A three-dimensional micromechanical model of brain white matter with histology-informed probabilistic distribution of axonal fibers

A Comprehensive Analysis of Inconsistencies in the Brain's Conventional Ex Vivo Mechanical Experiments

In 2020, a review titled Fifty Shades of Brain: A Review on the Mechanical Testing and Modeling of Brain Tissue was published, offering a comprehensive overview of brain mechanics. While this work stands out for its insightful analysis of brain mechanics, there are certain points it did not fully address, as well as key areas that require more detailed examination. The goal of this review is not merely to summarize and report on previous studies but to highlight discrepancies in the root causes of the extensive data reported in the literature. By examining the wide-ranging data, the progression of research over six decades, and the knowledge developed during this period, we aim to identify the sources of these discrepancies and propose feasible directions for future research. Additionally, while micromechanical models have attracted significant attention in recent years, we provide evidence to emphasize that, despite their advantages, these models are not yet reliable enough to replace conventional mechanical experiments and macro-scale models. By compiling, visualizing, and analyzing data from the past six decades and integrating challenging issues into a cohesive framework, this approach provides a more actionable analysis. It simplifies navigation through the field and equips researchers with a clearer understanding of its historical progression, challenges, and opportunities.

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.

Validation of a computational biomechanical mouse brain model for rotational head acceleration

Recent mouse brain injury experiments examine diffuse axonal injury resulting from accelerative head rotations. Evaluating brain deformation during these events would provide valuable information on tissue level thresholds for brain injury, but there are many challenges to imaging the brain's mechanical response during dynamic loading events, such as a blunt head impact. To address this shortcoming, we present an experimentally validated computational biomechanics model of the mouse brain that predicts tissue deformation, given the motion of the mouse head during laboratory experiments. First, we developed a finite element model of the mouse brain that computes tissue strains, given the same head rotations as previously conducted in situ hemicephalic mouse brain experiments. Second, we calibrated the model using a single brain segment, and then validated the model based on the spatial and temporal strain responses of other regions. The result is a computational tool that will provide researchers with the ability to predict brain tissue strains that occur during mouse laboratory experiments, and to link the experiments to the resulting neuropathology, such as diffuse axonal injury.

Statistical distribution of micro and macro pores in acrylic bone cement- effect of amount of antibiotic content

Aseptic loosening due to mechanical failure of bone cement is considered to be a leading cause of revision of joint replacement systems. Detailed quantified information on the number, size and distribution pattern of pores can help to obtain a deeper understanding of the bone cement's fatigue behavior. The objective of this study was to provide statistical descriptions for the pore distribution characteristics of laboratory bone cement specimens with different amounts of antibiotic contents. For four groups of bone cement (Palacos) specimens, containing 0.3, 0.6, 1.2 and 2.4 wt/wt% of telavancin antibiotic, seven samples per group were micro computed tomography scanned (38.97 μm voxel size). The images were first preprocessed in Mimics and then analyzed in Dragonfly, with the level of threshold being set such that single-pixel pores become visible. The normalized pore volume data of the specimens were then used to extract the logarithmic histograms of the pore densities for antibiotic groups, as well as their three-parameter Weibull probability density functions. Statistical comparison of the pore distribution data of the antibiotic groups using the Mann-Whitney non-parametric test revealed a significantly larger porosity (p < 0.05) in groups with larger added antibiotic contents (2.4 and 0.6 wt/wt% vs 0.3 wt/wt%). Further analysis revealed that this effect was associated with the significantly larger frequency of micropores of 0.1-0.5 mm diameter (p < 0.05) in groups with larger antibiotic content (2.4 wt/wt% vs and 0.6 and 0.3 wt/wt%), implying that the elution of the added antibiotic produces micropores in this diameter range mainly. Based on this observation and the fatigue test results in the literature, it was suggested that micropore clusters have a detrimental effect on the mechanical properties of bone cement and play a major role in initiating fatigue cracks in highly antibiotic added specimens.

