Ultrasound Elastography for Biomedical Applications and Medicine

2 Theory of Ultrasound Physics and Imaging

Roberto Lavarello¹ and Michael L. Oelze²

¹ Laboratorio de Imágenes Médicas, Departamento de Ingeniería, Pontificia Universidad Católica del Perú, Lima, Peru

² Bioacoustics Research Laboratory, Department of Electrical and Computer Engineering, University of Illinois at Urbana‐Champaign, Champaign, IL, USA

2.1 Introduction

An image is a representation of specific properties of a physical object. The properties of the object that are utilized to form an image depend upon the manner in which the object is perceived. The final representation of the object depends on how the perception of the object's properties is translated into the image space.

In ultrasonic imaging, the properties that are imaged are related to the mechanical structure of the underlying tissue. The manner in which these mechanical properties are perceived is through the transmission and reception of ultrasound waves through the tissue. Signals corresponding to these ultrasound waves are collected by an ultrasonic transducer, converted to a voltage, and processed to convert the perceived properties into an image.

Mathematically, such a process can be described through a processing operation that is a function of the perceived signal

(2.1)

where I is the image, represents the perceived signal, and represents the operation on the perceived signal that ...