The Influence of Strain Rate Dependency on the Structure–Property Relations of Porcine Brain

Needle-induced cavitation: A method to probe the local mechanics of brain tissue

Traditional mechanical characterization of extremely soft tissues is challenging given difficulty extracting tissue, satisfying geometric requirements, keeping tissues hydrated, and securing the tissue in an apparatus without slippage. The heterogeneous nature and structural complexity of brain tissues on small length scales makes it especially difficult to characterize. Needle-induced cavitation (NIC) is a technique that overcomes these issues and can mechanically characterize brain tissues at precise, micrometer-scale locations. This small-scale capability is crucial in order to spatially characterize diseased tissue states like fibrosis or cancer. NIC consists of inserting a needle into a tissue and pressurizing a fluid until a deformation occurs at the tip of the needle at a critical pressure. NIC is a convenient, affordable technique to measure mechanical properties, such as modulus and fracture energy, and to assess the performance of soft materials. Experimental parameters such as needle size and fluid flowrate are tunable, so that the end-user can control the length and time scales, making it uniquely capable of measuring local mechanical properties across a wide range of strain rates. The portable nature of NIC and capability to conduct in vivo experiments makes it a particularly appealing characterization technique compared to traditional methods. Despite significant developments in the technique over the last decade, wide implementation in the biological field is still limited. Here, we address the limitations of the NIC technique specifically when working with soft tissues and provide readers with expected results for brain tissue. Our goal is to assist others in conducting reliable and reproducible mechanical characterization of soft biomaterials and tissues.

Rate- and Region-Dependent Mechanical Properties of Göttingen Minipig Brain Tissue in Simple Shear and Unconfined Compression

Traumatic brain injury (TBI), particularly from explosive blasts, is a major cause of casualties in modern military conflicts. Computational models are an important tool in understanding the underlying biomechanics of TBI but are highly dependent on the mechanical properties of soft tissue to produce accurate results. Reported material properties of brain tissue can vary by several orders of magnitude between studies, and no published set of material parameters exists for porcine brain tissue at strain rates relevant to blast. In this work, brain tissue from the brainstem, cerebellum, and cerebrum of freshly euthanized adolescent male Göttingen minipigs was tested in simple shear and unconfined compression at strain rates ranging from quasi-static (QS) to 300 s-1. Brain tissue showed significant strain rate stiffening in both shear and compression. Minimal differences were seen between different regions of the brain. Both hyperelastic and hyper-viscoelastic constitutive models were fit to experimental stress, considering data from either a single loading mode (unidirectional) or two loading modes together (bidirectional). The unidirectional hyper-viscoelastic models with an Ogden hyperelastic representation and a one-term Prony series best captured the response of brain tissue in all regions and rates. The bidirectional models were generally able to capture the response of the tissue in high-rate shear and all compression modes, but not the QS shear. Our constitutive models describe the first set of material parameters for porcine brain tissue relevant to loading modes and rates seen in blast injury.

Mechanisms of mechanical load transfer through brain tissue

Brain injuries are often characterized by diffusely distributed axonal and vascular damage invisible to medical imaging techniques. The spatial distribution of mechanical stresses and strains plays an important role, but is not sufficient to explain the diffuse distribution of brain lesions. It remains unclear how forces are transferred from the organ to the cell scale and why some cells are damaged while neighboring cells remain unaffected. To address this knowledge gap, we subjected histologically stained fresh human and porcine brain tissue specimens to compressive loading and simultaneously tracked cell and blood vessel displacements. Our experiments reveal different mechanisms of load transfer from the organ or tissue scale to single cells, axons, and blood vessels. Our results show that cell displacement fields are inhomogeneous at the interface between gray and white matter and in the vicinity of blood vessels-locally inducing significant deformations of individual cells. These insights have important implications to better understand injury mechanisms and highlight the importance of blood vessels for the local deformation of the brain's cellular structure during loading.

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.

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.

