counterparts; this asymmetry was most pronounced for the dorsal cingulate bundle, as has been previously reported (Gong et al., 2005; Wakana et al., 2007). The generally lower RD values in the left-sided tracts also reflect their higher FA compared to the right cerebral hemisphere.

Mean and standard deviation of tract-based DTI parameters. Mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD) are in units of 10^{−3} mm^{2}/sec. Fractional anisotropy (FA) is dimensionless.

Spatial overlap between tracts in the same hemisphere was computed as the percentage of shared voxels, as specified in the Methods. The only significant overlaps were found between the IFO and the ILF and between the IFO and the UF. The mean percent shared voxels between left IFO and left ILF was 10.7% ± 3.3% and that between left IFO and left UF was 11.0% ± 3.7%. The mean percent shared voxels between right IFO and right ILF was 11.4% ± 3.7% and that between right IFO and right UF was 7.3% ± 3.1%. Negligible degrees of overlap were seen between the AF and the ILF and between the ILF and the UF in each hemisphere, with 1% or fewer shared voxels.

Matrices for the Spearman’s rank correlation coefficient *ρ* for each of the four DTI parameters are given in Tables 2–5, with the trivial values of unity along the main diagonal excluded. All of the computed correlation values were positive; there were no inverse correlations between white matter tracts for any of the DTI parameters. Each of the four correlation matrices was evaluated for equivalence to the identity matrix using the test statistic *u*_{I}, as detailed in the Methods. The null hypothesis was rejected for all four matrices. The four subjects for whom the right arcuate fasciculus could not be tracked were excluded from this particular analysis since the test statistic cannot be used with missing values. This is valid *u*_{I} because, if a subset of a matrix differs from identity, then the entire matrix also differs from identity. The value of for the FA correlation matrix was 310.6, corresponding to p < 0.0001 *u*_{I} for rejecting the null hypothesis. The value of for the MD correlation matrix was 431.4, *u*_{I} corresponding to p < 0.0001. The value of for the AD correlation matrix was 285.5, *u*_{I} corresponding to p < 0.0001. The value of for the RD correlation matrix was 365.6, *u*_{I} corresponding to p < 0.0001. Hence, it is concluded that statistically significant correlations between tracts exist for all four DTI parameters.

Each of the four correlation matrices was evaluated for homogenous structure, implying equal correlations throughout the off-diagonal elements in the correlation matrix, using the test statistic as *u*_{H} detailed in the Methods. The null hypothesis was rejected for all four matrices. The four subjects for whom the right arcuate fasciculus could not be tracked were excluded from this particular analysis since the test statistic *u*_{H} cannot be used with missing *u*_{H} values. This is valid because, if a subset of a matrix deviates from homogenous structure, then the entire matrix also deviates from homogenous structure. The value of *u*_{H} for the FA correlation matrix was 141.6, corresponding to p < 0.0001 for rejecting the null hypothesis. The value of *u*_{H} for the MD correlation matrix was 121.9, corresponding to p < 0.001. The value of *u*_{H} for the AD correlation matrix was 109.5, corresponding to p < 0.01. The value of for the *u*_{H} RD correlation matrix was 127.5, corresponding to p < 0.001. Hence, it is concluded that there are statistically significant variations in inter-tract correlations for all four DTI parameters. Based on the test statistic *u*_{H}, FA was the DTI parameter with the greatest variation in inter-tract correlations and AD was the DTI parameter with the least variation. The range of inter-tract FA correlations was also the greatest among the four DTI parameters, with the lowest value of *ρ* = 0.15 found between the right UF and the right CST and the highest value of *ρ* = 0.88 observed between the left and right IFO.

