Dynamic Behavior of Brain Tissue under Transient Loading

Authors: Y. J. Zhou, G. Lu

Abstract:

In this paper, an analytical study is made for the dynamic behavior of human brain tissue under transient loading. In this analytical model the Mooney-Rivlin constitutive law is coupled with visco-elastic constitutive equations to take into account both the nonlinear and time-dependent mechanical behavior of brain tissue. Five ordinary differential equations representing the relationships of five main parameters (radial stress, circumferential stress, radial strain, circumferential strain, and particle velocity) are obtained by using the characteristic method to transform five partial differential equations (two continuity equations, one motion equation, and two constitutive equations). Analytical expressions of the attenuation properties for spherical wave in brain tissue are analytically derived. Numerical results are obtained based on the five ordinary differential equations. The mechanical responses (particle velocity and stress) of brain are compared at different radii including 5, 6, 10, 15 and 25 mm under four different input conditions. The results illustrate that loading curves types of the particle velocity significantly influences the stress in brain tissue. The understanding of the influence by the input loading cures can be used to reduce the potentially injury to brain under head impact by designing protective structures to control the loading curves types.

Keywords: Analytical method, mechanical responses, spherical wave propagation, traumatic brain injury.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1093952

References:

[1] D.J. Thurman, C. Alverson, K.A. Dunn, J. Guerrero, and J.E. Sniezek, "Traumatic brain injury in the United States: A public health perspective,” J. Head. Trauma. Rehab., vol. 14, pp. 602-15, 1999.
[2] A. Anzelius, "The effect of an impact on a spherical liquid mass,” Acta. Pathol. Mic. Sc. , vol. 48, pp. 153-159, 1943.
[3] E. Engin, "Axisymmetric response of a fluid-filled spherical shell to a local radial impulse: a model for head injury,” J. Biomech., vol. 2, pp. 325-341, 1969.
[4] O. Talhouni and F. DiMaggio, "Dynamic response of a fluid-filled spheroidal shell—An improved model for studying head injury,” J. Biomech., vol. 8, pp. 219-228, 1975.
[5] P.G. Young, "An analytical model to predict the response of fluid-filled shells to impact - a model for blunt head impacts,”J. Sound. Vib., vol. 267, pp. 1107-1126, 2003.
[6] M. Heydari and S. Jani, "An ellipsoidal model for studying response of head impacts,”Acta. Bioeng. Biomech., vol. 12, pp. 47-53, 2010.
[7] R.C. Chivers and R.J. Parry, "Ultrasonic velocity and attenuation in mammalian tissues,”J. Acoust. Soc. Am., vol. 63, pp. 940-953, 1978.
[8] F.W. Kremkau, R.W. Barnes, and C.P. McGraw, "Ultrasonic attenuation and propagation speed in normal human brain,”J. Acoust. Soc. Am., vol. 70, pp. 29-38, 1981.
[9] M. Valdez and B. Balachandran, "Longitudinal nonlinear wave propagation through soft tissue,”J. Mech. Behav. Biomed. Mater., vol. 20, pp. 192-208, 2013.
[10] D.W.A. Brands, G.W.M. Peters, and P.H.M. Bovendeerd, "Design and numerical implementation of a 3-D non-linear viscoelastic constitutive model for brain tissue during impact,”J. Biomech., vol. 37, pp. 127-134, 2004.
[11] L.-L. Wang, H.-W. Lai, Z.-J. Wang, and L.-M. Yang, "Studies on nonlinear visco-elastic spherical waves by characteristics analyses and its application,”Int. J. Impact. Eng., vol. 55, pp. 1-10, 2013.
[12] K. Miller and K. Chinzei, "Constitutive modelling of brain tissue: experiment and theory,”J. Biomech., vol. 30, pp. 1115-1121, 1997.
[13] K.K. Mendis, R.L. Stalnaker, and S.H. Advani, "A constitutive relationship for large deformation finite element modeling of brain tissue,”J. Biomech. Eng., vol. 117, pp. 279-85, 1995.
[14] S. Kleiven and W.N. Hardy, "Correlation of an FE model of the human head with local brain motion--consequences for injury prediction,”Stapp Car Crash J., vol. 46, pp. 123-44, 2002.
[15] R.M. Wright, A computational model for traumatic brain injury based on an axonal injury criterion. Ann Arbor: The Johns Hopkins University, 2012.