# Deep Machine Learning for Path Length Characterization Using Acoustic Diffraction
## 1 Introduction
### Motivation  
This research draws motivation from the necessity to produce a methodology for assessing the health of biofilms in situ. The formation and spread of biofilms has been a long-standing challenge in the medical field as well as industrial settings. These biofilms often lead to the contamination of delicate systems and corrosion of industrial systems [6]. The EPS in which biofilms form allows microbes to form large colonies where they undergo physiological changes that increase their resistance to chemical challenges [11]. This often leads to the need for multiple treatment routes, particularly in the medical field. The health of the biofilm, and therefore susceptibility to treatment, can be understood based on the density and uniformity of the biofilm [11]. Most methods of studying biofilms require destructive methodologies or staining of the microbes [11; 12]. Newer techniques use microscopic approaches to study the biofilms; however, these approaches require the biofilm to be spread uniformly on flat surfaces, which is not conducive to an in situ study [11; 12]. In 2010 a study was performed to understand how the growth of biofilm impacts acoustic properties in porous media [13]. The authors collected acoustic samples over 29 days and found that this time, the signals began the same for the individual and stimulated samples, but near day 29, the signals changed. The lower-frequency components begin to arrive later while the high-frequency components begin to arrive earlier [13]. This research indicates that the acoustic properties of the biofilm are clearly exhibited in the resulting acoustic signal. In 2015 a study was conducted on the early detection of biofilm growth in immunocompromised patients, which demonstrated the increased complexity of analyzing biofilms in situ [14]. The authors demonstrated that the acoustic impedance of the biofilm (1.9 MRayl) is so similar to that of human soft tissue (1.35 to 1.85 MRayl), that imaging the biofilm using ultrasound in-vivo was too difficult using ultrasound alone. The authors saw a large improvement after coupling the high-frequency acoustic microscopy with targeted ultrasound contrast agents to enhance the images to overcome the low acoustic contrast [14]. As the average soft-tissue density is roughly the same as water, the same complications are likely to arise when trying to determine the health of a biofilm [15]. While the similar acoustic impedance of biofilm components to their surroundings may lead to low acoustic contrast, one property that may be exploited to account for the difference in signal strength and arrival time seen by [PERSON] et. al. [13] is the acoustic path length of the constituent cells in the biofilm. The change in acoustic velocity after Day 29 indicates that the acoustic velocity becomes dependent on the frequency. This means the media between the source and the receiver begins to demonstrate properties of dispersion. Since the water is unchanged, we can interpret all changes in the signal as the column becoming dispersive [13]. Normal dispersion is the dispersion where the wave velocity decreases with the frequency, so the dispersion exhibited by the column is normal dispersion. The acoustic path length is the product of the physical distance from the source to the receiver and the wave number (the reciprocal of the wavelength). This physical distance is unchanged regardless of the time. On the other hand, being proportional to the frequency, the acoustic path length shows the above effect of dispersion. Thus, it would be reasonable to use a property such as acoustic path length for detecting constituent biofilm cells. Similar to the work in [13], we aim to develop an approach for analyzing biofilms using properties of acoustics. Our research differs, however, in that we aim to conduct this analysis by using the property of acoustic diffraction. Biofilm density is typically approximately 1.14 g/cm\({}^{3}\), with a thickness ranging from 50 to 100 \(\upmu\)m, depending on the species [12].