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Research Papers

Characterizing Heterogeneous Properties of Cerebral Aneurysms With Unknown Stress-Free Geometry: A Precursor to In Vivo Identification

[+] Author and Article Information
Xuefeng Zhao1

Department of Mechanical and Industrial Engineering, Center for Computer Aided Design, University of Iowa, Iowa City, IA 52242-1527

Madhavan L. Raghavan

Department of Biomedical Engineering, University of Iowa, Iowa City, IA 52242

Jia Lu2

Department of Mechanical and Industrial Engineering, Center for Computer Aided Design, University of Iowa, Iowa City, IA 52242-1527jia-lu@uiowa.edu

1

Present address: Department of Biomedical Engineering, Indiana University Purdue University Indianapolis, Indianapolis, IN 46202.

2

Corresponding author.

J Biomech Eng 133(5), 051008 (May 03, 2011) (12 pages) doi:10.1115/1.4003872 History: Received December 09, 2010; Revised March 10, 2011; Posted March 28, 2011; Published May 03, 2011; Online May 03, 2011

Knowledge of elastic properties of cerebral aneurysms is crucial for understanding the biomechanical behavior of the lesion. However, characterizing tissue properties using in vivo motion data presents a tremendous challenge. Aside from the limitation of data accuracy, a pressing issue is that the in vivo motion does not expose the stress-free geometry. This is compounded by the nonlinearity, anisotropy, and heterogeneity of the tissue behavior. This article introduces a method for identifying the heterogeneous properties of aneurysm wall tissue under unknown stress-free configuration. In the proposed approach, an accessible configuration is taken as the reference; the unknown stress-free configuration is represented locally by a metric tensor describing the prestrain from the stress-free configuration to the reference configuration. Material parameters are identified together with the metric tensor pointwisely. The paradigm is tested numerically using a forward-inverse analysis loop. An image-derived sac is considered. The aneurysm tissue is modeled as an eight-ply laminate whose constitutive behavior is described by an anisotropic hyperelastic strain-energy function containing four material parameters. The parameters are assumed to vary continuously in two assigned patterns to represent two types of material heterogeneity. Nine configurations between the diastolic and systolic pressures are generated by forward quasi-static finite element analyses. These configurations are fed to the inverse analysis to delineate the material parameters and the metric tensor. The recovered and the assigned distributions are in good agreement. A forward verification is conducted by comparing the displacement solutions obtained from the recovered and the assigned material parameters at a different pressure. The nodal displacements are found in excellent agreement.

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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Schematic representation of local fiber distribution in the stress-free state, with respect to a local basis G1−G2 (adapted from Refs. 39-40)

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Figure 2

The reference distributions of the elastic parameters E1 and E2. Upper row: case I. Lower row: case II.

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Figure 3

Distribution of the first principal direction η1 (red lines) and the second principal direction η2 (blue lines), which correspond to the first and fifth collagen fiber directions, respectively (color online only)

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Figure 4

Distribution of the relative maximum stretch ratio from 80 mm Hg to 160 mm Hg: (a) case I and (b) case II

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Figure 5

Absolute relative percentage difference of the first principal stress at variously pressures after increasing the baseline material parameters in the modified neo-Hookean model by 100 times, i.e., ν1=ν2=500 N/mm

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Figure 6

Three of the 17 loaded configurations and the distribution of the first principal stress computed from forward finite element analyses (first row) and finite element inverse elastostatics method (second row). Third row: Absolute relative percentage difference of the first principal stress between the inverse and forward solutions.

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Figure 7

Identification results for case I. First row: The identified distributions. Second row: Distribution of the identification errors. Third row: Scatter dot plots of the identification errors. The total number of dots at particular y is the occurrence of that value. The horizontal line indicates the mean.

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Figure 8

Comparison between the identified (red solid lines) and true (blue dashed lines) first principal direction η1, which correspond to the first collagen fiber direction. The fiber directions are plotted at the Gauss points (color online only).

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Figure 9

Identification results for case II. First row: The identified distributions. Second row: Distribution of the identification errors. Third row: Scatter dot plots of the identification errors.

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Figure 10

Predictability of the identified elastic property distribution for case I: (a) Predicted loaded configurations from the reference material (solid surface) and the identified material (mesh) at 170 mm Hg. (b) Percentage deviation in nodal displacement.

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Figure 11

Distribution of the relative maximum stretch ratio from 50 mm Hg to 200 mm Hg for case I with a widened pressure range.

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Figure 12

Identification results for case I with larger in vivo deformation. Upper row: Distribution of the identification errors. Lower row: Scatter dot plots of the identification errors.

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