Principles of Ultrasound Wave Attenuation and Scatter

Clinical Note: Because attenuation increases with both frequency and depth, higher frequency transducers are excellent for superficial structures but struggle to penetrate deep into the body.

Scatter and the Texture of Organs

While specular reflection occurs when sound hits a large, smooth surface (like the diaphragm), scatter occurs when the sound beam interacts with interfaces that are rough or smaller than a single wavelength.

The Mechanics of Scattering

Scatter typically occurs in heterogeneous media, such as cells or suspended particles. When the incident sound beam hits these small reflectors, it breaks up into many different echoes that can reflect in any direction. Because these directions are unpredictable, the term "scatter" is used. The amount of scatter is determined by two main factors:

1. Frequency: Higher frequencies result in greater amounts of scatter.
2. Reflector Size: Smaller reflectors result in greater amounts of scatter.

Backscatter and Parenchyma

When the scattered sound is directed back toward the ultrasound probe, it is specifically called backscatter. Backscatter is the physical mechanism responsible for the appearance of the parenchyma (the functional tissue of an organ) on an ultrasound screen.

. Because RBCs are so small relative to the wavelength, Rayleigh scatter is very weak, which is why it can be difficult to visualize blood flow at high velocities.

Acoustic Speckle and Interference

Because scattering is a random process, it can lead to non-uniformities in the brightness of an image. This phenomenon is known as acoustic speckle. Speckle is the result of interference patterns created by echoes that have undergone multi-path scattering. While speckle can obscure fine detail, modern ultrasound equipment utilizes various techniques to minimize its impact on image quality.

Mathematical Summary of Attenuation

To quantify the loss of sound, clinicians use the decibel (dB) scale. The decibel is a relative unit used to express the intensity level of sound waves.

Calculating Decibels

The formula for decibels is:

$$dB = 10 \log \left(\frac{\text{new } I}{\text{original } I}\right)$$

Where $I$ represents intensity.

The Attenuation Coefficient

In soft tissue, attenuation is often calculated using an attenuation coefficient. In soft tissue, approximately 0.5 dB of attenuation occurs for every 1 cm traveled per 1 MHz of frequency. This can be expressed as:

$$\text{Attenuation Coefficient} = \frac{1}{2} f$$

To find the Total Attenuation (TAtt) for a specific depth, use:

$$\text{TAtt} = \frac{1}{2} f \times \text{Path Length (cm)}$$

Note: The path length must account for the sound traveling to the target and back to the probe.

Exam Tip: Remember the "Rule of Thumb" for decibels: A 3 dB drop represents a reduction to $1/2$ of the original intensity, while a 10 dB drop represents a reduction to $0.1$ (or 10%) of the original intensity.