### Abstract

Shear modulus imaging, often called elastography, enables detection and characterization of tissue abnormalities. In this paper the data are two displacement components obtained from successive MR or ultrasound data sets acquired while the tissue is excited mechanically. A 2D plane strain elastic model is assumed to govern the 2D displacement, u. The shear modulus, μ, is unknown and whether or not the first Lamé parameter, λ, is known the pressure p = λ∇ u which is present in the plane strain model cannot be measured and is unreliably computed from measured data and can be shown to be an order one quantity in the units kPa. So here we present a 2D log-elastographic inverse algorithm that (1) simultaneously reconstructs the shear modulus, μ, and p, which together satisfy a first-order partial differential equation system, with the goal of imaging μ; (2) controls potential exponential growth in the numerical error and (3) reliably reconstructs the quantity p in the inverse algorithm as compared to the same quantity computed with a forward algorithm. This work generalizes the log-elastographic algorithm in Lin et al (2009 Inverse Problems 25) which uses one displacement component, is derived assuming that the component satisfies the wave equation and is tested on synthetic data computed with the wave equation model. The 2D log-elastographic algorithm is tested on 2D synthetic data and 2D in vivo data from Mayo Clinic. We also exhibit examples to show that the 2D log-elastographic algorithm improves the quality of the recovered images as compared to the log-elastographic and direct inversion algorithms.

Original language | English (US) |
---|---|

Article number | 085007 |

Journal | Inverse Problems |

Volume | 26 |

Issue number | 8 |

DOIs | |

State | Published - 2010 |

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### ASJC Scopus subject areas

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

### Cite this

*Inverse Problems*,

*26*(8), [085007]. https://doi.org/10.1088/0266-5611/26/8/085007

**Calculating tissue shear modulus and pressure by 2D log-elastographic methods.** / McLaughlin, Joyce R.; Zhang, Ning; Manduca, Armando.

Research output: Contribution to journal › Article

*Inverse Problems*, vol. 26, no. 8, 085007. https://doi.org/10.1088/0266-5611/26/8/085007

}

TY - JOUR

T1 - Calculating tissue shear modulus and pressure by 2D log-elastographic methods

AU - McLaughlin, Joyce R.

AU - Zhang, Ning

AU - Manduca, Armando

PY - 2010

Y1 - 2010

N2 - Shear modulus imaging, often called elastography, enables detection and characterization of tissue abnormalities. In this paper the data are two displacement components obtained from successive MR or ultrasound data sets acquired while the tissue is excited mechanically. A 2D plane strain elastic model is assumed to govern the 2D displacement, u. The shear modulus, μ, is unknown and whether or not the first Lamé parameter, λ, is known the pressure p = λ∇ u which is present in the plane strain model cannot be measured and is unreliably computed from measured data and can be shown to be an order one quantity in the units kPa. So here we present a 2D log-elastographic inverse algorithm that (1) simultaneously reconstructs the shear modulus, μ, and p, which together satisfy a first-order partial differential equation system, with the goal of imaging μ; (2) controls potential exponential growth in the numerical error and (3) reliably reconstructs the quantity p in the inverse algorithm as compared to the same quantity computed with a forward algorithm. This work generalizes the log-elastographic algorithm in Lin et al (2009 Inverse Problems 25) which uses one displacement component, is derived assuming that the component satisfies the wave equation and is tested on synthetic data computed with the wave equation model. The 2D log-elastographic algorithm is tested on 2D synthetic data and 2D in vivo data from Mayo Clinic. We also exhibit examples to show that the 2D log-elastographic algorithm improves the quality of the recovered images as compared to the log-elastographic and direct inversion algorithms.

AB - Shear modulus imaging, often called elastography, enables detection and characterization of tissue abnormalities. In this paper the data are two displacement components obtained from successive MR or ultrasound data sets acquired while the tissue is excited mechanically. A 2D plane strain elastic model is assumed to govern the 2D displacement, u. The shear modulus, μ, is unknown and whether or not the first Lamé parameter, λ, is known the pressure p = λ∇ u which is present in the plane strain model cannot be measured and is unreliably computed from measured data and can be shown to be an order one quantity in the units kPa. So here we present a 2D log-elastographic inverse algorithm that (1) simultaneously reconstructs the shear modulus, μ, and p, which together satisfy a first-order partial differential equation system, with the goal of imaging μ; (2) controls potential exponential growth in the numerical error and (3) reliably reconstructs the quantity p in the inverse algorithm as compared to the same quantity computed with a forward algorithm. This work generalizes the log-elastographic algorithm in Lin et al (2009 Inverse Problems 25) which uses one displacement component, is derived assuming that the component satisfies the wave equation and is tested on synthetic data computed with the wave equation model. The 2D log-elastographic algorithm is tested on 2D synthetic data and 2D in vivo data from Mayo Clinic. We also exhibit examples to show that the 2D log-elastographic algorithm improves the quality of the recovered images as compared to the log-elastographic and direct inversion algorithms.

UR - http://www.scopus.com/inward/record.url?scp=77953792370&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77953792370&partnerID=8YFLogxK

U2 - 10.1088/0266-5611/26/8/085007

DO - 10.1088/0266-5611/26/8/085007

M3 - Article

AN - SCOPUS:77953792370

VL - 26

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 8

M1 - 085007

ER -