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Research Papers

On Sources of Error in Finite Element Simulations of Blast Effects in the Human Brain

[+] Author and Article Information
Krysl Petr1

Department of Structural Engineering,Jacobs School of Engineering,  University of California, San Diego, La Jolla, CA 92093pkrysl@ucsd.edu

Mark W. Bondi

Department of Psychiatry,  University of California, San Diego,VA San Diego Healthcare System,La Jolla, CA 92093

Samuel R. Ward

Departments of Radiology,Orthopaedic Surgery and Bioengineering,  University of California, San Diego, La Jolla, CA 92093

Lawrence R. Frank

UCSD Center for Functional MRI,  University of California, San Diego, VA San Diego Healthcare System, La Jolla, CA 92093

1

Corresponding author.

J. Comput. Nonlinear Dynam 7(3), 031008 (Apr 04, 2012) (9 pages) doi:10.1115/1.4006143 History: Received June 22, 2011; Revised December 07, 2011; Published April 03, 2012; Online April 04, 2012

Recent military conflicts in Iraq and Afghanistan have resulted in an increase in the number of blast related traumatic brain injuries (blast-TBI). It is assumed that the primary mechanism for blast-TBI is the interaction between the blast pressure wave and the central nervous system, but the details of this mechanism are poorly understood. The conditions of such blast injuries are highly variable, and the presence or absence of protective devices such as vehicles or helmets is presumed to have a strong influence on pressure waves. Because of the complexity of this problem and the difficulty of in situ measurement of these effects in actual combat scenarios, one approach is to develop efficient numerical simulations that have the fidelity to reliably model the interaction of the brain and the pressure and shear waves. Here we examine the distribution of pressures and principal strains (stretches) in a brain impinged upon by a blast wave incident from orthogonal directions as simulated by a finite element coupled fluid-solid dynamic interaction framework. We assess the various sources of errors in finite element simulations of wave propagating through tissue, the modeling error, the discretization error, and the error of input parameters (data uncertainty). We conclude that the least important source of error is the assumption of linear kinematics and linear constitutive equation. The discretization error is significant, and controlling it will remain a challenge. The most significant source of error is found to be the input parameter uncertainty (experimental variability) and lack of knowledge of the detailed mechanics of deformation of the brain tissues under conditions of blast loading.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Friedlander-type lateral and frontal blast wave, peak pressure 5.2 atm (0.53 MPa), Mach number M = 2.23. Lateral (top two rows) and Frontal (bottom two rows) blast wave pressure distributions. Unprotected human head.

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Figure 2

Pressure in the blast wave. Friedlander-type lateral and frontal blast wave, peak pressure 5.2 atm (0.53 MPa), Mach number M = 2.23. Unprotected head. Locations of pressure sensors indicated by letters.

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Figure 3

Acoustic pressure (color online: red positive, blue negative, grayscale: high pressure shown as opaque surface) in the cortex. (Snapshots spaced 0.035 ms).

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Figure 4

Friedlander-type lateral and frontal blast wave, peak pressure 5.2 atm, Mach number M = 2.23. Maximum intensity projection over time of largest principal strain distribution. The maximum intensity projection over time is defined as mip(ε1(i,j,k),t)=max⁡0≤τ≤tε1(i,j,k)τ) for all voxels i,j,k that correspond to the brain soft tissues. Here ɛ1 is the largest principal strain, where a positive value corresponds to stretching (and negative value would correspond to contraction). Highest strain (∼1.5%) occurs near the corpus callosum. The maximum of the largest principal strain (stretch) maximum intensity projection over time was recorded as 3.3%.

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Figure 5

Friedlander-type lateral blast wave, peak pressure 5.2 atm (0.53 MPa), Mach number M = 2.23. Pressure at the indicated location in the white matter on the left-hand side. Curves of pressure versus time shown for three grids with successively finer mesh size, 2.0, 1.0, and 0.5 mm.

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Figure 6

Friedlander-type lateral blast wave, peak pressure 5.2 atm (0.53 MPa), Mach number M = 2.23. Time-dependent pressure for brainstem (BS), corpus callosum (CC), and white matter (WM_L on the left side) and (WM_R on the right side of the brain) for three different values of the shear modulus of the white and gray matter with mesh size 2.0 mm. Pressure shown: in dotted line for shear modulus multiplier m = 1, in dashed line for shear modulus multiplier m = 5, and in solid line for multiplier m = 25.

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Figure 7

Friedlander-type lateral blast wave, peak pressure 5.2 atm (0.53 MPa), Mach number M = 2.23. Correlation coefficient for the pressure versus time for brainstem (BS), corpus callosum (CC), and white matter (WM_L on the left side) and (WM_R on the right side of the brain). Correlation coefficient of results for grids with mesh size 2.0 and 1.0 mm in black, and correlation coefficient of results for grids with mesh size 1.0 and 0.5 mm in white.

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Figure 8

Friedlander-type lateral blast wave, peak pressure 5.2 atm (0.53 MPa), Mach number M = 2.23. Positive and negative peak pressure for brainstem (BS), corpus callosum (CC), and white matter (WM_L on the left side) and (WM_R on the right side of the brain). Results with mesh size 2.0 mm in black, with mesh size 1.0 mm in gray, and with mesh size 0.5 mm in white.

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