Our study population consisted of data from the expanded DTI (eDTI) protocol of the NIH Pediatric MRI Data database (NIHPD) (36). The study included 182 brain scans from 152 unique individuals ranging in ages from 0 to 21 years. Please refer to Supplementary Figure S.1 for details regarding the age group distribution and number of subjects within each group.

The image acquisition for the eDTI protocol was designed with adequate b-values and directions with a goal of assessing brain scans from infants and young children with greater sensitivity. The image acquisition and processing are described elsewhere (36). Briefly, the eDTI protocol included b = 0 s/mm²; 9 images (GE), 10 images (Siemens), b = 100 s/mm²; 10 images, b = 300 s/mm²; 10 images, b = 500 s/mm²; 10 images, b = 800 s/mm²; 30 images, and b = 1,100 s/mm²; 50 images, with full brain coverage using 60 slices, 2.5 mm slice thickness, FOV = 240 mm with a 96 × 96 matrix resulting in 2.5 × 2.5 × 2.5 mm³ voxels. All data were processed using TORTOISE software (37) and the processed data went through rigorous quality control (36, 38). The DWI processing steps included: (1) correction of eddy and motion distortion artifacts, (2) correction of susceptibility induced EPI distortions, and (3) reorientation of the corrected data to its respective AC-PC structural reference image.

To achieve accurate registration in all brain regions, specifically for the alignment of individual WM pathways, we employed DRTAMAS (36), a diffusion tensor-based diffeomorphic registration and atlas creation pipeline. A young adult template was initially generated using DRTAMAS using 38 subjects [male (n = 20, mean = 19.7, SD = 1.3 yrs.), and female (n = 18, mean = 19.8 yrs., SD = 1.2 yrs.)] within the 18–21-year age group, with an average age of 19.5 years. Subsequently, the diffusion tensors from all study subjects were diffeomorphically aligned to this reference template to enable voxelwise and ROI-wise analysis. The term young adult template and reference template will be used interchangeably for the rest of the paper.

As described in the previous section, the goal was to evaluate the changes in volume and DTI metrics of individual brains across the different age groups relative to the values from the young adult template. Due to the large age range of the subjects included in the study, brain size differences were significant. To avoid potential misregistration due to such large morphometric differences, we adopted a two-step registration strategy: the first step involved the creation of age specific group templates and the second step involved the registration of these age-specific templates to the young adult template. We hypothesized that this approach would be less susceptible to registration local minima compared to the direct approach where very young brains are registered to the adult template. To achieve this two-step strategy, individual scans were first grouped to create nineteen age-specific groups. An individual template was created for each age-specific group using the registration strategies described in the previous section (39). Age-specific group templates were created initially in increments of 6 months until 2 years to capture the rapid changes in morphology and DTI metrics at the youngest ages, and thereafter age-specific group templates were created in increments of 1 year. Please refer to Supplementary Figure S.1 for details describing the age distribution and number of subjects included in each age group.

The image registration process generates a transformation that maps the moving (source) image to the fixed (target) image. Therefore, in our two-step registration framework, two sets of transformations were computed: the first set mapping each individual brain onto its corresponding age-specific template and the second set mapping the age-specific template to the young adult template. Supplementary Figure S.2 provides a schematic representation of the template creation pipeline.

These two transformations are subsequently combined to capture the overall mapping of individual brains to the adult template. The DTI-derived scalar maps, such as FA, MD, RD and AD were computed in the native space of the subjects, then warped onto the reference template space using the combined transformations, thereby normalizing all the DTI metrics across the study. Since the transformation map contains the amount of size and shape change a brain had to undergo to match the reference template, the volume of each brain and its local structures in relation to the adult brain could be assessed. In order to extract the quantitative volume change information, the Jacobian matrices of the combined transformation fields were first computed and the determinant of these voxelwise matrices were extracted to be used as a measure of local volume change. Figure 1 provides an example of a few salient age groups, showing large changes in brain morphometry and the resulting determinant of Jacobian maps. It should be noted that color brightness in the directionally encoded color maps is modulated by FA. Therefore, in very young brains the color brightness is low, with the brightness increasing with each age group, due to increasing FA with age.

