Ultrasound-driven microbubbles, typically between 1 and 8 µm in diameter, are resonant scatterers that are employed as diagnostic contrast agents and emerging as potentiators of targeted therapies. Microbubbles are administered in populations whereby their radial dynamics – key to their effectiveness - are greatly affected by intrinsic (e.g. bubble size) and extrinsic (e.g. boundaries) factors. In this work, we aim to understand how two neighbouring microbubbles influence each other. We developed a finite element model of a system of two individual phospholipid-encapsulated microbubbles vibrating in proximity to each other to study the effect of inter-bubble distance on microbubble radial resonance response. For the case of two equal-sized and identical bubbles, each bubble exhibits a decrease between 7 and 10% in the frequency of maximum response ($f_{\mathit{MR}}$) and an increase in amplitude of maximum response ($A_{\mathit{MR}}$) by 9–11% as compared to its isolated response in free-space, depending on the bubble size examined. For a system of two unequal-sized microbubbles, the large bubble shows no significant change, however the smaller microbubble shows an increase in $f_{\mathit{MR}}$ by 7–11% and a significant decrease in $A_{\mathit{MR}}$ by 38–52%. Furthermore, in very close proximity the small bubble shows a secondary off-resonance peak at the corresponding $f_{\mathit{MR}}$ of its larger companion microbubble. Our work suggests that frequency-dependent microbubble response is greatly affected by the presence of another bubble, which has implications in both imaging and therapy applications. Furthermore, our work suggests a mechanism by which nanobubbles show significant off-resonance vibrations in the clinical frequency range, a behaviour that has been observed experimentally but heretofore unexplained.

超声驱动的微泡，通常直径在 1 到 8 µm 之间，是共振散射体，被用作诊断造影剂并成为靶向治疗的增强剂。微泡在人群中给药，因此它们的径向动力学 - 其有效性的关键 - 受到内在（例如气泡大小）和外在（例如边界）因素。在这项工作中，我们旨在了解两个相邻的微泡如何相互影响。我们开发了一个由两个单独的磷脂封装微泡组成的系统的有限元模型，这些微泡彼此靠近振动，以研究气泡间距离对微泡径向共振响应的影响。对于两个大小相同且相同的气泡，每个气泡的最大响应频率都降低了 7% 到 10%（$F_{\mathit{先生}}$) 和最大响应振幅的增加 (${\mathrm{一个}}_{\mathit{先生}}$) 与其在自由空间中的孤立响应相比提高了 9–11%，具体取决于所检查的气泡大小。对于两个大小不等的微泡系统，大气泡没有显着变化，但较小的微泡显示增加$F_{\mathit{先生}}$7-11%，显着减少${\mathrm{一个}}_{\mathit{先生}}$38–52%。此外，在非常接近的地方，小气泡在相应的位置显示出二次偏共振峰$F_{\mathit{先生}}$它较大的同伴微泡。我们的工作表明，频率相关的微泡响应受另一个气泡的存在的影响很大，这对成像和治疗应用都有影响。此外，我们的工作提出了一种机制，通过该机制纳米气泡在临床频率范围内显示出显着的偏共振振动，这种行为已通过实验观察到但迄今为止无法解释。