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Often the network relied on portions of the ECG which are also considered by cardiologists to detect the same cardiac abnormalities, but this was not always the case. In conclusion, the proposed frameworks may unveil whether the network relies on features which are clinically significant for the detection of cardiac abnormalities from 12-lead ECG signals, thus increasing the trust in the DL models. This article is part of the theme issue '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'.Recent advancements in detrended fluctuation analysis (DFA) allow evaluating multifractal coefficients scale-by-scale, a promising approach for assessing the complexity of biomedical signals. The multifractality degree is typically quantified by the singularity spectrum width (WSS), a method that is critically unstable in multiscale applications. Thus, we aim to propose a robust multiscale index of multifractality, compare it with WSS and illustrate its performance on real biosignals. The proposed index is the cumulative function of squared increments between consecutive DFA coefficients at each scale n αCF(n). We compared it with WSS calculated scale-by-scale considering monofractal/monoscale, monofractal/multiscale, multifractal/monoscale and multifractal/multiscale random processes. The two indices provided qualitatively similar descriptions of multifractality, but αCF(n) differentiated better the multifractal components from artefacts due to crossovers or detrending overfitting. Applied on 24 h heart rate recordings of 14 participants, the singularity spectrum failed to always satisfy the concavity requirement for providing meaningful WSS, while αCF(n) demonstrated a statistically significant heart rate multifractality at night in the scale ranges 16-100 and 256-680 s. Furthermore, αCF(n) did not reject the hypothesis of monofractality at daytime, coherently with previous reports of lower nonlinearity and monoscale multifractality during the day. Thus, αCF(n) appears a robust index of multiscale multifractality that is useful for quantifying complexity alterations of physiological series. This article is part of the theme issue 'Advanced computation in cardiovascular physiology new challenges and opportunities'.Spontaneous beat-to-beat variations of heart rate (HR) have intrigued scientists and casual observers for centuries; however, it was not until the 1970s that investigators began to apply engineering tools to the analysis of these variations, fostering the field we now know as heart rate variability or HRV. Since then, the field has exploded to not only include a wide variety of traditional linear time and frequency domain applications for the HR signal, but also more complex linear models that include additional physiological parameters such as respiration, arterial blood pressure, central venous pressure and autonomic nerve signals. Most recently, the field has branched out to address the nonlinear components of many physiological processes, the complexity of the systems being studied and the important issue of specificity for when these tools are applied to individuals. When the impact of all these developments are combined, it seems likely that the field of HRV will soon begin to realize its potential as an important component of the toolbox used for diagnosis and therapy of patients in the clinic. This article is part of the theme issue 'Advanced computation in cardiovascular physiology new challenges and opportunities'.While Granger causality (GC) has been often employed in network neuroscience, most GC applications are based on linear multivariate autoregressive (MVAR) models. However, real-life systems like biological networks exhibit notable nonlinear behaviour, hence undermining the validity of MVAR-based GC (MVAR-GC). Most nonlinear GC estimators only cater for additive nonlinearities or, alternatively, are based on recurrent neural networks or long short-term memory networks, which present considerable training difficulties and tailoring needs. We reformulate the GC framework in terms of echo-state networks-based models for arbitrarily complex networks, and characterize its ability to capture nonlinear causal relations in a network of noisy Duffing oscillators, showing a net advantage of echo state GC (ES-GC) in detecting nonlinear, causal links. We then explore the structure of ES-GC networks in the human brain employing functional MRI data from 1003 healthy subjects drawn from the human connectome project, demonstrating the existence of previously unknown directed within-brain interactions. In addition, we examine joint brain-heart signals in 15 subjects where we explore directed interaction between brain networks and central vagal cardiac control in order to investigate the so-called central autonomic network in a causal manner. This article is part of the theme issue 'Advanced computation in cardiovascular physiology new challenges and opportunities'.The study of functional brain-heart interplay has provided meaningful insights in cardiology and neuroscience. Regarding biosignal processing, this interplay involves predominantly neural and heartbeat linear dynamics expressed via time and frequency domain-related