Integrable Pressure Gradients via Harmonics-Based Orthogonal Projection
Integrable Pressure Gradients via Harmonics-Based Orthogonal Projection
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DOI：
10.1007/11505730_36
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发表时间：
2005-07
期刊：
影响因子：
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通讯作者：
Yuehuang Wang;A. Amini
中科院分区：
文献类型：
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作者：
Yuehuang Wang;A. Amini
在过去，已经开发了几种基于压力-泊松方程迭代解的方法用于从相衬磁共振（PC-MR）数据测量压力。本文讨论了一种非迭代的基于调和函数的正交投影方法，该方法可以使基于Navier-Stokes方程的压力测量值与积分路径无关，将基于Navier-Stokes方程的压力梯度用一系列正交基函数展开，然后投影到一个可积子空间上。然而，在投影步骤之前，设计了一个方案来消除血管边界处的不连续性，该方法被应用于从狭窄流的计算流体动力学（CFD）模拟获得的速度，并与通过CFD独立获得的压力进行比较。此外，在不同程度的狭窄和不同的流速的体外体模模型中测量的MR速度数据被用来测试该算法，并将结果与CFD模拟进行比较。从新方法获得的压力结果也进行了比较，通过迭代求解的压力泊松方程计算的压力。实验表明，该方法具有速度快，对噪声不敏感等优点。
In the past, several methods based on iterative solution of pressure-Poisson equation have been developed for measurement of pressure from phase-contrast magnetic resonance (PC-MR) data. In this paper, a non-iterative harmonics-based orthogonal projection method is discussed which can keep the pressures measured based on the Navier-Stokes equation independent of the path of integration.The gradient of pressure calculated with Navier-Stokes equation is expanded with a series of orthogonal basis functions, and is subsequently projected onto an integrable subspace. Before the projection step however, a scheme is devised to eliminate the discontinuity at the vessel boundaries.The approach was applied to velocities obtained from computational fluid dynamics (CFD) simulations of stenotic flow and compared with pressures independently obtained by CFD. Additionally, MR velocity data measured in in-vitro phantom models with different degree of stenoses and different flow rates were used to test the algorithm and results were compared with CFD simulations. The pressure results obtained from the new method were also compared with pressures calculated by an iterative solution to the pressure-Poisson equation. Experiments have shown that the proposed approach is faster and is less sensitive to noise.