Department of Numerical Analysis and Scientific Computing, Simula Research Laboratory, Norway.
Mathematical Science, Chalmers University of Technology, Gothenburg, Sweden.
Int J Numer Method Biomed Eng. 2019 Jan;35(1):e3152. doi: 10.1002/cnm.3152. Epub 2018 Oct 15.
Several cardiovascular diseases are caused from localised abnormal blood flow such as in the case of stenosis or aneurysms. Prevailing theories propose that the development is caused by abnormal wall shear stress in focused areas. Computational fluid mechanics have arisen as a promising tool for a more precise and quantitative analysis, in particular because the anatomy is often readily available even by standard imaging techniques such as magnetic resonance and computed tomography angiography. However, computational fluid mechanics rely on accurate initial and boundary conditions, which are difficult to obtain. In this paper, we address the problem of recovering high-resolution information from noisy and low-resolution physical measurements of blood flow (for example, from phase-contrast magnetic resonance imaging [PC-MRI]) using variational data assimilation based on a transient Navier-Stokes model. Numerical experiments are performed in both 3D (2D space and time) and 4D (3D space and time) and with pulsatile flow relevant for physiological flow in cerebral aneurysms. The results demonstrate that, with suitable regularisation, the model accurately reconstructs flow, even in the presence of significant noise.
几种心血管疾病是由局部异常血流引起的，例如狭窄或动脉瘤。流行的理论认为，这种发展是由聚焦区域的壁切应力异常引起的。计算流体力学已成为一种更精确和定量分析的有前途的工具，特别是因为解剖结构通常很容易通过标准成像技术（如磁共振和计算机断层血管造影）获得。然而，计算流体力学依赖于准确的初始和边界条件，而这些条件很难获得。在本文中，我们使用基于瞬态纳维-斯托克斯模型的变分数据同化方法，解决了从血流的噪声和低分辨率物理测量中（例如，从相衬磁共振成像 [PC-MRI]）恢复高分辨率信息的问题。在 3D（2D 空间和时间）和 4D（3D 空间和时间）中以及与大脑动脉瘤中生理流动相关的脉动流动中进行了数值实验。结果表明，在适当的正则化条件下，即使存在显著噪声，该模型也能准确地重建流动。
