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Accurate characterization of the mechanical properties of the human brain at both microscopic and macroscopic length scales is a critical requirement for modeling of traumatic brain injury and brain folding. To date, most experimental studies that employ classical tension/compression/shear tests report the mechanical properties of the brain averaged over both the gray and white matter within the macroscopic regions of interest. As a result, there is a missing correlation between the independent mechanical properties of the microscopic constituent elements and the composite bulk macroscopic mechanical properties of the tissue. This microstructural computational study aims to inversely predict the hyperelastic mechanical properties of the axonal fibers and their surrounding extracellular matrix (ECM) from the bulk tissue's mechanical properties. We develop a representative volume element (RVE) model of the bulk tissue consisting of axonal fibers and ECM with the embedded element technique. A multiobjective optimization technique is implemented to calibrate the model and establish the independent mechanical properties of axonal fibers and ECM based on seven previously reported experimental mechanical tests for bulk white matter tissue from the corpus callosum. The result of the study shows that the discrepancy between the reported values for the elastic behavior of white matter in literature stems from the anisotropy of the tissue at the microscale. The shear modulus of the axonal fiber is seven times larger than the ECM, with axonal fibers that also show greater nonlinearity, contrary to the common assumption that both components exhibit identical nonlinear characteristics. Statement of significance The reported mechanical properties of white matter microstructure used in traumatic brain injury or brain mechanics studies vary widely, in some cases by up to two orders of magnitude. Currently, the material parameters of the white matter microstructure are identified by a single loading mode or ultimately two modes of the bulk tissue. The presented material models only define the response of the bulk and homogenized white matter at a macroscopic scale and cannot explicitly capture the connection between the material properties of microstructure and bulk structure. To fill this knowledge gap, our study characterizes the hyperelastic material properties of axonal fibers and ECM using microscale computational modeling and multiobjective optimization. The hyperelastic material properties for axonal fibers and ECM presented in this study are more accurate than previously proposed because they have been optimized using seven or six loading modes of the bulk tissue, which were previously limited to only two of the seven possible loading modes. As such, the predicted values with high accuracy could be used in various computational modeling studies. The systematic characterization of the material properties of the human brain tissue at both macro- and microscales will lead to more accurate computational predictions, which will enable a better understanding of injury criteria, and has a positive impact on the improved development of smart protection systems, and more accurate prediction of brain development and disease progression.
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A theoretical framework for predicting the heterogeneous stiffness map of brain white matter tissue
Abstract Finding the stiffness map of biological tissues is of great importance in evaluating their healthy or pathological conditions. However, due to the heterogeneity and anisotropy of biological fibrous tissues, this task presents challenges and significant uncertainty when characterized only by single-mode loading experiments. In this study, we propose a new theoretical framework to map the stiffness landscape of fibrous tissues, specifically focusing on brain white matter tissue. Initially, a finite element (FE) model of the fibrous tissue was subjected to six loading cases, and their corresponding stress–strain curves were characterized. By employing multiobjective optimization, the material constants of an equivalent anisotropic material model were inversely extracted to best fit all six loading modes simultaneously. Subsequently, large-scale FE simulations were conducted, incorporating various fiber volume fractions and orientations, to train a convolutional neural network capable of predicting the equivalent anisotropic material properties solely based on the fibrous architecture of any given tissue. The proposed method, leveraging brain fiber tractography, was applied to a localized volume of white matter, demonstrating its effectiveness in precisely mapping the anisotropic behavior of fibrous tissue. In the long-term, the proposed method may find applications in traumatic brain injury, brain folding studies, and neurodegenerative diseases, where accurately capturing the material behavior of the tissue is crucial for simulations and experiments.
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- Award ID(s):
- 2123061
- PAR ID:
- 10552921
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Physical Biology
- Volume:
- 21
- Issue:
- 6
- ISSN:
- 1478-3967
- Format(s):
- Medium: X Size: Article No. 066004
- Size(s):
- Article No. 066004
- Sponsoring Org:
- National Science Foundation
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