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The arithmetic mean is usually skewed towards the larger values in the data set. Therefore, to avoid this inherent bias towards smaller values, the harmonic mean is used.
Take the example of the speed of a car, which is the measure of the rate of distance traveled. If the vehicle traverses the same distance back-and-forth, its average speed equals the total distance traveled divided by the total time taken. However, if the car moves with varying speeds, then the arithmetic mean is more skewed...
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Simple harmonic motion is the name given to oscillatory motion for a system where the net force can be described by Hooke's law. If the net force can be described by Hooke's law and there is no damping (by friction or other non-conservative forces), then a simple harmonic oscillator will oscillate with equal displacement on either side of the equilibrium position. To derive an equation for period and frequency, the equation of motion is used. The period of a simple harmonic oscillator is given...
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To determine the energy of a simple harmonic oscillator, consider all the forms of energy it can have during its simple harmonic motion. According to Hooke's Law, the energy stored during the compression/stretching of a string in a simple harmonic oscillator is potential energy. As the simple harmonic oscillator has no dissipative forces, it also possesses kinetic energy. In the presence of conservative forces, both energies can interconvert during oscillation, but the total energy remains...
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The key characteristic of the simple harmonic motion is that the acceleration of the system and, therefore, the net force are proportional to the displacement and act in the opposite direction to the displacement. Additionally, the period and frequency of a simple harmonic oscillator are independent of its amplitude. For example, diving boards move faster or slower based on their thickness. A stiff, thick diving board has a large force constant, which causes it to have a smaller period, while a...
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Simple harmonic motion (SHM) is a type of periodic motion in time and position, in which an object oscillates back and forth around an equilibrium position with a constant amplitude and frequency. In SHM, there is a continuous exchange between the potential and kinetic energy, which results in the oscillation of the object.
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While simple harmonic motion and uniform circular motion may be two separate concepts, they correlate and interlink with each other. Simple harmonic motion is an oscillatory motion in a system where the net force can be described by Hooke's law, while uniform circular motion is the motion of an object in a circular path at constant speed.
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Second harmonic inversion for ultrasound contrast harmonic imaging.

Mirza Pasovic1, Mike Danilouchkine, Telli Faez

  • 1THORAXCENTER, Department of Biomedical Engineering Ee2302, Erasmus MC, Rotterdam, The Netherlands. mirza.pasovic@creatis.insa-lyon.fr

Physics in Medicine and Biology
|May 5, 2011
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Second harmonic inversion (SHI) reduces unwanted ultrasound harmonics from tissue, improving contrast agent imaging. This method enhances ultrasound contrast agent imaging by suppressing competing signals, boosting agent-to-tissue ratio.

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Area of Science:

  • Medical Imaging
  • Acoustics
  • Biomedical Engineering

Background:

  • Ultrasound contrast agents (UCAs) are microbubbles exhibiting nonlinear behavior under ultrasound waves.
  • Harmonics generated by UCAs are crucial for imaging, but compete with harmonics from tissue propagation.
  • Existing techniques struggle to isolate UCA-generated harmonics from medium-generated harmonics.

Purpose of the Study:

  • To introduce a novel method, second harmonic inversion (SHI), for reducing second harmonic generation from nonlinear propagation in ultrasound imaging.
  • To derive a general expression for suppression signals used in SHI.
  • To evaluate the effectiveness of SHI in improving ultrasound contrast agent imaging.

Main Methods:

  • The SHI technique utilizes two pulses of identical frequency and amplitude to cancel second harmonic signals generated by tissue nonlinearities.
  • A general expression for the suppression signals was mathematically derived.
  • Simulations and experimental B-mode imaging using a tissue-mimicking phantom and UCAs were performed.

Main Results:

  • Simulations demonstrated a 40 dB reduction in the second harmonic over a large axial range.
  • Experimental SHI imaging showed a 20 dB improvement in the agent-to-tissue ratio (ATR) compared to standard second harmonic imaging.
  • An improvement of 13 dB in harmonic power Doppler was observed with SHI.

Conclusions:

  • Second harmonic inversion effectively suppresses nonlinear propagation artifacts in ultrasound imaging.
  • SHI significantly enhances the contrast-to-tissue ratio, improving the visualization of ultrasound contrast agents.
  • The developed technique offers a substantial advancement for ultrasound contrast imaging applications.