Biomechanical Sensing Using Gas Bubbles Oscillations in Liquids and Adjacent Technologies: Theory and Practical Applications

Abstract

Gas bubbles present in liquids underpin many natural phenomena and human-developed technologies that improve the quality of life. Since all living organisms are predominantly made of water, they may also contain bubbles—introduced both naturally and artificially—that can serve as biomechanical sensors operating in hard-to-reach places inside a living body and emitting signals that can be detected by common equipment used in ultrasound and photoacoustic imaging procedures. This kind of biosensor is the focus of the present article, where we critically review the emergent sensing technologies based on acoustically driven oscillations of bubbles in liquids and bodily fluids. This review is intended for a broad biosensing community and transdisciplinary researchers translating novel ideas from theory to experiment and then to practice. To this end, all discussions in this review are written in a language that is accessible to non-experts in specific fields of acoustics, fluid dynamics and acousto-optics.

Analogue and Physical Reservoir Computing Using Water Waves: Applications in Power Engineering and Beyond

“…To provide an intuitive example of how a liquid-based system might implement the standard ESN algorithm, let us consider a mm-sized bubble in a bulk of water (Figure 4c). When the bubble is irradiated with a sound pressure wave, it harmonically oscillates, i.e., it periodically inflates and deflates while maintaining a spherical shape [99][100][101][102]. The natural frequency of such oscillations is associated with the Minnaert resonance [103] that occurs at the frequency given by the well-known formula…”

“…where the polytropic exponent of the gas trapped inside the bubble is κ = 4/3, P a is the pressure in the bulk of the liquid outside the bubble, R 0 is the equilibrium radius of the bubble and ρ is the density of the liquid. In this formula, the surface tension and the effect of the viscosity of the liquid are neglected due to their insignificant impacts on the oscillation frequency of mm-sized bubbles [101,102].…”

“…From a mathematical point of view, to implement a physics-informed network, the standard ESN, LSM or a similar algorithm needs to be combined with a mathematical model of a physical process that can be described using partial differential equations (PDEs) [104]. The so-designed RC systems have been shown to produce ML models that remain robust in the presence of noise or poorly defined data, which is often the case, for example, in biosensing [102].…”

“…From a theoretical point of view, the implementation of this idea implies that Equation ( 1) is replaced with the Rayleigh-Plesset equation, which describes the nonlinear dynamics of spherical bubble oscillations [100,102] in a cluster consisting of N b bubbles that do not undergo translational motion (see [102,108] for a relevant discussion of translation motion):…”

“…Once the Rayleigh-Plesset equation has been solved, the acoustic power scattered by the pth bubble is calculated as [102]…”