DCM for complex-valued data: cross-spectra, coherence and phase-delays.

Area of Science:

• Neuroscience
• Computational Neuroscience
• Systems Neuroscience

Background:

• Dynamic Causal Modeling (DCM) is a powerful tool for inferring directed connectivity and causal interactions in neural systems.
• Analyzing complex-valued data, such as cross-spectra, offers richer insights into neural dynamics than real-valued data alone.
• Multivariate ergodic time-series analysis is crucial for understanding complex brain network interactions.

Purpose of the Study:

• To extend Bayesian model inversion procedures for Dynamic Causal Modeling (DCM) to handle complex-valued data.
• To generalize DCM for steady-state responses, modeling both real and imaginary parts of sample cross-spectra.
• To enable inference of biophysical parameters and system architecture from complex data in neuroscience.

Main Methods:

• Developed an extension of Bayesian model inversion for complex-valued Dynamic Causal Modeling (DCM).
• Generalized DCM for steady-state responses to model real and imaginary parts of sample cross-spectra.
• Applied the extended DCM to local field potential recordings from the subthalamic nucleus and globus pallidus.

Main Results:

• The extended DCM successfully infers underlying biophysical parameters (synaptic time constants, connection strengths, conduction delays) from complex-valued time-series data.
• Conventional linear systems measures (coherence, phase-delay, cross-correlation) can be derived from the inferred parameters in both sensor and source space.
• Demonstrated the relationship between conduction delays and phase relationships/cross-correlation time lags in neural population activities.

Conclusions:

• The extended DCM provides a robust framework for analyzing complex-valued neural time-series data.
• This approach allows for a more comprehensive understanding of neural system architecture and causal interactions.
• The findings highlight the utility of complex data analysis in uncovering detailed relationships between neural conduction delays and population activity dynamics.