Fractal dimension of cortical functional connectivity networks & severity of disorders of consciousness.

Recent evidence suggests that the quantity and quality of conscious experience may be a function of the complexity of activity in the brain and that consciousness emerges in a critical zone between low and high-entropy states. We propose fractal shapes as a measure of proximity to this critical point, as fractal dimension encodes information about complexity beyond simple entropy or randomness, and fractal structures are known to emerge in systems nearing a critical point. To validate this, we tested several measures of fractal dimension on the brain activity from healthy volunteers and patients with disorders of consciousness of varying severity. We used a Compact Box Burning algorithm to compute the fractal dimension of cortical functional connectivity networks as well as computing the fractal dimension of the associated adjacency matrices using a 2D box-counting algorithm. To test whether brain activity is fractal in time as well as space, we used the Higuchi temporal fractal dimension on BOLD time-series. We found significant decreases in the fractal dimension between healthy volunteers (n = 15), patients in a minimally conscious state (n = 10), and patients in a vegetative state (n = 8), regardless of the mechanism of injury. We also found significant decreases in adjacency matrix fractal dimension and Higuchi temporal fractal dimension, which correlated with decreasing level of consciousness. These results suggest that cortical functional connectivity networks display fractal character and that this is associated with level of consciousness in a clinically relevant population, with higher fractal dimensions (i.e. more complex) networks being associated with higher levels of consciousness. This supports the hypothesis that level of consciousness and system complexity are positively associated, and is consistent with previous EEG, MEG, and fMRI studies.This work was supported by grants from the Wellcome Trust Clinical Research Training 509 Fellowship to RMA (Contract grant number: 083660/Z/07/Z); the UK Medical 510 Research Council [U.1055.01.002.00001.01 to JDP; the James S. McDonnell Foundation 511 to JDP; the Evelyn Trust, Cambridge to JA, the National Institute for Health Research 512 (NIHR, UK), Cambridge Biomedical Research Centre and NIHR Senior Investigator 513 Awards to JDP and DKM; The Canadian Institute for Advanced Research (CIFAR) to 514 DKM and EAS; the Stephen Erskine Fellowship (Queens’ College, Cambridge) to EAS; 515 the British Oxygen Professorship of the Royal College of Anaesthetists to DKM. MC 516 was supported by the Cambridge International Trust and the Howard Sidney Sussex 517 Research Studentship. TFV is supported by NSF-NRT grant 1735095, Interdisciplinary 518 Training in Complex Networks and Systems. The Evelyn Trust, Cambridge and the 519 EoE CLAHRC fellowship to J.A; this research was also supported by the NIHR Brain 520 Injury Healthcare Technology Co-operative based at Cambridge University Hospitals 521 NHS Foundation Trust and University of Cambridge