After establishing that microstructural correlations between white matter tracts exist and have statistically significant variation, specific patterns of inter-tract relationships were sought in the correlation matrices. For all of the correlation analyses described below, missing data points from the four subjects in whom the right AF could not be tracked were excluded on a case-wise basis, i.e. correlations between the right AF and other tracts were limited to those 40 subjects in which the right AF was tracked, but the full 44 subjects were still used to perform correlations between tracts other than the right AF. We begin with the FA correlation matrix because FA is widely accepted as the most sensitive measure of white matter microstructural integrity among the four DTI parameters examined herein. Unsurprisingly, homologous pathways of the left and right cerebral hemispheres had high correlation coefficients for FA; however, there was wide disparity in the strengths of coupling (Figure 2). The strongest correlation among homologous tracts was found between FA of the left and right IFO (*ρ* = 0.88), whereas the weakest correlation was between the left and right AF (*ρ* = 0.50). The relationship between FA of left and right CB was also relatively weak (*ρ* = 0.57), with an intermediate correlation coefficient found between left and right CST(*ρ* = 0.62), and relatively stronger associations between left and right UF (*ρ* = 0.70) and left and right ILF (*ρ* = 0.73). As expected, FA correlation coefficients between non-homologous tracts were generally lower than that between homologous tracts. Nevertheless, some of these non-homologous FA correlation coefficients exceeded those of the more weakly linked homologous tracts (Table 2, Figure 2). There were five pairwise FA correlation coefficients between non-homologous pathways that were greater than or equal to 0.7: left ILF - left IFO (*ρ* = 0.75); left ILF - right IFO (*ρ* = 0.73); left UF - left IFO (*ρ* = 0.70); right UF - left IFO (*ρ* = 0.70); and right UF - right IFO (*ρ* = 0.71). The weakest FA correlation coefficients were almost uniformly found between the CST on either side and the five pairs of association fiber pathways (Table 2, Figure 2). All values of *ρ* between CST and association tracts were less than 0.3 except for right CST - right ILF (*ρ* = 0.35) and right CST - left AF (*ρ* = 0.34). In contradistinction, all values of *ρ* among the association pathways were greater than 0.3. Similar to the findings in the FA correlation matrix, it can also be ascertained from the other three correlation matrices that homologous tracts had generally greater degrees of correlation than non-homologous tracts; however, for each DTI parameter, there were specific examples of non-homologous axonal pathways that were more strongly correlated than many, or even all, of the homologous ones.

Scatterplots of FA values show wide variation of inter-tract correlations between homologous pairs (*A*, *B*) and non-homologous pairs (*C*, *D*), as measured by the Spearman rank correlation coefficient ρ. The left and right IFO (*A*) are the most strongly **...**

To more systematically investigate the specific patterns of covariation among white matter tracts, agglomerative hierarchical clustering using average distance linkage was applied to each of the four correlation matrices. The degree of uncertainty for each of the linkages was calculated from multiscale bootstrapping, with statistical significance at a 95% confidence level threshold which is equivalent to *α* =0.05. The resulting dendrogram for FA (Figure 3) shows that there are three statistically significant clusters at a confidence level of 95% or greater. Since FA in the left and right IFO had the strongest correlation of any two tracts (*ρ* = 0.88), they represent the first linkage in the hierarchical clustering, with a statistical significance level approaching 100%. The left and right CST also represented a significant cluster at a virtually 100% confidence level. Furthermore, the ten association tracts formed a statistically significant grouping distinct from the bilateral CST at a 99% confidence level. Hence, the paired corticospinal tracts represent an outgroup that was found to be the most dissimilar of the twelve white matter pathways based on the FA correlation matrix. This partition between the association and projection tracts resulted naturally from the large FA correlational distances between the bilateral CST and the other ten axonal pathways. Of the ten association tracts, the cingulum bundles were the most distant outgroup; this pair of limbic association tracts clustered separately from the eight neocortical association pathways at an 85% confidence level. Homologous tracts of the left and right cerebral hemispheres had shorter FA correlational distances than those between most non-homologous tracts, with certain exceptions such as for the left ILF, which was more closely related to the left IFO and the right IFO than to the right ILF with at least a 91% confidence level.

