Experimental verification of brain tissue incompressibility using digital image correlation

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.

Dynamic strain fields of the mouse brain during rotation

Mouse models are used to better understand brain injury mechanisms in humans, yet there is a limited understanding of biomechanical relevance, beginning with how the murine brain deforms when the head undergoes rapid rotation from blunt impact. This problem makes it difficult to translate some aspects of diffuse axonal injury from mouse to human. To address this gap, we present the two-dimensional strain field of the mouse brain undergoing dynamic rotation in the sagittal plane. Using a high-speed camera with digital image correlation measurements of the exposed mid-sagittal brain surface, we found that pure rotations (no direct impact to the skull) of 100-200 rad/s are capable of producing complex strain fields that evolve over time with respect to rotational acceleration and deceleration. At the highest rotational velocity tested, the largest tensile strains (≥ 21% elongation) in selected regions of the mouse brain approach strain thresholds previously associated with axonal injury in prior work. These findings provide a benchmark to validate the mechanical response in biomechanical computational models predicting diffuse axonal injury, but much work remains in correlating tissue deformation patterns from computational models with underlying neuropathology.

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.

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.

Distinguishing poroelasticity and viscoelasticity of brain tissue with time scale

Brain tissue is considered to be biphasic, with approximately 80% liquid and 20% solid matrix, thus exhibiting viscoelasticity due to rearrangement of the solid matrix and poroelasticity due to fluid migration within the solid matrix. However, how to distinguish poroelastic and viscoelastic effects in brain tissue remains challenging. In this study, we proposed a method of unconfined compression-isometric hold to measure the force versus time relaxation curves of porcine brain tissue samples with systematically varied sample lengths. Upon scaling the measured relaxation force and relaxation time with different length-dependent physical quantities, we successfully distinguished the poroelasticity and viscoelasticity of the brain tissue. We demonstrated that during isometric hold, viscoelastic relaxation dominated the mechanical behavior of brain tissue in the short-time regime, while poroelastic relaxation dominated in the long-time regime. Furthermore, compared with poroelastic relaxation, viscoelastic relaxation was found to play a more dominant role in the mechanical response of porcine brain tissue. We then evaluated the differences between poroelastic and viscoelastic effects for both porcine and human brain tissue. Because of the draining of pore fluid, the Young's moduli in poroelastic relaxation were lower than those in viscoelastic relaxation; brain tissue changed from incompressible during viscoelastic relaxation to compressible during poroelastic relaxation, resulting in reduced Poisson ratios. This study provides new insights into the physical mechanisms underlying the roles of viscoelasticity and poroelasticity in brain tissue. STATEMENT OF SIGNIFICANCE: Although the poroviscoelastic model had been proposed to characterize brain tissue mechanical behavior, it is difficult to distinguish the poroelastic and viscoelastic behaviors of brain tissue. The study distinguished viscoelasticity and poroelasticity of brain tissue with time scales and then evaluated the differences between poroelastic and viscoelastic effects for both porcine and human brain tissue, which helps to accurate selection of constitutive models suitable for application in certain situations (e.g., pore-dominant and viscoelastic-dominant deformation).

On multiscale tension-compression asymmetry in skeletal muscle

Skeletal muscle tissue shows a clear asymmetry with regard to the passive stresses under tensile and compressive deformation, referred to as tension-compression asymmetry (TCA). The present study is the first one reporting on TCA at different length scales, associated with muscle tissue and muscle fibres, respectively. This allows for the first time the comparison of TCA between the tissue and one of its individual components, and thus to identify the length scale at which this phenomenon originates. Not only the passive stress-stretch characteristics were recorded, but also the volume changes during the axial tension and compression experiments. The study reveals clear differences in the characteristics of TCA between fibres and tissue. At tissue level TCA increases non-linearly with increasing deformation and the ratio of tensile to compressive stresses at the same magnitude of strain reaches a value of approximately 130 at 13.5% deformation. At fibre level instead it initially drops to a value of 6 and then rises again to a TCA of 14. At a deformation of 13.5%, the tensile stress is about 6 times higher. Thus, TCA is about 22 times more expressed at tissue than fibre scale. Moreover, the analysis of volume changes revealed little compressibility at tissue scale whereas at fibre level, especially under compressive stress, the volume decreases significantly. The data collected in this study suggests that the extracellular matrix has a distinct role in amplifying the TCA, and leads to more incompressible tissue behaviour. STATEMENT OF SIGNIFICANCE: This article analyses and compares for the first time the tension-compression asymmetry (TCA) displayed by skeletal muscle at tissue and fibre scale. In addition, the volume changes of tissue and fibre specimens with application of passive tensile and compressive loads are studied. The study identifies a key role of the extracellular matrix in establishing the mechanical response of skeletal muscle tissue: It contributes significantly to the passive stress, it is responsible for the major part of tissue-scale TCA and, most probably, prevents/balances the volume changes of muscle fibres during deformation. These new results thus shed light on the origin of TCA and provide new information to be used in microstructure-based approaches to model and simulate skeletal muscle tissue.

