Computational simulation of the mechanical response of brain tissue under blast loading

MFC: An open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver

MFC is an open-source tool for solving multi-component, multi-phase, and bubbly compressible flows. It is capable of efficiently solving a wide range of flows, including droplet atomization, shock-bubble interaction, and bubble dynamics. We present the 5- and 6-equation thermodynamically-consistent diffuse-interface models we use to handle such flows, which are coupled to high-order interface-capturing methods, HLL-type Riemann solvers, and TVD time-integration schemes that are capable of simulating unsteady flows with strong shocks. The numerical methods are implemented in a flexible, modular framework that is amenable to future development. The methods we employ are validated via comparisons to experimental results for shock-bubble, shock-droplet, and shock-water-cylinder interaction problems and verified to be free of spurious oscillations for material-interface advection and gas-liquid Riemann problems. For smooth solutions, such as the advection of an isentropic vortex, the methods are verified to be high-order accurate. Illustrative examples involving shock-bubble-vessel-wall and acoustic-bubble-net interactions are used to demonstrate the full capabilities of MFC.

The effect of large deformation on Poisson's ratio of brain white matter: An experimental study

A more Accurate description of the mechanical behavior of brain tissue could improve the results of computational models. While most studies have assumed brain tissue as an incompressible material with constant Poisson's ratio of almost 0.5 and constructed their modeling approach according to this assumption, the relationship between this ratio and levels of applied strains has not yet been studied. Since the mechanical response of the tissue is highly sensitive to the value of Poisson's ratio, this study was designed to investigate the characteristics of the Poisson's ratio of brain tissue at different levels of applied strains. Samples were extracted from bovine brain tissue and tested under unconfined compression at strain values of 5%, 10%, and 30%. Using an image processing method, the axial and transverse strains were measured over a 60-s period to calculate the Poisson's ratio for each sample. The results of this study showed that the Poisson's ratio of brain tissue at strain levels of 5% and 10% was close to 0.5, and assuming brain tissue as an incompressible material is a valid assumption at these levels of strain. For samples under 30% compression, this ratio was higher than 0.5, which could suggest that under strains higher than the brain injury threshold (approximately 18%), tissue integrity was impaired. Based on these observations, it could be concluded that for strain levels higher than the injury threshold, brain tissue could not be assumed as an incompressible material, and new material models need to be proposed to predict the material behavior of the tissue. In addition, the results showed that brain tissue under unconfined compression uniformly stretched in the transverse direction, and the bulging in the samples is negligible.

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.

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.

Multi-Directional Dynamic Model for Traumatic Brain Injury Detection

Given the worldwide adverse impact of traumatic brain injury (TBI) on the human population, its diagnosis and prediction are of utmost importance. Historically, many studies have focused on associating head kinematics to brain injury risk. Recently, there has been a push toward using computationally expensive finite element (FE) models of the brain to create tissue deformation metrics of brain injury. Here, we develop a new brain injury metric, the brain angle metric (BAM), based on the dynamics of a 3 degree-of-freedom lumped parameter brain model. The brain model is built based on the measured natural frequencies of an FE brain model simulated with live human impact data. We show that it can be used to rapidly estimate peak brain strains experienced during head rotational accelerations that cause mild TBI. In our data set, the simplified model correlates with peak principal FE strain (R² = 0.82). Further, coronal and axial brain model displacement correlated with fiber-oriented peak strain in the corpus callosum (R² = 0.77). Our proposed injury metric BAM uses the maximum angle predicted by our brain model and is compared against a number of existing rotational and translational kinematic injury metrics on a data set of head kinematics from 27 clinically diagnosed injuries and 887 non-injuries. We found that BAM performed comparably to peak angular acceleration, translational acceleration, and angular velocity in classifying injury and non-injury events. Metrics that separated time traces into their directional components had improved model deviance compare with those that combined components into a single time trace magnitude. Our brain model can be used in future work to rapidly approximate the peak strain resulting from mild to moderate head impacts and to quickly assess brain injury risk.

Optimization of a Multifrequency Magnetic Resonance Elastography Protocol for the Human Brain

BACKGROUND AND PURPOSE

The brain's stiffness measurements from magnetic resonance elastography (MRE) strongly depend on actuation frequencies, which makes cross-study comparisons challenging. We performed a preliminary study to acquire optimal sets of actuation frequencies to accurately obtain rheological parameters for the whole brain (WB), white matter (WM), and gray matter (GM).

METHODS

Six healthy volunteers aged between 26 and 72 years old went through MRE with a modified single-shot spin-echo echo planar imaging pulse sequence embedded with motion encoding gradients on a 3T scanner. Frequency-independent brain material properties and best-fit material model were determined from the frequency-dependent brain tissue response data (20 -80 Hz), by comparing four different linear viscoelastic material models (Maxwell, Kelvin-Voigt, Springpot, and Zener). During the material fitting, spatial averaging of complex shear moduli (G*) obtained under single actuation frequency was performed, and then rheological parameters were acquired. Since clinical scan time is limited, a combination of three actuation frequencies that would provide the most accurate approximation and lowest fitting error was determined for WB, WM, and GM by optimizing for the lowest Bayesian information criterion (BIC).

RESULTS

BIC scores for the Zener and Springpot models showed these models approximate the multifrequency response of the tissue best. The best-fit frequency combinations for the reference Zener and Springpot models were identified to be 30-60-70 and 30-40-80 Hz, respectively, for the WB.

CONCLUSIONS

Optimal sets of actuation frequencies to accurately obtain rheological parameters for WB, WM, and GM were determined from shear moduli measurements obtained via 3-dimensional direct inversion. We believe that our study is a first-step in developing a region-specific multifrequency MRE protocol for the human brain.

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.

Recursive Least Squares Filtering Algorithms for On-Line Viscoelastic Characterization of Biosamples

The mechanical characterization of biological samples is a fundamental issue in biology and related fields, such as tissue and cell mechanics, regenerative medicine and diagnosis of diseases. In this paper, a novel approach for the identification of the stiffness and damping coefficients of biosamples is introduced. According to the proposed method, a MEMS-based microgripper in operational condition is used as a measurement tool. The mechanical model describing the dynamics of the gripper-sample system considers the pseudo-rigid body model for the microgripper, and the Kelvin–Voigt constitutive law of viscoelasticity for the sample. Then, two algorithms based on recursive least square (RLS) methods are implemented for the estimation of the mechanical coefficients, that are the forgetting factor based RLS and the normalised gradient based RLS algorithms. Numerical simulations are performed to verify the effectiveness of the proposed approach. Results confirm the feasibility of the method that enables the ability to perform simultaneously two tasks: sample manipulation and parameters identification.

Mechanistic Insights into Human Brain Impact Dynamics through Modal Analysis

Although concussion is one of the greatest health challenges today, our physical understanding of the cause of injury is limited. In this Letter, we simulated football head impacts in a finite element model and extracted the most dominant modal behavior of the brain's deformation. We showed that the brain's deformation is most sensitive in low frequency regimes close to 30 Hz, and discovered that for most subconcussive head impacts, the dynamics of brain deformation is dominated by a single global mode. In this Letter, we show the existence of localized modes and multimodal behavior in the brain as a hyperviscoelastic medium. This dynamical phenomenon leads to strain concentration patterns, particularly in deep brain regions, which is consistent with reported concussion pathology.