features. However, the dynamics of central and autonomous nervous systems show nonlinear and multifractal behaviours, and the extent to which this behaviour influences brain-heart interactions is currently unknown. Here, we report a novel signal processing framework aimed at quantifying nonlinear functional brain-heart interplay in the non-Gaussian and multifractal domains that combines electroencephalography (EEG) and heart rate variability series. This framework relies on a maximal information coefficient analysis between nonlinear multiscale features derived from EEG spectra and from an inhomogeneous point-process model for heartbeat dynamics. Experimental results were gathered from 24 healthy volunteers during a resting state and a cold pressor test, revealing that synchronous changes between brain and heartbeat multifractal spectra occur at higher EEG frequency bands and through nonlinear/complex cardiovascular control. BAY-876 cost We conclude that significant bodily, sympathovagal changes such as those elicited by cold-pressure stimuli affect the functional brain-heart interplay beyond second-order statistics, thus extending it to multifractal dynamics. These results provide a platform to define novel nervous-system-targeted biomarkers. This article is part of the theme issue 'Advanced computation in cardiovascular physiology new challenges and opportunities'.While cross-spectral and information-theoretic approaches are widely used for the multivariate analysis of physiological time series, their combined utilization is far less developed in the literature. This study introduces a framework for the spectral decomposition of multivariate information measures, which provides frequency-specific quantifications of the information shared between a target and two source time series and of its expansion into amounts related to how the sources contribute to the target dynamics with unique, redundant and synergistic information. The framework is illustrated in simulations of linearly interacting stochastic processes, showing how it allows us to retrieve amounts of information shared by the processes within specific frequency bands which are otherwise not detectable by time-domain information measures, as well as coupling features which are not detectable by spectral measures. Then, it is applied to the time series of heart period, systolic and diastolic arterial pressure and respiration variability measured in healthy subjects monitored in the resting supine position and during head-up tilt. We show that the spectral measures of unique, redundant and synergistic information shared by these variability series, integrated within specific frequency bands of physiological interest and reflect the mechanisms of short-term regulation of cardiovascular and cardiorespiratory oscillations and their alterations induced by the postural stress. This article is part of the theme issue 'Advanced computation in cardiovascular physiology new challenges and opportunities'.Stress test electrocardiogram (ECG) analysis is widely used for coronary artery disease (CAD) diagnosis despite its limited accuracy. Alterations in autonomic modulation of cardiac electrical activity have been reported in CAD patients during acute ischemia. We hypothesized that those alterations could be reflected in changes in ventricular repolarization dynamics during stress testing that could be measured through QT interval variability (QTV). However, QTV is largely dependent on RR interval variability (RRV), which might hinder intrinsic ventricular repolarization dynamics. In this study, we investigated whether different markers accounting for low-frequency (LF) oscillations of QTV unrelated to RRV during stress testing could be used to separate patients with and without CAD. Power spectral density of QTV unrelated to RRV was obtained based on time-frequency coherence estimation. Instantaneous LF power of QTV and QTV unrelated to RRV were obtained. LF power of QTV unrelated to RRV normalized by LF power f the theme issue 'Advanced computation in cardiovascular physiology new challenges and opportunities'.The electrocardiogram (ECG) is a widespread diagnostic tool in healthcare and supports the diagnosis of cardiovascular disorders. Deep learning methods are a successful and popular technique to detect indications of disorders from an ECG signal. However, there are open questions around the robustness of these methods to various factors, including physiological ECG noise. In this study, we generate clean and noisy versions of an ECG dataset before applying symmetric projection attractor reconstruction (SPAR) and scalogram image transformations. A convolutional neural network is used to classify these image transforms. For the clean ECG dataset, F1 scores for SPAR attractor and scalogram transforms were 0.70 and 0.79, respectively. Scores decreased by less than 0.05 for the noisy ECG datasets. Notably, when the network trained on clean data was used to classify the noisy datasets, performance decreases of up to 0.18 in F1 scores were seen. However, when the network trained on the noisy data was used to classify the clean dataset, the decrease was less than 0.

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