Structural Anisotropy vs. Mechanical Anisotropy: The Contribution of Axonal Fibers to the Material Properties of Brain White Matter

Systematic analysis of constitutive models of brain tissue materials based on compression tests

It's crucial to understand the biomechanical properties of brain tissue to comprehend the potential mechanisms of traumatic brain injury. This study, distinct from homogeneous models, integrates axonal coupling in both axial and transverse compressive experiments within a continuum mechanics framework to capture its intricate mechanical behaviors. Fresh porcine brains underwent unconfined compression at strain rates of 0.001/s and 0.1/s to 0.3 strain, allowing for a comprehensive statistical analysis of the directional, regional, and strain-rate-dependent mechanical properties of brain tissue. The established constitutive model, fitted to experimental data, delineates material parameters providing intuitive insights into the stiffness of gray/white matter isotropic matrices and neural fibers. Additionally, it predicts the mechanical performance of white matter matrix and axonal fibers under compressive loading. Results reveal that gray matter is insensitive to loading direction, exhibiting insignificant stiffness variations within regions. White matter, however, displays no significant differences in mechanical properties under axial and transverse loading, with an overall higher average stress than gray matter and a more pronounced strain-rate effect. Stress-strain curves indicate that, under axial compression, white matter axons primarily resist the load before transitioning to a matrix-dominated response. Under transverse loading, axonal fibers exhibit weaker resistance to lateral pressure. The mechanical behavior of brain tissue is highly dependent on loading rate, region, direction, and peak strain. This study, by combining experimentation with phenomenological modeling, elucidates certain phenomena, contributing valuable insights for the development of precise computational models.

Discovering 3D hidden elasticity in isotropic and transversely isotropic materials with physics-informed UNets

Three-dimensional variation in structural components or fiber alignments results in complex mechanical property distribution in tissues and biomaterials. In this paper, we use a physics-informed UNet-based neural network model (El-UNet) to discover the three-dimensional (3D) internal composition and space-dependent material properties of heterogeneous isotropic and transversely isotropic materials without a priori knowledge of the composition. We then show the capabilities of El-UNet by validating against data obtained from finite-element simulations of two soft tissues, namely, brain tissue and articular cartilage, under various loading conditions. We first simulated compressive loading of 3D brain tissue comprising of distinct white matter and gray matter mechanical properties undergoing small strains with isotropic linear elastic behavior, where El-UNet reached mean absolute relative errors under 1.5 % for elastic modulus and Poisson's ratio estimations across the 3D volume. We showed that the 3D solution achieved by El-UNet was superior to relative stiffness mapping by inverse of axial strain and two-dimensional plane stress/plane strain approximations. Additionally, we simulated a transversely isotropic articular cartilage with known fiber orientations undergoing compressive loading, and accurately estimated the spatial distribution of all five material parameters, with mean absolute relative errors under 5 %. Our work demonstrates the application of the computationally efficient physics-informed El-UNet in 3D elasticity imaging and provides methods for translation to experimental 3D characterization of soft tissues and other materials. The proposed El-UNet offers a powerful tool for both in vitro and ex vivo tissue analysis, with potential extensions to in vivo diagnostics. STATEMENT OF SIGNIFICANCE: Elasticity imaging is a technique that reconstructs mechanical properties of tissue using deformation and force measurements. Given the complexity of this reconstruction, most existing methods have mostly focused on 2D problems. Our work is the first implementation of physics-informed UNets to reconstruct three-dimensional material parameter distributions for isotropic and transversely isotropic linear elastic materials by having deformation and force measurements. We comprehensively validate our model using synthetic data generated using finite element models of biological tissues with high bio-fidelity-the brain and articular cartilage. Our method can be implemented in elasticity imaging scenarios for in vitro and ex vivo mechanical characterization of biomaterials and biological tissues, with potential extensions to in vivo diagnostics.