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.

Development and Validation of a New Anisotropic Visco-Hyperelastic Human Head Finite Element Model Capable of Predicting Multiple Brain Injuries

This paper reports on the latest refinement of the Finite Element Global Human Body Models Consortium 50th percentile (GHBMC M50) adult male head model by the development and incorporation of a new material model into the white matter tissue of the brain. The white matter is represented by an anisotropic visco-hyperelastic material model capable of simulating direction-dependent response of the brain tissue to further improve the bio-fidelity and injury predictive capability of the model. The parameters representing the material were optimized by comparing model responses to seven experimentally reported strain responses of brains of postmortem human subjects (PMHS) subjected to head impact. The head model was subjected to rigorous validation against experimental data on force–deflection responses in the skull and face, intracranial pressure, and brain strain responses from over 34 PMHS head impact experiments. Crash-induced injury indices (CIIs) for facial bone fracture, skull fracture, cerebral contusion, acute subdural hematomas (ASDHs), and diffuse brain injury were developed by reconstructing 32 PMHS and real-world injury cases with the model. Model predicted maximum principal strain (MPS) and stress were determined as fracture CIIs for compact bone and spongy bones, respectively, in the skull and face. Brain responses in terms of MPS, MPS rates, and pressure distribution in injury producing experimental impacts were determined using the model and analyzed with logistic regression and survival analysis to develop CIIs for brain contusions, diffuse brain injuries, and ASDH. The statistical models using logistic regression and survival analysis showed high accuracy with area under the receiver operating curve greater than 0.8. Because of lack of sufficient moderate diffuse brain injury data, a statistical model was not created, but all indications are that the MPS rate is an essential brain response that discriminates between moderate and severe brain injuries. The authors stated that the current GHBMC M50 v.6.0 is an advanced tool for injury prediction and mitigation of injuries in automotive crashes, sports, recreational, and military environments.

Full-field MRI measurements of in-vivo positional brain shift reveal the significance of intra-cranial geometry and head orientation for stereotactic surgery

Positional brain shift (PBS), the sagging of the brain under the effect of gravity, is comparable in magnitude to the margin of error for the success of stereotactic interventions ([Formula: see text] 1 mm). This non-uniform shift due to slight differences in head orientation can lead to a significant discrepancy between the planned and the actual location of surgical targets. Accurate in-vivo measurements of this complex deformation are critical for the design and validation of an appropriate compensation to integrate into neuronavigational systems. PBS arising from prone-to-supine change of head orientation was measured with magnetic resonance imaging on 11 young adults. The full-field displacement was extracted on a voxel-basis via digital volume correlation and analysed in a standard reference space. Results showed the need for target-specific correction of surgical targets, as a significant displacement ranging from 0.52 to 0.77 mm was measured at surgically relevant structures. Strain analysis further revealed local variability in compressibility: anterior regions showed expansion (both volume and shape change), whereas posterior regions showed small compression, mostly dominated by shape change. Finally, analysis of correlation demonstrated the potential for further patient- and intervention-specific adjustments, as intra-cranial breadth and head tilt correlated with PBS reaching statistical significance.

Group characterization of impact-induced, in vivo human brain kinematics

Brain movement during an impact can elicit a traumatic brain injury, but tissue kinematics vary from person to person and knowledge regarding this variability is limited. This study examines spatio-temporal brain-skull displacement and brain tissue deformation across groups of subjects during a mild impact in vivo. The heads of two groups of participants were imaged while subjected to a mild (less than 350 rad s^-2) impact during neck extension (NE, n = 10) and neck rotation (NR, n = 9). A kinematic atlas of displacement and strain fields averaged across all participants was constructed and compared against individual participant data. The atlas-derived mean displacement magnitude was 0.26 ± 0.13 mm for NE and 0.40 ± 0.26 mm for NR, which is comparable to the displacement magnitudes from individual participants. The strain tensor from the atlas displacement field exhibited maximum shear strain (MSS) of 0.011 ± 0.006 for NE and 0.017 ± 0.009 for NR and was lower than the individual MSS averaged across participants. The atlas illustrates common patterns, containing some blurring but visible relationships between anatomy and kinematics. Conversely, the direction of the impact, brain size, and fluid motion appear to underlie kinematic variability. These findings demonstrate the biomechanical roles of key anatomical features and illustrate common features of brain response for model evaluation.

