The data used in the present study were selected from the publicly released dataset “the Nathan Kline Institute/Rockland Sample (NKI–RS)”¹ (Nooner et al., 2012). The data acquisition was approved by the institutional review board of the Nathan Kline Institute. The initial release of the NKI-RS dataset included 207 participants, each of whom underwent multimodal brain scans and a battery of clinical assessments. One hundred and eleven healthy adult subjects aged 18~55 years (mean age: 35.00 ± 11.19 years, 71 males), whose DTI data were available, were included in the present study.

The MRI data were acquired using a 3.0 T SIEMENS Trio scanner. The DTI images were acquired using the following parameters: TR/TE = 10,000/91 ms, FOV = 256 mm, spatial resolution = 2.0 × 2.0 × 2.0 mm, slices = 58, 64 diffusion encoding directions, b-value = 1000 s/mm² and 12 non-diffusion volumes. Further details about the image acquisition protocol could be found on the INDI website provided above. Other images not used in the present study will not be described here.

FMRIB’s Diffusion Toolbox (FDT) in FMRIB’S Software Library (FSL)² was used for image preprocessing. The images were first skull stripped and then were corrected for eddy currents. A diffusion tensor model was fit to each voxel to generate FA, MD, AD and RD images. The standard TBSS procedure (Smith et al., 2006) was applied in this study to obtain the skeletonized images of the four DTI metrics. Specifically, all subjects’ FA images were first nonlinearly aligned to the FA template in the MNI space³. The aligned FA images were averaged to create a mean FA image, which was then thinned to create a skeletonized mean FA image, and a skeleton mask was finally created by thresholding the mean FA skeleton with FA ≥ 0.3 (Smith et al., 2006; Chiang et al., 2009; Mwangi et al., 2013). Here, we used a threshold of FA ≥ 0.3 mainly for consistency with the study by Mwangi et al. (2013), which was also based on the dataset “NKI–RS”. In addition, false positives may be reduced with the use of a higher FA threshold, as voxels which are primarily gray matter or cerebral spinal fluid in some subjects would be largely excluded (Smith et al., 2006). Each subject’s (aligned) FA image was finally projected onto the skeleton by filling the skeleton with FA values from the nearest relevant tract center. The skeletons for the MD, RD and AD images were created by first nonlinearly aligning to the FA template in the MNI space and then projecting onto the mean FA skeleton. All further analyses were based on the skeletonized images of the DTI metrics.

We first performed global-level statistical analyses to test whether there were general changes in any metric. We obtained the mean of each DTI metric (across the voxels within the FA skeleton mask) of each subject using “fslmeants” command in FSL, and then each mean DTI metric was correlated with age across subjects. As the DTI metrics were reported to change nonlinearly throughout life (Hasan et al., 2009; Westlye et al., 2010; Lebel et al., 2012), we also modeled the mean of each DTI metric as a quadratic function of age (A × (age − B)² + C) to check whether age-related changes of the DTI metrics from early to mid-adulthood can be well fitted using a nonlinear model.

To test for regional microstructural changes, age was then correlated with each DTI metric of the voxels within the FA skeleton mask in a voxel-wise manner. For this purpose, 5000 permutations were performed on the skeletonized images of each DTI metric across subjects using “randomize” command in FSL. The voxel-wise correlation maps were thresholded at p < 0.05 (family-wise error (FWE) corrected) and cluster size ≥ 10 mm³. Statistically significant clusters were filled using the “TBSS_fill” command in FSL beforehand for display convenience.

We then estimated individuals’ ages based on each DTI metric to test whether the microstructural changes of the human brain are specific enough to decode individuals’ ages using E-Net. Specifically, for each DTI metric, we entered the metric of all voxels within the FA skeleton mask into the following linear model in a voxel-wise manner: (1)y = ∑j = 1dβjxj+β0+ε

where y is the age of the subject; d is the number of variables, and here d was 97602; x_js (j = 0, 2, …, d) are voxel-wise DTI metrics; β_js (j = 0, 2, …, d) are the model parameters, and ε is the error term. Penalized least squares approach with E-Net penalty (a weighted sum of the least absolute shrinkage and selection operator (LASSO) penalty and ridge penalty) was used to estimate the parameters of the model (Zou and Hastie, 2005). The aim of the approach is to minimize the E-Net cost function: (2)∑i = 1N(yi−∑j = 1dβjxij − β0)2+λ∑j = 1d(α|βj|+ 0.5(1 − α)(βj)2)

where y_i is the age of subject i; N is the number of subjects; x_ij is the jth variable (DTI metric of a voxel) of subject i; λ and α are regularization parameters. The LASSO penalty ∑j = 1d|βj| leads to sparse models by setting some parameters (β_js) to zero, and the ridge penalty ∑j = 1d(βj)2 encourages the β_js for the correlated variables (voxel-wise DTI metrics) to have approximately the same value. The regularization parameters λ and α set the sparsity of the model and tune the ratio between the ridge and LASSO penalties, respectively.

