High angular resolution diffusion imaging of neurodevelopment in children through data creation with deep learning

Abstract

High-angular resolution diffusion imaging (HARDI) is an advanced method for characterizing brain microstructure and function. However, HARDI is time-consuming limiting real-world applications, especially in children. We aimed to address the challenge by creating non-acquired HARDI data through deep learning and testing utility in neurodevelopment. Brain diffusion magnetic resonance imaging from 95 children aged 2–10 years (49 females) were examined. Each subject included two source b-value datasets: 750 s/mm² and 2000 s/mm², 30 directions each with five b0 volumes. Deep learning was voxel-wise, approximately 1,620,000 voxels from 12-subject each matched on age and sex for training and validation, respectively, to predict b2000 s/mm² from b750 s/mm² dataset. Different training samples, window sizes, and tissue inputs were also assessed. The remaining 71 individuals were used for tract-based analysis of neurodevelopment, which involved eight brain white matter tracts. Results showed that model performance improved with an increasing training sample, large window size, and additional brain segmentation input. HARDI outcomes including predicted data were similar in pattern to source-only data across tracts and metrics, with all appeared to increase with age. Additionally, tract volumes showed consistent sex differences between prediction-integrated and source-only datasets in all but pyramidal tract. Collectively, deep learning-enabled HARDI is feasible for pediatric imaging, which may help reduce scan time by half and characterize sex-specific neurodevelopment.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1038/s41598-026-60107-7.

Introduction

Understanding maturation changes of brain white matter in children is important for interpreting various functional outcomes^1,2. Diffusion-weighted magnetic resonance imaging (MRI) is a valuable tool for probing brain white matter characteristics by assessing water movement properties in a tissue such as myelin and axons³. Studies using diffusion tensor imaging (DTI) suggest that fractional anisotropy (FA) increases and mean diffusivity (MD) decreases by 5–15% in regional brain white matter tracts over 2–8 years old^4,5. However, DTI is limited in resolving crossing-fiber architectures and therefore further investigation is required⁶.

High angular resolution diffusion imaging (HARDI) has advantages over DTI^7,8. By acquiring additional diffusion weightings (b values) and directions, HARDI can provide measures with increased sensitivity and specificity to tissue microstructure, such as the neurite density index (NDI) and orientation dispersion index (ODI) from neurite orientation dispersion and density imaging (NODDI)⁹. Prior research suggests the potential of NDI and ODI for understanding neurodevelopment in children¹⁰. However, HARDI is typically time consuming and therefore prone to motion artifacts¹¹, limiting routine applications especially in children where tolerance is particularly a concern. Nonetheless, enabling HARDI in clinical practice with more specific measures of neural substrates may foster more nuanced monitoring of developmental health and disease.

Novel computational methods such as machine learning and deep learning may overcome the challenges by creating new datasets post hoc. These methods learn from examples, and with proper training, they can capture robust representations of the relationship between input and output data such as high and low b-value acquisitions. Previously deep learning using convolutional neural networks (CNNs) helped process undersampled data for robust diffusion spectrum imaging and then NODDI to predict stroke outcomes¹². Based on voxel-wise machine learning with just one individual using a multi-layer perceptron (MLP), another study showed the potential to directly predict NODDI-like metrics from multiple-weighting diffusion data that enabled 12X reduction of scan time¹³. Further, a combined CNN and MLP framework was found to be better than MLP alone and feasible for predicting high b-value from low b-value brain diffusion MRI, facilitating source-equivalent NODDI in adults with multiple sclerosis¹⁴. However, these algorithms are subject to verification in pediatric imaging.

Additionally both HARDI and DTI studies suggest region-specific developmental patterns present among brain white matter in young adulthood. There seemed to be earlier maturation in commissural and projection fibers such as the corpus callosum and pyramidal tracts than association and frontal-temporal fibers, and even differences between corpus callosum segments^15,16. These tract-based neurodevelopmental patterns were also observed in tract volumes and were sex-specific⁴. However, whether these observations hold in analyses integrating predicted data is unclear.