Stereo Digital Image Correlation in MATLAB

Digital Image Correlation (DIC) has found widespread use in measuring full-field displacements and deformations experienced by a body from images captured of it. Stereo-DIC has received significantly more attention than two-dimensional (2D) DIC since it can account for out-of-plane displacements. Although many aspects of Stereo-DIC that are shared in common with 2D DIC are well documented, there is a lack of resources that cover the theory of Stereo-DIC. Furthermore, publications which do detail aspects of the theory do not detail its implementation in practice. This literature gap makes it difficult for newcomers to the field of DIC to gain a deep understanding of the Stereo-DIC process, although this knowledge is necessary to contribute to the development of the field by either furthering its capabilities or adapting it for novel applications. This gap in literature acts as a barrier thereby limiting the development rate of Stereo-DIC. This paper attempts to address this by presenting the theory of a subset-based Stereo-DIC framework that is predominantly consistent with the current state-of-the-art. The framework is implemented in practice as a 202 line MATLAB code. Validation of the framework shows that it performs on par with well-established Stereo-DIC algorithms, indicating it is sufficiently reliable for practical use. Although the framework is designed to serve as an educational resource, its modularity and validation make it attractive as a means to further the capabilities of DIC.

Novel Mechanical Strain Characterization of Ventilated ex vivo Porcine and Murine Lung using Digital Image Correlation

Respiratory illnesses, such as bronchitis, emphysema, asthma, and COVID-19, substantially remodel lung tissue, deteriorate function, and culminate in a compromised breathing ability. Yet, the structural mechanics of the lung is significantly understudied. Classical pressure-volume air or saline inflation studies of the lung have attempted to characterize the organ’s elasticity and compliance, measuring deviatory responses in diseased states; however, these investigations are exclusively limited to the bulk composite or global response of the entire lung and disregard local expansion and stretch phenomena within the lung lobes, overlooking potentially valuable physiological insights, as particularly related to mechanical ventilation. Here, we present a method to collect the first non-contact, full-field deformation measures of ex vivo porcine and murine lungs and interface with a pressure-volume ventilation system to investigate lung behavior in real time. We share preliminary observations of heterogeneous and anisotropic strain distributions of the parenchymal surface, associative pressure-volume-strain loading dependencies during continuous loading, and consider the influence of inflation rate and maximum volume. This study serves as a crucial basis for future works to comprehensively characterize the regional response of the lung across various species, link local strains to global lung mechanics, examine the effect of breathing frequencies and volumes, investigate deformation gradients and evolutionary behaviors during breathing, and contrast healthy and pathological states. Measurements collected in this framework ultimately aim to inform predictive computational models and enable the effective development of ventilators and early diagnostic strategies.

Mechanosensation in traumatic brain injury

Traumatic brain injury (TBI) is distinct from other neurological disorders because it is induced by a discrete event that applies extreme mechanical forces to the brain. This review describes how the brain senses, integrates, and responds to forces under both normal conditions and during injury. The response to forces is influenced by the unique mechanical properties of brain tissue, which differ by region, cell type, and sub-cellular structure. Elements such as the extracellular matrix, plasma membrane, transmembrane receptors, and cytoskeleton influence its properties. These same components also act as force-sensors, allowing neurons and glia to respond to their physical environment and maintain homeostasis. However, when applied forces become too large, as in TBI, these components may respond in an aberrant manner or structurally fail, resulting in unique pathological sequelae. This so-called "pathological mechanosensation" represents a spectrum of cellular responses, which vary depending on the overall biomechanical parameters of the injury and may be compounded by repetitive injuries. Such aberrant physical responses and/or damage to cells along with the resulting secondary injury cascades can ultimately lead to long-term cellular dysfunction and degeneration, often resulting in persistent deficits. Indeed, pathological mechanosensation not only directly initiates secondary injury cascades, but this post-physical damage environment provides the context in which these cascades unfold. Collectively, these points underscore the need to use experimental models that accurately replicate the biomechanics of TBI in humans. Understanding cellular responses in context with injury biomechanics may uncover therapeutic targets addressing various facets of trauma-specific sequelae.

Protective Headgear Attenuates Forces on the Inner Table and Pressure in the Brain Parenchyma During Blast and Impact: An Experimental Study Using a Simulant-Based Surrogate Model of the Human Head

Military personnel sustain head and brain injuries as a result of ballistic, blast, and blunt impact threats. Combat helmets are meant to protect the heads of these personnel during injury events. Studies show peak kinematics and kinetics are attenuated using protective headgear during impacts; however, there is limited experimental biomechanical literature that examines whether or not helmets mitigate peak mechanics delivered to the head and brain during blast. While the mechanical links between blast and brain injury are not universally agreed upon, one hypothesis is that blast energy can be transmitted through the head and into the brain. These transmissions can lead to rapid skull flexure and elevated pressures in the cranial vault, and, therefore, may be relevant in determining injury likelihood. Therefore, it could be argued that assessing a helmet for the ability to mitigate mechanics may be an appropriate paradigm for assessing the potential protective benefits of helmets against blast. In this work, we use a surrogate model of the head and brain to assess whether or not helmets and eye protection can alter mechanical measures during both head-level face-on blast and high forehead blunt impact events. Measurements near the forehead suggest head protection can attenuate brain parenchyma pressures by as much as 49% during blast and 52% during impact, and forces on the inner table of the skull by as much as 80% during blast and 84% during impact, relative to an unprotected head.