Hierarchical clustering of FA correlational distances displayed as a dendrogram. The distance measure is *1 - ρ*, where *ρ* is the Spearman rank correlation coefficient. The statistical confidence level of each linkage in the dendrogram is **...**

The dendrogram of MD correlational distances (Figure 4) showed some similarities to the FA dendrogram, but also many important differences. Again, homologous tracts tended to form pairs, with the bilateral CST forming a statistically significant cluster at a 97% confidence level. However, the other two significant clusters were of mostly non-homologous tracts, specifically the left IFO with the left AF and the left ILF, as well as the bilateral CST with the aforementioned three pathways. The bilateral CB constituted the most distant outgroup by MD correlational distances, with the bilateral UF as the second most distant outgroup. The bilateral IFO, which was so tightly coupled by FA values, showed a relatively large MD correlational distance.

The dendrogram of AD correlational distances (Figure 5) did not have any statistically significant clusters at the 95% confidence level, likely due to a more homogenous correlation matrix structure than for FA or MD, as also reflected by the *u*_{H} test statistic results reported above. The configuration of the AD dendrogram resembled that of the MD dendrogram more than the FA dendrogram, with the bilateral CB and the bilateral UF comprising the first and second most distant outgroups, respectively. The RD dendrogram (Figure 6) also did not show any significant clusters; however, the bilateral CST approached significance as a cluster at the 94% confidence level and the ten association tracts also formed a nearly significant cluster at the 94% confidence level. This partitioning of the projection tracts from the association tracts in the RD dendrogram was similar to the FA dendrogram. Another point of correspondence between the FA and RD dendrograms was that the left and right IFO were linked by the first edge since they had the shortest correlational distance among all tracts for both these DTI parameters.

In this initial survey of microstructural correlations among white matter tracts of the human brain, we have established that there are statistically significant inter-tract correlations across normal adults in tract-based measures of FA, MD, AD, and RD. Furthermore, there are statistically significant differences in the strength of these pairwise correlations, meaning that DTI parameters in some pairs of tracts are more tightly correlated than in others. Finally, we used hierarchical clustering of correlational distances to form a dendrogram of microstructural relationships among the examined axonal pathways for each DTI parameter, with multiscale bootstrapping of the results to estimate the uncertainty in the linkages of the dendrogram. This is a data-driven analysis method that, combined with the nonparametric Spearman’s rank correlation coefficient as the distance measure, makes minimal assumptions about the underlying diffusion tensor imaging measurements.

These dendrograms showed that many, but not all, of the strongest correlations were between homologous tracts in the left and right hemispheres. Furthermore, even among homologous pairs of tracts, there were wide variations in the degree of coupling. The left and right inferior fronto-occipital fasciculi in particular were the most tightly correlated pair of tracts in terms of their FA (*ρ* = 0.88) and RD (*ρ* = 0.81). The weakest FA correlations between homologous tracts were found between the left and right arcuate fasciculi (*ρ* = 0.50), with the right AF forming an outgroup compared to the other seven neocortical association pathways. This might reflect the well-known structural and functional hemispheric asymmetry of the AF, with the left AF showing larger size and greater FA values in most individuals (Powell et al., 2006; Catani et al., 2007b, Rodrigo et al., 2007; Wakana et al., 2007), the latter also demonstrated in Table 1. Evidence that this macrostructural and microstructural asymmetry in the AF is related to left hemispheric language specialization is provided by a study showing that greater leftward FA lateralization correlated with stronger left-sided dominance for language activation on fMRI (Powell et al., 2006). Interestingly, the IFO is thought to be a phylogenetically novel tract in humans which is not found in non-human primates, whereas the AF may have derived from the further elaboration and left lateralization of a perisylvian white matter network present in apes (Catani, 2006; Catani, 2007a). It is known that the right AF causes greater difficulties for DTI tractography than is encountered with the left AF, often resulting in asymmetrically small size of the computed right AF fiber tracks (Wakana et al., 2007). It is not clear the extent to which the smaller size of the right AF fiber tracks has its basis in underlying gross anatomic and microstructural differences with the left AF. The right AF may not be found at all by DTI tractography in some healthy adults (Catani et al., 2007b). In our cohort, the right AF was not trackable in four subjects; these missing data points were excluded from the correlation analyses. Additionally, the CB showed relatively weak inter-hemispheric correlation for FA (*ρ* = 0.57), which may also reflect the known functional and microstructural hemispheric asymmetry between these tracts as reflected in the higher average FA for the left CB than the right CB (Gong et al., 2005; Wakana et al., 2007).

