Measured wave dispersion in tubes excited with acoustic radiation force matches theoretical guided wave dispersion

Acoustic radiation force (ARF) has been used to generate shear waves in many different tissues for the purpose of quantifying material properties of those tissues. This method has also been applied to arteries, but care must be taken in this application because waves produced in the arterial wall are guided waves. To obtain accurate measurements of mechanical properties of arteries, guided wave inversion can be used, where experimental wave dispersion is iteratively matched with theoretical dispersion curves. In this paper we study wave propagation in three sets of rubber tubes with different mechanical properties, and compare their measured and theoretical dispersion curves. Three sets of tubes were made with outer diameters of 8 mm and wall thicknesses of 1 mm to mimic an adult carotid artery. A different rubber mixture was used for each set of tubes, VytaFlex 10, VytaFlex20, and ReoFlex 30. Reference samples were also poured for testing with hyper-frequency viscoelastic spectroscopy (HFVS) instrument for measurement of the material complex modulus. Wave propagation measurements were made with a Verasonics system and linear array with water inside and surrounding the tubes. Acoustic radiation force was used to generate the waves with a 200 μs push at 4.1 MHz and plane wave imaging at a frame rate of 14.9 kHz was used for measuring the propagating waves. A two-dimensional Fourier transform method was used to extract the dispersion curves from the measured particle velocity. Theoretical dispersion curves for flexural modes with circumferential wavenumber n = 1, 2, 3 were calculated from the material properties measured with HFVS for comparison with the ultrasound-based results. The measured dispersion curve matches well with theoretical results. However, the match is not with a single theoretical dispersion curve, but with different theoretical curves at different frequencies. This new approach of matching with multiple theoretical curves can be used for better understanding of wave propagation in arterial walls and improved characterization of their mechanical properties.