In this study, E-Net was performed using Glmnet (Friedman et al., 2010)⁴. Leave one out cross validation (LOOCV) was used to estimate the performance of the predictors. Within each of the 111 LOOCV loops, one sample was set as the test sample, all the other 110 samples were set as the training samples, and the brain age of the test sample was estimated using the predictive model trained completely on the 110 training samples. With the use of LOOCV, the test sample was assumed to be independent of the training samples. It should be noted that this assumption of independence may sometimes not strictly hold, though LOOCV has been widely accepted in the region (Dosenbach et al., 2010; Mwangi et al., 2013; Tian et al., 2016). A more reliable way may be training the model using one dataset and evaluating the model using another dataset, if a second dataset were available.

The regularization parameters λ and α were optimized for each LOOCV loop. Specifically, for each training-set (including 110 samples), we tried 10 α values (α ∈ [0.5, 0.95] in steps of 0.05, we set α ≥ 0.5 to give more weight for the LASSO penalty) and 100 λ values. Based on each λ-α pair, “inner” cross validation was then performed, and the λ-α pair that maximize the correlation between the estimated and chronological ages (based on the 110 training samples) were selected as the optimal regularization parameters for the current training samples (Tian et al., 2016). Brain age estimation was then performed on the corresponding testing data using the optimal λ-α pair.

Pearson’s correlation coefficient and mean absolute error (MAE) between the estimated and chronological ages were used to evaluate the performance of the estimations. Using 500 permutations, we estimated how likely we were to observe the same brain age estimation performance by chance. Specifically, the chronological ages of the subjects were randomly permuted 500 times (randomly assign the age of one subject to another), and the entire estimation process was carried out with each set of the permuted ages.

In this study, we observed both global and regional negative age-vs-FA correlations (Figures 1A, 2, Table 1) and suggest that the correlations indicate microstructural aging of the human brain from early to mid-adulthood. FA decrease is an important characteristic of aging. Decreases in FA in the elderly have been suggested to signify worsening white matter integrity, and quite a few studies linked decreases in FA in the elderly to mild demyelination and loss of myelinated axons in them (Benedetti et al., 2006; Ardekani et al., 2007; Grieve et al., 2007; Charlton et al., 2008; Madden et al., 2009; Lebel et al., 2010; Ly et al., 2014). Accordingly, the statistically significant negative age-vs-FA correlations observed in the current study (Figures 1A, 2, Table 1) may indicate an overall microstructural aging of the human brain from early to mid-adulthood.

