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A new method for incorporating weighted temporal and spatial smoothing in the inverse problem of electrocardiography.

In this paper, we present a method for incorporating temporal smoothing (TS) into the estimate of epicardial potentials from body surface potential data. Our algorithm employs a different spatial smoothing parameter, chosen by the composite residual error and smoothing operator criteria, at each time step in the sequence. The total spatial smoothing term is then simply partitioned between temporal and spatial smoothing. The algorithm appears to be quite robust with regard to this partitioning. The new method was evaluated in the setting of additive Gaussian noise, but otherwise realistic conditions of body geometry and reference epicardial potentials. In examining the match between estimated and measured electrograms, or the match between estimated isopotential maps and measured isopotential maps, the estimates constructed using the new TS algorithm produced consistently smaller relative errors than those constructed using a quasi-static (QS) algorithm or those constructed by postprocessing the QS estimate with a moving average filter.

Algorithms↗

Exploratory analysis of the spatio-temporal deformation of the myocardium during systole from tagged MRI.

Myocardial contractile function is, with perfusion, one of the main affected factors in ischemic heart diseases. In this paper, we propose an original framework based on functional data analysis for the quantitative study of spatio-temporal parameters related to the myocardial contraction mechanics. The mechanical strains in the left-ventricular (LV) myocardium are computed from tagged magnetic resonance imaging cardiac sequences. A statistical functional model of the normal contractile function of the LV is build from the study of eight examinations on healthy subjects. We show that it is possible to detect abnormal strain patterns comparatively to this model, by generating distance maps at rest and under pharmacological stress. We demonstrate the consistency of the results for the circumferential deformation parameter on healthy and pathological data sets.

Algorithms↗

A novel algorithm for cardiac biosignal filtering based on filtered residue method.

In this paper, a new algorithm is presented for the filtering (de-noising) of cardiac bioelectrical signals. The primary target of this algorithm is the class of cardiac action potentials recorded using voltage-sensitive dyes, although the method is also applied to electrocardiographic signals. High periodicity is one of the main features of cardiac biosignals. The proposed algorithm exploits this feature in filtering signals with a minimum amount of distortion. The basic idea is to use signal averaging in time to find the stationary portion of the signal. The residue is found by subtracting the signal average from the corresponding points of the input. After passing through a low-pass filter, the filtered residue (FR) is added back to the signal average to reconstruct the output. The practical implementation of the filter residue algorithm is discussed. Stretching and shrinking operations are the basis for the conversion of quasi-periodic signals into periodic signals, which can then be subjected to the FR algorithm. Various examples are presented, and error estimation is performed to guide the selection of optimal parameters for the algorithm. The ability of the algorithm to reconstruct the variation among beats is demonstrated, and its limitations are discussed.

Action Potentials↗

Removal of cardiopulmonary resuscitation artifacts from human ECG using an efficient matching pursuit-like algorithm.

We present a computationally efficient and numerically robust solution to the problem of removing artifacts due to precordial compressions and ventilations from the human electrocardiogram (ECG) in an emergency medicine setting. Incorporated into automated external defibrillators, this would allow for simultaneous ECG signal analysis and administration of precordial compressions and ventilations, resulting in significant clinical improvement to the treatment of cardiac arrest patients. While we have previously demonstrated the feasibility of such artifact removal using a multichannel Wiener filter, we here focus on an efficient matching pursuit-like approach making practical real-time implementations of such a scheme feasible for a wide variety of sampling rates and filter lengths. Using more realistic data than what have been previously available, we present evidence showing the excellent performance of our approach and quantify its computational complexity.

Algorithms↗

Estimation of plasma insulin from plasma glucose.

Two plasma insulin estimators are derived and evaluated in this paper. The estimators use continuously monitored plasma glucose, and they are based on a simple mathematical model of glucose-insulin metabolism. The first estimator (Estimator 1) was obtained from the glucose subsystem of the simplified model, which includes plasma glucose and interstitial insulin compartments. The second estimator (Estimator 2) was developed from the insulin kinetics subsystem of the simplified model. The performances of the estimators were compared using computer simulations and data from clinical intravenous glucose tolerance test procedures and from animal experiments.

