Inferring Causality in Aperiodic and Periodic Components of Brain and Cardiac Dynamics.

UNLABELLED: Background: Aperiodic $1/f-$like neural activity is thought to reflect fundamental properties of population-level excitation-inhibition balance, yet no existing framework provides directional causal inference between this component and neuroautonomic dynamics. Current brain-heart models also lack formulations accounting for both aperiodic and oscillatory spectral components. OBJECTIVES: To develop a mathematical framework for directional causal inference between time-resolved aperiodic ($1/f-$like) electroencephalographic (EEG) components and heartbeat dynamics. We also aim to extend the same formalism to periodic narrow-band EEG oscillations. METHODS: We introduce the directional causality for brain-heart interplay (DiCa-BHI) framework, a stochastic modelling approach in which each EEG spectral parameter is treated as a time-varying process governed by autoregressive dynamics with exogenous neuroautonomic inputs. Aperiodic exponent, offset, and oscillatory peak amplitudes are modelled within a parametric spectral representation, while heartbeat dynamics are characterized via an extended, stochastic integral pulse frequency modulation model. Directional causal coefficients are estimated using a Granger-predictive causal ARX formalism. Validation employed synchronized EEG-ECG recordings from 27 healthy adults undergoing supine rest, postural changes, and emotional video elicitation. Subject-specific estimations are performed and then compared across experimental conditions. RESULTS: The aperiodic $1/f-$-like EEG component exhibited predominant bottom-up heart-to-brain causality, attenuated during orthostasis but strengthened during emotional stimulation across widespread cortical regions. Conversely, periodic narrowband components showed strong top-down brain-to-heart dominance, exceeding 90% for vagal and 70% for sympathovagal contributions. CONCLUSIONS: DiCa-BHI provides a novel methodological framework for directional causal inference in the $1/f-$ aperiodic component of neural activity and generalizes seamlessly to narrow-band oscillatory components. SIGNIFICANCE: The framework advances mathematical modelling of the brain-heart axis and provides a quantitative tool for applications in cardiology, neurology, and psychophysiological research.