Accuracy of Quadratic Versus Linear Interpolation in Noninvasive Electrocardiographic Imaging (ECGI)

Electrocardiographic Imaging (ECGI) is a cardiac functional imaging modality, noninvasively reconstructing epicardial potentials, electrograms and isochrones (activation maps) from multi-channel body surface potential recordings. The procedure involves solving Laplace’s equation in the source-free volume conductor between torso and epicardial surfaces, using Boundary Element Method (BEM). Previously, linear interpolation (LI) on three-noded triangular surface elements was used in the BEM formulation. Here, we use quadratic interpolation (QI) for potentials over six-noded linear triangles. The performance of LI and QI in ECGI is evaluated through direct comparison with measured data from an isolated canine heart suspended in a human-torso-shaped electrolyte tank. QI enhances the accuracy and resolution of ECGI reconstructions for two different inverse methods, Tikhonov regularization and Generalized Minimal Residual (GMRes) method, with the QI-GMRes combination providing the highest accuracy and resolution. QI reduces the average relative error (RE) between reconstructed and measured epicardial potentials by 25%. It preserves the amplitude (average RE reduced by 48%) and morphology of electrograms better (average correlation coefficient for QI ∼ 0.97, LI ∼ 0.92). We also applied QI to ECGI reconstructions in human subjects during cardiac pacing, where QI locates ventricular pacing sites with higher accuracy (≤ 10 mm) than LI (≤ 18 mm).     

Coronary artery mapping: A method for three-dimensional reconstruction of epicardial anatomy

Evaluation of coronary anatomy with conventional coronary angiography requires visual integration of multiple images from different viewing orientations to generate a mental interpretation of three-dimensional (3D) structure. The epicardial surface is, in many ways, analogous to the earth’s surface topography and may be effectively depicted using cartographic methods. To show coronary anatomy visualized as topographic maps, we used cartographic projection methods to analyze the coronary vessels of a canine heart after immediate postmortem injection with a radio-opaque gelatinous solution. A volumetric image data set was obtained with x-ray spiral computed tomography. The principal axis of the image volume was calculated and the image volume reformatted to a reference coordinate system defined by the principal axis as the ordinate. A cylindrical projection map of the epicardial surface was created using a maximum-intensity projection volume-rendering technique. After converting the Cartesian reference coordinate system to a polar coordinate system, additional mapping projections from user-defined orientations were generated. The results show that interpretative difficulties of coronary angiography may be diminished by generating 3D maps of coronary anatomy using volumetric datasets acquired noninvasively and displayed with cartographic methods.     

Three-dimensional simulation of epicardial potentials using a microcomputer-based heart-torso model

Previous cardiac simulation studies have focused on simulating the activation isochrones and subsequently the body surface potentials. Epicardial potentials, which are important for clinical applications as well as for electrocardiography inverse problem studies, however, have usually been neglected. This paper presents a procedure of simulating epicardial potentials using a microcomputer-based heart-torso model with real geometry. The heart model developed earlier which was composed of more than 60,000 cell units was used in this study. To simulate the epicardial potentials, an epicardial surface model which enclosed the whole heart was constructed. The heart model, together with the epicardial surface model, 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 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 patients with left bundle branch block (LBBB) are in close agreement with those reported in the literature.     

Application of the Method of Fundamental Solutions to Potential-based Inverse Electrocardiography

Potential-based inverse electrocardiography is a method for the noninvasive computation of epicardial potentials from measured body surface electrocardiographic data. From the computed epicardial potentials, epicardial electrograms and isochrones (activation sequences), as well as repolarization patterns can be constructed. We term this noninvasive procedure Electrocardiographic Imaging (ECGI). The method of choice for computing epicardial potentials has been the Boundary Element Method (BEM) which requires meshing the heart and torso surfaces and optimizing the mesh, a very time-consuming operation that requires manual editing. Moreover, it can introduce mesh-related artifacts in the reconstructed epicardial images. Here we introduce the application of a meshless method, the Method of Fundamental Solutions (MFS) to ECGI. This new approach that does not require meshing is evaluated on data from animal experiments and human studies, and compared to BEM. Results demonstrate similar accuracy, with the following advantages: 1. Elimination of meshing and manual mesh optimization processes, thereby enhancing automation and speeding the ECGI procedure. 2. Elimination of mesh-induced artifacts. 3. Elimination of complex singular integrals that must be carefully computed in BEM. 4. Simpler implementation. These properties of MFS enhance the practical application of ECGI as a clinical diagnostic tool.     

