The arrow of time in Parkinson's disease

Background: Parkinson's disease (PD) is a system-level disorder that implicates brain network dynamics across multiple scales. Detecting the ‘arrow of time’, or temporal reversibility of the brain's information processing flow enables quantification of equilibrium in the brain and inferences on the hierarchical organization. Therefore we aimed to explore disturbances in resting-state equilibrium levels as well as changes in the hierarchical organization due to PD. Methods: Structural and functional MRI of 29 PD patients and 19 healthy controls were acquired and analyzed. Empirical non-reversibility was computed as the distance between time-shifted forward- and artificially-reversed time series. Levels of equilibrium were subsequently assessed globally and within two cortico-subcortical motor networks implicated in PD. Moreover, whole-brain generative computational models consisting of 1051 Hopf oscillators were constructed to evaluate effective connectivities and alterations of the functional hierarchical organization. Results: We found that PD is characterized by disrupted equilibrium regimes, marked by distinct effective connectivity patterns, particularly within the motor networks. Additionally, we observed a flatter hierarchical organization in PD, with the cerebellum and thalamus exerting increased influence. Conclusion: The arrow of time methodology effectively identifies distinct and informative characteristics of PD. Our analyses suggest that PD shifts the brain towards less efficient, non-equilibrium dynamics that impair intrinsic flexibility and disrupt motor coordination. Thus, these findings not only provide insight into widespread system alterations in PD that could serve as potential biomarkers, but also lay the groundwork for next-generation stimulation techniques aimed at restoring balance in the Parkinsonian brain.