Estimation of displacement vectors and strain tensors in elastography using angular insonifications

U. Techavipoo, Q. Chen, T. Varghese, J. A. Zagzebski

Research output: Contribution to journalArticlepeer-review

97 Scopus citations


In current practice, only one out of three components of the tissue displacement vector and one of nine components of the strain tensor are accurately estimated and imaged in ultrasound elastography. Since, only the axial component of both the displacement and strain are imaged, other important elastic parameters, such as shear strains and the Poisson's ratio, also are not imaged. Moreover, reconstruction of the Young's modulus would be significantly improved if all components of the strain tensor were available. In this paper, we describe a new method for estimating all the components of the tissue displacement vector following a quasi-static compression. The method uses displacements estimated from radiofrequency echo-signals along multiple ultrasound beam insonification directions. At each spatial location in the compressed medium, orthogonal tissue displacements in both the axial and lateral direction with respect to the direction of the applied compression are estimated by curve fitting angular displacement vector data calculated for all insonification directions. Following displacement estimation in orthogonal directions, components of the corresponding normal and shear strain tensors are estimated. Simulation and experimental results demonstrate the utility of this technique for the computation of the normal and shear strain tensors.

Original languageEnglish
Pages (from-to)1479-1489
Number of pages11
JournalIEEE Transactions on Medical Imaging
Issue number12
StatePublished - Dec 2004

Bibliographical note

Funding Information:
Manuscript received March 5, 2004; revised July 27, 2004. This work was supported in part by the Wisconsin Alumni Research Foundation (WARF) and in part by the National Institutes of Health (NIH) under Grant R21 EB003853 and Grant 1R21EB002722. The work of T. Varghese was supported in part by start-up grant funds from the University of Wisconsin-Madison. The Associate Editor responsible for coordinating the review of this paper and recommending its publication was M. Insana. Asterisk indicates corresponding author.


  • Angular strain
  • Axial strain
  • Displacement
  • Elasticity
  • Elasticity imaging
  • Elastogram
  • Elastography
  • Imaging
  • Lateral strain
  • Least squares
  • Linear model
  • Poisson's ratio
  • Shear
  • Shear strain
  • Strain

ASJC Scopus subject areas

  • Software
  • Radiological and Ultrasound Technology
  • Computer Science Applications
  • Electrical and Electronic Engineering


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