In the framework of cardiac electrophysiology for the human heart, we apply multipatch NURBS-based Isogeometric Analysis for the space discretization of the Monodomain model. Isogeometric Analysis (IGA) is a technique for the solution of Partial Differential Equations (PDEs) that facilitates encapsulating the exact representation of the computational geometry by using basis functions with high-order continuity. IGA features very small numerical dissipation and dispersion when compared to other methods for the solution of PDEs. The use of multiple patches allows to overcome the conventional limitations of single patch IGA, thanks to the gained flexibility in the design of the computational domain, especially when its representation is quite involved as in bioengineering applications. We propose two algorithms for the preprocessing of CAD models of complex surface and volumetric NURBS geometries with cavities, such as atria and ventricles: our purpose is to obtain geometrically and parametrically conforming NURBS multipatch models starting from CAD models. We employ those algorithms for the construction of an IGA realistic representation of a human heart. We apply IGA for the discretization of the Monodomain equation, which describes the evolution of the cardiac action potential in space and time at the tissue level. This PDE is coupled with suitable microscopic models to define the behavior at cellular scale: the Courtemanche–Ramirez–Nattel model for the atrial simulation, and the Luo–Rudy model for the ventricular one. Numerical simulations on realistic human atria and ventricle geometries are carried out, obtaining accurate and smooth excitation fronts by combining IGA with the multipatch approach for the geometrical representation of the computational domains, either surfaces for the atria or solids for the ventricles.

在人类心脏的心脏电生理学框架中，我们将基于NURBS的多补丁等距分析应用于Monodomain模型的空间离散化。等轴测分析（IGA）是一种用于解决偏微分方程（PDE）的技术，该技术有助于通过使用具有高阶连续性的基函数来封装计算几何的精确表示。与其他解决PDE的方法相比，IGA具有非常小的数值耗散和色散。由于在计算领域的设计中获得了灵活性，尤其是当它的表示形式像在生物工程应用中一样涉及时，使用多个补丁可以克服单个补丁IGA的常规限制。我们提出了两种算法来预处理具有空腔（例如心房和心室）的复杂曲面和体积NURBS几何形状的CAD模型：我们的目的是从CAD模型开始获得几何和参数一致的NURBS多面体模型。我们采用这些算法来构建人心脏的IGA逼真表示。我们将IGA应用于Monodomain方程的离散化，该方程描述了组织水平上时空动作的心脏动作电位的演变。该PDE结合合适的微观模型来定义细胞尺度的行为：用于心房模拟的Courtemanche-Ramirez-Nattel模型和用于心室模拟的Luo-Rudy模型。对真实的人心房和心室几何形状进行了数值模拟，