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

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.

Concomitant evaluation of cardiovascular and cerebrovascular controls via Geweke spectral causality to assess the propensity to postural syncope

The evaluation of propensity to postural syncope necessitates the concomitant characterization of the cardiovascular and cerebrovascular controls and a method capable of disentangling closed loop relationships and decomposing causal links in the frequency domain. We applied Geweke spectral causality (GSC) to assess cardiovascular control from heart period and systolic arterial pressure variability and cerebrovascular regulation from mean arterial pressure and mean cerebral blood velocity variability in 13 control subjects and 13 individuals prone to develop orthostatic syncope. Analysis was made at rest in supine position and during head-up tilt at 60°, well before observing presyncope signs. Two different linear model structures were compared, namely bivariate autoregressive and bivariate dynamic adjustment classes. We found that (i) GSC markers did not depend on the model structure; (ii) the concomitant assessment of cardiovascular and cerebrovascular controls was useful for a deeper comprehension of postural disturbances; (iii) orthostatic syncope appeared to be favored by the loss of a coordinated behavior between the baroreflex feedback and mechanical feedforward pathway in the frequency band typical of the baroreflex functioning during the postural challenge, and by a weak cerebral autoregulation as revealed by the increased strength of the pressure-to-flow link in the respiratory band. GSC applied to spontaneous cardiovascular and cerebrovascular oscillations is a promising tool for describing and monitoring disturbances associated with posture modification.

Static autoregulation in humans

The process by which cerebral blood flow (CBF) remains approximately constant in response to short-term variations in arterial blood pressure (ABP) is known as cerebral autoregulation. This classic view, that it remains constant over a wide range of ABP, has however been challenged by a growing number of studies. To provide an updated understanding of the static cerebral pressure-flow relationship and to characterise the autoregulation curve more rigorously, we conducted a comprehensive literature research. Results were based on 143 studies in healthy individuals aged 18 to 65 years. The mean sensitivities of CBF to changes in ABP were found to be 1.47 ± 0.71%/% for decreased ABP and 0.37 ± 0.38%/% for increased ABP. The significant difference in CBF directional sensitivity suggests that cerebral autoregulation appears to be more effective in buffering increases in ABP than decreases in ABP. Regression analysis of absolute CBF and ABP identified an autoregulatory plateau of approximately 20 mmHg (ABP between 80 and 100 mmHg), which is much smaller than the widely accepted classical view. Age and sex were found to have no effect on autoregulation strength. This data-driven approach provides a quantitative method of analysing static autoregulation that can be easily updated as more experimental data become available.

Statistical Approaches to Characterize Functional Connectivity in Brain and Physiologic Networks on a Single-Subject Basis

The trend toward personalized medicine necessitates drawing conclusions from descriptive indexes of physiopathological states estimated from individual recordings of biomedical signals, using statistical analyses that focus on subject-specific differences between experimental conditions. In this context, the present work introduces an approach to assess functional connectivity in brain and physiologic networks by pairwise information-theoretic measures of coupling between signals, whose significance and variations between conditions are statistically validated on a single-subject basis through the use of surrogate and bootstrap data analyses. The approach is illustrated on single-subject recordings of (i) resting-state functional magnetic resonance imaging (rest-fMRI) signals acquired in a pediatric patient with hepatic encephalography associated to a portosystemic shunt and undergoing liver vascular shunt correction, and of (ii) cardiovascular and cerebrovascular time series acquired at rest and during head-up tilt in a subject suffering from orthostatic intolerance.

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.

Comparison of discretization strategies for the model-free information-theoretic assessment of short-term physiological interactions

This work presents a comparison between different approaches for the model-free estimation of information-theoretic measures of the dynamic coupling between short realizations of random processes. The measures considered are the mutual information rate (MIR) between two random processes X and Y and the terms of its decomposition evidencing either the individual entropy rates of X and Y and their joint entropy rate, or the transfer entropies from X to Y and from Y to X and the instantaneous information shared by X and Y. All measures are estimated through discretization of the random variables forming the processes, performed either via uniform quantization (binning approach) or rank ordering (permutation approach). The binning and permutation approaches are compared on simulations of two coupled non-identical Hènon systems and on three datasets, including short realizations of cardiorespiratory (CR, heart period and respiration flow), cardiovascular (CV, heart period and systolic arterial pressure), and cerebrovascular (CB, mean arterial pressure and cerebral blood flow velocity) measured in different physiological conditions, i.e., spontaneous vs paced breathing or supine vs upright positions. Our results show that, with careful selection of the estimation parameters (i.e., the embedding dimension and the number of quantization levels for the binning approach), meaningful patterns of the MIR and of its components can be achieved in the analyzed systems. On physiological time series, we found that paced breathing at slow breathing rates induces less complex and more coupled CR dynamics, while postural stress leads to unbalancing of CV interactions with prevalent baroreflex coupling and to less complex pressure dynamics with preserved CB interactions. These results are better highlighted by the permutation approach, thanks to its more parsimonious representation of the discretized dynamic patterns, which allows one to explore interactions with longer memory while limiting the curse of dimensionality.