## 5 How Acoustic Traps Work  
A hypothesis able to explain the genesis of vertical lung artifacts in hyperdense non consolidative pathology of the lung cortex states that the artifacts represent acoustic information relative to the full/empty ratio of the sub-pleural tissue [23; 24]. Vertical artifacts are thus the visual representations of the signals originating from the multiple reflections experienced by ultrasound waves when trapped inside the channels that can form between the air spaces when a pathologic condition exists [18]. Because the acoustic trap configuration and volume, its shape and its content are variable, it is not surprising that the vertical artifacts look different in different diseases and in different stages of a single disease. It is interesting to note that in theory every acoustic trap has its own spectral signature [39], which can be approximated accordingly to the simplified Equation [33]:  
\[f_{n,m,l}=\frac{c_{s}}{2}\sqrt{\left(\frac{n}{d_{1}}\right)^{2}+\left(\frac{m }{d_{2}}\right)^{2}+\left(\frac{l}{d_{3}}\right)^{2}}\]  
where \(f_{n,m,l}\) represents the harmonics generated inside the acoustic trap, \(n\), \(m\), and \(l\) are integer numbers (harmonic components of the spectral signature of the trap), and \(d_{1}\), \(d_{2}\), and \(d_{3}\) refer to the shape of the  
Figure 5: **(A)**: Acute cardiogenic pulmonary edema, histopathologic picture. **(B)**: Idiopatic Pulmonary Fibrosis (IPF), histopathologic picture. In acute pulmonary edema the lung shows little structural changes and this is especially evident in early hydrostatic edema, when only the interlobular septa show a moderate smooth thickening. On the contrary, in IPF the lung is involved by variable amount of fibrosis and it is deeply subverted in the structure. **(C)** and **(D)**: The related ultrasound pictures. In cardiogenic pulmonary edema **(C)** pleural line is regular and smooth (Image obtained with a commercially available machine, Esaote MyLab 25 equipped with a Convex probe), in IPF **(D)**, pleural line is irregular and the artefacts are very heterogeneous (Image obtained with a commercially available machine, Toshiba Aplio XV, equipped with a convex probe, 3 MHz, without harmonic imaging). acoustic trap (in this case simply defined by three spatial dimensions \(d_{1}\), \(d_{2}\), and \(d_{3}\)). Finally, \(C_{s}\) is the speed of sound within the trap, which is relative to the content of the trap itself. Therefore, the determinants of the spectral signature of the traps are their content, and the dimensions and shape of their volume. For example, a spherical volume can be described by a single spatial measure, the diameter. In general, the lowest native frequency of a trap increases as the size of the trap decreases [33; 39]. Obviously, the shape of a real acoustic trap, given by any transonic volume surrounded by alveoli, often cannot be described by single spatial measure. It follows that, in many cases, a more complex spectral signature is expected. In practical terms the sequence of events producing vertical artifacts arising from a diseased pleura covering a hyperdense non-consolidated lung can be exemplified as follows: (a) the ultrasonic pulse that reach the pleura is characterized by a frequency band; (b) Such a pulse can activate specific native frequencies of the acoustic trap, in this process the access channel must allow the penetration of sufficient acoustic energy, able to generate a visible artifact on the ultrasound images; (c) The trap acts as a secondary ultrasound source and part of the trapped energy is reradiated to the probe across the entry/exit of the trap; and (d) The probe, accordingly to its transfer function, is able to capture only those signals which fall within a specific frequency range, which are then converted by pre-defined signal processing operations into vertical artifacts that assume a specific visual structure observable on the screen.