Spatial Dynamic Subspaces Encode Sex-Specific Schizophrenia Disruptions in Transient Network Overlap and its Links to Genetic Risk

Background

Recent advances in resting-state fMRI allow us to study spatial dynamics, the phenomenon of brain networks spatially evolving over time. However, most dynamic studies still use subject-specific, spatially-static nodes. As recent studies have demonstrated, incorporating time-resolved spatial properties is crucial for precise functional connectivity estimation and gaining unique insights into brain function. Nevertheless, estimating time-resolved networks poses challenges due to the low signal-to-noise ratio, limited information in short time segments, and uncertain identification of corresponding networks within and between subjects.

Methods

We adapt a reference-informed network estimation technique to capture time-resolved spatial networks and their dynamic spatial integration and segregation. We focus on time-resolved spatial functional network connectivity (spFNC), an estimate of network spatial coupling, to study sex-specific alterations in schizophrenia and their links to multi-factorial genomic data.

Results

Our findings are consistent with the dysconnectivity and neurodevelopment hypotheses and align with the cerebello-thalamo-cortical, triple-network, and frontoparietal dysconnectivity models, helping to unify them. The potential unification offers a new understanding of the underlying mechanisms. Notably, the posterior default mode/salience spFNC exhibits sex-specific schizophrenia alteration during the state with the highest global network integration and correlates with genetic risk for schizophrenia. This dysfunction is also reflected in high-dimensional (voxel-level) space in regions with weak functional connectivity to corresponding networks.

Conclusions

Our method can effectively capture spatially dynamic networks, detect nuanced SZ effects, and reveal the intricate relationship of dynamic information to genomic data. The results also underscore the potential of dynamic spatial dependence and weak connectivity in the clinical landscape.

The timing and directional connectivity of human frontoparietal and ventral visual attention networks in emotional scene perception

Electrocortical and hemodynamic measures reliably identify enhanced activity in the ventral and dorsal visual cortices during the perception of emotionally arousing versus neutral images, an effect that may reflect directive feedback from the subcortical amygdala. However, other brain regions strongly modulate visual attention, such as frontal eye fields (FEF) and intraparietal sulcus (IPS). Here we employ rapid sampling of BOLD signal (4 Hz) in the amygdala, fusiform gyrus (FG), FEF and IPS in 42 human participants as they viewed a series of emotional and neutral natural scene photographs balanced for luminosity and complexity, to test whether emotional discrimination is evident in dorsal structures prior to such discrimination in the amygdala and FG. Granger causality analyses were used to assess directional connectivity within dorsal and ventral networks. Results demonstrate emotionally-enhanced peak BOLD signal in the amygdala, FG, FEF, and IPS, with the onset of BOLD signal discrimination occurring between 2 and 3s after stimulus onset in ventral structures, and between 4 and 5s in FEF and IPS. Granger causality estimates yield stronger directional connectivity from IPS to FEF than the reverse in this emotional picture paradigm. Consistent with a reentrant perspective of emotional scene perception, greater directional connectivity was found from the amygdala to FG compared to the reverse. These data support a perspective in which the registration of emotional scene content is orchestrated by the amygdala and rostral inferotemporal visual cortex.

Analyses of transient chaotic time series

We address the calculation of correlation dimension, the estimation of Lyapunov exponents, and the detection of unstable periodic orbits, from transient chaotic time series. Theoretical arguments and numerical experiments show that the Grassberger-Procaccia algorithm can be used to estimate the dimension of an underlying chaotic saddle from an ensemble of chaotic transients. We also demonstrate that Lyapunov exponents can be estimated by computing the rates of separation of neighboring phase-space states constructed from each transient time series in an ensemble. Numerical experiments utilizing the statistics of recurrence times demonstrate that unstable periodic orbits of low periods can be extracted even when noise is present. In addition, we test the scaling law for the probability of finding periodic orbits. The scaling law implies that unstable periodic orbits of high period are unlikely to be detected from transient chaotic time series.

Detecting unstable periodic orbits from transient chaotic time series

We address the detection of unstable periodic orbits from experimentally measured transient chaotic time series. In particular, we examine recurrence times of trajectories in the vector space reconstructed from an ensemble of such time series. Numerical experiments demonstrate that this strategy can yield periodic orbits of low periods even when noise is present. We analyze the probability of finding periodic orbits from transient chaotic time series and derive a scaling law for this probability. The scaling law implies that unstable periodic orbits of high periods are practically undetectable from transient chaos.

Estimating generating partitions of chaotic systems by unstable periodic orbits

An outstanding problem in chaotic dynamics is to specify generating partitions for symbolic dynamics in dimensions larger than 1. It has been known that the infinite number of unstable periodic orbits embedded in the chaotic invariant set provides sufficient information for estimating the generating partition. Here we present a general, dimension-independent, and efficient approach for this task based on optimizing a set of proximity functions defined with respect to periodic orbits. Our algorithm allows us to obtain the approximate location of the generating partition for the Ikeda-Hammel-Jones-Moloney map.

Unstable periodic orbits and the natural measure of nonhyperbolic chaotic saddles

Chaotic saddles are nonattracting dynamical invariant sets that physically lead to transient chaos. We examine the characterization of the natural measure by unstable periodic orbits for nonhyperbolic chaotic saddles in dissipative dynamical systems. In particular, we compare the natural measure obtained from a long trajectory on the chaotic saddle to that evaluated from unstable periodic orbits embedded in it. Our systematic computations indicate that the periodic-orbit theory of the natural measure, previously shown to be valid only for hyperbolic chaotic sets, is applicable to nonhyperbolic chaotic saddles as well.