A Non-invasive Method to Estimate the Stress–Strain Curve of Soft Tissue Using Ultrasound Elastography

Yuqi Wang, Daniel S. Jacobson, Matthew W. Urban

Research output: Contribution to journalArticlepeer-review


Ultrasound elastography performed under small strain conditions has been intensively studied. However, small deformations may be not sufficiently large to differentiate some abnormal tissues. By combining quasi-static and shear wave elastography, we developed a non-invasive method to estimate the localized stress– strain curve of materials. This method exerts progressive multistep uniaxial compression on the materials, and shear wave measurements were performed at every compression step. This method estimates the 2-D displacements between steps via a 2-D region growing motion tracking method and accumulates these displacements to obtain the large material displacements with respect to the initial configuration. At each step, the shear modulus and stress were calculated according to linear elastic theory. The proposed method was tested on custom-made tissue-mimicking phantoms. Mechanical compression testing was conducted on the samples made of the same material as the phantoms and taken as the reference. The stress–strain curves for the same material from the proposed method and from mechanical testing are in good agreement. The root mean square error (RMSE) and area percentage error (APE) of the stress–strain curve between ultrasound measurement and mechanical testing for soft materials ranged from 0.18 to 0.26 kPa and from 5.6% to 7.8%, respectively. The RMSE and APE for stiff materials ranged from 0.56 to 1.17 kPa and 8.0% to 17.9%. Therefore, our method was able to provide good estimates of the stress–strain curve for tissue-mimicking materials.

Original languageEnglish (US)
Pages (from-to)786-807
Number of pages22
JournalUltrasound in Medicine and Biology
Issue number5
StatePublished - May 2022


  • Large strain
  • Non-linear elasticity
  • Stress–strain curve
  • Ultrasound elastography

ASJC Scopus subject areas

  • Radiological and Ultrasound Technology
  • Biophysics
  • Acoustics and Ultrasonics


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