Deep 3D Convolution Neural Network Methods for Brain White Matter Hybrid Computational Simulations

Material properties of brain white matter (BWM) exhibit high anisotropy attributed to the complex internal three-dimensional microstructure and the heterogeneity of the brain-tissue (axon, myelin, and glia). Previous studies indicate that brain injury depends on the strain magnitude and the strain rate delineating the non-linear dynamic viscoelastic behavior of BWM as an important parametric consideration. Our group has previously exploited finite element methods to merge micro-scale Representative Volume Elements (RVE) with orthotropic frequency domain viscoelasticity to formulate a macro-scale BWM.  The goal of the current study is the calculation of the anisotropic frequency domain viscoelastic properties of a micro-scale RVE in a reliable and repeatable manner based on 3D CNN hybrid computational simulations.

The RVE behavior is expressed by a viscoelastic constitutive material model, in which manifestation of the frequency-related viscoelastic properties is expressed via the storage and loss moduli of a composite biostructure comprised of axonal fibers and extracellular glia. The location-architecture pertinent information (such as axon diameter, axon distribution, axon orientation, and volume fraction of axon-myelin-glia) is not analyzed separately but naturally merged as a hybrid integrated bundle based on a voxelization method.

Using finite elements to build an RVE with anisotropic viscoelastic material properties in a frequency domain is computationally demanding. Besides, it is nearly impossible to build arrays of RVES with distinct architecture that comprise all the possibilities encountered in any anisotropic brain tissue as the number of the distinct RVEs is arbitrary in an infinite data set. Therefore, a more flexible method that uses variational information is adopted, which is less time-consuming and can provide accuracy comparable to finite element methods.

Specifically, the analysis feasibility calls for a 3D convolution neural network (CNN) that can intrinsically handle 3D input information. The input data, comprised of voxelized location-architecture information and viscoelastic material properties of the axon-myelin-glia biocomposite system, are incorporated into a deep 3D CNN-based model that cross-references the RVEs' material properties as output data. The output data is calculated using finite element analysis of RVE samples with distinct architecture and axon-myelin-glia constituent properties. The anisotropic viscoelastic material properties in the frequency domain for the RVE samples are determined through a steady-state dynamics analysis.

Since the original material properties of axon-myelin-glia are variant and hard to define, we adopt a more flexible description of material properties to interpret the RVE behavior. We postulate that the proposed method is more reliable than adopting constituent values from homogenized composite brain tissues. Instead of adopting a fixed value for the original material properties, this study applies the layers merge method in CNN to include the original material properties of axon-myelin-glia as variables with a certain value range to increase the model's flexibility. Utilizing the trained CNN, the anisotropic frequency domain viscoelasticity of an RVE can be interpretable. The computational time using this method was significantly reduced compared to the computational time employed using finite elements