Our study aimed to investigate how the CNN-MLP model worked with brain diffusion MRI of early childhood collected using a clinical scanner, and how NODDI parameters generated along with predicted data compared with source-only data. Further, using longitudinal datasets, we also aimed to evaluate how prediction-integrated and source-only outcomes compared in assessing neurodevelopment stratified by tracts, diffusion parameters, and sex. Finally, to compare with the literature, FA-based neurodevelopmental analyses were also done.

Results

Data characteristics

Quality assurance excluded seven scans from three subjects. The final cohort included 226 scans from 95 individuals (49 females). The mean age was 5.64 ± 1.58 years, equivalent between sexes. Each subject had one to seven scans.

Model refinement and testing outcomes

According to spherical harmonics loss and NODDI quality metrics (Supplementary Figs. 1–5), the model performed better with more training samples involved, the best with voxels from all 12 subjects. Most models performed better with a larger window, except for NDI that favored a small window of three voxels in width. Eventually a window of 7 × 7 × 7 voxels was selected to balance. Subsequently, an input feature inclusive of probability and binary segmentations was chosen since it led to an overall better model performance than other options.

Model assessment using voxels of the 12 testing individuals showed that NDI and ODI appeared similar anatomically based on prediction-integrated versus source-only data (Figs. 1 and 2). The testing loss was persistently low at ≤ 0.03; PSNR and SSIM were high at ≥ 21 and ≥ 0.92, and RMSE and MAE were low at ≤ 0.08 and ≤ 0.05, respectively.

Fig. 1.

Template fiber orientation distribution and tractography images. Top row shows the template zero-order spherical harmonics that are computed from the source and predicted b2000 diffusion data. Bottom row shows tractography images derived from the above, with the four major white matter tracts shown.

Fig. 2.

Example images from a testing individual. Shown are raw diffusion MRI (top two rows) and NODDI parametric maps from both source-only and prediction-integrated data. The predicted NDI and ODI are computed using the predicted b2000 and source b750 data of a subject. NDI, neurite density index; ODI, orientation dispersion index.

Developmental trajectories by NODDI and DTI

Across tracts and associated metrics, positive trends were generally seen over 2–8 years of age, which showed no sex differences or age-sex interactions. The specific changes among metrics slightly differed as seen below.

In NDI, the growth rates were found to be slower in prediction-integrated than source-only data over the age range. Among major tracts, the pyramidal tract showed the fastest growing rate in source-only data (0.933 ± 0.150), followed by the Genu, Body, and then Splenium of corpus callosum (0.910 ± 0.148, 0.806 ± 0.155, and 0.748 ± 0.126, respectively; Table 1). In prediction- integrated data, while still led by the pyramidal tract (0.746 ± 0.076), the changing rate in corpus callosum was the highest in the Body, and then Genu and Splenium (0.655 ± 0.068, and 0.573 ± 0.069 and 0.510 ± 0.061, Table 1; Fig. 3). Between data sources, the NDI was significantly greater in the pyramidal tract and Body of corpus callosum in source-only than prediction- integrated results (p < 0.0001 and p < 0.05, respectively, Fig. 6). For the four other tracts, similar trends were found (first column, Supplementary Table 1; Supplementary Fig. 6). The growth rate was faster in source-only data, where the NDI was also greater in the arcuate tract (p < 0.05), than prediction-integrated data. In both datatypes, the tracts showed the same order of ranking in growth rates, with inferior fronto-occipital fasciculus being the fastest (1.008 ± 0.134 in source-only and 0.651 ± 0.065 with prediction) and cingulum being the slowest (0.794 ± 0.128 in source-only and 0.479 ± 0.066 with prediction).

Table 1.

Neurodevelopmental trajectories of neurite density index (NDI) based on source-only and predicted plus source b750 data.

