Lu Minhua, Wu Dan, Lin Wan-hua, Li Weifang, Zhang Heye, Huang WenHua
Key Lab for Health Informatics of the Chinese Academy of Sciences, Shenzhen Advanced Institutes of Technology, Chinese Academic of Sciences, Shenzhen, China.
Biomed Eng Online. 2014 Feb 12;13:15. doi: 10.1186/1475-925X-13-15.
Model-based reconstruction algorithms have shown potentials over conventional strain-based methods in quasi-static elastographic image by using realistic finite element (FE) or bio-mechanical model constraints. However, it is still difficult to properly handle the discrepancies between the model constraint and ultrasound data, and the measurement noise.
In this paper, we explore the usage of Kalman filtering algorithm for the estimation of strain imaging in quasi-static ultrasound elastography. The proposed strategy formulates the displacement distribution through biomechanical models, and the ultrasound-derived measurements through observation equations. Through this filtering strategy, the discrepancies are quantitatively modelled as one Gaussian white noise, and the measurement noise of ultrasound data is modelled as another independent Gaussian white noise. The optimal estimation of kinematic functions, i.e. the full displacement and velocity field, are computed through this Kalman filter. Then the strain images can be easily calculated from the estimated displacement field.
The accuracy and robustness of our proposed framework is first evaluated in synthetic data in controlled conditions, and the performance of this framework is then evaluated in the real data collected from elastography phantoms and patients with favourable results.
The potential of our algorithm is to provide the distribution of mechanically meaningful strain under a proper biomechanical model constraint. We address the model-data discrepancy and measurement noise by introducing process noise and measurement noise in our framework, and then the mechanically meaningful strain is estimated through the Kalman filter in the minimum mean square error (MMSE) sense.
基于模型的重建算法通过使用逼真的有限元（FE）或生物力学模型约束，在准静态弹性成像中已显示出优于传统基于应变方法的潜力。然而，仍然难以妥善处理模型约束与超声数据之间的差异以及测量噪声。
在本文中，我们探索了卡尔曼滤波算法在准静态超声弹性成像应变估计中的应用。所提出的策略通过生物力学模型来制定位移分布，并通过观测方程来制定超声衍生测量值。通过这种滤波策略，将差异定量建模为一个高斯白噪声，将超声数据的测量噪声建模为另一个独立的高斯白噪声。通过此卡尔曼滤波器计算运动学函数（即全位移和速度场）的最优估计值。然后可以从估计的位移场轻松计算出应变图像。
首先在受控条件下的合成数据中评估了我们提出的框架的准确性和鲁棒性，然后在从弹性成像体模和患者收集的真实数据中评估了该框架的性能，结果良好。
我们算法的潜力在于在适当的生物力学模型约束下提供具有机械意义的应变分布。我们通过在框架中引入过程噪声和测量噪声来解决模型 - 数据差异和测量噪声问题，然后通过卡尔曼滤波器在最小均方误差（MMSE）意义下估计具有机械意义的应变。