Animals↗

Electrical coupling of single cardiac rat myocytes to field-effect and bipolar transistors.

A novel bipolar transistor for extracellular recording the electrical activity of biological cells is presented, and the electrical behavior compared with the field-effect transistor (FET). Electrical coupling is examined between single cells separated from the heart of adults rats (cardiac myocytes) and both types of transistors. To initiate a local extracellular voltage, the cells are periodically stimulated by a patch pipette in voltage clamp and current clamp mode. The local extracellular voltage is measured by the planar integrated electronic sensors: the bipolar and the FET. The small signal transistor currents correspond to the local extracellular voltage. The two types of sensor transistors used here were developed and manufactured in the laboratory of our institute. The manufacturing process and the interfaces between myocytes and transistors are described. The recordings are interpreted by way of simulation based on the point-contact model and the single cardiac myocyte model.

Action Potentials↗

Automated detection and elimination of periodic ECG artifacts in EEG using the energy interval histogram method.

An automated method for electrocardiogram (ECG)-artifact detection and elimination is proposed for application to a single-channel electroencephalogram (EEG) without a separate ECG channel for reference. The method is based on three characteristics of ECG artifacts: the spike-like property, the periodicity and the lack of correlation with the EEG. The method involves a two-step process: ECG artifact detection using the energy interval histogram (EIH) method and ECG artifact elimination using a modification of ensemble average subtraction. We applied a smoothed nonlinear energy operator to the contaminated EEG, which significantly emphasized the ECG artifacts compared with the background EEG. The EIH method was initially proposed to estimate the rate of false positives (FPs) and false negatives (FNs) that were necessary to determine the optimal threshold for the detection of the ECG artifact. As a postprocessing step, we used two types of threshold adjusting algorithms that were based on the periodicity of the ECG R-peaks. The technique was applied to four whole-night sleep EEG recordings from four subjects with severe obstructive sleep apnea syndrome, from which a total of 132878 heartbeats were monitored over 31.8 h. We found that ECG artifacts were successfully detected and eliminated with FP = 0.017 and FN = 0.074 for the epochs where the elimination process is necessarily required.

Algorithms↗

Field stimulation of cardiac fibers with random spatial structure.

Polarization of individual cells ("sawtooth") has been proposed as a mechanism for field stimulation and defibrillation. To date, the modeling work has concentrated on the myocardium with periodic spatial structure; this paper investigates potentials arising in cardiac fibers with random spatial structure. Ten different random fibers consisting of cells with varying length (l(c) = 100 +/- 50 microm), diameter (d(c) = 20 +/- 10 microm), thickness of extracellular space (t(e) = 1.18 +/- 0.59 microm), and junctional resistance (R(j) = 2 +/- 1 M(omega)) are studied. Simulations demonstrate that randomizing spatial structure introduces to the field-induced potential (V(m)) a randomly varying baseline, which arises due to polarization of groups of cells. This polarization appears primarily in response to randomizing t(e); R(j), l(c), and d(c) have less influence. The maximum V(m) increases from 3.5 mV in a periodic fiber to 20.5+/-4.7 mV in random fibers (1 V/cm field applied for 5 ms). Field stimulation threshold E(th) decreases from 6.9 to 1.59 +/- 0.43 V/cm, which is within the range of experimental measurements. Thresholds for normal and reversed field polarities are statistically equivalent: 1.59 +/- 0.43 versus 1.44 +/- 0.41 V/cm (p value = 0.453). Thus, V(m) arising due to random structure of the myocardium may play an important role in field stimulation and defibrillation.

Computer Simulation↗

Real-time signal processing for fetal heart rate monitoring.

