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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

Predicted evolution of undulation with stretch. Simulation results are compared to experimental results from Bain et al. (2003) and to simulation results from Karami et al. (2009) and Pan et al. (2011).
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Figure 5: Predicted evolution of undulation with stretch. Simulation results are compared to experimental results from Bain et al. (2003) and to simulation results from Karami et al. (2009) and Pan et al. (2011).

Mentions: The axons’ tortuosity is plotted against the applied stretch in Figure 5. It is shown that the undulated axons become less wavy when the applied stretch increases. In this pseudo-3D RVE model, the tortuosity decreased faster at smaller applied stretches as compared to other simulation models. The experimental data from Bain et al. (2003) and the simulation data from Karami et al. (2009), who employed a unit-cell method with fully constrained coupling between axons and glia, are included for comparison, as well as our results from our previous TKM using a unit-cell approach (Pan et al., 2011). Clearly, fractional coupling between the axons and glia yields more accurate stretch-undulation data than Karami et al.’s model with perfectly bonded axons and glia. The current pseudo-3D RVE approach also gives consistent axon kinematics. Curves obtained from RVE1 and RVE3 in this study are close to that from the unit-cell model and experimental measurements. The curve from RVE2 is slightly off the trend since its initial undulation was slightly higher than 1.13. In this case, the evolution of axonal coupling to matrix with stretch is delayed. A drawback of these simulations is that the percentage of axon embedment was held constant and only updated at discrete stretch levels, whereas in reality axon kinematics transition continuously. We expect that allowing the constraints to evolve with stretch will allow us to capture the non-affine, independent behavior of axons and glia at lower stretch levels and enable a more rapid change in undulation at low stretch levels.


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)

Predicted evolution of undulation with stretch. Simulation results are compared to experimental results from Bain et al. (2003) and to simulation results from Karami et al. (2009) and Pan et al. (2011).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 5: Predicted evolution of undulation with stretch. Simulation results are compared to experimental results from Bain et al. (2003) and to simulation results from Karami et al. (2009) and Pan et al. (2011).
Mentions: The axons’ tortuosity is plotted against the applied stretch in Figure 5. It is shown that the undulated axons become less wavy when the applied stretch increases. In this pseudo-3D RVE model, the tortuosity decreased faster at smaller applied stretches as compared to other simulation models. The experimental data from Bain et al. (2003) and the simulation data from Karami et al. (2009), who employed a unit-cell method with fully constrained coupling between axons and glia, are included for comparison, as well as our results from our previous TKM using a unit-cell approach (Pan et al., 2011). Clearly, fractional coupling between the axons and glia yields more accurate stretch-undulation data than Karami et al.’s model with perfectly bonded axons and glia. The current pseudo-3D RVE approach also gives consistent axon kinematics. Curves obtained from RVE1 and RVE3 in this study are close to that from the unit-cell model and experimental measurements. The curve from RVE2 is slightly off the trend since its initial undulation was slightly higher than 1.13. In this case, the evolution of axonal coupling to matrix with stretch is delayed. A drawback of these simulations is that the percentage of axon embedment was held constant and only updated at discrete stretch levels, whereas in reality axon kinematics transition continuously. We expect that allowing the constraints to evolve with stretch will allow us to capture the non-affine, independent behavior of axons and glia at lower stretch levels and enable a more rapid change in undulation at low stretch levels.

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