Ch 17. Harmonics Physics

HARMONIC IMAGING AND CONTRAST AGENTS

Chapter 17: Harmonics

Objectives

  • What is Harmonic Imaging

  • Non-linear vs Linear behavior

  • Two types of Harmonics

  • Two other special types of harmonics

  • What are contrast agents

  • How is contrast harmonics different from tissue harmonics

  • Mechanical Index and harmonic relationship

Harmonic Imaging Overview

  • Definition: Harmonic imaging creates images through reflections at frequencies that are twice the transmitted frequency.

    • Fundamental Frequency: The frequency of the transducer, denoted as f.

    • Fundamental Image: The image created by the fundamental frequency f.

    • Harmonic Frequency: Equal to twice the fundamental frequency, or the second harmonic frequency, given as 2f. Improves signal to noise ratio

    • Harmonic Image: An image created by processing reflections that occur at the harmonic frequency 2f. 

Advantages of Harmonic Imaging

  • Suboptimal Situations: Harmonic imaging is particularly useful when fundamental imaging is suboptimal.

    • Reduction of Distortion: Helps reduce image distortions.

    • Improvement of Poor Quality Images: Enhancement of overall image quality.

Sound Wave Behavior in Tissue

  • Pressure Wave Dynamics: Sound is a pressure wave, which deforms as it travels through the tissue.

    • Uneven Travel Speeds: Pressure peaks travel faster than pressure valleys, leading to deformations as sound travels deeper.

    • Harmonics Generation: As sound travels deeper, it vibrates the patient’s tissues, creating harmonics.

Fundamental to Harmonic Frequency Transition

  • Example: If the fundamental frequency is 2MHZ , the harmonic frequency will return at 4MHZ (i.e., 2f).

Non-Linear vs Linear Behavior

  • Definitions:

    • Linear Behavior: Symmetrical, proportional change.

    • Non-Linear Behavior: Irregular, disproportionate, and asymmetrical changes in output relative to input.

Tissue Harmonics

  • Energy Conversion: During transmission, energy converts from the fundamental frequency to harmonic frequency due to non-linear behavior.

  • Sound Speed Variations:

    • Sound travels faster through compressions and slower through rarefactions, demonstrating non-linear behavior.

    • Impact on Wave Shape: Change in sound wave shape due to these speed variations.

  • Strength Development: The strength of the harmonic wave increases as the sound wave progresses deeper into the tissue.

  • Depth Dependency:

    • No tissue harmonics are created at superficial depths.

    • As depth increases, the speed of sound changes, leading to stronger harmonic signals.

Tissue Harmonic Imaging Benefits

  • Superficial Development Issues: Harmonic signals are not created superficially but rather develop deep in the tissue without distortion.

  • Image Quality Improvement: Tissue harmonic imaging vividly demonstrates the delineation of cystic and solid lesions compared to conventional grayscale imaging.

Beam Strength and Tissue Harmonics

  • Beam Strength Influence:

    • Weak beams fail to create harmonics.

    • Moderately strong beams produce minimal harmonics.

    • Strong beams generate significant harmonics due to non-linear relationships with tissue strength.

  • Harmonic Production Location:

    • Harmonics are primarily produced along the main axis where the beam strength is highest.

    • No harmonic production occurs in side or grating lobes, making effective beams less prone to artifacts. 

    • Want a narrow bandwidth

Summary of Tissue Harmonic Imaging

  • Key Characteristics:

    • Created during transmission of sound.

    • Generated by the patient’s tissues, not the transducer.

    • Enabled by the non-linear behavior of sound speed.

    • Predominantly produced along the main axis of the beam.

Technologies for Harmonics

  • Pulse Inversion Harmonics:

    • Technique to differentiate between fundamental frequency distortions and harmonic signals in the receiver.

    • Utilizes two pulses per scan line:

    • One typical pulse and one inverted pulse (180 degrees out of phase with the first).

    • Fundamental signals cancel out, allowing harmonic signals to remain. 

    • Harmonic Signals are in phase and combine and create a 2x bigger signal/wave 

    • Decreases axial resolution degrades frame rate

  • Power Modulation Harmonic Imaging:

    • Technique aimed at increasing harmonic signals while eliminating distorted fundamental signals.