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.

Determining constitutive behavior of the brain tissue using digital image correlation and finite element modeling

Detailed knowledge about the mechanical properties of brain can improve numerical modeling of the brain under various loading conditions. The success of this modeling depends on constitutive model and reliable extraction of its material constants. The isotropy of the brain tissue is a key factor which affects the form of constitutive models. In this study, compression tests were performed on different parts of the sheep brain tissue. Also, the digital image correlation (DIC) method was utilized to investigate the direction dependency of brain parts considering their microstructures. To this aim, the DIC method was employed to measure the transverse strain of two lateral sides of the tissue samples. The results of DIC method revealed that the brain stem and corona radiata were isotropic, while the mixed white and gray matter showed an unrepeatable behavior depending on the extracted sample. To examine and validate DIC method, stress-strain diagrams were also used to investigate the isotropy. It could be concluded that axonal fibers had no reinforcing role in the brain tissue. Furthermore, the DIC method indicated incompressibility of the brain tissue. Then, the significance of using a correct method to extract the material constants of brain was discussed. In other words, the effect of the real boundary conditions in experiments, which was neglected in most previous studies, was taken into account here. Finally, the particle swarm optimization algorithm along with the finite element modeling was used to estimate the hyper-viscoelastic constants of different parts of the brain tissue.

Homogenization of heterogeneous brain tissue under quasi-static loading: a visco-hyperelastic model of a 3D RVE

Researches, in the recent years, reveal the utmost importance of brain tissue assessment regarding its mechanical properties, especially for automatic robotic tools, surgical robots and helmet producing. For this reason, experimental and computational investigation of the brain behavior under different conditions seems crucial. However, experiments do not normally show the distribution of stress and injury in microscopic scale, and due to various factors are costly. Development of micromechanical methods, which could predict the brain behavior more appropriately, could highly be helpful in reducing these costs. This study presents computational analysis of heterogeneous part of the brain tissue under quasi-static loading. Heterogeneity is created by irregular distribution of neurons in a representative volume element (RVE). Considering time-dependent behavior of the tissue, a visco-hyperelastic constitutive model is developed to predict the RVE behavior more realistically. The RVE is studied in different loads and load rates; 1, 2, 3, 10 and 15% strain load are applied at 0.03 and 0.2 s on the RVE as tensile and shear loads. Due to complexity in geometry, self-consistent approximation method is employed to increase the volume fraction of neurons and analyze RVE behavior in various NVFs. The results show increasing the load rate leads to a raise in the maximum stress that indicates the tissue is more vulnerable at higher rates. Moreover, stiffness of the tissue is enhanced in higher NVFs. Additionally, it is found that axons undergo higher stresses; hence, they are more sensitive in accidents which lead to axonal death and would cause TBI and DAI.

Craniofacial skeletal response to encephalization: How do we know what we think we know?

Dramatic changes in cranial capacity have characterized human evolution. Important evolutionary hypotheses, such as the spatial packing hypothesis, assert that increases in relative brain size (encephalization) have caused alterations to the modern human skull, resulting in a suite of traits unique among extant primates, including a domed cranial vault, highly flexed cranial base, and retracted facial skeleton. Most prior studies have used fossil or comparative primate data to establish correlations between brain size and cranial form, but the mechanistic basis for how changes in brain size impact the overall shape of the skull resulting in these cranial traits remains obscure and has only rarely been investigated critically. We argue that understanding how changes in human skull morphology could have resulted from increased encephalization requires the direct testing of hypotheses relating to interaction of embryonic development of the bones of the skull and the brain. Fossil and comparative primate data have thoroughly described the patterns of association between brain size and skull morphology. Here we suggest complementing such existing datasets with experiments focused on mechanisms responsible for producing the observed patterns to more thoroughly understand the role of encephalization in shaping the modern human skull.

