Biomechanics and Modeling in Mechanobiology

, Volume 14, Issue 5, pp 1119–1128 | Cite as

Measuring the linear and nonlinear elastic properties of brain tissue with shear waves and inverse analysis

  • Yi Jiang
  • Guoyang Li
  • Lin-Xue Qian
  • Si Liang
  • Michel DestradeEmail author
  • Yanping CaoEmail author
Original Paper


We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the plane shear waves induced by acoustic radiation force at different states of pre-deformation when the ultrasonic probe is pushed into the soft tissue. We relied on an inverse method based on the theory governing the propagation of small-amplitude acoustic waves in deformed solids to interpret the experimental data. We found that, depending on the subjects, the resulting initial shear modulus \(\mu _0 \) varies from 1.8 to 3.2 kPa, the stiffening parameter \(b\) of the hyperelastic Demiray–Fung model from 0.13 to 0.73, and the third- \((A)\) and fourth-order \((D)\) constants of weakly nonlinear elasticity from \(-\)1.3 to \(-\)20.6 kPa and from 3.1 to 8.7 kPa, respectively. Paired \(t\) test performed on the experimental results of the left and right lobes of the brain shows no significant difference. These values are in line with those reported in the literature on brain tissue, indicating that the SSI method, combined to the inverse analysis, is an efficient and powerful tool for the mechanical characterization of brain tissue, which is of great importance for computer simulation of traumatic brain injury and virtual neurosurgery.


Supersonic shear wave imaging technique Inverse method Brain tissue Elastic and hyperelastic properties 



Supports from the National Natural Science Foundation of China (Grant No. 11172155), Tsinghua University (2012Z02103) and 973 Program of MOST (2010CB631005) are gratefully acknowledged. We also thank the referees for helping us improve greatly previous versions of the article.

Conflict of interest

The authors have no financial and personal relationships that could inappropriately influence or bias this work.

Supplementary material

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Supplementary material 1 (gif 3222 KB)
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institute of Biomechanics and Medical Engineering, AML, Department of Engineering MechanicsTsinghua UniversityBeijingPeople’s Republic of China
  2. 2.Department of Ultrasound, Beijing Friendship HospitalCapital Medical UniversityBeijingPeople’s Republic of China
  3. 3.School of Mathematics, Statistics and Applied MathematicsNational University of Ireland GalwayGalwayIreland

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