Cavitation induced fracture of intact brain tissue

Nonpenetrating traumatic brain injuries (TBIs) are linked to cavitation. The structural organization of the brain makes it particularly susceptible to tears and fractures from these cavitation events, but limitations in existing characterization methods make it difficult to understand the relationship between fracture and cavitation in this tissue. More broadly, fracture energy is an important, yet often overlooked, mechanical property of all soft tissues. We combined needle-induced cavitation with hydraulic fracture models to induce and quantify fracture in intact brains at precise locations. We report here the first measurements of the fracture energy of intact brain tissue that range from 1.5 to 8.9 J/m2, depending on the location in the brain and the model applied. We observed that fracture consistently occurs along interfaces between regions of brain tissue. These fractures along interfaces allow cavitation-related damage to propagate several millimeters away from the initial injury site. Quantifying the forces necessary to fracture brain and other soft tissues is critical for understanding how impact and blast waves damage tissue in vivo and has implications for the design of protective gear and tissue engineering.

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.

Unraveling the Local Relation Between Tissue Composition and Human Brain Mechanics Through Machine Learning

The regional mechanical properties of brain tissue are not only key in the context of brain injury and its vulnerability towards mechanical loads, but also affect the behavior and functionality of brain cells. Due to the extremely soft nature of brain tissue, its mechanical characterization is challenging. The response to loading depends on length and time scales and is characterized by nonlinearity, compression-tension asymmetry, conditioning, and stress relaxation. In addition, the regional heterogeneity-both in mechanics and microstructure-complicates the comprehensive understanding of local tissue properties and its relation to the underlying microstructure. Here, we combine large-strain biomechanical tests with enzyme-linked immunosorbent assays (ELISA) and develop an extended type of constitutive artificial neural networks (CANNs) that can account for viscoelastic effects. We show that our viscoelastic constitutive artificial neural network is able to describe the tissue response in different brain regions and quantify the relevance of different cellular and extracellular components for time-independent (nonlinearity, compression-tension-asymmetry) and time-dependent (hysteresis, conditioning, stress relaxation) tissue mechanics, respectively. Our results suggest that the content of the extracellular matrix protein fibronectin is highly relevant for both the quasi-elastic behavior and viscoelastic effects of brain tissue. While the quasi-elastic response seems to be largely controlled by extracellular matrix proteins from the basement membrane, cellular components have a higher relevance for the viscoelastic response. Our findings advance our understanding of microstructure - mechanics relations in human brain tissue and are valuable to further advance predictive material models for finite element simulations or to design biomaterials for tissue engineering and 3D printing applications.

Deformation of an airfoil-shaped brain surrogate under shock wave loading

Improvised explosive devices (IEDs), during military operations, has increased the incidence of blast-induced traumatic brain injuries (bTBI). The shock wave is created following detonation of the IED. This shock wave propagates through the atmosphere and may cause bTBI. As a result, bTBI research has gained increased attention since this injury's mechanism is not thoroughly understood. To develop better protection and treatment against bTBI, further studies of soft material (e.g. brain and brain surrogate) deformation due to shock wave exposure are essential. However, the dynamic mechanical behavior of soft materials, subjected to high strain rates from shock wave exposure, remains unknown. Thus, an experimental approach was applied to study the interaction between the shock wave and an unconfined brain surrogate fabricated from a biomaterial (i.e. polydimethylsiloxane (PDMS)). The 1:70 ratio of curing agent-to-base determined the stiffness of the PDMS (Sylgard 184, Dow Corning Corporation). A stretched NACA 2414 (upper airfoil surface) geometry was utilized to resemble the shape of a porcine brain. Digital image correlation (DIC) technique was applied to measure the deformation on the brain surrogate's surface following shock wave exposure. A shock tube was utilized to create the shock wave and pressure transducers measured the pressure in the vicinity of the brain surrogate. A transient structural analysis using ANSYS Workbench was performed to predict the elastic modulus of 1:70 airfoil-shaped PDMS, at a strain rate on the order of 6 × 10³ s^-1. Both compression and protrusion of the PDMS surface were found due to the shock wave exposure. Negative pressure was found in a semi-ring area, which was the cause of protrusion. Oscillation of the brain surrogate, due to the shock wave loading, was found. The frequency of oscillation does not depend on the geometry. This work will add to the limited data describing the dynamic behavior of soft materials due to shock wave loading.

