Effect of Cardiac Motion on Solution of the Electrocardiography Inverse Problem

Previous studies of the ECG inverse problem often assumed that the heart was static during the cardiac cycle; consequently, a time-dependent geometrical error was thought to be unavoidably introduced. In this paper, cardiac motion is included in solutions to the electrocardiographic inverse problem. Cardiac dynamics are simulated based on a previously developed biventricular model that coupled the electrical and mechanical properties of the heart, and simulated the ventricular wall motion and deformation. In the forward computation, the heart surface source model method is employed to calculate the epicardial potentials from the action potentials, and then, the simulated epicardial potentials are used to calculate body surface potentials. With the inclusion of cardiac motion, the calculated body surface potentials are more reasonable than those in the case of static assumption. In the epicardial potential-based inverse studies, the Tikhonov regularization method is used to handle ill-posedness of the ECG inverse problem. The simulation results demonstrate that the solutions obtained from both the static ECG inverse problem and the dynamic ECG inverse problem approaches are approximately the same during the QRS complex period, due to the minimal deformation of the heart in this period. However, with the most obvious deformation occurring during the ST-T segment, the static assumption of heart always generates something akin to geometry noise in the ECG inverse problem causing the inverse solutions to have large errors. This study suggests that the inclusion of cardiac motion in solving the ECG inverse problem can lead to more accurate and acceptable inverse solutions.      

Switched Gain?A Technique for Simplifying Ultrasonic Measurement of Cardiac Wall Thickness

Pulse-echo ultrasound, a valuable tool for noninvasive cardiac examination, has been used extensively to determine left ventricular volume and wall thickness. It is often difficult, however, to visualize simultaneously the endocardial and epicardial surfaces of the left ventricular posterior wall because of dynamic range and grey scale limitations. Although the signal reflected at the epicardial-lung interface is much stronger than the signal from surrounding myocardium and lung, it is often obliterated when the receiver gain is increased sufficiently to record the endocardial echo. We have developed a switched gain technique which allows both wall surfaces to be visualized in real time. An oscillator rapidly switches the receiver gain between two levels that are independently set to display the two wall surfaces; thus, echograms are generated with high and low gain portions closely mixed. The endocardial surface is seen best at high gain; the epicardial surface at lower amplification.     

Estimation of Local Cardiac Wall Deformation and Regional Wall Stress from Biplane Coronary Cineangiograms

A new mathematical method was developed to estimate the local epicardial deformation, wall thickness, and the regional circumferential and longitudinal wall stress using biplane coronary cineangiograms. In this method, the motion images of the coronary artery bifurcation points were used as natural landmarks for the kinematic analysis of the ventricular deformation. In four dogs and a normal patient's coronary cineangiograms, the estimation results show the validity of the present analysis, compared to the experimental results based upon the implanted markers. Thus, the present method provides a new method of evaluating the regional wall deformation and wall stress together with the blood vessel conditions using the coronary cineangiography procedure.     

A bioelectric inverse imaging technique based on surface Laplacians

A new approach is proposed to solve bioelectric inverse problems by employing the surface Laplacian of the bioelectrical potential. A theoretical investigation was conducted to test the feasibility of epicardial inverse imaging of cardiac electrical activity. A two-sphere homogeneous volume conductor model, where the inner sphere represents the epicardium and the outer sphere the body surface, was used. Radial and tangential current dipoles were used to approximate localized wavefronts propagating from the endocardium to the epicardium, and ectopic myocardial activities. The epicardial potential distribution was reconstructed from the body surface Laplacians with the aid of the Tikhonov zero-order regularization technique, which then was compared with the results obtained from the body surface potentials using the same regularization scheme. The two inverse solutions were compared qualitatively via visual inspection of the reconstructed epicardial potential maps, and quantitatively by examining relative errors and correlation coefficients between the “true” and the reconstructed epicardial potentials. Both qualitative and quantitative results indicate that the surface Laplacians play a positive role in improving the ill-posed nature of the bioelectric inverse problem, which would enhance one's capability of reconstructing important epicardial events such as extrema in the epicardial potential distribution. The present theoretical study suggests that the Laplacian-based inverse imaging technique may have important applications to epicardial inverse imaging and other bioelectric inverse imaging     