Another major finding of our study was the strong degree of microstructural correlation between specific non-homologous white matter pathways. Indeed, some of these heterologous associations were stronger than those between most homologous pairs of tracts. In the dendrograms, these heterologous relationships are reflected as shorter correlational distances between non-homologous tracts than between some homologous pairs. For FA values, particularly strong non-homologous correlations were found between IFO, ILF, and UF both within and across hemispheres. These findings that correlations of DTI parameters between certain pairs of homologous tracts are weaker than those between specific non-homologous tracts call into question the increasingly common practice in the DTI literature of using the contralateral tract as a control for the ipsilateral homologous tract in clinical studies where the pathology is presumed to be unilateral, for example in traumatic brain injury (Mayer et al., 2010). Even besides the known hemispheric asymmetry of the mean FA values of tracts such as the AF and the CB (Gong et al., 2005; Wakana et al., 2007), the relatively weak inter-hemispheric microstructural correlations of these pathways means that there is no reason to expect that the contralateral tract would be particularly representative of the premorbid status of the tract ipsilateral to the pathology.

The pairwise correlations of FA values showed that the eight neocortical association pathways (four pairs: AF, IFO, ILF, and UF) formed a separate cluster from the two limbic association pathways (left and right CB). Also, the only non-association tracts (the left and right CST) constituted the most distant outgroup of the FA dendrogram. Hence, the correlational patterns of FA appear to reflect known phylogenetic and functional differences between white matter pathways. The partition between the two projection tracts and the ten association tracts was statistically significant at a 99% confidence level. The separation between the limbic and the neocortical association tracts reached trend-level significance at an 85% confidence level.

Among the four DTI parameters, FA showed the greatest variation in the strength of these pairwise correlations between white matter pathways. Also, the FA correlational matrix appeared to reflect known functional similarities and differences between tracts better than the other three DTI metrics. With a larger sample size, it seems likely that many of the linkages in the FA dendrogram that did not reach the 95% confidence level with the current cohort of 44 subjects would then become significant. FA has become the consensus measure of white matter microstructural “integrity” throughout the DTI literature due to its sensitivity to changes of maturation, senescence, and diverse forms of brain pathology in humans and in experimental animal models. However, even other DTI parameters that are thought to be less sensitive to white matter microstructural integrity than FA, such as the mean diffusivity, did show variations in inter-tract correlations that were manifested as statistically significant clusters in the dendrogram analysis. Importantly, there were differences between the statistically significant groupings of tracts found with FA and with MD, suggesting that each metric may emphasize at least partially distinct microstructural properties of white matter pathways. Of course, the four DTI parameters that were examined herein do not provide completely independent information. In fact, the AD and RD are completely determined by the values of MD and FA, and vice versa (Hasan & Narayana, 2006). Therefore, it is anticipated that the AD and RD correlational structures share information with those of FA and MD. Diffusion anisotropy in large white matter tracts is reflected by the much lower values of the minor eigenvalues than the major eigenvalue. This prolate shape of the diffusion tensor emerges during human brain maturation from decreases in the two minor eigenvalues, i.e. the radial diffusivity, with relatively little change in the major eigenvalue, i.e. the axial diffusivity (Mukherjee et al., 2002). Conversely, dysmyelination has been shown in animal models to reduce anisotropy by preferentially increasing the radial diffusivity of white matter but not altering the axial diffusivity (Song et al., 2002). Hence, it might be expected that the RD dendrogram would more closely resemble FA than would the AD dendrogram. The relative lack of inter-tract correlational structure for AD suggests that it does not convey as much interesting white matter microstructural information as does FA or RD.

