基于虚拟心脏的心电逆问题求解

心电逆问题研究的目标是要从无损测得的体表电位来找出心脏的对应状态。以往的心电逆问题求解方法有二类，一类是基于等效心电源法，另一类是基于心外膜电位解法。这二类方法都存在病态问题，同时所求出的解并不是真正的心脏状态解，而是一种中间解。本文提出了一种新的心电逆问题求解方法，即从体表电位求出虚拟心脏的模型参数，由所求得的虚拟心脏的模型参数即可确定心脏所处的状态。该法把欠定的逆问题求解问题转化为正问题的参数优化问题，避免了以往心电逆问题求解方法中的病态问题。为了检验该法的有效性，我们做了对ＷＰＷ预激综合征旁道室内预激点进行定位的模型试验，结果表明逆解得出的预激点位置误差一般不超过４．５ｍｍ。     

求解心外膜电位的有限元方法研究

由体表电位分布求解心电源 称力心电逆问题 它是现代心电理论研究的方向之一 具有重要的理论价值和临床意义 本文推导了用有限元方法求解心外膜电位的算法 着重介绍了为改善逆问题解的稳定性所做的努力 在作者研制的100通道体表电位系统上 利用实测的体表电位数据进行了心外膜电位的实际计算 得到了具有生理意义的结果 从而证明本算法是合理的。     

心电逆问题的研究现状

心电逆问题研究是心电学的基础理论研究之一，具有重要的临床和实验价值。本文全面地讨论了当前国内外心电逆问题研究情况，首先介绍了心电逆问题的基本特性和研究方法。然后着重介绍了基于心外膜电位的逆问题研究方法，其中包括逆问题的数值解法、正则化技术以及心脏～躯干模型、几何参数、电导参数及噪声对心电逆问题解的影响。最后介绍了逆问题研究成果、临床应用，并对逆问题研究存在的困难和发展趋势提出了自己的看法。     

心电逆问题的研究现状

心电逆问题研究是心电学的基础理论研究之一，具有重要的临床和实验价值。本文全面地讨论了当前国内外心电逆问题研究情况，首先介绍了心电逆问题的基本特性和研究方法。然后着重介绍了基于心外膜电位的逆问题研究方法，其中包括逆问题的数值解法、正则化技术以及心脏￣躯干模型、几何参数、电导参数及噪声对心电逆问题解的影响。最后介绍了逆问题研究成果、临床应用，并对逆问题研究存在的困难和发展趋势提出了自己的看法。     

心电图逆问题研究动态

心电体表电位逆问题是心电学的基础理论研究。本文全面讨论了当前国内外心电逆问题研究的情况。文章首先回顾了心电逆问题的发展历史,在讨论了研究心电逆问题的基本方法后,文章通过几个典型实例说明了其中一些方法的具体应用。对心电逆问题研究的发展趋势作者提出了自己的看法。     

心电体外层电位仿真研究：一种检测心脏电位活动的新方法

体表电位测量中常要面对一些难以克服的问题。例如电极数量受限、电极与人体体表固定困难以及人体体形个体差异对测量数据影响较大等。为解决上述问题，本文提出了一种检测心电活动的新方法：心电体外层电位法。并建立了体外层电位标测系统的仿真模型，对不同的人体体形算例进行了仿真计算。结果表明，体外层电位法是比传统体表电位测量更可行的一种新方法。     

基于最大似然算法的心电逆问题研究

心电逆问题是通过测得的体表电势分布求取心外膜电势分布的过程,具有重要的临床意义和生理意义.本文采用有限元方法对心脏和体腔进行二维建模并求解心电正问题,然后构建状态空间方程,建模得到的体表电势与心外膜电势之间的关系为系统的测量方程,相邻时刻状态之间的关系为系统的状态方程.对于参数的不确定性问题,建立似然函数,引入期望最大化(Expectation Maximization,EM)算法来求解,步骤E(Expectation)采用卡尔曼滤波对参数进行估计,步骤M(Maximization)利用似然函数重新估计约束,步骤E,步骤M循环迭代.最后对整个过程进行仿真,结果显示采用期望最大化(EM)算法时,解的收敛性要好于传统的卡尔曼滤波的解,相对误差也可以得到大幅度的降低.     

