Parker Kevin J, Ormachea Juvenal, Zvietcovich Fernando, Castaneda Benjamin
Department of Electrical and Computer Engineering, University of Rochester, Hopeman Building, Box 270126, Rochester, NY 14627, USA.
Phys Med Biol. 2017 Feb 7;62(3):1046-1061. doi: 10.1088/1361-6560/aa5201. Epub 2017 Jan 12.
The determination of shear wave speed is an important subject in the field of elastography, since elevated shear wave speeds can be directly linked to increased stiffness of tissues. MRI and ultrasound scanners are frequently used to detect shear waves and a variety of estimators are applied to calculate the underlying shear wave speed. The estimators can be relatively simple if plane wave behavior is assumed with a known direction of propagation. However, multiple reflections from organ boundaries and internal inhomogeneities and mode conversions can create a complicated field in time and space. Thus, we explore the mathematics of multiple component shear wave fields and derive the basic properties, from which efficient estimators can be obtained. We approach this problem from the historic perspective of reverberant fields, a conceptual framework used in architectural acoustics and related fields. The framework can be recast for the alternative case of shear waves in a bounded elastic media, and the expected value of displacement patterns in shear reverberant fields are derived, along with some practical estimators of shear wave speed. These are applied to finite element models and phantoms to illustrate the characteristics of reverberant fields and provide preliminary confirmation of the overall framework.
剪切波速度的测定是弹性成像领域的一个重要课题，因为剪切波速度升高可直接与组织硬度增加相关联。磁共振成像（MRI）和超声扫描仪经常用于检测剪切波，并且应用了各种估计器来计算潜在的剪切波速度。如果假设平面波行为且传播方向已知，估计器可能相对简单。然而，来自器官边界和内部不均匀性的多次反射以及模式转换会在时间和空间上产生复杂的场。因此，我们探索多分量剪切波场的数学原理并推导其基本特性，从中可以获得有效的估计器。我们从混响场的历史角度来处理这个问题，混响场是建筑声学及相关领域中使用的一个概念框架。该框架可以针对有界弹性介质中剪切波的替代情况进行重塑，推导剪切混响场中位移模式的期望值以及一些剪切波速度的实用估计器。这些被应用于有限元模型和体模，以说明混响场的特性并为整个框架提供初步确认。
