基于速度测量误差的加权最小二乘四维流场MRI压力估计
4D-Flow MRI Pressure Estimation Using Velocity Measurement-Error based Weighted Least-Squares
摘要：
本文介绍了一种基于加权最小二乘（WLS）压力积分的四维流磁共振成像（MRI）压力重建方法。压力梯度由速度场计算，速度误差由不可压缩流的速度发散估计。压力梯度误差通过Navier-Stokes动量方程传播速度误差来估计。基于压力梯度误差生成权矩阵，然后用于压力重构。使用合成速度场以及使用体外4D流动MRI测量的Poiffille流来演示和分析压力重建方法。所提出的WLS方法的性能进行了比较的方法求解的压力泊松方程，这一直是在以前的研究中使用的主要方法。误差分析表明，该方法对速度测量误差具有较强的鲁棒性。压力结果的改善被认为是更显着的情况下，空间变化的速度误差水平，减少误差范围从50%到超过200%。最后，将该方法应用于患者特定脑动脉瘤中的流动。使用粒子跟踪测速法（PTV）和摇箱法（STB）收集的体外流量数据以及使用4D-流量MRI获得的体内流量测量值进行验证。与Poisson方程相比，WLS计算的压力与流动结构更一致，并且体内和体外数据之间显示出更好的一致性。这些结果表明，WLS方法的实用性，以获得可靠的压力场从临床流量测量数据。
英文摘要：
This work introduces a 4D-flow magnetic resonance imaging (MRI) pressure reconstruction method which employs weighted least-squares (WLS) for pressure integration. Pressure gradients are calculated from the velocity fields, and velocity errors are estimated from the velocity divergence for incompressible flow. Pressure gradient errors are estimated by propagating the velocity errors through Navier-Stokes momentum equation. A weight matrix is generated based on the pressure gradient errors, then employed for pressure reconstruction. The pressure reconstruction method was demonstrated and analyzed using synthetic velocity fields as well as Poiseuille flow measured using in vitro 4D-flow MRI. Performance of the proposed WLS method was compared to the method of solving the pressure Poisson equation which has been the primary method used in the previous studies. Error analysis indicated that the proposed method is more robust to velocity measurement errors. Improvement on pressure results was found to be more significant for the cases with spatially-varying velocity error level, with reductions in error ranging from 50% to over 200%. Finally, the method was applied to flow in a patient-specific cerebral aneurysm. Validation was performed with in vitro flow data collected using Particle Tracking Velocimetry (PTV) and Shake the Box (STB) method, and in vivo flow measurement obtained using 4D-flow MRI. Pressure calculated by WLS, as opposed to the Poisson equation, was more consistent with the flow structures and showed better agreement between the in vivo and in vitro data. These results suggest the utility of WLS method to obtain reliable pressure field from clinical flow measurement data.
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