### Abstract

Transient elastography and supersonic imaging are promising new techniques for characterizing the elasticity of soft tissues. Using this method, an 'ultrafast imaging' system (up to 10 000 frames s^{-1}) follows in real time the propagation of a low frequency shear wave. The displacement of the propagating shear wave is measured as a function of time and space. The objective of this paper is to develop and test algorithms whose ultimate product is images of the shear wave speed of tissue mimicking phantoms. The data used in the algorithms are the front of the propagating shear wave. Here, we first develop techniques to find the arrival time surface given the displacement data from a transient elastography experiment. The arrival time surface satisfies the Eikonal equation. We then propose a family of methods, called distance methods, to solve the inverse Eikonal equation: given the arrival times of a propagating wave, find the wave speed. Lastly, we explain why simple inversion schemes for the inverse Eikonal equation lead to large outliers in the wave speed and numerically demonstrate that the new scheme presented here does not have any large outliers. We exhibit two recoveries using these methods: one is with synthetic data; the other is with laboratory data obtained by Mathias Fink's group (the Laboratoire Ondes et Acoustique, ESPCI, Université Paris VII).

Original language | English |
---|---|

Pages (from-to) | 681-706 |

Number of pages | 26 |

Journal | Inverse Problems |

Volume | 22 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Apr 2006 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Signal Processing
- Mathematical Physics
- Computer Science Applications
- Applied Mathematics

### Cite this

*Inverse Problems*,

*22*(2), 681-706. https://doi.org/10.1088/0266-5611/22/2/018

**Shear wave speed recovery in transient elastography and supersonic imaging using propagating fronts.** / McLaughlin, Joyce; Renzi, Paul.

Research output: Contribution to journal › Article

*Inverse Problems*, vol. 22, no. 2, pp. 681-706. https://doi.org/10.1088/0266-5611/22/2/018

}

TY - JOUR

T1 - Shear wave speed recovery in transient elastography and supersonic imaging using propagating fronts

AU - McLaughlin, Joyce

AU - Renzi, Paul

PY - 2006/4/1

Y1 - 2006/4/1

N2 - Transient elastography and supersonic imaging are promising new techniques for characterizing the elasticity of soft tissues. Using this method, an 'ultrafast imaging' system (up to 10 000 frames s-1) follows in real time the propagation of a low frequency shear wave. The displacement of the propagating shear wave is measured as a function of time and space. The objective of this paper is to develop and test algorithms whose ultimate product is images of the shear wave speed of tissue mimicking phantoms. The data used in the algorithms are the front of the propagating shear wave. Here, we first develop techniques to find the arrival time surface given the displacement data from a transient elastography experiment. The arrival time surface satisfies the Eikonal equation. We then propose a family of methods, called distance methods, to solve the inverse Eikonal equation: given the arrival times of a propagating wave, find the wave speed. Lastly, we explain why simple inversion schemes for the inverse Eikonal equation lead to large outliers in the wave speed and numerically demonstrate that the new scheme presented here does not have any large outliers. We exhibit two recoveries using these methods: one is with synthetic data; the other is with laboratory data obtained by Mathias Fink's group (the Laboratoire Ondes et Acoustique, ESPCI, Université Paris VII).

AB - Transient elastography and supersonic imaging are promising new techniques for characterizing the elasticity of soft tissues. Using this method, an 'ultrafast imaging' system (up to 10 000 frames s-1) follows in real time the propagation of a low frequency shear wave. The displacement of the propagating shear wave is measured as a function of time and space. The objective of this paper is to develop and test algorithms whose ultimate product is images of the shear wave speed of tissue mimicking phantoms. The data used in the algorithms are the front of the propagating shear wave. Here, we first develop techniques to find the arrival time surface given the displacement data from a transient elastography experiment. The arrival time surface satisfies the Eikonal equation. We then propose a family of methods, called distance methods, to solve the inverse Eikonal equation: given the arrival times of a propagating wave, find the wave speed. Lastly, we explain why simple inversion schemes for the inverse Eikonal equation lead to large outliers in the wave speed and numerically demonstrate that the new scheme presented here does not have any large outliers. We exhibit two recoveries using these methods: one is with synthetic data; the other is with laboratory data obtained by Mathias Fink's group (the Laboratoire Ondes et Acoustique, ESPCI, Université Paris VII).

UR - http://www.scopus.com/inward/record.url?scp=33645275457&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645275457&partnerID=8YFLogxK

U2 - 10.1088/0266-5611/22/2/018

DO - 10.1088/0266-5611/22/2/018

M3 - Article

VL - 22

SP - 681

EP - 706

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 2

ER -