Clustering methods have previously been used in DTI studies for purposes such as the automatic segmentation of white matter tracts (Jonasson et al., 2005; O’Donnell et al., 2006; Awate et al., 2007; Hasan et al., 2007; Voineskos et al., 2009) and thalamic nuclei (Wiegell et al., 2003) as well as for unsupervised voxel-based tissue classification (Li et al., 2004; Wang & Vemuri, 2005; Freidlin et al., 2009). To our knowledge, this is the first investigation of correlations in white matter tract-based DTI parameters across individuals and the first to use these inter-tract correlations to determine whether there are specific microstructural relationships between fiber pathways. Hierarchical clustering analysis suggests that the strength of the observed correlations might reflect anatomic, phylogenetic, and/or functional similarities between tracts. This would explain why homologous tracts tended to cluster together, except in cases like the AF where known anatomic and functional hemispheric asymmetries exist. Phylogenetic and functional differences may also explain why neocortical and limbic association tracts group separately on the FA dendrogram, yet are more closely related to each other microstructurally than to a cortical-subcortical projection pathway such as the corticospinal tract.

The best current evidence is that the biophysical basis of white matter anisotropy is related to the effect of longitudinally oriented axonal membranes, the coherence of the parallel organization of axons within fibers, the packing density of the fibers, and their degree of myelination (Beaulieu et al., 2002). Presently, the question of which of these underlying biophysical substrates govern the microstructural relationships among different tracts remains unresolved and is worthy of further investigation in animal models. On the clinical side, there are many possible variables that might influence inter-tract correlations in the human brain. Demographic attributes such as age, gender, and intelligence quotient, among many other factors, may contribute to these microstructural relationships. These await future research on larger cohorts, in which such dependencies can be evaluated with adequate statistical power. Of these demographic variables, age is the one that has been best studied in the DTI literature (Pfefferbaum et al., 2000; Mukherjee et al., 2001; Salat et al., 2005; Snook et al., 2005; Hermoye et al., 2006). Based on what is known about the age dependence of the DTI parameters that we have investigated, it is unlikely to be the primary factor driving the correlations. Our sample consisted of adults from 20–50 years old, with a mean age of approximately 31 and a standard deviation of less than 8 years, so any effects of maturation or senescence would be minimized in the age range studied. Also, there is no known mechanism by which age or other demographic factors might produce the specific patterns of inter-tract correlations observed in this study.

Another potential cause of these microstructural correlations is spatial overlap in the course of the white matter tracts due to intravoxel partial volume averaging where two fiber pathways are in close proximity. The effects of partial volume averaging between tracts were minimized in this study by the relatively high spatial resolution of the DTI acquisition, with 1.8-mm voxels in all three dimensions, as well as the high angular resolution provided by 55 diffusion-weighted gradient directions, which serves to reduce error in the estimation of the principal diffusion tensor eigenvector at each voxel and enable more accurate fiber tracking (Jones 2004). Among the six pairs of tracts examined, regions of overlap were found between the IFO and the UF in the subinsular white matter (the external and extreme capsules), the temporal stem, and the inferior frontal lobe. An average of 7–11% of voxels were shared between the IFO and UF in each hemisphere. Spatial overlap between the IFO and ILF along the posterior aspect of their courses resulted in an average of 10–11% shared voxels in each hemisphere. While spatial overlap between these tracts may possibly contribute to the observed microstructural correlations, the low percentage of shared voxels and the high correlation coefficients show that it cannot be the decisive factor. Tables 2–5 show many instances of tracts correlating as well with non-homologous tracts of the contralateral hemisphere as with overlapping ipsilateral tracts. For example, the FA correlation between the left IFO and the left UF (*ρ* = 0.70), which have an average of 11% voxels in common, is identical to that between the left IFO and the right UF (*ρ* = 0.70), which have no shared voxels. Hence, if the high FA correlation between left IFO and left UF is explained only by spatial overlap, then the left and right UF would have to be perfectly correlated to account for the similarly high correlation between left IFO and right UF. Yet, the measured FA correlation between left and right UF is only at the same 0.70 level as that between left ILF and either UF.

