心电活动的可视并行计算模型
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摘要
准确阐明正常与各种异常心电图如何产生于心肌细胞的电活动和考察各种心律失
常的形成与持续机制对于心脏疾病的诊断具有重要意义。由于受临床与实验手段的限
制，对于心电学领域中存在的许多不清楚和有争议的问题，建模与仿真一直是一个受
到高度重视的研究手段。迄今为止，大多数的心电模型以经典的Miller-Geselowitz模
型为基础，使用偶极子表达抽象的心肌细胞的电活动，并由偶极矩计算场点电势得到
仿真心电图。其它重要的模型种类包括电生理模型和使用Fitzhugh-Nagumo方程考察
心律失常动力学性质的模型。已报道的电生理模型都是一维和二维的多细胞模型，旨
在详细考察细胞间连接通讯与兴奋传播的关系，未与体表心电图联系起来。大规模并
行计算是发展全心脏电生理模型的主要障碍，所涉及的问题有两个方面，即如何高效
地执行和如何方便地描述几千至几百万组心肌细胞动作电位方程的并行求解。
细胞自动机是一种完全并行的计算模式，具有固有的并行性，作为离散动力学仿
真系统近年来受到广泛注意。尽管按标准定义的细胞自动机是基于规则的，但可以有
基于语言的实现，使之具备更灵活的描述能力。作为建模的前提，我们对一种基于语
言实现的细胞自动机系统Cellular3.0在语言和可视化设施方面进行了扩展，使之能
够描述大规模并行数值计算。
为了在细胞与亚细胞层次精细地和可视化地考察心电图的产生与心律失常的形
成，我们使用经扩展的Cellular3.0为工具设计与实现了一个全心脏电生理模型，该模
型的两个构成要素分别是细胞自动机式的大规模并行计算和各种心肌细胞的动作电位
模型。所包含的心肌组织为窦房结、房室结、心房肌、心室肌、心房传导束以及心室
传导束。限于我们现有计算机的性能，模型是二维的，包含五千余个细胞。根据心室
的分层特性以及不同层次细胞具有不同电学性质的事实，我们提出了一个与模型解析
度和几何特性无关的运行时心壁分层算法，将室壁分层以及使心肌细胞的电活动与其
所在层次联系起来。兴奋在同层细胞间是沿轴向端到端传导，在不同层细胞间是沿径
向边到边传导，两种传导具有不同的速度。细胞间共有24种跨缝隙连结结构，用于
准确描述各种细胞间不同的兴奋传导特性。靠并行求解数千组心肌细胞动作电位方程
和计算各个细胞对之间的跨结兴奋传播，心电活动的时空过程，包括许多心律失常的
形成与演绎过程，能够得到可视化地展现。单个心肌细胞的电活动可使用跟踪窗口进
行跟踪与显示。对于建模中所遇到的问题我们也进行了讨论。
基于全心脏电生理模型，我们还提出了一个新的心电图仿真算法，在细胞层次计
算每一个处于相互连接与通讯中的心肌细胞对各种导联位置心电图的贡献，仿真的正
常与多种异常心电图波形与临床记录十分一致。根据仿真结果，我们讨论了若干心电
图波形的形成机制及诊断意义，包括右胸R波的意义、病理性Q波的形成机制和一
侧
心室电活动对对侧胸表心电场的影响，处于不同位置心肌细胞动作电位波形变井’3
心电图波形变异之间的关系得到形式和定量的说明。已完成的仿真表明该模型对十考
察心律失常的形成具有极大的助益，论文给出了若干心律失常的仿真例，包括缺血诱
导的心动过速及M纠1胞独特的电学性质在心律失常形成中。】能起到的作川。
最后，我们简要讨论了大规模多层次并行i；算在解决广泛存在的复杂性问题方面
的作川，心电问题只是生物医学领域中复杂性问题的一个典型例了。
Answering how normal and various abnormal ECGs generate from the electrical
activities of cardiac cells and investigating how various arrhythmias form and sustain have
been questions of great significance to the diagnosis of heart diseases. Restricted by the
limited means of clinical and experimental investigation, quite a few of unclear and
debatable questions in cardioelectricity still exist and modeling and simulation has been
valued as an important research approach. So far, most cardioelectrical models have been
built based on the classical Miller-Geselowitz model that employs a dipole to represent the
electrical activity of each abstract cardiac cell. Other kinds of models include the
electrophysiological models and the models employing the Fitzhugh-Nagumo equation to
investigate the dynamic behavior of arrhythmia. The reported electrophysiological models
are one- or two-dimensional multicellular models, aiming at investigating the intercellular
connection and communication, but lacking an imbedded ECG computing algorithm to link
the cardioelectrical activity with the recordings of ECG. The massive parallel computing has
been the main obstacle to develop a whole-heart electrophysiological model. Difficulties
come from two aspects: the efficiency of executing and the convenience of describing
thousands to millions groups of nonlinear action potential equations of cardiac cells.