Porosity-permeability tensor relationship of closely and randomly packed fibrous biomaterials and biological tissues: Application to the brain white matter

The constitutive model for the porosity-permeability relationship is a powerful tool to estimate and design the transport properties of porous materials, which has attracted significant attention for the advancement of novel materials. However, in comparison with other materials, biomaterials, especially natural and artificial tissues, have more complex microstructures e.g. high anisotropy, high randomness of cell/fibre dimensions/position and very low porosity. Consequently, a reliable microstructure-permeability relationship of fibrous biomaterials has proven elusive. To fill this gap, we start a mathematical derivation from the fundamental brain white matter (WM) formed by nerve fibres. This is augmented by a numerical characterisation and experimental validations to obtain an anisotropic permeability tensor of the brain WM as a function of the tissue porosity. A versatile microstructure generation software (MicroFiM) for fibrous biomaterial with complex microstructure and low porosity was built accordingly and made freely accessible here. Moreover, we propose an anisotropic poro-hyperelastic model enhanced by the newly defined porosity-permeability tensor relationship which precisely captures the tissues macro-scale permeability changes due to the microstructural deformation in an infusion scenario. The constitutive model, theories and protocols established in this study will both provide improved design strategies to tailor the transport properties of fibrous biomaterials and enable the non-invasive characterisation of the transport properties of biological tissues. This will lead to the provision of better patient-specific medical treatments, such as drug delivery. STATEMENT OF SIGNIFICANCE: Due to the microstructural complexity, a reliable microstructure-permeability relationship of fibrous biomaterials has proven elusive, which hinders our way of tuning the fluid transport property of the biomaterials by directly programming their microstructure. The same problem hinders non-invasive characterisations of fluid transport properties in biological tissues, which can significantly improve the efficiency of treatments e.g. drug delivery, directly from the tissues accessible microstructural information, e.g. porosity. Here, we developed a validated mathematical formulation to link the random microstructure to a fibrous material's macroscale permeability tensor. This will advance our capability to design complex biomaterials and make it possible to non-invasively characterise the permeability of living tissues for precise treatment planning. The newly established theory and protocol can be easily adapted to various types of fibrous biomaterials.

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.

Sex Differences in Axonal Dynamic Responses Under Realistic Tension Using Finite Element Models

Existing axonal finite element models do not consider sex morphological differences or the fidelity in dynamic input. To facilitate a systematic investigation into the micromechanics of diffuse axonal injury, we develop a parameterized modeling approach for automatic and efficient generation of sex-specific axonal models according to specified geometrical parameters. Baseline female and male axonal models in the corpus callosum with random microtubule (MT) gap configurations are generated for model calibration and evaluation. They are then used to simulate a realistic tensile loading consisting of both a loading and a recovery phase (to return to an initial undeformed state) generated from dynamic corpus callosum fiber strain in a real-world head impact simulation. We find that MT gaps and the dynamic recovery phase are both critical to successfully reproduce MT undulation as observed experimentally, which has not been reported before. This strengthens confidence in model dynamic responses. A statistical approach is further employed to aggregate axonal responses from a large sample of random MT gap configurations for both female and male axonal models (n = 10,000 each). We find that peak strains in MTs and the Ranvier node and associated neurofilament failures in female axons are substantially higher than those in male axons because there are fewer MTs in the former and also because of the random nature of MT gap locations. Despite limitations in various model assumptions as a result of limited experimental data currently available, these findings highlight the need to systematically characterize MT gap configurations and to ensure a realistic model input for axonal dynamic simulations. Finally, this study may offer fresh and improved insight into the biomechanical basis of sex differences in brain injury, and sets the stage for more systematic investigations at the microscale in the future, both numerically and experimentally.

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.