Shear-deformation based continuum-damage constitutive modeling of brain tissue

Traumatic brain injury (TBI) is a leading cause of death in the United States. Depending on the severity of injury, complications such as memory loss and emotional changes are common. While the exact mechanisms are still unclear, these cognitive deficiencies are thought to arise from microstructural damages to the brain tissue, such as in diffuse-axonal injury where neuron fibers are sheared. Constitutive models can predict such damage at a microstructural level and allow for insight into the mechanisms of injury initiating at lower length scales. In this study, we developed a continuum damage model of brain tissue that is validated by experimental quasi-static stress-strain tests in tension, compression, and shear. The present work shows that damage is most present in the shear stress state, making the tissue suitable for damage modeling via shear interaction terms. Using this model, new insights into microstructural breakdown due to shear stresses and strains can be gained by application to simulations.

Tension Strain-Softening and Compression Strain-Stiffening Behavior of Brain White Matter

Brain, the most important component of the central nervous system (CNS), is a soft tissue with a complex structure. Understanding the role of brain tissue microstructure in mechanical properties is essential to have a more profound knowledge of how brain development, disease, and injury occur. While many studies have investigated the mechanical behavior of brain tissue under various loading conditions, there has not been a clear explanation for variation reported for material properties of brain tissue. The current study compares the ex-vivo mechanical properties of brain tissue under two loading modes, namely compression and tension, and aims to explain the differences observed by closely examining the microstructure under loading. We tested bovine brain samples under uniaxial tension and compression loading conditions, and fitted hyperelastic material parameters. At 20% strain, we observed that the shear modulus of brain tissue in compression is about 6 times higher than in tension. In addition, we observed that brain tissue exhibited strain-stiffening in compression and strain-softening in tension. In order to investigate the effect of loading modes on the tissue microstructure, we fixed the samples using a novel method that enabled keeping the samples at the loaded stage during the fixation process. Based on the results of histology, we hypothesize that during compressive loading, the strain-stiffening behavior of the tissue could be attributed to glial cell bodies being pushed against surroundings, contacting each other and resisting compression, while during tension, cell connections are detached and the tissue displays softening behavior.

A knowledge map analysis of brain biomechanics: Current evidence and future directions

Although brain, one of the most complex organs in the mammalian body, has been subjected to many studies from physiological and pathological points of view, there remain significant gaps in the available knowledge regarding its biomechanics. This article reviews the research trends in brain biomechanics with a focus on injury. We used published scientific articles indexed by Web of Science database over the past 40 years and tried to address the gaps that still exist in this field. We analyzed the data using VOSviewer, which is a software tool designed for scientometric studies. The results of this study showed that the response of brain tissue to external forces has been one of the significant research topics among biomechanicians. These studies have addressed the effects of mechanical forces on the brain and mechanisms of traumatic brain injury, as well as characterized changes in tissue behavior under trauma and other neurological diseases to provide new diagnostic and monitoring methods. In this study, some challenges in the field of brain injury biomechanics have been identified and new directions toward understanding the gaps in this field are suggested.

