A Three-Dimensional Statistical Volume Element for Histology Informed Micromechanical Modeling of Brain White Matter

Do human brain white matter and brain stem structures show direction-dependent mechanical behavior?

Since the corpus callosum and the brain stem are both vulnerable to diffuse axonal injury during head impacts, there is a high interest in modeling the mechanical behavior of these brain structures. In recent years, different versions of fiber-reinforced material models have been proposed for the corpus callosum and other white matter regions, as well as for the brain stem, even though there is currently no consensus on whether those structures exhibit a significant direction-dependent behavior during mechanical loading. Here, we present the first large-strain, multimodal experimental study on human brain tissue that includes the corpus callosum and the lower brain stem (medulla oblongata) tested along two different directions. Additionally, we compare those two structures with other white matter (corona radiata, cerebellar white matter) and brain stem structures (pons, midbrain) to highlight differences in their material response. Cyclic compression-tension and shear tests reveal statistically significant direction-dependent material behavior in the corpus callosum. Directional differences in the brain stem are not statistically significant and do not indicate a clear directionality. Combined with histological findings, our results suggest that the mechanical behavior of white matter structures is influenced not only by axon caliber, orientation and density, but also by the architectural organization, i.e., clustering versus even distribution, of cells and tracts, and possibly vascular density. These findings highlight the need for micromechanical constitutive models for brain white matter that do not merely include axons embedded in a matrix. Statement of significance Mechanical head injuries often result in insults like diffuse axonal injury in white matter regions of the human brain. Therefore, there is a high interest in understanding and predicting the mechanical properties of those regions in order to prevent injury and advance diagnosis and treatment strategies of neurological disorders. There has been a long controversy regarding the question whether human brain white matter regions show an anisotropic, direction-dependent mechanical response. With the goal of providing experimental evidence to conclusively answer this question, we here present large-strain, multimodal experimental data and representative histological analyses of different human brain white matter regions and brain stem structures, including directional investigations for both the corpus callosum and the medulla oblongata (lower brain stem).

From structure to mechanics: exploring the role of axons and interconnections in anisotropic behavior of brain white matter

According to various experimental studies, the role of axons in the brain's white matter (WM) is still a subject of debate: Is the role of axons in brain white matter (WM) limited to their functional significance, or do they also play a pivotal mechanical role in defining its anisotropic behavior? Micromechanics and computational models provide valuable tools for scientists to comprehend the underlying mechanisms of tissue behavior, taking into account the contribution of microstructures. In this review, we delve into the consideration of strain level, strain rates, and injury threshold to determine when WM should be regarded as anisotropic, as well as when the assumption of isotropy can be deemed acceptable. Additionally, we emphasize the potential mechanical significance of interconnections between glial cells-axons and glial cells-vessels. Moreover, we elucidate the directionality of WM stiffness under various loading conditions and define the possible roles of microstructural components in each scenario. Ultimately, this review aims to shed light on the significant mechanical contributions of axons in conjunction with glial cells, paving the way for the development of future multiscale models capable of predicting injuries and facilitating the discovery of applicable treatments.

Stress landscape of folding brain serves as a map for axonal pathfinding

Understanding the mechanics linking cortical folding and brain connectivity is crucial for both healthy and abnormal brain development. Despite the importance of this relationship, existing models fail to explain how growing axon bundles navigate the stress field within a folding brain or how this bidirectional and dynamic interaction shapes the resulting surface morphologies and connectivity patterns. Here, we propose the concept of "axon reorientation" and formulate a mechanical model to uncover the dynamic multiscale mechanics of the linkages between cortical folding and connectivity development. Simulations incorporating axon bundle reorientation and stress-induced growth reveal potential mechanical mechanisms that lead to higher axon bundle density in gyri (ridges) compared to sulci (valleys). In particular, the connectivity patterning resulting from cortical folding exhibits a strong dependence on the growth rate and mechanical properties of the navigating axon bundles. Model predictions are supported by in vivo diffusion tensor imaging of the human brain.

A theoretical framework for predicting the heterogeneous stiffness map of brain white matter tissue

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.

Toward understanding the brain tissue behavior due to preconditioning: an experimental study and RVE approach

Brain tissue under preconditioning, as a complex issue, refers to repeated loading-unloading cycles applied in mechanical testing protocols. In previous studies, only the mechanical behavior of the tissue under preconditioning was investigated; However, the link between macrostructural mechanical behavior and microstructural changes in brain tissue remains underexplored. This study aims to bridge this gap by investigating bovine brain tissue responses both before and after preconditioning. We employed a dual approach: experimental mechanical testing and computational modeling. Experimental tests were conducted to observe microstructural changes in mechanical behavior due to preconditioning, with a focus on axonal damage. Concurrently, we developed multiscale models using statistically representative volume elements (RVE) to simulate the tissue's microstructural response. These RVEs, featuring randomly distributed axonal fibers within the extracellular matrix, provide a realistic depiction of the white matter microstructure. Our findings show that preconditioning induces significant changes in the mechanical properties of brain tissue and affects axonal integrity. The RVE models successfully captured localized stresses and facilitated the microscopic analysis of axonal injury mechanisms. These results underscore the importance of considering both macro and micro scales in understanding brain tissue behavior under mechanical loading. This comprehensive approach offers valuable insights into mechanotransduction processes and improves the analysis of microstructural phenomena in brain tissue.