Semiautomated border tracking of cine echocardiographic ventnrcular images

Two-dimensional ultrasound sector scans of the left ventricle (LV) are commonly used to diagnose cardiac mechanical function. Present quantification procedures of wall motion by this technique entail inaccuracies, mainly due to relatively poor image quality and the absence of a definition of the relative position of the probe and the heart. The poor quality dictates subjective determination of the myocardial edges, while the absence of a position vector increases the errors in the calculations of wall displacement, LV blood volume, and ejection fraction. An improved procedure is proposed here for automatic myocardial border tracking (AMBT) of the endocardial and epicardial edges in a sequence of video images. The procedure includes nonlinear filtering of whole images, debiasing of gray levels, and location-dependent contrast stretching. The AMBT algorithm is based upon tracking movement of a small number of predefined set of points, which are manually defined on the two myocardial borders. Information from one image is used, by utilizing predetermined statistical criteria to iteratively search and detect the border points on the next one. Border contours are reconstructed by Spline interpolation of the border points. The AMBT procedure is tested by comparing processed sequences of cine echocardiographic scan images to manual tracings by an objective observer and to results from previously published data.     

The Effects of Thoracic Inhomogeneities on the Relationship Between Epicardial and Torso Potentials

This study examines the effects of the lungs, spine, sternum, and the anisotropic skeletal muscle layer on the relationship between torso and epicardial potentials. Boundary integral equations representing potentials on the epicardial surface, the torso surface, and the internal conductivity interfaces were solved yielding a set of transfer coefficients valid for any source inside the epicardium and for any conductivity configuration outside the epicardial surface. These transfer coefficients relate potentials on the torso to potentials on the epicardial surface. Calculated torso potentials are generated via the transfer coefficients and measured epicardial potentials for comparison to measured torso potentials. This comparison indicates whether including the thoracic inhomogeneities improves attainable accuracy in calculations relating torso potentials to epicardial potentials.     

Effects of Geometrical Uncertainties on Electrocardiography

This paper investigates the influence of uncertainties in geometrical coordinates on calculated torso and epicardial potentials. Two types of sources, spherical epicardial and multipolar, are both considered. A concentric sphere model with the epicardial surface represented by a unit sphere and the torso surface represented by a spherical surface of radius 1.4 is utilized. While the representation of biological surfaces with spheres is a highly idealized situation, the dimensions chosen and the approximations utilized are such that the results should be indicative of those using measured biological coordinates.     

Fusion of body surface potential and body surface Laplacian signals for electrocardiographic imaging

Various approaches to the solution to the inverse problem of electrocardiography have been proposed over the years. Recently, the use of inverse algorithms using measured body surface Laplacians has been proposed, and in various studies this technique has been shown to outperform the traditional use of body surface potentials in certain model problems. In this paper, we compare the use of body surface potentials and body surface Laplacians on two model problems with different assumed cardiac sources. For the spherical cap model problems with an anterior source, the epicardial estimates using body surface potentials had smaller average relative errors than when body surface Laplacians were used. For the spherical cap model problems with a posterior source, the epicardial estimates using body surface potential or body surface Laplacian sensors generally produced similar relative errors. For the radial dipole model, the epicardial estimates using body surface Laplacians had smaller errors than when body surface potentials were used. We introduce a fusion algorithm that combines the different types of signals and generally produces a good estimate for both model problems.     

An Analysis of Transfer Coefficients Calculated Directly from Epicardial and Body Surface Potential Measurements in the Intact Dog

This study dealt with the question of how to estimate body surface potentials from epicardial potential distributions in intact dogs; in particular, the study considered the feasibility of obtaining transfer coefficients directly from sequences of epicardial and body surface measurements of ventricular excitation and repolarization potential distributions, rather than from measurements of the geometry of the volume conductor. The transfer coefficients were calculated from the measured potentials via the mathematical method of using a Bayes estimator. The merit of this approach was that it offered the possibility of accurately representing the characteristics of the volume conductor without directly measuring either the volume conductor's geometry or its inhomogeneities. The experimental protocol made use of measurements from two dogs. Data from the first dog were used to obtain two sets of transfer coefficients, one by the Bayes method as applied to measured sequences of epicardial and body surface potentials, and the other by a method based on the geometric position of each epicardial and body surface electrode. These two sets of transfer coefficients were found to be similar in pattern and value size. Additionally, results of forward simulations in the first dog, based on the measured epicardial potentials and each set of transfer coefficients, were compared to the measured body potentials. The results showed that the simulated potentials were closer to the measured potentials when the transfer coefficients obtained from the potentials were used, rather than when the geometric coefficients were used.     

