Finite element methods for the simulation of wave propagation in soft viscoelastic biotissue

研究用有限元法模拟粘弹性软生物组织中的波传播。材料将使用Voigt和麦克斯韦型本构律建模，空间离散化可以是连续或不连续的Galerkin或谱有限元法，时间离散化可以是经典的有限差分方案或不连续或连续的有限元法。本研究涉及应用数学、数值分析、生物力学和科学计算等学科，主要目的是：1.设计并网格化一系列人体胸部配置，包括肌肉、肺、骨骼、皮肤、脂肪和运动心脏，以建模和模拟从冠状动脉相关区域到胸部表面的剪切波传播。2.实现从上述技术中得出的各种数值方案，以确定在精度和速度权衡方面最合适的方法。该软件将使用现有的开源资源，并根据需要定制编码。这项工作是一个正在进行的多站点和跨学科项目的一部分，该项目研究了使用计算数学进行冠状动脉疾病非侵入性诊断的可行性。

Undertake research into finite element methods for the simulation of wave propagation in soft viscoelastic biotissue. The material will be modelled using Voigt and Maxwell type constitutive laws, the spatial discretization may be a continuous or discontinuous Galerkin or spectral finite element method, and the time discretization may be a classical finite difference scheme or a discontinuous or continuous finite element method. The research involves applied mathematics, numerical analysis, biomechanics and scientific computing, and its main aims are: 1. To design and mesh a family of human chest configurations, incorporating muscle, lung, bone, skin, fat, and a moving heart, for the purpose of modelling and simulating shear wave propagation from the areas associated with the coronary arteries to the chest surface. 2. To implement various numerical schemes, drawn from the techniques above, to determine the most suitable methods in terms of the accuracy and speed trade-off. This software will use existing open source resources and bespoke coding as necessary. This work is part of an ongoing multi-site and interdisciplinary project investigating the feasibility of non-invasive diagnosis of coronary artery disease using computational mathematics.