Linking fluid-axons interactions to the macroscopic fluid transport properties of the brain

Many brain disorders, including Alzheimer's Disease and Parkinson's Disease, and drug delivery procedures are linked to fluid transport in the brain; yet, while neurons are extremely soft and can be easily deformed, how the microscale channel flow interacts with the neuronal structures (especially axons) deformation and how these interactions affect the macroscale tissue function and transport properties is poorly understood. Misrepresenting these relationships may lead to the erroneous prediction of e.g. disease spread, drug delivery, and nerve injury in the brain. However, understanding fluid-neuron interactions is an outstanding challenge because the behaviours of both phases are not only dynamic but also occur at an extremely small length scale (the width of the flow channel is ∼100 nm), which cannot be captured by state-of-the-art experimental techniques. Here, by explicitly simulating the dynamics of the flow and axons at the microstructural level, we, for the first time, establish the link between micromechanical tissue response to the physical laws governing the macroscopic transport property of the brain white matter. We found that interactions between axons and the interstitial flow are very strong, thus playing an essential role in the brain fluid/mass transport. Furthermore, we proposed the first anisotropic pressure-dependent permeability tensor informed by microstructural dynamics for more accurate brain modelling at the macroscale, and analysed the effect of the variation of the microstructural parameters that influence such tensor. These findings will shed light on some unsolved issues linked to brain functions and medical treatments relying on intracerebral transport, and the mathematical model provides a framework to more realistically model the brain and design brain-tissue-like biomaterials. STATEMENT OF SIGNIFICANCE: This study reveals how neurons interact with the fluid flowing around them and how these microscale interactions affect macroscale transport behaviour of the brain tissue. The findings provide unprecedented insights into some unsolved issues linked to brain functions and medical treatments relying on intracerebral fluid transport. Furthermore, we, for the first time, established a microstructure-informed permeability tensor as a function of local hydraulic pressure and pressure gradient for the brain tissue, which inherently captures the dynamic transport property of the brain. This study is a cornerstone to advance the predicting accuracy of brain tissue transport property and neural tissue engineering.

Bidirectional hyperelastic characterization of brain white matter tissue

Biomechanical study of brain injuries originated from mechanical damages to white matter tissue requires detailed information on mechanical characteristics of its main components, the axonal fibers and extracellular matrix, which is very limited due to practical difficulties of direct measurement. In this paper, a new theoretical framework was established based on microstructural modeling of brain white matter tissue as a soft composite for bidirectional hyperelastic characterization of its main components. First the tissue was modeled as an Ogden hyperelastic material, and its principal Cauchy stresses were formulated in the axonal and transverse directions under uniaxial and equibiaxial tension using the theory of homogenization. Upon fitting these formulae to the corresponding experimental test data, direction-dependent hyperelastic constants of the tissue were obtained. These directional properties then were used to estimate the strain energy stored in the homogenized model under each loading scenario. A new microstructural composite model of the tissue was also established using principles of composites micromechanics, in which the axonal fibers and surrounding matrix are modeled as different Ogden hyperelastic materials with unknown constants. Upon balancing the strain energies stored in the homogenized and composite models under different loading scenarios, fully coupled nonlinear equations as functions of unknown hyperelastic constants were derived, and their optimum solutions were found in a multi-parametric multi-objective optimization procedure using the response surface methodology. Finally, these solutions were implemented, in a bottom-up approach, into a micromechanical finite element model to reproduce the tissue responses under the same loadings and predict the tissue responses under unseen non-equibiaxial loadings. Results demonstrated a very good agreement between the model predictions and experimental results in both directions under different loadings. Moreover, the axonal fibers with hyperelastic characteristics stiffer than the extracellular matrix were shown to play the dominant role in directional reinforcement of the tissue.

