Measuring the linear and nonlinear elastic properties of brain tissue with shear waves and inverse analysis
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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.
KeywordsSupersonic 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.
- Chatelin S, Constantinesco A, Willinger R (2010) Fifty years of brain tissue mechanical testing: from in vitro to in vivo investigations. Biorheology 47:255–276Google Scholar
- Hrapko M, Van Dommelen JAW, Peters GWM, Wismans JSHM (2006) The mechanical behaviour of brain tissue: large strain response and constitutive modelling. Biorheology 43:623–636Google Scholar
- Kleiven S, Hardy WN (2002) Correlation of an FE model of the human head with local brain motion-consequences for injury prediction. Stapp Car Crash J 46:123–144Google Scholar
- Nicolle S, Lounis M, Willinger R, Palierne JF (2005) Shear linear behavior of brain tissue over a large frequency range. Biorheology 42:209–223Google Scholar
- Ogden RW (2007) Incremental statics and dynamics of pre-stressed elastic materials. In: Destrade M, Saccomandi G (eds) Waves in nonlinear pre-stressed materials. Springer, Vienna, pp 1–26Google Scholar
- Streitberger KJ, Wiener E, Hoffmann J, Freimann FB, Klatt D, Braun J, Sack I (2011) In vivo viscoelastic properties of the brain in normal pressure hydrocephalus. NMR Biomed 24:385–392Google Scholar
- Zhang L, Yang KH, Dwarampudi R, Omori K, Li T, Chang K, Hardy WN, Khalil TB, King AI (2001) Recent advances in brain injury research: a new human head model development and validation. Stapp Car Crash J 45:369–394Google Scholar