A Transversely Isotropic Viscoelastic Constitutive Equation for Brainstem Undergoing Finite Deformation

[+] Author and Article Information
Xinguo Ning, Qiliang Zhu, Yoram Lanir

Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104-6382

Susan S. Margulies1

Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104-6382margulie@seas.upenn.edu


Corresponding author.

J Biomech Eng 128(6), 925-933 (Jun 29, 2006) (9 pages) doi:10.1115/1.2354208 History: Received September 15, 2005; Revised June 29, 2006

The objective of this study was to define the constitutive response of brainstem undergoing finite shear deformation. Brainstem was characterized as a transversely isotropic viscoelastic material and the material model was formulated for numerical implementation. Model parameters were fit to shear data obtained in porcine brainstem specimens undergoing finite shear deformation in three directions: parallel, perpendicular, and cross sectional to axonal fiber orientation and determined using a combined approach of finite element analysis (FEA) and a genetic algorithm (GA) optimizing method. The average initial shear modulus of brainstem matrix of 4-week old pigs was 12.7Pa, and therefore the brainstem offers little resistance to large shear deformations in the parallel or perpendicular directions, due to the dominant contribution of the matrix in these directions. The fiber reinforcement stiffness was 121.2Pa, indicating that brainstem is anisotropic and that axonal fibers have an important role in the cross-sectional direction. The first two leading relative shear relaxation moduli were 0.8973 and 0.0741, respectively, with corresponding characteristic times of 0.0047 and 1.4538s, respectively, implying rapid relaxation of shear stresses. The developed material model and parameter estimation technique are likely to find broad applications in neural and orthopaedic tissues.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Schematic diagram of shearing directions relative to axonal fiber orientations

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Figure 2

Anatomic locations of specimens of 4-week old pig brainstem for three shearing directions

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Figure 3

3D finite element model of brainstem specimen

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Figure 4

Flowchart to identify optimal material parameters—a combined approach of finite element analysis and genetic algorithm optimizing method

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Figure 5

Variation of cost function with the increase of generation number at the first optimizing step

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Figure 6

Fitting results at the strain level of 50% for experiments: (a) A and (b) B



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