Ultrasound intensity calculations for a vessel with simulated wall lesion

Vascular disease alters the shape of the lumen of a blood vessel. The lumen is not circular from the early stages of the disease, where there is intimal thickening, through to advanced stages where a large plaque may protrude into the lumen. Using a mathematical model we investigated the ultrasound intensity distribution, both within the vessel wall and across the lumen, in the presence of a simulated wall lesion. Acoustic impedance interfaces due to wall lesions have dimensions (typically ∼ 1 mm) only slightly greater than the wavelength (∼ 0.3 mm for 5 MHz ultrasound). Full wave solutions for the acoustic field are therefore required. Exact solutions in terms of Bessel functions are known for the case of a cylindrical vessel, and a collocation method based on this was developed for non-circular interfaces. By considering two such interfaces we developed a novel model representation of a vessel with a simulated wall lesion. The results of this study show how vessel wall properties may alter the ultrasound intensity distribution within the vessel wall and across the lumen. In the case of non-circular impedance interfaces there can be significant effects due to the local curvature and orientation of the interface.