Copula as a dynamic measure of cardiovascular signal interactions

Objectives: Copula is a tool for measuring linear and non-linear interactions between two or more time series. The aim of this paper is to prove that a copula approach can accurately capture and visualize the spatial and temporal fluctuations in dependency structures of cardiovascular signals, and to outline the application possibilities. Methods: The method for measuring the level of interaction between systolic blood pressure and the corresponding pulse interval is validated statistically and pharmacologically. The time series are recorded from the freely moving male Wistar rats equipped with radio-telemetry device for blood pressure recording, before and after administration of autonomic blockers scopolamine, atenolol, prazosin and hexamethonium. Implicit (Gaussian and t) and explicit (Clayton, Frank and Gumbel) copulas were calculated and compared to the conventional bivariate methods (Kendal, Pearson, Spearman and classical correlation). Further statistical validation was done using artificially generated surrogate data. A window sliding procedure for dynamic monitoring the signals' coupling strength is implemented. Results: Under the baseline physiological conditions, SBP-PI dependency is significant for time lags 0 s-4 s. Hexamethonium completely abolished the dependency, scopolamine abolished it for time lags 0 s-2 s, atenolol first slightly increased, than for lags greater than 2 s decreased the dependency and prazosin had no effect. Isospectral and isodistributional surrogate data tests confirm that copulas successfully notify the absence of dependency as well. Conclusion: Copula approach accurately captures the temporal fluctuations in dependency structures of SBP and PI, simultaneously enabling a visualization of dependency levels within the particular signal zones. An analysis showed that copulas are more sensitive than the conventional statistical measures, with Frank copula exhibiting the best characterization of SBP and PI dependency

Voronoi Decomposition of Cardiovascular Dependency Structures in Different Ambient Conditions: An Entropy Study

This paper proposes a method that maps the coupling strength of an arbitrary number of signals D, D >= 2, into a single time series. It is motivated by the inability of multiscale entropy to jointly analyze more than two signals. The coupling strength is determined using the copula density defined over a [0 1](D) copula domain. The copula domain is decomposed into the Voronoi regions, with volumes inversely proportional to the dependency level (coupling strength) of the observed joint signals. A stream of dependency levels, ordered in time, creates a new time series that shows the fluctuation of the signals' coupling strength along the time axis. The composite multiscale entropy (CMSE) is then applied to three signals, systolic blood pressure (SBP), pulse interval (PI), and body temperature (t(B)), simultaneously recorded from rats exposed to different ambient temperatures (t(A)). The obtained results are consistent with the results from the classical studies, and the method itself offers more levels of freedom than the classical analysis

On entropy of probability integral transformed time series

Abstract The goal of this paper is to investigate the changes of entropy estimates when the amplitude distribution of the time series is equalized using the probability integral transformation. The data we analyzed were with known properties—pseudo-random signals with known distributions, mutually coupled using statistical or deterministic methods that include generators of statistically dependent distributions, linear and non-linear transforms, and deterministic chaos. The signal pairs were coupled using a correlation coefficient ranging from zero to one. The dependence of the signal samples is achieved by moving average filter and non-linear equations. The applied coupling methods are checked using statistical tests for correlation. The changes in signal regularity are checked by a multifractal spectrum. The probability integral transformation is then applied to cardiovascular time series—systolic blood pressure and pulse interval—acquired from the laboratory animals and represented the results of entropy estimations. We derived an expression for the reference value of entropy in the probability integral transformed signals. We also experimentally evaluated the reliability of entropy estimates concerning the matching probabilities

Dependency Structures in Differentially Coded Cardiovascular Time Series

Objectives. This paper analyses temporal dependency in the time series recorded from aging rats, the healthy ones and those with early developed hypertension. The aim is to explore effects of age and hypertension on mutual sample relationship along the time axis. Methods. A copula method is applied to raw and to differentially coded signals. The latter ones were additionally binary encoded for a joint conditional entropy application. The signals were recorded from freely moving male Wistar rats and from spontaneous hypertensive rats, aged 3 months and 12 months. Results. The highest level of comonotonic behavior of pulse interval with respect to systolic blood pressure is observed at time lags τ=0, 3, and 4, while a strong counter-monotonic behavior occurs at time lags τ=1 and 2. Conclusion. Dynamic range of aging rats is considerably reduced in hypertensive groups. Conditional entropy of systolic blood pressure signal, compared to unconditional, shows an increased level of discrepancy, except for a time lag 1, where the equality is preserved in spite of the memory of differential coder. The antiparallel streams play an important role at single beat time lag

Stroke-related alterations in inter-areal communication

Beyond causing local ischemia and cell damage at the site of injury, stroke strongly affects long-range anatomical connections, perturbing the functional organization of brain networks. Several studies reported functional connectivity abnormalities parallelling both behavioral deficits and functional recovery across different cognitive domains. FC alterations suggest that long-range communication in the brain is altered after stroke. However, standard FC analyses cannot reveal the directionality and time scale of inter-areal information transfer. We used resting-state fMRI and covariance-based Granger causality analysis to quantify network-level information transfer and its alteration in stroke. Two main large-scale anomalies were observed in stroke patients. First, inter-hemispheric information transfer was significantly decreased with respect to healthy controls. Second, stroke caused inter-hemispheric asymmetries, as information transfer within the affected hemisphere and from the affected to the intact hemisphere was significantly reduced. Both anomalies were more prominent in resting-state networks related to attention and language, and they correlated with impaired performance in several behavioral domains. Overall, our findings support the hypothesis that stroke provokes asymmetries between the affected and spared hemisphere, with different functional consequences depending on which hemisphere is lesioned