Three-dimensional panoramic imaging of cardiac arrhythmias in rabbit heart

Cardiac fluorescent optical imaging provides the unique opportunity to investigate the dynamics of propagating electrical waves during ventricular arrhythmias and the termination of arrhythmias by strong electric shocks. Panoramic imaging systems using charge-coupled device (CCD) cameras as the photodetector have been developed to overcome the inability to monitor electrical activity from the entire cardiac surface. Photodiode arrays (PDAs) are known to have higher temporal resolution and signal quality, but lower spatial resolution compared to CCD cameras. We construct a panoramic imaging system with three PDAs and image Langendorff perfused rabbit hearts (n=18) during normal sinus rhythm, epicardial pacing, and arrhythmias. The recorded spatiotemporal dynamics of electrical activity is texture mapped onto a reconstructed 3-D geometrical heart model specific to each heart studied. The PDA-based system provides sufficient spatial resolution (1.72 mm without interpolation) for the study of wavefront propagation in the rabbit heart. The reconstructed 3-D electrical activity provides us with a powerful tool to investigate the fundamental mechanisms of arrhythmia maintenance and termination.     

Developing integrative computational models of pulmonary structure

Integrative computational modeling of the pulmonary system aims to incorporate interactions between the lung's subsystems by means of a hierarchy of structural and functional models. This requires detailed imaging-based data, along with a wide range of functional information from experiments. Advances in computed tomography imaging technology ensure that high-resolution data are now readily available upon which the structure of these models can be based. We present methods for constructing anatomically realistic finite element models of interrelated pulmonary structures from such data. Segmented human lung lobe data are fit to high-order (cubic Hermite) volume elements. Meshes for the conducting airways and pulmonary arteries and veins are constructed within the lobe mesh, using a combination of fitting to imaging data and a bifurcating-distributive algorithm. The algorithm generates an airway-consistent mesh within a host volume, and this airway mesh is then used as a template for generating blood vessel models. The lung parenchyma is modeled as a space-filling three-dimensional (3D) Voronoi mesh, with generated geometry consistent with the alveolated airway structure. Pulmonary capillaries are generated over the alveolar model, as a 2D Voronoi mesh. These structural models have been compared extensively with morphometric data to verify that their geometry is representative of the pulmonary system. The models are designed to be integrative: they relate multiple structural systems within the same individual, and their use as computational meshes allows application of spatially distributed properties.     

Automated detection of qualitative spatio-temporal features in electrocardiac activation maps

OBJECTIVE: This paper describes a piece of work aiming at the realization of a tool for the automated interpretation of electrocardiac maps. Such maps can capture a number of electrical conduction pathologies, such as arrhytmia, that can be missed by the analysis of traditional electrocardiograms. But, their introduction into the clinical practice is still far away as their interpretation requires skills that belongs to very few experts. Then, an automated interpretation tool would bridge the gap between the established research outcome and clinical practice with a consequent great impact on health care. METHODS AND MATERIAL: Qualitative spatial reasoning can play a crucial role in the identification of spatio-temporal patterns and salient features that characterize the heart electrical activity. We adopted the spatial aggregation (SA) conceptual framework and an interplay of numerical and qualitative information to extract features from epicardial maps, and to make them available for reasoning tasks. RESULTS: Our focus is on epicardial activation isochrone maps as they are a synthetic representation of spatio-temporal aspects of the propagation of the electrical excitation. We provide a computational SA-based methodology to extract, from 3D epicardial data gathered over time, (1) the excitation wavefront structure, and (2) the salient features that characterize wavefront propagation and visually correspond to specific geometric objects. CONCLUSION: The proposed methodology provides a robust and efficient way to identify salient pieces of information in activation time maps. The hierarchical structure of the abstracted geometric objects, crucial in capturing the prominent information, facilitates the definition of general rules necessary to infer the correlation between pathophysiological patterns and wavefront structure and propagation.     

心外膜电位仿真研究

以往的心电理论研究，一方面强调从体表电位分布到心外膜电位分布的求逆；另一方面利用计算机心脏仿真模型只侧重于体表电位的仿真，而忽视了对心外膜电位的仿真，不利于心电逆问题研究的发展。本文阐明了心外膜电位对临床诊断和心电逆问题研究的重要性，并在ＬＦＸ计算机心脏仿真模型［１～３］的基础上建立了心外膜电位仿真的数学描述和心外膜模型。文中对正常心脏和左束支传导阻滞的心外膜电位进行了仿真研究，获得了一些有价值的结论     

Workflow for Visualization of Neuroimaging Data with an Augmented Reality Device

Commercial availability of three-dimensional (3D) augmented reality (AR) devices has increased interest in using this novel technology for visualizing neuroimaging data. Here, a technical workflow and algorithm for importing 3D surface-based segmentations derived from magnetic resonance imaging data into a head-mounted AR device is presented and illustrated on selected examples: the pial cortical surface of the human brain, fMRI BOLD maps, reconstructed white matter tracts, and a brain network of functional connectivity.     

