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Related Concept Videos

NMR Spectrometers: Radiofrequency Pulses and Pulse Sequences01:17

NMR Spectrometers: Radiofrequency Pulses and Pulse Sequences

A pulse is a short burst of radio waves distributed over a range of frequencies that simultaneously excites all the nuclei in the sample. Upon passing a radio frequency pulse along the x-axis, the nuclei absorb energy corresponding to their Larmor frequencies and achieve resonance. This shifts the net magnetization vector from the z-axis toward the transverse plane. This angle of rotation of the magnetization vector, or the flip angle, is proportional to the duration and intensity of the pulse.
Magnetic Resonance Imaging01:24

Magnetic Resonance Imaging

Magnetic resonance imaging (MRI) is a noninvasive medical imaging technique based on a phenomenon of nuclear physics discovered in the 1930s, in which matter exposed to magnetic fields and radio waves was found to emit radio signals. In 1970, a physician and researcher named Raymond Damadian noticed that malignant (cancerous) tissue gave off different signals than normal body tissue. He applied for a patent for the first MRI scanning device in clinical use by the early 1980s. The early MRI...
Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis. This...
NMR Spectrometers: Resolution and Error Correction01:14

NMR Spectrometers: Resolution and Error Correction

When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the others.

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MRI pulse sequence design with first-order gradient moment nulling in arbitrary directions by solving a polynomial

Kurt Majewski1, Oliver Heid, Thomas Kluge

  • 1Siemens AG, Corporate Technology, 81739 Munich, Germany. kurt.majewski@siemens.com

IEEE Transactions on Medical Imaging
|March 23, 2010
PubMed
Summary

We developed a polynomial program to optimize gradient waveforms for magnetic resonance tomography pulse sequences, improving image quality by reducing motion artifacts.

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Area of Science:

  • Medical Imaging
  • Applied Mathematics
  • Magnetic Resonance Imaging

Background:

  • Magnetic Resonance Imaging (MRI) relies on precisely controlled gradient waveforms.
  • Optimizing these waveforms is crucial for image quality and artifact reduction.
  • Current methods may not fully capture complex system constraints or desired imaging properties.

Purpose of the Study:

  • To introduce a novel polynomial programming approach for designing optimized gradient waveforms in MRI.
  • To demonstrate the capability of this method in handling gradient system limitations, k-space trajectories, and timing constraints.
  • To incorporate gradient moment nulling for artifact reduction.

Main Methods:

  • Formulation of gradient waveform optimization as a non-linear mathematical program.
  • Inclusion of gradient system capabilities, k-space trajectory specifications, and timing conditions.
  • Implementation of gradient moment nulling constraints in arbitrary spatial directions.
  • Utilizing the interior point solver Ipopt for solving the optimization problem.

Main Results:

  • Successful application of polynomial programming for calculating optimized gradient waveforms.
  • Demonstrated ability to meet complex sequence design specifications.
  • Effective incorporation of gradient moment nulling to mitigate flow motion artifacts.

Conclusions:

  • Polynomial programming offers a powerful framework for automatic pulse sequence design in MRI.
  • This approach enables the generation of sophisticated gradient waveforms tailored to specific imaging needs.
  • The method shows promise for enhancing image quality by reducing motion-related artifacts.