Nodes

Nodes in a brain graph can be defined on many levels, representing, for example, synapses or entire brain regions. Over the past few decades a variety of definitions of brain regions or parcels were developed based on anatomical landmarks (sulci and gyri) and functional coherence, for example the Automated Anatomical Labeling (AAL) atlas, or using random parcellation methods which define regions based on criteria such as equal region size. Importantly, depending on whom you ask, you might end up with a different definition.

Different node definition

Random parcellation methods are particularly interesting in the developing brain. Developmental processes such as myelination and cortical folding change both the structural and functional aspects of the brain and therefore the definition based on atlases becomes challenging.

Atlases

The most prominent brain atlas was introduced in 1909 by Brodmann, based on the cytoarchitecture, the cellular composition of the brain. Brodmann defined 50 regions on the human brain post-mortem over a set of brain samples. Studies trying to learn the cytoarchitecture of individual parts of the brain are currently being conducted. The efforts, however, are limited by the spatial and temporal resolution of the MRI sequences used.

Another approach defines regions of interest in the brain by using its functional activation pattern measured with fMRI. One atlas which uses this principle is the so called Automated Anatomical Labeling (AAL) introduced by Tzourio-Mazoyer and colleagues in 2002. In their work, they defined 45 regions within each hemisphere, using the underlying sulcation patterns of the brain.

Random Parcellations

In particular during early brain development, when the sulcation patterns are not fully developed, registering the atlas to the changing brain becomes difficult. It has even been indicated that some approaches developed for the adult brain won't work in such populations. This motivates the use of random parcellation schemes which do not rely on the structural patterns of the brain.

Poisson disk sampling

One principles way of generating random parcellations on a 3D volume is based on Poisson disk sampling. It generates regions of approximately equal size, by ensuring that two region centres are not closer than a given threshold. Given any type of volume, Poisson disk sampling first selects a starting centre at random (b). Additional region centres are placed close to the existing region centres, under the condition that they cannot be closer than the threshold (c-f). When there is no space anymore to place an additional region centres, the volume elements are assigned to their closest centre, resulting in a parcellation of the volume (g).

One benefit of random this parcellation scheme lies in the fact that it does not rely on any anatomical landmarks. However, two execution on the same brain might not result in the same number of regions. This is a result of the random nature of the approach and therefore it is important to create many parcellations of the same brain, to avoid biases.

Poisson disk sampling of the brain