人体骨骼肌肉层对心电传导和体表电位标测的影响

应用电磁场数值计算方法求解三维心电图正问题,重点考察了人体骨骼肌肉层的各向异性导电性对心电传导的影响。推导了描述人类心电场的有限元模型和边界元模型,以及二者结合的形式,并在一个包含各向异性导电性肌肉层的三维人体模型下进行了模拟计算。讨论了骨骼肌肉层在不同的肌肉纤维方向组合下的胸腔模型,以及纤维的各向异性导电性对体表电位图的影响     

基于小波变换的心肌梗塞体表电位特征分析

小波变换已被很多心电学者用于ＥＣＧ信号的特征分析检测,在虚拟心脏基础上,选取合适的小波,对心肌梗塞的仿真体表电位进行小波变换细节分量处理,提出了一种新的体表电位形态特征的分析方法。结果表明,基于小波变换处理后体表电位图可以更地提示不同部位心肌在体表电位分布的特征,其表征出的拓扑形态对体表电位和虚拟心脏方法用于心肌梗塞临床诊断提供了一种新的途径。     

心肌电兴奋传导速度对心律失常影响的仿真研究

心电场是由心肌的电活动产生的。心肌细胞的电特性及心肌细胞间的传导关系决定了体表电位的分布及心电图的变化。心肌电兴奋传导速度则是影响心肌间兴奋传导关系的重要参数之一。由于很难通过实验方法来人为改变电兴奋传导速度,因而临床上有关该参数对心律影响的定量知识相当缺乏。本文采用真实三雏躯干模型及心脏模型,对心肌电兴奋传导速度与心律变化的关系进行定量仿真研究。结果表明,兴奋传导速度决定了整个心电图的变化,而局部普通心肌的传导速度在相当范围内变化似乎对心电图影响不明显,但传导速度超过一定范围后可能产生突变。     

人体和动物模型的体表物理信息地形图的研究

对人体头面、躯干、四肢、耳廓各局部几十个及整个人体等体表部位正、背面等210个部位进行超微弱冷光和温度测量,输入电子计算机,经特殊的自编程序处理,获得十分清晰的,由3000多数据构成的各个局部或人体整体的冷光和温度地形图。 对家兔左、右耳廓、胸腹部、背部都分别观察32个部位的冷光与体表温度,经计算机分析处理,每观察区域获得约由2000个数据构成的精确的冷光、温度地形分市图。并可见不同生理、病理状态及不同病程家兔体表冷光、温度等地形图呈有规律的改变。 此外,我们还编制了以体表左右相应对称部位差值为分析数据进行地形图分析的程序,用以人体和动物体表物理信息对称规律的研究。 本工作以图形的形式显示物理参量在体表的广泛的分布规律,以揭示机体内部的不同生理、病理状态。本方法定位准确、直观醒目,为研究体表信息及机体生命活动规律提供了与逐点直接测量方法相互补充的有益的新手段。     

中域效应模型中物种分布幅度梯度的影响

中域效应（Mid-domain effect）模型量化了几何限制对物种丰富度空间分布格局的影响．然而,目前的研究缺乏对该模型的生物学意义作进一步的阐明,以及对物种分布幅度的梯度变化进行数量评价．本文利用已发表的马达加斯加蝴蝶的多样性数据,通过模拟方法和物种幅度频度分布（RSFD）的分析,研究了几何限制和物种幅度非随机分布的共同效应．研究发现,尽管马达加斯加蝴蝶物种丰富度的分布格局满足中域效应模型,但并不符合该模型的特征RSFD变化．如果在模型中加入物种分布幅度的梯度变化,则能较好地模拟实际RSFD的变化,表明物种丰富度的空间格局确实存在物种分布幅度的梯度变化．同时还发现,物种分布幅度梯度的存在对最终丰富度格局影响不大,表明中域效应模型的生物学意义难以从物种分布幅度的行为上来解释．     