Towards microstructure-informed material models for human brain tissue

Emerging evidence suggests that the mechanical behavior of the brain plays a critical role in development, disease, and aging. Recent studies have begun to characterize the mechanical behavior of gray and white matter tissue and to identify sets of material models that best reproduce the stress-strain behavior of different brain regions. Yet, these models are mainly phenomenological in nature, their parameters often lack clear physical interpretation, and they fail to correlate the mechanical behavior to the underlying microstructural composition. Here we make a first attempt towards identifying general relations between microstructure and mechanics with the ultimate goal to develop microstructurally motivated constitutive equations for human brain tissue. Using histological staining, we analyze the microstructure of brain specimens from different anatomical regions, the cortex, basal ganglia, corona radiata, and corpus callosum, and identify the regional stiffness and viscosity under multiple loading conditions, simple shear, compression, and tension. Strikingly, our study reveals a negative correlation between cell count and stiffness, a positive correlation between myelin content and stiffness, and a negative correlation between proteoglycan content and stiffness. Additionally, our analysis shows a positive correlation between lipid and proteoglycan content and viscosity. We demonstrate how understanding the microstructural origin of the macroscopic behavior of the brain can help us design microstructure-informed material models for human brain tissue that inherently capture regional heterogeneities. This study represents an important step towards using brain tissue stiffness and viscosity as early diagnostic markers for clinical conditions including chronic traumatic encephalopathy, Alzheimer's and Parkinson's disease, or multiple sclerosis. STATEMENT OF SIGNIFICANCE: The complex and heterogeneous mechanical properties of brain tissue play a critical role for brain function. To understand and predict how brain tissue properties vary in space and time, it will be key to link the mechanical behavior to the underlying microstructural composition. Here we use histological staining to quantify area fractions of microstructural components of mechanically tested specimens and evaluate their individual contributions to the nonlinear macroscopic mechanical response. We further propose a microstructure-informed material model for human brain tissue that inherently captures regional heterogeneities. The current work provides unprecedented insights into the biomechanics of human brain tissue, which are highly relevant to develop refined computational models for brain tissue behavior or to advance neural tissue engineering.

The Influence of Shear Anisotropy in mTBI: A White Matter Constitutive Model

We examine the influence of shear anisotropy of brain tissue on the potential for mild traumatic brain injury. First we develop a new constitutive description for the white matter in the brain that can capture the anisotropic behavior of the white matter in both tension and shear. The material parameters for the models are determined using a set of three experiments already published in the literature. The calibrated and parameterized model is then implemented in a computational (finite element) model of the head. This computational model is two-dimensional and is used to simulate a previously published injury-causing event in the National Hockey League, using axonal strain as criterion to assess the level of diffuse axonal injury. It is demonstrated that the inclusion of shear anisotropy affects both the nature and the extent of predicted injury. Further, the locations of the predicted injury are more consistent with observations in the literature.

Compressive Mechanical Properties of Porcine Brain: Experimentation and Modeling of the Tissue Hydration Effects

Designing protective systems for the human head—and, hence, the brain—requires understanding the brain’s microstructural response to mechanical insults. We present the behavior of wet and dry porcine brain undergoing quasi-static and high strain rate mechanical deformations to unravel the effect of hydration on the brain’s biomechanics. Here, native ‘wet’ brain samples contained ~80% (mass/mass) water content and ‘dry’ brain samples contained ~0% (mass/mass) water content. First, the wet brain incurred a large initial peak stress that was not exhibited by the dry brain. Second, stress levels for the dry brain were greater than the wet brain. Third, the dry brain stress–strain behavior was characteristic of ductile materials with a yield point and work hardening; however, the wet brain showed a typical concave inflection that is often manifested by polymers. Finally, finite element analysis (FEA) of the brain’s high strain rate response for samples with various proportions of water and dry brain showed that water played a major role in the initial hardening trend. Therefore, hydration level plays a key role in brain tissue micromechanics, and the incorporation of this hydration effect on the brain’s mechanical response in simulated injury scenarios or virtual human-centric protective headgear design is essential.

A fully nonlinear viscohyperelastic model for the brain tissue applicable to dynamic rates

Understanding the mechanical response of the brain to external loadings is of critical importance in investigating the pathological conditions of this tissue during injurious conditions. Such injurious loadings may occur at high rates, for example among others, during road traffic or sport accidents, falls, or due to explosions. Hence, investigating the injury mechanism and design of protective devices for the brain requires constitutive modeling of this tissue at such rates. Accordingly, this paper is aimed at critically investigating the physical background for viscohyperelastic modeling of the brain tissue with scrutinizing the elastic fields pertinent to large, time dependent deformations, and developing a fully nonlinear multimode Maxwell model that can mathematically explain such deformations. The proposed model can be calibrated using the simple monotonic uniaxial deformation of the sample extracted from the tissue, and does not require additional information from relaxation or creep experiments. The performance of the proposed model is examined using the experimental results of two different studies, which reveals a desirable agreement. The usefulness, limitations, and future developments of the proposed model are discussed in this paper.

