Determination of nonlinear medium parameter B/ A using model assisted variable-length measurement approach

Abstract

This work addresses the difficulties in the measurements of the nonlinear medium parameter B/ A and presents a modification of the finite amplitude method (FAM), one of the accepted procedures to determine this parameter. The modification is based on iterative, hybrid approach and entails the use of the versatile and comprehensive model to predict distortion of the pressure–time waveform and its subsequent comparison with the one experimentally determined. The measured p– t waveform contained at least 18 harmonics generated by 2.25 MHz, 29 mm effective diameter, single element, focused PZT source (f-number 3.5) and was recorded by Sonora membrane hydrophone calibrated in the frequency range 1–40 MHz. The hydrophone was positioned coaxially at the distal end of the specially designed, two-section assembly comprising of one, fixed length (60 mm), water-filled cylindrical container and the second, variable length (60–120 mm) container that was filled with unknown medium. The details of the measurement chamber are described and the reasons for this specific design are analyzed. The data were collected with the variable length chamber filled with 1.3-butanediol, which was used as a close approximation of tissue mimicking phantom. The results obtained provide evidence that a novel combination of the FAM with the semi-empirical nonlinear propagation model based on the hyperbolic operator is capable of reducing the overall uncertainty of the B/ A measurements as compared to those reported in the literature. The overall uncertainty of the method reported here was determined to be ±2%, which enhances the confidence in the numerical values of B/ A measured for different, clinically relevant media. Optimization of the approach is also discussed and it is shown that it involves an iterative procedure that entails a careful selection of the acoustic source and its geometry and the axial distance over which the measurements need to be performed. The optimization also depends critically on the experimental determination of the source surface pressure amplitude.