A finite element and data-science assisted deep learning framework to interpret the constitutive behavior of brain white matter

The finite element methods (FEM) are widely utilized in numerical modeling of Brain White Matter (BWM) to depict traumatic brain injuries (TBI). These injuries could manifest in several forms such as tensile, compressive or shear loads on axons in both quasi-static and dynamic forms. Novel data-driven multi-scale numerical models are formulated to characterize BWM response when subjected to ensemble of traumatic loading scenarios. The purpose of this study is to propose computational solutions that connects AI (data-science), optimizations, medical imaging, multi-scale biomechanics and soft tissue modeling. These models would act as foundation studies for attaining highly repeatable and accurate data driven FEM and Machine-Learning (ML) models for multi-scale depiction of brain by incorporating axon/neuroglia composite anisotropy, axonal tracts tortuosity and brain aging/softening effects due to demyelination. Firstly, a bi-phasic 3D finite element model (FEM) has been proposed to study the mechanical response of axons embedded in ECM when subjected to tensile loads. The Ogden hyper-elastic (HE) material model describes the axons and the ECM materials. The developed model investigates several tethering scenarios between axons and oligodendrocytes using two FEM sub-models (single-OL and multi-OL) configurations. These tethering are deployed as linear spring-dashpot element. To gauge dynamic response and stress accumulation & relaxation effects, a hyper-viscoelastic (HVE) model is also proposed leveraging both analytical and optimization based frameworks. This generalizable approach enables a comprehensive analysis of the role of oligodendrocytes on stress redistribution and propagation, under static and repeated loading using a combination of static, steady-state (SSD), and explicit (ED) dynamic models. Next, a series of novel 3D micromechanical FEM proof-of-concept (POC) models are developed in house using Representative volume element (RVE) with axons embedded in extra-cellular glial matrix (ECM) for simulating the BWM response under shear. These models exhibit the Poynting effect (PE) in brain matter. PE is a nonlinear phenomenon associated with soft materials whereby they tend to elongate (positive) or contract (negative Poynting effect) in a direction perpendicular to the shearing or twisting plane. In-depth investigation is carried out using single, scaled-up and biconically modeled myelinated axons-ECM tri-phasic RVEs (Ogden hyperelastic) to characterize trends in degree of Poynting effect when subjected to ensemble of simple and pure shear loads. Leveraging the developed 3D FEMs built for simulating the Poynting effect, a deep 3D convolution neural network (CNN) algorithm combined with the 3D anisotropic REV FEM was employed to predict the WM's anisotropic stress & stiffness/material properties. 3D FEM geometrical information encoded in the voxelated locations & isotropic Ogden material properties are used as input data and consequently incorporated into a 3D CNN model that cross-references the RVEs' stress and stiffness (output). These output data are calculated in parallel using in-house developed tri-phasic 3D FEM, which depicts RVE samples as axon-myelin-glia composites. This novel hybrid CNN-FEM framework dramatically reduced the computation time compared to conventional FEMs to generate stress-stiffness tensor for sheared brain. In continuing the data-science based BWM modeling efforts, a synthetic 2D-FEM viscoelastic modeled BWM simulation dataset generated from previous research was used to build an end-to-end predictive ML forward model workflow to predict brain tissue properties (i.e., storage modulus) of a visco-elastic modeled brain. Developed framework incorporates uncertainty quantification in property estimations and also achieves model interpretability & explainability by analyzing sensitivity of constituent RVE components on predicted target BWM properties. The proposed transferable ML framework will aid soft tissue-characterization, tissue sensitivity & inverse model research for non-linear composites. Lastly, a novel high-order 3D FEM Ogden hyper-elastic brain aging model has been put forward to depict physiological aging and tissue degeneration in BWM. Magnetic Resonance Imaging (MRI) data from test subjects’ of different ages are analyzed using image processing libraries in python and MATLAB scripts used to calculate white matter volume fraction (VF) shrinkage and shear moduli depreciation functions with age. An ensemble of RVE models are developed with straight and tortuous myelinated axonal tracts embedded in glial matrix to characterize and interpret an aging brain response. Proposed novel proof-of-concept aging brain micro-mechanical FEMs would enable advanced pathology identification (brain tissue decay) and facilitate preventive health measures planning for TBI/aged brain.