虚拟心脏解剖及电生理数学建模
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摘要
虚拟心脏建模仿真工作是对心脏结构和功能的模拟，集电生理学、动力学、血液流体力学以及神经、生化控制于一身的极其复杂的综合系统，是一项难度和复杂度极高的技术工作。目前，心脏生理病理学家大多从细胞、基因、蛋白、分子等微观层次来研究心脏机理，实验反映出来的大多是单细胞或局部的特性，不能很好地阐明从微观病理变化如何演变成整体心脏的异常，而临床心脏学家则更多地关注整体心脏的宏观综合表现特征，对病症微观起源较少深究，对于病因复杂的心脏病诊治很大程度上依靠经验决断。连接心脏微观宏观研究的有效手段之一就是虚拟心脏模型，基于虚拟心脏模型我们可以非常方便地研究心肌微观生理病理变化是如何发展成整体心脏的宏观变化，而且是定量的，从而有助于提高心脏病的诊治水平和创新药物的开发。近些年生物医学工程领域和其它学科快速发展，出现了很多新方法、新理论，将这些成果引入心脏建模领域，会帮助我们建立更为复杂和完善的虚拟心脏模型，深入认识心血管系统的运动规律和本质，从而朝着建立复合虚拟心脏仿真模型的最终目标深入下去，推动虚拟心脏建模正逆问题研究的进一步发展。
本文以虚拟心脏解剖结构数学建模和虚拟心脏电生理数学建模为研究方向，在原有浙江大学第一代LFX虚拟心脏模型基础之上，综合应用虚拟人技术、图像处理、信号处理、并行计算、三维科学可视化等技术手段，尝试求解虚拟心脏建模中关键的生物计算问题，建立了代表国际先进水平的Cardiome-CN虚拟心脏电生理数学模型。在若干性能指标上领先于国际同类模型，对推动Cardiome计划相关技术的向前发展具有重要影响力。其中基于细胞离子通道和双域模型方程的超大计算量心肌兴奋传播并行算法的实现，对其它大型生物计算技术的发展也具有一定的借鉴作用。本文主要工作和研究成果包括：
(1)基于医学影像数据、生理标本数据、虚拟人数据建立了虚拟心脏解剖结构数据库，包含兔子、犬、人体等心脏解剖模型样本。其中以人体心脏模型为例，数据结构空间分辨率为0．33mm，包含了完整的心房、心室结构。对心室壁分层、心肌纤维旋向设定、传导通路设定、组织功能分类定义等虚拟心脏解剖结构建模的关键问题进行了研究，并给出了解决方案。针对各模型建立了相应的计算、可视化网格。这是国际上目前结构完整、精度高，且包含完整心肌纤维旋向和电传导通路信息的人体心脏解剖结构模型之一。
(2)基于心肌细胞离子通道水平的实验数据，开创性的建立了国内首个犬、人体心肌细胞动作电位模型库。其中包含了起搏细胞、心房肌细胞、心室肌细胞等多样性、特异性的模型定义。模型还包含了完整的钙循环以及兴奋收缩耦联机制。针对细胞模型的计算和分析方法进行了深入研究，首次提出了使用非标准有限差分方法(NSFD)和DVODE算子来加速细胞模型的运算速度。总结扩展了心肌细胞模型静态和动态的分析方法，丰富了模型研究的手段。并应用细胞模型针对心力衰竭、短QT综合症、Brugada综合症等相关疾病进行了初步的探索研究。
(3)基于MPI和OPENMP并行计算协议库，设计并实现了基于双域模型模拟的各向异性的心肌兴奋传播并行算法，实现了离子通道细胞模型和双域模型兴奋扩散方程的耦合，建立了从一维结构模型到三维解剖模型的各种层次的传导模型，仿真了正常心脏组织的兴奋传导时序，并对折返性心律失常的兴奋传导机制进行了模型研究。其中并行扩散算法属国际先进水平，国内虚拟器官建模领域还没有类似的研究工作。
(4)构建了基于真实人体心脏解剖生理结构，具有仿真心肌缺血、多种心律失常、基因变异类离子通道疾病等功能的达到国际领先和先进水平的Cardiome-CN虚拟人体心脏模型。
(5)基于美国虚拟人断层数据，构建了真实完整的男性和女性人体躯干结构模型。使用Cardiome-CN虚拟心脏模型，模拟了心电场分布，计算了体表电位、心电图和心电向量图。
未来虚拟心脏模型具有很大的应用潜力，不仅仅在生物医学领域，还可以为临床服务，包括介入治疗，为病人定制个体化的心脏信息数据库等等。特别是对于临床需求迫切的房颤、室颤等心律失常疾病的诊断和导管介入消融治疗技术的提升具有直接的应用价值。虽然目前还无法针对个体案例进行实时重建，但随着计算能力的提高，基于病人个体化定制的虚拟心脏模型辅助治疗必将成为现实。
By setting electrophysiology, dynamics, fluid mechanics of blood, nerves and chemical biological control together within an extremely complex integrated system, virtual heart modeling can be used to simulate the structure and function of the real heart, which is a technical work with high degree of difficulty and complexity. At present, most pathologists study the mechanism of the heart from micro-level, such as physiological cardiac cells, genes, proteins, molecules, while the majority of the experiments can only reflect in single-cell or partial identity, which can not be used to well explain how the cardiac abnormalities in micro-pathological level evolved into the macro-pathological level, and clinical cardiac experts, however, pay more attention to the overall comprehension of macro cardiac performance characteristics, less concern the micro-origined cause of the heart diseases. Their decisions of the diagnosis and treatment on complex heart disease are largely depend on experience. The virtual heart model is the effective means of connection between the micro and macro level heart research. Based on virtual heart model, doctor can study the physiological and pathological quantitative changes of myocardial conveniently in micro level and also test how the micro changes develop into the overall macro-change, which can contribute to improve the diagnosis and treatment of heart disease and the development of innovative medicines. In recent years, with the rapid development of biomedical engineering and other disciplines, there are a lot of new methods and new theories are introduced in these fields. The introduction of these methods and theories to virtual heart modeling areas can help us set up more complex and sophisticated model and sequentially in-depth understand the laws and the nature of cardiovascular system, which can eventually contribute to promote the further developing of forward and inverse problem of heart modeling studies.
