Doinikov Alexander A, Sheeran Paul S, Bouakaz Ayache, Dayton Paul A
Inserm U930, Université François Rabelais, Tours 37044, France.
Joint Department of Biomedical Engineering, The University of North Carolina and North Carolina State University, Chapel Hill, North Carolina 27599.
Med Phys. 2014 Oct;41(10):102901. doi: 10.1118/1.4894804.
Perfluorocarbon (PFC) microdroplets, called phase-change contrast agents (PCCAs), are a promising tool in ultrasound imaging and therapy. Interest in PCCAs is motivated by the fact that they can be triggered to transition from the liquid state to the gas state by an externally applied acoustic pulse. This property opens up new approaches to applications in ultrasound medicine. Insight into the physics of vaporization of PFC droplets is vital for effective use of PCCAs and for anticipating bioeffects. PCCAs composed of volatile PFCs (with low boiling point) exhibit complex dynamic behavior: after vaporization by a short acoustic pulse, a PFC droplet turns into a vapor bubble which undergoes overexpansion and damped radial oscillation until settling to a final diameter. This behavior has not been well described theoretically so far. The purpose of our study is to develop an improved theoretical model that describes the vaporization dynamics of volatile PFC droplets and to validate this model by comparison with in vitro experimental data.
The derivation of the model is based on applying the mathematical methods of fluid dynamics and thermodynamics to the process of the acoustic vaporization of PFC droplets. The used approach corrects shortcomings of the existing models. The validation of the model is carried out by comparing simulated results with in vitro experimental data acquired by ultrahigh speed video microscopy for octafluoropropane (OFP) and decafluorobutane (DFB) microdroplets of different sizes.
The developed theory allows one to simulate the growth of a vapor bubble inside a PFC droplet until the liquid PFC is completely converted into vapor, and the subsequent overexpansion and damped oscillations of the vapor bubble, including the influence of an externally applied acoustic pulse. To evaluate quantitatively the difference between simulated and experimental results, the L2-norm errors were calculated for all cases where the simulated and experimental results are compared. These errors were found to be in the ranges of 0.043-0.067 and 0.037-0.088 for OFP and DFB droplets, respectively. These values allow one to consider agreement between the simulated and experimental results as good. This agreement is attained by varying only 2 of 16 model parameters which describe the material properties of gaseous and liquid PFCs and the liquid surrounding the PFC droplet. The fitting parameters are the viscosity and the surface tension of the surrounding liquid. All other model parameters are kept invariable.
The good agreement between the theoretical and experimental results suggests that the developed model is able to correctly describe the key physical processes underlying the vaporization dynamics of volatile PFC droplets. The necessity of varying the parameters of the surrounding liquid for fitting the experimental curves can be explained by the fact that the parts of the initial phospholipid shell of PFC droplets remain on the surface of vapor bubbles at the oscillatory stage and their presence affects the bubble dynamics.
全氟化碳（PFC）微滴，即所谓的相变造影剂（PCCA），是超声成像和治疗中一种很有前景的工具。对PCCA的兴趣源于这样一个事实，即它们可以通过外部施加的声脉冲触发从液态转变为气态。这一特性为超声医学的应用开辟了新途径。深入了解PFC微滴的汽化物理过程对于有效使用PCCA和预测生物效应至关重要。由挥发性PFC（低沸点）组成的PCCA表现出复杂的动态行为：在短声脉冲汽化后，PFC微滴变成一个蒸汽泡，该蒸汽泡会经历过度膨胀和阻尼径向振荡，直至稳定到最终直径。到目前为止，这种行为在理论上尚未得到很好的描述。我们研究的目的是开发一个改进的理论模型，描述挥发性PFC微滴的汽化动力学，并通过与体外实验数据进行比较来验证该模型。
该模型的推导基于将流体动力学和热力学的数学方法应用于PFC微滴的声汽化过程。所采用的方法纠正了现有模型的缺点。通过将模拟结果与通过超高速视频显微镜获得的不同尺寸的八氟丙烷（OFP）和十氟丁烷（DFB）微滴的体外实验数据进行比较，对模型进行验证。
所开发的理论能够模拟PFC微滴内蒸汽泡的生长，直至液态PFC完全转化为蒸汽，以及随后蒸汽泡的过度膨胀和阻尼振荡，包括外部施加声脉冲的影响。为了定量评估模拟结果与实验结果之间的差异，对所有比较模拟结果和实验结果的情况计算了L2范数误差。对于OFP和DFB微滴，这些误差分别在0.043 - 0.067和0.037 - 0.088范围内。这些值使人们可以认为模拟结果与实验结果之间的一致性良好。仅通过改变描述气态和液态PFC以及PFC微滴周围液体材料特性的16个模型参数中的2个就实现了这种一致性。拟合参数是周围液体的粘度和表面张力。所有其他模型参数保持不变。
理论结果与实验结果之间的良好一致性表明，所开发的模型能够正确描述挥发性PFC微滴汽化动力学背后的关键物理过程。为了拟合实验曲线而改变周围液体参数的必要性可以通过以下事实来解释，即在振荡阶段，PFC微滴初始磷脂壳的部分仍留在蒸汽泡表面，它们的存在会影响气泡动力学。