一种处理人体骨骼肌肉层各向异性导电性的数值方法

重点讨论了应用电磁场数值计算方法求解心电图正问题和逆问题中人体骨骼肌肉层的各向异性导电性的处理方法．文中应用有限元和边界元结合的方法,构造了一个包含不同的纤维方向组合的骨骼肌肉层的三维胸腔模型,并在此模型下引入了局部坐标内的各向异性导电率向整体坐标转换的方法．据此进行的模拟计算结果以图像的方式清晰地展示了各向异性导电性对体表电位图的影响．     

由体表电位分布推算心脏外膜电位——心脏电活动的逆解

心脏外膜电位分布对研究心脏电活动机制和诊断心脏某些疾病有重要意义。本文介绍由体表电位估算心外膜电位的原理、方法和实验装置,并着重叙述从体表到心外膜电位传输系数的两种估算方法——几何测量法和有限元法——及它们的结果。     

红松种群生态场特性函数初步分析

文中给出生态空间、生态场、红松种群生态场的定义,分析了由单株母树繁衍而成的红松后代的时空分布,并依据其分布特性给出了以个体数量u和密度ρ为标度的红松种群数量场的函数描述。函数刻画了非均匀场的空间分布特征,在此基础上进一步讨论了非均匀场形成的生态机理及生态场研究的经济意义。     

非均匀人群SIR模型的稳态分布

文章利用测度论的方法研究非均匀人群中疾病传播的SIR模型,建立了动态模型中感染人群的演化方程,在此基础上我们得到了非均匀SIR模型的稳态分布.     

空间异质性对植物种群动态的影响:三种模拟方法的比较

为了讨论单一物种在异质性景观中的空间传播,将平均场近似模型和偶对近似模型的结果进行对比研究.本研究选择了有代表性的四邻域和八邻域时物种的传播情况,首先运用细胞自动机建立了理想模型,对偶对近似模型和平均场近似模型在全局密度和局域密度固定时随着出生率与死亡率比值变化的结果比较,以细胞自动机模型结果为依据,判断偶对近似与平均场近似哪个结果更加接近细胞自动机模型的结果.通过分析得到四邻域时在近似细胞自动机模型结果时偶对近似的结果优于平均场近似的结果,但是在八邻域时三个模型之间的差异性不再那么明显,偶对近似依然能够很好的预测细胞自动机模型的结果.     

Computational issues of importance to the inverse recovery of epicardial potentials in a realistic heart-torso geometry

In vitro data from a realistic-geometry electrolytic tank were used to demonstrate the consequences of computational issues critical to the ill-posed inverse problem in electrocardiography. The boundary element method was used to discretize the relationship between the body surface potentials and epicardial cage potentials. Variants of Tikhonov regularization were used to stabilize the inversion of the body surface potentials in order to reconstruct the epicardial surface potentials. The computational issues investigated were (1) computation of the regularization parameter; (2) effects of inaccuracy in locating the position of the heart; and (3) incorporation of a priori information on the properties of epicardial potentials into the regularization methodology. Two methods were suggested by which a priori information could be incorporated into the regularization formulation: (1) use of an estimate of the epicardial potential distribution everywhere on the surface and (2) use of regional bounds on the excursion of the potential. Results indicate that the a posteriori technique called CRESO, developed by Colli Franzone and coworkers, most consistently derives the regularization parameter closest to the optimal parameter for this experimental situation. The sensitivity of the inverse computation in a realistic-geometry torso to inaccuracies in estimating heart position are consistent with results from the eccentric spheres model; errors of 1 cm are well tolerated, but errors of 2 cm or greater result in a loss of position and amplitude information. Finally, estimates and bounds based on accurate, known information successfully lower the relative error associated with the inverse and have the potential to significantly enhance the amplitude and feature position information obtainable from the inverse-reconstructed epicardial potential map.     

