Characterization of the multifractal spatial scaling of brain dynamics and its breakdown in disorders of consciousness
Marian Martínez-Marín*1, Yonatan Sanz Perl1,2,3, Gustavo Deco1,4
1 Computational Neuroscience Group, Center for Brain and Cognition, Universitat Pompeu Fabra, Barcelona, Catalonia, Spain
2 Institut du Cerveau et de la Moelle épinière, ICM Paris, Paris, France
3 Universidad de San Andrés, Buenos Aires, Argentina
4 Institució Catalana de la Recerca i Estudis Avançats (ICREA), Universitat Pompeu Fabra, Barcelona, Spain
*Email: marian.martinez@upf.edu
Introduction
Understanding the spatial organization of brain dynamics across scales is key to modelling information transmission. Spatiotemporal complexity in phase synchronization can be addressed using turbulence theory [1,2,3,4], which reveals a range of distances in which fluctuations are self-similar and energy cascades from large to small scales. However, self-similarity across scales is not uniform across the brain [5] (Fig. 1, top left). We characterize this multifractal spatial scaling using fluid dynamics' predictions [6,7,8], and study its alteration in disorders of consciousness (DoC). The rate of energy transfer is used a biomarker of consciousness level and explained through a Ginzburg-Landau neural field model.
Methods
Functional MRI data from healthy controls, minimally conscious (MCS), and unresponsive wakefulness syndrome (UWS) patients were analysed for evidence of turbulent energy cascades, following Kolmogorov's rationale on self-similarity. We computed the spatial distribution of fluctuations using high-order statistical moments (1st-10th) in a parcellated atlas. Scaling exponents, extracted from subject-specific self-similar spatial scales, quantify multifractal deviation from ideally-fractal global invariance. The results are validated on full-resolution data and modelled using a Ginzburg-Landau neural field.
Results
In conscious controls, scaling exponents deviate from ideal scale-invariance in line with multifractal turbulence predictions (Fig. 1, bottom left). As consciousness decreases, dynamics become closer to global invariance, indicating reduced communication between regions. The spatial range of consistent self-similarity shortens in DoC, and the third-order moment slope steepens, reflecting disrupted information flow from large to small scales. Analyses at acquisition resolution demonstrate intermittency explicitly (non-Gaussian distribution of fluctuations), lost in DoC. Last, the Ginzburg-Landau neural field model accounts for observed spatial scaling features (Fig. 1, top right).
Discussion
The spatial scaling of brain dynamics is well characterized by a multifractal (probabilistic and local self-similarity). With reduced consciousness, dynamics approach global invariance, and self-similarity is confined to shorter distances from region centroids. The rate of energy transfer across scales (reflecting information dissipation) may serve as a biomarker and is measurable in both atlas and voxel resolution, offering different levels of detail of individual dynamics. These findings extend prior work on desynchronization in DoC and enable refined modelling and monitoring of information transmission. The Ginzburg-Landau field explains observed multifractal deviation due to the brain's hierarchical organization, and its breakdown in DoC.
M.M.M is supported by the PRE2022-101417 (Spanish AEI/EU). Y.S.P by Project NEMESIS (101071900) funded by EU ERC Synergy Horizon Europe. G.D. by PSI2016-75688-P (Spanish AEI/EU); by the EU's Horizon 2020 Research and Innovation Grants 720270 (Human Brain Project [HBP] SGA1) and 785907 (HBP SGA2); and Catalan Agency for Management of University and Research Grants 2017 SGR 1545.
1) https://doi.org/10.1016/j.neubiorev.2024.105988
2 https://doi.org/10.1016/j.celrep.2020.108471
3) https://doi.org/10.1007/978-3-642-69689-3
4) https://doi.org/10.1038/s42003-022-03576-6
5) https://doi.org/10.1103/PhysRevResearch.5.033183
6) https://doi.org/10.1088/0305-4470/17/18/021
7) https://doi.org/10.1098/rspa.1991.0082
8) https://doi.org/10.1007/s12210-022-01078-5
