Linear and Nonlinear Directed Connectivity Analysis of the Cardio-Respiratory System in Type 1 Diabetes

In this study, we explored the possibility of developing non-invasive biomarkers for patients with type 1 diabetes (T1D) by quantifying the directional couplings between the cardiac, vascular, and respiratory systems, treating them as interconnected nodes in a network configuration. Towards this goal, we employed a linear directional connectivity measure, the directed transfer function (DTF), estimated by a linear multivariate autoregressive modelling of ECG, respiratory and skin perfusion signals, and a nonlinear method, the dynamical Bayesian inference (DBI) analysis of bivariate phase interactions. The physiological data were recorded concurrently for a relatively short time period (5 min) from 10 healthy control subjects and 10 T1D patients. We found that, in both control and T1D subjects, breathing had greater influence on the heart and perfusion with respect to the opposite coupling direction and that, by both employed methods of analysis, the causal influence of breathing on the heart was significantly decreased (p < 0.05) in T1D patients compared to the control group. These preliminary results, although obtained from a limited number of subjects, provide a strong indication for the usefulness of a network-based multi-modal analysis for the development of biomarkers of T1D-related complications from short-duration data, as well as their potential in the exploration of the pathophysiological mechanisms that underlie this devastating and very widespread disease.

Time-evolving coupling functions for evaluating the interaction between cerebral oxyhemoglobin and arterial blood pressure with hypertension

PURPOSES

This study aimed to investigate the network coupling between arterial blood pressure (ABP) and changes in cerebral oxyhemoglobin concentration (Δ [O₂ Hb]/Δ [HHb]) oscillations based on dynamical Bayesian inference in hypertensive subjects.

METHODS

Two groups of subjects, consisting of 30 healthy (Group Control, 55.1 ± 10.6 y), and 32 hypertensive individuals (Group AH, 58.9 ± 8.7 y), participated in this study. A functional near-infrared spectroscopy system was used to measure the Δ [O₂ Hb] and Δ [HHb] signals in the bilateral prefrontal cortex (LPFC/RPFC), motor cortex (LMC/RMC), and occipital lobe (LOL/ROL) during the resting state (12 min). Based on continuous wavelet analysis and coupling functions, the directed coupling strength (CS) between ABP and cerebral hemoglobin was identified and analyzed in three frequency intervals (I: 0.6-2 Hz, II: 0.145-0.6 Hz, III: 0.01-0.08 Hz). The Pearson correlations between the CS and blood pressure parameters were calculated in the hypertension group.

RESULTS

In interval I, Group AH exhibited a significantly higher CS for the coupling from ABP to Δ [O₂ Hb] than Group Control in LMC, RMC, LOL, and ROL. In interval III, the CS from ABP to Δ [O₂ Hb] in LPFC, RPFC, LMC, RMC, LOL, and ROL was significantly higher in Group AH than in Group Control. For the patients with hypertension, diastolic blood pressure was negatively and pulse pressure was positively related to the CS from ABP to Δ [O₂ Hb] oscillations in interval III.

CONCLUSIONS

The higher CS from ABP to Δ [O₂ Hb] in interval I indicated that the components of cardiac activity in cerebral hemoglobin oscillations were more directly responsive to the changes in systematic ABP in patients with hypertension than in healthy subjects. Meanwhile, the higher CS from ABP to Δ [O₂ Hb] in interval III indicated that the cerebral hemoglobin oscillations were susceptible to changes in blood pressure in hypertensive subjects. The results may serve as evidence of impairment in cerebral autoregulation after hypertension. The Pearson correlation results showed that diastolic blood pressure and pulse pressure might be regarded as predictors of cerebral autoregulation function in patients with hypertension, and may be useful for hypertension stratification. This study provides novel insights into the interaction mechanism between ABP and cerebral hemodynamics and could help in the development of new assessment techniques for cerebral vascular disease.

Time Window Determination for Inference of Time-Varying Dynamics: Application to Cardiorespiratory Interaction

Interacting dynamical systems abound in nature, with examples ranging from biology and population dynamics, through physics and chemistry, to communications and climate. Often their states, parameters and functions are time-varying, because such systems interact with other systems and the environment, exchanging information and matter. A common problem when analysing time-series data from dynamical systems is how to determine the length of the time window for the analysis. When one needs to follow the time-variability of the dynamics, or the dynamical parameters and functions, the time window needs to be resolved first. We tackled this problem by introducing a method for adaptive determination of the time window for interacting oscillators, as modeled and scaled for the cardiorespiratory interaction. By investigating a system of coupled phase oscillators and utilizing the Dynamical Bayesian Inference method, we propose a procedure to determine the time window and the propagation parameter of the covariance matrix. The optimal values are determined so that the inferred parameters follow the dynamics of the actual ones and at the same time the error of the inference represented by the covariance matrix is minimal. The effectiveness of the methodology is presented on a system of coupled limit-cycle oscillators and on the cardiorespiratory interaction. Three cases of cardiorespiratory interaction were considered-measurement with spontaneous free breathing, one with periodic sine breathing and one with a-periodic time-varying breathing. The results showed that the cardiorespiratory coupling strength and similarity of form of coupling functions have greater values for slower breathing, and this variability follows continuously the change of the breathing frequency. The method can be applied effectively to other time-varying oscillatory interactions and carries important implications for analysis of general dynamical systems.

Chance, long tails, and inference in a non-Gaussian, Bayesian theory of vocal learning in songbirds

Traditional theories of sensorimotor learning posit that animals use sensory error signals to find the optimal motor command in the face of Gaussian sensory and motor noise. However, most such theories cannot explain common behavioral observations, for example, that smaller sensory errors are more readily corrected than larger errors and large abrupt (but not gradually introduced) errors lead to weak learning. Here, we propose a theory of sensorimotor learning that explains these observations. The theory posits that the animal controls an entire probability distribution of motor commands rather than trying to produce a single optimal command and that learning arises via Bayesian inference when new sensory information becomes available. We test this theory using data from a songbird, the Bengalese finch, that is adapting the pitch (fundamental frequency) of its song following perturbations of auditory feedback using miniature headphones. We observe the distribution of the sung pitches to have long, non-Gaussian tails, which, within our theory, explains the observed dynamics of learning. Further, the theory makes surprising predictions about the dynamics of the shape of the pitch distribution, which we confirm experimentally.

Neural Cross-Frequency Coupling Functions

Although neural interactions are usually characterized only by their coupling strength and directionality, there is often a need to go beyond this by establishing the functional mechanisms of the interaction. We introduce the use of dynamical Bayesian inference for estimation of the coupling functions of neural oscillations in the presence of noise. By grouping the partial functional contributions, the coupling is decomposed into its functional components and its most important characteristics—strength and form—are quantified. The method is applied to characterize the δ-to-α phase-to-phase neural coupling functions from electroencephalographic (EEG) data of the human resting state, and the differences that arise when the eyes are either open (EO) or closed (EC) are evaluated. The δ-to-α phase-to-phase coupling functions were reconstructed, quantified, compared, and followed as they evolved in time. Using phase-shuffled surrogates to test for significance, we show how the strength of the direct coupling, and the similarity and variability of the coupling functions, characterize the EO and EC states for different regions of the brain. We confirm an earlier observation that the direct coupling is stronger during EC, and we show for the first time that the coupling function is significantly less variable. Given the current understanding of the effects of e.g., aging and dementia on δ-waves, as well as the effect of cognitive and emotional tasks on α-waves, one may expect that new insights into the neural mechanisms underlying certain diseases will be obtained from studies of coupling functions. In principle, any pair of coupled oscillations could be studied in the same way as those shown here.