Multiscale modelling as a tool to prescribe realistic boundary conditions for the study of surgical procedures.
Multiscale modelling as a tool to prescribe realistic boundary conditions for the study of surgical procedures.
复制标题
多尺度建模作为一种工具，为外科手术研究规定现实的边界条件。
作者：
K. Laganà;G. Dubini;F. Migliavacca;R. Pietrabissa;G. Pennati;A. Veneziani;A. Quarteroni
这项工作的动机是分析复杂解剖结构的血管区的详细3D模型的问题。它提出了一种方法，以规定现实的边界条件，以获得当地以及全球血液动力学的信息。发展了一种方法，该方法同时求解局部信息的Navier-Stokes方程和全局信息的非线性常微分方程系统。这是基于这样的原理，即通过使用有限元方法可以实现心血管区的解剖学上详细的3D模型。反过来，有限元方法需要特定的边界条件集。在这项工作中概述的方法是包括系统的常微分方程的边界条件集。这种多尺度方法首先应用于两个控制：（i）在一个简单的液压网络中的直管的3D模型和（ii）在心血管系统的集中参数模型中的直冠状血管的3D模型。得到的结果是非常接近的解决方案可用于管道的几何形状。本文还介绍了一个特定的血液动力学问题的方法的应用程序的初步结果：即在儿科心脏手术的系统到肺分流的流体动力学。
This work was motivated by the problems of analysing detailed 3D models of vascular districts with complex anatomy. It suggests an approach to prescribing realistic boundary conditions to use in order to obtain information on local as well as global haemodynamics. A method was developed which simultaneously solves Navier-Stokes equations for local information and a non-linear system of ordinary differential equations for global information. This is based on the principle that an anatomically detailed 3D model of a cardiovascular district can be achieved by using the finite element method. In turn the finite element method requires a specific boundary condition set. The approach outlined in this work is to include the system of ordinary differential equations in the boundary condition set. Such a multiscale approach was first applied to two controls: (i) a 3D model of a straight tube in a simple hydraulic network and (ii) a 3D model of a straight coronary vessel in a lumped-parameter model of the cardiovascular system. The results obtained are very close to the solutions available for the pipe geometry. This paper also presents preliminary results from the application of the methodology to a particular haemodynamic problem: namely the fluid dynamics of a systemic-to-pulmonary shunt in paediatric cardiac surgery.