Region-Dependent Mechanical Properties of Human Brain Tissue Under Large Deformations Using Inverse Finite Element Modeling

This study aims to facilitate intracranial simulation of traumatic events by determining the mechanical properties of different anatomical structures of the brain. Our experimental indentation paradigm used fresh, post-operative human tissue, which is highly advantageous in determining mechanical properties without being affected by postmortem time. This study employed an inverse finite element approach coupled with experimental indentation data to characterize mechanical properties of the human hippocampus (CA1, CA3, dentate gyrus), cortex white matter, and cortex grey matter. We determined that an uncoupled viscoelastic Ogden constitutive formulation was most appropriate to represent the mechanical behavior of these different regions of brain. Anatomical regions were significantly different in their mechanical properties. The cortex white matter was stiffer than cortex grey matter, and the CA1 and dentate gyrus were both stiffer than cortex grey matter. Although no sex dependency was observed, there were trends indicating that male brain regions were generally stiffer than corresponding female regions. In addition, there were no statistically significant age dependent differences. This study provides a structure-specific description of fresh human brain tissue mechanical properties, which will be an important step toward explicitly modeling the heterogeneity of brain tissue deformation during TBI through finite element modeling.

Head injury: Importance of the deep brain nuclei in force transmission to the brain

Finite element modeling provides a digital representation of the human body. It is currently the most pertinent method to study the mechanisms of head injury, and is becoming a scientific reference in forensic expert reports. Improved biofidelity is a recurrent aim of research studies in biomechanics in order to improve earlier models whose mechanical properties conformed to simplified elastic behavior and mechanic laws. We aimed to study force transmission to the brain following impacts to the head, using a finite element head model with increased biofidelity. To the model developed by the Laboratory of Applied Biomechanics of Marseille, we added new brain structures (thalamus, central gray nuclei and ventricular systems) as well as three tracts involved in the symptoms of head injury: the corpus callosum, uncinate tracts and corticospinal tracts. Three head impact scenarios were simulated: an uppercut with the prior model and an uppercut with the improved model in order to compare the two models, and a lateral impact with an impact velocity of 6.5 m/s in the improved model. In these conditions, in uppercuts the maximum stress values did not exceed the injury risk threshold. On the other hand, the deep gray matter (thalamus and central gray nuclei) was the region at highest risk of injury during lateral impacts. Even if injury to the deep gray matter is not immediately life-threatening, it could explain the chronic disabling symptoms of even low-intensity head injury.

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.

Strain-rate-dependent material properties of human lung parenchymal tissue using inverse finite element approach

Automobile crashes and blunt trauma often lead to life-threatening thoracic injuries, especially to the lung tissues. These injuries can be simulated using finite element-based human body models that need dynamic material properties of lung tissue. The strain-rate-dependent material parameters of human parenchymal tissues were determined in this study using uniaxial quasi-static (1 mm/s) and dynamic (1.6, 3, and 5 m/s) compression tests. A bilinear material model was used to capture the nonlinear behavior of the lung tissue, which was implemented using a user-defined material in LS-DYNA. Inverse mapping using genetic algorithm-based optimization of all experimental data with the corresponding FE models yielded a set of strain-rate-dependent material parameters. The bilinear material parameters are obtained for the strain rates of 0.1, 100, 300, and 500 s-1. The estimated elastic modulus increased from 43 to 153 kPa, while the toe strain reduced from 0.39 to 0.29 when the strain rate was increased from 0.1 to 500 s-1. The optimized bilinear material properties of parenchymal tissue exhibit a piecewise linear relationship with the strain rate.

Improving the quality and processing efficiency of beef jerky via drying in confined conditions of pre-stretching

Inspired by the mechanical enhancement of hydrogel via drying in confined conditions, we applied this strategy to beef jerky manufacture for improving the quality and processing efficiency. In our study, beef strips were pre-stretched and then dried in a tensile state, and the confined conditions were achieved by controlling the stretched strains from 20% to 120%. Compared with the sample dried freely, beef jerky dried in confined conditions of different pre-stretching strains exhibited improved quality based on texture and sensory analysis. Additionally, this method also enhanced processing efficiency by reducing approximately 50% drying time. The excellent sensory quality and good texture of beef jerky were obtained as the pre-stretching strain was 80%. Drying beef strips in confined conditions made muscle fibers tense and enhanced hydrophobicity of myofibrillar proteins, leading to a compact structure with high shear force and anisotropy, and rapid water loss in beef jerky. This facile and green method provides a promising route to enrich the existing technologies of jerky processing.