Harmonic viscoelastic response of 3D histology-informed white matter model

White matter (WM) consists of bundles of long axons embedded in a glial matrix, which lead to anisotropic mechanical properties of brain tissue, and this complicates direct numerical simulations of WM viscoelastic response. The detailed axonal geometry contains scales that range from axonal diameter (microscale) to many diameters (mesoscale) imposing an additional challenge to numerical simulations. Here we describe the development of a 3D homogenization model for the central nervous system (CNS) that accounts for the anisotropy introduced by the axon/neuroglia composite, the axonal trace curvature, and the tissue dynamic response in the frequency domain. Homogenized models that allow the incorporation of all the above factors are important for accurately simulating the tissue's mechanical behavior, and this in turn is essential in interpreting non-invasive elastography measurements. Geometric and material parameters affect the material properties and thus the response of the brain tissue. More complex, orthotropic, or anisotropic material properties are to be considered as necessitated by the 3D tissue structure. An assembly of micro-scale 3D representative elemental volumes (REVs) is constructed, leading to an integrated mesoscale WM finite element model. Assemblies of microscopic REVs, with orientations based on geometrical reconstructions driven by confocal microscopy data are employed to form the elements of the WM model. Each REV carries local material properties based on a finite element model of biphasic (axon-glial matrix) unidirectional composite. The viscoelastic response of the microscopic REVs is extracted based on geometric information and fiber volume fractions calculated from the relative distance between the local elements and global axonal trace. The response of the WM tissue model is homogenized by averaging the shear moduli over the total volume (thus deriving effective properties) under realistic external loading conditions. Under harmonic shear loading, it is proven that that the effective transverse shear moduli are higher than the axial moduli when the axon moduli are higher than the glial. Methodologically, the process of using micro-scale 3D REVs to describe more complex axon geometries avoids the partition process in traditional composite finite element methods (based on partition of finite element grids) and constitutes a robust algorithm to automatically build a WM model based on available axonal trace information. Analytically, the model provides unmatched simulation flexibility and computational power as the position, orientation, and the magnitude of each tissue building block is calculated using real tissue data, as are the training and testing processes at each level of the multiscale WM tissue.

Morphological changes in glial cells arrangement under mechanical loading: A quantitative study

The mechanical properties and microstructure of brain tissue, as its two main physical parameters, could be affected by mechanical stimuli. In previous studies, microstructural alterations due to mechanical loading have received less attention than the mechanical properties of the tissue. Therefore, the current study aimed to investigate the effect of ex-vivo mechanical forces on the micro-architecture of brain tissue including axons and glial cells. A three-step loading protocol (i.e., loading-recovery-loading) including eight strain levels from 5% to 40% was applied to bovine brain samples with axons aligned in one preferred direction (each sample experienced only one level of strain). After either the first or secondary loading step, the samples were fixed, cut in planes parallel and perpendicular to the loading direction, and stained for histology. The histological images were analyzed to measure the end-to-end length of axons and glial cell-cell distances. The results showed that after both loading steps, as the strain increased, the changes in the cell nuclei arrangement in the direction parallel to axons were more significant compared to the other two perpendicular directions. Based on this evidence, we hypothesized that the spatial pattern of glial cells is highly affected by the orientation of axonal fibers. Moreover, the results revealed that in both loading steps, the maximum cell-cell distance occurred at 15% strain, and this distance decreased for higher strains. Since 15% strain is close to the previously reported brain injury threshold, this evidence could suggest that at higher strains, the axons start to rupture, causing a reduction in the displacement of glial cells. Accordingly, it was concluded that more attention to glial cells' architecture during mechanical loading may lead to introduce a new biomarker for brain injury.

Effect of Particle Size and Surface Charge on Nanoparticles Diffusion in the Brain White Matter

Purpose

Brain disorders have become a serious problem for healthcare worldwide. Nanoparticle-based drugs are one of the emerging therapies and have shown great promise to treat brain diseases. Modifications on particle size and surface charge are two efficient ways to increase the transport efficiency of nanoparticles through brain-blood barrier; however, partly due to the high complexity of brain microstructure and limited visibility of Nanoparticles (NPs), our understanding of how these two modifications can affect the transport of NPs in the brain is insufficient.

Methods

In this study, a framework, which contains a stochastic geometric model of brain white matter (WM) and a mathematical particle tracing model, was developed to investigate the relationship between particle size/surface charge of the NPs and their effective diffusion coefficients (D) in WM.

Results

The predictive capabilities of this method have been validated using published experimental tests. For negatively charged NPs, both particle size and surface charge are positively correlated with D before reaching a size threshold. When Zeta potential (Zp) is less negative than -10 mV, the difference between NPs’ D in WM and pure interstitial fluid (IF) is limited.

Conclusion

A deeper understanding on the relationships between particle size/surface charge of NPs and their D in WM has been obtained. The results from this study and the developed modelling framework provide important tools for the development of nano-drugs and nano-carriers to cure brain diseases.

