论文标题
PDE引起的运动帧连接2D中庭的心脏电气传播地图集
PDE-induced connection of moving frames for the Atlas of the cardiac electric propagation on 2D atrium
论文作者
论文摘要
作为针对部分微分方程的移动帧的另一个关键实现，本文提出了一种新颖的数值方案，该方案是通过将每个网格点的三个正交单元向量对准沿波传播的方向，以构建一个有组织的框架集，称为A连接。这种连接根据（1）初始点，（2）波的类型和（3）具有传导性能的域的形状来表征波传播的几何形状。再次区分了构造的连接，以得出与波传播中重要的物理和生物学意义相对应的正顺序碱基的riemann曲率张量。作为一种实际应用，提出的方案被应用于扩散反应方程，以获得带有心脏纤维的中庭的地图集，或带有连接的几何图，以对心脏动作电位传播的定量和定性分析，这可能有助于临床和外科手术纤维化的临床和外科手术计划。
As another critical implementation of moving frames for partial differential equations, this paper proposes a novel numerical scheme by aligning one of three orthogonal unit vectors at each grid point along the direction of a wave propagation to construct an organized set of frames, called a connection. This connection characterizes the geometry of wave propagation depending on (1) the initial point, (2) type of wave, and (3) shape of the domain with conduction properties. The constructed connection is differentiated again to derive the Riemann curvature tensor of orthonormal bases corresponding to important physical and biological meanings in wave propagation. As a practical application, the proposed scheme is applied to diffusion-reaction equations to obtain the Atlas, or a geometric map with connections, of an atrium with cardiac fibers, for the quantitative and qualitative analysis of cardiac action potential propagation, which could contribute to the clinical and surgical planning of atrial fibrillation.