Application of the time-strain superposition - Part I: Prediction of the nonlinear constant shear rate response of brain tissue

Modern surgical training, better understanding of the biomechanics of traumatic brain injury, and precise quantification of the difference between mechanical response of healthy and disease-modified brain tissue, require reliable experimental data and efficient mathematical/computational models. In this paper, a new methodology is proposed for prediction of the nonlinear viscoelastic behaviour of porcine brain. Time-strain superposition is applied to the brain stress relaxation data for construction of the overall master curve. The nonlinear internal-clock viscoelastic model, which is based on the free volume concept, is utilized to predict the constant shear rate (CSR) response, based on the known stress relaxation master curve. Demonstrated theoretical procedure is evaluated on the porcine brain experimental data available from the literature.

RESULTS

show good agreement between the predicted CSR response and the previously published CSR measurements. We may justifiably speculate that the proposed approach serves well for prediction of the nonlinear CSR behaviour of the porcine brain tissue. Since the methodology is strongly supported by the physical background, it exhibits the potential to be utilized for prediction of nonlinear behaviour in other loading modes, as well as of other tissues or viscoelastic materials.

Region and species dependent mechanical properties of adolescent and young adult brain tissue

Traumatic brain injuries, the leading cause of death and disability in children and young adults, are the result of a rapid acceleration or impact of the head. In recent years, a global effort to better understand the biomechanics of TBI has been undertaken, with many laboratories creating detailed computational models of the head and brain. For these models to produce realistic results they require accurate regional constitutive data for brain tissue. However, there are large differences in the mechanical properties reported in the literature. These differences are likely due to experimental parameters such as specimen age, brain region, species, test protocols, and fiber direction which are often not reported. Furthermore, there is a dearth of reported viscoelastic properties for brain tissue at large-strain and high rates. Mouse, rat, and pig brains are impacted at 10/s to a strain of ~36% using a custom-built micro-indenter with a 125 μm radius. It is shown that the resultant mechanical properties are dependent on specimen-age, species, and region, under identical experimental parameters.

Protection of cortex by overlying meninges tissue during dynamic indentation of the adolescent brain

Traumatic brain injury (TBI) has become a recent focus of biomedical research with a growing international effort targeting material characterization of brain tissue and simulations of trauma using computer models of the head and brain to try to elucidate the mechanisms and pathogenesis of TBI. The meninges, a collagenous protective tri-layer, which encloses the entire brain and spinal cord has been largely overlooked in these material characterization studies. This has resulted in a lack of accurate constitutive data for the cranial meninges, particularly under dynamic conditions such as those experienced during head impacts. The work presented here addresses this lack of data by providing for the first time, in situ large deformation material properties of the porcine dura-arachnoid mater composite under dynamic indentation. It is demonstrated that this tissue is substantially stiffer (shear modulus, μ=19.10±8.55kPa) and relaxes at a slower rate (τ₁=0.034±0.008s, τ₂=0.336±0.077s) than the underlying brain tissue (μ=6.97±2.26kPa, τ₁=0.021±0.007s, τ₂=0.199±0.036s), reducing the magnitudes of stress by 250% and 65% for strains that arise during indentation-type deformations in adolescent brains.

STATEMENT OF SIGNIFICANCE

We present the first mechanical analysis of the protective capacity of the cranial meninges using in situ micro-indentation techniques. Force-relaxation tests are performed on in situ meninges and cortex tissue, under large strain dynamic micro-indentation. A quasi-linear viscoelastic model is used subsequently, providing time-dependent mechanical properties of these neural tissues under loading conditions comparable to what is experienced in TBI. The reported data highlights the large differences in mechanical properties between these two tissues. Finite element simulations of the indentation experiments are also performed to investigate the protective capacity of the meninges. These simulations show that the meninges protect the underlying brain tissue by reducing the overall magnitude of stress by 250% and up to 65% for strains.

A study of the progression of damage in an axially loaded Branta leucopsis femur using X-ray computed tomography and digital image correlation

This paper uses X-ray computed tomography to track the mechanical response of a vertebrate (Barnacle goose) long bone subjected to an axial compressive load, which is increased gradually until failure. A loading rig was mounted in an X-ray computed tomography system so that a time-lapse sequence of three-dimensional (3D) images of the bone’s internal (cancellous or trabecular) structure could be recorded during loading. Five distinct types of deformation mechanism were observed in the cancellous part of the bone. These were (i) cracking, (ii) thinning (iii) tearing of cell walls and struts, (iv) notch formation, (v) necking and (vi) buckling. The results highlight that bone experiences brittle (notch formation and cracking), ductile (thinning, tearing and necking) and elastic (buckling) modes of deformation. Progressive deformation, leading to cracking was studied in detail using digital image correlation. The resulting strain maps were consistent with mechanisms occurring at a finer-length scale. This paper is the first to capture time-lapse 3D images of a whole long bone subject to loading until failure. The results serve as a unique reference for researchers interested in how bone responds to loading. For those using computer modelling, the study not only provides qualitative information for verification and validation of their simulations but also highlights that constitutive models for bone need to take into account a number of different deformation mechanisms.