In this paper, we will focus on the mathematical modeling of the anatomical structure and electrophysiology of the heart. Based on the original LFX virtual heart model, the first generation of virtual heart model of Zhejiang University, with comprehensive application of the Virtual Human technology, image processing, signal processing, parallel computing, three-dimensional scientific visualization and other technical means, we try to solve the key biological computing problems and set up the new generation of Cardiome-CN virtual heart electrophysiology model, which performance indicators is on the top of the international similar models and the related technology has an important influence on promoting the development of Cardiome project. The design and implementiaon of the parallel algorithms for ionic-channel based and bidomain model equations of myocardial excitation propagation can also be used for reference of other large-scale development of bio-computing technology. In this paper, the main research work and findings include:
1. Based on medical image data, physiological data samples, virtual human project dataset, we construct the database of virtual heart anatomical structure, including rabbit, dog, and human heart models. For the human heart model as an example, the spatial resolution of data structure is 0.33mm, which contains a complete atrial and ventricular structure, stratification of ventricular wall, myocardial fiber orientation, conduction pathway settings, organizations such as the definition of functional classification of heart tissue, etc. The calculation method, visualization grid of these models was also set up. The constructed human virtual heart model is one of the best virtual heart models in the world with detailed anatomy structure.
2. Based on experimental data of ion channels in cardiac myocytes, we pioneeringly set up the first cardiac myocyte action potential model library of dogs, human in the domestic, which contain the pacemaker cells, atrial myocytes, ventricular myocytes and other heterogeneous models with a complete cycle of calcium and excitation-contraction coupling mechanism. We carried out in-depth research on calculation and analysis for cell model. By using of non-standard finite difference method (NSFD) and operator DVODE, we accelerate cell model computational speed and sum up the expansion of the static and dynamic analysis methods, enriching the model means. The cell models have been used for simulation of heart failure, short-QT syndrome, Brugada syndrome-related diseases.
3. Based on MPI and OpenMP parallel computing protocol library, we design and implement parallel algorithms of the bidomain model, and use them to simulate the anisotropic spread of the cardiac excitation propagation. By coupling ionic channel cell model and bidomain reaction and diffusion model, we setup the one-dimensional structural conduction models to the three-dimensional anatomical conduction models and simulate the normal heart tissue conduction sequences. Then, we study the mechanism of reentrant arrhythmia by using these conduction models, which is international advanced level in the field of domestic virtual organ modeling.
4. Based on real physiological structures, a virtual human heart model, Cardiome-CN, has been constructed. This model can be used to simulate myocardial ischemia, a variety of arrhythmias, genetic variation, and ionic channel function diseases.