Regional negative age-vs-FA correlations were observed in such fibers as the CCg, the CST, the fornix, the SLF and the ILF (Figure 2). Each of the fibers has been reported to show statistically significant FA decreases in former aging studies (Abe et al., 2002; Zahr et al., 2009; Teipel et al., 2010; Lövdén et al., 2014). Specifically, the CCg, which connects the bilateral prefrontal lobes, have been reported to be rather susceptible to aging (Pfefferbaum et al., 2000; Abe et al., 2002; Bhagat and Beaulieu, 2004; Ota et al., 2006; Hsu et al., 2010; Zhang et al., 2010). The early aging of CCg has been related to the fact that up to 20%–30% of its axons are unmyelinated (Lamantia and Rakic, 1990; Pagani et al., 2008). FA declines in the CCg in the elderly have been reported to be associated with lower perceptual speed and longer episodic retrieval reaction time (Schulte et al., 2005; Bucur et al., 2008), as well as poor performance in reasoning in them (Monge et al., 2016). CST is a major neural tract in the human brain for motor function. Numerous studies on aging reported FA decreases in the CST (Terao et al., 1994; Lövdén et al., 2014; Vik et al., 2015), and these decreases have been reported to be accompanied by reduction in the number of myelinated fibers and thinning of the tissue it originates (Terao et al., 1994). FA decreases in the CST have been reported to contribute much to decreases of perceptual speed in the elderly (Lövdén et al., 2014; Johnson et al., 2015; Vik et al., 2015). The SLF connects the temporo-parietal junction area and parietal lobe with the frontal lobe (Makris et al., 2005), and its FA decreases in the elderly have been linked with poor performance in cognitive tasks in them (Perry et al., 2009; Stamatakis et al., 2011; Lockhart et al., 2012; Sasson et al., 2012). Quite a few studies on aging reported age-related FA decreases in the fornix (Pagani et al., 2008; Stadlbauer et al., 2008; Lee et al., 2009; Zahr et al., 2009; Sullivan et al., 2010), a part of the limbic system important for episodic memory recall (Tsivilis et al., 2008), and declines of memory performance in the elderly have been reported to be associated with FA decreases in the fornix (Li et al., 2016; Oishi and Lyketsos, 2016). Closely relevant to the current results, the fornix, the CCg, the CCs and the ILF have been reported to be the four fibers that exhibit the earliest FA decreases in the lifespan study by Lebel et al. (2012). According to these former findings, we suggest that the statistically significant negative age-vs-FA correlations in the CCg, the CST, the fornix, the SLF and the ILF observed in the current study may indicate that the fibers are the earliest to change with aging.

In addition to FA decreases, aging of the human brain has also been associated with MD increases (Benedetti et al., 2006; Lebel et al., 2012; Ly et al., 2014). Age-vs-MD correlations in the current study, however, were not statistically significant at global level (Figure 1B) and relatively weaker than those with FA at regional level (Supplementary Figure S2, Table 2). We suggest that age-related MD increases might lag behind age-related FA decreases. This suggestion is supported by reports that MD minima significantly lags behind FA peaks, with minimum MD values occurring 6–18 years after FA peaks (Lebel et al., 2010, 2012).

The negative age-vs-FA correlations in the current study were associated primarily with negative age-vs-AD and positive age-vs-RD correlations (Figures 1A,C,D, 3). This finding is consistent with the reports of a study by Kodiweera et al. (2016), in which significant RD increases and AD decreases were observed in middle-aged adult brains. Both RD and AD have been reported to decrease with development, reach a minimum and then increase in later life (Lebel et al., 2010, 2012). RD increases and AD decreases in the elderly have often been linked to age-related demyelination (Song et al., 2002, 2005; Bennett et al., 2010) and axonal shrinkage (Song et al., 2003; Bennett et al., 2010), respectively. We speculate that the present finding of statistically significant negative age-vs-AD and positive age-vs-RD correlations may reflect an RD-preceding-AD sequence of change of the two metrics, with AD having not reached its respective minimum, while RD has already passed its minimum at the time. This speculation is supported by the report that RD reaches its minimum and begins to increase before AD (Lebel et al., 2010). If our suggestion of “RD-preceding-AD” hypothesis were valid, we suggest that our finding of the fornix being the only region exhibiting AD increase (Figure 3K) might be due to its earlier change with aging relative to other fibers: AD increases in the fornix begin at an earlier time, when other fibers still exhibit AD decreases. This suggestion is consistent with former studies that reported the earliest maturation and degeneration of the fornix (Lebel et al., 2012). Further studies based on longitudinal data, rather than cross-sectional data, as was used in the current study, are needed to test the hypothesis.

Using multivariate pattern analyses, several studies have been performed on brain age estimations based on MRI and reported relatively high accuracies (Dosenbach et al., 2010; Brown et al., 2012; Mwangi et al., 2013; Erus et al., 2015; Tian et al., 2016). Of particular interest, the study by Mwangi et al. (2013) was based on DTI data of subjects aged 4–85 years, and the study by Erus et al. (2015) was based on DTI data of subjects aged 8–22 years. As both studies included child and adolescent subjects, whose brain structures undergo great changes, successful brain age estimations are expected.

The current study included only young and middle-aged adults, whose brain structures have traditionally been deemed to be relatively stable. Our results indicate that, in contrast to the opinion that the microstructural changes from early to mid-adulthood are rather subtle as to be negligible, these changes were specific enough to decode individuals’ ages (Figure 4). In combination with the findings of statistically significant age-vs-DTI-metrics correlations, the present results highlight the necessity of considering age effects in related studies. Specifically, in studies including adult subjects covering large age span (Welcome and Joanisse, 2014; Boltzmann et al., 2017), possible age effects should be considered carefully, otherwise spurious results possibly reflecting age-effects, rather than the effect under investigation, may be obtained.

