# Ultrasound: physical principles and image formation

Ultrasounds, like all sound waves, can be described as phenomena of compression and rarefaction of matter on a Cartesian plane. It is a sinusoidal line whose positive peaks coincide with the maximum compression and the negative ones with the maximum rarefaction. A sound wave can also be represented by concentric circles that widen starting from a central point, in the same way as waves that ripple the surface of a body of water after we have dropped a stone. Of a sound wave (and, therefore, also of an ultrasound), we can define the frequency, the propagation speed, the intensity, and the period time that elapses between the passage of two wavefronts at the same point.

## Intensity of ultrasound

Ultrasound, like other forms of radiation, possesses energy. It is represented by the intensity of the sound (I) and can be measured in watts/cm 2 (power per unit area) or in Pascal (pressure per unit area). Most commonly, the intensity of a sound is measured in Bel (B) or, better, in its decimal subunit, the deciBel.

The deciBel is a "comparative" unit of the intensity of two sounds, expressed on a logarithmic basis 10, which takes the threshold of audibility as a reference point.

The more intense a sound, the more energy it gives to the medium through which it propagates. The ultrasounds used in Diagnostic Imaging have intensity below the threshold capable of causing permanent changes in the medium crossed.

## Ultrasound propagation

The propagation speed of a sound wave depends on the atomic density and the elastic properties of the medium. The speed is expressed in meters per second (m / s). The speed of propagation of ultrasound is constant in a homogeneous medium and proportional to its density. Sound waves propagate better and faster in liquids than in air. Therefore, soft tissues, which are made up mostly of water, are particularly suitable for ultrasound study.

However, each medium opposes a certain "resistance" to the propagation of a sound wave. This resistance is called "impedance." Impedance represents a fundamental property of matter and is the basis of the formation of echoes. The impedance is directly proportional to the density of the material traversed and the speed of sound. Its unit of measurement is the Rayl, The formula for calculating the Rayl is:

Z = ρ c

Where

Z = acoustic impedance

ρ = density (g / cm 3)

c = speed of sound in the middle.

## Ultrasound: how they are produced

The ultrasound machine has an instrument called a probe or transducer, which is used for the production and reception of ultrasound. In the probe, there are crystals that have the property of vibrating when subjected to an electrical voltage. These crystals are called piezoelectrics, and their molecular structure is such that the electric charges are arranged in an orderly and polarized way, and each molecule represents a small dipole. The piezoelectric effect was discovered in 1880 by the brothers Pierre and Jacques Curie on quartz crystals.

So if these crystals are placed in an electric field, they deform because the charges of the molecules are oriented at 90 ° with respect to the electric field. As soon as the voltage ceases, the crystals quickly return to their original shape. This sudden elastic return causes the crystals to resonate, causing a small series of vibrations, which, therefore, will generate an ultrasound.

The phenomenon can occur in both directions; the electrical impulse is transformed into deformation/vibration (mechanical energy); if the crystal is hit by ultrasound. It enters into resonance and, therefore, the deformation/vibration that follows causes a disturbance in its electromagnetic field, generating a small electric current.

This property of piezoelectric materials causes the probes to function as both emitters and antennas.

## Ultrasound: formation of echoes

The reflection and diffusion of ultrasound occur at the points where there is a passage between two tissues with different impedance. The acoustic interfaces define as areas where there is a change in the acoustic impedance. For example, between the skin and subcutaneous tissue, between soft tissues and hard tissues, etc., beyond the interface, an ultrasound with reduced intensity continues its path towards the deeper structures for transmission/refraction. When the difference in impedance is greater, the reflection will also be greater. For this reason, bone tissue and lungs are not suitable for ultrasound study, at the level of the interface between soft tissues and bone tissue or lung parenchyma, ultrasound is almost completely reflected and, therefore, attenuated.

During operation, the probe transmits small ultrasound "packets" (usually 2 or 3 cycles) for 1% of the time (generally around 1-2 millionths of a second). For the remaining 99% (100-200 millionths of a second), the probe listens for the return echoes. The echoes returned to the probe cause the piezoelectric crystals to resonate, causing the production of an electrical signal.

### Characteristics of the ultrasound beam

The ultrasound beam, a few slides ago, we described it as a "brush." In fact, the hair on this brush tends to widen shortly after coming out of the probe. They remain parallel to each other only for a short distance; the beam remains coherent and the diameter equal to that of the crystal up to a distance which is proportional to the diameter of the crystal. The section in which the beam is coherent is called the "Fresnel zone," the next one, "Fraunhofer zone."

### Spatial resolution

The ultrasound beam emitted by the probe has three dimensions:

- Axial (Y, depth)

- Lateral (X, width)

- Height (Z, thickness).

The depth depends on the frequency and the width and thickness, depending on the size of the emitting crystal. The spatial resolution (ability to distinguish two very close objects as separate) depends on:

- Axial resolution (along the beam axis: Y)

- Lateral resolution (along the perpendicular planes to the beam: X and Z).

The axial resolution is given by the ability to distinguish two points along the Y-axis of the ultrasound beam. This type of resolution depends on the frequency of the ultrasounds, the higher the frequency, the lower the wavelength, and therefore, the greater the axial resolution.

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