It should also be noted that the Jacobian maps (row B of Figure 1) capture the morphometric changes various brain structures had to undergo to match the adult template. These features appear less detailed as age increases.

With the registration steps detailed in section 2.4–2.5 we had achieved a voxel-wise correspondence between each subject and the reference template. Therefore, ROIs defined on the reference template can be used to extract measurements from the spatially normalized volume and DTI metrics maps. While the JHU (Johns Hopkins University) WM ROIs (40) are informative and readily available to be used in this type of analysis, it is defined on a single subject brain. Moreover, the ROIs are available only using registration to an FA template, with the ROIs larger in size and with some left and right discrepancies (41). The large ROIs can be problematic when extracting information from brains of very young subjects, because they may be more prone to partial volume effects, confounding the measurements for these very young age groups. Therefore, for this study, we used subcortical WM ROIs defined on a Human Connectome DTI template (42). These WM ROIs were drawn on the HCP template with the JHU WM ROIs as a reference but making sure that ROIs were restricted more to the core of the tract. Tensor based registration was performed between the HCP DTI template and the reference template for the study to transform the ROIs defined on the HCP template into the young adult template space using nearest neighbor interpolation. Putamen and Thalamus ROIs were defined on the young adult template. Due to anatomical variability, diffeomorphism in image registration is violated and accurate registration of data in the cortical folding cannot be achieved. Therefore, the only gray matter regions that could be reasonably assessed are the deep gray matter regions included in this study, namely, Putamen and Thalamus. These regions are added as control regions and were appropriate to be included due to reliability of registration in these regions compared to the cortex. Please refer to Supplementary Figure S.3 for information regarding the anatomical locations of the ROIs used in the analysis.

Thirty-four WM ROIs (inclusive of left and right structures) used for the study are grouped under commissural, associative, projection, and cerebellar pathways. The following section details the structures categorized under each pathway.

Commissural: Genu, Body, and Splenium of the Corpus Callosum, and Pontine Crossing Tract.

Association: External Capsule, Cingulum Cingulate Gyrus, Cingulum Hippocampus, Fornix Cres Stria Terminalis, Fornix, Superior Longitudinal Fasciculus, Superior Fronto-Occipital Fasciculus, Uncinate Fasciculus.

Projection: Cerebral Peduncle, Posterior Limb of Internal Capsule, Retro-lenticular part of Internal Capsule, Corticospinal Tract, and Medial Lemniscus.

Cerebellar: Inferior, superior, and middle cerebellar peduncle.

From visual observation, the percentage change in whole brain volume per subject, with respect to age, shows a nonlinear growth trajectory with a steep increase in volume in the initial years from birth, followed by a flattening of the trajectory (refer to Supplementary Figure S.4a). The ‘change-point’ in the trajectory of whole brain volume growth can be identified using two linear regressions (refer to section S.4 in the supplement). This approach allowed for a data driven approach of dividing the data into groups informed by the behavior of the growth trajectory of the whole brain volume across the age span of the study. Following this, ROI values, which were quantitively normalized from DTI metrics and for volume, were split into two groups; segment 1 before the ‘change-point’ (< 2.69 years) and segment 2 after the ‘change-point’ (> 2.69 years). Quantile regression was performed on each segment of the data, per ROI and metric. This regression step generated three parameters about the fitting performed in each segment from which we made some biological inferences. The parameters and their biological inferences are detailed below:

Intercept 1 = The estimated value at birth (age = 0) derived from a regression model of metrics already normalized to the young adult template.

Slope 1 = The rate of change in normalized metric values per year for segment 1, inferred as rate of growth until the ‘change-point’ age, expressed in percentage points relative to the young adult reference.

Slope 2 = The rate of change in normalized metric values per year for segment 2, inferred as rate of growth after the ‘change-point’ age, expressed in percentage points relative to the young adult reference.

