The human brain undergoes rapid and dynamic development early in life.

Assessment of brain growth patterns relevant to neurological disorders and disease requires a normative population model of growth and variability in order to evaluate deviation from typical development.

In this work, we focus on maturation of brain white matter as shown in diffusion tensor MRI (DT-MRI), measured by fractional anisotropy (FA), mean diffusivity (MD), as well as axial and radial diffusivities (AD, RD). We present a novel methodology to model temporal changes of white matter diffusion from longitudinal DT-MRI data taken at discrete time points. Our proposed framework combines nonlinear modeling of trajectories of individual subjects, population analysis, and testing for regional differences in growth pattern. We first perform deformable mapping of longitudinal DT-MRI of healthy infants imaged at birth, 1 year, and 2 years of age, into a common unbiased atlas. An existing template of labeled white matter regions is registered to this atlas to define anatomical regions of interest. Diffusivity prop- erties of these regions, presented over time, serve as input to the longitudinal characterization of changes. We use non-linear mixed effect (NLME) modeling where temporal change is described by the Gompertz function. The Gompertz growth function uses intuitive parameters related to delay, rate of change, and expected asymp- totic value; all descriptive measures which can answer clinical questions related to quantitative analysis of growth patterns. Results suggest that our proposed framework provides descriptive and quantitative informa- tion on growth trajectories that can be interpreted by clinicians using natural language terms that describe growth. Statistical analysis of regional differences between anatomical regions which are known to mature differently demonstrates the potential of the proposed method for quantitative assessment of brain growth and differences thereof. This will eventually lead to a prediction of white matter diffusion properties and associ- ated cognitive development at later stages given imaging data at early stages.

Contribution We have presented a framework for the processing of longitudinal im- ages in order to characterize longitudinal development of white matter regions at both the individual and group level. By utilizing nonlinear mixed effects modeling, we jointly estimate the population trajectory along with each individual trajectories. Gompertz parameterization of diffusion changes provides an intuitive parameterization of growth trajecto- ry in terms of asymptote, delay and speed. This provides a description of longitudinal changes with potential for detecting deviations from a typical growth trajectory sensitive to multiple neurodevelopmental phenomena.

Findings We applied our framework to longitudinal pediatric DTI data of 26 subjects. In total, we selected 13 regions in the unbiased atlas as shown in Fig. 4. The regions are as follows: anterior limb of internal capsule (right and left; ALIC), posterior limb of internal capsule (right and left; PLIC), genu, body of corpus callosum (BCC), splenium (Sp), external capsule (right and left; ExCap), retrolenticular part of internal capsule (right and left; RLIC), and posterior thalamic radia- tion which includes optic radiation (right and left; PTR). The right and left of each anatomical region were combined giving a total of eight regions. Fig. 5 plots the average FA, MD, RD, and AD of each region for each subject. In all the regions, FA increases with age, whereas MD, RD and AD decrease with age. Interestingly, each region develops in a distinctly different temporal pattern.

Papers/abstracts: Sadeghi et al., NeuroImage 2013