基于动态心脏模型的体表心电图仿真研究

以往的电生理心脏模型大多是静态的,而非动态模型.这样在用准静电场理论求解体表电位时,整个心动周期中等效心电偶极子（源点）与体表（场点）之间的距离假设为恒定不变,从而会引入较大的系统误差.因此,为了更准确仿真心电图,有必要采用动态或跳动的心脏模型.基于原来静态心脏模型,构造了一个动态心脏模型,并对体表12导联心电图进行仿真比较研究.在动态心脏模型中考虑了心肌电兴奋引起的心脏机械力学收缩,通过计算心动周期中心室壁的位移,从而将心脏与体表之间的相对距离变化考虑进体表电位计算过程.仿真结果表明,对于正常心电图,基于动态心脏模型的仿真结果比基于静态心脏模型的仿真结果更符合临床记录心电图,特别是V1-V6胸导联的ST段和T波.对于前壁轻微缺血情况,在动态心脏模型的仿真心电图中能明显看出ST段和T波的变化,而在静态心脏模型的仿真心电图中与正常心电图相比看不出什么变化.本研究的仿真研究证实了动态心脏模型的确能更准确地仿真体表心电图.     

心脏外膜电势传播过程的三维立体显示

我们借助于一组心脏的X－CT图片重构人体心脏的几何模型，并采用边界元算法从体表电位求得心外膜电位的数值解，利用计算机图形技术在1BM－PC／XT微型机上实现了心外膜电势传播过程的三维立体显示。     

全心电生理建模及体表电位标测图的仿真

虚拟心脏建模是连接心脏宏观和微观研究的有效手段之一。本研究利用微型计算机和可视人断层数据,通过图像增强、组织分割和三维重建,建立了分辨率为0.5 mm×0.5 mm×0.5 mm的心脏结构和胸前表面几何模型;以单细胞动作电位仿真为基础,使用改进的规则型算法,基于惠更斯原理的各向同性和各相异性波面型算法,分别完成了特殊传导系统、心房和心室电活动的仿真,时间精度可达1 ms;结合双域模型理论,使用偶极子等效心脏的电活动,同时结合躯体模型,完成了心脏电活动到体表心电的映射,进行正常和异常情况下体表电位标测图(BSPM)及12导联心电图的仿真。通过此模型得到的由窦房结起搏的体表12导联心电图,满足正常心电的诊断标准,证明了模型的真实性和可靠性,为进一步探讨传导和起搏异常的体表心电建立基础。     

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.     

Value and limitations of an inverse solution for two equivalent dipoles in localising dual accessory pathways

Investigations were carried out into whether an equivalent generator consisting of two dipoles could be used to detect dual sites of ventricular activity. A computer model of the human ventricular myocardium was used to simulate activation sequences initiated at eight different pairs of sites positioned on the epicardial surface of the atrio-ventricular ring. From these sequences, 117-lead body surface potentials (covering the anterior and posterior torso), 64-lead magnetic field maps (above the anterior chest) and 128-lead magnetic field maps (above the anterior and posterior chest) were simulated and were then used to localise dual accessory pathways employing pairs of equivalent dipoles. Average localisation errors were 12 mm, 12mm and 9mm, respectively, when body surface potentials, 64-lead and 128-lead magnetic fields were used. The results of the study suggest that solving the inverse problem for two dipoles could provide additional information on dual accessory pathways prior to electrophysiological study.     

The inverse problem in electrocardiography: solutions in terms of equivalent sources

This paper reviews those inverse electrocardiographic solutions that compute the electrical activity of the heart in terms of equivalent sources such as multipoles or multiple dipoles, as opposed to more realistic source formulations such as epicardial potentials. It treats, in succession, inverse solutions in terms of a single fixed-location dipole, a multipole series, moving dipoles, and, finally, multiple fixed-location dipoles. For each category of solution, simulation studies, animal experiments, and work involving human subjects are reviewed. Finally, more recent work that seeks to compute the cardiac activation isochrones, from the time integrals of the torso potentials during the QRS complex of the electrocardiogram, is described. The paper concludes with a discussion on the future of inverse electrocardiographic solutions in terms of equivalent sources.     