Tract	Age  ± SE (×10−2)	Sex  ± SE (×10−2)	Age*Sex  ± SE (×10−2)	2 years (predicted)	Absolute change 2–8 years	Percent change 2–8 years (%)
Source-only
Global ODI	0.263 ± 0.076***	0.100 ± 0.596	−0.057 ± 0.100	0.349	0.014	4.029
Genu (CC)	0.463 ± 0.079***	− 0.044 ± 0.622	− 0.062 ± 0.106	0.325	0.026	7.983
Body (CC)	0.221 ± 0.079**	0.081 ± 0.629	− 0.059 ± 0.108	0.346	0.011	3.320
Splenium (CC)	0.204 ± 0.098*	0.579 ± 0.768	− 0.094 ± 0.129	0.374	0.009	2.523
Pyramidal	0.158 ± 0.067*	− 0.035 ± 0.525	− 0.057 ± 0.089	0.295	0.008	2.634
Predicted + Source b750
Global ODI	0.118 ± 0.035***	− 0.406 ± 0.287	0.018 ± 0.044	0.375	0.008	2.025
Genu (CC)	0.295 ± 0.051***	− 0.151 ± 0.409	− 0.024 ± 0.066	0.339	0.017	5.010
Body (CC)	0.102 ± 0.050*	− 0.254 ± 0.395	0.001 ± 0.064	0.357	0.006	1.719
Splenium (CC)	0.015 ± 0.042	− 0.381 ± 0.365	0.030 ± 0.053	0.388	0.002	0.462
Pyramidal	0.048 ± 0.045	− 0.343 ± 0.360	0.007 ± 0.059	0.302	0.003	1.023

SE for standard error; the stars indicate significance, with *** p < 0.0001. CC for corpus callosum.

Fig. 3.

Comparison of neurodevelopmental trajectories in neurite density index modeled with source (top) and predicted (bottom) b2000 diffusion data along with source b750 data for both (n = 71). The thick black lines in plots highlight the mean regression across both males and females. The thin red and blue lines highlight linear fits of data points per participant independent of the overall linear model fit to data.

Fig. 6 .

Comparison of HARDI metric values derived using source-only (original) versus prediction-integrated (predicted) data. Shown are outcomes with the four major tracts investigated. The stars highlight significant findings, with *≤0.05, and ****≤0.0001.

In ODI, the Genu and global tracts showed the most significant positive changes over age (p < 0.0001, first column, Table 2; Fig. 4). This pattern was seen based on either data source, while the growth rates were greater using source-only than prediction-integrated datasets. The relative rankings of the tracts in rates were also the same between data sources used. Pair-wise, the ODI was significantly higher in all four major tracts using prediction-integrated data than source-only data (p < 0.0001 in all assessments, see Fig. 6). Regarding the four other tracts, the growth rates were also higher in most tracts, and ODI values were lower in all tracts, in source-only than prediction-integrated results (first column, Supplementary Table 2; Supplementary Fig. 7).

Table 2.

Neurodevelopmental trajectories of orientation dispersion index (ODI) based on source-only and predicted plus source b750 data.

Tract	Age  ± SE (×10−2)	Sex  ± SE (×10−2)	Age*Sex  ± SE (×10−2)	2 years (predicted)	Absolute change 2–8 years	Percent change 2–8 years (%)
Source-only
Global ODI	0.263 ± 0.076***	0.100 ± 0.596	− 0.057 ± 0.100	0.349	0.014	4.029
Genu (CC)	0.463 ± 0.079***	− 0.044 ± 0.622	− 0.062 ± 0.106	0.325	0.026	7.983
Body (CC)	0.221 ± 0.079**	0.081 ± 0.629	− 0.059 ± 0.108	0.346	0.011	3.320
Splenium (CC)	0.204 ± 0.098*	0.579 ± 0.768	− 0.094 ± 0.129	0.374	0.009	2.523
Pyramidal	0.158 ± 0.067*	− 0.035 ± 0.525	− 0.057 ± 0.089	0.295	0.008	2.634
Predicted + Source b750
Global ODI	0.118 ± 0.035***	− 0.406 ± 0.287	0.018 ± 0.044	0.375	0.008	2.025
Genu (CC)	0.295 ± 0.051***	− 0.151 ± 0.409	− 0.024 ± 0.066	0.339	0.017	5.010
Body (CC)	0.102 ± 0.050*	− 0.254 ± 0.395	0.001 ± 0.064	0.357	0.006	1.719
Splenium (CC)	0.015 ± 0.042	− 0.381 ± 0.365	0.030 ± 0.053	0.388	0.002	0.462
Pyramidal	0.048 ± 0.045	− 0.343 ± 0.360	0.007 ± 0.059	0.302	0.003	1.023

SE for standard error; the stars indicate significance, with *p < 0.05, **p < 0.01, and ***p < 0.0001. CC for corpus callosum.

