An analytical solution to the dispersion-by-inversion problem in magnetic resonance elastography

Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine
Joaquin MuraIngolf Sack

Abstract

Magnetic resonance elastography (MRE) measures stiffness of soft tissues by analyzing their spatial harmonic response to externally induced shear vibrations. Many MRE methods use inversion-based reconstruction approaches, which invoke first- or second-order derivatives by finite difference operators (first- and second-FDOs) and thus give rise to a biased frequency dispersion of stiffness estimates. We here demonstrate analytically, numerically, and experimentally that FDO-based stiffness estimates are affected by (1) noise-related underestimation of values in the range of high spatial wave support, that is, at lower vibration frequencies, and (2) overestimation of values due to wave discretization at low spatial support, that is, at higher vibration frequencies. Our results further demonstrate that second-FDOs are more susceptible to noise than first-FDOs and that FDO dispersion depends both on signal-to-noise ratio (SNR) and on a lumped parameter A, which is defined as wavelength over pixel size and over a number of pixels per stencil of the FDO. Analytical FDO dispersion functions are derived for optimizing A parameters at a given SNR. As a simple rule of thumb, we show that FDO artifacts are minimized when A/2 is in the rang...Continue Reading

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Citations

Dec 17, 2020·Acta Biomaterialia·Helge HerthumIngolf Sack
Dec 10, 2020·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Armando ManducaBernard E Van Beers
Jun 30, 2021·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Ledia LilajIngolf Sack
Oct 30, 2021·Journal of Magnetic Resonance Imaging : JMRI·Andrew T Trout, Jean A Tkach
Nov 10, 2021·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Jakob Ernst Luis JordanIngolf Sack

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