Department of Medical Physics, University of Wisconsin, Madison, WI, USA.
Med Phys. 2012 Apr;39(4):1779-92. doi: 10.1118/1.3691905.
Accurate cardiac deformation analysis for cardiac displacement and strain imaging over time requires Lagrangian description of deformation of myocardial tissue structures. Failure to couple the estimated displacement and strain information with the correct myocardial tissue structures will lead to erroneous result in the displacement and strain distribution over time.
Lagrangian based tracking in this paper divides the tissue structure into a fixed number of pixels whose deformation is tracked over the cardiac cycle. An algorithm that utilizes a polar-grid generated between the estimated endocardial and epicardial contours for cardiac short axis images is proposed to ensure Lagrangian description of the pixels. Displacement estimates from consecutive radiofrequency frames were then mapped onto the polar grid to obtain a distribution of the actual displacement that is mapped to the polar grid over time.
A finite element based canine heart model coupled with an ultrasound simulation program was used to verify this approach. Segmental analysis of the accumulated displacement and strain over a cardiac cycle demonstrate excellent agreement between the ideal result obtained directly from the finite element model and our Lagrangian approach to strain estimation. Traditional Eulerian based estimation results, on the other hand, show significant deviation from the ideal result. An in vivo comparison of the displacement and strain estimated using parasternal short axis views is also presented.
Lagrangian displacement tracking using a polar grid provides accurate tracking of myocardial deformation demonstrated using both finite element and in vivo radiofrequency data acquired on a volunteer. In addition to the cardiac application, this approach can also be utilized for transverse scans of arteries, where a polar grid can be generated between the contours delineating the outer and inner wall of the vessels from the blood flowing though the vessel.
准确的心脏变形分析需要对心肌组织结构的变形进行拉格朗日描述，以便对心脏位移和应变进行成像。如果不能将估计的位移和应变信息与正确的心肌组织结构相匹配，那么在随时间推移的位移和应变分布中就会出现错误的结果。
本文中的基于拉格朗日的跟踪将组织结构分为固定数量的像素，这些像素的变形在心脏周期内被跟踪。提出了一种利用估计的心内膜和心外膜轮廓之间生成的极坐标网格的算法，以确保像素的拉格朗日描述。然后将来自连续射频帧的位移估计值映射到极坐标网格上，以获得实际位移的分布，该分布随时间映射到极坐标网格上。
使用基于有限元的犬心模型和超声模拟程序验证了这种方法。对一个心动周期内累积位移和应变的节段分析表明，直接从有限元模型获得的理想结果与我们的应变估计拉格朗日方法之间存在极好的一致性。另一方面，传统的基于欧拉的估计结果显示出与理想结果的显著偏差。还提出了一种基于胸骨旁短轴视图的位移和应变估计的体内比较。
使用极坐标网格的拉格朗日位移跟踪通过对志愿者的射频数据进行的有限元和体内比较，展示了心肌变形的准确跟踪。除了心脏应用外，这种方法还可以用于动脉的横切面扫描，在这种情况下，可以在血管的轮廓之间生成极坐标网格，这些轮廓描绘了血管的内外壁以及流经血管的血液。