Fig. 4.

Comparison of neurodevelopmental trajectories in orientation dispersion index modeled with source (top) and predicted (bottom) b2000 diffusion data along with source b750 data for both (n = 71). The thick black lines in plots highlight the mean regression across both males and females. The thin red and blue lines highlight linear fits of data points per participant independent of the overall linear model fit to data.

In FA, the patterns of growth were highly similar in major tracts between data sources, with the changing rates and tract values being slightly lower in source-only than prediction-integrated data (first column, Supplementary Table 3; Supplementary Fig. 8). In both data sources, the growth rate was the largest in the pyramidal tract (0.461 ± 0.075 in source-only and 0.504 ± 0.046 with prediction) and smallest in the Genu (0.200 ± 0.060 in source-only and 0.259 ± 0.042 with prediction). For the four other tracts, similar patterns were seen, with greater growth rates and higher tract values detected using prediction-integrated than source-only data (first column, Supplementary Table 4; Supplementary Fig. 9). The changes were led by the inferior longitudinal fasciculus (0.423 ± 0.041 with prediction) and inferior fronto-occipital fasciculus (0.291 ± 0.050 in source-only), respectively.

Developmental trajectories by tract volume

Major Tract volumes showed an increasing trend with age, and their growth rates appearing greater in source-only than prediction-integrated datasets (first column, Table 3; Fig. 5). In both data sources, the tract volume was the highest in the splenium (746.725 ± 74.933 in source-only and 500.006 ± 66.478 with prediction) and lowest in the pyramidal tract (175.414 ± 14.695 in source-only and 146.538 ± 13.249 with prediction). Pair-wise, the tract volume was greater in prediction-integrated than source-only data in all major tracts but the splenium (see Fig. 6). In addition, these tract volumes were found to be greater in males than females (see Fig. 5—thick blue and thick red fitting lines) except for the pyramidal tract from source-only data (thick black fitting line only), with the Genu and Splenium being the most distinct areas (p < 0.001 and p < 0.05, see Table 3—second column). For the four other tracts, similar patterns were identified. The tract volumes showed a consistent growing trend between data sources in each tract, with the rates being higher while tract volumes being lower in source-only than prediction-integrated datasets. Between sexes, the tract volumes were also greater in males than females (Supplementary Tables 5—second column; Supplementary Fig. 10—thick blue and thick red fitting lines). No significant age-sex interactions were found in any tract.

Table 3.

Neurodevelopmental trajectories of tract volumes based on source-only and predicted plus source (b750) data.

Tract	Age  ± SE (×10−2)	Sex  ± SE (×10−2)	Age*Sex  ± SE (×10−2)	2 years (predicted)	Absolute change 2–8 years	Percent change 2–8 years (%)
Source-only
Global tract volume	2547.546 ± 229.721***	9544.846 ± 2257.906***	− 275.037 ± 284.988	623.283	144.602	23.200
Genu (CC)	488.000 ± 71.844***	2503.399 ± 671.298***	− 72.512 ± 89.385	148.511	27.105	18.251
Body (CC)	621.116 ± 61.597***	1236.658 ± 526.548*	− 10.753 ± 77.356	112.912	36.944	32.720
Splenium (CC)	746.725 ± 74.933***	2769.777 ± 713.822***	− 48.254 ± 93.115	177.090	43.356	24.482
Pyramidal	175.414 ± 14.695***	204.195 ± 121.433	3.274 ± 18.589	29.377	10.623	36.161
Predicted + Source b750
Global tract volume	1900.584 ± 178.789***	7605.212 ± 1945.978***	95.150 ± 220.993	618.082	116.890	18.912
Genu (CC)	410.898 ± 62.447***	2585.505 ± 636.487***	− 49.816 ± 77.351	158.278	23.159	14.632
Body (CC)	485.414 ± 50.626***	1273.929 ± 467.502**	25.698 ± 63.039	126.130	29.896	23.702
Splenium (CC)	500.006 ± 66.478***	1980.030 ± 658.651**	112.130 ± 82.440	183.166	33.364	18.215
Pyramidal	146.538 ± 13.249***	227.150 ± 112.147*	5.431 ± 16.668	31.032	8.955	28.858

SE for standard error; the stars indicate significance, with *p < 0.05, **p < 0.01, and ***p < 0.0001. CC for corpus callosum.

