Electrophysiological modelling of hearts with diseases

仅在英国，就有大约150万人背负着心脏病的负担。不幸的是，发生心力衰竭的确切机制还知之甚少。该项目的目标包括设计更有效的算法，在细胞、组织和整个器官水平上对患有疾病的心脏的电行为进行数值模拟。目前，心脏活动的数值模拟在计算上是昂贵的，因为相对缓慢的机械过程和快得多的电过程在空间和时间尺度上存在着巨大的差距，必须加以解决。然而，并不是所有的电行为都是快速的，所以该项目将利用心脏渐近性的进展来开发一种简化的传播电信号的运动学描述。这些简化的模型将完全耦合到原始的偏微分方程组，用于慢速非线性动态场的时空演化。这将允许在整体数值格式中使用大得多的空间和时间步长，并为临床应用铺平道路，特别是为梗死后的冠状动脉灌注。所开发的模型将应用于感兴趣的具体问题，包括(1)肌细胞-成纤维细胞-胶原瘢痕之间的偶联；(2)瘢痕组织的形状分析及其对电信号传播的影响；(3)使用人类数据的个性化3D心脏模型。该项目将需要并将发展数学建模、偏微分方程的渐近和数值方法以及软件开发的知识，以及一些生理学的基本知识。

In the United Kingdom alone, there are about 1.5 million people living with the burden of a heart disease. Unfortunately, the exact mechanisms by which heart failure occurs are poorly understood. The goals of this project include designing more efficient algorithms for numerical simulation of the electrical behaviour of hearts with diseases on cell, tissue and on whole-organ levels. At present numerical simulations of cardiac activity are computationally expensive as a huge disparity in spatial and temporal scales between relatively slow mechanical and much faster electrical processes exists and must be resolved. However, not all electrical behaviour is fast so the project will exploit advances in cardiac asymptotics to develop a reduced kinematic description of propagating electrical signals. These reduced models will be fully coupled to the original partial-differential equations for spatio-temporal evolution of the slow nonlinear dynamic fields. This will allow significantly larger spatial and time steps to be used in monolithic numerical schemes and pave the way for clinical applications, particularly coronary perfusion post infarction. The models thus developed will be applied to specific problems of interest, including (1) coupling among myocyte-fibroblast-collagen scar;(2) shape analysis of scar tissue and their effects on electric signal propagation; (3) personalized 3D heart models using human data. The project will require and will develop knowledge of mathematical modelling, asymptotic and numerical methods for PDEs and software development and some basic knowledge of physiology.