Cardiac electric field on the epicardial and body surfaces during the period of depolarization and repolarization of ventricular myocardium in pikes

Body surface and ventricular epicardial potential distributions during the electrocardiographic QRST interval were studied in pikes with the aid of potential mapping. The earliest epicardial activation was observed at the posterior base near the atrioventricular orifice. The areas of the earliest repolarization were found at the apex and the posterior base, whereas the area of the latest repolarization was detected at the anterior base. In the initial period of the QRS, the minimum was developed in the middle third of the right lateral body surface, and the maximum in the middle third of the ventral body surface. The body surface potential distribution during the ST-Twas characterized by the clear-cut negative potential zone in the cranial ventral area with the rest of the body surface having positive potentials, a pattern being largely unchanged throughout the period of the T-wave. The ventricular epicardial repolarization sequence differed from the activation sequence. The ventricular epicardial depolarization and repolarization sequences as well as epicardial potential distributions are expressed in the cardiac electric field on the body surface during the QRS and ST-T complexes.     

Inverse electrocardiographic transformations: dependence on the number of epicardial regions and body surface data points

The inverse problem of electrocardiography, the computation of epicardial potentials from body surface potentials, is influenced by the desired resolution on the epicardium, the number of recording points on the body surface, and the method of limiting the inversion process. To examine the role of these variables in the computation of the inverse transform, Tikhonov's zero-order regularization and singular value decomposition (SVD) have been used to invert the forward transfer matrix. The inverses have been compared in a data-independent manner using the resolution and the noise amplification as endpoints. Sets of 32, 50, 192, and 384 leads were chosen as sets of body surface data, and 26, 50, 74, and 98 regions were chosen to represent the epicardium.The resolution and noise were both improved by using a greater number of electrodes on the body surface. When 60% of the singular values are retained, the results show a trade-off between noise and resolution, with typical maximal epicardial noise levels of less than 0.5% of maximum epicardial potentials for 26 epicardial regions, 2.5% for 50 epicardial regions, 7.5% for 74 epicardial regions, and 50% for 98 epicardial regions. As the number of epicardial regions is increased, the regularization technique effectively fixes the noise amplification but markedly decreases the resolution, whereas SVD results in an increase in noise and a moderate decrease in resolution. Overall the regularization technique performs slightly better than SVD in the noise-resolution relationship.There is a region at the posterior of the heart that was poorly resolved regardless of the number of regions chosen. The variance of the resolution was such as to suggest the use of variable-size epicardial regions based on the resolution.     

改善心电图逆问题病态条件的两个有效方法

本文对应用数值方法求解三维心电图逆问题时出现的解的不稳定现象,提出了两种有效的解决办法,即提高电导率值和选用包含适当的正则因子的阻尼最小二乘法。文中应用有限元和边界元结合的方法,在一个包含各向异性导电性肌肉层的三维人体模型下进行了心外膜电位的重构计算。其结果证明这种方法对提高心电图逆问题的数值稳定性和解的精度非常有效。     

A model study of instability of the inverse problem in electrocardiography.

The inverse problem in electrocardiography is studied analytically using a concentric spheres model with no symmetry assumptions on the potential distribution. The mathematical formulation is presented, and existence and uniqueness of the solution are briefly discussed. Solution to the inverse problem is inherently very unstable. The magnitude of this instability is demonstrated using the derived analytical inverse solution for the spherical model. Regularization methods used to date are based on a regularization parameter that does not relate to any measurable physiological parameters. This paper presents a regularization method that is based on a parameter in the form of an a priori bound on the L2 norm of the inverse solution. Such a bound can be obtained from the theoretical estimates based on the measured values of the body surface potentials together with experimental knowledge about the magnitudes of the epicardial potentials. Based on the presented regularization, an exact form of the regularized solution and estimates of its accuracy are derived.     