An algorithm based on digital filtering, adaptive thresholding, statistical properties in the time domain, and differencing of local maxima and minima has been developed for the simultaneous measurement of the fetal and maternal heart rates from the maternal abdominal electrocardiogram during pregnancy and labor for ambulatory monitoring. A microcontroller-based system has been used to implement the algorithm in real-time. A Doppler ultrasound fetal monitor was used for statistical comparison on five volunteers with low risk pregnancies, between 35 and 40 weeks of gestation. Results showed an average percent root mean square difference of 5.32% and linear correlation coefficient from 0.84 to 0.93. The fetal heart rate curves remained inside a +/- 5-beats-per-minute limit relative to the reference ultrasound method for 84.1% of the time.

Algorithms↗

Ischemic modulation of vulnerable period and the effects of pharmacological treatment of ischemia-induced arrhythmias: a simulation study.

First identified in the 1930s (Ferris et al., 1936 and Wiggers and Wegria, 1939), the concept of vulnerability applies perfectly to biological oscillators. We can safely say that vulnerability is an inherent property of any excitable media. The duration of vulnerable period (VP) (the time interval during which single stimuli can initiate self-sustaining propagation) is sensitive to medium properties and stimulus parameters (stimulus field, timing behind the conditioning wave, and stimulus amplitude). Apart from medium properties and stimulus characteristics, heart vulnerability is affected by any intervention targeting the excitatory and recovery process. Therefore, we can expect that any pathological condition disturbing heart excitation or tissue recovery will most probably alter the duration of VP. In this paper, we shall explore the implications of ischemia and one of the arrhythmia counteracting methods widely used in clinical practice-antiarrhythmic drugs--in changing the boundaries of VP. The Cardiac Arrhythmia Suppression Trial (CAST) studies, as well as classification based on functional characteristics, revealed the arrhythmogenic potential of both Class I and Class III agents, but failed to identify the proarrhythmic mechanisms. This study presents results from a mathematical model (Cimponeriu et al., 2001) of the ventricle based on Luo-Rudy cellular formulation Luo and Rudy, 1991) modified for studying the ischemic modulation of VP and the effects of pharmacological treatment of ischemia-induced arrhythmia. Simulations revealed the link between the cellular antiarrhythmic properties and the proarrhythmic effect at the multicellular level in the case of Na+ channel blockade. Na+ channel blockade delayed recovery of cellular excitability, but also introduced a nonuniform dispersion of refractoriness along the cardiac fiber that can serve as a substrate for initiating a new arrhythmia. Our initial analysis proved that fast unbinding rates are essential in reducing the proarrhythmic potential of Class I drugs. However, further investigations led us to believe that binding properties are equally important. An antiarrhythmic drug with high affinity for drug-channel complex formation elicits a higher level of blockade per time unit. Under this light, we hypothesize that even the modern, fast unbinding drugs are not necessarily safe.

Action Potentials↗

Improved alignment method for noisy high-resolution ECG and Holter records using multiscale cross-correlation.

The coherent signal averaging process requires accurate estimation of a fiducial point in all beats to be averaged. The temporal cross-correlation between each detected beat and a template beat is the typical alignment method used with high-resolution electrocardiogram (HRECG) records. However, this technique does not produce a precise fiducial mark in records with high noise levels, like those found in Holter HRECG systems. In this study, we propose a new alignment method based on the multiscale cross-correlation between the template and each detected beat. We report the results of tests comparing multiscale and temporal methods for 3000 beats of simulated HRECG records corrupted separately with white noise, electromyographic noise and power line interference (50 Hz) of different root mean square levels. A second study with simulated records constructed from real Holter HRECG records is also presented. The results indicate that the multiscale alignment method produces a lower trigger jitter than the temporal method in all tests. We conclude that the proposed alignment method can be used in HRECG records with high noise levels.

Algorithms↗

Analysis of heart rate variability in the presence of ectopic beats using the heart timing signal.

