Extending the spectral decomposition of Granger causality to include instantaneous influences: application to the control mechanisms of heart rate variability

The contribution of granger causality analysis to our understanding of cardiovascular homeostasis: from cardiovascular and respiratory interactions to central autonomic network control

Homeostatic regulation plays a fundamental role in maintenance of multicellular life. At different scales and in different biological systems, this principle allows a better understanding of biological organization. Consequently, a growing interest in studying cause-effect relations between physiological systems has emerged, such as in the fields of cardiovascular and cardiorespiratory regulations. For this, mathematical approaches such as Granger causality (GC) were applied to the field of cardiovascular physiology in the last 20 years, overcoming the limitations of previous approaches and offering new perspectives in understanding cardiac, vascular and respiratory homeostatic interactions. In clinical practice, continuous recording of clinical data of hospitalized patients or by telemetry has opened new applicability for these approaches with potential early diagnostic and prognostic information. In this review, we describe a theoretical background of approaches based on linear GC in time and frequency domains applied to detect couplings between time series of RR intervals, blood pressure and respiration. Interestingly, these tools help in understanding the contribution of homeostatic negative feedback and the anticipatory feedforward mechanisms in homeostatic cardiovascular and cardiorespiratory controls. We also describe experimental and clinical results based on these mathematical tools, consolidating previous experimental and clinical evidence on the coupling in cardiovascular and cardiorespiratory studies. Finally, we propose perspectives allowing to complete the understanding of these interactions between cardiovascular and cardiorespiratory systems, as well as the interplay between brain and cardiac, and vascular and respiratory systems, offering a high integrative view of cardiovascular and cardiorespiratory homeostatic regulation.

A Method to Assess Granger Causality, Isolation and Autonomy in the Time and Frequency Domains: Theory and Application to Cerebrovascular Variability

OBJECTIVE

Concepts of Granger causality (GC) and Granger autonomy (GA) are central to assess the dynamics of coupled physiologic processes. While causality measures have been already proposed and applied in time and frequency domains, measures quantifying self-dependencies are still limited to the time-domain formulation and lack of clear spectral representation.

METHODS

We embed into the linear parametric framework for computing GC from a driver X to a target process Y a measure of Granger Isolation (GI) quantifying the part of the dynamics of Y not originating from X, and a new spectral measure of GA assessing frequency-specific patterns of self-dependencies in Y. The measures are illustrated in theoretical simulations and applied to time series of arterial pressure and cerebral blood flow obtained in syncope subjects and healthy controls.

RESULTS

Simulations show that GI is complementary to GC but not trivially related to it, while GA reflects the regularity of the internal dynamics of the target process. In the application to cerebrovascular interactions, spectral GA quantified the physiological response to postural stress of slow cerebral blood flow oscillations, while spectral GC and GI detected an altered response to orthostasis in syncope subjects, likely related to impaired cerebral autoregulation.

CONCLUSION AND SIGNIFICANCE

The new spectral measures of GI and GA are useful complements to GC for the analysis of interacting oscillatory processes, and detect pathophysiological responses to postural stress which cannot be traced in the time domain. The thorough assessment of causality, isolation and autonomy opens new perspectives for the analysis of coupled processes in both physiological and clinical investigations.

Connectivity Analysis in EEG Data: A Tutorial Review of the State of the Art and Emerging Trends

Understanding how different areas of the human brain communicate with each other is a crucial issue in neuroscience. The concepts of structural, functional and effective connectivity have been widely exploited to describe the human connectome, consisting of brain networks, their structural connections and functional interactions. Despite high-spatial-resolution imaging techniques such as functional magnetic resonance imaging (fMRI) being widely used to map this complex network of multiple interactions, electroencephalographic (EEG) recordings claim high temporal resolution and are thus perfectly suitable to describe either spatially distributed and temporally dynamic patterns of neural activation and connectivity. In this work, we provide a technical account and a categorization of the most-used data-driven approaches to assess brain-functional connectivity, intended as the study of the statistical dependencies between the recorded EEG signals. Different pairwise and multivariate, as well as directed and non-directed connectivity metrics are discussed with a pros-cons approach, in the time, frequency, and information-theoretic domains. The establishment of conceptual and mathematical relationships between metrics from these three frameworks, and the discussion of novel methodological approaches, will allow the reader to go deep into the problem of inferring functional connectivity in complex networks. Furthermore, emerging trends for the description of extended forms of connectivity (e.g., high-order interactions) are also discussed, along with graph-theory tools exploring the topological properties of the network of connections provided by the proposed metrics. Applications to EEG data are reviewed. In addition, the importance of source localization, and the impacts of signal acquisition and pre-processing techniques (e.g., filtering, source localization, and artifact rejection) on the connectivity estimates are recognized and discussed. By going through this review, the reader could delve deeply into the entire process of EEG pre-processing and analysis for the study of brain functional connectivity and learning, thereby exploiting novel methodologies and approaches to the problem of inferring connectivity within complex networks.