Fig. 5.

Comparison of neurodevelopmental trajectories in tract volumes modeled with source (top) and predicted (bottom) b2000 diffusion data (n = 71). The thick blue and red lines represent group fits for males and females, respectively, for tracts that show sex differences that include all but the pyramidal tract based on source-only data (top right). For the latter, only a thick black fitting line is shown that highlights mean regression across both sex groups. The thin red and blue lines highlight linear fits of data points per participant independent of the overall linear model fit to data.

Discussion

Using brain diffusion MRI scans of young children, this study demonstrated the utility of our deep learning approach for generating high b-value data, enabling advanced analysis of brain microstructure and neurodevelopment. The best models favored a larger training sample and window size, and combined segmentation input. Over time, while diffusion metric values appeared mostly higher in prediction-integrated than source-only data, the neurodevelopmental trajectories were essentially similar between the two data sources applied.

Hyperparameter refinement is essential in transfer learning. For this study, we began with a model used in adults with multiple sclerosis¹⁴. While the study directions overlapped, the pediatric cohort used here differed in imaging protocol, image quality, and likely brain geometry, requiring considerable model adjustment. Additionally, unlike classical deep learning, these models were often trained on a voxel basis, which might not require large numbers of subjects¹³. Our experiments suggested that training using 1.62 million voxels from 12 subjects was feasible along with a larger window (patch) size and segmentation input. Further, loss was typically evaluated in model development. However, given our focus of HARDI outcomes, both loss and HARDI-based quality metrics were considered, as done previously^14,17. Eventually, a balance between these measures was struck. Notably, data quality could be another critical factor in modeling diffusion MRI given their strong susceptibility to motion artifacts especially in young children. Our results suggested that applying motion thresholds and controlling for the number of outlier images were helpful.

The utility of our model for predicting high b-value data was manifest in each quality metric examined. Based on NODDI ODI and NDI, our metrics were in the preferred end of common value ranges, equivalent to the literature as seen in PSNR (23–26) and SSIM (0.96–0.97)^12,17. While not many associated studies assessed both RMSE and MAE, our measures were preferably low (≤ 8%) in both. Furthermore, there were notable inter-individual quality differences in the study, which however appeared similar to published work¹².

Additional neurodevelopmental analyses seemed to support the feasibility of our deep learning results. Across tracts, the diffusion measures showed a highly similar increasing trend over age between source-only and prediction-integrated datasets. With the latter, the changing rates appeared to be slower in HARDI associated metrics (NDI, ODI, and tract volume) than source-only data, but not in DTI FA that showed the opposite. Considering the mostly greater diffusion values out of prediction-integrated data than source-only data in pair-wise assessments, caution would be advised in future applications and interpretation of the methods when high b value (e.g. b = 2000 s/mm²) data is heavily involved. Tract-wise, the pyramidal tract showed the highest rates of increase in NDI and FA regardless of data source used, which might indicate the most avid growth in myelination and fiber packing in this tract over 2–8 years old¹⁸. For ODI and tract volume, the most increases were seen in the Genu and Splenium of corpus callosum, respectively, likely indicating their most development in fiber orientation and amount. These patterns seemed to agree with previous studies within a similar age range although the exact evolving rates shown were different^5,19. The difference in data fitting approaches could be a contributor. In contrast to linear mixed-effects models used here, prior work (in DTI only) applied quadratic models that might have contributed to an initial fast and later slow rate observation⁴. In addition, both our source-only and prediction-integrated results indicated higher tract volumes in males than females in all but the source pyramidal tract, supporting further investigation on sex-specific analyses⁴. Notably, there were a few outliers in NDI and ODI of the evaluated tracts, especially seen for source-only data. While pending further confirmation, we speculated that imaging ‘noise’ associated with the source b2000 data was a cause as that was the main difference between the input data sources. The lack of outliers in NDI and ODI using prediction-integrated data was likely due to the nature of prediction algorithms applied. These methods were trained on b750 data, which were inherently less noisy, to infer values of new b2000 data points. The inference was done based on common patterns associated with the majority of source data points, and therefore the outliers as part of the minority were not necessarily reflected in the predicted data. Nevertheless, the observed neurodevelopmental trends were consistent between source-only and prediction-integrated results.