The brain age estimation based on FA was not as good as that based on RD (Figure 4). Specifically, the correlation between the estimated and chronological ages based on FA (0.62) was weaker than that based on RD (0.68), and the MAE based on FA (7.28 years) was larger than that based on RD (6.66 years). This is a bit unexpected, as the age-vs-FA correlation was the strongest at the global-level (Figure 1), and the number of statistically significant voxels was the largest in voxel-wise statistical analyses (Tables 1, 2). We suggest that strong FA-vs-age correlations do not necessarily mean better brain age estimations. That is, if there existed strong associations among the FA changes of different voxels, for an extreme example, the FA changes of all statistically significant voxels were fully correlated with each other, then the contributions of all statistically significant voxels to brain age estimations would be just the same as that of a single voxel. This suggestion is in line with the finding that the changes of FA in a tract often go together with changes in other tracts, while the changes of MD are weakly associated among each other (Lövdén et al., 2014). In addition, the present results were consistent with those in the study by Mwangi et al. (2013), in which brain age estimation based on FA was also poorer than that based on RD. Further studies are needed to evaluate the hypothesis.

Quite a few studies reported nonlinear changes of the DTI metrics in most white matter tracts of the human brain throughout life (Hasan et al., 2009; Westlye et al., 2010; Lebel et al., 2012; Sexton et al., 2014). In those studies, nonlinear models work well, as substantial microstructural changes of the human brain occur with maturation and aging, and the changes are obviously nonlinear throughout life. In those studies, it was often the changes with maturation and aging that play predominant roles (e.g., driving the evolution curve; Lebel et al., 2012; Zhao et al., 2015), though the maximum/minimum of the DTI metrics were often reported to occur during 25–45 years old (Lebel et al., 2010, 2012).

In the current study, we chose to use linear models because of the following two facts: (1) we observed no obvious nonlinear relationship between age and any DTI metric by visual inspection (Figure 1); and (2) when we modeled the mean of each DTI metric as a quadratic function of age (A × (age − B)² + C), absurd results were obtained (Supplementary Figure S1): based on the current dataset, the maximum of mean FA was estimated to occur at −18.92 years (Supplementary Figure S1A), and the minimum of mean RD was estimated to occur at 18.87 years (Supplementary Figure S1D), which was much earlier than those reported in literatures (Lebel et al., 2010, 2012). These results based on nonlinear models indicate that wrong conclusions may be drawn if nonlinear models were used inappropriately. With the use of linear models, the nonlinear changes of the DTI metrics with age, if there are, could not be detected. Therefore, it should be strengthened that the present results reflect only “overall tendencies” of the changes of the DTI metrics (e.g., FA decreases with age) from early to mid-adulthood.

There are several other methodical issues that should be addressed. First, the current study was based on cross-sectional data, rather than longitudinal data. As cross-sectional data can provide only one measurement per subject, possible bias may occur. In fact, we could not rule out the possibility that the current results may, to some degree, be influenced by such factors as cohort effects, which are inevitable in studies based on cross-sectional data. Future longitudinal studies may be better able to depict the trajectories of the microstructural changes of the human brain from early to mid-adulthood. Second, the estimation errors of the DTI metrics in crossing fibers are not negligible. Therefore, the statistically significant regional age-related correlations observed in the current study, especially those in crossing fibers, should be further evaluated, for instance, by incorporating measures of intervoxel coherence (Bennett et al., 2010). Third, with the use of TBSS, later statistical analyses and brain age estimations were all restricted to major white matter tracts. TBSS may benefit reducing false positives (Smith et al., 2006; Mwangi et al., 2013), but some true positives may be excluded, as it is possible that age-related correlations exist in regions away from major white matter tracts. Finally, gender effects were not specially considered in the current study, as there was no significant difference in age between the two genders (t = 1.08, p = 0.28). Indeed, when we included gender as a covariate into our global-level statistical analyses, little change was observed on the age-vs-FA, -MD, -AD and -RD correlations: they changed from −0.44, 0.077, −0.38 and 0.30 to −0.43, 0.078, −0.36 and 0.29, respectively.