An atlas of the heterogeneous viscoelastic brain with local power-law attenuation synthesised using Prony-series

This review addresses the acute need to acknowledge the mechanical heterogeneity of brain matter and to accurately calibrate its local viscoelastic material properties accordingly. Specifically, it is important to compile the existing and disparate literature on attenuation power-laws and dispersion to make progress in wave physics of brain matter, a field of research that has the potential to explain the mechanisms at play in diffuse axonal injury and mild traumatic brain injury in general. Currently, viscous effects in the brain are modelled using Prony-series, i.e., a sum of decaying exponentials at different relaxation times. Here we collect and synthesise the Prony-series coefficients appearing in the literature for twelve regions: brainstem, basal ganglia, cerebellum, corona radiata, corpus callosum, cortex, dentate gyrus, hippocampus, thalamus, grey matter, white matter, homogeneous brain, and for eight different mammals: pig, rat, human, mouse, cow, sheep, monkey and dog. Using this data, we compute the fractional-exponent attenuation power-laws for different tissues of the brain, the corresponding dispersion laws resulting from causality, and the averaged Prony-series coefficients. STATEMENT OF SIGNIFICANCE: Traumatic brain injuries are considered a silent epidemic and finite element methods (FEMs) are used in modelling brain deformation, requiring access to viscoelastic properties of brain. To the best of our knowledge, this work presents 1) the first multi-frequency viscoelastic atlas of the heterogeneous brain, 2) the first review focusing on viscoelastic modelling in both FEMs and experimental works, 3) the first attempt to conglomerate the disparate existing literature on the viscoelastic modelling of the brain and 4) the largest collection of viscoelastic parameters for the brain (212 different Prony-series spanning 12 different tissues and 8 different animal surrogates). Furthermore, this work presents the first brain atlas of attenuation power-laws essential for modelling shear waves in brain.

Modeling the damage-induced softening behavior of brain white matter using a coupled hyperelasticty-damage model

White matter in the brain is structurally anisotropic consisting of large bundle of aligned axonal fibers. Hyperelastic, transversely isotropic constitutive models are typically used in the modeling and simulation of such tissues. However, most studies constrain the material models to describe the mechanical behavior of white matter in the limit of small deformation, without considering the experimentally observed damage initiation and damage-induced material softening in large strain regime. In this study, we extend a previously developed transversely isotropic hyperelasticity model for white matter by coupling it with damage equations within the framework of thermodynamics and using continuum damage mechanics method. Two homogeneous deformation cases are used to demonstrate the proposed model's capability in capturing the damage-induced softening behaviors of white matter under uniaxial loading and simple shear, along with the investigation of fiber orientation effect on such behaviors and material stiffness. As a demonstration case of inhomogeneous deformation, the proposed model is also implemented into finite element codes to reproduce the experimental data (nonlinear material behavior and damage initiation) from an indentation configuration of porcine white matter. Good agreement between numerical results and experimental data is achieved indicating the potential of the proposed model in characterizing the mechanical behaviors of white matter considering damage at large strain.

Elasticity imaging using physics-informed neural networks: Spatial discovery of elastic modulus and Poisson's ratio

Elasticity imaging is a technique that discovers the spatial distribution of mechanical properties of tissue using deformation and force measurements under various loading conditions. Given the complexity of this discovery, most existing methods approximate only one material parameter while assuming homogeneous distributions for the others. We employ physics-informed neural networks (PINN) in linear elasticity problems to discover the space-dependent distribution of both elastic modulus (E) and Poisson's ratio (ν) simultaneously, using strain data, normal stress boundary conditions, and the governing physics. We validated our model on three examples. First, we experimentally loaded hydrogel samples with embedded stiff inclusions, representing tumorous tissue, and compared the approximations against ground truth determined through tensile tests. Next, using data from finite element simulation of a rectangular domain containing a stiff circular inclusion, the PINN model accurately localized the inclusion and estimated both E and ν. We observed that in a heterogeneous domain, assuming a homogeneous ν distribution increases estimation error for stiffness as well as the area of the stiff inclusion, which could have clinical importance when determining size and stiffness of tumorous tissue. Finally, our model accurately captured spatial distribution of mechanical properties and the tissue interfaces on data from another computational model, simulating uniaxial loading of a rectangular hydrogel sample containing a human brain slice with distinct gray matter and white matter regions and complex geometrical features. This elasticity imaging implementation has the potential to be used in clinical imaging scenarios to reliably discover the spatial distribution of mechanical parameters and identify material interfaces such as tumors. STATEMENT OF SIGNIFICANCE: Our work is the first implementation of physics-informed neural networks to reconstruct both material parameters - Young's modulus and Poisson's ratio - and stress distributions for isotropic linear elastic materials by having deformation and force measurements. We comprehensively validate our model using experimental measurements and synthetic data generated using finite element modeling. Our method can be implemented in clinical elasticity imaging scenarios to improve diagnosis of tumors and for mechanical characterization of biomaterials and biological tissues in a minimally invasive manner.