The time-domain signals representing the heart rate variability (HRV) in the presence of an ectopic beat exhibit a sharp transient at the position of the ectopic beat, which corrupts the signal, particularly the power spectral density (PSD) of the HRV. Consequently, there is a need for correction of this type of beat prior to any HRV analysis. This paper deals with the PSD estimation of the HRV by means of the heart timing (HT) signal when ectopic beats are present. These beat occurrence times are modeled from a generalized, continuous time integral pulse frequency modulation model and, from this point of view, a specific method for minimizing the effect of the presence of ectopic beats is presented to work together with the HT signal. By using both, a white noise driven autoregressive model of the HRV signal with artificially introduced ectopic beats and actual heart rate series including ectopic beats, the more usual methods of HRV spectral estimation are compared. Results of the PSD estimation error function of the number of ectopic beats are presented. These results demonstrate that the proposed method has one order of magnitude lower error than usual ectopic beats removal strategies in preserving PSD, thus, this strategy better recovers the original clinical indexes of interest.

Algorithms↗

The effect of torso impedance on epicardial and body surface potentials: a modeling study.

Experimental results have been published that report marked changes in measured epicardial potentials when the conductivity of the material surrounding the heart is altered. These reports raise a question as to the validity of the traditional two step, equivalent cardiac source approach to modeling the forward problem of electrocardiology as the equivalent source calculation occurs in what is effectively an isolated cardiac region. In the physical situation the heart is surrounded by a torso that contains many different tissue types with different conductivities and is certainly not isolated. Here, a fully coupled model of the problem is employed where the electrical pathways are continuous from a cellular level through to the body surface. This model is used to investigate the effects that torso inhomogeneities have on epicardial and body surface potentials, including comparisons with a traditional two step approach. In particular, it is shown that adding lungs changes the epicardial potentials by 17%, which is consistent with the reported experimental results. In none of the tested situations did the equivalent source approach completely reproduce the fully coupled results, supporting the notion that a fully coupled approach is required to properly solve the forward problem of electrocardiology.

Abdomen↗

Statistical accuracy of a moving equivalent dipole method to identify sites of origin of cardiac electrical activation.

While radio frequency (RF) catheter ablation (RCA) procedures for treating ventricular arrhythmias have evolved significantly over the past several years, the use of RCA has been limited to treating slow ventricular tachycardias (VTs). In this paper, we present preliminary results from computer and animal studies to evaluate the accuracy of an algorithm that uses the single equivalent moving dipole (SEMD) model in an infinite homogeneous volume conductor to guide the RF catheter to the site of origin of the arrhythmia. Our method involves measuring body surface electrocardiographic (ECG) signals generated by arrhythmic activity and by bipolar current pulses emanating from a catheter tip, and representing each of them by a SEMD model source at each instant of the cardiac cycle, thus enabling rapid repositioning of the catheter tip requiring only a few cycles of the arrhythmia. We found that the SEMD model accurately reproduced body surface ECG signals with a correlation coefficients > 0.95. We used a variety of methods to estimate the uncertainty of the SEMD parameters due to measurement noise and found that at the time when the arrhythmia is mostly localized during the cardiac cycle, the estimates of the uncertainty of the spatial SEMD parameters (from ECG signals) are between 1 and 3 mm. We used pacing data from spatially separated epicardial sites in a swine model as surrogates for focal ventricular arrhythmic sources and found that the spatial SEMD estimates of the two pacing sites agreed with both their physical separation and orientation with respect to each other. In conclusion, our algorithm to estimate the SEMD parameters from body surface ECG can potentially be a useful method for rapidly positioning the catheter tip to the arrhythmic focus during an RCA procedure.

Algorithms↗

Prediction of ultrasound-mediated disruption of cell membranes using machine learning techniques and statistical analysis of acoustic spectra.