Effect of collagen degradation on the mechanical behavior and wrinkling of skin

Chronological skin aging is a complex process that is controlled by numerous intrinsic and extrinsic factors. One major factor is the gradual degradation of the dermal collagen fiber network. As a step toward understanding the mechanistic importance of dermal tissue in the process of aging, this study employs analytical and multiscale computational models to elucidate the effect of collagen fiber bundle disintegration on the mechanical properties and topography of skin. Here, human skin is modeled as a soft composite with an anisotropic dermal layer. The anisotropy of the tissue is governed by collagen fiber bundles with varying densities, average fiber alignments, and normalized alignment distributions. In all finite element models examined, collagen fiber bundle degradation results in progressive decreases in dermal and full-thickness composite stiffness. This reduction is more profound when collagen bundles align with the compression axis. Aged skin models with low collagen fiber bundle densities under compression exhibit notably smaller critical wrinkling strains and larger critical wavelengths than younger skin models, in agreement with in vivo wrinkling behavior with age. The propensity for skin wrinkling can be directly attributable to the degradation of collagen fiber bundles, a relationship that has previously been assumed but unsubstantiated. While linear-elastic analytical models fail to capture the postbuckling behavior in skin, nonlinear finite element models can predict the complex bifurcations of the compressed skin with different densities of collagen bundles.

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.

Regional Neurodegeneration in vitro: The Protective Role of Neural Activity

Traumatic brain injury is a devastating public health problem, the eighth leading cause of death across the world. To improve our understanding of how injury at the cellular scale affects neural circuit function, we developed a protocol to precisely injure individual neurons within an in vitro neural network. We used high speed calcium imaging to estimate alterations in neural activity and connectivity that occur followed targeted microtrauma. Our studies show that mechanically injured neurons inactivate following microtrauma and eventually re-integrate into the network. Single neuron re-integration is dependent on its activity prior to injury and initial connections in the network: more active and integrated neurons are more resistant to microtrauma and more likely to re-integrate into the network. Micromechanical injury leads to neuronal death 6 h post-injury in a subset of both injured and uninjured neurons. Interestingly, neural activity and network participation after injury were associated with survival in linear discriminate analysis (77.3% correct prediction, Wilks' Lambda = 0.838). Based on this observation, we modulated neuronal activity to rescue neurons after microtrauma. Inhibition of neuronal activity provided much greater survivability than did activation of neurons (ANOVA, p < 0.01 with post-hoc Tukey HSD, p < 0.01). Rescue of neurons by blocking activity in the post-acute period is partially mediated by mitochondrial energetics, as we observed silencing neurons after micromechanical injury led to a significant reduction in mitochondrial calcium accumulation. Overall, the present study provides deeper insight into the propagation of injury within networks, demonstrating that together the initial activity, network structure, and post-injury activity levels contribute to the progressive changes in a neural circuit after mechanical trauma.

Visco-hyperelastic characterization of human brain white matter micro-level constituents in different strain rates

In this study, we propose a computational characterization technique for obtaining the material properties of axons and extracellular matrix (ECM) in human brain white matter. To account for the dynamic behavior of the brain tissue, data from time-dependent relaxation tests of human brain white matter in different strain rates are extracted and formulated by a visco-hyperelastic constitutive model consisting of the Ogden hyperelastic model and the Prony series expansion. Through micromechanical finite element simulation, a derivative-free optimization framework designed to minimize the difference between the numerical and experimental data is used to identify the material properties of the axons and ECM. The Prony series expansion parameters of axons and ECM are found to be highly affected by the Prony series expansion coefficients of the brain white matter. The optimal parameters of axons and ECM are verified through micromechanical simulation by comparing the averaged numerical response with that of the experimental data. Moreover, the initial shear modulus and the reduced shear modulus of the axons are found for different strain rates of 0.0001, 0.01, and 1 s^-1. Consequently, first- and second-order regressions are used to find relations for the prediction of the shear modulus at the intermediate strain rates. Graphical Abstract The applied procedure for characterization of brain white matter micro-level constituents. The macro-level experimental data in different strain rates are used in the context of simulation-based optimization to obtain the properties of axons and extracellular matrix material.