This study had some limitations. The scans were associated with different degrees of ‘noise’ impacting consistency of inter-individual results. While denoising was done and our voxel-wise modeling strategy could have also helped, the current implementation might not be sufficient²⁰. Additionally, to handle the complex diffusion MRI data structure, we used spherical harmonics as done previously^14,21; however, due to the wide range of their values ranging from ± 1e−4 to 5, the contribution of higher-order coefficients that had smaller values could be missed. Our calculation of loss functions in the signal intensity domain likely provided complementary information. Further, the number of longitudinal scans varied between children. While that might impact the mean value of neurodevelopmental measures, our focus was on comparing between prediction-integrated and source-only results, which appeared consistent. Likewise, our measurement of tract volumes was not normalized by the brain size of an individual. While that might have imposed influence on the computed values as males appeared to have a larger brain size than females²², the changing patterns in tract volume were equivalent between data sources applied in this study. Furthermore, all the current data were acquired using a single scanner with virtually the same acquisition parameters. This relatively uniform setting might make it uncertain in translating the methods directly to different clinical applications. In the future, we seek to confirm our findings using multi-site datasets of different imaging protocols to verify generalizability, explore alternative denoising strategies, and develop new models to optimize the handling of spherical harmonics.

In summary, this study demonstrated the utility of our deep learning approach for predicting high b-value diffusion MRI data enabling robust HARDI analysis in a much-needed pediatric population, potentially permitting 2X reductions of imaging time and cost. The predicted data can be used together with source data to characterize neurodevelopment in brain white matter tracts of children and sex-specific analysis of tract volume. Additionally, the predicted data can be used in many other tasks required to improve the training capacity of deep learning models as shown previously in different scenarios²³. Ultimately, our findings could help expand the impact of diffusion imaging in children in centers of both high and low resources.

Methods

Participants

We used archived data from 128 typically developing children aged 2–10 years as part of a prior prospective observational study of brain development and function²⁴. All children were born at 35 or more weeks of gestation. Each child was imaged one to eight times at 6 to 12 month intervals, one to two diffusion-weighted brain MRI scans per timepoint. For the current study, 98 of 128 children who had complete demographic data and two b-value acquisitions (two shells) per timepoint were included. Following quality control, 95 of them (49 females) were eventually examined, totaling 226 scans (Fig. 7; Supplementary Fig. 11). This study was approved by the institutional Research Information Services Solution ethics board (REB13-0020), and all research was performed in accordance with the Declaration of Helsinki guidelines and regulations. Parental/guardian written informed consent was obtained, along with assent from each child.

Fig. 7.

Flowchart of the datasets used in this study

Imaging protocol

All MRI was done using a 3T scanner (MR750w, GE Healthcare, Waukesha, USA). Diffusion-weighted imaging used a two-dimensional single-shot spin-echo echo-planar sequence, one excitation per slice. The matrix size was 256 × 256, field of view was 20 × 20 cm², slice thickness was 2.2 mm, b values were 750 s/mm² (b750) and 2000 s/mm² (b2000), 30 directions each, and five interleaved non-diffusion-weighted (b = 0 s/mm²) volumes. The repetition/echo time was 6750/79 ms and 9000/97 ms for b750 and b2000, respectively.

