Analytical modeling and non-dimensionalization study for endoscopic ultrasound acoustic field in tubular structure

Abstract

The concept of endoscopic ultrasound (EUS) has been introduced to non-destructive testing for the internal inspection of tubular structure. It is a typical inspection application on layered media with a non-planar interface. Existing research in this area is hindered by two significant limitations: i) the absence of an EUS acoustic field model that is adaptable to the layered medium with non-planar interfaces; ii) the lack of a generalizable analysis and regularity of the EUS acoustic field distribution. This paper derives a refraction model for the tube interface and delay law. By combining these with the angular spectrum model, an analytical acoustic field model for EUS in tubular structure is developed, providing the theoretical framework for acoustic field analysis and interpretation. Subsequently, the geometric and acoustic parameters of the transducer and the tubular object are non-dimensionalized to normalize diverse EUS inspection scenarios. A parametric analysis is then conducted to identify and comprehend the regularity of the EUS acoustic field distribution, which is the main object of this study. The derived EUS acoustic field regularity is validated through an EUS inspection experiment of a tube using control variate method. The quantitative analysis result of the EUS imaging aligns with the expectations from beam analysis. The proposed analytical model is applicable to any scenarios with multi-layered media and with arbitrary interfaces. Its primary strength lies in its intuitive ability to demonstrate the impact of various parameters on the acoustic field distribution. The methodology of non-dimensionalization provides a paradigm for deriving generalizable regularities in the field of ultrasonic testing and imaging.