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Temple University

1. Laksari, Kaveh. Nonlinear Viscoelastic Wave Propagation in Brain Tissue.

Degree: PhD, 2013, Temple University

Mechanical Engineering

A combination of theoretical, numerical, and experimental methods were utilized to determine that shock waves can form in brain tissue from smooth boundary conditions. The conditions that lead to the formation of shock waves were determined. The implication of this finding was that the high gradients of stress and strain that could occur at the shock wave front could contribute to mechanism of brain injury in blast loading conditions. The approach consisted of three major steps. In the first step, a viscoelastic constitutive model of bovine brain tissue under finite step-and-hold uniaxial compression with 10 1/s ramp rate and 20 s hold time has been developed. The assumption of quasi-linear viscoelasticity (QLV) was validated for strain levels of up to 35%. A generalized Rivlin model was used for the isochoric part of the deformation and it was shown that at least three terms (C_10, C_01 and C_11) are needed to accurately capture the material behavior. Furthermore, for the volumetric deformation, a linear bulk modulus model was used and the extent of material incompressibility was studied. The hyperelastic material parameters were determined through extracting and fitting to two isochronous curves (0.06 s and 14 s) approximating the instantaneous and steady-state elastic responses. Viscoelastic relaxation was characterized at five decay rates (100, 10, 1, 0.1, 0 1/s) and the results in compression and their extrapolation to tension were compared against previous models. In the next step, a framework for understanding the propagation of stress waves in brain tissue under blast loading was developed. It was shown that tissue nonlinearity and rate dependence are key parameters in predicting the mechanical behavior under such loadings, as they determine whether traveling waves could become steeper and eventually evolve into shock discontinuities. To investigate this phenomenon, the QLV material model developed based on finite compression results mentioned above was extended to blast loading rates, by utilizing the stress data published on finite torsion of brain tissue at high rates (up to 700 1/s). It was shown that development of shock waves is possible inside the head in response to compressive pressure waves from blast explosions. Furthermore, it was argued that injury to the nervous tissue at the microstructural level could be attributed to the high stress and strain gradients with high temporal rates generated at the shock front and this was proposed as a mechanism of injury in brain tissue. In the final step, the phenomenon of shock wave formation and propagation in brain tissue was further studied by developing a one-dimensional model of brain tissue using the Discontinuous Galerkin finite element method. This model is capable of capturing high-gradient waves with higher accuracy than commercial finite element software. The deformation of brain tissue was investigated under displacement input and pressure input boundary conditions relevant to blast over-pressure reported in the…

Advisors/Committee Members: Darvish, Kurosh;, Sadeghipour, Keya, Margulies, Susan, Seibold, Benjamin, Crandall, Jeff R.;.

Subjects/Keywords: Engineering; Mechanical engineering; Biomechanics;

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APA (6th Edition):

Laksari, K. (2013). Nonlinear Viscoelastic Wave Propagation in Brain Tissue. (Doctoral Dissertation). Temple University. Retrieved from,242293

Chicago Manual of Style (16th Edition):

Laksari, Kaveh. “Nonlinear Viscoelastic Wave Propagation in Brain Tissue.” 2013. Doctoral Dissertation, Temple University. Accessed October 31, 2020.,242293.

MLA Handbook (7th Edition):

Laksari, Kaveh. “Nonlinear Viscoelastic Wave Propagation in Brain Tissue.” 2013. Web. 31 Oct 2020.


Laksari K. Nonlinear Viscoelastic Wave Propagation in Brain Tissue. [Internet] [Doctoral dissertation]. Temple University; 2013. [cited 2020 Oct 31]. Available from:,242293.

Council of Science Editors:

Laksari K. Nonlinear Viscoelastic Wave Propagation in Brain Tissue. [Doctoral Dissertation]. Temple University; 2013. Available from:,242293