Background: A multitude of complex methods is available to quantify interactions in highly complex physiological systems. Brain–heart interactions play an important role in identifying couplings between the central nervous system and the autonomic nervous system during defined physiological states or specific diseases. The crucial point of those interaction analyses is adequate pre-processing taking into account nonlinearity of data, intuitive graphical representation and suitable statistical evaluation of the achieved results. Objective: The aim of this study is to provide generalized processing schemes for such investigations taking into account pre-processing, graphical representation and statistical analysis. Approach: Two defined data sets were used to develop these processing schemes. Brain–heart interactions in children with temporal lobe epilepsy during the pre-ictal, ictal and post-ictal periods as well as in patients with paranoid schizophrenia and healthy control subjects during the resting state period were investigated by nonlinear convergent cross mapping (CCM). Surrogate data, bootstrapping and linear mixed-effects model approaches were utilized for statistical analyses. Main results: CCM was able to reveal specific and statistically significant time- and frequency-dependent patterns of brain–heart interactions for children with temporal lobe epilepsy and provide a statistically significant pattern of topographic- and frequency-dependent brain–heart interactions for schizophrenic patients, as well as to show the differences from healthy control subjects. Suitable statistical models were found to quantify group differences. Significance: Generalized processing schemes and crucial points of pre-processing, adapted interaction analysis and performed statistical analysis are provided. The general concept of analyses is transferable also to other methods of interactions analysis and data representing even more complex physiological systems.

Objective: Epileptic seizure activity influences the autonomic nervous system (ANS) in different ways. Heart rate variability (HRV) is used as indicator for alterations of the ANS. It was shown that linear, nondirected interactions between HRV and EEG activity before, during, and after epileptic seizure occur. Accordingly, investigations of directed nonlinear interactions are logical steps to provide, e.g., deeper insight into the development of seizure onsets. Methods: Convergent cross mapping (CCM) investigates nonlinear, directed interactions between time series by using nonlinear state space reconstruction. CCM is applied to simulated and clinically relevant data, i.e., interactions between HRV and specific EEG components of children with temporal lobe epilepsy (TLE). In addition, time-variant multivariate Autoregressive model (AR)-based estimation of partial directed coherence (PDC) was performed for the same data. Results: Influence of estimation parameters and time-varying behavior of CCM estimation could be demonstrated by means of simulated data. AR-based estimation of PDC failed for the investigation of our clinical data. Time-varying interval-based application of CCM on these data revealed directed interactions between HRV and delta-related EEG activity. Interactions between HRV and alpha-related EEG activity were visible but less pronounced. EEG components mainly drive HRV. The interaction pattern and directionality clearly changed with onset of seizure. Statistical relevant interactions were quantified by bootstrapping and surrogate data approach. Conclusion and Significance: In contrast to AR-based estimation of PDC CCM was able to reveal time-courses and frequency-selective views of nonlinear interactions for the further understanding of complex interactions between the epileptic network and the ANS in children with TLE.

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.

Summary: Objectives: Empirical mode decomposition (EMD) is a frequently used signal processing approach which adaptively decomposes a signal into a set of narrow-band components known as intrinsic mode functions (IMFs). For multi-trial, multivariate (multiple simultaneous recordings), and multi-subject analyses the number and signal properties of the IMFs can deviate from each other between trials, channels and subjects. A further processing of IMFs, e.g. a simple ensemble averaging, should determine which IMFs of one signal correspond to IMFs from another signal. When the signal properties have similar characteristics, the IMFs are assigned to each other. This problem is known as correspondence problem.Methods: From the mathematical point of view, in some cases the correspondence problem can be transformed into an assignment problem which can be solved e.g. by the Kuhn-Munkres algorithm (KMA) by which a minimal cost matching can be found. We use the KMA for solving classic assignment problems, i.e. the pairwise correspondence between two sets of IMFs of equal cardinalities, and for pairwise correspondences between two sets of IMFs with different cardinalities representing an unbalanced assignment problem which is a special case of the k-cardinality assignment problem.Results: A KMA-based approach to solve the correspondence problem was tested by using simulated, heart rate variability (HRV), and EEG data. The KMA-based results of HRV decomposition are compared with those obtained from a hierarchical cluster analysis (state-of-the-art). The major difference between the two approaches is that there is a more consistent assignment pattern using KMA. Integrating KMA into complex analysis concepts enables a comprehensive exploitation of the key advantages of the EMD. This can be demonstrated by non-linear analysis of HRV-related IMFs and by an EMD-based cross-frequency coupling analysis of the EEG data.Conclusions: The successful application to HRV and EEG analysis demonstrates that our solutions can be used for automated EMD-based processing concepts for biomedical signals.

We address the correspondence problem which arises when applying empirical mode decomposition (EMD) to multi-trial and multi-subject data. EMD decomposes a signal into a set of narrow-band components named intrinsic mode functions (IMFs). The number of IMFs and their signal properties can be different between trials, channels and subjects. In order to assign IMFs with similar characteristics to each other, we compare two assignment methods, unbalanced assignment and k-cardinality assignment and two clustering algorithms, namely hierarchical clustering and density-based spatial clustering of applications with noise based on heart rate variability data of children with temporal lobe epilepsy

Introduction: This article is part of the Focus Theme of Methods of Information in Medicine on “Biosignal Interpretation: Advanced Methods for Neural Signals and Images“. Objectives: The aim of this study was to compare rhythmicities in the quadratic phase coupling (QPC) in the tracé discontinue EEG patterns (TD) of premature newborns and the tracé alternant EEG patterns (TA) of full-term newborns by means of time-variant bispectral analysis. Both pattern occur during quiet sleep and are characterized by an ongoing sequence of interburst and burst patterns. The courses of time-variant bispectral measures during the EEG burst most likely indicate specific interrelations between cortical and thalamocortical brain structures. Methods: The EEG of a group of premature (n = 5) and of full-term (n = 5) newborns was analysed. Time-variant QPC was investigated by means of time-variant parametric bispectral analysis. The frequency plain [0.5 Hz, 1.5 Hz] × [3 Hz, 6 Hz] was used as the region-of-interest (ROI). Results: QPC rhythms with a frequency of 0.1 Hz (8 – 11 s) were found in all full-term newborns at all electrodes. For the premature newborns the QPC rhythms were less stable and slower (< 0.1 Hz, 11 – 17 s) at all electrodes and showed a higher inter-individual variation than for the full-term newborns. Statistically, the adaptation of a linear mixed model revealed a difference of about 5 s between both groups of newborns. Conclusions: The comparison of the results of both groups of newborns indicates a development in the interaction between cortical, thalamocortical and neurovegetative structures in the neonatal brain.