Although biological effects of ultrasound must be avoided for safe diagnostic applications, ultrasound's ability to disrupt cell membranes has attracted interest as a method to facilitate drug and gene delivery. This paper seeks to develop "prediction rules" for predicting the degree of cell membrane disruption based on specified ultrasound parameters and measured acoustic signals. Three techniques for generating prediction rules (regression analysis, classification trees and discriminant analysis) are applied to data obtained from a sequence of experiments on bovine red blood cells. For each experiment, the data consist of four ultrasound parameters, acoustic measurements at 400 frequencies, and a measure of cell membrane disruption. To avoid over-training, various combinations of the 404 predictor variables are used when applying the rule generation methods. The results indicate that the variable combination consisting of ultrasound exposure time and acoustic signals measured at the driving frequency and its higher harmonics yields the best rule for all three rule generation methods. The methods used for deriving the prediction rules are broadly applicable, and could be used to develop prediciton rules in other scenarios involving different cell types or tissues. These rules and the methods used to derive them could be used for real-time feedback about ultrasound's biological effects.

Animals↗

Combined phase singularity and wavefront analysis for optical maps of ventricular fibrillation.

Much of the research into the mechanisms of ventricular fibrillation (VF) employs high-resolution mapping of electrical activation and recovery patterns. We previously developed a method for analyzing electrically mapped VF patterns that was based on identifying individual VF wavefronts. We now introduce a related method designed to take into account the information on repolarization that is present in optically mapped VF data. The new method first converts raw fluorescence data to an angular variable that tracks the phase of the mapped tissue through the depolarization-repolarization cycle. We define wavefronts in this context as isolines of phase that terminate either at boundaries or at singular points within the phase field. These singularities are the pivots of functional reentry and are important determinants of VF patterns. We parameterize VF by constructing data structures that describe wavefronts and singularities and also maintain wavefront-wavefront, wavefront-singularity, and singularity-singularity relationships. We describe one important application of this parameterization, which is to identify, localize, and characterize the importance of occurrences of propagation block during VF.

Action Potentials↗

Filament behavior in a computational model of ventricular fibrillation in the canine heart.

The aim of this paper was to quantify the behavior of filaments in a computational model of re-entrant ventricular fibrillation. We simulated cardiac activation in an anisotropic monodomain with excitation described by the Fenton-Karma model with Beeler-Reuter restitution, and geometry by the Auckland canine ventricle. We initiated re-entry in the left and right ventricular free walls, as well as the septum. The number of filaments increased during the first 1.5 s before reaching a plateau with a mean value of about 36 in each simulation. Most re-entrant filaments were between 10 and 20 mm long. The proportion of filaments touching the epicardial surface was 65%, but most of these were visible for much less than one period of re-entry. This paper shows that useful information about filament dynamics can be gleaned from models of fibrillation in complex geometries, and suggests that the interplay of filament creation and destruction may offer a target for antifibrillatory therapy.

Action Potentials↗

A new spatiotemporal regularization approach for reconstruction of cardiac transmembrane potential patterns.

The single-beat reconstruction of electrical cardiac sources from body-surface electrocardiogram data might become an important issue for clinical application. The feasibility and field of application of noninvasive imaging methods strongly depend on development of stable algorithms for solving the underlying ill-posed inverse problems. We propose a novel spatiotemporal regularization approach for the reconstruction of surface transmembrane potential (TMP) patterns. Regularization is achieved by imposing linearly formulated constraints on the solution in the spatial as well as in the temporal domain. In the spatial domain an operator similar to the surface Laplacian, weighted by a regularization parameter, is used. In the temporal domain monotonic nondecreasing behavior of the potential is presumed. This is formulated as side condition without the need of any regularization parameter. Compared to presuming template functions, the weaker temporal constraint widens the field of application because it enables the reconstruction of TMP patterns with ischemic and infarcted regions. Following the line of Tikhonov regularization, but considering all time points simultaneously, we obtain a linearly constrained sparse large-scale convex optimization problem solved by a fast interior point optimizer. We demonstrate the performance with simulations by comparing reconstructed TMP patterns with the underlying reference patterns.

Algorithms↗