Heart and Ventilatory Measures in Crayfish During Copulation

Monitoring heart rate (HR) and ventilatory rate (VR) during defined sensory stimuli and during aggressive and submissive social interactions has provided additional information of a crayfish\u27s physiological state which is not achieved by behavioral observations. In this study, the HR and VR of crayfish were monitored before, during and after the act of copulation in both heterosexual partners. The female crayfish abruptly reduces HR and VR during copulation but the male maintains HR and VR. After separation from copulation the female HR and VR are elevated, potentially paying back the O2 debt. The tight relationship with HR and VR in direction of change indicates a potential neural coupling. These physiological changes in cardiac and respiratory systems suggest an autonomic-like regulation of HR and VR. How these neuronal functions are driven and regulated remains to be determined. Olfactory cues from the female to the male during copulation may be reduced by the reduction in VR in the female. These studies offer experimental paradigms for future neuronal and pharmacological investigations into autonomic regulation of HR and VR as well as the neural circuitry involved

Disambiguating the role of blood flow and global signal with partial information decomposition

Global signal (GS) is an ubiquitous construct in resting state functional magnetic resonance imaging (rs-fMRI), associated to nuisance, but containing by definition most of the neuronal signal. Global signal regression (GSR) effectively removes the impact of physiological noise and other artifacts, but at the same time it alters correlational patterns in unpredicted ways. Performing GSR taking into account the underlying physiology (mainly the blood arrival time) has been proven to be beneficial. From these observations we aimed to: 1) characterize the effect of GSR on network-level functional connectivity in a large dataset; 2) assess the complementary role of global signal and vessels; and 3) use the framework of partial information decomposition to further look into the joint dynamics of the global signal and vessels, and their respective influence on the dynamics of cortical areas. We observe that GSR affects intrinsic connectivity networks in the connectome in a non-uniform way. Furthermore, by estimating the predictive information of blood flow and the global signal using partial information decomposition, we observe that both signals are present in different amounts across intrinsic connectivity networks. Simulations showed that differences in blood arrival time can largely explain this phenomenon, while using hemodynamic and calcium mouse recordings we were able to confirm the presence of vascular effects, as calcium recordings lack hemodynamic information. With these results we confirm network-specific effects of GSR and the importance of taking blood flow into account for improving de-noising methods. Additionally, and beyond the mere issue of data denoising, we quantify the diverse and complementary effect of global and vessel BOLD signals on the dynamics of cortical areas

Numerical Simulation in Biomechanics and Biomedical Engineering

In the first contribution, Morbiducci and co-workers discuss the theoretical and methodological bases supporting the Lagrangian- and Euler-based methods, highlighting their application to cardiovascular flows. The second contribution, by the Ansón and van Lenthe groups, proposes an automated virtual bench test for evaluating the stability of custom shoulder implants without the necessity of mechanical testing. Urdeitx and Doweidar, in the third paper, also adopt the finite element method for developing a computational model aim to study cardiac cell behavior under mechano-electric stimulation. In the fourth contribution, Ayensa-Jiménez et al. develop a methodology to approximate the multidimensional probability density function of the parametric analysis obtained developing a mathematical model of the cancer evolution. The fifth paper is oriented to the topological data analysis; the group of Cueto and Chinesta designs a predictive model capable of estimating the state of drivers using the data collected from motion sensors. In the sixth contribution, the Ohayon and Finet group uses wall shear stress-derived descriptors to study the role of recirculation in the arterial restenosis due to different malapposed and overlapping stent conditions. In the seventh contribution, the research group of Antón demonstrates that the simulation time can be reduced for cardiovascular numerical analysis considering an adequate geometry-reduction strategy applicable to truncated patient specific artery. In the eighth paper, Grasa and Calvo present a numerical model based on the finite element method for simulating extraocular muscle dynamics. The ninth paper, authored by Kahla et al., presents a mathematical mechano-pharmaco-biological model for bone remodeling. Martínez, Peña, and co-workers propose in the tenth paper a methodology to calibrate the dissection properties of aorta layer, with the aim of providing useful information for reliable numerical tools. In the eleventh contribution, Martínez-Bocanegra et al. present the structural behavior of a foot model using a detailed finite element model. The twelfth contribution is centered on the methodology to perform a finite, element-based, numerical model of a hydroxyapatite 3D printed bone scaffold. In the thirteenth paper, Talygin and Gorodkov present analytical expressions describing swirling jets for cardiovascular applications. In the fourteenth contribution, Schenkel and Halliday propose a novel non-Newtonian particle transport model for red blood cells. Finally, Zurita et al. propose a parametric numerical tool for analyzing a silicone customized 3D printable trachea-bronchial prosthesis

Risks

This book is a collection of feature articles published in Risks in 2020. They were all written by experts in their respective fields. In these articles, they all develop and present new aspects and insights that can help us to understand and cope with the different and ever-changing aspects of risks. In some of the feature articles the probabilistic risk modeling is the central focus, whereas impact and innovation, in the context of financial economics and actuarial science, is somewhat retained and left for future research. In other articles it is the other way around. Ideas and perceptions in financial markets are the driving force of the research but they do not necessarily rely on innovation in the underlying risk models. Together, they are state-of-the-art, expert-led, up-to-date contributions, demonstrating what Risks is and what Risks has to offer: articles that focus on the central aspects of insurance and financial risk management, that detail progress and paths of further development in understanding and dealing with...risks. Asking the same type of questions (which risk allocation and mitigation should be provided, and why?) creates value from three different perspectives: the normative perspective of market regulator; the existential perspective of the financial institution; the phenomenological perspective of the individual consumer or policy holder

Multivariate financial econometrics: with applications to volatility modelling, option pricing and asset allocation

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