As a computation mode with intrinsic parallel features, cellular automata have received
increasing attentions in recent years as the tool of discrete dynamic system simulation.
Although the standard defined cellular automata are rule-based, they can be implemented as
languages, with much flexibility in computation describing. As the basis of our work, we
made extensions to both the language compiler and the viewing facility of Celltilae3.O, a
language-based cellular automata system, and made it applicable to describe the massive
parallel numerical computing.
To investigate the ECG generation and the arrhythmia formation problems
quantitatively and visibly at cellular and subcellular level, taking the extended cellular3.O as
tool, we designed and implemented a whole-heart electrophysiological model. The two key
components of this model are the cellular automata style massive parallel computing and the
action potential models of cardiac cells. The included cardiac tissues are sinoatiial node,
atrioventricular node, atrium, ventricle, intra-atrial conduction bundle, and intra-ventricular
conduction bundle (Purkinje fiber). Restricted by the power of computer we equip now, the
current model is two-dimensional now and consists of about more than four thousand
cardiac cells. According to the fact that the walls of ventricles are layered and cells at
ND
different layer have different electrical properties, we developed a resolution- nd geometry-
independent run-time make-layer algorithm to layer the was of ventricles, linking the
electrical property of cardiac ll with its layer position. The excitation propagation among
cells of same layer is end-to-end conduction along longitudinal direction and the
propagation among cells of different layer is side-to-side conduction along radial direction.
Twenty-four kinds of intercellular gap junctions are designed to describe the intercellular
excitation propagation among cells of different kinds and cells along different direction. By
parallely solving thousands groups of action potential equations of cardiac cells and
computing the trans-junctional excitation propagation between every cell pairs, the
spatiotemporal process of ca
常的形成与持续机制对于心脏疾病的诊断具有重要意义。由于受临床与实验手段的限
制，对于心电学领域中存在的许多不清楚和有争议的问题，建模与仿真一直是一个受
到高度重视的研究手段。迄今为止，大多数的心电模型以经典的Miller-Geselowitz模
型为基础，使用偶极子表达抽象的心肌细胞的电活动，并由偶极矩计算场点电势得到
仿真心电图。其它重要的模型种类包括电生理模型和使用Fitzhugh-Nagumo方程考察
心律失常动力学性质的模型。已报道的电生理模型都是一维和二维的多细胞模型，旨
在详细考察细胞间连接通讯与兴奋传播的关系，未与体表心电图联系起来。大规模并
行计算是发展全心脏电生理模型的主要障碍，所涉及的问题有两个方面，即如何高效
地执行和如何方便地描述几千至几百万组心肌细胞动作电位方程的并行求解。
细胞自动机是一种完全并行的计算模式，具有固有的并行性，作为离散动力学仿
真系统近年来受到广泛注意。尽管按标准定义的细胞自动机是基于规则的，但可以有
基于语言的实现，使之具备更灵活的描述能力。作为建模的前提，我们对一种基于语
言实现的细胞自动机系统Cellular3.0在语言和可视化设施方面进行了扩展，使之能
够描述大规模并行数值计算。
为了在细胞与亚细胞层次精细地和可视化地考察心电图的产生与心律失常的形
成，我们使用经扩展的Cellular3.0为工具设计与实现了一个全心脏电生理模型，该模
型的两个构成要素分别是细胞自动机式的大规模并行计算和各种心肌细胞的动作电位
模型。所包含的心肌组织为窦房结、房室结、心房肌、心室肌、心房传导束以及心室
传导束。限于我们现有计算机的性能，模型是二维的，包含五千余个细胞。根据心室
的分层特性以及不同层次细胞具有不同电学性质的事实，我们提出了一个与模型解析
度和几何特性无关的运行时心壁分层算法，将室壁分层以及使心肌细胞的电活动与其
所在层次联系起来。兴奋在同层细胞间是沿轴向端到端传导，在不同层细胞间是沿径
向边到边传导，两种传导具有不同的速度。细胞间共有24种跨缝隙连结结构，用于
准确描述各种细胞间不同的兴奋传导特性。靠并行求解数千组心肌细胞动作电位方程
和计算各个细胞对之间的跨结兴奋传播，心电活动的时空过程，包括许多心律失常的
形成与演绎过程，能够得到可视化地展现。单个心肌细胞的电活动可使用跟踪窗口进
行跟踪与显示。对于建模中所遇到的问题我们也进行了讨论。
基于全心脏电生理模型，我们还提出了一个新的心电图仿真算法，在细胞层次计
算每一个处于相互连接与通讯中的心肌细胞对各种导联位置心电图的贡献，仿真的正
常与多种异常心电图波形与临床记录十分一致。根据仿真结果，我们讨论了若干心电
图波形的形成机制及诊断意义，包括右胸R波的意义、病理性Q波的形成机制和一
侧
心室电活动对对侧胸表心电场的影响，处于不同位置心肌细胞动作电位波形变井’3
心电图波形变异之间的关系得到形式和定量的说明。已完成的仿真表明该模型对十考
察心律失常的形成具有极大的助益，论文给出了若干心律失常的仿真例，包括缺血诱
导的心动过速及M纠1胞独特的电学性质在心律失常形成中。】能起到的作川。
最后，我们简要讨论了大规模多层次并行i；算在解决广泛存在的复杂性问题方面
的作川，心电问题只是生物医学领域中复杂性问题的一个典型例了。
Answering how normal and various abnormal ECGs generate from the electrical