Image preprocessing

Five typical steps were applied. These were: denoising, Gibbs ringing removal, N4 bias field correction, brain extraction, and motion and eddy current correction, using MRtrix3 (mrtrix.org) and FSL (FMRIB, Oxford, UK) with default settings. The fifth step involved eight iterations to reduce movement artifacts, including corrections for intra-volume movement, and susceptibility-by-movement interaction²⁵. These were accompanied by outlier replacement²⁶ and then quality assessment²⁷. Diffusion volumes with > 20% of slices affected by signal dropout were excluded, and diffusion scans with > 10% of volumes removed were excluded from the study²⁶.

The two shell datasets were then combined, with zero-padding when slice numbers were different, and aligned using FSL eddy-correction and bvector rotation tools. The average b0 volume for a subject was calculated using interleaved volumes from the b750 scans. Inter-subject image variations were addressed by group intensity normalization with ‘dwinormalise’ from MRtrix3. The NDI and ODI were calculated using NODDI (MATLAB toolbox), and FA analysis used the DIPY library²⁸.

Model development

Model architecture

The prepared diffusion scans with absolute inter-volume motion less than 2 mm for both shells that had also no excluded volumes were identified, totaling 95 individuals. For model development, scans representing different age groups from four to 9 years old were randomly chosen, one scan per individual. Specifically, these subjects included two each (one per sex of the same age) from each age group. Eventually, 24 individuals were involved, who were then divided into two age- and sex- balanced sub-cohorts, 12 each (half being females or males) for training and testing, respectively. Each cohort consisted of 1,620,000 voxel samples, ~ 135,000 voxels per individual. The remaining scans from these 24 subjects were excluded in follow-up analyses to avoid information leakage between cohorts used here and in final assessment. Further, given the relatively low availability of high b-value data, the models were trained to predict b2000 from b750 datasets.

The base model architecture (Fig. 8) was similar to a published design¹⁴. Prior to training, the b750 images were converted to spherical harmonics with an order of eight (45 coefficients per voxel)²⁹. A cubic window of coefficients central to each voxel was used as model input. Voxels were sampled per scan with a stride of two across all axes and randomly split into training and validation at 80:20. The models were trained to predict the 45-spherical harmonic coefficients of individual b2000 voxels, which were eventually converted back to the signal intensity domain for further analysis.

Fig. 8.

Architecture of the deep learning model used in this study. The 45 spherical harmoniccoefficients based on the b=750 s/mm2 data are used as model input. These values extractedfrom individual three-dimensional voxel windows (dark blue cubes) are applied to the modelstarting with two three-dimensional convolutional layers (light orange). The resultingfeatures are flattened and passed through 10 hidden layers (light blue) with 200 neuronseach. The final outputs are 45 coefficients (dark orange) representing the predicted b=2000s/mm2 signal for an individual voxel, which are converted to the image domain forsubsequent analysis

Model refinement was done in stages. Sequentially these involved: training size (n ∈ 1, 3, 6, 9, 12 subjects X 135,000 voxels), window width (k ∈ 3, 5, 7, 9, 11 voxels), and additional inputs (feature ∈ None, probability segmentation (pSeg), binary segmentation (Seg), or pSeg & Seg of brain parenchyma). All represented common factors impacting deep learning with diffusion MRI^17,30. The segmentations were obtained with ‘Atropos’ in ANTs³¹ based on the average b0, average b750, and b750-based FA.

Model hyperparameters included a starting learning rate of 1e-4, batch size of 32, and normalized mean squared error (shNMSE) loss. The loss was calculated on signal intensity data between predicted and original b2000 datasets. Based on validation loss, the development used early stopping with a patience of 20 epochs, and a plateau-based learning rate schedule that reduced 50% with a patience of 10 epochs. The lowest validation loss defined the best model.

Model testing

Based on 1,620,000 voxel samples from the 12 held-out subjects, NDI and ODI were computed using the predicted b2000 and original b750 datasets, at each model refinement stage. Peak signal to noise ratio (PSNR), structural similarity index metric (SSIM), root mean squared error (RMSE), and mean absolute error (MAE) were calculated on respective sets of NODDI metrics. These quality measures were compared using linear mixed-effects modeling in R (v4.3.3), followed by pairwise comparisons, with a 0.05 false discovery rate for multiple-comparison corrections. Combined analyses determined the best training size, window size, and input feature for the final CNN-MLP model.

