Introduction to Ultrasound Imaging and Elastography

Transducer Design: Frequency and Depth

The fundamental properties of a transducer are dictated by the physical dimensions of its PZT crystals. A transducer operates most efficiently at its natural frequency, which occurs when the crystal thickness is exactly half of the wavelength:

$\text{Thickness} = \frac{\lambda}{2}$

This creates an inverse relationship between frequency and crystal thickness:

• Thinner crystals produce higher frequencies (e.g., $7.5\text{ MHz} \approx 0.3\text{ mm}$).
• Thicker crystals produce lower frequencies (e.g., $2\text{ MHz} \approx 1\text{ mm}$).

This relationship is critical for clinical selection because frequency determines the balance between resolution and penetration:

Electronic Beam Scanning and Image Formation

To create a two-dimensional image, the machine must determine the distance and direction of returning echoes. Modern systems use electronic beam scanning rather than moving the probe mechanically.

In a linear array transducer, which contains between 128 and 256 individual elements, the machine sequentially activates small groups of elements to steer or focus the beam. Two key techniques are used:

• Beam Steering: Activating elements in a specific sequence across the transducer face to direct the beam in different directions.
• Beam Focusing: Applying a phase delay to specific elements so that the wave fronts arrive at a specific point simultaneously, concentrating the energy.

Different transducer geometries are used depending on the clinical target:

• Linear Arrays: Used for superficial structures.
• Curvilinear Arrays: Used for deep abdominal and obstetric imaging.
• Phased Arrays: Electronically steered to "see" between ribs, ideal for cardiac imaging.

The quality of these images is defined by spatial resolution in three planes: axial, lateral, and elevational.

Elastography: "Palpation by Imaging"

While B-mode imaging shows echogenicity (how tissue reflects sound), elastography maps tissue stiffness. Since many malignancies (such as breast carcinoma) are stiffer than surrounding healthy tissue, elastography provides a vital adjunct to standard imaging.

The physics of stiffness is defined by Young’s Modulus ($E$), which is the ratio of stress to strain:

$E = \frac{\text{stress}}{\text{strain}}$

Where:

• Stress: The force applied per unit area (e.g., probe pressure).
• Strain: The fractional change in size (unitless).
• $E$: Measured in kilopascals (kPa).

There are two primary families of elastography:

1. Strain Elastography (Quasi-static)

This method measures relative deformation. It relies on manual compression by the operator, physiological motion (like breathing), or an Acoustic Radiation Force Impulse (ARFI) "push". Because it measures how much one tissue deforms compared to another, the results are qualitative or semi-quantitative (e.g., the Tsukuba 5-point score) and are highly operator-dependent.

2. Shear Wave Elastography (SWE) (Dynamic)

SWE is a quantitative method that measures shear wave speed. An acoustic "push" generates lateral shear waves that travel through the tissue; stiffer tissue results in faster shear wave speeds. Results are provided in absolute values of $\text{m/s}$ or $\text{kPa}$. While more reproducible and less operator-dependent, SWE can be weakened by excessive probe pressure (pre-compression) or depth.

Clinical Applications of Elastography

• Breast Imaging: Helps increase specificity and reduce unnecessary biopsies. A stiffness threshold (e.g., $80\text{ kPa}$) can help categorize masses within the BI-RADS system.
• Thyroid Imaging: Used to differentiate benign from malignant nodules. While the Rago score has shown high predictive value, some studies suggest it is more useful for identifying benign nodules than for deciding on fine-needle aspiration (FNA).
• Liver: Used to assess the severity of fibrosis, reducing the need for invasive biopsies.

Worked Example: Calculating Stiffness If a shear wave is measured traveling at $5.2\text{ m/s}$ through tissue, and assuming a tissue density ($\rho$) of approximately $1000\text{ kg/m}^3$, the Young's Modulus ($E$) can be estimated: $E \approx \rho \cdot c^2$ $E \approx 1000 \cdot (5.2)^2 \approx 27,040\text{ Pa} \approx 27\text{ kPa}$ (Note: Actual clinical calculations may vary based on specific mathematical models used by the machine).

Contrast-Enhanced Ultrasound (CEUS)

To improve the detection of blood flow and tumor vascularity, clinicians use microbubbles as contrast agents. These are tiny spheres (1–10 $\mu\text{m}$) containing gas (such as $\text{SF}_6$) enclosed in a stabilizing shell.

Because microbubbles are much more compressible than soft tissue, they resonate strongly when hit by ultrasound waves. This resonance produces harmonics—signals at multiples of the fundamental frequency (e.g., $2f$). By using filters to isolate these harmonic signals, the machine can significantly improve the signal-to-noise ratio (SNR) and depict microvasculature more clearly than standard B-mode.