scholarly journals Detecting phase singularities and rotor center trajectories based on the Hilbert transform of intraatrial electrograms in an atrial voxel model

2015 ◽  
Vol 1 (1) ◽  
pp. 38-41 ◽  
Author(s):  
Laura Anna Unger ◽  
Markus Rottmann ◽  
Gunnar Seemann ◽  
Olaf Dössel
Keyword(s):  
Atrial Fibrillation ◽  
Blood Volume ◽  
Hilbert Transform ◽  
Rf Ablation ◽  
Voxel Model ◽  
Rotor Center ◽  
Phase Singularities ◽  
Endocardial Surface ◽  
The Hilbert Transform ◽  
Unipolar Electrograms

AbstractThis work aimed at the detection of rotor centers within the atrial cavity during atrial fibrillation on the basis of phase singularities. A voxel based method was established which employs the Hilbert transform and the phase of unipolar electrograms. The method provides a 3D overview of phase singularities at the endocardial surface and within the blood volume. Mapping those phase singularities from the inside of the atria at the endocardium yielded rotor center trajectories. We discuss the results for an unstable and a more stable rotor. The side length of the areas covered by the trajectories varied from 1.5 mm to 10 mm. These results are important for cardiologists who target rotors with RF ablation in order to cure atrial fibrillation.

Dynamic synchronization analysis of venous pressure-driven cardiac output in rainbow trout

2003 ◽  
Vol 285 (4) ◽  
pp. R889-R896 ◽  
Author(s):  
Adrienne Robyn Minerick ◽  
Hsueh-Chia Chang ◽  
Todd M. Hoagland ◽  
Kenneth R. Olson
Keyword(s):  
Cardiac Output ◽  
Rainbow Trout ◽  
Blood Volume ◽  
Hilbert Transform ◽  
Venous Pressure ◽  
Time Lag ◽  
Venous Compliance ◽  
Pressure Transducers ◽  
The Hilbert Transform

Measurement of venous function in vivo is inherently difficult. In this study, we used the Hilbert transform to examine the dynamic relationships between venous pressure and cardiac output (CO) in rainbow trout whose blood volume was continuously increased and decreased by ramp infusion and withdrawal (I/W). The dorsal aorta and ductus Cuvier were cannulated percutaneously and connected to pressure transducers; a flow probe was placed around the ventral aorta. Whole blood from a donor was then I/W via the dorsal aortic cannula at a rate of 10% of the estimated blood volume per minute, and the duration of I/W was varied from 40, 60, 80, 90, 120, 230, 240, 260, 300, and 340 s. Compliance [change in (Δ) blood vol/Δvenous pressure] was 2.8 ± 0.2 ml · mmHg-1 · g-1 ( N = 25 measurements; 6 fish with closed pericardium) and 2.8 ± 0.3 ml · mmHg-1 · kg-1 ( N = 19 measurements, 4 fish with open pericardium). Compliance was positively correlated with the duration of I/W, indicative of cardiovascular reflex responses at longer I/W durations. In trout with closed pericardium, CO followed venous pressure oscillations with an average time lag of 4.2 ± 1.0 s ( N = 9); heart rate (HR) was inversely correlated with CO. These studies show that CO is entrained by modulation of venous pressure, not by HR. Thus, although trout have a rigid pericardium, venous pressure (vis-a-tergo), not cardiac suction (vis-a-fronte), appears to be the primary determinant of CO. Estimation of venous compliance by ramp-modulation of venous pressure is faster and less traumatic than classical capacitance measurements and appears applicable to a variety of vertebrate species, as does the Hilbert transform, which permits analysis of signals with disparate frequencies.