5. Based on the US virtual human project data, we build both male and female human torso models. Together with the Cardiome-CN model, we simulate the cardiac electric field distribution and body surface potential, calculate electrocardiogram and vectorcardiogram, study the the cellular mechanism of ECG morphological characteristics in arrhythmia condition.
In the future, virtual heart models have great potential applications not only in the biomedical field, bu also in clinical services, including interventional treatment, the individual custom database information and so on. Especially for the clinical diagnosis needs of atrial fibrillation, ventricular fibrillation and other arrhythmias diseases, the virtual heart model can help to enhance the application value of transcatheter interventional ablation techniques. Although it can not realize the real-time reconstruction of individual cases at the present, with the improvement of the calculation ability, the individual customized virtual heart model for clinical therapy application must become a reality in the future.
本文以虚拟心脏解剖结构数学建模和虚拟心脏电生理数学建模为研究方向，在原有浙江大学第一代LFX虚拟心脏模型基础之上，综合应用虚拟人技术、图像处理、信号处理、并行计算、三维科学可视化等技术手段，尝试求解虚拟心脏建模中关键的生物计算问题，建立了代表国际先进水平的Cardiome-CN虚拟心脏电生理数学模型。在若干性能指标上领先于国际同类模型，对推动Cardiome计划相关技术的向前发展具有重要影响力。其中基于细胞离子通道和双域模型方程的超大计算量心肌兴奋传播并行算法的实现，对其它大型生物计算技术的发展也具有一定的借鉴作用。本文主要工作和研究成果包括：
(1)基于医学影像数据、生理标本数据、虚拟人数据建立了虚拟心脏解剖结构数据库，包含兔子、犬、人体等心脏解剖模型样本。其中以人体心脏模型为例，数据结构空间分辨率为0．33mm，包含了完整的心房、心室结构。对心室壁分层、心肌纤维旋向设定、传导通路设定、组织功能分类定义等虚拟心脏解剖结构建模的关键问题进行了研究，并给出了解决方案。针对各模型建立了相应的计算、可视化网格。这是国际上目前结构完整、精度高，且包含完整心肌纤维旋向和电传导通路信息的人体心脏解剖结构模型之一。
(2)基于心肌细胞离子通道水平的实验数据，开创性的建立了国内首个犬、人体心肌细胞动作电位模型库。其中包含了起搏细胞、心房肌细胞、心室肌细胞等多样性、特异性的模型定义。模型还包含了完整的钙循环以及兴奋收缩耦联机制。针对细胞模型的计算和分析方法进行了深入研究，首次提出了使用非标准有限差分方法(NSFD)和DVODE算子来加速细胞模型的运算速度。总结扩展了心肌细胞模型静态和动态的分析方法，丰富了模型研究的手段。并应用细胞模型针对心力衰竭、短QT综合症、Brugada综合症等相关疾病进行了初步的探索研究。
(3)基于MPI和OPENMP并行计算协议库，设计并实现了基于双域模型模拟的各向异性的心肌兴奋传播并行算法，实现了离子通道细胞模型和双域模型兴奋扩散方程的耦合，建立了从一维结构模型到三维解剖模型的各种层次的传导模型，仿真了正常心脏组织的兴奋传导时序，并对折返性心律失常的兴奋传导机制进行了模型研究。其中并行扩散算法属国际先进水平，国内虚拟器官建模领域还没有类似的研究工作。
(4)构建了基于真实人体心脏解剖生理结构，具有仿真心肌缺血、多种心律失常、基因变异类离子通道疾病等功能的达到国际领先和先进水平的Cardiome-CN虚拟人体心脏模型。
(5)基于美国虚拟人断层数据，构建了真实完整的男性和女性人体躯干结构模型。使用Cardiome-CN虚拟心脏模型，模拟了心电场分布，计算了体表电位、心电图和心电向量图。
未来虚拟心脏模型具有很大的应用潜力，不仅仅在生物医学领域，还可以为临床服务，包括介入治疗，为病人定制个体化的心脏信息数据库等等。特别是对于临床需求迫切的房颤、室颤等心律失常疾病的诊断和导管介入消融治疗技术的提升具有直接的应用价值。虽然目前还无法针对个体案例进行实时重建，但随着计算能力的提高，基于病人个体化定制的虚拟心脏模型辅助治疗必将成为现实。
By setting electrophysiology, dynamics, fluid mechanics of blood, nerves and chemical biological control together within an extremely complex integrated system, virtual heart modeling can be used to simulate the structure and function of the real heart, which is a technical work with high degree of difficulty and complexity. At present, most pathologists study the mechanism of the heart from micro-level, such as physiological cardiac cells, genes, proteins, molecules, while the majority of the experiments can only reflect in single-cell or partial identity, which can not be used to well explain how the cardiac abnormalities in micro-pathological level evolved into the macro-pathological level, and clinical cardiac experts, however, pay more attention to the overall comprehension of macro cardiac performance characteristics, less concern the micro-origined cause of the heart diseases. Their decisions of the diagnosis and treatment on complex heart disease are largely depend on experience. The virtual heart model is the effective means of connection between the micro and macro level heart research. Based on virtual heart model, doctor can study the physiological and pathological quantitative changes of myocardial conveniently in micro level and also test how the micro changes develop into the overall macro-change, which can contribute to improve the diagnosis and treatment of heart disease and the development of innovative medicines. In recent years, with the rapid development of biomedical engineering and other disciplines, there are a lot of new methods and new theories are introduced in these fields. The introduction of these methods and theories to virtual heart modeling areas can help us set up more complex and sophisticated model and sequentially in-depth understand the laws and the nature of cardiovascular system, which can eventually contribute to promote the further developing of forward and inverse problem of heart modeling studies.
