Identification of growth seeds in preterm brain using Helmholtz decomposition: a longitudinal study

Introduction:
The emergence of cortical folding in the developing human brain is a complex process which begins at about 14 weeks of gestation and continues in the rest of antenatal life and after birth [1]. Although its underlying mechanisms are still unclear (genetic, epigenetic, mechanical or environmental) [1], models of cortical growth trying to overcome the folding patterns variability have been proposed [2, 3] based on 'sulcal roots' (first folding locations during antenatal life) and 'sulcal pits' (deepest location of the fold in adult brain). Following these concepts and our previous work in [4], we aim at identifying elementary units ('growth seeds') in the developing cortical surface shape of preterm newborns using longitudinal MRI data.

Methods:
Data.
The sample of this study consists of 2 preterm infants with no apparent neuroanatomical abnormality. The infants were scanned twice with a T2-weighted MRI sequence: at around 30 weeks of gestation (gestational age: 29.6 and 30.1 weeks), and at term equivalent age (TEA) (gestational age: 40.6 and 41.1 weeks). Details on the MR image acquisition and reconstruction have been described elsewhere [5].

Image and surface pre-processing.
Brain MRI images are automatically segmented into masks of the major brain tissue types using supervised classification [6]. Triangulated meshes of the inner cortical surfaces of each hemisphere are then obtained from the segmented masks using the anatomical pipeline of the Brainvisa software http://brainvisa.info/ enriched with tools dedicated to the processing of infant brains [7, 8]. After being visually inspected and manually corrected where necessary, cortical surfaces are processed by an expert to delineate the major sulci using the SurfPaint module of BrainVisa. Next, the early cerebral hemispheric meshes of each infant are remapped into the corresponding TEA using a model-driven harmonic parameterization of the cortical surface [9].

Helmholtz decomposition.
Once a point-to-point correspondence between early and TEA meshes is achieved for each infant (and each hemisphere separately), they are affinely registered to each other. Finally a deformation field F is calculated between the early and TEA meshes, and decomposed via Helmholtz decomposition.
Helmholtz decomposition can decompose a vector field into the sum of its rotational part and divergential part. Particularly, for a given vector field F, there exists 2 unique functions U and V, and a vector field H such that
F=∇U+curl V+H
where ∇U and curl V denote the divergential and rotational parts of F, respectively [4,10]. This allows to locate the points of singularity (source, sink or rotation center) of a vector field. The identification of such points for a brain growth field can reveal important information on the underlying spatiotemporal grow trajectory [4].

Results:
In Fig. 1, the divergential part of the field F is depicted along with the potential map and local minima of U for each infant and each hemisphere. Following our previous work in [4], these minima points can be interpreted as 'growth seeds', that is locations in the brain around which the cortical growth fields tend to grow. A certain level of across-subjects reproducibly in the location of the growth seeds can be noticed in Fig. 1.




Conclusions:
In this work, we have used surfacic Helmholtz decomposition of the deformation growth field (computed from the cortical surfaces of each infant, separately for left and right hemispheres) to identify growth centers in preterm newborns at a critical age for folding formation. This was obtained by applying dedicated image processing routines to high-quality longitudinal MR images acquired shortly after birth in infants with no apparent neuroanatomical abnormality. Although small, this is a rare and therefore precious dataset. In future studies we aim to confirm these results using a large dataset which is available to us.