Department of Physics, Ryerson University, Toronto, Canada; Institute for Biomedical Engineering, Science and Technology (iBEST) a partnership between Ryerson University and St. Michael's Hospital, Toronto, Ontario, Canada.
Department of Physics, Ryerson University, Toronto, Canada; Institute for Biomedical Engineering, Science and Technology (iBEST) a partnership between Ryerson University and St. Michael's Hospital, Toronto, Ontario, Canada.
Ultrason Sonochem. 2020 Sep;66:105070. doi: 10.1016/j.ultsonch.2020.105070. Epub 2020 Mar 29.
This study presents the fundamental equations governing the pressure dependent disipation mechanisms in the oscillations of coated bubbles. A simple generalized model (GM) for coated bubbles accounting for the effect of compressibility of the liquid is presented. The GM was then coupled with nonlinear ODEs that account for the thermal effects. Starting with mass and momentum conservation equations for a bubbly liquid and using the GM, nonlinear pressure dependent terms were derived for power dissipation due to thermal damping (Td), radiation damping (Rd) and dissipation due to the viscosity of liquid (Ld) and coating (Cd). The pressure dependence of the dissipation mechanisms of the coated bubble have been analyzed. The dissipated energies were solved for uncoated and coated 2-20 μm in bubbles over a frequency range of 0.25f-2.5f (f is the bubble resonance) and for various acoustic pressures (1 kPa-300 kPa). Thermal effects were examined for air and C3F8 gas cores. In the case of air bubbles, as pressure increases, the linear thermal model looses accuracy and accurate modeling requires inclusion of the full thermal model. However, for coated C3F8 bubbles of diameter 1-8 μm, which are typically used in medical ultrasound, thermal effects maybe neglected even at higher pressures. For uncoated bubbles, when pressure increases, the contributions of Rd grow faster and become the dominant damping mechanism for pressure dependent resonance frequencies (e.g. fundamental and super harmonic resonances). For coated bubbles, Cd is the strongest damping mechanism. As pressure increases, Rd contributes more to damping compared to Ld and Td. For coated bubbles, the often neglected compressibility of the liquid has a strong effect on the oscillations and should be incorporated in models. We show that the scattering to damping ratio (STDR), a measure of the effectiveness of the bubble as contrast agent, is pressure dependent and can be maximized for specific frequency ranges and pressures.
本研究提出了控制涂层气泡振动中压力相关耗散机制的基本方程。提出了一个简单的考虑液体可压缩性影响的涂层气泡广义模型 (GM)。然后，GM 与考虑热效应的非线性常微分方程耦合。从考虑热效应的多相流方程出发，利用 GM，推导了由于热阻尼 (Td)、辐射阻尼 (Rd) 和液体 (Ld) 和涂层 (Cd) 粘性耗散而导致的非线性压力相关项。分析了涂层气泡的耗散机制的压力依赖性。在频率范围为 0.25f-2.5f（f 为气泡共振频率）和各种声压（1kPa-300kPa）下，求解了未涂层和涂层 2-20μm 气泡的耗散能量。研究了空气和 C3F8 气体核的热效应。在空气气泡的情况下，随着压力的增加，线性热模型的准确性降低，需要包括完整的热模型来进行精确建模。然而，对于典型用于医学超声的直径为 1-8μm 的涂覆 C3F8 气泡，即使在较高的压力下，热效应也可能被忽略。对于未涂层气泡，随着压力的增加，Rd 的贡献增长更快，成为压力相关共振频率（例如基频和超谐波共振）的主要阻尼机制。对于涂层气泡，Cd 是最强的阻尼机制。随着压力的增加，Rd 对阻尼的贡献比对 Ld 和 Td 的贡献更大。对于涂层气泡，通常被忽略的液体可压缩性对振动有很大影响，应将其纳入模型中。我们表明，作为对比剂的气泡的散射到阻尼比 (STDR)，是压力相关的，可以在特定的频率范围和压力下最大化。