Model of multicomponent narrow-band periodical non-stationary random signal

2020 ◽  
Vol 2020 (48) ◽  
pp. 17-24
Author(s):  
I.M. Javorskyj ◽  
◽  
R.M. Yuzefovych ◽  
P.R. Kurapov ◽  
◽  
...  
Keyword(s):  
Time Series ◽  
Real Time ◽  
Hilbert Transform ◽  
Spectral Properties ◽  
Narrow Band ◽  
Analytic Signal ◽  
Random Signal ◽  
Hilbert Transformation ◽  
The Hilbert Transform

The correlation and spectral properties of a multicomponent narrowband periodical non-stationary random signal (PNRS) and its Hilbert transformation are considered. It is shown that multicomponent narrowband PNRS differ from the monocomponent signal. This difference is caused by correlation of the quadratures for the different carrier harmonics. Such features of the analytic signal must be taken into account when we use the Hilbert transform for the analysis of real time series.

A Bayesian View on the Hilbert Transform and the Kramers-Kronig Transform of Electrochemical Impedance Data: Probabilistic Estimates and Quality Scores

2020 ◽  
Author(s):  
Jiapeng Liu ◽  
Ting Hei Wan ◽  
Francesco Ciucci
Keyword(s):  
Power Generation ◽  
Electrochemical Impedance Spectroscopy ◽  
Hilbert Transform ◽  
Electrochemical Impedance ◽  
The Self ◽  
Impedance Data ◽  
The Hilbert Transform ◽  
Validation Tests ◽  
Self Consistency ◽  
Mathematical Relations

<p>Electrochemical impedance spectroscopy (EIS) is one of the most widely used experimental tools in electrochemistry and has applications ranging from energy storage and power generation to medicine. Considering the broad applicability of the EIS technique, it is critical to validate the EIS data against the Hilbert transform (HT) or, equivalently, the Kramers–Kronig relations. These mathematical relations allow one to assess the self-consistency of obtained spectra. However, the use of validation tests is still uncommon. In the present article, we aim at bridging this gap by reformulating the HT under a Bayesian framework. In particular, we developed the Bayesian Hilbert transform (BHT) method that interprets the HT probabilistic. Leveraging the BHT, we proposed several scores that provide quick metrics for the evaluation of the EIS data quality.<br></p>

scholarly journals A Radial Basis Function Finite Difference Scheme for the Benjamin–Ono Equation

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 65
Author(s):  
Benjamin Akers ◽  
Tony Liu ◽  
Jonah Reeger
Keyword(s):  
Radial Basis Function ◽  
Hilbert Transform ◽  
Basis Function ◽  
Differential Operators ◽  
Convergence Rates ◽  
Traveling Wave Solutions ◽  
Algebraic Decay ◽  
Pseudo Differential Operators ◽  
Radial Basis ◽  
The Hilbert Transform

A radial basis function-finite differencing (RBF-FD) scheme was applied to the initial value problem of the Benjamin–Ono equation. The Benjamin–Ono equation has traveling wave solutions with algebraic decay and a nonlocal pseudo-differential operator, the Hilbert transform. When posed on R, the former makes Fourier collocation a poor discretization choice; the latter is challenging for any local method. We develop an RBF-FD approximation of the Hilbert transform, and discuss the challenges of implementing this and other pseudo-differential operators on unstructured grids. Numerical examples, simulation costs, convergence rates, and generalizations of this method are all discussed.

scholarly journals Phase Synchronization Is the Amplified Result by the Hilbert Transform

2015 ◽  
Vol 2015 ◽  
pp. 1-3 ◽  
Author(s):  
Ming-Chi Lu ◽  
Hsing-Chung Ho ◽  
Chen-An Chan ◽  
Chia-Ju Liu ◽  
Jiann-Shing Lih ◽  
...  
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Hilbert Transform ◽  
Phase Synchronization ◽  
Nonlinear Dynamical Systems ◽  
The State ◽  
Nonlinear Dynamical ◽  
Large Correlation ◽  
Current Usage ◽  
The Hilbert Transform

We investigate the interplay between phase synchronization and amplitude synchronization in nonlinear dynamical systems. It is numerically found that phase synchronization intends to be established earlier than amplitude synchronization. Nevertheless, amplitude synchronization (or the state with large correlation between the amplitudes) is crucial for the maintenance of a high correlation between two time series. A breakdown of high correlation in amplitudes will lead to a desynchronization of two time series. It is shown that these unique features are caused essentially by the Hilbert transform. This leads to a deep concern and criticism on the current usage of phase synchronization.

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