0
TECHNICAL PAPERS: Soft Tissue

# 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

1

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

## Abstract

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.

<>

## Figures

Figure 1

Schematic diagram of shearing directions relative to axonal fiber orientations

Figure 2

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

Figure 3

3D finite element model of brainstem specimen

Figure 4

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

Figure 5

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

Figure 6

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

## Discussions

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections