Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50011, USA.
Ultrasonics. 2011 Feb;51(2):115-22. doi: 10.1016/j.ultras.2010.06.005. Epub 2010 Jul 15.
Medical ultrasound has shown great potential as a minimally invasive therapy technique. It can be used in areas such as histotripsy, thermal ablation, and administering medication. The success of these therapies is improved by the cavitation of small microbubbles, and often it is useful to know which bubbles might provide the most effective therapy. When using therapies based on stable cavitation, the optimal bubble size is approximately given by R(0)≅3MHzμm/f(0)(lin). However, a similar expression is not available for therapies involving inertial cavitation. Therefore, the goal of our study was to develop an approximate expression relating the initial size of the bubble that resulted in the maximum response to the ultrasound operating frequency and pressure of the ultrasound wave when inertial cavitation is expected. The study was conducted by simulating the response of air bubbles in water to linearly propagating sine waves using the Gilmore-Akulichev formulation to solve for the bubble response. The frequency of the sine wave varied from 0.5 to 5MHz while the amplitude of the sine wave varied from 0.0001 to 5MPa. The optimal initial size for a particular frequency of excitation and amplitude, which is normally only established for stable cavitation, was defined in the study as the initial bubble size that resulted in the maximum bubble expansion prior to bubble radius dropping below its initial radius. A fit over pressure and frequency then yielded that the optimal size was approximately given by R(optimal)=(0.0327f(2)+0.0679f+16.5P(2))(-0.5) where R(optimal) is in μm, f is the frequency of the ultrasound wave in MHz, and P the pressure amplitude of the ultrasound wave in MPa.
医学超声已显示出作为一种微创治疗技术的巨大潜力。它可以用于组织破碎、热消融和给药等领域。这些治疗方法的成功得益于小微泡的空化作用，因此通常需要知道哪种微泡可能提供最有效的治疗效果。在使用基于稳定空化的治疗方法时，最佳的气泡尺寸大约由 R(0)≅3MHzμm/f(0)(lin)给出。然而，对于涉及惯性空化的治疗方法，类似的表达式并不适用。因此，我们的研究目标是开发一个近似表达式，将产生最大响应的气泡初始尺寸与预计发生惯性空化时的超声工作频率和压力联系起来。该研究通过使用 Gilmore-Akulichev 公式模拟水中气泡对线性传播正弦波的响应来进行，该公式用于求解气泡的响应。正弦波的频率从 0.5MHz 到 5MHz 变化，而正弦波的振幅从 0.0001MPa 到 5MPa 变化。在研究中，对于特定频率的激励和振幅，通常仅在稳定空化的情况下确定最佳初始尺寸，定义为导致气泡在半径降至初始半径以下之前最大膨胀的初始气泡尺寸。然后对压力和频率进行拟合，得到最佳尺寸大约由 R(optimal)=(0.0327f(2)+0.0679f+16.5P(2))(-0.5)给出，其中 R(optimal)以 μm 为单位，f 是超声波的频率（MHz），P 是超声波的压力振幅（MPa）。
