LSD-induced increase of Ising temperature and algorithmic complexity of brain dynamics
Authors: Ruffini Giulio , Damiani Giada , Lozano-Soldevilla Diego , Deco Nikolas , Rosas Fernando E. , Kiani Narsis A. , Ponce-Alvarez Adrián , Kringelbach Morten L. , Carhart-Harris Robin , Deco Gustavo 
Published: August 2022

A topic of growing interest in computational neuroscience is the discovery of fundamental principles underlying global dynamics and the self-organization of the brain. In particular, the notion that the brain operates near criticality has gained considerable support, and recent work has shown that the dynamics of different brain states may be modeled by pairwise maximum entropy Ising models at various distances from a phase transition, i.e., from criticality. Here we aim to characterize two brain states (psychedelics-induced and placebo) as captured by functional magnetic resonance imaging (fMRI), with features derived from the Ising spin model formalism (system temperature, critical point, susceptibility) and from algorithmic complexity. We hypothesized, along the lines of the entropic brain hypothesis, that psychedelics drive brain dynamics into a more disordered state at a higher Ising temperature and increased complexity. We analyze resting state blood-oxygen-level-dependent (BOLD) fMRI data collected in an earlier study from fifteen subjects in a control condition (placebo) and during ingestion of lysergic acid diethylamide (LSD). Working with the automated anatomical labeling (AAL) brain parcellation, we first create “archetype” Ising models representative of the entire dataset (global) and of the data in each condition. Remarkably, we find that such archetypes exhibit a strong correlation with an average structural connectome template obtained from dMRI (r= 0.6). We compare the archetypes from the two conditions and find that the Ising connectivity in the LSD condition is lower than the placebo one, especially at homotopic links (interhemispheric connectivity), reflecting a significant decrease of homotopic functional connectivity in the LSD condition. The global archetype is then personalized for each individual and condition by adjusting the system temperature. The resulting temperatures are all near but above the critical point of the model in the paramagnetic (disordered) phase. The individualized Ising temperatures are higher in the LSD condition than the placebo condition (p= 9 × 10-5). Next, we estimate the Lempel-Ziv-Welch (LZW) complexity of the binarized BOLD data and the synthetic data generated with the individualized model using the Metropolis algorithm for each participant and condition. The LZW complexity computed from experimental data reveals a weak statistical relationship with condition (p= 0.04 one-tailed Wilcoxon test) and none with Ising temperature (r(13) = 0.13,p= 0.65), presumably because of the limited length of the BOLD time series. Similarly, we explore complexity using the block decomposition method (BDM), a more advanced method for estimating algorithmic complexity. The BDM complexity of the experimental data displays a significant correlation with Ising temperature (r(13) = 0.56,p= 0.03) and a weak but significant correlation with condition (p = 0.04, one-tailed Wilcoxon test). This study suggests that the effects of LSD increase the complexity of brain dynamics by loosening interhemispheric connectivity—especially homotopic links. In agreement with earlier work using the Ising formalism with BOLD data, we find the brain state in the placebo condition is already above the critical point, with LSD resulting in a shift further away from criticality into a more disordered state.

Author summary

In this study, we aim to characterize two brain states (psychedelics-induced and placebo), as captured in functional magnetic resonance imaging (fMRI) data, with features derived from the Ising model formalism (system temperature, critical point, susceptibility) and from algorithmic complexity. Under the hypothesis that psychedelics drive the brain into a more disordered state, we study criticality features of brain dynamics under LSD in a within-subject study using the Ising model formalism and algorithmic complexity using Lempel-Ziv and the Block Decomposition methods. Personalized Ising models are created by first using BOLD fMRI data from all the subjects and conditions to create a single Ising “archetype” model—which we can interpret as the average model of the data at unit temperature—and then by adjusting the model temperature for each subject and condition. We find that the effects of LSD translate into increased BOLD signal complexity and Ising temperature, in agreement with earlier findings and predictions from existing theories of the effects of psychedelics, such as the relaxed beliefs under psychedelics (REBUS), the anarchic brain hypothesis [1], and the algorithmic information theory of consciousness (KT) [2, 3]. However, in contrast with some of the previously cited theories, we find that the system in the placebo condition is already in the paramagnetic phase—above the critical point—with ingestion of LSD resulting in a shift away from Ising criticality into a more disordered state. Finally, we highlight the fact that the structural connectome can be recovered to a good degree by fitting an Ising model and that the reduction of homotopic links appears to play an important role in the slide to disorder under psychedelics.