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

This study presents a novel statistical volume element (SVE) for micromechanical modeling of the white matter structures, with histology-informed randomized distribution of axonal tracts within the extracellular matrix. The model was constructed based on the probability distribution functions obtained from the results of diffusion tensor imaging as well as the histological observations of scanning electron micrograph, at two structures of white matter susceptible to traumatic brain injury, i.e. corpus callosum and corona radiata. A simplistic representative volume element (RVE) with symmetrical arrangement of fully alligned axonal fibers was also created as a reference for comparison. A parametric study was conducted to find the optimum grid and edge size which ensured the periodicity and ergodicity of the SVE and RVE models. A multi-objective evolutionary optimization procedure was used to find the hyperelastic and viscoelastic material constants of the constituents, based on the experimentally reported responses of corpus callosum to axonal and transverse loadings. The optimal material properties were then used to predict the homogenized and localized responses of corpus callosum and corona radiata. The results indicated similar homogenized responses of the SVE and RVE under quasi-static extension, which were in good agreement with the experimental data. Under shear strain, however, the models exhibited different behaviors, with the SVE model showing much closer response to the experimental observations. Moreover, the SVE model displayed a significantly better agreement with the reports of the experiments at high strain rates. The results suggest that the randomized fiber architecture has a great influence on the validity of the micromechanical models of white matter, with a distinguished impact on the model's response to shear deformation and high strain rates. Moreover, it can provide a more detailed presentation of the localized responses of the tissue substructures, including the stress concentrations around the low caliber axonal tracts, which is critical for studying the axonal injury mechanisms.

Nonlinear mechanics of soft composites: hyperelastic characterization of white matter tissue components

This paper presents a bi-directional closed-form analytical solution, in the framework of nonlinear soft composites mechanics, for top-down hyperelastic characterization of brain white matter tissue components, based on the directional homogenized responses of the tissue in the axial and transverse directions. The white matter is considered as a transversely isotropic neo-Hookean composite made of unidirectional distribution of axonal fibers within the extracellular matrix. First, two homogenization formulations are derived for the homogenized axial and transverse shear moduli of the tissue, based on definition of the strain energy density function. Next, the rule of mixtures and Hashin-Shtrikman theories are used to derive two coupled nonlinear equations which correlates the tissue shear moduli to these of its components. Closed-form solutions for shear moduli of the components are then obtained by solving these equations simultaneously. In order to validate the hyperelastic characteristics of components obtained in previous step, they are used in a bottom-up approach in a micromechanical model of the tissue with the aim of predicting the directional homogenized responses of the tissue. Comparison of model predictions with the experimental test results reported for corona radiata and corpus callosum white matter structures reveals very good agreements with the experimental results in both directions. The model predictions are also in good agreement with the analytical solution obtained by the iterated homogenization technique. Results indicate that axonal fibers are almost ten times stiffer than the extracellular matrix under large deformations.

Axons Embedded in a Tissue May Withstand Larger Deformations Than Isolated Axons Before Mechanoporation Occurs

Diffuse axonal injury (DAI) is the pathological consequence of traumatic brain injury (TBI) that most of all requires a multiscale approach in order to be, first, understood and then possibly prevented. While in fact the mechanical insult usually happens at the head (or macro) level, the consequences affect structures at the cellular (or microlevel). The quest for axonal injury tolerances has so far been addressed both with experimental and computational approaches. On one hand, the experimental approach presents challenges connected to both temporal and spatial resolution in the identification of a clear axonal injury trigger after the application of a mechanical load. On the other hand, computational approaches usually consider axons as homogeneous entities and therefore are unable to make inferences about their viability, which is thought to depend on subcellular damages. Here, we propose a computational multiscale approach to investigate the onset of axonal injury in two typical experimental scenarios. We simulated single-cell and tissue stretch injury using a composite finite element axonal model in isolation and embedded in a matrix, respectively. Inferences on axonal damage are based on the comparison between axolemma strains and previously established mechanoporation thresholds. Our results show that, axons embedded in a tissue could withstand higher deformations than isolated axons before mechanoporation occurred and this is exacerbated by the increase in strain rate from 1/s to 10/s.