Geodesic Based Registration of Sensor Data and Anatomical Surface Image Data

This paper presents two related methods for registering an image of an anatomical object with data from sensors arranged on the object. One method is described with reference to a test case involving a rectangular electrode plaque disposed on a heart surface, which is imaged with MRI. Data from the electrodes is fused with the MRI image at the appropriate locations. The registration scheme involves four parts. First, selected landmarks on a data surface (e.g., electrode plaque) are registered to known locations on a target anatomical surface image. Second, the anatomical surface is represented numerically with a spherical harmonic expansion. Third, given the registration of the select data surface landmarks, the location of the outer four corners of the rectangular electrode plaque are located on the anatomical surface. Fourth, a quasi-evenly spaced grid within these four corners is formed on the anatomical surface. The third and fourth steps involve calculating geodesics on the anatomical surface, preferably by utilizing the spherical harmonic expansion. According to the second registration method, spherical harmonics and geodesics are used to extract a mesh from the anatomical surface. Laplace’s equation is solved on this mesh to generate a mapping from the anatomical surface to the data surface (electrode plaque).     

Generalized training subset selection for statistical estimation of epicardial activation maps from intravenous catheter measurements

Catheter-based electrophysiological studies of the epicardium are limited to regions near the coronary vessels or require transthoracic access. We have developed a statistical approach by which to estimate high-resolution maps of epicardial activation from very low-resolution multi-electrode venous catheter measurements. This technique uses a linear estimation model that derives a relationship between venous catheter measurements and unmeasured epicardial sites from a set of previously recorded, high-resolution epicardial activation-time maps used as a training data set based on the spatial covariance of the measurement sites. We performed 14 dog experiments with various interventions to create an epicardial activation-time map database. This database included a total of 592 epicardial activation maps which were recorded using a sock array placed on the ventricles of dog hearts. We present five approaches, which examined sequential addition and removal of maps to select a generalized training set for the estimation technique. The selection consisted of choosing a subset of epicardial ectopic activation-time maps from the database of beats which resulted in estimation accuracy levels better than or at least similar to using all the maps in database. Our aim was to minimize the redundancy in the database and to be able to guide the eventual procedures required to obtain training data from open-chest surgery patients. The results from this study illustrated this redundancy and suggested that by including an optimal subset (around 100 maps) of the full database the estimation technique was able to perform as well as and even in some cases better than including all the maps in the database. The results also suggest that such an approach is feasible for providing accurate reconstruction of complete epicardial activation-time maps in a clinical setting and with fewer maps we can obtain similar reconstruction accuracy levels.     

基于CT断层数据的仿X线全景图生成技术

本文提出了一种利用口腔的三维CT断层数据生成牙齿的仿X线全景图的新技术。该技术通过从靠近牙弓面的一个曲面上沿法向量投射仿X线进入三维图像区域而生成牙齿的仿X线全景图。利用该技术可以在口腔的三维CT图像与牙齿的二维全景图之间建立对应关系,有助于克服真实牙X线全景图存在的结构叠加、显示内容不可选择的缺陷。所提出的技术在牙科相关的计算机辅助诊断及手术规划中有重要应用。     

数字化全景齿科成像系统中医学图像处理软件的开发

目的开发一套数字化全景齿科成像系统专用的图像处理软件。方法借助DCMTK开发包和OpenGL开发包,用VC＋＋语言编程实现。结果本软件不但具有医学图像的显示、几何变换、平滑、锐化、窗宽窗位调节、图像测量等功能,而且具有二维图像的立体显示及三维图形的旋转功能。结论通过实验验证,本软件是一套运行稳定、相对完整的图像处理软件,可成功用于数字化全景齿科成像系统中。     

