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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

Finite element model of the undulated axons (A) and the extracellular matrix (B).
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Figure 1: Finite element model of the undulated axons (A) and the extracellular matrix (B).

Mentions: The FE model of an RVE is developed using ABAQUS 6.11 and Python scripting. An RVE is a sub-domain of a composite material whose size needs to be sufficiently large to include necessary fiber information such that the macroscopic homogeneous mechanical behavior of the composite material can be derived. To reduce computational demands in a FEA, one might need to limit the size of an RVE while retain necessary fibers. The interested reader is referred to Iorga et al. (2008). In this study, a pseudo-3D RVE for the CNS white matter is composed of many undulated axons that are embedded in the ECM. A cuboid (x = 0.4 μm, y = 10 μm, z = 5.68 μm) is created representing the matrix surrounding the axons as shown in Figure 1. The axons are undulated and their geometry is complex. The undulation varies from axon-to-axon as well as along an individual axon. The distribution of undulation of the axons within the RVE model is based on those found by Bain et al. (2003). An undulated axon is represented by a poly-line and a cubic spline: a poly-line is composed of multiple connecting line segments extending from random points on one face of the cuboid (z = 0 plane) to its opposite face (z = 5.68 plane); and the cubic spline, representing the backbone of an axon, is generated by depicting every key point on the poly-line. Sweeping a circle along the cubic spline then generates the axons. In this study, the diameter of an axon is fixed to 0.4 μm, although it may vary from axon-to-axon in the range of sub-micron to about 20 μm for porcine optic and sciatic nerves (Assaf et al., 2008). The portion of an axon that falls outside of the cuboid is trimmed. The volume fraction of axons is set to 53% (Karami et al., 2009). The total number of axons in the matrix is 33, which is determined by the volume fraction, as shown in Figure 2. The average undulation of the axons ranges from 1.05 to 1.25.


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)

Finite element model of the undulated axons (A) and the extracellular matrix (B).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: Finite element model of the undulated axons (A) and the extracellular matrix (B).
Mentions: The FE model of an RVE is developed using ABAQUS 6.11 and Python scripting. An RVE is a sub-domain of a composite material whose size needs to be sufficiently large to include necessary fiber information such that the macroscopic homogeneous mechanical behavior of the composite material can be derived. To reduce computational demands in a FEA, one might need to limit the size of an RVE while retain necessary fibers. The interested reader is referred to Iorga et al. (2008). In this study, a pseudo-3D RVE for the CNS white matter is composed of many undulated axons that are embedded in the ECM. A cuboid (x = 0.4 μm, y = 10 μm, z = 5.68 μm) is created representing the matrix surrounding the axons as shown in Figure 1. The axons are undulated and their geometry is complex. The undulation varies from axon-to-axon as well as along an individual axon. The distribution of undulation of the axons within the RVE model is based on those found by Bain et al. (2003). An undulated axon is represented by a poly-line and a cubic spline: a poly-line is composed of multiple connecting line segments extending from random points on one face of the cuboid (z = 0 plane) to its opposite face (z = 5.68 plane); and the cubic spline, representing the backbone of an axon, is generated by depicting every key point on the poly-line. Sweeping a circle along the cubic spline then generates the axons. In this study, the diameter of an axon is fixed to 0.4 μm, although it may vary from axon-to-axon in the range of sub-micron to about 20 μm for porcine optic and sciatic nerves (Assaf et al., 2008). The portion of an axon that falls outside of the cuboid is trimmed. The volume fraction of axons is set to 53% (Karami et al., 2009). The total number of axons in the matrix is 33, which is determined by the volume fraction, as shown in Figure 2. The average undulation of the axons ranges from 1.05 to 1.25.

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