    • Uses two pulses per scan line, with one pulse having extra power:

    • This power is doubled during reception, effectively extracting the harmonic signal.

    • Decreases Temporal Resolution

Advantages and Disadvantages of Techniques

  • Pulse Inversion & Power Modulation:

    • Advantages: Reduced distortion in images.

    • Disadvantages: Impact on frame rate (temporal resolution) due to the doubling of pulses.

Contrast Agents / Microbubbles

Introduction to Contrast Agents

  • Functionality: Contrast agents enhance image quality significantly.

  • High Echogenicity: Faciliate the ‘lighting up’ of areas of interest (e.g., blood in chambers, vessels, tissue, lesions).

  • Microbubbles Characteristics:

    • Composed of gas encapsulated in a shell.

    • Can be administered orally or intravenously.

    • Must possess certain properties:

    • Safe for use.

    • Metabolically inert (do not react with body tissues).

    • Long-lasting within the body.

    • Strong inductors of sound reflection.

    • Small enough to transit through capillaries.

Contrast Harmonics

  • Interaction with Microbubbles:

    • When ultrasound strikes a microbubble, some reflected frequencies convert to harmonic frequencies.

    • Generated based on the non-linear behavior of the microbubbles and the sound.

Microbubble Dynamics

  • Oscillation Effect:

    • Microbubbles oscillate—shrink during high-pressure phases and expand during low-pressure phases of sound waves.

    • This oscillation phenomenon reflects a non-linear alteration in size, hence creating harmonic signals.

Mechanical Index (MI)

  • Definition: MI estimates the quantity of contrast harmonics produced.

    • There exists a direct relationship between harmonic production and mechanical index (MI).

    • Factors Influencing MI:

    • Frequency (f) of transmitted wave.

    • Peak pressure (P) of the wave.

    • MI Relationships:

    • High MI correlates with high pressure and low frequency.

    • Low MI connects to lower pressure and high frequency.

  • Mechanical Index Equation

    • Mechanical Index = peak rarefaction pressure / \sqrt{frequency}

MI Effects on Harmonic Generation

  • Linear vs Non-linear Behavior:

    • Low MI: Exhibits linear behavior with minimal harmonic generation.

    • High MI: Exhibits non-linear behavior, which enhances harmonic production.

    • Extremely high MI may lead to destructive responses like cavitation (explosive resonances).

Important Characteristics of Contrast Agents

  • Microbubble Shell: Flexible, non-permeable to gases.

  • Gas Properties: Comprising larger molecules that remain within the bubble, enhancing stability.

Contrast-enhanced Ultrasound Applications

  • Illustrations:

    • Contrast-enhanced sonograms demonstrate various tumors in the liver, one benign and another indicative of hypervascular malignancy.

Summary of Contrast Harmonics

  • Key Points:

    • Created during reflection processes.

    • Resulting from non-linear behavior characteristic of microbubbles.

    • Directly related to mechanical index (MI) where high MI correlates strongly with greater harmonic production.

    • Influenced by the characteristics of the shell and gas in the contrast agent.

Comparison of Harmonics

  • Which Harmonics Are Stronger?: Discussion point on whether contrast harmonics or tissue harmonics exhibit stronger responses.

Tissue Harmonics Summary

  • Key Features:

    • Created during sound transmission influenced by the non-linear behavior of sound speed within tissues.

    • More likely produced along the beam’s primary axis.

    • Formed at greater depths as sound propagates further into tissues.

Review Questions

  • Harmonic Frequency Calculation: For a 3 MHz transducer, what is the harmonic frequency produced? 6MZ

  • Basis for Non-linear Behavior: Understanding the underlying reasoning for non-linear behaviors seen in tissue harmonics. 

  • Pulse Inversion Technique Usage: Detailed understanding of how to isolate harmonic frequencies through specific pulse configurations.

  • Contrast Harmonics Occurrence: Investigation into whether the contrast harmonics occur during transmission, reception, propagation, or reflection.

  • Non-linear Behavior in Contrast Harmonics: Analysis of what type of non-linear behavior contributes to the development of contrast harmonics.

  • and frequencies.