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

Q3 Computer Science

Open Bioinformatics Journal Pub Date : 2021-11-19 DOI:10.2174/1875036202114010087

Z. Nytrebych, V. Il'kiv, O. Malanchuk

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引用次数: 1

Abstract

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. 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. 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. 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.

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具有给定轮廓的松弛环境中超声波在三个时刻传播过程的数学模型

在已知声波在三个时间时刻的分布的情况下，超声波在松弛环境中的振荡过程用三阶偏微分方程的三点问题来建模。该方程作为部分情况包含一个三阶双曲方程，在超声诊断中得到了广泛的应用。应用微分符号法研究了一个三点准时问题。这种方法的优点是可以只通过微分运算就得到问题的解。我们提出了一个公式来构造问题的解析解，它描述了超声振荡在松弛环境中的传播过程。由于这一点，超声波的轮廓是已知的，在任何时间和在任意一点的空间。将拟多项式类区分为三点问题的唯一性可解类。利用所提出的方法，可以分析超声诊断问题的主要参数在宽松环境下对声振荡传播的影响。给出了一个具体的三点问题的研究实例。

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来源期刊

Open Bioinformatics Journal Computer Science-Computer Science (miscellaneous)

CiteScore

2.40

自引率

0.00%

发文量

期刊介绍： The Open Bioinformatics Journal is an Open Access online journal, which publishes research articles, reviews/mini-reviews, letters, clinical trial studies and guest edited single topic issues in all areas of bioinformatics and computational biology. The coverage includes biomedicine, focusing on large data acquisition, analysis and curation, computational and statistical methods for the modeling and analysis of biological data, and descriptions of new algorithms and databases. The Open Bioinformatics Journal, a peer reviewed journal, is an important and reliable source of current information on the developments in the field. The emphasis will be on publishing quality articles rapidly and freely available worldwide.