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Updated: Jan 24, 2026

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
Published on: July 28, 2013
Statistical tensor analysis of the MQ MR signals generated by weak quadrupole interactions
1CIMAR, National High Magnetic Field Laboratory/FSU, Tallahassee, FL, USA.
Abstract:
Multiple quantum NMR signals that appear in the presence of weak quadrupole interactions were formulated using statistical tensors (Fano, 1957). The approach aimed to present a concise and a computer-based tool for a detailed analysis and modification of the MQ pulse sequences. The calculation avoids a lengthy procedure of utilizing exponential operators and, moreover, the same formulae are applicable for any interval in the TQ pulse sequence, as well as any spin value. The quantum operator algebra was implemented using "Mathematica" software (Wolfram Inc.). The results of tensor's evolutions in the TQ pulse sequence were graphically illustrated using corresponding spherical harmonics. The visualization takes into consideration the parity properties of irreducible tensors and the corresponding spherical harmonics.
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