受损心脏电力耦合问题高效数值模拟方法及其应用研究

Injury of the heart can lead to dysfunction, decline and even loss of pump blood function of the heart. It is urgent to study how to construct computable models and numerical methods for the accurate medical treatment of the injured heart. In this project, some researches on modeling, computation and application of the human atriums, ventricles, vessels, valves and stents of the injured heart are investigated. Based on the large deformation diffeomorphic metric mapping, the new image mapping method is proposed to obtain the high accuracy strain. Combining the action potential model of the cardiac myocytes with the monodomain electrical potential model of atriums and ventricles, the electro-mechanical coupling model of the injured heart is presented. The model is more consistent with electrophysiological characteristics. By using the stable schemes and the immersed boundary method without generating complex body fitted grids, the hybrid immersed boundary method is established to solve the FSI problems of the injured heart. On the basis of local grid generation method and the task equilibrium principle, the high efficient node-based finite method is proposed to solve the obtained electrophysiological model. Finally, a platform for the computation and application of electro-mechanical coupling problems of the injured heart is founded. In the platform, the key scientific problems in the numerical methods for the corresponding FSI and electro-mechanical coupling problems of the injured heart can be solved successfully. Based on the obtained results, an efficient, reliable and complete research framework for the modeling, computation, analysis and its application of the injured heart can be provided. The obtained achievements will promote the interdisciplinary researches between different fields, such as computational mathematics, image processing, computational cardiology and clinical medicine on some relevant issues.

心脏受损会导致其泵血功能紊乱、衰退甚至丧失，故急需为受损心脏的精准医疗提供可计算模型与数值方法支撑。本项目以受损心脏为研究对象，拟开展相应的建模、计算与应用研究：基于大形变微分同胚映射方法，建立适用于高精度应变计算的图像配准方法；基于心肌细胞动作电势模型与心房室单域电势模型，建立更符合电生理特性的受损心脏电力耦合模型；构造稳定、高效的数值格式，与无需生成复杂贴体网格的浸没边界方法结合，建立高效求解受损心脏流固耦合问题的混合浸没边界方法；基于局部网格生成方法与任务均衡原则，建立求解受损心脏电势模型的基于节点的高性能有限元方法。本项目将建立受损心脏电力耦合计算与应用平台，解决受损心脏流固耦合、电力耦合相关问题的数值模拟方法中的关键科学问题，为受损心脏的建模、计算、分析与应用提供高效、可靠、完整的研究框架。本项目的研究将推进计算数学与图像处理、计算心脏力学、临床医学等领域在相关问题上的交叉研究。

心血管疾病是我国居民首要致死和致残的原因，而心脏功能的好坏直接影响人类的健康与生命。由于心脏结构复杂，任何一部分受损，都可能导致其泵血功能紊乱、衰退甚至丧失，故急需为受损心脏的精准医疗提供可计算模型与数值方法支撑。本项目以受损心脏为研究对象，围绕相关的电力耦合问题开展了建模、计算与应用研究，建立了基于心脏电势传播模型与心脏流固耦合模型的受损心脏电力耦合模型，提出了求解该电力耦合模型的高性能数值方法，揭示了心脏相关部位受损后的力学特性。..项目组主要针对心肌本构参数识别问题提出了快速有效的机器学习方法，针对主动脉、心脏瓣膜等建模问题提出了基于医学图像的重构方法，针对主动脉、心脏瓣膜、心房室等流固耦合系统数值模拟问题提出了混合浸没边界（IB）方法，针对整数阶与分数阶心脏电势模型提出了高效数值模拟方法，最终建立了求解心脏电力耦合系统的数值模拟方法，并基于IBAMR建立了以混合IB方法为核心的受损心脏电力耦合计算平台——IB-NPUHeart计算平台。..本项目解决了受损心脏流固耦合、电力耦合相关问题的数值模拟方法中的关键科学问题，为受损心脏的建模、计算、分析与应用提供了高效、可靠、完整的研究框架，推进计算数学与计算心脏病学、临床医学等领域在相关问题上的交叉研究。

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