Mathematical Model of the Process of Ultrasonic wave Propagation in a Relax Environment with its Given Profiles at three Time Moments

Objective: The process of ultrasound oscillations in a relaxed environment, provided that the profiles of the acoustic wave at three time moments are known, is modeled by a three-point problem for the partial differential equation of the third order in time. This equation as a partial case contains a hyperbolic equation of the third order, which is widely used in ultrasound diagnostics. Methods: The differential-symbol method is applied to study a three-point in-time problem. The advantage of this method is the possibility to obtain a solution of the problem only through operations of differentiation. Results: We propose the formula to construct the analytic solution of the problem, which describes the process of ultrasound oscillations propagation in a relax environment. Due to this, the profile of the ultrasonic wave is known at any time and at an arbitrary point of space. The class of quasi-polynomials is distinguished as a class of uniqueness solvability of a three-point problem. Conclusion: Using the proposed method, it is possible to analyze the influence of the main parameters of ultrasound diagnostics problems on the propagation of acoustic oscillations in a relaxed environment. The research example of a specific three-point problem is given.

High Frequency Ultrasonic Wave Propagation in Anisotropic Materials

<p>The influence of highly regular, anisotropic, microstructured materials on high frequency ultrasonic wave propagation was investigated in this work. Microstructure, often only treated as a source of scattering, significantly influences high frequency ultrasonic waves, resulting in unexpected guided wave modes. Tissues, such as skin or muscle, are treated as homogeneous by current medical ultrasound systems, but actually consist of highly anisotropic micron-sized fibres. As these systems increase towards 100 MHz, these fibres will significantly influence propagating waves leading to guided wave modes. The effect of these modes on image quality must be considered. However, before studies can be undertaken on fibrous tissues, wave propagation in more ideal structures must be first understood. After the construction of a suitable high frequency ultrasound experimental system, finite element modelling and experimental characterisation of high frequency (20-200 MHz) ultrasonic waves in ideal, collinear, nanostructured alumina was carried out. These results revealed interesting waveguiding phenomena, and also identified the potential and significant advantages of using a microstructured material as an alternative acoustic matching layer in ultrasonic transducer design. Tailorable acoustic impedances were achieved from 4-17 MRayl, covering the impedance range of 7-12 MRayl most commonly required by transducer matching layers. Attenuation coefficients as low as 3.5 dBmm-1 were measured at 100 MHz, which is excellent when compared with 500 dBmm-1 that was measured for a state of the art loaded epoxy matching layer at the same frequency. Reception of ultrasound without the restriction of critical angles was also achieved, and no dispersion was observed in these structures (unlike current matching layers) until at least 200 MHz. In addition, to make a significant step forward towards high frequency tissue characterisation, novel microstructured poly(vinyl alcohol) tissue-mimicking phantoms were also developed. These phantoms possessed acoustic and microstructural properties representative of fibrous tissues, much more realistic than currently used homogeneous phantoms. The attenuation coefficient measured along the direction of PVA alignment in an example phantom was 8 dBmm-1 at 30 MHz, in excellent agreement with healthy human myocardium. This method will allow the fabrication of more realistic and repeatable phantoms for future high frequency tissue characterisation studies.</p>

High Frequency Ultrasonic Wave Propagation in Anisotropic Materials

<p>The influence of highly regular, anisotropic, microstructured materials on high frequency ultrasonic wave propagation was investigated in this work. Microstructure, often only treated as a source of scattering, significantly influences high frequency ultrasonic waves, resulting in unexpected guided wave modes. Tissues, such as skin or muscle, are treated as homogeneous by current medical ultrasound systems, but actually consist of highly anisotropic micron-sized fibres. As these systems increase towards 100 MHz, these fibres will significantly influence propagating waves leading to guided wave modes. The effect of these modes on image quality must be considered. However, before studies can be undertaken on fibrous tissues, wave propagation in more ideal structures must be first understood. After the construction of a suitable high frequency ultrasound experimental system, finite element modelling and experimental characterisation of high frequency (20-200 MHz) ultrasonic waves in ideal, collinear, nanostructured alumina was carried out. These results revealed interesting waveguiding phenomena, and also identified the potential and significant advantages of using a microstructured material as an alternative acoustic matching layer in ultrasonic transducer design. Tailorable acoustic impedances were achieved from 4-17 MRayl, covering the impedance range of 7-12 MRayl most commonly required by transducer matching layers. Attenuation coefficients as low as 3.5 dBmm-1 were measured at 100 MHz, which is excellent when compared with 500 dBmm-1 that was measured for a state of the art loaded epoxy matching layer at the same frequency. Reception of ultrasound without the restriction of critical angles was also achieved, and no dispersion was observed in these structures (unlike current matching layers) until at least 200 MHz. In addition, to make a significant step forward towards high frequency tissue characterisation, novel microstructured poly(vinyl alcohol) tissue-mimicking phantoms were also developed. These phantoms possessed acoustic and microstructural properties representative of fibrous tissues, much more realistic than currently used homogeneous phantoms. The attenuation coefficient measured along the direction of PVA alignment in an example phantom was 8 dBmm-1 at 30 MHz, in excellent agreement with healthy human myocardium. This method will allow the fabrication of more realistic and repeatable phantoms for future high frequency tissue characterisation studies.</p>

Ultrasound simulation technique as state-of-health estimation method of lithium-ion batteries

Ultrasound is a non-destructive technique recently proposed to estimate Lithium-ion batteries degradation. However, recent research has been devoted towards understanding the physical phenomena behind the ultrasonic wave propagation through a Lithium-ion battery. To achieve this, the second-order-scalar elastic and acoustic wave equations are solved with explicit and implicit finite difference method, considering the interfaces between materials with different physical properties. Results showed that implicit method presents less noise than the explicit scheme. In addition, changes in the physical properties of battery materials that occur in charge and discharge processes, highly affect the ultrasonic wave propagation inside the battery. Finally, this study demonstrates the feasibility of using numerical methods as a precursor of battery degradation estimator.

Parametric Model Order Reduction of Guided Ultrasonic Wave Propagation in Fiber Metal Laminates with Damage

This paper focuses on parametric model order reduction (PMOR) of guided ultrasonic wave propagation and its interaction with damage in a fiber metal laminate (FML). Structural health monitoring in FML seeks to detect, localize and characterize the damage with high accuracy and minimal use of sensors. This can be achieved by the inverse problem analysis approach, which employs the signal measurement data recorded by the embedded sensors in the structure. The inverse analysis requires us to solve the forward simulation of the underlying system several thousand times. These simulations are often exorbitantly expensive and trigger the need for improving their computational efficiency. A PMOR approach hinged on the proper orthogonal decomposition method is presented in this paper. An adaptive parameter sampling technique is established with the aid of a surrogate model to efficiently update the reduced-order basis in a greedy fashion. A numerical experiment is conducted to illustrate the parametric training of the reduced-order model. The results show that the reduced-order solution based on the PMOR approach is accurately complying with that of the high fidelity solution.