It remains currently unresolved whether the microstructural correlations revealed herein are present from birth or whether they gradually develop during postnatal life. Studies of brain development in fetuses, newborns, infants, and children will hopefully elucidate the extent to which these findings are the result of genetic programming and how much may instead reflect usage-dependent neuroplasticity, perhaps even extending into adulthood and modulated over time by changes in cognition and other aspects of behavior. Under this hypothesis, long-term repetitive activation of brain networks subserving particular forms of cognition and behavior, or of the so-called resting state brain networks (Biswal et al., 1995; Greicius et al., 2003; Fox et al., 2005), may result in microstructural changes specific to the tracts interconnecting those networks. Variation in this network-based activity may drive inter-individual differences in tract-based DTI parameters that are correlated for pathways belonging to the same functional networks. This premise remains to be tested in studies of neuroplasticity that combine functional imaging with diffusion-based white matter microstructural analysis.

The study of microstructural correlations between white matter tracts might provide a new perspective with which to examine neurological and psychiatric diseases, including the effects of brain malformations, brain injury, and neurodegeneration. For example, in adults with agenesis of the corpus callosum, one might hypothesize that microstructural correlations between homologous tracts in the left and right cerebral hemispheres would be less than that in the normally formed brain due to the reduced interhemispheric functional connectivity that has been demonstrated in these acallosal subjects with both task activation and resting state fMRI (Quigley et al., 2003). In traumatic brain injury, reduced FA has been reported in numerous white matter pathways (Arfanakis et al., 2002; Kraus et al. 2007; Niogi et al. 2008a) and injury to specific tracts is associated with particular cognitive deficits (Niogi et al. 2008b). It would be interesting to ascertain whether traumatic axonal injury reduces the microstructural correlations seen in the uninjured brain, or whether networks of tracts correlated at the microstructural level might show synchronous post-traumatic degeneration. Similarly, recent work in neurodegenerative disorders using functional connectivity fMRI techniques has emphasized the importance of network-based neurodegeneration, with involvement of distinct cortical networks for each type of clinical disorder such as Alzheimer disease and frontotemporal dementia (Seeley et al. 2009). The examination of altered microstructural correlations in the affected white matter pathways could add a new dimension to the pathophysiological understanding of neurodegenerative diseases.

Knowledge of the underlying correlation structure of white matter microarchitecture should aid studies of the effect of white matter on cognition and behavior, as well as studies of genetic influences on white matter microstructure (Nierenberg et al., 2005; Persson et al., 2006; McIntosh et al., 2008; Winterer et al., 2008; Chiang et al., 2009). In particular, microstructural correlation matrices might be useful as prior information for Bayesian inferences in relating genes to white matter and in relating white matter to cognition and behavior. For these purposes, maps of white matter correlational structure at a finer spatial scale than that of whole tracts, such as at the voxel level, would be more powerful. However, voxel-level correlation matrices would have vastly greater dimensionality than those from tract-based measures, and would therefore require much larger datasets to provide statistically significant information. The recently developed tract-based morphometry approach (O’Donnell et al., 2009) might represent a more practical alternative, as it has already been used to reveal regions within the left and right CB that have statistically significant microstructural asymmetry between hemispheres. This methodology might be extended to explore more generally microstructural correlations at a spatial scale less than that of whole tracts. Of note, our study explored correlations using univariate scalar quantities derived from the diffusion tensor, such as FA and MD. More microstructural information might be obtained about human white matter architecture by employing a tensor-variate measure of distance instead (Pasternak et al., 2009). This is another promising avenue for further investigation.