In this paper, we will focus on the mathematical modeling of the anatomical structure and electrophysiology of the heart. Based on the original LFX virtual heart model, the first generation of virtual heart model of Zhejiang University, with comprehensive application of the Virtual Human technology, image processing, signal processing, parallel computing, three-dimensional scientific visualization and other technical means, we try to solve the key biological computing problems and set up the new generation of Cardiome-CN virtual heart electrophysiology model, which performance indicators is on the top of the international similar models and the related technology has an important influence on promoting the development of Cardiome project. The design and implementiaon of the parallel algorithms for ionic-channel based and bidomain model equations of myocardial excitation propagation can also be used for reference of other large-scale development of bio-computing technology. In this paper, the main research work and findings include:
1. Based on medical image data, physiological data samples, virtual human project dataset, we construct the database of virtual heart anatomical structure, including rabbit, dog, and human heart models. For the human heart model as an example, the spatial resolution of data structure is 0.33mm, which contains a complete atrial and ventricular structure, stratification of ventricular wall, myocardial fiber orientation, conduction pathway settings, organizations such as the definition of functional classification of heart tissue, etc. The calculation method, visualization grid of these models was also set up. The constructed human virtual heart model is one of the best virtual heart models in the world with detailed anatomy structure.
2. Based on experimental data of ion channels in cardiac myocytes, we pioneeringly set up the first cardiac myocyte action potential model library of dogs, human in the domestic, which contain the pacemaker cells, atrial myocytes, ventricular myocytes and other heterogeneous models with a complete cycle of calcium and excitation-contraction coupling mechanism. We carried out in-depth research on calculation and analysis for cell model. By using of non-standard finite difference method (NSFD) and operator DVODE, we accelerate cell model computational speed and sum up the expansion of the static and dynamic analysis methods, enriching the model means. The cell models have been used for simulation of heart failure, short-QT syndrome, Brugada syndrome-related diseases.
3. Based on MPI and OpenMP parallel computing protocol library, we design and implement parallel algorithms of the bidomain model, and use them to simulate the anisotropic spread of the cardiac excitation propagation. By coupling ionic channel cell model and bidomain reaction and diffusion model, we setup the one-dimensional structural conduction models to the three-dimensional anatomical conduction models and simulate the normal heart tissue conduction sequences. Then, we study the mechanism of reentrant arrhythmia by using these conduction models, which is international advanced level in the field of domestic virtual organ modeling.
4. Based on real physiological structures, a virtual human heart model, Cardiome-CN, has been constructed. This model can be used to simulate myocardial ischemia, a variety of arrhythmias, genetic variation, and ionic channel function diseases.
5. Based on the US virtual human project data, we build both male and female human torso models. Together with the Cardiome-CN model, we simulate the cardiac electric field distribution and body surface potential, calculate electrocardiogram and vectorcardiogram, study the the cellular mechanism of ECG morphological characteristics in arrhythmia condition.
In the future, virtual heart models have great potential applications not only in the biomedical field, bu also in clinical services, including interventional treatment, the individual custom database information and so on. Especially for the clinical diagnosis needs of atrial fibrillation, ventricular fibrillation and other arrhythmias diseases, the virtual heart model can help to enhance the application value of transcatheter interventional ablation techniques. Although it can not realize the real-time reconstruction of individual cases at the present, with the improvement of the calculation ability, the individual customized virtual heart model for clinical therapy application must become a reality in the future.
引文
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