Traumatic brain injury (TBI) studies on the living human brain are experimentally infeasible due to ethical reasons and the elastic properties of the brain degrade rapidly postmortem. We present a simulation approach that models ultrasound propagation in the human brain, while it is moving due to the complex shear shock wave deformation from a traumatic impact. Finite difference simulations can model ultrasound propagation in complex media such as human tissue. Recently, we have shown that the fullwave finite difference approach can also be used to represent displacements that are much smaller than the grid size, such as the motion encountered in shear wave propagation from ultrasound elastography. However, this subresolution displacement model, called impedance flow, was only implemented and validated for acoustical media composed of randomly distributed scatterers. Herein, we propose a generalization of the impedance flow method that describes the continuous subresolution motion of structured acoustical maps, and in particular of acoustical maps of the human brain. It is shown that the average error in simulating subresolution displacements using impedance flow is small when compared to the acoustical wavelength ( $\lambda $ /1702). The method is then applied to acoustical maps of the human brain with a motion that is imposed by the propagation of a shear shock wave. This motion is determined numerically with a custom piecewise parabolic method that is calibrated to ex vivo observations of shear shocks in the porcine brain. Then the fullwave simulation tool is used to model transmit-receive imaging sequences based on an L7-4 imaging transducer. The simulated radio frequency data are beamformed using a conventional delay-and-sum method and a normalized cross-correlation method designed for shock wave tracking is used to determine the tissue motion. This overall process is an in silico reproduction of the experiments that were previously performed to observe shear shock waves in fresh porcine brain. It is shown that the proposed generalized impedance flow method accurately captures the shear wave motion in terms of the wave profile, shock front characteristics, odd harmonic spectrum generation, and acceleration at the shear shock front. We expect that this approach will lead to improvements in image sequence design that takes into account the aberration and multiple reflections from the brain and in the design of tracking algorithms that can more accurately capture the complex brain motion that occurs during a traumatic impact. These methods of modeling ultrasound propagation in moving media can also be applied to other displacements, such as those generated by shear wave elastography or blood flow.

中文翻译：

---

超声在运动大脑中的传播模型：在剪切冲击波和颅脑外伤中的应用

由于道德原因，对活人脑进行颅脑外伤（TBI）的研究在实验上是不可行的，并且死后大脑的弹性会迅速下降。我们提出了一种模拟方法，该方法可以模拟超声波在人脑中的传播，而超声波在运动中是由于创伤冲击引起的复杂的剪切冲击波变形。有限差分仿真可以模拟超声在复杂介质（例如人体组织）中的传播。最近，我们已经表明，全波有限差分方法也可以用于表示比网格尺寸小得多的位移，例如在超声弹性成像的剪切波传播中遇到的运动。但是，这种亚分辨率位移模型称为阻抗流，仅对由随机分布的散射体组成的声学介质实施和验证。在此，我们提出了一种阻抗流方法的一般化方法，该方法描述了结构化声学图，尤其是人脑声学图的连续亚分辨率运动。结果表明，与声波波长相比，使用阻抗流模拟亚分辨率位移的平均误差很小（ $ \ lambda $ / 1702）。该方法然后通过剪切激波的传播施加的运动应用于人脑的声学图。该运动是通过自定义分段抛物线法数值确定的，该方法已校准为离体猪脑中的剪切电击的观察。然后，将全波仿真工具用于基于L7-4成像换能器的收发成像序列建模。使用常规的延迟和求和方法对模拟的射频数据进行波束成形，并使用为冲击波跟踪而设计的归一化互相关方法来确定组织运动。这个整体过程是在计算机上复制以前在新鲜猪脑中观察剪切冲击波的实验。结果表明，所提出的广义阻抗流动方法可以准确地捕获横波运动，包括波轮廓，激波锋面特征，奇次谐波谱的产生以及横波激波前沿的加速度。我们期望这种方法将导致图像序列设计的改进，该设计考虑到大脑的像差和多次反射，以及跟踪算法的设计，这些算法可以更准确地捕获在创伤性撞击中发生的复杂的大脑运动。这些对移动介质中的超声波传播进行建模的方法也可以应用于其他位移，例如由剪切波弹性成像或血流产生的位移。