The effect of nontransmural necroses on epicardial potential maps during paced activation: a simulation study

A number of studies have indicated that epicardial potentials provide detailed spatiotemporal information about the spread of electrical activation within the ventricular wall. Here, we used a computer model to simulate activation sequences and corresponding epicardial potential maps in the ventricles damaged by localized necroses. Our findings agreed with those of experimental studies performed for epicardial pacing locus in a complete transient loss of one of the positive areas when the necrosis was located subepicardially, and in a transient gap in the expanding positive areas when the necrosis was located intramurally and subendocardially. This study--by systematically comparing simulated epicardial potential maps with those recorded on the exposed canine hearts--constitutes an important step in validation of our model.     

The Effect of Conductivity on ST-Segment Epicardial Potentials Arising from Subendocardial Ischemia

We quantify and provide biophysical explanations for some aspects of the relationship between the bidomain conductivities and ST-segment epicardial potentials that result from subendocardial ischemia. We performed computer simulations of ischemia with a realistic whole heart model. The model included a patch of subendocardial ischemic tissue of variable transmural thickness with reduced action potential amplitude. We also varied both intracellular and extracellular conductivities of the heart and the conductivity of ventricular blood in the simulations. At medium or high thicknesses of transmural ischemia (i.e., at least 40% thickness through the heart wall), a consistent pattern of two minima of the epicardial potential over opposite sides of the boundary between healthy and ischemic tissue appeared on the epicardium over a wide range of conductivity values. The magnitude of the net epicardial potential difference, the epicardial maximum minus the epicardial minimum, was strongly correlated to the intracellular to extracellular conductivity ratios both along and across fibers. Anisotropy of the ischemic source region was critical in predicting epicardial potentials, whereas anisotropy of the heart away from the ischemic region had a less significant impact on epicardial potentials. Subendocardial ischemia that extends through at least 40% of the heart wall is manifest on the epicardium by at least one area of ST-segment depression located over a boundary between ischemic and healthy tissue. The magnitude of the depression is a function of the bidomain conductivity values.     

Noninvasive characterisation of multiple ventricular events using electrocardiographic imaging

Distributions of epicardial potentials, calculated from body surface electrocardiograms (ECGs), were investigated to determine if they could enable detection of multiple sites of ventricular activity. An anatomical model of the human ventricular myocardium was used to simulate activation sequences initiated at nine different ventricular pairs of sites. From these sequences, body surface ECGs were simulated at 352 sites on the torso surface and then used to reconstruct epicardial potentials at 202 sites. The criterion for detection of dual ventricular events was the presence of two distinct primary potential minima in the reconstructed epicardial potentials. The shortest distance between the two events in the right ventricle that resulted in the reconstruction of epicardial potential patterns, featuring two minima, was 27 mm; the distance between the two events in the left ventricle was 23 mm. When Gaussian white noise in the simulated body surface potentials was increased from 3μV to 15μV and 50μV, dual events became more difficult to distinguish. Findings indicate that calculated epicardial potentials provide useful visual information about the presence of multiple ventricular events that is not apparent in features of body surface ECGs, and could be particularly helpful in optimising mapping procedures during difficult or unsuccessful radiofrequency ablations of accessory pathways.     

Deriving the Standard 12-lead ECGbased on Weighed Epicardial Potential

INTRODUCTION　　 Many methods are routinely used in diagnosing and locating myocardial ischemiaand myocardial infarction,such as the standard 1 2 -lead ECG and body surfaceisopotential maps.All of them are to measure multi-pointbody surface potentialsnoni…     

Effects of rotational myocardial anisotropy in forward potential computations with equivalent heart dipoles

Rotating fibers in the heart lead to a myocardium of inhomogeneous anisotropic conductivity. Besides affecting the activation isochrones, this anisotropy modifies the equivalent dipoles used in calculating extracardiac potentials, rendering them oblique rather than normal to the activation wavefront due to an added axial dipole component oriented along the fibers. Herein, however, consequences of the assumption usually made in forward potential calculations that the equivalent dipoles act in a myocardium that is homogeneous and isotropic are examined. A layered inner block representing the heart was placed inside an outer block representing an isotropic volume conductor. Fiber direction in the inner block rotated uniformly from layer to layer. Current dipoles of different orientations were placed in the inner block and the potentials calculated everywhere. Effects of the anisotropy of the inner block were gauged by computing an equivalent dipole that best fit the outer block surface potentials. For volume conductor conductivities close to that of the torso, the anisotropy diminished dipoles oriented along the fibers. Since the intraventricular blood masses in the heart also diminish such dipoles, these reductions of the axial component may explain the success of heart model simulations that ignore this component.     

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.