Comparison and testing of least-squares time domain inverse solutions in electrocardiography

The use of several mathematical methods for estimating epicardial ECG potentials from arrays of body surface potentials has been reported in the literature; most of these methods are based on least-squares reconstruction principles and operate in the time-space domain. In this paper we introduce a general Bayesian maximum a posteriori (MAP) framework for time domain inverse solutions in the presence of noise. The two most popular previously applied least-squares methods, constrained (regularized) least-squares and low-rank approximation through the singular value decomposition, are placed in this framework, each of them requiring the a priori knowledge of a ‘regularization parameter’, which defines the degree of smoothing to be applied to the inversion. Results of simulations using these two methods are presented; they compare the ability of each method to reconstruct epicardial potentials. We used the geometric configuration of the torso and internal organs of an individual subject as reconstructed from CT scans. The accuracy of each method at each epicardial location was tested as a function of measurement noise, the size and shape of the subarray of torso sensors, and the regularization parameter. We paid particular attention to an assessment of the potential of these methods for clinical use by testing the effect of using compact, small-size subarrays of torso potentials while maintaining a high degree of resolution on the epicardium.     

A new method for regularization of the inverse problem of electrocardiography.

The inverse problem of electrocardiography (specifically, that part concerned with the computation of the ventricular surface activation isochrones) is shown to be formally equivalent to the problem of identification and measurement of discontinuities in derivatives of body surface potentials. This is based on the demonstration that such measurements allow localization of the relative extrema of the ventricular surface activation map (given a forward problem solution), which in turn restricts the space of admissible solution maps to a compact set. Although the inverse problem and the problem of identifying derivative discontinuities are both ill-posed, it is possible that the latter may be more easily or justifiably resolved with available information, particularly as current methods for regularizing the inverse problem typically rely on a regularization parameter chosen in an a posteriori fashion. An example of the power of the approach is the demonstration that a recent Uniform Dipole Layer Hypothesis-based method for producing the ventricular surface activation map is largely independent on that hypothesis and capable in principle of generating maps that are very similar in a precise sense to those that would result from the usual epicardial potential formulation (assuming the latter were capable of producing intrinsic deflections in computed epicardial electrograms sufficiently steep to accurately compute the activation map). This is consistent with the preliminary success of the former method, despite the significant inaccuracy of its underlying assumption.     

Sequence of ventricular repolarization under body cooling in the frog

Lowering the temperature is known to prolong the repolarization of cardiomyocytes. However, whether the prolongation of action potentials is uniform throughout the myocardium, and whether this prolongation is obvious in ECG, remains unclear. Ventricular repolarization sequences and body surface potential distributions were studied in 20 frogs Rana temporaria using epicardial and body surface potential mapping. An apex-to-base ventricular repolarization sequence corresponded to the distribution of local repolarization durations was demonstrated at the temperature of 18 degrees C. The body surface potential distribution during the ST-T complex was characterized by the cranial negative and caudal positive potential areas. Under the body cooling to 10 degrees C, repolarization prolonged to a greater extent at the apex that resulted in the base-to-apex repolarization sequence, which, in turn, caused an inversion in the body surface potential distribution with cranial portion of the body being positive and caudal portion being negative.     

Correlation in the of the process of cardiac ventricle intramural depolarization and distribution of cardioelectric field potentials of the dog Canis familiaris

Based on a multichannel synchronous mapping of heart electric potentials, the sequence in time of the ventricle myocardium depolarization was compared with dynamics of distribution of cardioelectric potentials on the body surface in a dog. The cardioelectric field on the dog body surface at the period of the initial ventricular activity has been shown to be characterized by the presence of two inversions of the mutual disposition of areas of positive and negative potentials. Contribution to formation of distribution of the cardioelectric potentials on the body surface at each moment of the period of initial ventricular activity was made by all myocardial layers involved by excitation.     

Correlation in time of the process of cardiac ventricle intramural depolarization and of distribution of cardioelectric field potentials of the dog <Emphasis Type="Italic">Canis famjliaris</Emphasis>

Based on a multichannel synchronous mapping of heart electric potentials, the sequence in time of the ventricle myocardium depolarization was compared with dynamics of distribution of cardioelectric potentials on the dog body surface. The cardioelectric field on the dog body surface at the period of the initial ventricular activity has been shown to be characterized by the presence of two inversions of the mutual disposition of areas of positive and negative potentials. Contribution to formation of distribution of the cardioelectric potentials on the body surface at each moment of the period of initial ventricular activity was made by all myocardial layers involved in excitation.