Sketching a Space of Brain States

Abstract

Brain functional connectivity alterations, that is, pathological changes in the signal exchange between areas of the brain, occur in several neurological diseases, including neurodegenerative and neuropsychiatric ones. They consist in changes in how brain functional networks operate. By conceptualising a brain space as a space whose points are connectome configurations representing brain functional states, changes in brain network functionality can be represented by paths between these points. Paths from a healthy state to a diseased one, or between diseased states as instances of disease progression, are modelled as the action of the Krankheit-Operator, which produces changes from a brain functional state to another. This study proposes a formal representation of the space of brain states and presents its computational definition. References to patients affected by Parkinson's disease, schizophrenia, and Alzheimer-Perusini's disease are included to discuss the proposed approach and possible developments of the research toward a generalisation.

Figures (6)

• Figure 1: Different perspectives of a human connectome
• Figure 2: Left: pictorial representation of the brain as a nested network, from neurons, to neuronal agglomerates, to the connectome. Right: Space of brain states, where each connectome is a point, and the transformation of a specific brain over time can be represented as a path from one state to another. Bottom right: the path from a brain of person A from state $\mathcal{G}_{A,i}$ to state $\mathcal{G}_{A,j}$ lies within the healthy states, while the pathological evolution brings the brain towards the state $\mathcal{G}^{k'}_{A,j}$ within one of the diseased states' subspaces. (Drawing and graphics by Maria Mannone).
• Figure 3: Pictorial representation of the $K$-operator on a brain. Drawing by Maria Mannone.
• Figure 4: A quantitative example of brain space for a selection of patients. For the explanation of the points' labels, see Table \ref{['list_patients']} (right). The labels contain a weighted sum of the regions of interest, automatically computed (Table \ref{['labels_ROIs_MDS']}). The states belonging to the same patients are identified with the same symbol. The arrows, indicating time evolution, are added as post-processing.
• Figure 5: A quantitative example of brain space for the selected patients, where we also use the same symbol for the same patient, with the exception of the two normal ones, with the same symbol, an $\times$ (limitation of the available marker shapes in 3D in Python). Here: Euclidean dissimilarity.