activities of cardiac cells and investigating how various arrhythmias form and sustain have
been questions of great significance to the diagnosis of heart diseases. Restricted by the
limited means of clinical and experimental investigation, quite a few of unclear and
debatable questions in cardioelectricity still exist and modeling and simulation has been
valued as an important research approach. So far, most cardioelectrical models have been
built based on the classical Miller-Geselowitz model that employs a dipole to represent the
electrical activity of each abstract cardiac cell. Other kinds of models include the
electrophysiological models and the models employing the Fitzhugh-Nagumo equation to
investigate the dynamic behavior of arrhythmia. The reported electrophysiological models
are one- or two-dimensional multicellular models, aiming at investigating the intercellular
connection and communication, but lacking an imbedded ECG computing algorithm to link
the cardioelectrical activity with the recordings of ECG. The massive parallel computing has
been the main obstacle to develop a whole-heart electrophysiological model. Difficulties
come from two aspects: the efficiency of executing and the convenience of describing
thousands to millions groups of nonlinear action potential equations of cardiac cells.
As a computation mode with intrinsic parallel features, cellular automata have received
increasing attentions in recent years as the tool of discrete dynamic system simulation.
Although the standard defined cellular automata are rule-based, they can be implemented as
languages, with much flexibility in computation describing. As the basis of our work, we
made extensions to both the language compiler and the viewing facility of Celltilae3.O, a
language-based cellular automata system, and made it applicable to describe the massive
parallel numerical computing.
To investigate the ECG generation and the arrhythmia formation problems
quantitatively and visibly at cellular and subcellular level, taking the extended cellular3.O as
tool, we designed and implemented a whole-heart electrophysiological model. The two key
components of this model are the cellular automata style massive parallel computing and the
action potential models of cardiac cells. The included cardiac tissues are sinoatiial node,
atrioventricular node, atrium, ventricle, intra-atrial conduction bundle, and intra-ventricular
conduction bundle (Purkinje fiber). Restricted by the power of computer we equip now, the
current model is two-dimensional now and consists of about more than four thousand
cardiac cells. According to the fact that the walls of ventricles are layered and cells at
ND
different layer have different electrical properties, we developed a resolution- nd geometry-
independent run-time make-layer algorithm to layer the was of ventricles, linking the
electrical property of cardiac ll with its layer position. The excitation propagation among
cells of same layer is end-to-end conduction along longitudinal direction and the
propagation among cells of different layer is side-to-side conduction along radial direction.
Twenty-four kinds of intercellular gap junctions are designed to describe the intercellular
excitation propagation among cells of different kinds and cells along different direction. By
parallely solving thousands groups of action potential equations of cardiac cells and
computing the trans-junctional excitation propagation between every cell pairs, the
spatiotemporal process of ca
引文
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[12]杨均国，李治安．主编 现代心电图学．科学出版社．1997；p153．