A viscoelastic analysis of the P56 mouse brain under large-deformation dynamic indentation

The brain is a complex organ made up of many different functional and structural regions consisting of different types of cells such as neurons and glia, as well as complex anatomical geometries. It is hypothesized that the different regions of the brain exhibit significantly different mechanical properties which may be attributed to the diversity of cells within individual brain regions. The regional viscoelastic properties of P56 mouse brain tissue, up to 70μm displacement, are presented and discussed in the context of traumatic brain injury, particularly how the different regions of the brain respond to mechanical loads. Force-relaxation data obtained from micro-indentation measurements were fit to both linear and quasi-linear viscoelastic models to determine the time and frequency domain viscoelastic response of the pons, cortex, medulla oblongata, cerebellum, and thalamus. The damping ratio of each region was also determined. Each region was found to have a unique mechanical response to the applied displacement, with the pons and thalamus exhibiting the largest and smallest force-response, respectively. All brain regions appear to have an optimal frequency for the dissipation of energies which lies between 1 and 10Hz.

STATEMENT OF SIGNIFICANCE

We present the first mechanical characterization of the viscoelastic response for different regions of mouse brain. Force-relaxation tests are performed under large strain dynamic micro-indentation, and viscoelastic models are used subsequently, providing time-dependent mechanical properties of brain tissue under loading conditions comparable to what is experienced in TBI. The unique mechanical properties of different brain regions are highlighted, with substantial variations in the viscoelastic properties and damping ratio of each region. Cortex and pons were the stiffest regions, while the thalamus and medulla were most compliant. The cerebellum and thalamus had highest damping ratio values and those of the medulla were lowest. The reported material parameters can be implemented into finite element computer models of the mouse to investigate the effects of trauma on individual brain regions.

An anisotropic hyperelastic constitutive model of brain white matter in biaxial tension and structural-mechanical relationships

Computational models of the brain require accurate and robust constitutive models to characterize the mechanical behavior of brain tissue. The anisotropy of white matter has been previously demonstrated; however, there is a lack of data describing the effects of multi-axial loading, even though brain tissue experiences multi-axial stress states. Therefore, a biaxial tensile experiment was designed to more fully characterize the anisotropic behavior of white matter in a quasi-static loading state, and the mechanical data were modeled with an anisotropic hyperelastic continuum model. A probabilistic analysis was used to quantify the uncertainty in model predictions because the mechanical data of brain tissue can show a high degree of variability, and computational studies can benefit from reporting the probability distribution of model responses. The axonal structure in white matter can be heterogeneous and regionally dependent, which can affect computational model predictions. Therefore, corona radiata and corpus callosum regions were tested, and histology and transmission electron microscopy were performed on tested specimens to relate the distribution of axon orientations and the axon volume fraction to the mechanical behavior. These measured properties were implemented into a structural constitutive model. Results demonstrated a significant, but relatively low anisotropic behavior, yet there were no conclusive mechanical differences between the two regions tested. The inclusion of both biaxial and uniaxial tests in model fits improved the accuracy of model predictions. The mechanical anisotropy of individual specimens positively correlated with the measured axon volume fraction, and, accordingly, the structural model exhibited slightly decreased uncertainty in model predictions compared to the model without structural properties.

A Novel Method for Optical High Spatiotemporal Strain Analysis for Transcatheter Aortic Valves In Vitro

The transcatheter aortic valve implantation (TAVI) valve is a bioprosthetic valve within a metal stent frame. Like traditional surgical bioprosthetic valves, the TAVI valve leaflet tissue is expected to calcify and degrade over time. However, clinical studies of TAVI valve longevity are still limited. In order to indirectly assess the longevity of TAVI valves, an estimate of the mechanical wear and tear in terms of valvular deformation and strain of the leaflets under various conditions is warranted. The aim of this study was, therefore, to develop a platform for noncontact TAVI valve deformation analysis with both high temporal and spatial resolutions based on stereophotogrammetry and digital image correlation (DIC). A left-heart pulsatile in vitro flow loop system for mounting of TAVI valves was designed. The system enabled high-resolution imaging of all three TAVI valve leaflets simultaneously for up to 2000 frames per second through two high-speed cameras allowing three-dimensional analyses. A coating technique for applying a stochastic pattern on the leaflets of the TAVI valve was developed. The technique allowed a pattern recognition software to apply frame-by-frame cross correlation based deformation measurements from which the leaflet motions and the strain fields were derived. The spatiotemporal development of a very detailed strain field was obtained with a 0.5 ms time resolution and a spatial resolution of 72 μm/pixel. Hence, a platform offering a new and enhanced supplementary experimental evaluation of tissue valves during various conditions in vitro is presented.