Tables 1, 2 show the intercept (Segment 1) and slope values (Segments 1 and 2), respectively for all global volume and DTI measurements. For the rest of the manuscript, the intercept corresponding to Segment 1 will be referred to as ‘Intercept 1’ and the slopes corresponding to Segments 1 and 2 will be referred to as ‘Slope 1’ and ‘Slope 2’, respectively. All values reported in the tables are normalized with respect to the median value observed in the developed young-adult brain template, which is defined as 100%. Therefore, the regression intercept reflects the estimated value for a metric at birth (i.e age = 0), derived from a regression model of metrics already normalized to the adult template. For example, an intercept with a value of 40% indicates that the metric at birth is 40% of the young adult reference value, whereas an intercept of 140% indicates a value that is 40% greater than the adult reference value. The slopes represent the rate of change in normalized metric values per year, expressed in percentage points relative to the adult reference value.

In the context of the current analysis, for example, at birth, (Intercept 1, at age = 0 years) the whole brain volume is 45% (last row, Table 1) of the young adult brain volume, indicating that the brain of children younger than 3 years old have only developed 45% of the reference young-adult brain volume. The volume changes at a rapid rate of 20% per year (Slope 1, last row, Table 1) until 2.69 years, thereafter, considerably slows down in growth to 0.1% per year (Slope 2, last row, Table 2) to reach the adult brain size.

Furthermore, at birth, the global WM is 32% (Table 1, row 2) of the volume in young-adults. In comparison, WM anisotropy (FA) is 65% of the adult FA values (Table 1, row 2), while diffusivity (MD, RD and AD) values are at 134, 158 and 112% of the young-adult WM diffusivity values, respectively (Table 1, row 2).

In the first few years following birth, Slope 1 for global WM volume and FA are comparable at 13.9 and 11.7% per year, respectively (Table 2, row 2). It indicates that WM volume and its maturation are progressing at a similar rate, albeit at a slightly slower trajectory compared to the rapidly increasing whole brain volume. It should be noted that while MD changes by −15.6% per year, (Table 2, row 2), it is comparable to the rate of increase in FA in these initial years. RD decreases slightly more rapidly at −26.4% per year to arrive at adult brain RD values. The change in AD is noticeably slower in comparison at −7.1% per year (Table 2).

The rate of change considerably slows down for all metrics after 2.69 years, as seen from Slope 2 values in Table 2. In general, both anisotropy (FA = 0.4% per year) and diffusivity (MD = −0.4%, AD = 0.2% and RD = 0.7% per year) rates go down significantly. Interestingly, while the global brain volume can be observed to change at a very slow rate of 0.1% per year (last row), the change in WM volume was still noticeable at a yearly rate of 1.3% (row 2) to reach the adult brain size.

For the purpose of simplicity and clarity, here we present results from ‘pathway-averaged’ statistical estimates. For each pathway group, the intercept 1, slope 1 and slope 2 parameters are averaged and presented in Tables 3, 4. Please note, we also refer to some relevant estimates of specific ROIs. However, all ROI-wise estimates are tabulated in Supplementary Tables S1and S2 in the supplement for reference. Considering all intercept 1 values from specific ROIs in Supplementary Table S1, we observe that there is a high variability in magnitude of the relative volume change across the WM pathways. When grouped under specific pathway categories, they do not show any noticeable behavior across metrics (Table 3). However, while the differences are not large among Commissural, Association, and Cerebellar pathways for average slope 1 in the first 2.69 years, Commissural pathways on average have a steeper rate of change at 20.8% per year, (Table 4, row 1) compared to the Projection pathways changing 8.7% per year (Table 4, row 3). In addition, on average, the projection pathways have an average higher yearly rate of growth (slope 2 = 2.4% per year) compared to the slower yearly rate of growth of the Commissural pathways (slope 2 = 0.8% per year).

