Medical-image-based aorta modeling with zero-stress-state estimation
Medical-image-based aorta modeling with zero-stress-state estimation
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DOI：
10.1007/s00466-019-01669-4
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发表时间：
2019-02
影响因子：
4.1
通讯作者：
Takafumi Sasaki;K. Takizawa;T. Tezduyar
中科院分区：
文献类型：
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作者：
Takafumi Sasaki;K. Takizawa;T. Tezduyar
因为在患者特定动脉流体-结构相互作用计算中使用的基于医学图像的几何形状不是来自动脉的零应力状态（ZSS），所以我们需要估计计算中所需的ZSS。对于具有复杂几何形状的动脉（例如主动脉），任务变得更具挑战性。在我们前面介绍的方法中，估计是基于动脉壁的T样条离散化，并且是基于积分点的ZSS（IPBZSS）的形式。T样条离散化能够处理复杂的动脉几何形状，例如具有分支的主动脉模型，同时保留等几何离散化的期望特征。使用等几何离散化的高阶基函数，我们可以实现与线性基函数类似的精度水平，但使用更大尺寸和更少的元素。此外，高阶基函数允许在元素内表示更复杂的形状。IPBZSS是ZSS的方便表示，因为使用等几何离散化，特别是T样条离散化，在积分点指定条件比在控制点上施加条件更直接。该方法有两个主要组成部分。1.迭代技术，其开始于计算的ZSS初始猜测，用于计算IPBZSS，使得当施加给定的压力负载时，匹配基于医学图像的目标形状。2.一个设计过程，这是基于Kirchhoff-Love壳模型的动脉，用于计算ZSS初始猜测。在这里，我们通过引入一个新的ZSS初始猜测的设计过程来增加该方法的范围和鲁棒性。新的设计程序有两个特点。(a)IPB壳状坐标系，可将设计范围扩大到计算空间中的一般参数化。(b)基于Kirchhoff-Love壳模型的法向力平衡的解析解，该模型对设计参数施加了适当的约束。这提高了估计精度，这又提高了迭代的鲁棒性和收敛速度。为了展示ZSS初始猜测的新设计过程如何执行，我们首先用直管和Y形管进行了3D测试计算。然后，我们提出了一个三维计算的目标几何形状是来自医学图像的人体主动脉，我们包括在模型中的分支。
Because the medical-image-based geometries used in patient-specific arterial fluid–structure interaction computations do not come from the zero-stress state (ZSS) of the artery, we need to estimate the ZSS required in the computations. The task becomes even more challenging for arteries with complex geometries, such as the aorta. In a method we introduced earlier the estimate is based on T-spline discretization of the arterial wall and is in the form of integration-point-based ZSS (IPBZSS). The T-spline discretization enables dealing with complex arterial geometries, such as an aorta model with branches, while retaining the desirable features of isogeometric discretization. With higher-order basis functions of the isogeometric discretization, we may be able to achieve a similar level of accuracy as with the linear basis functions, but using larger-size and fewer elements. In addition, the higher-order basis functions allow representation of more complex shapes within an element. The IPBZSS is a convenient representation of the ZSS because with isogeometric discretization, especially with T-spline discretization, specifying conditions at integration points is more straightforward than imposing conditions on control points. The method has two main components. 1. An iteration technique, which starts with a calculated ZSS initial guess, is used for computing the IPBZSS such that when a given pressure load is applied, the medical-image-based target shape is matched. 2. A design procedure, which is based on the Kirchhoff–Love shell model of the artery, is used for calculating the ZSS initial guess. Here we increase the scope and robustness of the method by introducing a new design procedure for the ZSS initial guess. The new design procedure has two features. (a) An IPB shell-like coordinate system, which increases the scope of the design to general parametrization in the computational space. (b) Analytical solution of the force equilibrium in the normal direction, based on the Kirchhoff–Love shell model, which places proper constraints on the design parameters. This increases the estimation accuracy, which in turn increases the robustness of the iterations and the convergence speed. To show how the new design procedure for the ZSS initial guess performs, we first present 3D test computations with a straight tube and a Y-shaped tube. Then we present a 3D computation where the target geometry is coming from medical image of a human aorta, and we include the branches in the model.