Mechanical Characterization of Immature Porcine Brainstem in Tension at Dynamic Strain Rates

Background

Many brain injury cases involve pediatric road traffic accidents, and among these, brainstem injury causes disastrous outcomes. A thorough understanding of the tensile characterization of immature brainstem tissue is crucial in modeling traumatic brain injury sustained by children, but limited experimental data in tension is available for the immature brain tissue at dynamic strain rates.

Material/Methods

We harvested brainstem tissue from immature pigs (about 4 weeks old, and at a developmental stage similar to that of human toddlers) as a byproduct from a local slaughter house and very carefully prepared the samples. Tensile tests were performed on specimens at dynamic strain rates of 2/s, 20/s, and 100/s using a biological material instrument. The constitutive models, Fung, Ogden, Gent, and exponential function, for immature brainstem tissue material property were developed for the recorded experimental data using OriginPro^® 8.0 software. The t test was performed for infinitesimal shear modules.

Results

The curves of stress-versus-stretch ratio were convex in shape, and inflection points were found in all the test groups at the strain of about 2.5%. The average Lagrange stress of the immature brainstem specimen at the 30% strain at the strain rates of 2, 20, and 100/s was 273±114, 515±107, and 1121±197 Pa, respectively. The adjusted R-Square (R²) of Fung, Ogden, Gent, and exponential model was 0.820≤R²≤0.933, 0.774≤R²≤0.940, 0.650≤R²≤0.922, and 0.852≤R²≤0.981, respectively. The infinitesimal shear modulus of the strain energy functions showed a significant association with the strain rate (p<0.01).

Conclusions

The immature brainstem is a rate-dependent material in dynamic tensile tests, and the tissue becomes stiffer with increased strain rate. The reported results may be useful in the study of brain injuries in children who sustain injuries in road traffic accidents. Further research in more detail should be performed in the future.

Müller glia provide essential tensile strength to the developing retina

When the formation of Müller glia is inhibited in the zebrafish retina, a major consequence is that the retina begins to rip apart due to a loss of the mechanical resilience that these glial cells provide to the neural tissue.

To investigate the cellular basis of tissue integrity in a vertebrate central nervous system (CNS) tissue, we eliminated Müller glial cells (MG) from the zebrafish retina. For well over a century, glial cells have been ascribed a mechanical role in the support of neural tissues, yet this idea has not been specifically tested in vivo. We report here that retinas devoid of MG rip apart, a defect known as retinoschisis. Using atomic force microscopy, we show that retinas without MG have decreased resistance to tensile stress and are softer than controls. Laser ablation of MG processes showed that these cells are under tension in the tissue. Thus, we propose that MG act like springs that hold the neural retina together, finally confirming an active mechanical role of glial cells in the CNS.

Viscoelastic properties of the rat brain in the sagittal plane: effects of anatomical structure and age

Rat is the most commonly used animal model for the study of traumatic brain injury. Recent advances in imaging and computational modeling technology offer the promise of biomechanical models capable of resolving individual brain structures and offering greater insight into the causes and consequences of brain injury. However, there is insufficient data on the mechanical properties of brain structures available to populate these models. In this study, we used microindentation to determine viscoelastic properties of different anatomical structures in sagittal slices of juvenile and adult rat brain. We find that the rat brain is spatially heterogeneous in this anatomical plane supporting previous results in the coronal plane. In addition, the brain becomes stiffer and more heterogeneous as the animal matures. This dynamic, region-specific data will support the development of more biofidelic computational models of brain injury biomechanics and the testing of hypotheses about the manner in which different anatomical structures are injured in a head impact.