Spatial Methods of Epicardial Activation Time Determination in Normal Hearts

The purpose of this study was to demonstrate errors in activation time maps created using the time derivative method on fractionated unipolar electrograms, to characterize the epicardial distribution of those fractionated electrograms, and to investigate spatial methods of activation time determination. Electrograms (EGs) were recorded using uniform grids of electrodes (1 or 2 mm spacing) on the epicardial surface of six normal canine hearts. Activation times were estimated using the time of the minimum time derivative, maximum spatial gradient, and zero Laplacian and compared with the time of arrival of the activation wave front as assessed from a time series of potential maps as the standard. When comparing activation times from the time derivative for the case of epicardial pacing, spatial gradient and Laplacian methods with the standard for EGs without fractionation, correlations were high (R²=0.98, 0.98, 0.97, respectively). Similar comparisons using results from only fractionated EGs (R²=0.85,0.97,0.95) showed a lower correlation between times from the time derivative method and the standard. The results suggest an advantage of spatial methods over the time derivative method only for the case of epicardial pacing where large numbers of fractionated electrograms are found. © 2003 Biomedical Engineering Society. PAC2003: 8719Hh, 8719Nn, 8780Tq     

Forward problem of electrocardiography: construction of human torso models and field calculations using finite element method

Finite element models of the human torso were constructed using anatomical data measured by serial computerised tomography scans in a subject. A first set of three models with a mesh resolution of 5517 nodes and 29810 elements included an homogeneous conductivity, lungs inhomogeneity, and heart, lungs and spinal region inhomogeneities. A second set comprised similar models with a mesh resolution of 12084 nodes and 67045 elements. A cylindrically shaped volume conductor was also constructed to evaluate the convergency and accuracy of the finite element solutions by comparison with the analytical solution. Forward simulations were performed using different excitation sites on the cardiac surface. The inclusion of conductivity inhomogeneities altered the maximum and minimum values of the body surface potentials, but did not substantially modify the pattern of the potential distributions. The greatest effect was due to the inclusion of the lungs. Increasing the mesh resolution from 5517 to 12084 nodes did not change noticeably the shape or amplitude of the simulated body surface potential maps. These models can readily be used for other bioelectromagnetic problems.     

Source localization of focal ventricular arrhythmias using linear estimation, correlation, and back propagation networks

Catheter-based approaches used in the localization and treatment of the source of heart rhythm disturbances (arrhythmias) have become popular, because they do not require highly invasive and risky open-chest operations. In most of the existing approaches, mapping of the outer surface (epicardium) is not possible even though arrhythmic substrates involving epicardial and subepicardial layers account for about 15% of the ventricular tachycardias. In this study, we report a feasibility study of a novel mapping approach targeting the epicardium which is based on the measurements of multielectrode catheters placed in the coronary veins. We investigated three methods in determining the most probable region of early activation, i.e., the region that contains the source of the abnormal activation on the heart, using only a set of sparse venous catheter recordings. The methods we proposed here were the linear estimation, correlation, and the back propagation networks. The linear estimation technique hypothesized the relationship between venous catheter measurements and unmeasured epicardial sites based on a previously recorded training data set. The correlation method included a comparative analysis between test and training epicardial activation time maps based on the measured values from the venous sites. In the back propagation method, the input layer consisted of the source data in the form of 42 nodes which were the activation time values from the intravenous catheter leads. We used two hidden layers with 600 and 500 nodes, respectively. The output layer consisted of 28 nodes in the output layer that corresponded to the manually selected early activation regions on the epicardium. The results of the linear estimation and the correlation methods showed that they could be used as a good predictor for the region of early activation, and thus, these approaches may be employed to direct a subsequent more focused electrophysiological study and curative radiofrequency (RF) ablation. The back propagation network approach performed relatively well for the right ventricularly paced beats and the results demonstrated its potential as a supporting technique to the estimation and correlation methods. The results of this study encourage further investigation and provides evidence that an epicardial mapping approach based on the venous catheter recordings is feasible and can provide adequate accuracy for clinical applications.     

Epicardial potential distribution reconstruction from recordings of intravenous and transthoracic mapping catheters: a feasibility study

