1 Sonography

1.1 Introduction and overview

Sonography works with ultrasound waves. Medical sonography is an imaging modality that uses ultrasound (US) for taking static images of organs and tissues, dynamic images of heart and lung movement, and kinetic images of blood flow. A well-known and common example of sonography is imaging fetuses as part of prenatal checkups. Sonography is not limited to medicine. Many other fields use US techniques such as submarine navigation, seafloor mapping, food control, security screening, surface cleaning, nondestructive material testing, and ultrasonic welding of plastics.

US imaging is much more practical to handle by a physician than any radiation-based imaging modality. It can be applied locally at the bedside or the site of an accident and does not require special safety procedures for the patient or the examining staff. Direct communication with the patient is possible during the examination, which is a significant advantage compared to other imaging modalities such as magnetic resonance imaging (MRI), computed tomography (CT), or positron emission tomography. Conversely, conventional US images have lower resolution and require considerable experience to interpret them correctly for useful diagnostics. US imaging for medical diagnostics are mainly in the following areas:

• Cardiovascular system

• Abdominal organs

• Urology/prostate

• Obstetrics/gynecology

• Ophthalmology

• Mammography

After discovering the piezoelectric effect by Paul-Jacques Curie1 and Pierre Curie2 in 1880, Langevin3 first used it to produce ultrasonic waves, mainly for industrial and military applications. It was not until the 1940s to 1950s of the twentieth century that US was applied for medical investigations. In the 1960s, the first handheld contact B-mode scanner was produced and commercialized.

The basic properties and terms of sound waves are presented and defined in Section 12.2 of Volume 1: pressure amplitude, sound velocity, particle velocity, acoustic impedance, sound intensity, reflection, and transmission at interfaces. It is recommended to refresh these terms before continuing with the following discussions. Table 1.1 reviews the most important relationships. The frequencies used for sonography are much beyond audible sound, i.e., more than 20 kHz. In fact, most sonographic systems use frequencies in the range of 2–20 MHz. Although these have much higher frequencies than considered in Chapter 12 of Volume 1, the physics of sound waves is the same.

1.2 Ultrasound transducer

1.2.1 Piezoelectric effect

For generating and detecting US waves, a piezoelectric head is used, also called a transducer. In general, transducers are devices that convert one form of energy into another. In the present case, US transducers convert electrical energy into vibrational energy of a crystal lattice using the piezoelectric effect. The exploitation of the piezoelectric effect requires a single crystal with appropriate properties. Piezoelectric crystals are ionic and insulating materials with high electrical polarizability that is strongly coupled to the crystal lattice. Mechanical compressive or tensile strain generates electrical potentials, and vice versa, electric potentials are converted into elastic strain. In either case, a polarization of electric dipole moments in the crystal is induced via strain or electrical potential. The direct piezoelectrical effect relates the polarization P of these electric dipole moments to the stress σ applied, as illustrated in Fig. 1.1:

Fig. 1.1: Working principle of the direct piezoelectric effect. Application of compressive or tensile stress induces an electric polarization and a voltage change. Conversely, the application of a voltage changes the length of the piezoelectric crystal.

where g is the piezoelectric coefficient with the unit g=m/V. The converse piezoelectric effect relates the length change Δl of the crystal to the applied voltage change ΔU:

Note that the expansion of the crystal does not depend on its size but only on the voltage applied. The magnitude of the piezoelectric coefficient g is on the order of 500 pC/N or 0.5 nm/V. The piezoelectric coefficient  g is actually a tensor, but for simplicity, we keep it here as a scalar. A more complete discussion can be found in the review [1].

The piezoelectric transduction can be utilized in a static or dynamic mode up to high frequencies. Piezoelectric crystals have numerous applications in physics and technology as actuators, sensors, and for nano-positioning. For instance, the sensing head of scanning tunneling microscopes and atomic force microscopes is driven by piezoelectric crystals.

What are piezoelectric materials made of? There is a large variety of piezoelectric materials [1, 2]. The most common ones are crystals of insulating ceramic materials, which lack inversion symmetry. The best-known example is the piezoelectric compound PbTiO3 (short notation, PT) or the Zr-doped version Pb(Zr1–xTix)O3 (short notation, PZT). The movement of Zr4+/Ti4+ ions in and out of the oxygen plane (see Fig. 1.2) by application of an electrical field or by stress induces an electrical dipole moment. Therefore, these piezoelectric materials can either be used as actuators by applying a voltage or as...