Numerical methods for analysing physiological flows and cardiac electrophysiology

数值模拟在生理系统和病理分析以及生物医学治疗的发展中已成为越来越重要的工具。来自连续介质力学的技术和模型是传统工程的一部分，现在逐渐被引入医学，考虑到生命系统的相对复杂性，通常需要开发新的模拟方法。目前的建议正是沿着这一目标发展模型和数值技术，适用于两个生物医学领域，即生理流动和心脏电生理学。所谓生理流动，我们指的是血液流动，也包括气道中的流动和气溶胶传播，这与我们之前在这两个领域的工作有关。这些领域的共性问题，即用时变非线性偏微分方程模拟多个时空尺度的现象，需要一种共性的模拟方法，即在空间和时间上控制误差水平的自适应数值方法。我们的研究计划集中在这些数值方法的发展，但也包括建模方面，特别是改进我们目前的欧拉气溶胶模型。拟议的研究计划最终将导致从医学图像分割=>患者特异性几何=>物理模型=>数值模拟=>可视化过程的集成分析工具。

Numerical simulations are becoming an increasingly important tool in the analysis of physiological systems and pathologies, and the development of biomedical treatment. Techniques and models from continuum mechanics and that were part of traditional engineering are now progressively introduced in medicine, often requiring the development of new simulation methods given the relative complexity of living systems. The current proposal works precisely along this objective of developing models and numerical techniques that apply to two biomedical fields, namely to physiological flows and to cardiac electrophysiology. By physiological flows, we mean blood flows but also flows and aerosol propagation in airways, linking to our previous work in these two areas. A commonality of problems in these fields, i.e. phenomena with several spatial and temporal scales modelled with time-dependent nonlinear partial differential equations, requires a commonality of simulation methods, i.e. adaptative numerical methods with a controlled level of error in space and time. Our research program concentrates on the development of such numerical methods but also includes modelling aspects, in particular for improving our current Eulerian aerosol model. The proposed research program will eventually lead to integrated analysis tools for the process from medical image segmentation => patient-specific geometry => physical model => numerical simulations => visualization.