White matter template construction for tractography

The template was constructed using b2000 data from another 30 individuals as commonly done to balance quality and computational time, one template each for predicted and source dataset, following the single-shell fixel-based analysis pipeline^32,33. To optimize representativity of our templates, the subjects were sampled to cover current age and sex distributions. Briefly, fiber orientation distribution (FOD) was estimated per subject using the Single-Shell 3-Tissue Constrained Spherical Deconvolution approach³⁴. A FOD template was then created for both predicted and original b2000 data, with which the individual subject FODs from corresponding sources were nonlinearly aligned. Over template construction processes, FA maps from the common b750 data of an individual were used as references to improve alignment of the final FOD templates created from the respective b2000 sources.

Whole-brain tractography and automatic tract segmentation

Whole-brain anatomically constrained tractography was done based on corresponding template FODs using the iFOD2 tracking algorithm³⁵. This was supported by nonlinear co-registrations from standard MNI T1-weighted and T2-weighted images to the zero-order spherical harmonics coefficient of the template FOD (see Fig. 1). Tractography applied a maximum angle of 22.5 degrees per step, maximum/minimum length of 250 mm/10 mm, backtracking with cropping at the GM and WM interface, and dynamic seeding. 20 million streamlines were tracked initially, which were filtered to two million to match streamline densities to FOD volumes³⁶.

In addition to whole brain white matter, representative white matter tracts were evaluated as done in a prior study⁴. These included major tracts: corpus callosum and pyramidal tracts, with the former subdivided into Genu, Body, and Splenium, as well as four additional tracts: arcuate, cingulum, inferior fronto-occipital fasciculus, and inferior longitudinal fasciculus. The main paper essentially covered the major tracts (see Fig. 1), while details about the four other tracts were reported in Supplementary materials (Supplementary Fig. 12). All of the tracts were delineated using the TractSeg method³⁷. Peaks of the template FOD were extracted with ‘MRtrix3 sh2peaks’ for input to TractSeg that tracked 10,000 streamlines per tract with enforced inclusion and termination regions. Resultant tracts were then transformed into voxel-wise binary regions of interest (ROI) with a threshold of one streamline per voxel.

Analysis of neurodevelopmental trajectories

For the 71 participants (95 minus 24, totaling 138 scans) not included in model development, age-related changes in NDI and ODI from both b-values, FA from b750, and tract volumes were assessed in the segmented white matter tracts and across the whole brain.

To compare the relative rates of neurodevelopment in imaging measures between source-only and prediction-integrated data, we performed linear mixed-effects modeling. Age was set as fixed effects interacting with sex, and subjects as random effects. The number of outlier slices was included as a covariate, from b750 and b2000 datasets for the source-only model, and from b750 dataset alone for the prediction-included model. For literature comparison⁴, the absolute change and percent change (absolute_change/predicted_age2) were also calculated using regression values at 2 and 8 years of age. Bonferroni correction was conducted to account for multiple comparisons, with p ≤ 0.00156 [p < 0.05/(four diffusion metrics X eight tract groups)] considered significant. Finally, to assess how the absolute values of diffusion outcomes compare between source-only and prediction-integrated data, paired student’s t-tests were performed for each tract followed by correction for multiple comparisons as noted above. Similar analyses were done for all tract groups investigated.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

O.O. and Y.Z. wrote the main manuscript text. O.O. and F.L. performed data analysis and O.O. prepared the figures and tables. B.G. and C.L. acquired the source MRI data. All authors reviewed the manuscript.

Funding

Data acquisition was funded by the Alberta Children’s Hospital, Canada, and Canadian Institutes of Health Research (CIHR). Data analysis was funded in part by the Natural Sciences and Engineering Research Council of Canada and CIHR.

Data availability

The datasets generated during the current study may be available from the corresponding author upon reasonable request. The initial single b-value diffusion data can be accessed from https://doi.org/10.17605/OSF.IO/AXZ5R.

Declarations

Competing interests

The authors declare no competing interests.