Brain pressure responses in translational head impact: a dimensional analysis and a further computational study

Brain pressure responses resulting from translational head impact are typically related to focal injuries at the coup and contrecoup sites. Despite significant efforts characterizing brain pressure responses using experimental and modeling approaches, a thorough investigation of the key controlling parameters appears lacking. In this study, we identified three parameters specific and important for brain pressure responses induced by isolated linear acceleration a(lin) via a dimensional analysis: a(lin) itself (magnitude and directionality), brain size and shape. These findings were verified using our recently developed Dartmouth Head Injury Model (DHIM). Applying a(lin) to the rigid skull, we found that the temporal profile of the given a(lin) directly determined that of pressure. Brain pressure was also found to be linearly proportional to brain size and dependent on impact direction. In addition, we investigated perturbations to brain pressure responses as a result of non-rigid skull deformation. Finally, DHIM pressure responses were quantitatively validated against two representative cadaveric head impacts (categorized as "good" to "excellent" in performance). These results suggest that both the magnitude and directionality of a(lin) as well as brain size and shape should be considered when interpreting brain pressure responses. Further, a model validated against pressure responses alone is not sufficient to ensure its fidelity in strain-related responses. These findings provide important insights into brain pressure responses in translational head impact and the resulting risk of pressure-induced injury. In addition, they establish the feasibility of creating a pre-computed atlas for real-time tissue-level pressure responses without a direct simulation in the future.

Effect of needle insertion speed on tissue injury, stress, and backflow distribution for convection-enhanced delivery in the rat brain

Flow back along a needle track (backflow) can be a problem during direct infusion, e.g. convection-enhanced delivery (CED), of drugs into soft tissues such as brain. In this study, the effect of needle insertion speed on local tissue injury and backflow was evaluated in vivo in the rat brain. Needles were introduced at three insertion speeds (0.2, 2, and 10 mm/s) followed by CED of Evans blue albumin (EBA) tracer. Holes left in tissue slices were used to reconstruct penetration damage. These measurements were also input into a hyperelastic model to estimate radial stress at the needle-tissue interface (pre-stress) before infusion. Fast insertion speeds were found to produce more tissue bleeding and disruption; average hole area at 10 mm/s was 1.87-fold the area at 0.2 mm/s. Hole measurements also differed at two fixation time points after needle retraction, 10 and 25 min, indicating that pre-stresses are influenced by time-dependent tissue swelling. Calculated pre-stresses were compressive (0 to 485 Pa) and varied along the length of the needle with smaller average values within white matter (116 Pa) than gray matter (301 Pa) regions. Average pre-stress at 0.2 mm/s (351.7 Pa) was calculated to be 1.46-fold the value at 10 mm/s. For CED backflow experiments (0.5, 1, and 2 µL/min), measured EBA backflow increased as much as 2.46-fold between 10 and 0.2 mm/s insertion speeds. Thus, insertion rate-dependent damage and changes in pre-stress were found to directly contribute to the extent of backflow, with slower insertion resulting in less damage and improved targeting.

STUDY OF PLAQUE VULNERABILITY IN CORONARY ARTERY USING MOONEY–RIVLIN MODEL: A COMBINATION OF FINITE ELEMENT AND EXPERIMENTAL METHOD

Atherosclerosis is a disease in which plaque builds up inside arteries. It is also considered as one of the most serious and common forms of cardiovascular disease which can lead to heart attack and stroke. In the current research, finite element method is used to anticipate plaque vulnerability based on peak plaque stress using human samples. A total of 23 healthy and atherosclerotic human coronary arteries, including 14 healthy and 9 atherosclerotic are removed within 5 h postmortem. The samples are mounted on a uniaxial tensile test machine and the obtained mechanical properties are used in finite element models. The results, including the Mooney–Rivlin hyperelastic constants of the samples as well as peak plaque stresses, are computed. It is demonstrated that the atherosclerotic human coronary arteries have significantly (p < 0.05) higher stiffness compared to healthy ones. The hypocellular plaque, in addition, has the highest stress values compared to the cellular and calcified ones and, consequently, is so prone to rupture. The calcified plaque type, nevertheless, has the lowest stress values and, remains stable. The results of this study can be used in the plaque vulnerability prediction and could have clinical implications for interventions and surgeries, such as balloon angioplasty, bypass and stenting.

