Frontiers in Applied Mathematics and Statistics (Sep 2020)
Validation of Critical Ages in Regional Adult Brain Maturation
Abstract
Some aspects of the brain change volume at a fairly constant rate across the life span, i.e., linear maturation rate with respect to age, whereas other aspects of the brain change volume at different rates for younger vs. older age ranges, i.e., non-linear changes. Various forms of non-linear maturation likely reflect different biological mechanisms such that theoretical distinctions between maturation patterns ought to be considered. Simulated data with known maturation patterns and a single critical age characterizing a qualitative change in maturation were used to establish the validity of a non-parametric fitting method, the smoothing spline, combined with processing steps for determining the form of the pattern and the associated critical age. Multiple classes of models were assessed, including model-free, bottom up approaches. Three categories of maturation patterns were explored: U-shaped, with a change in direction; sigmoidal, with an isolated period of change; accelerating, with changes in amplitude but not direction. As noise is a limiting factor in curve fitting, smoothing splines were fit to data with idealized low and realistic noise levels. The smoothing spline was shown to contain the relevant information to extract the critical ages of all maturation patterns in the form of derivative zero points, but the previously proposed method of using third derivative zero points worked only for the accelerating category. Therefore, an additional classification step was included to first determine the category of maturation pattern. Classification accuracy and identification of the calculated critical age within 5 years of the actual critical age was found to be perfect for low noise and high for realistic noise levels. To demonstrate the applicability of the method, a reevaluation of published biological data previously analyzed using third derivative zero points to determine critical ages was carried out for 17 aspects of MRI scans from 1,100 subjects. For a majority of non-linear areas, new critical ages were identified. Further modifications to the analysis procedure could include a wider set of maturation patterns and the inclusion of multiple critical ages to help determine distinctions between brain areas in the timing of developmental or degenerative events that influence their volume.
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