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.

Viscoelastic damage evaluation of the axon

In this manuscript, we have studied the microstructure of the axonal cytoskeleton and adopted a bottom-up approach to evaluate the mechanical responses of axons. The cytoskeleton of the axon includes the microtubules (MT), Tau proteins (Tau), neurofilaments (NF), and microfilaments (MF). Although most of the rigidity of the axons is due to the MT, the viscoelastic response of axons comes from the Tau. Early studies have shown that NF and MF do not provide significant elasticity to the overall response of axons. Therefore, the most critical aspect of the mechanical response of axons is the microstructural topology of how MT and Tau are connected and construct the cross-linked network. Using a scanning electron microscope (SEM), the cross-sectional view of the axons revealed that the MTs are organized in a hexagonal array and cross-linked by Tau. Therefore, we have developed a hexagonal Representative Volume Element (RVE) of the axonal microstructure with MT and Tau as fibers. The matrix of the RVE is modeled by considering a combined effect of NF and MF. A parametric study is done by varying fiber geometric and mechanical properties. The Young’s modulus and spacing of MT are varied between 1.5 and 1.9 GPa and 20–38 nm, respectively. Tau is modeled as a 3-parameter General Maxwell viscoelastic material. The failure strains for MT and Tau are taken to be 50 and 40%, respectively. A total of 4 RVEs are prepared for finite element analysis, and six loading cases are inspected to quantify the three-dimensional (3D) viscoelastic relaxation response. The volume-averaged stress and strain are then used to fit the relaxation Prony series. Next, we imposed varying strain rates (between 10/sec to 50/sec) on the RVE and analyzed the axonal failure process. We have observed that the 40% failure strain of Tau is achieved in all strain rates before the MT reaches its failure strain of 50%. The corresponding axonal failure strain and stress vary between 6 and 11% and 5–19.8 MPa, respectively. This study can be used to model macroscale axonal aggregate typical of the white matter region of the brain tissue.

Correlating the microstructural architecture and macrostructural behaviour of the brain

The computational simulation of pathological conditions and surgical procedures, for example the removal of cancerous tissue, can contribute crucially to the future of medicine. Especially for brain surgery, these methods can be important, as the ultra-soft tissue controls vital functions of the body. However, the microstructural interactions and their effects on macroscopic material properties remain incompletely understood. Therefore, we investigated the mechanical behaviour of brain tissue under three different deformation modes, axial tension, compression, and semi-confined compression, in different anatomical regions, and for varying axon orientation. In addition, we characterised the underlying microstructure in terms of myelin, cells, glial cells and neuron area fraction, and density. The correlation of these quantities with the material parameters of the anisotropic Ogden model reveals a decrease in shear modulus with increasing myelin area fraction. Strikingly, the tensile shear modulus correlates positively with cell and neuronal area fraction (Spearman's correlation coefficient of r_s=0.40 and r_s=0.33), whereas the compressive shear modulus decreases with increasing glial cell area (r_s=-0.33). Our study finds that tissue non-linearity significantly depends on the myelin area fraction (r_s=0.47), cell density (r_s=0.41) and glial cell area (r_s=0.49). Our results provide an important step towards understanding the micromechanical load transfer that leads to the non-linear macromechanical behaviour of the brain. STATEMENT OF SIGNIFICANCE: Within this article, we investigate the mechanical behaviour of brain tissue under three different deformation modes, in different anatomical regions, and for varying axon orientation. Further, we characterise the underlying microstructure in terms of various constituents. The correlation of these quantities with the material parameters of the anisotropic Ogden model reveals a decrease in shear modulus with increasing myelin area fraction. Strikingly, the tensile shear modulus correlates positively with cell and neuronal area fraction, whereas the compressive shear modulus decreases with increasing glial cell area. Our study finds that tissue non-linearity significantly depends on the myelin area fraction, cell density, and glial cell area. Our results provide an important step towards understanding the micromechanical load transfer that leads to the non-linear macromechanical behaviour of the brain.

