### Abstract

Magnetic resonance elastography (MRE) is a phase-contrast MRI based technique that allows quantitative, noninvasive assessment of the mechanical properties of tissues by the introduction of shear waves into the body and measurement of the resulting displacements. In MRE, the calculated stiffness values are affected by noise, which is amplified by the inversion process. It would be useful to know that beyond some SNR threshold, the stiffness values are accurate within some confidence limit. The most common methods to calculate SNR values in MRE are variations of displacement SNR, which estimate the noise in the measured displacement. However, the accuracy of stiffness determination depends not only on the displacement SNR, but also on the wavelength of the shear wave, in turn dependent on the stiffness of the underlying material. More recently, the SNR of the octahedral shear strain (OSS) has been proposed as a more appropriate measure, since shear deformation is the signal in MRE. We also propose here another measure based on the SNR of the Laplacian of the data, since this is the most noise sensitive quantity calculated when performing direct inversion of the Helmholtz equation. The three SNR measures were compared on simulated data for materials of different stiffness with varying amounts of noise using three inversion algorithms commonly used in MRE (phase gradient, local frequency estimation, and direct inversion). We demonstrate that the proper SNR measure for MRE depends on the inversion algorithm used, and, more precisely, on the order of derivatives used in the inversion process.

Original language | English (US) |
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Title of host publication | Progress in Biomedical Optics and Imaging - Proceedings of SPIE |

Publisher | SPIE |

Volume | 9417 |

ISBN (Print) | 9781628415070 |

DOIs | |

State | Published - 2015 |

Event | Medical Imaging 2015: Biomedical Applications in Molecular, Structural, and Functional Imaging - Orlando, United States Duration: Feb 24 2015 → Feb 26 2015 |

### Other

Other | Medical Imaging 2015: Biomedical Applications in Molecular, Structural, and Functional Imaging |
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Country | United States |

City | Orlando |

Period | 2/24/15 → 2/26/15 |

### Fingerprint

### Keywords

- Direct inversion
- Helmholtz equation
- Laplacian
- Local frequency estimation
- Magnetic resonance elastography
- Octahedral shear strain
- Phase gradient
- Shear stiffness
- Signal-to-noise ratio

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Electronic, Optical and Magnetic Materials
- Biomaterials
- Radiology Nuclear Medicine and imaging

### Cite this

*Progress in Biomedical Optics and Imaging - Proceedings of SPIE*(Vol. 9417). [94171K] SPIE. https://doi.org/10.1117/12.2083371

**A Laplacian-based SNR measure : Shear stiffness estimation in MR elastography.** / Eon, Rehman S.; Huynh, Khang T.; Lake, David S.; Manduca, Armando.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Progress in Biomedical Optics and Imaging - Proceedings of SPIE.*vol. 9417, 94171K, SPIE, Medical Imaging 2015: Biomedical Applications in Molecular, Structural, and Functional Imaging, Orlando, United States, 2/24/15. https://doi.org/10.1117/12.2083371

}

TY - GEN

T1 - A Laplacian-based SNR measure

T2 - Shear stiffness estimation in MR elastography

AU - Eon, Rehman S.

AU - Huynh, Khang T.

AU - Lake, David S.

AU - Manduca, Armando

PY - 2015

Y1 - 2015

N2 - Magnetic resonance elastography (MRE) is a phase-contrast MRI based technique that allows quantitative, noninvasive assessment of the mechanical properties of tissues by the introduction of shear waves into the body and measurement of the resulting displacements. In MRE, the calculated stiffness values are affected by noise, which is amplified by the inversion process. It would be useful to know that beyond some SNR threshold, the stiffness values are accurate within some confidence limit. The most common methods to calculate SNR values in MRE are variations of displacement SNR, which estimate the noise in the measured displacement. However, the accuracy of stiffness determination depends not only on the displacement SNR, but also on the wavelength of the shear wave, in turn dependent on the stiffness of the underlying material. More recently, the SNR of the octahedral shear strain (OSS) has been proposed as a more appropriate measure, since shear deformation is the signal in MRE. We also propose here another measure based on the SNR of the Laplacian of the data, since this is the most noise sensitive quantity calculated when performing direct inversion of the Helmholtz equation. The three SNR measures were compared on simulated data for materials of different stiffness with varying amounts of noise using three inversion algorithms commonly used in MRE (phase gradient, local frequency estimation, and direct inversion). We demonstrate that the proper SNR measure for MRE depends on the inversion algorithm used, and, more precisely, on the order of derivatives used in the inversion process.

AB - Magnetic resonance elastography (MRE) is a phase-contrast MRI based technique that allows quantitative, noninvasive assessment of the mechanical properties of tissues by the introduction of shear waves into the body and measurement of the resulting displacements. In MRE, the calculated stiffness values are affected by noise, which is amplified by the inversion process. It would be useful to know that beyond some SNR threshold, the stiffness values are accurate within some confidence limit. The most common methods to calculate SNR values in MRE are variations of displacement SNR, which estimate the noise in the measured displacement. However, the accuracy of stiffness determination depends not only on the displacement SNR, but also on the wavelength of the shear wave, in turn dependent on the stiffness of the underlying material. More recently, the SNR of the octahedral shear strain (OSS) has been proposed as a more appropriate measure, since shear deformation is the signal in MRE. We also propose here another measure based on the SNR of the Laplacian of the data, since this is the most noise sensitive quantity calculated when performing direct inversion of the Helmholtz equation. The three SNR measures were compared on simulated data for materials of different stiffness with varying amounts of noise using three inversion algorithms commonly used in MRE (phase gradient, local frequency estimation, and direct inversion). We demonstrate that the proper SNR measure for MRE depends on the inversion algorithm used, and, more precisely, on the order of derivatives used in the inversion process.

KW - Direct inversion

KW - Helmholtz equation

KW - Laplacian

KW - Local frequency estimation

KW - Magnetic resonance elastography

KW - Octahedral shear strain

KW - Phase gradient

KW - Shear stiffness

KW - Signal-to-noise ratio

UR - http://www.scopus.com/inward/record.url?scp=84943418418&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84943418418&partnerID=8YFLogxK

U2 - 10.1117/12.2083371

DO - 10.1117/12.2083371

M3 - Conference contribution

AN - SCOPUS:84943418418

SN - 9781628415070

VL - 9417

BT - Progress in Biomedical Optics and Imaging - Proceedings of SPIE

PB - SPIE

ER -