The Corticospinal tract and Corpus Callosum, belonging to the Commissural and Projection pathways respectively, show distinct behavior for intercept 1, slopes 1 and 2 (see Supplementary Tables S1 and S2). The Corticospinal tract and Genu and Splenium of Corpus Callosum have similar intercept 1 values approximately ranging between 12 and 16% of the adult brain volume. However, a distinction can be observed at their yearly rate of change. For example, slope 1 of the Corticospinal tract indicates a comparatively slower rate of change of less than 7% per year, (see Supplementary Table S2, rows 5 and 6) compared to the Corpus Callosum, where the Genu and Splenium change at a similar rate of 23.9–29.9% per year, respectively (Supplementary Table S2, rows 1 and 3). Interestingly, the body of the Corpus Callosum shows a rate of change of 10.3% per year, which is close to that of the Corticospinal tract. The plots in Figures 2, 3 show the distinct behavior of the growth trajectories for the two pathways. Please refer to section Supplementary Figures S.5A–P of the supplement for plots presented on remaining WM ROIs not shown here.

Although MRI is clearly sensitive to compositional, structural, and architectural changes occurring in brain tissue during development, it is much more difficult to establish the specificity of different MRI derived metrics to distinctly occuring biological processes. Moreover, a complete picture of the postnatal changes occurring in the brain is still not available even from anatomical post-mortem studies in humans and studies with invasive methods in animals. There is a general agreement that the number of long range axonal fibers would not increase after birth (if anything it may decrease due to selective pruning) (44), therefore the increase in volume should not be attributed to an increase in the number of fibers. However, during postnatal development, the overall axon diameter increases both for an increase in the cross-section of the axon itself and for the deposition of additional myelin wraps (45). In the immature brain, there is a higher content of water in the interstitial (inter-axonal) space with respect to the adult brain, resulting in larger inter-axonal distances and lower extra-axonal tortuosity (46). As the brain matures, the water content of the interstitial space decreases (46), which in theory should contribute to a decrease of the local volume of the fiber we measure with DTBM. The volumetric changes that we measure with DTBM are probably the result of these two opposite mechanisms: growth of axon diameter and thickness of myelin sheet, with a shrinkage of the extracellular space. These phenomena also affect the diffusion tensor metrics, although in a different way. It is not completely clear how myelination affects diffusion anisotropy. It is clear that unmyelinated fibers show diffusional anisotropy (46), although myelination may contribute to increased anisotropy by reducing the rate of exchange between intra- and extra-axonal water. For sure, as also demonstrated by methods other than MRI, there is an increased tortuosity of the interstitial space which increases anisotropy, with a reduction of radial diffusivity, and consequently a reduction of mean diffusivity in WM (46).

One strength of our study is that we were able to examine ages ranging from infancy to early adulthood. Imaging the brain at a very young age is challenging due to limitations posed by recruitment, retainment, and data quality due to motion artifacts. This large age range has allowed us to normalize age specific measurements to the values reached in young adulthood. Another strength is the novelty of the methodology used for volumetric measurements and the ability to compare and contrast volumetric and DTI metrics in each region. The DTI-based diffeomorphic registration has allowed visually reliable coregistration of structures across different subjects over a large age range. However, we cannot rule out regional differences in the quality of the registration, resulting in inaccurate information in some areas. For example, we did not include cortical areas in our analysis because, given the high interindividual variability in cortical folding, we were not confident that the intersubject registration would have been meaningful in the cortex. There are a few weaknesses with the study sample we have used for the analysis. We have performed the analysis on mostly cross-sectional data that were acquired on two different scanners. The cross-sectional design is not ideal to evaluate developmental trajectories and can only describe average developmental trends. The added effect of developmental changes with the small sample size for the study precluded the test for scanner-related variability on the results. In addition, the small number of subjects under the age of 2.7 years made it challenging to examine the rapid growth changes at smaller intervals within this period. Also, the relative scarcity of female subjects in the lower age range was not suitable for examination of potential sex related differences in developmental trajectories. Future studies should consider conducting similar analysis with DTBM in a larger sample with longitudinal data.