论文标题
使用气泡作为对比剂的数学分析在几乎共鸣的频率下用作对比剂
Mathematical analysis of the acoustic imaging modality using bubbles as contrast agents at nearly resonating frequencies
论文作者
论文摘要
我们在数学上使用气泡作为对比剂分析声学成像方式。这些气泡是由质量密度和散装模量建模的，具有对比度。这些对比量表使它们在某些事件频率上产生共鸣。我们考虑了两种类型的这种对比。在第一个中，与背景的气泡相比，气泡是带有小块状模量的光，因此它们产生了Minnaert共振（对应于局部表面波）。在第二个中，气泡具有中等的质量密度，但仍具有较小的散装模量，因此它们产生一系列共振（对应于局部体波）。 我们建议用作测量在注入气泡之前和之后收集的远场，该气泡设置为目标域中的给定位置点，在入射频率的带和固定的单个反向散射方向上生成。然后，我们用这样的气泡扫描目标域并收集相应的远场。目的是重建目标区域背景的，变量，质量密度和大量模量。 1。我们表明，对于每种固定的使用气泡，对比远场达到其最大值，在事件中，接近MinNeart共振的频率（或者根据我们使用的气泡的类型）。因此，我们可以从数据中重建这种共鸣。 Minnaert共振在背景的背景密度方面的明确依赖性使我们能够以直接的方式恢复质量密度。 2。此外，这种测得的对比远场使我们能够在气泡的位置点恢复总场（即在没有气泡的情况下的总场）。例如，一个数值分化参数使我们也能够恢复目标区域的大量模量。
We analyze mathematically the acoustic imaging modality using bubbles as contrast agents. These bubbles are modeled by mass densities and bulk moduli enjoying contrasting scales. These contrasting scales allow them to resonate at certain incident frequencies. We consider two types of such contrasts. In the first one, the bubbles are light with small bulk modulus, as compared to the ones of the background, so that they generate the Minnaert resonance (corresponding to a local surface wave). In the second one, the bubbles have moderate mass density but still with small bulk modulus so that they generate a sequence of resonances (corresponding to local body waves). We propose to use as measurements the far-fields collected before and after injecting a bubble, set at a given location point in the target domain, generated at a band of incident frequencies and at a fixed single backscattering direction. Then, we scan the target domain with such bubbles and collect the corresponding far-fields. The goal is to reconstruct both the, variable, mass density and bulk modulus of the background in the target region. 1. We show that, for each fixed used bubble, the contrasted far-fields reach their maximum value at, incident, frequencies close to the Minneart resonance (or the body-wave resonances depending on the types of bubbles we use). Hence, we can reconstruct this resonance from our data. The explicit dependence of the Minnaert resonance in terms of the background mass density of the background allows us to recover it, i.e. the mass density, in a straightforward way. 2. In addition, this measured contrasted far-fields allow us to recover the total field at the location points of the bubbles (i.e. the total field in the absence of the bubbles). A numerical differentiation argument, for instance, allows us to recover the bulk modulus of the targeted region as well.