Tissue-Scale Biomechanical Testing of Brain Tissue for the Calibration of Nonlinear Material Models

Brain tissue is one of the most complex and softest tissues in the human body. Due to its ultrasoft and biphasic nature, it is difficult to control the deformation state during biomechanical testing and to quantify the highly nonlinear, time-dependent tissue response. In numerous experimental studies that have investigated the mechanical properties of brain tissue over the last decades, stiffness values have varied significantly. One reason for the observed discrepancies is the lack of standardized testing protocols and corresponding data analyses. The tissue properties have been tested on different length and time scales depending on the testing technique, and the corresponding data have been analyzed based on simplifying assumptions. In this review, we highlight the advantage of using nonlinear continuum mechanics based modeling and finite element simulations to carefully design experimental setups and protocols as well as to comprehensively analyze the corresponding experimental data. We review testing techniques and protocols that have been used to calibrate material model parameters and discuss artifacts that might falsify the measured properties. The aim of this work is to provide standardized procedures to reliably quantify the mechanical properties of brain tissue and to more accurately calibrate appropriate constitutive models for computational simulations of brain development, injury and disease. Computational models can not only be used to predictively understand brain tissue behavior, but can also serve as valuable tools to assist diagnosis and treatment of diseases or to plan neurosurgical procedures. © 2022 The Authors. Current Protocols published by Wiley Periodicals LLC.

Mind the gap: A mechanobiological hypothesis for the role of gap junctions in the mechanical properties of injured brain tissue

Despite more than half a century of work on the brain biomechanics, there are still significant unknowns about this tissue. Since the brain is highly susceptible to injury, damage biomechanics has been one of the main areas of interest to the researchers in the field of brain biomechanics. In many previous studies, mechanical properties of brain tissue under sub-injury and injury level loading conditions have been addressed; however, to the best of our knowledge, the role of cell-cell interactions in the mechanical behavior of brain tissue has not been well examined yet. This note introduces the hypothesis that gap junctions as the major type of cell-cell junctions in the brain tissue play a pivotal role in the mechanical properties of the tissue and their failure during injury leads to changes in brain's material properties. According to this hypothesis, during an injury, the gap junctions are damaged, leading to a decrease in tissue stiffness, whereas following the injury, new junction proteins are expressed, leading to an increase in tissue stiffness. We suggest that considering the mechanobiological effect of gap junctions in the material properties of brain tissue may help better understand the brain injury mechanism.

Progress in the Applications of Smart Piezoelectric Materials for Medical Devices

Smart piezoelectric materials are of great interest due to their unique properties. Piezoelectric materials can transform mechanical energy into electricity and vice versa. There are mono and polycrystals (piezoceramics), polymers, and composites in the group of piezoelectric materials. Recent years show progress in the applications of piezoelectric materials in biomedical devices due to their biocompatibility and biodegradability. Medical devices such as actuators and sensors, energy harvesting devices, and active scaffolds for neural tissue engineering are continually explored. Sensors and actuators from piezoelectric materials can convert flow rate, pressure, etc., to generate energy or consume it. This paper consists of using smart materials to design medical devices and provide a greater understanding of the piezoelectric effect in the medical industry presently. A greater understanding of piezoelectricity is necessary regarding the future development and industry challenges.

Structural Anisotropy vs. Mechanical Anisotropy: The Contribution of Axonal Fibers to the Material Properties of Brain White Matter

Brain's micro-structure plays a critical role in its macro-structure material properties. Since the structural anisotropy in the brain white matter has been introduced due to axonal fibers, considering the direction of axons in the continuum models has been mediated to improve the results of computational simulations. The aim of the current study was to investigate the role of fiber direction in the material properties of brain white matter and compare the mechanical behavior of the anisotropic white matter and the isotropic gray matter. Diffusion tensor imaging (DTI) was employed to detect the direction of axons in white matter samples, and tensile stress-relaxation loads up to 20% strains were applied on bovine gray and white matter samples. In order to calculate the nonlinear and time-dependent properties of white matter and gray matter, a visco-hyperelastic model was used. The results indicated that the mechanical behavior of white matter in two orthogonal directions, parallel and perpendicular to axonal fibers, are significantly different. This difference indicates that brain white matter could be assumed as an anisotropic material and axons have contribution in the mechanical properties. Also, up to 15% strain, white matter samples with axons parallel to the force direction are significantly stiffer than both the gray matter samples and white matter samples with axons perpendicular to the force direction. Moreover, the elastic moduli of white matter samples with axons both parallel and perpendicular to the loading direction and gray matter samples at 15-20% strain are not significantly different. According to these observations, it is suggested that axons have negligible roles in the material properties of white matter when it is loaded in the direction perpendicular to the axon direction. Finally, this observation showed that the anisotropy of brain tissue not only has effects on the elastic behavior, but also has effects on the viscoelastic behavior.