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Finite Element Modeling of CNS White Matter Kinematics: Use of a 3D RVE to Determine Material Properties.

Pan Y, Sullivan D, Shreiber DI, Pelegri AA - Front Bioeng Biotechnol (2013)

Bottom Line: An inverse FE procedure was developed to identify material parameters of spinal cord white matter by combining the results of uniaxial testing with FE modeling.A satisfactory balance between simulation and experiment was achieved via optimization by minimizing the squared error between the simulated and experimental force-stretch curve.The combination of experimental testing and FE analysis provides a useful analysis tool for soft biological tissues in general, and specifically enables evaluations of the axonal response to tissue-level loading and subsequent predictions of axonal damage.

View Article: PubMed Central - PubMed

Affiliation: Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey , Piscataway, NJ , USA.

ABSTRACT
Axonal injury represents a critical target area for the prevention and treatment of traumatic brain and spinal cord injuries. Finite element (FE) models of the head and/or brain are often used to predict brain injury caused by external mechanical loadings, such as explosive waves and direct impact. The accuracy of these numerical models depends on correctly determining the material properties and on the precise depiction of the tissues' microstructure (microscopic level). Moreover, since the axonal microstructure for specific regions of the brain white matter is locally oriented, the stress, and strain fields are highly anisotropic and axon orientation dependent. Additionally, mechanical strain has been identified as the proximal cause of axonal injury, which further demonstrates the importance of this multi-scale relationship. In this study, our previously developed FE and kinematic axonal models are coupled and applied to a pseudo 3-dimensional representative volume element of central nervous system white matter to investigate the multi-scale mechanical behavior. An inverse FE procedure was developed to identify material parameters of spinal cord white matter by combining the results of uniaxial testing with FE modeling. A satisfactory balance between simulation and experiment was achieved via optimization by minimizing the squared error between the simulated and experimental force-stretch curve. The combination of experimental testing and FE analysis provides a useful analysis tool for soft biological tissues in general, and specifically enables evaluations of the axonal response to tissue-level loading and subsequent predictions of axonal damage.

No MeSH data available.


Related in: MedlinePlus

Plot of function value at various shear modulus. It shows that the squared error of the experimental curve and the simulated curve is minimized at μ = 36.63, 33.28, and 29.64 kPa for α = 6.95, 8.22, and 9.49, respectively.
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Figure 6: Plot of function value at various shear modulus. It shows that the squared error of the experimental curve and the simulated curve is minimized at μ = 36.63, 33.28, and 29.64 kPa for α = 6.95, 8.22, and 9.49, respectively.

Mentions: The stress-stretch curve was sampled at 20 equidistant intervals. The squared error was minimized with a golden search algorithm for this univariate problem in order to find the shear modulus of an axon, μ. An initial guess for μ was given for the algorithm. A pre-determined solution bracket (20, 50 kPa) was also provided to shorten the computational time. The solution tolerance was set to 1.0 kPa for the unknown parameter. The procedure was automated using Python scripts. After nine iterations, the optimized parameter μ = 33.28 kPa was obtained using the nominal value α = 8.22. The residual of each iteration was tabulated in Table 1 and plotted in Figure 6. It is shown that the unknown parameter converges to the optimized value as the residual reaches its minimum. The stress-stretch curves obtained in all iterations were plotted in Figure 7. The simulated stress-stretch curves converge to the experimental curve. To investigate the sensitivity of the results to the parameter α, the optimization process was also performed at α = 6.95 and 6.49. The respective optimized parameters are μ = 36.63 and 29.64 kPa and the respective residuals are tabulated in Table 1. The optimized parameters reside within the curve-fitting range of 32.8 ± 9.53 kPa obtained from the experimental data (Shreiber et al., 2009). It can be concluded that shear modulus is not sensitive to the non-linear parameter α since the change of μ is less than 11% and it is within the simulated range. The stress-stretch corresponding to the optimized parameter of μ = 33.28 kPa is also plotted in Figure 4 showing good agreement between the curves from the experiment and the optimization process.


