The transcranial Doppler (TCD) ultrasound is a method that uses a handheld low-frequency (2–2.5 MHz), pulsed Doppler phased array probe to measure blood velocity within the arteries located inside the brain. The problem with TCD lies in the low ultrasonic energy penetrating inside the brain through the skull, which leads to a low signal-to-noise ratio. This is due to several effects, including phase aberration, variations in the speed of sound in the skull, scattering, the acoustic impedance mismatch, and absorption of the three-layer medium constituted by soft tissues, the skull, and the brain. The goal of this article is to study the effect of transmission losses due to the acoustic impedance mismatch on the transmitted energies as a function of frequency. To do so, wave propagation was modeled from the ultrasonic transducer into the brain. This model calculates transmission coefficients inside the brain, leading to a frequency-dependent transmission coefficient for a given skin and bone thickness. This approach was validated experimentally by comparing the analytical results with measurements obtained from a bone phantom plate mimicking the skull. The average position error of the occurrence of the maximum amplitude between the experiment and analytical result was equivalent to a 0.06-mm error on the skin thickness given a fixed bone thickness. The similarity between the experimental and analytical results was also demonstrated by calculating correlation coefficients. The average correlation between the experimental and analytical results came out to be 0.50 for a high-frequency probe and 0.78 for a low-frequency probe. Further analysis of the simulation showed that an optimized excitation frequency can be chosen based on skin and bone thicknesses, thereby offering an opportunity to improve the image quality of TCD.

中文翻译：

---

经颅超声中骨-软组织界面处声阻抗不匹配的影响与频率的关系：模拟和 体外 实验研究

经颅多普勒超声（TCD）是一种使用手持式低频（2-2.5 MHz）脉冲多普勒相控阵探头测量大脑内部动脉内血流速度的方法。TCD的问题在于通过颅骨穿透大脑内部的超声能量较低，从而导致信噪比较低。这是由于几种影响，包括相差，颅骨中声速的变化，散射，声阻抗失配以及由软组织，颅骨和大脑构成的三层介质的吸收。本文的目的是研究由于声阻抗不匹配而引起的传输损耗对作为频率函数的传输能量的影响。为此，对从超声波换能器到大脑的波传播进行了建模。该模型计算大脑内部的传输系数，从而得出给定皮肤和骨骼厚度的频率相关的传输系数。通过将分析结果与从模仿头骨的骨幻影板获得的测量值进行比较，实验验证了该方法。在给定骨骼厚度的情况下，实验与分析结果之间出现最大振幅的平均位置误差相当于皮肤厚度的0.06-mm误差。通过计算相关系数也证明了实验结果与分析结果之间的相似性。实验和分析结果之间的平均相关性对于高频探头为0.50，对于低频探头为0.78。