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Updated: Jun 19, 2026

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
Published on: July 28, 2013
1-Norm waveform analysis for MR elastography-based quantification of inhomogeneity: Effects of the freeze-thaw cycle
Harish Palnitkar1, Rolf Reiter2, Shreyan Majumdar3
1Department of Mechanical and Industrial Engineering, University of Illinois Chicago, Chicago, IL, 60607, United States; Department of Radiology, Mayo Clinic, 200 First St SW, Rochester, MN, 55905, United States.
Background:
Despite its success in the mechanical characterization of biological tissues, magnetic resonance elastography (MRE) uses ill-posed wave inversions to estimate tissue stiffness. 1-Norm has been recently introduced as a mathematical measure for the scattering of mechanical waves due to inhomogeneities based on an analysis of the delineated contours of wave displacement.
Purpose:
To investigate 1-Norm as an MRE-based quantitative biomarker of mechanical inhomogeneities arising from microscopic structural tissue alterations caused by the freeze-thaw cycle (FTC) or Alzheimer's disease (AD).
Methods:
In this proof-of-concept study, we prospectively investigated excised porcine kidney (n = 6), liver (n = 6), and muscle (n = 6) before vs. after the FTC at 500-2000 Hz and excised murine brain of healthy controls (n = 3) vs. 5xFAD species with AD (n = 3) at 1200-1800 Hz using 0.5 T tabletop MRE. 1-Norm analysis was compared with conventional wave inversion.
Results:
While the FTC reduced both stiffness and inhomogeneity in kidney, liver, and muscle tissue, AD led to lower brain stiffness but more pronounced mechanical inhomogeneity.
Conclusion:
Our preliminary results show that 1-Norm is sensitive to tissue mechanical inhomogeneity due to FTC and AD without relying on ill-posed wave inversion techniques. 1-Norm has the potential to be used as an MRE-based diagnostic biomarker independent of stiffness to characterize abnormal conditions that involve changes in tissue mechanical inhomogeneity.