Catheter-based epicardial mapping is possible with two access methods: transthoracic pericardial access and transvenous access. Transthoracic pericardial access is based on the introduction of the catheters into the pericardial space using a percutaneous subxiphoid puncture and may at times require lengthy sequential mapping procedures. From the transthoracic pericardial approach major regions of the epicardium may also be inaccessible. Transvenous access uses the multielectrode (4-20 electrodes) catheters placed in the coronary veins thus increases the speed of the mapping procedure, however, leaves most of the epicardium inaccessible to direct measurement. The aim of this present study is to demonstrate that the reconstruction of the high-resolution maps using sparse measurements from different sites on the epicardium and on the multielectrode catheters is possible with a reasonably high accuracy in terms of locating the origin of the ventricular arrhythmia. In this study we investigated strategies for the reconstruction of epicardial potential distribution from recordings of intravenous and transthoracic epicardial mapping catheters, alone and in combination. For this purpose, we first examined the problem of best number of epicardial measurement sites (or best sampling resolution) using transthoracic mapping catheters and secondly studied the feasibility of the combined usage of both mapping approaches. In the prediction of the surrogate measurements at inaccessible sites from the measurements localized to the cardiac veins and sparse epicardial sites we evaluated two prediction methods: the Laplacian interpolation and statistical estimation, to overcome the sparsity of the measurements. We performed 14 dog experiments with various interventions to create a high-resolution epicardial potential map database. This database included a total of 592 beats which were recorded using a sock array placed on the ventricles of dog hearts. We found that 2 cm sampling resolution is quite feasible, which means that the time for the mapping procedure may be reduced considerably. Predictions from the combination of 21 intravenous catheter leads and 30 transthoracic catheter leads were better than when only 21 or 30 leads were used. The results of this study encourage further investigation and provide adequate evidence that an epicardial mapping approach based on the combined usage of transvenous and transthoracic pericardial access methods for the mapping of the outer surface of the heart is feasible and can provide adequate accuracy for clinical applications.     

Topographic approach to the study of the human body

Recent developments in medical imaging techniques such as ultrasound, computed tomography (CT), and magnetic resonance imaging (MRI) have been explosive. These modalities provide 3D information about the human body and assess tissue damage in various pathological conditions. To complement the diagnostic usefulness of these imaging techniques, we have designed a system of topographic coordinates based on the principles of global projection cartography in which lines of latitude and longitudes are assigned to the surface of the human body. We designated the median sagittal plane as corresponding to the Greenwich Meridian (zero longitude) in global cartography. From the median sagittal plane (M0), vertical lines of longitude or "great circles" divide the body into 12 zones that are 30 degrees apart. Parallel lines of latitude are assigned according to surface anatomy landmarks. Studying the 3D reconstruction of anatomical structures is important for: 1) devising a system of coordinates; 2) allowing biomedical measurements to be made; and 3) drawing maps that may be useful in some clinical procedures (e.g., biopsies).     

Maps of the brain

We review recent developments in brain mapping and computational anatomy that have greatly expanded our ability to analyze brain structure and function. The enormous diversity of brain maps and imaging methods has spurred the development of population-based digital brain atlases. These atlases store information on how the brain varies across age and gender, across time, in health and disease, and in large human populations. We describe how brain atlases, and the computational tools that align new datasets with them, facilitate comparison of brain data across experiments, laboratories, and from different imaging devices. The major methods are presented for the construction of probabilistic atlases, which store information on anatomic and functional variability in a population. Algorithms are reviewed that create composite brain maps and atlases based on multiple subjects. We show that group patterns of cortical organization, asymmetry, and disease-specific trends can be resolved that may not be apparent in individual brain maps. Finally, we describe the creation of four-dimensional (4D) maps that store information on the dynamics of brain change in development and disease. Digital atlases that correlate these maps show considerable promise in identifying general patterns of structural and functional variation in human populations, and how these features depend on demographic, genetic, cognitive, and clinical parameters.     

Cytokeratins as a marker for epicardial formation in the quail embryo

Several techniques have been used to visualize the migration pattern of the epicardial cells from the proepicardial organ over the myocardial surface. As the epicardial cells contain keratin tonofilament bundles, we have incubated 92 whole-mount quail hearts with an anti-keratin antibody. This immunohistochemical method showed that the complete epicardial covering of the embryonic heart is preceded by the formation of three epicardial rings. The epicardial rings are formed on the outer myocardial surface in the grooves that separate the cardiac segments from each other. We have also documented timing and patterning of isolated epicardial islands. They are not encountered at random over the myocardial surface, but only along the edge of the advancing epicardial front border and in two defined future epicardial ring areas on the ventral side of the outflow tract. The epicardial islands suggest that in the quail free-floating parts of epicardium can attach to the myocardium. Characteristics of the surface of the myocardium at the transitional zones between the cardiac segments, as well as the three-dimensional remodelling of the heart during cardiac morphogenesis seem to play a role in the pattern in which the epicardium eventually completely ensheaths the myocardial surface. Congenital heart defects are often related to malpositioned transitional zones that dictate the pattern of epicardial outgrowth. As the embryonic position of the epicardial rings is mirrored in the pattern of the main arterial stems, the coronary vascularization pattern might be altered in congenitally malformed hearts as well.