Histology-informed multiscale modeling of human brain white matter

In this study, we propose a novel micromechanical model for the brain white matter, which is described as a heterogeneous material with a complex network of axon fibers embedded in a soft ground matrix. We developed this model in the framework of RVE-based multiscale theories in combination with the finite element method and the embedded element technique for embedding the fibers. Microstructural features such as axon diameter, orientation and tortuosity are incorporated into the model through distributions derived from histological data. The constitutive law of both the fibers and the matrix is described by isotropic one-term Ogden functions. The hyperelastic response of the tissue is derived by homogenizing the microscopic stress fields with multiscale boundary conditions to ensure kinematic compatibility. The macroscale homogenized stress is employed in an inverse parameter identification procedure to determine the hyperelastic constants of axons and ground matrix, based on experiments on human corpus callosum. Our results demonstrate the fundamental effect of axon tortuosity on the mechanical behavior of the brain's white matter. By combining histological information with the multiscale theory, the proposed framework can substantially contribute to the understanding of mechanotransduction phenomena, shed light on the biomechanics of a healthy brain, and potentially provide insights into neurodegenerative processes.

Origins of brain tissue elasticity under multiple loading modes by analyzing the microstructure-based models

Constitutive behaviors and material properties of brain tissue play an essential role in accurately modeling its mechanical responses. However, the measured mechanical behaviors of brain tissue exhibit a large variability, and the reported elastic modulus can differ by orders of magnitude. Here we develop the micromechanical models based on the actual microstructure of the longitudinally anisotropic plane of brain tissue to investigate the microstructural origins of the large variability. Specifically, axonal fiber bundles with the specified configurations are distributed in an equivalent matrix. All micromechanical models are subjected to multiple loading modes, such as tensile, compressive, and shear loading, under periodic boundary conditions. The predicted results agree well with the experimental results. Furthermore, we investigate how brain tissue elasticity varies with its microstructural features. It is revealed that the large variability in brain tissue elasticity stems from the volume fraction of axonal fiber, the aspect ratio of axonal fiber, and the distribution of axonal fiber orientation. The volume fraction has the greatest impact on the mechanical behaviors of brain tissue, followed by the distribution of axonal fiber orientation, then the aspect ratio. This study provides critical insights for understanding the microstructural origins of the large variability in brain tissue elasticity.

Designing a hybrid reinforcement learning based algorithm with application in prediction of the COVID-19 pandemic in Quebec

World Health Organization (WHO) stated COVID-19 as a pandemic in March 2020. Since then, 26,795,847 cases have been reported worldwide, and 878,963 lost their lives due to the illness by September 3, 2020. Prediction of the COVID-19 pandemic will enable policymakers to optimize the use of healthcare system capacity and resource allocation to minimize the fatality rate. In this research, we design a novel hybrid reinforcement learning-based algorithm capable of solving complex optimization problems. We apply our algorithm to several well-known benchmarks and show that the proposed methodology provides quality solutions for most complex benchmarks. Besides, we show the dominance of the offered method over state-of-the-art methods through several measures. Moreover, to demonstrate the suggested method's efficiency in optimizing real-world problems, we implement our approach to the most recent data from Quebec, Canada, to predict the COVID-19 outbreak. Our algorithm, combined with the most recent mathematical model for COVID-19 pandemic prediction, accurately reflected the future trend of the pandemic with a mean square error of 6.29E-06. Furthermore, we generate several scenarios for deepening our insight into pandemic growth. We determine essential factors and deliver various managerial insights to help policymakers making decisions regarding future social measures.

Mechanism Exploration of 3-Hinge Gyral Formation and Pattern Recognition

The 3-hinge gyral folding is the conjunction of gyrus crest lines from three different orientations. Previous studies have not explored the possible mechanisms of formation of such 3-hinge gyri, which are preserved across species in primate brains. We develop a biomechanical model to mimic the formation of 3-hinge patterns on a real brain and determine how special types of 3-hinge patterns form in certain areas of the model. Our computational and experimental imaging results show that most tertiary convolutions and exact locations of 3-hinge patterns after growth and folding are unpredictable, but they help explain the consistency of locations and patterns of certain 3-hinge patterns. Growing fibers within the white matter is posited as a determining factor to affect the location and shape of these 3-hinge patterns. Even if the growing fibers do not exert strong enough forces to guide gyrification directly, they still may seed a heterogeneous growth profile that leads to the formation of 3-hinge patterns in specific locations. A minor difference in initial morphology between two growing model brains can lead to distinct numbers and locations of 3-hinge patterns after folding.

Effect of axonal fiber architecture on mechanical heterogeneity of the white matter-a statistical micromechanical model

A diffusion tensor imaging (DTI) -based statistical micromechanical model was developed to study the effect of axonal fiber architecture on the inter- and intra-regional mechanical heterogeneity of the white matter. Three characteristic regions within the white matter, i.e., corpus callosum, brain stem, and corona radiata, were studied considering the previous observations of locations of diffuse axonal injury. The embedded element technique was used to create a fiber-reinforced model, where the fiber was characterized by a Holzapfel hyperelastic material model with variable dispersion of axonal orientations. A relationship between the fractional anisotropy and the dispersion parameter of the hyperelastic model was used to introduce the statistical DTI data into the representative volume element. The FA-informed statistical micromechanical models of three characteristic regions of white matter were developed by deriving the corresponding probabilistic measures of FA variations. Comparison of the model predictions and experimental data indicated a good agreement, suggesting that the model could reasonably capture the inter-regional heterogeneity of white matter. Moreover, the standard deviations of experimental results correlated well with the model predictions, suggesting that the model could capture the intra-regional mechanical heterogeneity for different regions of white matter.