A finite element investigation on plaque vulnerability in realistic healthy and atherosclerotic human coronary arteries

Atherosclerosis is the most common arterial disease. It has been shown that stresses that are induced during blood circulation can cause plaque rupture and, in turn, lead to thrombosis and stroke. In this study, finite element method is used to predict plaque vulnerability based on peak plaque stress using human samples. A total of 23 healthy and atherosclerotic human coronary arteries of 14 healthy and 9 atherosclerotic patients are excised within 5 h postmortem. The samples are mounted on an uniaxial tensile test machine, and the obtained mechanical properties are used in two-dimensional and three-dimensional finite element models. The results including the Neo-Hookean hyperelastic coefficients of the samples as well as peak plaque stresses are analyzed. The results indicate that the atherosclerotic human coronary arteries have significantly (p < 0.05) higher stiffness compared with the healthy ones. The hypocellular plaque also has the highest stress values and, as a result, is most likely (vulnerable) to rupture, while the calcified type has the lowest stress values and, consequently, is expected to remain stable. The results could be used in the plaque vulnerability anticipation and have clinical implications in interventions and surgeries, including balloon angioplasty, bypass, and stenting.

Measurement of the uniaxial mechanical properties of rat brains infected by Plasmodium berghei ANKA

Degenerative and demyelinating diseases are known to alter the mechanical properties of brain tissue. While few studies have characterized these biomechanical changes, it is clear that accurate characterization of the mechanical properties of diseased brain tissue could be a substantial asset to neuronavigation and surgery simulation through haptic devices. In this study, samples of brain tissue from rats infected with Plasmodium berghei ANKA, an African murine malaria parasite, are evaluated using a uniaxial tensile test machine. Infected brains having different levels of parasitemia are mounted on the testing machine and extended until failure of the tissue. The stress–strain curve of each sample is obtained and compared to healthy rat brain tissue. Young’s modulus of each sample is extracted from the Hookean part of the stress–strain diagram. Young’s modulus of rats’ brain shows considerable difference among the samples having various levels of parasitemia compared with the controls. For instance, the brains with 0% (control), 1.5%, and 9% parasitemia showed a Young’s modulus of 46.15, 54.54, and 266.67 kPa, respectively. This suggests sequestration of the stiffened and less deformable parasitized red blood cells in the brain microvasculature.

Measurement of the uniaxial mechanical properties of healthy and atherosclerotic human coronary arteries

Atherosclerosis is a common arterial disease which alters the stiffness of arterial wall. Arterial stiffness is related to many cardiovascular diseases. In this investigation, maximum stress and strain as well as physiological and maximum elastic modulus of 22 human coronary arteries are measured. In addition, the force-displacement diagram of human coronary artery is obtained to discern the alterations between the healthy and atherosclerotic arterial wall stiffness. The age of each specimen and its effect on the elastic modulus of human coronary arteries is also considered. Twenty-two human coronary arteries, including eight atherosclerotic and fourteen healthy arteries are excised within 5 hours post-mortem. Samples are mounted on a tensile-testing machine and force is applied until breakage occurs. Elastic modulus coefficient of each specimen is calculated to compare the stiffness of healthy and atherosclerotic coronary arteries. The results show that the atherosclerotic arteries bear 44.55% more stress and 34.61% less strain compared to the healthy ones. The physiological and maximum elastic moduli of healthy arteries are 2.53 and 2.91 times higher than that of atherosclerotic arteries, respectively. The age of specimens show no correlation with the arterial wall stiffness. A combination of biomechanics and mathematics is used to characterize the mechanical properties of human coronary arteries. These results could be utilized to understand the extension and rupture mechanism of coronary arteries and has implications for interventions and surgeries, including balloon-angioplasty, bypass, and stenting.

Assessment of relative brain-skull motion in quasistatic circumstances by magnetic resonance imaging

Brain-skull relative motion plays a pivotal role in the etiology of traumatic brain injury (TBI). The present study aims to assess brain-skull relative motion in quasistatic circumstances, and to correlate cortical regions with high motion amplitudes with sites prone to cerebral contusions. The study includes 30 healthy volunteers scanned using a clinical 3-T MR scanner in four different head positions. Through image processing and 3D model registration, pairwise comparisons were performed to calculate the brain shift between sagittal and coronal head positional change. Next, local brain deformation was evaluated by comparison between cortical and ventricular amplitudes. Finally, the influence of age, sex, and skull geometry on the cortical and ventricular motion was investigated. The results describe complex brain shift patterns, with high regional and inter-individual variations, outweighing age and sex patterns. Regions with maximum motion amplitudes were identified at the inferolateral aspects of the frontal and temporal lobes, congruent with predilection sites for contusions. No significant influences of age and sex on the cortical shift amplitudes were detected. The 3D cortical deviations varied from -7.86 mm to +5.71 mm for the sagittal head movement, and from -11.46 mm to +7.30 mm for head movement in the coronal plane, for a 95% confidence interval. The present study contributes to a better understanding of the mechanopathogenesis of frontotemporal contusions, and is useful for the optimization of finite-element head models and neurosurgical navigation procedures. Moreover, our results prove that in vivo MRI allows for accurate assessment of brain-skull relative motion in quasistatic conditions.