Zoeppritz equations: from seismology to medical exploration

TL;DR

This paper explores how Zoeppritz equations, originally used in seismology, can be applied to medical ultrasound imaging to extract detailed information about tissue interfaces, potentially improving diagnosis and AI-assisted medical analysis.

Contribution

It demonstrates the potential of using full Zoeppritz equations and their generalizations for enhanced medical imaging and diagnosis, including layer thickness and tissue property estimation.

Findings

Separation of density and sound speed effects using AVA measurements

Detection of subwavelength layer thickness through waveform distortion analysis

Application of seismic wave analysis techniques to medical ultrasound imaging

Abstract

More than a century ago, Karl Bernhard Zoeppritz derived the equations that determine the reflected and transmitted coefficients at a planar interface for an incident seismic wave. The coefficients so obtained are a function of the elastic parameters of the media on each side of the interface and the angle of incidence. Approximations of the equations have been proposed and used in geophysical exploration, however, full use of the equations and their generalization to multiple layers could offer richer information about the properties of the media and be helpful in medical diagnosis via ultrasound. In this work, we investigate how to extract information from the angle-dependent reflection coefficients, including critical angles and the wave distortion at the interface between two and three media. It is shown that it is possible to separate the effect of density from speed of sound mismatch by measuring amplitudes as a function of angle of incidence (AVA). And examining the critical angle and waveform distortion of the reflected waves can reveal the thickness of an intermediate layer, even with subwavelength resolution. These studies could be integrated into medical imaging and also into the training of artificial intelligence systems that assist in diagnosis. In particular, they could help prevent cerebrovascular accidents by early detection of the formation and hardening of plaque in the arteries that irrigate the brain.