Forward and inverse problems of electrocardiography: modeling andrecovery of epicardial potentials in humans

To assess the accuracy of solutions to the inverse problem of electrocardiography in man, epicardial potentials computed from thoracic potential distributions were compared to potentials measured directly over the surface of the heart during arrhythmia surgery. Three-dimensional finite element models of the thorax with different mesh resolutions and conductivity inhomogeneities were constructed from serial computerized tomography scans of a patient. These torso models were used to compute transfer matrices relating the epicardial potentials to the thoracic potentials. Potential distributions over the torso and the ventricles were measured with 63 leads in the same patient whose anatomical data was used to construct the torso models. To solve the inverse problem, different methods based on Tykhonov regularization or regularization-truncation were applied. The recovered epicardial potential distributions closely resembled the epicardial potential distributions measured early during ventricular preexcitation, but not the more complex distributions measured later during the QRS complex. Several problems encountered as the validation process is applied in man are also discussed     

Computer simulation of epicardial potentials using a heart-torsomodel with realistic geometry

Previous cardiac simulation studies have focused on simulating the activation isochrones and subsequently the body surface potentials. Epicardial potentials, which are important for clinical application as well as for electrocardiographic inverse problem studies, however, have usually been neglected. This paper describes a procedure of simulating epicardial potentials using a microcomputer-based heart-torso model with realistic geometry. The authors' heart model developed earlier is composed of approximately 65000 cell units which are arranged in a cubic close-packed structure. An action potential waveform with variable in duration is assigned to each unit. The heart model, together with the epicardial surface model constructed recently, are mounted in an inhomogeneous human torso model. Electric dipoles, which are proportional to the spatial gradient of the action potential, are generated in all the cell units. These dipoles give rise to a potential distribution on the epicardial surface, which is calculated by means of the boundary element method. The simulated epicardial potential maps during a normal heart beat and in a preexcited beat to mimic Wolff-Parkinson-White (WPW) syndrome are in close agreement with those reported in the literature     

Tracking the left ventricle in echocardiographic images by learningheart dynamics

In this paper a temporal learning-filtering procedure is applied to refine the left ventricle (LV) boundary detected by an active-contour model. Instead of making prior assumptions about the LV shape or its motion, this information is incrementally gathered directly from the images and is exploited to achieve more coherent segmentation. A Hough transform technique is used to find an initial approximation of the object boundary at the first frame of the sequence. Then, an active-contour model is used in a coarse-to-fine framework, for the estimation of a noisy LV boundary. The PCA transform is applied to form a reduced ordered orthonormal basis of the LV deformations based on a sequence of noisy boundary observations. Then this basis is used to constrain the motion of the active contour in subsequent frames, and thus provide more coherent identification. Results of epicardial boundary identification in B-mode images are presented.     

Wearable Stretchable Dry and Self-Adhesive Strain Sensors with Conformal Contact to Skin for High-Quality Motion Monitoring

Wearable stretchable strain sensors can have important applications in many areas. However, the high noise is a big hurdle for their application to monitor body movement. The noise is mainly due to the motion artifacts related to the poor contact between the sensors and skin. Here, wearable stretchable dry and self-adhesive strain sensors that can always form conformal contact to skin even during body movement are demonstrated. They are prepared via solution coating and consist of two layers, a dry adhesive layer made of biocompatible elastomeric waterborne polyurethane and a sensing layer made of a non-adhesive composite of reduced graphene oxide and carbon nanotubes. The adhesive layer makes the sensors conformal to skin, while the sensing layer exhibits a resistance sensitive to strain. The sensors are used to accurately monitor both small- and large-scale body movements, including various joint movements and muscle movements. They can always generate high-quality signals even on curvilinear skin surface and during irregular skin deformation. The sensitivity is remarkably higher while the noise is saliently lower than the non-adhesive strain sensors. They can also be used to monitor the movements along two perpendicular directions, which cannot be achieved by the non-adhesive strain sensors.     

Effect of the Twisting Motion on the Nonunifornities of Transmyocardial Fiber Mechanics and Energy Demand A Theoretical Study

The contraction of the left ventricle (LV) is manifested by a distribution of strains and strain rates throughout the muscle thickness. Using a nested shell spheroidal model of the LV, which accounts for a fiber angle distribution from + 60°at the endocardium to ?60° at the epicardium, and the radial electrical activation pattern from the endocardium to the epicardium, it can be shown that endocardial layers undergo higher strains than the epicardial layers throughout the cardiac cycle, and higher length changes characterize the endocardial sarcomeres relative to the epicardial sarcomeres. However, the calculated nonuniformities in the sarcomeres' shortening are significantly moderated when the physiological twisting motion of the LV around the longitudinal axis is accounted for. Thus, the twisting motion of the heart is a basic mechanism by which the sarcomere function is maintained within its physiological range.     