Spectral decomposition of cerebrovascular and cardiovascular interactions in patients prone to postural syncope and healthy controls

We present a framework for the linear parametric analysis of pairwise interactions in bivariate time series in the time and frequency domains, which allows the evaluation of total, causal and instantaneous interactions and connects time- and frequency-domain measures. The framework is applied to physiological time series to investigate the cerebrovascular regulation from the variability of mean cerebral blood flow velocity (CBFV) and mean arterial pressure (MAP), and the cardiovascular regulation from the variability of heart period (HP) and systolic arterial pressure (SAP). We analyze time series acquired at rest and during the early and late phase of head-up tilt in subjects developing orthostatic syncope in response to prolonged postural stress, and in healthy controls. The spectral measures of total, causal and instantaneous coupling between HP and SAP, and between MAP and CBFV, are averaged in the low-frequency band of the spectrum to focus on specific rhythms, and over all frequencies to get time-domain measures. The analysis of cardiovascular interactions indicates that postural stress induces baroreflex involvement, and its prolongation induces baroreflex dysregulation in syncope subjects. The analysis of cerebrovascular interactions indicates that the postural stress enhances the total coupling between MAP and CBFV, and challenges cerebral autoregulation in syncope subjects, while the strong sympathetic activation elicited by prolonged postural stress in healthy controls may determine an increased coupling from CBFV to MAP during late tilt. These results document that the combination of time-domain and spectral measures allows us to obtain an integrated view of cardiovascular and cerebrovascular regulation in healthy and diseased subjects.

Pairwise and higher-order measures of brain-heart interactions in children with temporal lobe epilepsy

OBJECTIVE

While it is well-known that epilepsy has a clear impact on the activity of both the central nervous system (CNS) and the autonomic nervous system (ANS), its role on the complex interplay between CNS and ANS has not been fully elucidated yet. In this work, pairwise and higher-order predictability measures based on the concepts of Granger causality (GC) and Partial Information Decomposition (PID) were applied on time series of electroencephalographic (EEG) brain wave amplitude and heart rate variability (HRV) in order to investigate directed brain-heart interactions associated with the occurrence of focal epilepsy.

APPROACH

HRV and the envelopes of δ and α EEG activity recorded from ipsilateral (ipsi-EEG) and contralateral (contra-EEG) scalp regions were analyzed in 18 children suffering from temporal lobe epilepsy monitored during pre-ictal, ictal and post-ictal periods. After linear parametric model identification, we compared pairwise GC measures computed between HRV and a single EEG component with PID measures quantifying the unique, redundant and synergistic information transferred from ipsi-EEG and contra-EEG to HRV.

MAIN RESULTS

The analysis of GC revealed a dominance of the information transfer from EEG to HRV and negligible transfer from HRV to EEG, suggesting that CNS activities drive the ANS modulation of the heart rhythm, but did not evidence clear differences between δ and α rhythms, ipsi-EEG and contra-EEG, or pre- and post-ictal periods. On the contrary, PID revealed that epileptic seizures induce a reorganization of the interactions from brain to heart, as the unique predictability of HRV originated from the ipsi-EEG for the δ waves and from the contra-EEG for the α waves in the pre-ictal phase, while these patterns were reversed after the seizure.

SIGNIFICANCE

These results highlight the importance of considering higher-order interactions elicited by PID for the study of the neuro-autonomic effects of focal epilepsy, and may have neurophysiological and clinical implications.

Partial Directed Coherence and the Vector Autoregressive Modelling Myth and a Caveat

Here we dispel the lingering myth that Partial Directed Coherence is a Vector Autoregressive (VAR) Modelling dependent concept. In fact, our examples show that it is spectral factorization that lies at its heart, for which VAR modelling is a mere, albeit very efficient and convenient, device. This applies to Granger Causality estimation procedures in general and also includes instantaneous Granger effects. Care, however, must be exercised for connectivity between multivariate data generated through nonminimum phase mechanisms as it may possibly be incorrectly captured.

Advanced computation in cardiovascular physiology: new challenges and opportunities

Recent developments in computational physiology have successfully exploited advanced signal processing and artificial intelligence tools for predicting or uncovering characteristic features of physiological and pathological states in humans. While these advanced tools have demonstrated excellent diagnostic capabilities, the high complexity of these computational 'black boxes' may severely limit scientific inference, especially in terms of biological insight about both physiology and pathological aberrations. This theme issue highlights current challenges and opportunities of advanced computational tools for processing dynamical data reflecting autonomic nervous system dynamics, with a specific focus on cardiovascular control physiology and pathology. This includes the development and adaptation of complex signal processing methods, multivariate cardiovascular models, multiscale and nonlinear models for central-peripheral dynamics, as well as deep and transfer learning algorithms applied to large datasets. The width of this perspective highlights the issues of specificity in heartbeat-related features and supports the need for an imminent transition from the black-box paradigm to explainable and personalized clinical models in cardiovascular research. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.