Finite Element Modeling of CNS White Matter Kinematics: Use of a 3D RVE to Determine Material Properties.

Pan Y, Sullivan D, Shreiber DI, Pelegri AA - Front Bioeng Biotechnol (2013)

Plot of function value at various shear modulus. It shows that the squared error of the experimental curve and the simulated curve is minimized at μ = 36.63, 33.28, and 29.64 kPa for α = 6.95, 8.22, and 9.49, respectively.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4126384&req=5

Figure 6: Plot of function value at various shear modulus. It shows that the squared error of the experimental curve and the simulated curve is minimized at μ = 36.63, 33.28, and 29.64 kPa for α = 6.95, 8.22, and 9.49, respectively.
Mentions: The stress-stretch curve was sampled at 20 equidistant intervals. The squared error was minimized with a golden search algorithm for this univariate problem in order to find the shear modulus of an axon, μ. An initial guess for μ was given for the algorithm. A pre-determined solution bracket (20, 50 kPa) was also provided to shorten the computational time. The solution tolerance was set to 1.0 kPa for the unknown parameter. The procedure was automated using Python scripts. After nine iterations, the optimized parameter μ = 33.28 kPa was obtained using the nominal value α = 8.22. The residual of each iteration was tabulated in Table 1 and plotted in Figure 6. It is shown that the unknown parameter converges to the optimized value as the residual reaches its minimum. The stress-stretch curves obtained in all iterations were plotted in Figure 7. The simulated stress-stretch curves converge to the experimental curve. To investigate the sensitivity of the results to the parameter α, the optimization process was also performed at α = 6.95 and 6.49. The respective optimized parameters are μ = 36.63 and 29.64 kPa and the respective residuals are tabulated in Table 1. The optimized parameters reside within the curve-fitting range of 32.8 ± 9.53 kPa obtained from the experimental data (Shreiber et al., 2009). It can be concluded that shear modulus is not sensitive to the non-linear parameter α since the change of μ is less than 11% and it is within the simulated range. The stress-stretch corresponding to the optimized parameter of μ = 33.28 kPa is also plotted in Figure 4 showing good agreement between the curves from the experiment and the optimization process.

Bottom Line: An inverse FE procedure was developed to identify material parameters of spinal cord white matter by combining the results of uniaxial testing with FE modeling.A satisfactory balance between simulation and experiment was achieved via optimization by minimizing the squared error between the simulated and experimental force-stretch curve.The combination of experimental testing and FE analysis provides a useful analysis tool for soft biological tissues in general, and specifically enables evaluations of the axonal response to tissue-level loading and subsequent predictions of axonal damage.

View Article: PubMed Central - PubMed

Affiliation: Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey , Piscataway, NJ , USA.

ABSTRACT
Axonal injury represents a critical target area for the prevention and treatment of traumatic brain and spinal cord injuries. Finite element (FE) models of the head and/or brain are often used to predict brain injury caused by external mechanical loadings, such as explosive waves and direct impact. The accuracy of these numerical models depends on correctly determining the material properties and on the precise depiction of the tissues' microstructure (microscopic level). Moreover, since the axonal microstructure for specific regions of the brain white matter is locally oriented, the stress, and strain fields are highly anisotropic and axon orientation dependent. Additionally, mechanical strain has been identified as the proximal cause of axonal injury, which further demonstrates the importance of this multi-scale relationship. In this study, our previously developed FE and kinematic axonal models are coupled and applied to a pseudo 3-dimensional representative volume element of central nervous system white matter to investigate the multi-scale mechanical behavior. An inverse FE procedure was developed to identify material parameters of spinal cord white matter by combining the results of uniaxial testing with FE modeling. A satisfactory balance between simulation and experiment was achieved via optimization by minimizing the squared error between the simulated and experimental force-stretch curve. The combination of experimental testing and FE analysis provides a useful analysis tool for soft biological tissues in general, and specifically enables evaluations of the axonal response to tissue-level loading and subsequent predictions of axonal damage.

No MeSH data available.


Related in: MedlinePlus