This initial survey of the microstructural correlation patterns of the human brain was limited by modest sample size (*n* = 44). The number of subjects was sufficient to achieve the three primary objectives of this study: (1) to determine that there are statistically significant microstructural correlations among white matter tracts, (2) to establish that there are statistically significant variations in these microstructural correlations, and (3) to use these variations to preliminarily group the fiber tracts based on relatedness of microarchitecture. However, the number of white matter tracts that could be examined was constrained by the size of the cohort, since the number of pairwise comparisons increases quadratically with the number of pathways, rapidly leading to a loss of statistical power. Therefore, we chose to limit our evaluation to six pairs of white matter tracts which have diverse phylogenetic origins and functions, which can be compared across hemispheres, and for which reproducible quantitative fiber tracking protocols have been established (Wakana et al., 2007; Danielian et al., 2009). Although statistically significant groupings of the tracts could be ascertained from hierarchical clustering analysis of the FA and MD correlation matrices, those linkages with greater degrees of uncertainty in all four DTI correlational matrices must be regarded as provisional until confirmed by a larger-scale study. Furthermore, the statistical confidence levels of the four dendrograms were not corrected for multiple comparisons, one for each of the DTI parameters, in the absence of any known principled way to correct dendrograms for multiple comparisons across correlated variables such as FA, MD, AD, and RD. However, the central result that the two projection pathways cluster separately from the ten association pathways for FA has strong enough statistical confidence to survive even Bonferroni correction for the four comparisons. It is also important to note that the dendrogram structure for DTI parameters that are known to be highly correlated (e.g. FA and RD) are more similar than for DTI parameters that are less strongly associated (e.g. FA and MD). We believe that this correspondence represents further evidence for the accuracy of the clustering results.

This investigation was also limited by the rank-2 tensor model of diffusion, which has well known shortcomings for tractography in regions of complex white matter architecture such as intravoxel crossing fibers (Frank et al., 2001; Tuch et al., 2004). For example, the laterally oriented motor fibers representing the face and arm are typically not trackable using DTI; hence, CST tractography is limited to the motor representation of the lower half of the body, located at the vertex of the primary motor cortex (Figure 1F). Moreover, errors in fiber tracking due to intravoxel partial volume averaging of fiber populations with different orientations could potentially lead to sampling of non-equivalent portions of tracts across different subjects, which would be expected to artifactually reduce the measured microstructural correlations by introducing another source of variation. These problems could potentially be overcome by using fiber tracking based on newer mathematical models that do not assume Gaussian diffusion, such as *q*-ball imaging (Tuch et al., 2004; Hess et al., 2006; Barnett et al., 2009; Canales-Rodríguez et al., 2009), spherical deconvolution (Tournier et al., 2004), and the diffusion orientation transform (Ozarslan et al., 2006), to name a few. Extending the diffusion measurements to multiple b-values, including values well in excess of the 1000 s/mm^{2} used in this study, would permit full or hybrid *q*-space analysis (Cohen & Assaf, 2002; Wedeen et al., 2005; Wu & Alexander, 2007) combined with biophysical modeling (Assaf & Basser, 2005; Assaf et al., 2008) that may yield more and better microstructural parameters for correlational analysis than could be obtained from DTI.

Taken together, these initial results from DTI correlation analysis provide evidence for our hypotheses that specific relationships exist in the microstructural organization of different white matter pathways beyond those of homologous pairs of tracts in the two cerebral hemispheres, and that these relationships may reflect phylogenetic and/or functional similarities between tracts. Further studies of inter-tract DTI correlations encompassing many more pathways in a larger cohort will likely provide a wealth of novel and interesting information about the architecture of human brain networks, especially in combination with functional connectivity data from fMRI (Biswal et al., 1995; Greicius et al., 2003; Fox et al., 2005) as well as macrostructural covariance data from structural MRI measures of regional cortical thickness (He et al., 2007). Greater knowledge of the microstructural relationships between white matter pathways might aid studies of the genetics and of the behavioral effects of white matter architecture, as well as provide a revealing new perspective with which to investigate neurologic disorders such as brain malformations, brain injury, and neurodegeneration.

This study was supported by grants from the James S. McDonnell Foundation, the Charles A. Dana Foundation, the American Society of Neuroradiology, the U.S. National Institutes of Health (R01 NS060776), and the Academic Senate of the University of California, San Francisco. The authors would like to thank Ryota Suzuki for helpful discussions on hierarchical data clustering and for providing R code modifications for the pvclust algorithm to enable Spearman’s rank correlation coefficient as a distance measure.

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