The effect of conductivity values on ST segment shift in subendocardial ischaemia

The aim of this study was to investigate the effect of different conductivity values on epicardial surface potential distributions on a slab of cardiac tissue. The study was motivated by the large variation in published bidomain conductivity parameters available in the literature. Simulations presented are based on a previously published bidomain model and solution technique which includes fiber rotation. Three sets of conductivity parameters are considered and an alternative set of nondimensional parameters relating the tissue conductivities to blood conductivity is introduced. These nondimensional parameters are then used to study the relative effect of blood conductivity on the epicardial potential distributions. Each set of conductivity parameters gives rise to a distinct set of epicardial potential distributions, both in terms of morphology and magnitude. Unfortunately, the differences between the potential distributions cannot be explained by simple combinations of the conductivity values or the resulting dimensionless parameters.     

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.     

Use of the finite element method to determine epicardial from body surface potentials under a realistic torso model

This paper presents a new method of solution for the inverse problem in electrocardiography using the finite element procedure. It is an application of the authors' earlier work which derived a solution method by means of an integral equation under a generalized configuration of geometry and conductivity of the torso. Based on prior geometry information, the human torso region is discretized into a series offinite elements and, then, electric fields are computed when a set of linearly independent functions chosen as a basis is imposed on the epicardial surface. The set of these forward solutions defines the forward transfer coefficients which relate epicardial to body surface potentials. By the use of the forward transfer coefficients, a constrained least-squares estimate of the epicardial potential distribution can be obtained from measured body surface potentials. The solution method is examined through numerical experiments carried out for a realistic model of the human torso. It is demonstrated that the rapid decrease in voltage far from the heart generator makes this inverse problem ill conditioned and, as a result, the accuracy of the inverse epicardial potentials calculated depends greatly upon both the signal-to-noise ratio and the number of lead points in measuring the body surface potentials.     

The Laplacian inverse problem of electrocardiography: an eccentricspheres study

The eccentric spheres model of the heart-torso system is used to study the inverse problem of electrocardiography using measurements of the Laplacian of the body surface potential distribution. Electrical activity is simulated on the six main regions of the inner surface by considering a limited number of current dipoles placed within the inner sphere. The resulting outer surface potential and Laplacian distributions are then calculated in a forward sense. Varying amounts of random noise are added to these distributions before a zero-order Tikhonov regularization scheme is used to recover the inner surface potential distribution. Comparing the calculated and original inner surface distributions indicates that measurements of the outer surface Laplacian can more accurately reconstruct epicardial potentials than measurements of the outer surface potentials. These distributions are more accurate in that the extrema are placed very close to their original positions and are of nearly the same magnitude. Also, multiple extrema and high potential gradients are recovered     

Improved performance of bayesian solutions for inverse electrocardiography using multiple information sources

The usual goal in inverse electrocardiography (ECG) is to reconstruct cardiac electrical sources from body surface potentials and a mathematical model that relates the sources to the measurements. Due to attenuation and smoothing that occurs in the thorax, the inverse ECG problem is ill-posed and imposition of a priori constraints is needed to combat this ill-posedness. When the problem is posed in terms of reconstructing heart surface potentials, solutions have not yet achieved clinical utility; limitations include the limited availability of good a priori information about the solution and the lack of a "good" error metric. We describe an approach that combines body surface measurements and standard forward models with two additional information sources: statistical prior information about epicardial potential distributions and sparse simultaneous measurements of epicardial potentials made with multielectrode coronary venous catheters. We employ a Bayesian methodology which offers a general way to incorporate these information sources and additionally provides statistical performance analysis tools. In a simulation study, we first compare solutions using one or more of these information sources. Then, we study the effects of varying the number of sparse epicardial potential measurements on reconstruction accuracy. To evaluate accuracy, we used the Bayesian error covariance as well as traditional error metrics such as relative error. Our results show that including even sparsely sampled information from coronary venous catheters can substantially improve the reconstruction of epicardial potential distributions and that a Bayesian framework provides a feasible approach to using this information. Moreover, computing the Bayesian error standard deviations offers a means to indicate confidence in the results even in the absence of validation data.